Alternative Methods of Aircraft Braking · 2016. 4. 28. · 1 ABSTRACT Aircraft braking systems are required to convert large amounts of kinetic energy into thermal energy produced

Project Number: MQP MQF – 3317

Alternative Methods of Aircraft Braking

A Major Qualifying Project

Submitted to the Faculty of the

WORCESTER POLYTECHNIC INSTITUTE

In partial fulfillment of the requirements for the degree of

Bachelor of Science

in

Mechanical Engineering

by

Mathew R. Dunster Thomas R. Nuthmann

Mechanical Engineering Mechanical Engineering

Gregory S. Stockman Nathan T. Varney

Mechanical Engineering Mechanical Engineering

MIRAD Laboratory, April 26, 2016

Approved by:

Professor Mustapha. S. Fofana, Advisor

MIRAD Laboratory, Mechanical Engineering Department

1

ABSTRACT

Aircraft braking systems are required to convert large amounts of kinetic energy into

thermal energy produced by a rejected take off. Current aircraft wheel brakes accomplish this task

through the friction between rotating carbon disks, or brake pads. During a rejected take off, an

aircraft’s maximum energy event, the brakes absorb can reach maximum temperatures of 1500 °C,

causing damage to the wheel and brake structures. One alternative system which may be beneficial

over this current system is a fluidic braking system that stores heat in a magnetorheological fluid.

The advantage of this system is that the fluid is able to reject stored heat to the environment through

an active heat rejection system. Magnetorheological fluid allows for direct control over fluid

viscosity, which is related to friction generated by the wheel. The objectives of this Major

Qualifying Project are to identify alternative methods of braking for use in commercial aircraft

and to evaluate the feasibility of a fluidic braking system utilizing magnetorheological fluid.

To determine the kinetic to thermal energy conversion that is required of the brakes to stop

an aircraft safely on an airport runway, a set of equations is derived to model various aircraft

braking events. These equations were validated using a case study of the Boeing 737-800 single

aisle commercial passenger aircraft. The main result of the braking model is an evaluation of brake

power as a function of time. To evaluate the feasibility of a magnetorheological fluid based fluidic

aircraft brake a thermodynamic model was developed to determine the transient pressures and

temperatures within the brake over the course of a braking event. This thermodynamic system

includes a pump, which acts as the frictional brake, a heat exchanger that rejects the heat generated

within the working fluid, and a throttling valve that drops fluid pressure. Using the brake power

acquired from the derived landing equations as a system input, the model determined that to

achieve the energy dissipation necessary to stop the aircraft, extremely low pump efficiencies of

less than 0.1% would be required.

Using the thermodynamic model, the inlet and outlet temperatures and pressures were

calculated. Using these values, we used a thermal component sizing tool that was supplied to our

group by our sponsor to determine the weight and volume of the heat exchanger within the system.

With the given range of temperatures and pressure of our system, it was determined that the fluidic

braking system would be three times the mass of a current system.

2

TABLE OF CONTENTS

Abstract ......................................................................................................................................1

Table of Contents ........................................................................................................................2

List of Figures .............................................................................................................................5

List of Tables...............................................................................................................................8

Report Nomenclature ..................................................................................................................9

Acknowledgements .................................................................................................................... 11

Authorship ................................................................................................................................ 12

IMPROVING AIRCRAFT BRAKING SYSTEMS ............................................. 12

1. Introduction ....................................................................................................................... 13

EVALUATION OF CURRENT BRAKE SYSTEMS ......................................... 15

2. Introduction ....................................................................................................................... 15

2.1 Current Aircraft Braking Systems ................................................................................ 15

2.1.1 Mechanics and Components of Braking Systems .................................................. 15

2.1.2 Materials of Braking Systems ............................................................................... 18

2.1.3 Limitations of Current Braking Systems................................................................ 20

2.2 Aircraft Selection......................................................................................................... 21

2.3 Aircraft Braking Requirements .................................................................................... 21

2.3.1 Aircraft Landing Process ....................................................................................... 22

2.3.2 Rejected Take-Off................................................................................................. 25

2.3.3 Limitations of Current Braking Systems................................................................ 28

2.4 Brake Thermal Management Concepts......................................................................... 29

2.4.1 Air Cooling Systems ............................................................................................. 29

2.4.2 Liquid Cooling Systems ........................................................................................ 31

2.4.3 Energy Storage within Phase Change Material ...................................................... 33

2.4.4 Fluidic Braking Systems ....................................................................................... 33

2.5 Magnetorheological Fluid ............................................................................................ 35

2.5.1 Characteristics and Properties ............................................................................... 36

3

2.5.2 Various Modes of MR Fluids ................................................................................ 40

2.5.3 Existing Technologies ........................................................................................... 41

EXPLORING ALTERNATIVE BRAKE METHODS ........................................ 44

3. Introduction ....................................................................................................................... 44

3.1 Power Requirements Modeling .................................................................................... 44

3.1.1 Drag Force Model ................................................................................................. 45

3.1.2 Braking Force Modeling ....................................................................................... 46

3.1.3 Thrust Reverser Force Modeling ........................................................................... 47

3.1.4 Brake Power Determination .................................................................................. 47

3.2 Power Requirements Results........................................................................................ 48

3.2.1 Rejected Take-Off (RTO) Certification ................................................................. 49

3.2.2 Emergency Landing Certification .......................................................................... 53

3.2.3 Standard Landing .................................................................................................. 55

3.3 Water Deluge Brake Cooling ....................................................................................... 58

3.4 Open Evaporation Feasibility ....................................................................................... 59

3.5 Fluidic Brake Modeling ............................................................................................... 60

3.5.1 Centrifugal Pump Modeling .................................................................................. 63

3.5.2 Heat Sink Modeling .............................................................................................. 65

3.5.3 Heat Exchanger Modeling ..................................................................................... 66

3.5.4 Valve Modeling .................................................................................................... 68

3.6 Fluidic Brake Modeling Results ................................................................................... 69

3.6.1 Model Output ........................................................................................................ 69

3.6.2 Pump Efficiency ................................................................................................... 79

3.6.3 Heat Exchanger Sizing .......................................................................................... 81

3.6.4 Statement of Feasibility......................................................................................... 82

3.7 Experimental Testing of MRF: .................................................................................... 83

CONCLUSIONS AND RECOMMENDATIONS ............................................... 86

4

REFERENCES ......................................................................................................................... 88

Appendices ............................................................................................................................... 91

Experimental Procedure of Pump Performance with MRF ..................................................... 91

Boeing 777 Standard Landing Energy and Forces .................................................................. 93

Boeing 777 Low Power Standard Landing Energy And Forces .............................................. 95

Boeing 777 Standard Rejected Takeoff Energy and Forces .................................................... 97

Boeing 777 Low Power Rejected Takeoff Energy and Forces ................................................ 99

Boeing 777 Standard Emergency Landing Energy and Forces ............................................. 101

Boeing 777 Low Power Emergency Landing Energy and Forces ......................................... 103

Embraer 175 Standard Landing Energy and Forces .............................................................. 105

Embraer 175 Low Power Standard Landing Energy and Forces ........................................... 107

Embraer 175 Standard Rejected Takeoff Energy and Forces ................................................ 109

Embraer 175 Low Power Rejected Takeoff Energy and Forces ............................................ 111

Embraer 175 Standard Emergency Landing Energy and Forces ........................................... 113

Embraer 175 Low Power Emergency Landing Energy and Forces ....................................... 115

Main file for the fluidic braking system model ..................................................................... 117

Pump Model ........................................................................................................................ 120

Heat Exchanger Model ........................................................................................................ 122

Heat Sink Model .................................................................................................................. 124

Pump Model ........................................................................................................................ 125

Boeing 737 Parameters Definition ....................................................................................... 126

Event Energy ....................................................................................................................... 127

Get Event Parameters .......................................................................................................... 129

Drag Force Calculation ........................................................................................................ 131

BrakeForce .......................................................................................................................... 132

5

LIST OF FIGURES

Figure 1: Current Carbon-Carbon Braking System .................................................................... 16

Figure 2: Exploded View of Wheel Brake from Wheel Hub ...................................................... 17

Figure 3: Carbon-Carbon Wheel Brake Approximate Dimensions ............................................. 17

Figure 4: Aircraft Side View FBD ............................................................................................. 22

Figure 5: Schedule of aircraft landing procedure ....................................................................... 23

Figure 6: Schematic of landing maneuver (not to scale) [3]] ...................................................... 23

Figure 7: Image of Speed-brakes ............................................................................................... 24

Figure 8: Motor Fan Axle Kit FU1702A04 ................................................................................ 30

Figure 9: Ground Based Cooling - SuperVAC 724BC Fan [32] ................................................. 31

Figure 10: Proposed Fluidic Braking System [36] ..................................................................... 34

Figure 11: Pump Pressure vs Heat to Fluid at multiple efficiencies [8] ...................................... 35

Figure 12: Magnetorheological Fluid Effect .............................................................................. 36

Figure 13: Flow of Magnetorheological Fluid between Two Plates ............................................ 38

Figure 14: MRF Pressure vs. Flow Velocity for valve sizes: (a) 25.4mm (b) 6.35mm ................ 38

Figure 15: Response Time of Magnetorheological Fluid............................................................ 39

Figure 16: Flow mode of MR Fluid ........................................................................................... 40

Figure 17: Shear mode of MR Fluid .......................................................................................... 41

Figure 18: Squeeze mode of MR Fluid ...................................................................................... 41

Figure 19: Magnetorheological Fluid Damper ........................................................................... 42

Figure 20: A Magnetorheological Brake .................................................................................... 43

Figure 21: Aircraft Free-body Diagram ..................................................................................... 45

Figure 22: RTO Power Dissipation Constant Brake Force ......................................................... 50

Figure 23: RTO Velocity Constant Brake Force ........................................................................ 51

Figure 24: RTO Power Dissipation Constant Power .................................................................. 51

Figure 25: RTO Aircraft Forces Constant Power ....................................................................... 52

Figure 26: RTO Velocity Constant Power ................................................................................. 52

Figure 27: Emergency Landing Power Dissipation .................................................................... 53

Figure 28: Emergency Landing Velocity Constant Brake Force................................................. 54

Figure 29: Emergency Landing Power Dissipation Constant Power ........................................... 54

https://d.docs.live.net/e683b6bb8a1097be/Alternative%20Braking%20MQP/Report/Second%20Semester/D%20Term/D%20Term%20Final%20Report_V7.docx#_Toc449543969

6

Figure 30: Emergency Landing Forces Constant Power ............................................................. 55

Figure 31: Emergency Landing Velocity Constant Power .......................................................... 55

Figure 32: Standard Landing Power Dissipation ........................................................................ 56

Figure 33: Standard Landing Velocity Constant Brake Force .................................................... 56

Figure 34: Standard Landing Power Dissipation Constant Power .............................................. 57

Figure 35: Standard Landing Forces Constant Power ................................................................ 58

Figure 36: Standard Landing Velocity Constant Power.............................................................. 58

Figure 37: Torque Bar Open Loop Evaporator........................................................................... 60

Figure 38: Fluidic Brake System Diagram ................................................................................. 61

Figure 39: System Characteristic Pump Curve ........................................................................... 64

Figure 40: Heat Exchanger Effectiveness Map .......................................................................... 66

Figure 41: Hot Side Pressure Drop Correlation .......................................................................... 67

Figure 42: Fluidic Brake State Plot ............................................................................................ 70

Figure 43: State 1 - Valve outlet / Pump Inlet Pressure .............................................................. 71

Figure 44: State 1 – Valve Outlet / Pump Inlet Temperatures .................................................... 72

Figure 45: State 2 - Pump Outlet Pressure ................................................................................. 73

Figure 46: State 2 - Pump Outlet Temperature ........................................................................... 74

Figure 47: State 3 - Heat Sink Outlet Pressure ........................................................................... 75

Figure 48: State 3 - Heat Sink Outlet Temperature .................................................................... 75

Figure 49: State 4 - Heat Exchanger Outlet Temperature ........................................................... 76

Figure 50: State 4 - Heat Exchanger Outlet Pressure .................................................................. 77

Figure 51: Heat Exchanger Heat Rejection ................................................................................ 78

Figure 52: Fluidic Brake Mass Flow Rate .................................................................................. 79

Figure 53: Fluidic Brake Pump Efficiency ................................................................................. 80

Figure 54: Pump Outlet Pressure vs. Pump Efficiency ............................................................... 81

Figure 55: Experimental Set-Up ................................................................................................ 84

Figure 56: Boeing 777 Standard Landing Forces ....................................................................... 93

Figure 57: Boeing 777 Standard Landing Power Dissipation ..................................................... 93

Figure 58: Boeing 777 Standard Landing Velocity .................................................................... 94

Figure 59: Boeing 777 Low Power Standard Landing Forces .................................................... 95

Figure 60: Boeing 777 Low Power Standard Landing Power Dissipation .................................. 95

7

Figure 61: Boeing 777 Low Power Standard Landing Velocity ................................................. 96

Figure 62: Boeing 777 Standard Rejected Takeoff Forces ......................................................... 97

Figure 63: Boeing 777 Standard Rejected Takeoff Power Dissipation ....................................... 97

Figure 64: Boeing 777 Standard Rejected Takeoff Velocity ...................................................... 98

Figure 65: Boeing 777 Low Power Rejected Takeoff Forces ..................................................... 99

Figure 66: Boeing 777 Low Power Rejected Takeoff Power Dissipation ................................... 99

Figure 67: Boeing 777 Low Power Rejected Takeoff Velocity ................................................ 100

Figure 68: Boeing 777 Standard Emergency Landing Forces ................................................... 101

Figure 69: Boeing 777 Standard Emergency Landing Power Dissipation ................................. 101

Figure 70: Boeing 777 Standard Emergency Landing Velocity ................................................ 102

Figure 71: Boeing 777 Low Power Emergency Landing Forces .............................................. 103

Figure 72: Boeing 777 Low Power Emergency Landing Power Dissipation ............................ 103

Figure 73: Boeing 777 Low Power Emergency Landing Velocity ........................................... 104

Figure 74: Embraer 175 Standard Landing Forces ................................................................... 105

Figure 75: Embraer 175 Standard Landing Power Dissipation ................................................. 105

Figure 76: Embraer 175 Standard Landing Velocity ................................................................ 106

Figure 77: Embraer 175 Low Power Standard Landing Forces ................................................ 107

Figure 78: Embraer 175 Low Power Standard Landing Power Dissipation .............................. 107

Figure 79: Embraer 175 Low Power Standard Landing Velocity ............................................. 108

Figure 80: Embraer 175 Standard Rejected Takeoff Forces ..................................................... 109

Figure 81: Embraer 175 Standard Rejected Takeoff Power Dissipation ................................... 109

Figure 82: Embraer 175 Standard Rejected Takeoff Velocity .................................................. 110

Figure 83: Embraer 175 Low Power Rejected Takeoff Forces ................................................. 111

Figure 84: Embraer 175 Low Power Rejected Takeoff Power Dissipation ............................... 111

Figure 85: Embraer 175 Low Power Rejected Takeoff Velocity .............................................. 112

Figure 86: Embraer 175 Standard Emergency Landing Forces ................................................ 113

Figure 87: Embraer 175 Standard Emergency Landing Power Dissipation .............................. 113

Figure 88: Embraer 175 Standard Emergency Landing Velocity ............................................. 114

Figure 89: Embraer 175 Low Power Emergency Landing Forces ............................................ 115

Figure 90: Embraer 175 Low Power Emergency Landing Power Dissipation .......................... 115

Figure 91: Embraer 175 Low Power Emergency Landing Velocity ......................................... 116

8

LIST OF TABLES

Table 1: Properties of Steel and Carbon Brakes ......................................................................... 19

Table 2: 737 Aircraft Landing Parameters [24] .......................................................................... 21

Table 3: Brake Material Properties ............................................................................................ 27

Table 4: Typical Phase Change Materials Properties ................................................................. 33

Table 5: Typical Properties or Various MR Fluids ..................................................................... 39

Table 6: MRF Material Interaction ............................................................................................ 40

Table 7: Aircraft Drag Parameters [3] ....................................................................................... 46

Table 8: Aircraft Parameters [3] ................................................................................................ 48

Table 9: Energy Requirements Summary, Constant Brake Force ............................................... 49

Table 10: Energy Requirements Summary: Constant Brake Power ............................................ 49

Table 11: Fluid Mass Per Component ........................................................................................ 62

Table 12: Desired Test Cases for Cross Flow Heat Exchanger ................................................... 82

Table 13: Cross Flow Heat Exchanger Analysis Fluid Parameters ............................................. 82

Table 14: Heat Exchanger Size .................................................................................................. 82

Table 15: Experimental Bill of Materials ................................................................................... 84

9

REPORT NOMENCLATURE

English Symbols

Number Symbol Value Units

1 AR Aspect Ratio

2 b Wing Span 𝑚

3 C Specific Heat Capacity 𝑘𝐽

𝑘𝑔𝐾

4 CD Coefficient of Drag

5 CD0 Parasitic Drag

6 Cmin Maximum Heat Capacity

Rate

𝑘𝐽

𝐾𝑠

7 Fbrakes Force of Wheel Brakes N

8 Fdrag Force of Drag N

9 FG Force of Gravity N

10 FN Normal Force N

12 FThrust rev Force of Thrust Reversers N

13 G(h) Ground Effect

14 h Enthalpy 𝑘𝐽

𝑘𝑔

15 k

16 m Mass 𝑘𝑔

17 NTU Number of Transfer Units

18 P Pressure 𝑘𝑃𝑎

19 Pb Brake Power 𝑘𝑊

20 Q Heat 𝑘𝐽

21 R HEX Cmin Ratio

22 S Wing Area 𝑚2

23 T Temperature 𝐾

24 t Time 𝑠

25 UA HEX Transfer Capability 𝑘𝑊

𝐾

26 V Volume 𝑚3

27 W Weight 𝑁

10

English Derivative Symbols


28 m Mass Flow Rate 𝑘𝑔

𝑠

29 Q Rate of Heat 𝑘𝑊

30 x Acceleration 𝑚

𝑠2

31 �� Volumetric Flow Rate 𝑚3

𝑠

32 �� Work 𝑘𝑊

33 �� Velocity 𝑚

𝑠

Greek Symbols


34 ϵ Effectiveness

35 ρ Density 𝑘𝑔

𝑚3

36 𝜂 Efficiency

37 𝜈 Specific Volume 𝑚3

𝑘𝑔

11

ACKNOWLEDGEMENTS

We would like to thank Brian St. Rock, Steve Tongue, and Tom Filburn who were integral

in bringing this project to WPI. We would also like to thank them for the assistance and advice

that they provided to us throughout the course of this project. Additionally, we would like to thank

our advisor, Professor M. S. Fofana for his assistance and advice throughout the duration of the

project. We would also like to thank Professor John Blandino for his assistance in working with

fluid mechanics and thermodynamics. Finally, we would like to thank WPI for the opportunity to

work on this project.

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AUTHORSHIP

Matthew Dunster:

Undertook significant work on Chapter 1, Chapter 2, Chapter 3, and Chapter 4. Significant

contributions were also made on formatting and editing the report and appendices. Experimental

set up and mathematical derivations were additionally completed.

Thomas Nuthmann:

Listed and derived the equations in Chapter 3, and contributed significant work on Chapter

2 and the Matlab model. Edited portions of the report and appendices. Supported efforts with

deriving and computation of mathematical derivations.

Gregory Stockman:

Significant work was contributed to Chapter 1, Chapter 2, Chapter 3, and Chapter 4. Paper

formatting and editing was also contributed. Additionally, he assisted with mathematical

derivations described within the report.

Nathan Varney:

Parts of Chapter 2, Chapter 3, and our Matlab model were major contributions. Editing and

formatting of the report and appendices were largely contributed. Revised the entire report and

assisted with mathematical derivations described within the report.

13

IMPROVING AIRCRAFT BRAKING SYSTEMS

1. Introduction

Commercial aircraft landings are extremely high energy events that require considerable

aircraft braking capability. Modern commercial aircraft use three main forms of braking to

decelerate: drag, thrust reversers, and wheel brakes [1]. Aircraft wheel brakes are made up of

several layers of carbon or steel disks, called a stack. When the brakes are applied, a hydraulic

system applies pressure on the stack, causing the stationary and rotating disks to come in contact.

The friction between the brakes applies torque on the wheels and converts the kinetic energy of

the aircraft into heat. Due to the large amount of energy that needs to be converted to heat during

a landing or rejected take off, the braking systems are designed to act as a heat sink instead of as a

temporary energy transfer system [2]. For this reason, it is vital for the braking system to be able

to handle the maximum amount of energy created in any braking event without succumbing to

catastrophic thermal failures. There are four different scenarios in which aircraft wheel brakes are

used: standard landings, emergency landings, rejected take off, and taxi operations. The most

common landing procedure that utilizes the wheel brakes is a standard landing. During a standard

landing, the aircraft approaches the runway at its landing speed and end of mission weight, touches

down, and has the full length of the runway to bring the aircraft to a stop [3]. For emergency

landings, the aircraft brakes must operate at significantly higher energy and energy storage rates,

due to the aircraft’s increased weight and decreased runway length. The highest braking energy

that an aircraft will experience, and the sizing point for the brakes, is a high speed rejected takeoff

(RTO). In other words, since the brakes are designed to be able to handle the entire energy load, a

rejected take off determines a brakes overall mass and volume. A RTO occurs when an aircraft is

deemed unable to takeoff and has to abort the procedure [4]. When an RTO occurs at or near

takeoff speed, the energy conversion loads and heat the brakes to temperatures of 1500 °C [5].

Although current carbon-carbon brake pads can survive temperatures up to 7000 °C, the

surrounding structures including the wheel well, axel, landing gear, and hydraulic system are often

damaged by heat [6, 7]. Additionally, the hydraulic fluid has the potential to catch fire, spreading

damage to the undercarriage and if not put out quickly can reach the fuel tanks causing extensive

damage and threatening the lives of the passenger and crew.

14

A system that can reduce the temperature of the brakes by actively rejecting heat during

the braking event offers several operational advantages. A fluidic braking system concept has been

proposed by our sponsor [8]. A fluidic braking system utilizes a fluid for the kinetic to thermal

energy conversion of the brakes. Because the brake utilizes a fluid, the heat can be moved to a

thermal dissipation device, such as a heat exchanger, where the heat is actively rejected during the

event, rather than storing all of the heat within the system. The system proposed in this project

decreases the performance of a pump to convert the required energy to heat. In order to control the

performance of the pump, the system utilizes a magnetorheological fluid (MRF). MRF’s

viscosities can be increased in the presence of a magnetic field. By increasing the viscosity of the

working fluid, the frictional forces between the fluid and the wetted area of the pump increases,

decreasing the performance of the pump [9, 10]. The goal of this project is to determine the

feasibility of this fluidic braking concept. To determine this, a computational model is developed

to evaluate the thermodynamic requirements of the system and estimate component weights. The

model examined is composed of four major components: a pump, a thermal heat sink, a heat

exchanger, and a valve. The pump increases the temperature and pressure of the fluid through the

absorption of the aircraft’s kinetic energy. The heat sink removes a portion of the total energy

through conduction and its purpose is to lessen the load experienced by the heat exchanger. The

heat exchanger rejects this heat to the atmosphere during the braking event. Lastly, the valve

reduces the pressure of the fluid to the original inlet pressure of the pump. The model determines

that an efficiency of less than .1% would be required to keep the system within reasonable

pressures. The design of an experiment is proposed to determine the feasibility of achieving such

a low efficiency. The purpose of this experiment is to test pump performance degradation for

varying MRF viscosities.

First, chapter two of this report lays out a fundamental background of current braking

systems and major components. Next, chapter three evaluates the requirements and mechanics of

current braking systems, potential means of brake cooling systems, fluidic braking systems and

magnetorheological fluids. A computational fluidic model for the fluidic brake is then explored in

detail, with each section starting with a summary, before then going into further derivations. In

this same the results of the model and sizing of major components of the fluidic brake components

are discussed. Chapter 4 contains the conclusion and recommendation for future work.

15

EVALUATION OF CURRENT BRAKE SYSTEMS

2. Introduction

In this chapter, we discuss the current braking systems used by commercial aircraft during

runway operation to slow and stop the aircraft. We begin by outlining brake system design

requirements, followed by a detailed description of current aircraft braking systems, their major

components, and their function. Additionally, we describe various thermal management concepts

intended to mitigate excess heat generated during frictional braking. Following this, we describe

in detail the concept for an alternative fluidic braking system. We outline the properties and

applications of magnetorheological fluids, which are incorporated into the proposed alternative

aircraft braking system.

2.1 Current Aircraft Braking Systems

Aircraft carbon wheel braking systems have been used for over 50 years, and were first

utilized by military aircraft. Although the brakes were extremely expensive to make, the cost was

justified by the weight savings over long military flights [11]. However, developments starting in

the early to mid-1980’s made carbon braking systems more feasible for shorter flights, and

accordingly more feasible for the commercial airline industry. Since their implementation, carbon

brakes have proved to be a reliable and effective way of aircraft braking.

2.1.1 Mechanics and Components of Braking Systems

The wheel braking systems for commercial aircraft work in a similar manner to other

vehicular disk braking systems. With a standard stator-rotor mechanism, aircraft wheel brakes are

located on the axles, inside of the rear landing wheels [12]. The brake is made up of not one, but

several alternating layers of stators and rotors. For the Boeing 737-800, there are four sets of stators

and rotors which make up the brake [13]. Running along both the outer and inner diameters of the

brake stack, parallel to the axle are torque bars [6]. When the brakes are applied, a set of six

hydraulic pistons equally spaced around the rotor compress the stack of discs and pads together,

creating an equal pressure around the brake stack. The harder the pistons push the stack together,

the more friction increases between each layer of the brake stack, and thus the more braking force

is applied to the aircraft. For the Boeing 737-800, the carbon brake stacks include four rotors and

16

five stators, which have an approximate diameter of nineteen inches, and a depth of twelve. The

carbon brakes weigh 238.4 lbs. per assembly stack, and are located inside the wheel hubs of the

landing gear [11, 12]. A conceptual model of the brake components of a 737-800 aircraft braking

system is depicted in Figure 1.

Figure 1: Current Carbon-Carbon Braking System

Additionally, an exploded view of the brake, acting as a conceptual model of the brakes’

location within the wheel hubs of the aircraft wheels can be seen in Figure 2.

17

Figure 2: Exploded View of Wheel Brake from Wheel Hub

Basic dimensions of the Boeing 737-wheel brake are shown in Figure 3.

Figure 3: Carbon-Carbon Wheel Brake Approximate Dimensions

18

As the velocity of the aircraft decreases, the kinetic energy is converted to thermal energy,

and is temporarily stored as heat in the wheel brake stack, as well as the surrounding brake

structure, such as the face plate, torque bars, and heat shield. Contradictory to a traditional braking

system, the rate of cooling from the external atmospheric air is minimal during the braking process

[14]. Due to the magnitude of energy that needs to be stored during landing or rejected take off

procedures, airline braking systems are designed to act as a heat sink instead of as a temporary

energy transfer system [2]. For this reason, it is vital for the braking system to be able to handle

the maximum amount of energy without succumbing to thermal failures [15]. Once the landing

event has ended, the brakes then slowly dissipate the thermal the energy to the atmosphere through

means of convection. Once the brakes have cooled to the initial temperature of the environment,

they are cleared to take off again for the next flight.

2.1.2 Materials of Braking Systems

Early aircraft braking systems were made of steel. At the time, steel braking systems were

the best choice due to their material properties such as their high thermal energy storage capability

and their cheap manufacturing cost. Despite these desirable features, steel brakes have many

disadvantages. First, steel disc brakes have a poor life span, and are only able to make

approximately 1,100 landings before being replaced [12]. This is caused by the fact that steel

brakes have high wear rates at high temperature performance [11]. Once the steel braking systems

have worn, they must be replaced, a process which can take up to 24 hours to complete. This

turnaround maintenance time keeps the aircraft out of service, costing the airline companies money

as they are unable to make flights. The second major problem with steel braking systems is the

large mass of steel needed to hold the thermal load [17]. Even with modern material advancements,

a single steel braking system weighs 363.4 lbs., which is approximately double the mass of modern

carbon braking systems. The combination of these issues drove the initiative for airline companies

to find an alternative material, which was later discovered to be carbon [18].

By the 1980's, the manufacturing process for carbon braking systems had advanced to the

point where they began to be used in the commercial industry [19]. Although the initial cost of the

brakes was much higher, the advantage of weight saving that carbon brought to an airplane were

great enough to pay themselves off. Table 1 shows and compares important characteristics and

properties of both steel and carbon-carbon braking systems.

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Table 1: Properties of Steel and Carbon Brakes

Property Steel Brake Carbon-

Carbon Brake

Units

Density 7900 1700 kg

m3

Specific Heat 490 755 J

kg ∙ K

Thermal Conductivity 52 10-70 W

m ∙ K

Melting Point 1773 3573 K

Number of Landings 1100 2000 Landings

System Mass 363.4 238.4 lbs.

As shown in Table 1, steel used in aircraft brakes has a considerably higher density than

its carbon brake counterpart. Additionally, the specific heat of carbon-carbon is 35% greater than

that of steel. When looking at the Boeing 737-600/700, the carbon braking system can reduce the

weight of a conventional steel braking system by over five hundred pounds [20]. Carbon brakes

also have a higher thermal capacity, allowing the brakes to absorb more thermal energy before

damage occurs to the brake or surrounding components [21]. With the older steel braking systems,

if the temperatures were to reach the same upper limit, the brakes would melt and fuse together

into a single metal block, causing significant damage to the aircraft landing gear. Lastly, carbon

disc brakes provide an alternative mechanical advantage over the steel disc brakes, which is how

the brake wear. Steel brakes perform well under low temperature cycles such as braking during

taxiing, but poorly during hot temperatures such as landing procedures and rejected take offs.

Carbon-carbon braking systems perform in the exact opposite way [2]. During repetitive cycles at

lower temperatures, carbon brakes oxidize, causing increased wear rates during taxiing and

braking at the terminal. However, during landing and emergency stopping procedures, carbon

braking systems have significantly less wear around the upper temperature limit. There are also

external factors that have more impacts on carbon brakes than steel brakes, such as certain aircraft

chemicals. Current aircraft deicing chemicals, such as alkali-metal-salt-based products, have been

associated with damaging carbon brakes by oxidizing them as well. However, the overall

20

difference in wear rates still results in carbon braking systems having a lifespan of nearly double

the life of the steel disc brakes [17]. These factors of improved performance and longevity are the

reasons that the carbon-carbon wheel brake is the current preferred brake for commercial airlines.

Despite this, carbon-carbon wheel brakes do not exist without their own set of limitations.

2.1.3 Limitations of Current Braking Systems

Though commercial aircraft braking systems perform adequately, they are not without their

drawbacks. The foremost of these drawbacks is the performance of the aircraft brakes during a

rejected take-off. Because a rejected take-off is the highest energy event that the brakes can

withstand, there is often significant damage done to the wheels, brakes, and landing gear [22].

During rejected take-off, aircraft wheel brakes can reach temperatures of up to 1500° C.

While the carbon-carbon rotors and stators of the brakes can withstand such high temperatures

without failing, the surrounding landing gear and wheel structure is not designed to endure such

high temperatures [14]. As a result, the nitrogen gas inside the wheels can expand to the point

where the tires explode violently [23]. To prevent this, fuse plugs are installed on the wheels. These

fuse plugs are designed such that they melt before the gas inside the wheels causes the tires to

explode. If brake temperatures could be lowered, the use of fuse plugs would no longer be

necessary.

If there is any hydraulic fluid leaking in the breaking system during a high energy rejected

take-off, the fluid may heat to the point of ignition, causing the landing structure to catch fire. This

presents inherent danger to any passengers and cargo aboard the aircraft. Fires can also occur after

the aircraft has come to rest, as the same phenomenon occurs as the heat stored in the brakes is

distributed throughout the landing structure [2]. Fires cause extreme and irreparable damage to the

landing structure, resulting in a high cost replacement.

Carbon-carbon brake pads are difficult and costly to manufacture. To manufacture a single

brake pad takes nearly three weeks, which results in high production costs [17]. To try and make

the most out of each brake pad manufactured, most brake manufacturers attempt to recycle brake

pads by fusing multiple worn pad together to form a full sized rotor or stator. This costly process

requires coordination from both manufacturers and customers for recycling aircraft brakes [19].

21

2.2 Aircraft Selection

Before the wheel brakes can be discussed in detail, it is important to select an aircraft for

modeling, due to the wide variety of wheel brake properties across various sized aircraft. For the

sake of continuity through-out the modeling of this project, all brake power calculations focus on

a single aircraft, the Boeing 737. As the most frequently flown aircraft in the continental United

States, the Boeing 737 is a single-aisle regional aircraft. Table 1 shows some of the major aircraft

parameters:

Table 2: 737 Aircraft Landing Parameters [24]

Parameter Value

Maximum Take-Off Weight 174,200 lbs. (79016 kg)

Maximum Landing Weight 146,300 lbs. (66361 kg)

V1 (RTO Speed) 176.7 mph (79m/s)

FAR Take-off Field Length 7,874 ft. (2,400 m)

FAR Landing Field Length 4,500 ft. (1371.6 m)

Maximum Aircraft Range 3,115 mi (5013 km)

Number of Wheel Hubs 4

Sample energy calculations are also completed for the Boeing 777, as well as for the Embraer 175.

These sample energy calculations can be found at the end of the report in the appendices.

2.3 Aircraft Braking Requirements

The function of the brakes on an aircraft is to slow and stop the aircraft when the aircraft

is on the ground. The brakes are used during four types of events: standard landings, emergency

landings, taxi operation, and rejected takeoff. A standard landing takes place when the aircraft is

its post mission location, touches down on the runway, and decelerates to either taxi speed or to a

complete stop. An emergency landing occurs when the aircraft is forced to land without having

reached its final mission location, and has to touch down on the runway and decelerate to either

taxi speed or to a stop. Often times, emergency landings occur at the same airport as the takeoff,

meaning very little of the fuel mass has been expended. A rejected takeoff occurs when a pilot has

to abort lifting off during a takeoff run and slow the aircraft to a stop. Rejected takeoffs can occur

at low or high speeds. Taxiing occurs as the aircraft moves around on the ground, and generally

requires several applications of the brakes during turning maneuvers in addition to stopping the

aircraft.

22

2.3.1 Aircraft Landing Process

A landing can be divided into two phases: air approach and ground run. During approach,

the pilot maneuvers the aircraft such that it approaches the runway nose-up at 120 feet per minute

or less until the main landing gear makes contact with the ground, initiating the ground run [3].

The nose is then lowered over the next several seconds until all wheels contact the ground.

Between the main and nose gear touchdown, the speed-brakes are fully deployed. Typical speed-

brakes can be seen in Figure 7. Without the speed-brakes, the aircraft would still produce a large

amount of lift, reducing the normal force and therefore reducing the available friction force for

braking. Instead, the speed brakes are angled to further push the aircraft into the ground, thereby

increasing the frictional and wheel braking capabilities. A free body diagram of this concept can

be seen in Figure 4:

Figure 4: Aircraft Side View FBD

After all the wheels maintain contact with the ground, the thrust reversers are activated followed

quickly by the brakes being applied [25]. A schedule of the deployment of the aircraft’s braking

systems, demonstrating the order of brake application, is summarized in Figure 5.

23

Figure 5: Schedule of aircraft landing procedure

As can be seen from the figure, the order of landing operations of the aircraft is main gear

touchdown, speed brakes, nose gear touchdown, thrust reversers, and finally wheel brakes.

Additionally, the progression of a standard landing including initial touchdown, nose gear touch

down, and complete stop of the aircraft, is demonstrated in Figure 6. Connecting the two figures,

it can be seen that all of the braking operations demonstrated in Figure 6 occurs entirely within the

initial touchdown and complete aircraft stop shown in Figure 6: Schematic of landing maneuver

(not to scale) [3]:

Figure 6: Schematic of landing maneuver (not to scale) [3]]

24

Figure 7: Image of Speed-brakes

At the instant that the brakes are applied, the speed-brakes and thrust reversers have already

been initiated. As we are examining the wheel brakes of the aircraft, the time period most

interesting to us during the event is from the instant the frictional brakes are applied until the

aircraft comes to a full stop. The Federal Aviation Administration (FAA) certifies each aircraft for

a landing field length at various conditions [4]. The dry-runway demonstrated landing distance can

be no longer than 60% of the FAA certified landing field length for the aircraft. The typical

minimum landing field distance for the Boeing 737-800 is 1634m, however this length varies with

individual aircraft weight and runway conditions [26].

During an emergency landing the pilot is forced to land the plane immediately or shortly

after take-off due to a failure or emergency [4]. An emergency landing is a higher energy event

than a standard landing, because the aircraft is all or mostly full of fuel and therefore weighs more,

resulting in increased potential energy. In this case, the pilot would jettison fuel overboard in order

to bring the weight of the aircraft down to its maximum landing weight before initiating a landing.

Still, the aircraft weighs significantly more than it would during a typical landing in which the

aircraft is at its end-of-mission weight [27].

25

2.3.2 Rejected Take-Off

A rejected take-off occurs when an aircraft has started down the runway and experiences a

malfunction that requires the aircraft to abort the take-off. For rejected takeoffs, the aircraft is at

its maximum weight and it has burned minimal fuel, making it an extremely high energy event [3].

Furthermore, the aircraft is required to stop in a shorter distance, as a large portion of the runway

has already been covered. The decision to initiate an RTO must be made before the airplane

reaches V1, or the so called “Go/No Go” speed. This speed varies greatly depending on the aircraft,

airport, and conditions, but is generally within the range of 100-150 mph [4]. After the aircraft has

reached this speed the captain must continue with the take-off unless it is apparent that the aircraft

is not fit to fly. According to the National Aeronautics and Space Administration 13 of 107 rejected

takeoffs are caused by initiation and execution problems, while 94 of 107 are caused by flight crew

errors [28]. Because a rejected takeoff is the highest energy event for a brake, the overall volume

and mass of aircraft brakes are sized based on the need to safely stop the airplane during a high-

speed rejected takeoff (RTO). Although the speed that defines a high-speed rejected take off varies

for each aircraft, a typical “high-speed” RTO is above the speed of 120 knots.

Every aircraft is certified for operation on a given runway length, referred to as a Federal

Aviation Regulation (FAR) Take-off Field Length, typically based on how well the aircraft

performs a rejected takeoff [4]. In order to allow the aircraft to operate at most major airports, the

brakes must be sized to complete the maneuver within its current certification. The FAR take-off

field length is defined as the longest of the following three scenarios:

1. The distance required to accelerate with all engines, experience an engine failure one

second prior to V1, continue the take-off and reach a point 35 feet above the runway

(Accelerate-Go Distance).

2. The distance required to accelerate with all engines, experience an event at one second

prior to V1, recognize the event, initiate the stopping maneuver and stop within the

confines of the runway (Accelerate-Stop Distance).

3. 1.15 times the all engine take-off distance required to reach a point 35 feet above the

runway.

The take-off field length depends on take-off gross weight (TOGW), altitude, temperature,

and runway conditions [4].

26

RTO’s occur approximately once every 3,000 take-offs. The majority of these result in a

delayed flight; only two percent of these occur at “high speeds”, or above 120 knots. This means

that a high speed RTO occurs approximately once in every 150,000 take-offs [4]. Rejected take-

offs are uncommon events, but they are still the sizing condition for the wheel brakes, meaning

that the brakes still have to be able to perform the maneuver successfully at any time. Because of

this, the brakes are significantly oversized for normal operation. FAA brake certifications account

for a lack in thrust reversers, increasing the energy load requirement of the wheel brakes. By

finding a way to mitigate a portion of this brake energy to the external environment, the brakes

could be downsized, reducing weight and saving operation costs of the aircraft.

A high speed rejected take-off is an expensive operation, resulting in the need for brake

replacement or repair at a significant cost. In the case that the brakes or tires need to be replaced,

the consequential cost is $50,000 for each brake stack, or $800 per tire [29]. This does not include

parts such as the hydraulic lines, heat shield, electronics, or control systems. Even in the event that

that all mechanical components are intact, many parts are weakened by the heat of the brakes, such

as the tires or the plies. As a result, all aircraft components must be evaluated after a high speed

rejected take off, before the aircraft is allowed to fly again. In order to bring an airplane to a stop

at these speeds, the brakes must convert massive amounts of kinetic energy into heat. This results

in extremely high temperatures, around 1500 °C, of the brakes; steel brakes are designed to melt

during this condition, fusing the rotors and stators together, saving the aircraft but destroying the

brake [5]. While carbon-carbon brakes can handle maximum temperatures up to 7000 °C, they do

become hot enough to cause damage to the surrounding components. High temperatures that result

from the operation can cause the hydraulic lines to catch fire, which can reach the fuel tanks and

cause enormous amounts of damage. A brake that performs a rejected take-off without causing

damage to the aircraft could have the potential to save airlines a significant amount of money,

while improving the safety of the passengers, crew, and emergency services.

Early aircraft braking systems were made of steel. At the time, steel braking systems were

the best choice due to their material properties such as their high thermal energy storage capability

and their cheap manufacturing cost. Despite these desirable features, steel brakes have many

disadvantages. First, steel disc brakes have a poor life span, and are only able to make

approximately 1,100 landings before being replaced [16]. This is caused by the fact that steel

brakes have high wear rates at high temperature performance [11]. Once the steel braking systems

27

have worn, the aircraft must be temporarily removed from commission to replace the brakes. This

turnaround maintenance time keeps the aircraft out of service, costing the airline companies money

as they are unable to make flights. The second major problem with steel braking systems is the

large mass of steel needed to hold the thermal load [17]. Even with modern material advancements,

a single steel braking system weighs 363.4 lbs., which is approximately double the mass of modern

carbon braking systems. The combination of these issues drove the initiative for airline companies

to find an alternative material, which was later discovered to be carbon [18].

Table 3: Brake Material Properties

Property Steel Brake Carbon-

Carbon Brake

Units

Density 7900 1700 kg

m3

Specific Heat 490 755 J

kg ∙ K

Thermal Conductivity 52 10-70 W

m ∙ K

Melting Point 1773 3573 K

Number of Landings 1100 2000 Landings

System Mass 363.4 238.4 lbs

As shown in Table 3, steel used in aircraft brakes has a considerably higher density than

its carbon brake counterpart. Additionally, the specific heat of carbon-carbon is 35% greater than

that of steel. When looking at the Boeing 737-600/700, the carbon braking system can reduce the

weight of a conventional steel braking system by over five hundred pounds [20]. Carbon brakes

also have a higher thermal capacity, allowing the brakes to absorb more thermal energy before

damage occurs to the brake or surrounding components [21]. With the older steel braking systems,

if the temperatures were to reach the same upper limit, the brakes would melt and fuse together

into a single metal block, causing significant damage to the aircraft landing gear. Lastly, carbon

disc brakes provide an alternative mechanical advantage over the steel disc brakes, which is how

the brake wear. Steel brakes perform well under low temperature cycles such as braking during

taxiing, but poorly during hot temperatures such as landing procedures and rejected take offs.

Carbon-carbon braking systems perform in the exact opposite way [2]. During repetitive cycles at

lower temperatures, carbon brakes oxidize, causing increased wear rates during taxiing and

28

braking at the terminal. However, during landing and emergency stopping procedures, carbon

braking systems have significantly less wear around the upper temperature limit. There are also

external factors that have more impacts on carbon brakes than steel brakes, such as certain aircraft

chemicals. Current aircraft deicing chemicals, such as alkali-metal-salt-based products, have been

associated with damaging carbon brakes by oxidizing them as well. However, the overall

difference in wear rates still results in carbon braking systems having a lifespan of nearly double

the life of the steel disc brakes [17]. These factors of improved performance and longevity are the

reasons that the carbon-carbon wheel brake is the current preferred brake for commercial airlines.

Despite this, carbon-carbon wheel brakes do not exist without their own set of limitations.

2.3.3 Limitations of Current Braking Systems

Though commercial aircraft braking systems perform adequately, they are not without their

drawbacks [8]. The foremost of these drawbacks is the performance of the aircraft brakes during

a rejected take-off [11]. Because a rejected take-off is the highest energy event that the brakes can

withstand, there is often significant damage done to the wheels, brakes, and landing gear [22].

During rejected take-off, aircraft wheel brakes can reach temperatures of up to 1500° C.

While the carbon-carbon rotors and stators of the brakes can withstand such high temperatures

without failing, the surrounding landing gear and wheel structure is not designed to endure such

high temperatures [14]. As a result, the nitrogen gas inside the wheels can expand to the point

where the tires explode violently. To prevent this, fuse plugs are installed on the wheels. These

fuse plugs are designed such that they melt before the gas inside the wheels causes the tires to

explode. If brake temperatures could be lowered, the use of fuse plugs would no longer be

necessary.

If there is any hydraulic fluid leaking in the breaking system during a high energy rejected

take-off, the fluid may heat to the point of ignition, causing the landing structure to catch fire. This

presents inherent danger to any passengers and cargo aboard the aircraft. Fires can also occur after

the aircraft has come to rest, as the same phenomenon occurs as the heat stored in the brakes is

distributed throughout the landing structure [2]. The damage caused to the landing structure during

these fires is nearly always irreparable, and results in the replacement of the landing gear, which

is extremely costly.

29

Carbon-carbon brake pads are difficult and costly to manufacture. To manufacture a single

brake pad takes nearly three weeks, which results in high production costs [17]. To try and make

the most out of each brake pad manufactured, most brake manufacturers attempt to recycle brake

pads by fusing multiple worn pad together to form a full sized rotor or stator [2]. This process

again is costly and requires both manufacturers and customers to have processes to deliver and

recycle the aircraft brakes [19].

2.4 Brake Thermal Management Concepts

As previously described, current aircraft wheel brakes are designed as heat sinks to store

all energy created during a high speed rejected take off. There is potential to downsize these brakes

by cooling them during their highest energy event, thus reducing the sizing conditions.

Additionally, by reducing the maximum energy stored in the brakes, there is potential to increase

the safety for surrounding components and the passengers. Although they are not currently utilized,

there are several designs for aircraft brake cooling systems. Below we discuss five of these options:

air cooling, ground based, liquid cooling, phase change materials cooling, and a proposed fluidic

braking system. Since many of these alternative aircraft brake cooling systems utilize the potable

water stored on an aircraft, it is vital to explain what aircraft potable water is and the quantity of

water that resides on the Boeing 737. For emergency purposes a given amount of water has to

remain on the aircraft, so that if the vehicle is unable to land, the passengers have a source of

drinkable water for the period of time the aircraft is in the air. For the Boeing 737, this amount of

potable water is approximately 30 U.S. gallons, or approximately 250 pounds. This water could

be utilized in several brake cooling systems. Although water based cooling systems would not be

used during a standard landing, they could be used during situations such as a rejected take off, to

reduce the overall size of the brake for its maximum condition.

2.4.1 Air Cooling Systems

Air cooled airline brake cooling systems cool the brakes through increased rates of

convection, by adding structures such as fans to either the assembly such as on the axle, or by

having a separate system on the ground to cool the brakes between flights [30]. Brake cooling

systems do in fact succeed in reducing the temperature of the brake and the surrounding

components [22]. In a study from the International Journal of Science Technology & Management,

30

fans attached to the axles of the aircraft were found to be able to decrease the temperature of the

brake discs 42.3% more than just that of ambient air cooling [31]. These mounted wheel brake

fans are referred to as “BCF’s” which is short for Brake Cooling Fans. One company that makes

this type of product is Safran™, whose product model can be seen in Figure 8.

Figure 8: Motor Fan Axle Kit FU1702A04

Each of these brake assemblies weigh 2.75kg and have a flow rate of 250l/s. These axle

fans are to be used on the ground only and are used not only to decrease the temperature of the

brake but also to decrease the turnaround time of the aircraft [32]. While they are fairly light, they

do not offer any cooling during the braking event and therefore do not offer any potential to

decrease the size of the brakes.

Another form of air cooled braking systems are entirely ground based systems. One such

design is a ground based fan created by ResQTec, which is a mobile fan to increase convection of

the braking system. These ground based fans do not add weight to the aircraft, and they are

significantly less expensive due to their simple structure and lack of integration with the vehicle.

An example of a ground based air cooling system is shown in Figure 9.

31

Figure 9: Ground Based Cooling - SuperVAC 724BC Fan [32]

Systems similar to this can be used to reduce the turnaround time between flights, because

the brakes need to cool down enough to be able to perform a rejected take-off if necessary. There

is little evidence of any air cooled braking systems in existence that cool the brakes during the

event in order to downsize the brake. This is likely because air cooling braking systems come with

their own set of disadvantages [11]. In order for air cooled systems to be operational during

rejected take off scenarios, additional structures need to be added to an assembly, adding weight,

complexity, and cost to the system. Most significantly, with the implementation of carbon brakes,

drawing air into the brake increases oxidation. This type of brake wear is referred to as thermal

oxidation, caused by rapid increase and decrease in temperatures [22]. By increasing the airflow,

oxidation of the brakes also increases. As the brakes oxidize, the brakes wear significantly faster

and due to the high cost of replacing the brakes, utilizing an air cooled system becomes entirely

infeasible.

2.4.2 Liquid Cooling Systems

After ruling out air cooled systems, the natural next step would be to explore liquid cooling

options. There is little evidence of significant work done in this area with regard to aircraft braking

systems. Although there exist several patents on the concept of air cooling, none are currently

32

being used by the commercial airline industry. There are several variations of liquid cooled braking

systems that include but are not limited to liquid deluge systems, open loop evaporation systems,

and closed looped systems.

A liquid deluge system cools the brakes by actively spraying the cooling liquid onto the

brakes. This idea is outlined in the patent from John, J Bloomfield for the Lockheed Aircraft

Corporation. This patent specifies the delivery of a fluidic directly in contact with parts of the

braking system during high temperature situations, without significantly increasing the weight of

the braking system. This system would only be used at high threshold temperatures to avoid use

during minimal braking procedures such as taxiing. When needed, the system coolant fluid would

be applied to the hottest areas through a hydraulic pressure system. The fluid would then vaporize

and be released into the atmosphere. Lastly, the patent explains that the hydraulic system used to

push the fluid to the brake would be activated by the same hydraulic system that is used to brake

the plane. No additional systems would need to be added to the plane. It is important to note that

this design centralizes on using a drum brake, and not a disc brake systems similar to this could,

conceivably, be used to reduce the size of the brake stack, significantly reducing the weight.

However, the development of similar systems is limited, likely due to the significant increase in

complexity and weight of the system relative to the potential weight savings. Systems similar to

this could conceivably be used to reduce the size of the brake stack and significantly reduce the

weight of the aircraft. However, the development of similar systems is limited, likely due to the

significant increase in complexity and weight of the system relative to the potential weight savings.

An open loop liquid cooling system works in a similar manner, but has no direct contact

between the fluid and the braking system. Instead, the fluid runs through the braking system, and

is heated through one of the components in a similar fashion to a heat exchanger. After being

heated, the liquid is then released into the atmosphere as gaseous form, same as the deluge. The

advantage of this system over the prior system is that by controlling how much heat is released at

once, the integrity of the brake can be protected as fluid no longer has to be applied directly to the

material.

Lastly, a closed loop system works by cooling the brake through the evaporation of an

external fluid, which is then recaptured through a condenser or by avoiding evaporation all

together. Although this system is advantageous because it can be reused several times without

33

replacing or refilling the fluid, it does require more hardware in order to recapture the working

fluid.

2.4.3 Energy Storage within Phase Change Material

Phase-change materials (PCMs) are materials that are designed to store or release large

amounts of thermal energy in the heat required for a material to undergo a phase change. PCMs

are often used in applications requiring energy storage or dissipation, also known as latent heat

storage applications. Within these applications, the use of phase-change material is advantageous

due to the high latent heat of fusion of the materials in question. Because of this physical

characteristic, the amount of heat that can be stored per unit mass of material is significantly higher

than materials that do not undergo a change of phase [34, 35]. By utilizing a phase change material,

a significant amount of the thermal energy of the brake can be stored within the PCM while

maintaining the temperature of the system. Some typical phase change materials and their

properties are listed in Table 4.

Table 4: Typical Phase Change Materials Properties

Material Initial Phase Enthalpy of

State Change

(kJ/kg)

State Change Temperature (C)

Water Liquid 333.55 100

Paraffin Wax Solid 200-220 48-63

Salt Hydrate Solid 115-200 0-117

Enthalpy of state change is the amount of energy required to change the material from one

phase to another. The temperature remains constant through this process, but a significant amount

of heat can be stored. Water has one of the highest enthalpy of state changes, but transitions from

a liquid to a gas, meaning that there is a significant volume increase. Paraffin wax and salt hydrates

have similar enthalpies of state changes, but the paraffin wax has a narrower operating range. The

salt hydrates can be designed to have a phase change temperature over a large range, making it

useful for many applications [35].

2.4.4 Fluidic Braking Systems

An innovative concept, proposed by our sponsor, is the central focus of this project. The

concept involves using a fluid as the material that generates the heat required to stop the aircraft

34

[36]. By using a fluid, the system would be able to pump the heat to an external heat exchanger

where it can be actively cooled during the braking event, reducing the overall temperature of the

system, and potentially reducing the weight. A block diagram of the system from our sponsor is

shown in Figure 10.

Figure 10: Proposed Fluidic Braking System [36]

The braking system block shown in Figure 10 is what applies torque on the wheels to stop

the airplane. In order to do so it must convert the kinetic energy of the aircraft into heat within the

fluid. The fluid is then pumped in a close loop circuit to a thermal dissipation unit (TDU), where

the heat of the fluid is transferred to some other medium before returning to the braking system

where it is heated up again. The TDU’s goal is to remove the heat from the fluid quickly enough

so the system does not overheat. For instance, it could reject the heat to the air, to a phase change

material such as water or paraffin, or store it within the thermal mass of the structure of the aircraft.

There are two potential methods for generating and controlling the brake force. The first is

to pump the fluid through a controllable orifice, or valve, causing the pressure drop in a

controllable way. In this case the valve would be the braking component. Here, the pump would

generate a high pressure that would be reduced at the orifice, converting that pressure into heat

that would go on to be rejected in the TDU.

This system comes with several apparent issues. First, the orifice would require precise

moving parts that wear out over time, increasing the maintenance cost and reducing the reliability.

Furthermore, it requires very high pressure within the pump because the kinetic energy of the

35

aircraft is converted into pressure rather than heat until after the valve. A high pressure system

requires more weight in seals and other components to prevent the system from leaking or

rupturing. Furthermore, because a catastrophic failure would result in the aircraft being unable to

stop, this point of failure is undesirable. A low pressure system would be more feasible as it

requires less complexity and durability to prevent blow out.

The next concept allows the system to maintain a low pressure. Instead of generating the

heat outside of the pump, the heat could be generated within the pump. By having a very inefficient

pump, the majority of the shaft work exerted on the pump can be converted directly into fluidic

heat rather than pressure. This essentially combines the pump and braking system [8]. Figure 11

shows how a very low efficiency pump can expend the required amount of heat into the fluid with

reasonable pressures between 14-20 psi, and flowrates less than 25 kg/s, however this requires a

pump efficiency of 0.2%. Graphs given to our team from our sponsor demonstrate this concept,

which can be seen in Figure 11.

Figure 11: Pump Pressure vs Heat to Fluid at multiple efficiencies [8]

In order to degrade the efficiency of the pump, a variable viscosity fluid called

magnetorheological fluid (MRF) will be required. By increasing the viscosity of the fluid in a

pump you increase the frictional force between the pump working surface and the fluid, decreasing

the performance of the pump, and potentially reducing its efficiency to the required range.

2.5 Magnetorheological Fluid

Rheology is the study of flow of a non-Newtonian fluid that undergoes certain conditions.

These may also be classified as a “soft solid” or solids primarily in a liquid state. Rheological

36

materials are materials that can change their physical state when they are exposed to either an

electrical or magnetic field. Magnetorheological fluid (MRF) was discovered by Jacob Rainbow

in 1948 for the US National Bureau of Standards, which is made up of a carrier fluid containing

magnetized micron-sized particles, typically iron, which can be suspended in place when exposed

to a magnetic field [37,38].

2.5.1 Characteristics and Properties

The particles that are dissolved within the carrier fluid are attracted to one another when

under a magnetic field due to dipolar effects of the magnetized micron-sized particles [37]. These

particles will then align relatively in line with magnetic field lines, as seen in Figure 12.

Figure 12: Magnetorheological Fluid Effect

Because of the increased fluid shear force on the carrier fluid by the iron particles, the

viscosity of the fluid will vary depending on the strength of the magnetic field that it is exposed

to. As soon as the magnetic field is extinguished, the fluid will return to its original state. As shown

in Figure 5, the colored spheres represent the magnetized micron-sized particles outside of a

magnetic field, then exposed to a magnetic field [9, 38].

37

While the fluid may behave as a non-Newtonian fluid while under the influence of a

magnetic field, the fluid will behave as a Newtonian fluid when not under the presence of a

magnetic field. Some potential applications where this could be used in systems classified with the

requirement of three specific behaviors: shear, flow, and squeeze. Shear requirements typically

include systems such as brakes and clutches, or vibration control and isolation, where two

opposing faces rotate amongst one another, creating a shear stress on the liquid. Applications

where flow would be an ideal use would be systems such as, suspension system, seat dampers,

recoil dampers, landing gear, large stroke dampers, seismic dampers, and vibration isolation

mounts [8, 39]. Applications where squeeze would be ideal primarily focus around vibration

isolation for smaller magnitudes do to the limited variability.

One example of investigating the ability to control the damping and latching of a

suspension system without using power, control the overall displacement of the actuator up to

30mm, and have a computer response of only a few milliseconds. This experiment was set up using

a piston filled up with the magnetorheological fluid and fixed to a force gauge and a hydraulic

piston. The experiment was set up where a permanent magnet encased in a small coil was fixed

inside the actuator. This would provide a constant magnetic field to the fluid until a current was

put through the coil. By inducing a current, the magnetic field was canceled out, making the

magnetorheological fluid to become more viscous, therefore, requiring less force on the actuator.

This was done by utilizing a permanent magnet where power would remove the blocking action

of the actuator. This variable coil allowed for a more controllable resistive force which was proven

by applying different currents through the coil [10]. The more current that was put through the

coil, the less force was required for the actuator to operate. The last major goal was to improve the

reaction time to control the forces required, which was achieved through high performance

controls system.

Other testing has been completed to evaluate how magnetorheological behaves at higher

velocities. Researchers built a test fixture that would press magnetorheological fluid at a high

velocity through a small opening in a piston. This was then analyzed under different magnetic field

strengths. The purpose of this experiment was to establish a data set that could be used and tailored

to specific applications with the given data set. This information would be beneficial to designers

in all automotive and aviation applications because it will save a tremendous amount of time and

money for design and testing of each application. There were aspects in the testing phase that the

38

smaller the valve length of the actuator using the fluid, the less controllable the fluid becomes at

high velocities [38]. Figure 13 below shows the flow of the magnetorheological fluid between two

non-magnetized plates and two magnetized plates.

Figure 13: Flow of Magnetorheological Fluid between Two Plates

Calculating forces is one important when completing this project because we need to

understand all the situations that this fluid will be experiences. The forces will result in a variation

of velocities as well as the magnetic current that they are exposed to. Figure 14 shows two different

situations of the magnetorheological fluid flowing through two different valves, one being 25.4mm

and the other 6.35mm [40]. These forces are calculated in terms of the pressure that the fluid will

exert while flowing at a certain velocity under a specific magnetic field.

Figure 14: MRF Pressure vs. Flow Velocity for valve sizes: (a) 25.4mm (b) 6.35mm

The third crucial aspect that needs to be established is the amount of time it takes for the

fluid to reach its maximum viscosity. During this same study, researchers evaluated the

39

approximate time it would take the fluid to reach the Normalized Yield Stress in relation to the

dwell time. Dwell time is defined as the time that the fluid is being exposed to a magnetic field.

Figure 15 shows a plot of the response time of MRF when exposed to different magnetic fields.

Figure 15: Response Time of Magnetorheological Fluid

The key takeaway from Figure 15 is that the magnetorheological fluid has the ability to

achieve approximately 63.2% of the target yield stress within a window of about .6ms.

Table 5 is a specification sheet that compares various types of MR fluids in respect to

different physical and thermodynamic values [41].

Table 5: Typical Properties or Various MR Fluids

Property MRF-122DG MRF-132EG MRF-336AG MRF-430AG MRF-241ES

Carrier Fluid Hydrocarbon Hydrocarbon Silicone Oil Glycol Water

Particle volume fraction 0.22 0.32 0.36 0.30 0.41

Particle weight fraction 0.72 0.81 0.82 0.75 0.85

Density (g/cm3) 2.38 3.08 3.45 3.13 3.86

Yield Strength (kPa) at

100kA/m

22 30 29 27 48


200kA/m

32 42 46 41 67


saturation

34 49 53 48 80

Plastic Viscosity (mPa sec) at

40°C

41 92 100 81 88 at 25°C

Temperature Range (°C) -40 to 130 -40 to 130 -40 to 150 -40 to 140 -10 to 70

Magnetic permeability

relative a low field

≈4 ≈6 ≈7 ≈6 ≈8

Response Time (sec) <0.001 <0.001 <0.001 <0.001 <0.001

Flash point (°C) >150 >150 >150 >93 >93

Thermal conductivity (W/m

°C) at 25°C

0.21-0.81 0.20-1.88 0.20-1.88 1.1 0.85-3.77

Specific heat (J/g °C) at 25°C 0.94 0.80 0.94 - 0.65

Coefficient of thermal

expansion

6.5 x 10-4 5.5 x 10-4 5.8 x 10-4 1.7 x 10-4 2.2 x 10-4

40

MR Fluids have a wide range of materials that can and cannot be used with due to negative

interactions. For example, many softer materials such as plastics cannot be used with MRF because

the iron particles within the fluid will break down the material.

Table 6: MRF Material Interaction

MR Fluid MRF-336AG MRF-122-2ED MRF-132AD MRF-241ES

Carrier Fluid Silicone oil Hydrocarbon Hydrocarbon Water

Buna-n Good Poor Poor Good

Butyl Good Poor Poor Good

EPDM, EPR Good Poor Poor Good

Fluoro-elastomer Good Good Good Good

Natural Rubber Good Poor Poor Good

Neoprene Good Good Good Good

Nitrile Good Good Good Good

Silicone Poor Fair Fair Fair

Iron Good Good Good Good

Stainless Steel Good Good Good Good

Aluminum Good Good Good Fair

2.5.2 Various Modes of MR Fluids

Magnetorheological fluids have three major modes of operation that allow them to perform

optimally. Flow mode utilizes the movement of the fluid through two stationary walls, with the

magnetic field lines being perpendicular to the flow of the MR Fluid. This style of operation is

most effect for use with a linear damper application because of the fixed walls [41].

Figure 16: Flow mode of MR Fluid

Shear mode utilizes the idea of rotational motion of the walls in respect to the fluid. The

magnetic field lines run perpendicular to the direction of motion of the wall. A major application

41

for the shear mode consists but is not limited to brakes and clutches because of the motion of the

walls [42].

Figure 17: Shear mode of MR Fluid

Squeeze mode is utilized for applications similar to bearings where there is a need for a

low displacement but high forces. The magnetic field lines run parallel to the motion of the aircraft

of the wall. One plate will move compressing and decompressing the fluid, with the rate being

affected by the viscosity of the fluid [43].

Figure 18: Squeeze mode of MR Fluid

2.5.3 Existing Technologies

Several MRF technologies have been developed into commercially available products.

Magnetorheological fluid itself, for example, is commercially developed and sold by LORD

42

Corporation. LORD is the main company developing commercial magnetorheological fluid, as it

is a niche technology without much business outside of specialized applications [43]. The MRF

that can be commercially purchased through LORD is available in several composition types,

however each variant is made with a proprietary carrier fluid with iron particles dissolved within

it. Variants are offered with iron compositions of 72%, 81%, and 85% by mass, and are given the

titles of MRF-122EG, MRF-132DG, and MRF-140CG from LORD [43].

Some industries have developed devices that utilize MRF properties to create advanced

replacements for current physical systems. The best example of this is with magnetorheological

fluid dampers. Figure 19 illustrates the design of a magnetorheological fluid damper.

Figure 19: Magnetorheological Fluid Damper

As shown in Figure 19, the damper body is pushed and pulled through MRF as the damper

and connecting rod move [44]. By varying the viscosity of the fluid within the damper body

through the use of an electromagnetic coil, the damping coefficient of the entire system can be

controlled and varied as needed. This allows for fine control over applied damping force. MRF

dampers such as these are used in all-terrain military vehicles and Formula 1 racing cars [44, 45].

43

Magnetorheological fluids have also been used to produced brakes and clutches. The

systems that have been produced for these devices have been enclosed fluid systems, meaning

there is no fluid flow outside of the control volume [38, 46, 47]. Examples of these devices are

shown in Figure 20:

As shown in Figure 20, the brake works much like a conventional brake. However instead

of a brake pad that clamps onto the spinning disk to create friction, there is a small amount of MRF

there for the same purpose. The fluid is made viscous and the disk releases energy into the fluid

through friction, bringing the disk to a stop. Though this works well for low energy applications,

due to the small fluid volume within the brake and the relatively low flashpoint of MRF. If too

much thermal energy were to be released into the MRF, the brake would catch fire [48]. The MRF

clutch functions in the same way, however because the purpose of the clutch is not energy storage,

there is little to no risk of high temperatures within the fluid resulting in ignition [39].

Figure 20: B MRF Clutch Figure 20: A Magnetorheological Brake

44

EXPLORING ALTERNATIVE BRAKE METHODS

3. Introduction

This project is focused on evaluating alternative methods of braking systems for commercial

aircraft. The objectives of the project are:

1. Identify potential alternative methods to frictional braking for use in commercial

aircraft.

2. Evaluate the feasibility of a fluidic brake utilizing magnetorheological fluid.

In order to accomplish these objectives, we lay out the following methodology:

1. Determine the power requirements of the braking system on a Boeing 737 aircraft using a

kinetic to thermal energy balance.

2. Identify potential alternative methods of aircraft braking.

3. Mathematically evaluate each braking method and estimate component weights.

3.1 Power Requirements Modeling

During an aircraft stopping event, the aircraft is always flat on the ground, traveling at some

velocity when the brakes are applied. At this time, the aircraft begins to slow down and the brakes

convert a significant portion of the aircraft’s kinetic energy to thermal energy. In order to determine

this energy requirement, we identify the three major forces acting on the aircraft during a stopping

event: brake force (𝐹𝑏𝑟𝑎𝑘𝑖𝑛𝑔), drag force (𝐹𝑑𝑟𝑎𝑔) and thrust reverser force (𝐹𝑡ℎ𝑟𝑢𝑠𝑡 𝑟𝑒𝑣) [39, 48].

These forces are shown in Figure 21.

��(t)

𝐹𝑑𝑟𝑎𝑔

𝐹𝑡ℎ𝑟𝑢𝑠𝑡 𝑟𝑒𝑣

𝐹𝑏𝑟𝑎𝑘𝑒𝑠

𝐹𝑁 𝐹𝑁

𝐹𝐺

45

Figure 21: Aircraft Free-body Diagram

From the free-body diagram shown above and the mass of the airplane, m, we can say that

m��(t) = Fdrag + Fbraking + Fthrust rev , (1)

where 𝐹𝑑𝑟𝑎𝑔 is the drag force, 𝐹𝑏𝑟𝑎𝑘𝑖𝑛𝑔 is the brake force and 𝐹𝑡ℎ𝑟𝑢𝑠𝑡 𝑟𝑒𝑣 is the force applied by the

thrust reversers.

3.1.1 Drag Force Model

The drag force, 𝐹𝑑𝑟𝑎𝑔, is proportional to the velocity, ��, squared and is modeled by the

equation,

Fdrag = 1

2ρCDSx(t)2 , (2)

where 𝜌 is the density of the air, 𝐶𝐷 is the drag coefficient of the airplane during landing, and 𝑆 is

the wing area of the aircraft. The coefficient of drag during landing with the spoilers deployed is

calculated according to a method described in [3, 25] and is called 𝐶𝐷𝐺 the coefficient of drag on

the ground. Equation 3 represents this drag coefficient of an aircraft on the ground:

CDG = CD0

+ 𝛥CD0+ [k1 +

G(h)

πϵAR] CL

2 (3)

where 𝐶𝐷0 is the parasitic drag of the aircraft, Δ𝐶𝐷0

is the parasitic drag adjustment factor for

spoiler deployment, 𝑘1 is a constant of the drag polar, 𝐺(ℎ) is the ground effect on the lift as a

function of wing height, 𝜖 is Oswald’s efficiency factor, 𝐴𝑅 is the aspect ratio of the wing, and

𝐶𝐿 is the coefficient of lift of the aircraft. It follows that the ground effect on the lift is given by

G(h) =16(

h

b)

2

1+16(h

b)

2 , (4)

where ℎ is the height of the wing from the ground and 𝑏 is the total wingspan of the aircraft. The

parasitic drag adjustment factor Δ𝐶𝐷0 is given by:

𝛥CD0= 2.42 (

W

S) kucm−0.215, (5)

where 𝑊 is the weight of the aircraft, 𝑆 is the wing loading of the aircraft, 𝑘𝑢𝑐 is a component of

the drag polar of the aircraft as a function of the flap position during a landing, and 𝑚 is the mass

of the aircraft. The drag polar constant is given by

46

k1 = 0.02, (6)

which is the constant for the drag force due to lift, before accounting for ground effects. The other

major component of the drag force due to lift is the lift coefficient, given by

CL =2W

ρv2S, (7)

where 𝜌 is the density of the air, 𝑣 is the velocity of the aircraft on the ground, and 𝑆 is the total

wing surface area of the aircraft. Finally, the aspect ratio is defined as

AR = b2

S, (8)

where, as before, 𝑏 is the wingspan of the aircraft and 𝑆 is the wing area of the aircraft. Using this

method, 𝐶𝑑 was calculated to roughly 0.17, however this changes with the weight of the aircraft

so it varies with which event we are examining. The aircraft parameters used are shown in Table

7 [3, 25, 27].

Table 7: Aircraft Drag Parameters [3]

Variable Value Unit

𝐂𝐃𝟎 0.0159

𝐤𝐮𝐜 3.16e-5

𝛜 0.9

𝐡 3.05 m

𝐛 35.32 m

𝐖 (see Table 8) kg

𝐒 124.58 m2

Table 7 gives the values utilized for each aircraft parameter. The values given within this table for

wing span, wing height, wing area, and drag coefficient are all given by dimensions and

specifications of a Boeing 737.

3.1.2 Braking Force Modeling

We calculate the brake force in two ways. In the first, the braking force 𝐹𝑏𝑟𝑎𝑘𝑒𝑠 is assumed

to be constant during a braking event. This is how the current braking system operates. The brake

force is calculated based on the required force needed to stop the plane within the required distance.

47

The second method we use to calculate the brake force aims to minimize the peak heat

dissipation rate required by the brakes. To do this, the brake force increases as the velocity of the

plane decreases in such a way that the required brake power is held constant. At some point, the

maximum acceleration achievable by the plane is reached and the brake force has to be held

constant. At this point the heat dissipation rate decreases through the remainder of the braking

event. To hold the power constant, a relationship between the brake force and the velocity is

created. We begin with the definition of power

Pbrake = Fbrake ∙ x, (9)

where 𝑃𝑏𝑟𝑎𝑘𝑒 is the power requirement of the brake, 𝐹𝑏𝑟𝑎𝑘𝑒 is the braking force, and �� is

the velocity of the aircraft. In the first brake force calculation, we hold 𝐹𝑏𝑟𝑎𝑘𝑒 constant and let

𝑃𝑏𝑟𝑎𝑘𝑒 vary with velocity, however in this case we hold 𝑃𝑏𝑟𝑎𝑘𝑒 constant and the brake force varies

with time, and it varies according to

Fbrake =Pbrake

x. (10)

As the velocity approaches 0, the force approaches infinity, however there is some

maximum force that can be applied on the aircraft. When this limit is reached, the total force on

the aircraft is held constant at which point the power decreases.

3.1.3 Thrust Reverser Force Modeling

The thrust reverser force 𝐹𝑡𝑟𝑢𝑠𝑡 𝑟𝑒𝑣 is currently assumed to do 20% of the braking force.

This number is only used as a reference value, as during the sizing event (rejected-takeoff

certification) the thrust reversers are not used. Because we are currently focusing on sizing the

braking system, we are not concerned with the requirements of a standard landing.

3.1.4 Brake Power Determination

Combining equations (1) and (2) we obtain the equation

m��(t) = 1

2ρCdSx(t)2 + Fbraking + Fthrust rev , (11)

which is a non-linear differential equation describing the motion of the aircraft with the initial

conditions of ��(0) = 𝑉0 and 𝑥(𝑡𝑠𝑡𝑜𝑝) = 𝐷𝑠𝑡𝑜𝑝 , where 𝑡𝑠𝑡𝑜𝑝 is the time at which the airplane comes

to a stop. The equation can be numerically solved for ��(𝑡) and 𝐹𝑏𝑟𝑎𝑘𝑖𝑛𝑔. The stopping distance

48

𝐷𝑠𝑡𝑜𝑝 and initial velocity 𝑉0 are based on Federal Aviation Regulations takeoff and landing field

length requirements. To get the power requirement of the brakes, we use the equation

Pbrakes(t) = x(t)Fbraking , (12)

where 𝑃𝑏𝑟𝑎𝑘𝑒𝑠 is the rate of the brakes kinetic to thermal energy conversion. All parameters used

in these equations are summarized with the values given in Table 8 [25, 27].

Table 8: Aircraft Parameters [3]

Parameter Value Parameter Value

Max Takeoff Weight (W) 174,200 lbs Go/No-Go Velocity (V0) 154 knots

Max Landing Weight (W) 146,300 lbs Landing Velocity (V0) 155 knots

Standard Landing Weight (W) 131,400 lbs RTO Stop Distance (Dstop) 3,480 ft

Wing Area (S) 1341 sq. ft Landing Stop Distance (Dstop) 5,220 ft

Table 8 details parameters such as those on the left (maximum takeoff and landing weight, standard

landing weight, and wing area), which are specifications of the selected aircraft, the Boeing 737.

Additionally, specifications on the right (Go/No-Go Velocity, Landing Velocity, RTO stop

distance, and landing stop distance) are requirements created an enforced by the FAA.

The calculation works by choosing an initial guess of the required brake force and

calculating the distance required for the plane to stop by solving the differential equation, Equation

9, for 𝑥(𝑡) using a MatLab solver. It then checks to see if that distance is equal to the stopping

distance required, and chooses a new braking force based on how far off the value was and repeats

the calculation until the correct force is found. Then the forces velocity, and heat dissipation rates

are tracked and outputted.

3.2 Power Requirements Results

We ran three cases to determine the requirements of the brakes: rejected takeoff,

emergency landing, and a standard landing. The RTO proved to have the largest load on the brakes,

making it the sizing point for our system. Table 9 below summarizes our results for the constant

braking force case:

49

Table 9: Energy Requirements Summary, Constant Brake Force

Per Brake

Event Peak Power Average Power Brake Force

Rejected Takeoff Certification 4.4 MW 2.1 MW 55.7 kN

Emergency Landing

Certification

3.2 MW 1.5 MW 40.2 kN

Standard Landing 1.4 MW 0.62 MW 18.1 kN

As shown above in Table 9, the RTO certification required the most power and brake force

over the course of the braking event. The peak power of this braking event is 4.4 MW while the

average power was 2.1 MW. The brake force required to stop the aircraft in the required distance,

according to our calculations was 55.7 kN. The large peak power means that the heat exchanger

will increase in mass to be able to reject all of the heat, so we sought to reduce this peak power by

gradually increasing the force over the course of the braking event and holding the power constant

until the force exceeds the maximum force that the wheels and landing gear can apply. This means

the total kinetic to thermal energy conversion is the same as during a standard braking event, but

it is carried out at a constant, lower power. Table 9 summarizes the peak and average power with

holding the power constant for a significant portion of the braking event.

Table 10: Energy Requirements Summary: Constant Brake Power

Per Brake

Event Peak Power Average Power

Rejected Takeoff Certification 2.9 MW 2.1 MW

Emergency Landing Certification 2.0 MW 1.5 MW

Standard Landing .76 MW 0.62 MW

By holding the power constant over the braking event, we can drop the peak power of the

event significantly. The peak power for the “low-power” case for RTO shown in Table 10 has a

peak power of 2.9 MW compared to the 4.4 MW of the constant brake force case shown in Table

9. This allows us to downsize the heat exchanger required in the fluidic brake as much as possible.

3.2.1 Rejected Take-Off (RTO) Certification

During a rejected takeoff certification, in which spoilers are fully deployed and maximum

manual braking is applied, it was found that each brakes see a peak load of 4.41 MW, which

decreases to zero linearly over the 25.3 second braking event. Since there are four wheel hubs on

50

our modeled Boeing 737, this means that the peak load for the entire aircraft is approximately

17.64 MW. This event can be seen in Figure 22

Figure 22: RTO Power Dissipation Constant Brake Force

The drag power dissipation decreases exponentially because the drag force is proportional

to velocity squared, as Equation (2) describes. It can be seen in Figure 22 that the brakes are the

primary means of braking. This means that the aircraft’s wheel brakes are responsible for

managing the most amount of thermal energy, converting 211.7 MJ of kinetic energy to heat and

applying a total of 222.7 kN of force on the aircraft. This force and conversion from kinetic energy

to thermal energy is what slows the aircraft, and is shown in the following Figure 22. Because the

brake force is constant, the heat dissipation rate seen in Figure 22 follows the velocity curve, which

is nearly linear as seen in Figure 23.

51

Figure 23: RTO Velocity Constant Brake Force

In order to minimize the maximum sizing point of the brakes, it is beneficial to reduce the peak

power across the braking event. This is because the brakes are designed to handle the worst case

scenario to avoid failure. This can be accomplished by increasing the brake force over the duration

of the braking event. In this scenario, the peak power drops to 2.9 MW while still absorbing the

same 211.7 MJ of energy.

Figure 24: RTO Power Dissipation Constant Power

Figure 24 demonstrates this concept of reduced peak power. In this situation it is seen that

the power is held constant until about 12 seconds into the braking event, at which point it decreases

linearly. At this point, the force exerted has reached the maximum acceleration the aircraft can

52

withstand. To keep the power constant, the force must increase exponentially. The following

figure, Figure 25, shows this result.

Figure 25: RTO Aircraft Forces Constant Power

Rather than having a constant drag force, as is done with conventional braking systems,

Figure 25 shows how the braking force from Equation (1) can be increased over time to keep the

power constant. This also means that the velocity no longer follows a near linear trend, but is

concave down during the event, shown in Figure 26.

Figure 26: RTO Velocity Constant Power

53

3.2.2 Emergency Landing Certification

During an emergency landing situation, the spoilers are fully deployed, maximum manual

braking is applied, and the aircraft is at the maximum landing weight. It was found that each brake

experiences a peak load of 3.20 MW, which decreases to zero linearly over the 28.5 second braking

event. The total energy absorbed by the brakes during the procedure is 170.4 MJ. Again, during

an emergency landing, the brakes are the primary mode in which the kinetic energy of the aircraft

is absorbed. The brake has to apply 160.6 kN of force on the aircraft. A graph of the power

dissipated by the brakes calculated by solving Equation (1) is shown in Figure 27.

Figure 27: Emergency Landing Power Dissipation

As with the RTO, the velocity follows a nearly linear trend, shown in Figure 28. The main

difference between the emergency landing power dissipation figure and the rejected take off power

dissipation figure is the total amount of energy that is absorbed by the brakes as well as the peak

power experienced. Although the rejected take off is the most important situation to look at, as it

will determine the overall sizing of the brakes, it is important to understand how the brakes perform

during alternative operations. In the next figure, the velocity graph for the emergency landing is

shown.

54

Figure 28: Emergency Landing Velocity Constant Brake Force

As with the rejected take off, the next step was to reduce the peak power by making the

power more consistent across the entire braking event. Reducing the power by holding it constant

drops the peak power to 2.0 MW, as determined by Equation (1), while still absorbing the same

170.4 MJ of energy. This is achieved as discussed before with the RTO certification.

Figure 29: Emergency Landing Power Dissipation Constant Power

Figure 29 shows the emergency landing power dissipation with minimized peak power. The forces

required to accomplish this constant power are demonstrated in the following Figure 30.

55

Figure 30: Emergency Landing Forces Constant Power

Similar to the forces for the rejected take off, the force increases over time during the

braking event in accordance with Equation (1). This causes the velocity to have a concave-down

shape as shown in Figure 31. This means that although the velocity is decreasing from the initial

action, the aircraft has positive acceleration until the aircraft comes to a stop.

Figure 31: Emergency Landing Velocity Constant Power

3.2.3 Standard Landing

During a standard landing, the spoilers are fully deployed, thrust reversers are engaged,

and the aircraft is at its end of mission weight. It was found that each brake experiences a peak

56

load of 1.44 MW which decreases to zero linearly over the 46.8 second braking event. Again, this

calculation remains consistent with the other calculations resulting from Equation (1), as the

standard landing creates a peak load less than that of the rejected take off or the emergency landing.

Figure 32: Standard Landing Power Dissipation

The total energy absorbed by the brakes during the procedure is 115.4 MJ. The brakes have

to apply 72.6 kN of force on the aircraft. This result is shown below in Figure 32. Because the

brake force is constant, but the drag force, which decreases over time, is a significant portion of

the forces on the aircraft, the velocity curve is concave-up, as shown in Figure 33.

Figure 33: Standard Landing Velocity Constant Brake Force

57

The peak power can be reduced to .75 MW by increasing the brake force in Equation (1)

over the course of the event in order to hold the brake power constant, as shown in Figure 34.

Figure 34: Standard Landing Power Dissipation Constant Power

This value for peak power is the lowest of all the calculations. Although brakes would not

normally be sized to this condition, creating a sizing for the system at this design point would

provide a valuable comparison. If the entire fluidic braking system was significantly larger than

the current system (by a given magnitude), than the system could be demonstrated as in feasible,

without having to compare the maximum sizing condition.

The power during this event is constant through the majority of the time period, in order

to do so the brake force is increased over time as shown in Figure 35.

58

Figure 35: Standard Landing Forces Constant Power

Because the brake force is increasing over time, the velocity is again pulled into a concave-

down shape as shown in Figure 36, as it was for both the rejected take off as well as the emergency

landing.

Figure 36: Standard Landing Velocity Constant Power

3.3 Water Deluge Brake Cooling

The first alternative braking system that was explored was a water deluge brake cooling

system; a form of liquid cooled braking system that would utilize the potable water stored on the

59

aircraft for rejected takeoff scenarios. In a rejected takeoff scenario, the potable water could be

gravity fed through tubing to the brake stacks, to either downsize the amount of brake material, or

to simply increase the factor of safety of the aircraft. Although this has the potential to destroy the

brakes due to the thermal gradient, it could save surrounding components, the aircraft and

consequently the passengers aboard.

To begin the feasibility of this concept, it was necessary to find out how much thermal

energy could be stored in the fluid to be applied to the braking system. To do this, the mass of the

fluid, its thermal capacity, the change in temperature, and the heat of vaporization are all used in

a single equation, which is

𝑚𝑤𝑎𝑡𝑒𝑟 =��

𝐶𝑤𝑎𝑡𝑒𝑟Δ𝑇+ℎ𝑣𝑎𝑝 𝑤𝑎𝑡𝑒𝑟, (13)

where 𝑚𝑤𝑎𝑡𝑒𝑟 is the mass of the fluid, �� represents the excess heat of the braking system,

𝐶𝑤𝑎𝑡𝑒𝑟 represents the specific heat of the fluid, Δ𝑇 is the change in temperature within the brakes

and ℎ𝑣𝑎𝑝 is the heat of vaporization needed to turn the water into vapor. According to this

calculation, it would only take 24.9 kg, or just over 6.5 gallons of water needed to completely cool

the brake. By making the brake smaller in accordance to this amount of water, approximately 75

kg could be removed from the aircraft, assuming that the piping for the fluid is massless. The main

advantage of this system is that most of the mass needed to operate this system already exists on

the aircraft. Although tubing would need to be included, the mass of water is a system that already

exists on the aircraft and could be utilized for rejected take off.

Despite this massive amount of weight that could be cut from the aircraft, this design does

not exist without its own set of limitations and problems, such as how to apply the fluid to the

braking system. Current wheel brakes are designed to entrap all of the heat, which means there is

little to no room available for piping or spray nozzles. Additionally, such spraying creates

temperature gradients within the stack of carbon-carbon brake pads causing cracking and further

damage to the braking system.

3.4 Open Evaporation Feasibility

Although a different physical system, the open evaporation cooling system would cool

water in the same manner as the water deluge method outlined in the previous section. Instead of

spraying the extra potable water directly on the brake, this concept would run the water through a

60

component of the braking system, such as the torque bars, which would then evaporate the water.

In Figure 37, a possible configuration for the fluidic system illustrates how the fluid could run

through the torque bars to become evaporated.

Figure 37: Torque Bar Open Loop Evaporator

As shown, piping could be laid down through the torque bars to act as a heat exchanger. However,

the consequences of how this might affect the integrity of the torque bars, or the total force that

they would be able to withstand is unknown, and would have to be explored further if this idea

was to be implemented.

3.5 Fluidic Brake Modeling

Our model consists of four primary components: a pump, a heat sink, a heat exchanger,

and a throttling valve. The pump, located within the wheel hub, is the component that creates the

braking torque that converts the kinetic energy of the aircraft into heat. This heat is then stored

within the fluid. The heat sink stores a fraction of the braking power within the structure of the

landing gear. The heat exchanger actively rejects this heat to the atmosphere or other thermal

61

storage device. The valve reduces the pressure of the fluid to the inlet pressure of the pump. This

accounts for the thermal energy that can be stored within the fluid. A conceptual diagram of the

system is displayed below in Figure 38 [25, 27].

Figure 38: Fluidic Brake System Diagram

We modeled each component individually, with the inlet conditions associated with the

previous states outlet conditions. For example, the inlet pressure and temperature of the throttling

valve would be the same as the outlet pressure and temperature from the heat exchanger. The

model then steps through each stage for differential time-steps throughout the braking event.

Because the operating time steps for this system are very small (0.01 seconds), we assume that for

a given time step each component operates at steady state, with the state conditions changing for

62

each time step to approximate the transient nature of the system. Aside from the transient

temperatures and flowrate, there is an energy accumulation within the system, which is neglected

in steady state equations. We model this temperature accumulation using a thermal reservoir

method within each component. In this method, a total mass of working fluid is defined, with

specified fractions of this total mass associated with each state of the system model. The fluid mass

defined for each component are shown in Table 11.

Table 11: Fluid Mass Per Component

Component Fluid Mass (kg)

1 Pump 6.0

2 Heat Sink 6.0

3 Heat Exchanger 6.0

4 Valve 2.0

5 Total 20.0

We derived equations that model the fluid mass for any given component. Any excess heat,

that is not rejected by the heat exchanger, increases the temperature of the fluid throughout the

duration of a given braking event. This is modeled with a numerical integration of the net amount

of energy going into the component. We can say that the amount of energy that enters the

component over a small time-step, Δ𝑡, is

Uin = mC (Tin(t) − Tout(t − 𝛥t))𝛥t (14)

where 𝑇𝑖𝑛(𝑡) is the temperature of the fluid entering a given component at that instant and

𝑇𝑜𝑢𝑡(𝑡 − Δ𝑡) is the outlet temperature of the component at the previous time-step. We can also say

that the temperature change of a given mass of fluid is given by:

𝛥𝑇 =

Uin

mfluidC

(15)

Now, we can determine the outlet temperature of the component by the equation

Tout(t) =m( (t)−Tout(t−𝛥t))𝛥t

mfluid+ Tout(t − 𝛥𝑡). (16)

Equation (49) is implemented in each component of the model. This accounts for the

transient heat accumulation within the system. The remainder of the analysis is done using the

assumption of steady state components as previously discussed [8].

63

3.5.1 Centrifugal Pump Modeling

The pump converts the kinetic energy of the aircraft into thermal energy through frictional

losses between the impeller vanes and the variable viscosity magnetorheological fluid. To derive

the changes in temperature and pressure within the pump, we begin with the first law of

thermodynamics for a flowing system

W𝑐𝑣

��= ℎ2 − ℎ1, (17)

where ��𝑐𝑣 is the work done on the control volume of fluid within the pump, �� is the mass flow

rate through the pump, and ℎ1 and ℎ2 are the enthalpies at states 1 and 2 respectively. Assuming

that the MRF used as the working fluid within the system is an incompressible liquid, we can

approximate that

ℎ2 − ℎ1 = 𝐶(𝑇2 − 𝑇1) +𝑃2−𝑃1

𝜌, (18)

where 𝐶 is the specific heat capacity of the fluid, 𝑇1, 𝑃1, 𝑇2, and 𝑃2 are the temperatures and

pressures at states 1 and 2 respectively, and 𝜌 is the density of the working fluid. Furthermore, the

isentropic efficiency of the pump can be defined as

𝜂 =ℎ2𝑠−ℎ1

ℎ2−ℎ1, (19)

where ℎ2𝑠 is the enthalpy resultant from an entirely isentropic pump. Simplifying this expression,

we find that

ℎ2 − ℎ2𝑠 = (ℎ2 − ℎ1)(1 − 𝜂). (20)

Because the pressure ratio for an isentropic pump and a non-isentropic pump are equivalent, we

find that

ℎ2 − ℎ2𝑠 = 𝐶(𝑇2 − 𝑇2𝑠). (21)

Now, combining Equation (21) with the first law of a flowing system, we find that

𝑇2 = 𝑇2𝑠 +��

��𝐶(1 − 𝜂), (22)

Where 𝑇2𝑠 is the temperature change in an isentropic system and ��

��𝐶(1 − 𝜂) represents the

temperature increase greater than the change in temperature for an isentropic pump system. For an

aircraft fluidic braking system, the braking power is

𝑃𝑏𝑟𝑎𝑘𝑒𝑠 = ��, (23)

where �� is the total mechanical work done on the fluid within the control volume. By substituting

this expression into the first law representation of a pump, we find that

64

𝑃𝑏𝑟𝑎𝑘𝑒𝑠

��= 𝐶(𝑇2 − 𝑇1) +

Δ𝑃

𝜌. (24)

Equation (19) can be rewritten in terms of a different standard set of fluid parameters such that

𝑃𝑏𝑟𝑎𝑘𝑒𝑠 = 𝜌��𝐶(𝑇2 − 𝑇1) + 𝐻𝑔𝜌��, (25)

where �� is the volumetric flow rate of fluid through the system defined as

�� =��

𝜌, (26)

and 𝐻 is the hydraulic head of the system defined as

𝐻 =Δ𝑃

𝜌𝑔, (27)

where 𝑔 is the acceleration due to gravity. The head for a given pump is defined by a characteristic

pump curve that describes the performance of the pump as a function of volumetric flowrate 𝐻(��)

for a given pump angular velocity. The characteristic pump curve is a design requirement which

must be met for the system to be able to transfer the braking power to the fluid as heat. Because of

this, many possible characteristic pump curves can be used to define the fluidic braking system.

Figure 39 shows the characteristic pump curve requirement generated using our fluidic braking

system model in Matlab.

Figure 39: System Characteristic Pump Curve

This characteristic pump curve determines how the pump operates at a given angular

velocity of the impeller, however, as the angular velocity of the pump decreases over the duration

65

of the braking event, the pressure rise across the pump decreases according to the pump affinity

law

𝑃𝑓 = 𝑃𝑖 (

𝜔𝑓

𝜔𝑖)

2

, (28)

where 𝜔𝑓 and 𝜔𝑖 are the final and initial angular velocities of the pump and 𝑃𝑓 and 𝑃𝑖 are the final

and initial pressures where the initial pressure is dependent on the characteristic pump curve [49].

With this information, we can solve the equation

𝑇2 = 𝑇1 +𝑃𝑏𝑟𝑎𝑘𝑒𝑠−𝜌𝑔��𝐻

𝜌𝐶��, (29)

for the volumetric flow rate of the system, as the input temperature 𝑇1 is known and the output

temperature 𝑇2 is required to be the maximum operating temperature of the fluid of 200 °C.

Solving for this flowrate then allows us to calculate the pressure at the outlet of the pump according

to

𝑃2 = 𝑃1 + 𝜌𝑔𝐻, (30)

where, as above, 𝐻 is a function of volumetric flowrate. Solving for the outlet conditions of the

pump (𝑃2, 𝑇2, and ��) at each time step provides us with the inlet conditions within which we can

solve the next component in the fluidic braking model, the heat sink.

3.5.2 Heat Sink Modeling

The outputs of the pump model describe state 2 of our fluidic braking system. State 2 also

defines the inlet conditions of the heat sink. The heat sink is physically represented by the thermal

mass of the landing gear structure and fluidic system piping. This thermal mass has the capability

of storing energy, effectively reducing the required active heat rejection within the heat exchanger.

This heat sink is modeled by allotting a constant fraction of the time variant braking power to be

stored within the landing gear structure as described by

��1 = 𝑓𝑄𝑃𝑏𝑟𝑎𝑘𝑒𝑠 , (31)

where ��1 is the heat rejected from the fluid into the heat sink and 𝑓𝑄 is the fraction of the brake

power that is to be stored within the landing superstructure. Using Equation (31), we can now

calculate the temperature of state 3 as

𝑇3 = 𝑇2 −��1

��𝐶 . (32)

For the heat sink component, we assume that the output pressure

66

𝑃3 = 𝑃2, (33)

because of the lack of piping geometry required to calculate a pressure drop. This assumption

simply is corrected within the throttling valve model where the system pressure is dropped back

to the pump inlet pressure condition. With state 3 known, the heat exchanger inlet conditions are

determined and this component can be analyzed.

3.5.3 Heat Exchanger Modeling

To calculate outlet conditions of our heat exchanger, we use the effectiveness NTU method

for cross-flow heat exchangers. First, we calculate the heat capacity rate of both the hot and cold

sides, and use the minimum value [49, 50].

Cmin = 𝑚𝑖𝑛 (mc(t)Cc , mh(t)Ch) (34)

This minimum value represents the maximum power (in kW) that can be dissipated per degree

Kelvin of temperature. The effectiveness NTU method relies on knowing a quantity known as the

effectiveness of the heat exchanger. The effectiveness is defined as the fraction of the maximum

heat that can be transferred between the two fluid streams within the heat exchanger. This

effectiveness varies with hot and cold side flow rates, which changes the fluidic braking system’s

transient states. This variation can be expressed in terms of a heat exchanger effectiveness map.

Figure 40 shows the effectiveness map of the heat exchanger used within the mathematical model

for the fluidic braking system.

Figure 40: Heat Exchanger Effectiveness Map

67

In Figure 40, the effectiveness of the heat exchanger varies non-linearly with both hot and cold

side flow rate. The positive to negative change in slope occurs when the maximum heat capacity

rate is changed to be defined by the other fluid. Using this effectiveness map, we can find the

total active heat rejection achieved by the heat exchanger for a given time step by using

��2 = 𝜖𝐶𝑚𝑖𝑛(𝑇3 − 𝑇𝑎𝑡𝑚), (35)

where 𝜖 is the effectiveness of the heat exchanger based on the effectiveness map, 𝐶𝑚𝑖𝑛 is the

maximum achievable heat capacity rate from the hot side fluid to the cold side fluid, 𝑇3 is the

temperature of the working fluid entering the hot side, and 𝑇𝑎𝑡𝑚 is the temperature of atmospheric

air entering the cold side. The hot side of the heat exchanger refers to the channels where heated

fluid, in this case the MRF, is flowing. Conversely, the cold side of the heat exchanger refers to

channels in which cool fluid, in this case atmospheric air, is absorbing heat from the hot fluid.

Using the value for the total active heat rejection for a given time step, we can solve for the outlet

temperature of the heat exchanger

T4 = T3 −

��2

��𝐶 ,

(36)

where ��2 is the active heat rejection of the heat exchanger. To calculate the change in pressure

within the heat exchanger, we utilize pressure correlations provided by our sponsor. Figure 41

shows the variation of the pressure drop across the heat exchanger as a function of hot side flow

rate.

Figure 41: Hot Side Pressure Drop Correlation

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20 25 30 35 40 45

Pre

ssure

Dro

p (

Pa)

Flow Rate (kg/s)

Hot Side Pressure Drop Correlation

68

This correlation is also represented by the second order polynomial

𝑃4 = 𝑃3 − (28.67��2 + 517.1��2), (37)

where 𝑃4 is the outlet pressure of the heat exchanger and 𝑃3 is the inlet pressure of the heat

exchanger. With the outlet conditions now solved for, we can move on to the valve model.

3.5.4 Valve Modeling

Our valve model operates by dropping the pressure of the system after leaving the heat

exchanger back to the required pump inlet pressure. Because the pressure leaving the heat

exchanger as a function of time and the starting pressure are known, a required change in pressure

(Δ𝑃) is known for the valve.

To derive the model equations used for modeling a throttling valve to drop the pressure in

the system, we begin by defining enthalpy,

𝐻 = 𝑈 + 𝑃𝑉, (38)

where H is enthalpy, U is internal energy, P is pressure, and V is volume.

Now applying the second law of thermodynamics [51], we get:

𝑑𝐻 = 𝑇𝑑𝑠 + 𝑉𝑑𝑃 (39)

Entropy in incompressible liquids is:

𝑑𝑆 =

𝑑𝑈

𝑇

(40)

Now multiplying Equation (40) by 𝑑𝑇

𝑑𝑇 we get:

𝑑𝑆 =

𝑑𝑈

𝑑𝑇

𝑑𝑇

𝑇

(41)

Given that:

𝑑𝑈

𝑑𝑇= 𝐶𝑣(𝑇)

(42)

within the operating range of our system, 𝐶𝑣 = 𝑐𝑣𝑚 = 𝑐𝑚 = 𝐶 where 𝑐𝑣 is the specific heat of the

fluid and 𝑚 is the mass of the fluid in the control volume. 𝐶 is a constant, so that:

𝑑𝑆 = 𝐶

𝑑𝑇

𝑇

(43)

Substituting the result from Equation (43) into Equation (39) we get:

𝑑𝐻 = 𝐶𝑑𝑇 + 𝑉 ∙ 𝑑𝑃 (44)

This simplifies to:

𝐻2 − 𝐻1 = 𝐶(𝑇2 − 𝑇1) + 𝑉(𝑃2 − 𝑃1) (45)

69

Now normalize the result above by dividing the mass of the fluid within the control volume to get

Δℎ = 𝑐Δ𝑇 + 𝑣Δ𝑃 (46)

where 𝑣 is the specific volume of the fluid and ℎ is the specific enthalpy. Across a throttling valve

the enthalpy is constant so Δℎ = 0. Solving for Δ𝑇 now gives:

𝛥T = −

𝑣𝛥P

c

(47)

Where Δ𝑃 is the pressure drop across the valve, 𝑣 is the fluid specific volume (assumed to be an

incompressible liquid), and 𝑐 is the specific heat of the fluid [52].

3.6 Fluidic Brake Modeling Results

The model is designed to examine the thermodynamic feasibility of using a fluidic brake

to stop an aircraft, as well as provide us with conditions to size the major components to provide

an insight into the weight of the system so it could be compared to the current braking system.

This section will discuss the outputs from the model, including the transient pressures,

temperatures, and flowrates, as well as provide a statement of feasibility of utilizing a fluidic brake

on an airplane.

3.6.1 Model Output

The model examines the transient mass flow rate, as well as pressures and temperatures at

each state within the cycle as the system progresses through the braking event. The state plot of

the cycle at 2.5 seconds into a rejected takeoff certification is show in Figure 42.

70

Figure 42: Fluidic Brake State Plot

Figure 42 illustrates how the state of the fluid is changing throughout the braking event. The

pump increases the temperature and pressure from State 1 to State 2. The heat sink then decreases

the temperature and pressure some from State 2 to State 3. The goal of the heat sink is to reduce

the load on the main heat exchanger, which decreases the temperature significantly and reduces

the pressure between State 3 and State 4. Next, the fluid passes though the valve, which reduces

the pressure to the inlet pressure of the pump between State 4 and State 1 so the cycle may continue.

All of the heat generation takes place in the pump, and the majority of the heat is rejected by the

heat exchanger.

Each of the states shown in Figure 42 changes as the braking event progresses and the mass

flowrate and heat exchanger heat rejection change. This section examines each of these transient

variables in detail.

71

State 1: Valve Outlet / Pump Inlet

The valve is designed to always bring the pressure down to atmospheric so that there is not

pressure accumulation within the system, this allows the pump to operate with a constant pressure

inlet condition as described in Equation (30). Figure 43 shows this constant pressure of the pump

inlet.

Figure 43: State 1 - Valve outlet / Pump Inlet Pressure

The inlet temperature, however, is changing constantly. Figure 44 shows how the temperature

changes with time.

72

Figure 44: State 1 – Valve Outlet / Pump Inlet Temperatures

In Figure 44, it is seen that from 0-13 seconds the inlet temperature is increasing. This is

because the heat exchanger cannot possibly reduce the temperature of the fluid all the way to

atmospheric without being incredibly large, so temperature accumulates within the fluid as the

braking event progresses. From 0-2 seconds it is increasing more quickly because the pump outlet

temperature is not immediately at the fluid maximum temperature. There is some period required

to warm up the fluid within the pump, which happens more quickly than the temperature

accumulation within the whole system. At around 13 seconds, the inlet temperature mostly levels

off. This is a result of the input power beginning to decrease as shown in Figure 24. As the power

decreases the heat exchanger is able to reject enough heat to keep the system at near steady state

and around 19 seconds the heat exchanger is able to reject more heat than the pump is generating

so the temperature decreases. The wavy portion of the graph is a result of the interpolation method

used for the heat exchanger effectiveness map, which causes slightly discontinuous changes in

effectiveness resulting in a discontinuous line.

State 2: Pump Outlet / Heat Sink Inlet

The pump increases the pressure and temperature of the fluid in order to absorb the kinetic

energy of the aircraft. Figure 45 shows the pressure decreasing throughout the braking event.

73

Figure 45: State 2 - Pump Outlet Pressure

The pump increases the pressure and temperature of the fluid in order to absorb the kinetic

energy of the aircraft. The outlet pressure of the pump decreases as the event progresses because

the rotational speed of the pump is decreasing, which according to the pump affinity relationships

discussed in section 3.5.1, reduces the pressure generating capabilities of the pump.

The outlet temperature of the pump is nearly constant because the system is constrained to

increase the temperature of the fluid to its maximum temperature. Figure 46 shows the temperature

of the pump outlet increasing to the fluid’s maximum temperature before remaining constant.

74

Figure 46: State 2 - Pump Outlet Temperature

The outlet temperature increases between 0-2 seconds because there is a warmup time

associated with warming up the fluid that is already in the pump, so the output temperature is not

immediately the maximum temperature of the fluid.

State 3: Heat Sink Outlet / Heat Exchanger Inlet

The heat sink reduces the temperature and pressure of the fluid by storing some of the heat

from the braking event within the structure of the landing gear. Figure 47 shows the outlet pressure

of the heat sink, which is less than the outlet pressure of the pump because there is a pressure drop

associated with the heat sink.

75

Figure 47: State 3 - Heat Sink Outlet Pressure

The pressure decreases in the same manner as the pump outlet because the pressure drop

across the component is assumed to be some percentage of the total pressure. The temperature,

however, increases to near steady state, as shown in Figure 48.

Figure 48: State 3 - Heat Sink Outlet Temperature

76

The temperature increases from 0-2 seconds because of the warmup time associated with

the fluid within the system, and then remains mostly constant because it is assumed that this heat

sink absorbs a constant percentage of the input power.

State 4: Heat Exchanger Outlet / Valve Inlet

The heat exchanger actively rejects the heat generated during the braking event. Because

the fluid cannot store a significant portion of the heat generated during a rejected takeoff, the heat

exchanger must reject the majority of the heat during the event. However, because heat does

accumulate within the fluid because the heat exchanger cannot bring the temperature down to the

initial condition without being incredibly large, this causes the temperature to increase during the

braking event, as shown in Figure 49.

Figure 49: State 4 - Heat Exchanger Outlet Temperature

The reasons for the specific shape of this plot are discussed in the State 1 section. The outlet

pressure of the heat exchanger also reduces relative to the pump outlet pressure, which is

decreasing throughout the braking event. The heat exchanger outlet pressure is shown in Figure

50.

77

Figure 50: State 4 - Heat Exchanger Outlet Pressure

This plot follows the outlet pressure of the pump, as described by the pump curve and the

pump affinity laws described in section 3.5.1 Centrifugal Pump Modeling. The heat rejection of

the heat exchanger is closely related to the required brake power, because the amount of heat stored

in the fluid is very small in comparison to the total energy of the braking event. Figure 51 shows

the heat rejection of the heat exchanger.

78

Figure 51: Heat Exchanger Heat Rejection

The heat exchanger’s heat rejection increases for the first two seconds as the system’s fluid

mass warms up at which point it remains fairly constant until the point where the input power starts

decreasing, at which point the heat rejection also decreases.

79

Mass Flow Rate

Figure 52: Fluidic Brake Mass Flow Rate

Figure 52 shows the mass flowrate of the system during a rejected takeoff certification using

the low power force curve, discussed in Section 3. From 0 to about 13 seconds, the mass flowrate

is increasing. This is a result of the fluid accumulating heat, causing the pump inlet (State 1)

temperature to increase. This means the pump has to move more fluid through the system to keep

the fluid from reaching its maximum temperature. Between 0 and 2 seconds the mass flowrate is

increasing more quickly than for the rest of the period. This is because the pump output

temperature is not immediately the fluid maximum temperature because there is a warm up period

for the fluid already in the pump. As the fluid in the pump warms up, the mass flowrate must

increase to keep the temperature beneath the fluids maximum temperature. At about 13 seconds,

the flow rate starts to decrease. This is when the input power starts to decrease as shown in Figure

24, requiring less flow to keep the fluid within its operating range.

3.6.2 Pump Efficiency

The pump efficiency needs to be very low in order for the system to keep the pressure

within a reasonably low pressure because we want it to convert the majority of the shaft power

into heat rather than increasing the pressure. This means that the efficiency needs to be less than

80

.05% efficient in order to keep the pressure to 30 psi. Figure 53 shows the pump efficiency mostly

decreasing as the cycle moves through the event.

Figure 53: Fluidic Brake Pump Efficiency

The pump efficiency has to decrease as seen in Figure 53 because the output pressure of the

pump decreases as the rotational speed of the pump decreases, but the pump still has to complete

the required kinetic to thermal energy conversion and increase the temperature of the fluid to its

maximum temperature, reducing the efficiency as defined in section 3.5.1. This trend can be shown

by plotting the efficiency versus the pressure for a given fluid, as shown in Figure 54.

81

Figure 54: Pump Outlet Pressure vs. Pump Efficiency

As the outlet pressure decreases, the pump efficiency must increase to maintain the

required outlet temperature and absorb the shaft power required to stop the aircraft. The equations

outlined in Section 3.5.1 indicate that that the pressure rise of the pump is solely dependent on

fluid properties and the pump efficiency. The efficiency of the pump has to be extremely low in

order to keep the pressures within a reasonable bound. A high-pressure system is undesirable

because if the system were to leak or rupture, the aircraft would be unable to stop.

From Figure 54, is seen that the most desirable fluid is the hydrocarbon-oil because it can

maintain reasonable pressures with the highest efficiency, but it also requires a higher flow rate,

and consequently a higher total fluid. However, regardless of the fluid an incredibly low pump

efficiency is required. An optimization between heat exchanger size and pump efficiency can be

applied to the fluid selection of the system.

3.6.3 Heat Exchanger Sizing

The heat exchanger is a major component of the system whose size and weight greatly

affect the feasibility of the system. A heat exchanger that is too heavy or has a volume that is too

large to fit on the aircraft would greatly decrease the feasibility of a MRF braking system. As such,

the heat exchanger is the first component we looked at in terms of size and weight.

Using our sponsors’ heat exchanger sizing toolbox, we obtained a weight of the heat

exchanger as well as the heat exchanger effectiveness map as described in Section 0. The point

82

that the heat exchanger is sized for the maximum shaft power with the minimum cold side flow

rate, which occurs right before the input power begins to decrease, as shown in Figure 24. Table

12 shows the hot and cold side flow rates, temperatures, and pressures that are required for the

heat exchanger sizing toolbox to generate a heat exchanger design and output the desired weight,

dimensions, and effectiveness map. The hot and cold side fluid properties are shown in Table 13.

Table 12: Desired Test Cases for Cross Flow Heat Exchanger

Hot Side Parameters Cold Side Parameters

Inlet Temperature 190.62 C 20 C

Outlet Temperature 108.2 C N/A C

Inlet Flow rate 39.96 kg/s 50.3 kg/s

Inlet Pressure 150.6 kPa 10.3 kPag

Max dP 90.3 kPa 10.3 kPa

Table 13: Cross Flow Heat Exchanger Analysis Fluid Parameters

Hot Side Fluid Parameters (MRF-132DG) Cold Side Fluid Parameters (Air)

Density 3080 kg/m^3 Density 1.225 kg/m^3

Specific Heat 0.8 kJ/Kg K Specific Heat 1.005 kJ/kg K

Conductivity .20 W/m K Conductivity .024 kJ/kg K

According to the heat exchanging sizing tool provided by our sponsor, the heat exchanger

core would weigh 222.6 kg and have dimensions of 1.45x1.45x.29 meters. which can be seen in

Table 14.

Table 14: Heat Exchanger Size

Quantity Value Units

Mass 222.6 kg

Width 1.45 m

Height 1.45 m

Thickness .29 m

Volume .617 m3

3.6.4 Statement of Feasibility

The feasibility of this braking system concept relies on three primary concerns. These concerns

should be evaluated to decide on the continuation of this work. These concerns are as follows:

1. The heat exchanger, based on design parameters from our system model, is considerably

heavier than the weight of the current braking system. This weight may be able to be

reduced using one or more of the following options:

83

a. Utilization of phase change material for thermal storage

b. Greater thermal storage within the landing and/or aerostructure

c. Implementation of a three stream heat exchanger using water during high energy

braking events

2. Degrading pump efficiency while maintaining high flow rates as required at the beginning

of a given braking event may result in an excessively large pump. The feasibility of this

needs to be investigated using experimentation or high fidelity simulation of the behavior

within a centrifugal pump.

3. The volume of fluid required to fill the four components of the system may result in a fluid

weight.

3.7 Experimental Testing of MRF:

Although this project is unable to run a physical test, an experiment is created and it is

recommended for future work on this project. This main goal of this experiment would be to

experimentally test how pump performance is affected with a varying viscosity. To achieve this,

we planned a test to run MRF through a centrifugal drill pump, while measuring system flow,

pressure, and temperature to compare the power of the drill to the flow of the fluid. The following

diagram, Figure 55, demonstrates how this experimental set up is to be constructed [49]:

84

Figure 55: Experimental Set-Up

By measuring the pressure change and flow of the fluid at various motor powers, we can calculate

a pump efficiency, and ultimately a pump performance curve. By varying the magnetic field

around the pump, we can see how far we can degrade the pump efficiency by increasing the

viscosity. We are not expecting to achieve the incredibly low efficiencies required by the actual

system, but rather examine how significant of an impact the viscosity has on the efficiency. The

parts we are using for this experiment are outlined in the bill of materials in

Table 15: Experimental Bill of Materials

Component Unit Price Quantity Total Price

MRF per Liter $ 750.00 1 $ 750.00

Pump $ 43.54 3 $ 130.62

Tubing (Silicon) $ 14.60 1 $ 14.60

Pressure Meter $ 185.93 1 $ 185.93

Flow Meter (paddle) $ 310.00 1 $ 310.00

Total $ 1 ,304.07

This is an experiment that is expected to cost a total of $1,304, as shown in Table 15. This

experiment is expected to take a week to setup and one to two weeks to perform. Data acquisition

85

will be handled through the use of National Instruments LabVIEW software, and will consist of

data collection for all thermodynamic aspects of the experimental system.

86

CONCLUSIONS AND RECOMMENDATIONS

In conclusion, this Major Qualifying Project of investigating alternative methods of aircraft

braking fulfills the objectives and requirements proposed by the sponsor. First, current brake and

brake cooling technologies are researched to understand what technologies have already been

previously attempted, including problems with carbon-carbon aircraft wheel brakes. Second,

alternative methods of aircraft braking are explored, primarily focusing on an active heat rejection

fluid brake that utilizes magnetorheological fluid as the working fluid. Finally a thermodynamic

model is formulated and analyzed using Matlab. By calculating the inlet and outlet conditions of

the major components, we are able to use Matlab sizing tools provided to us by the sponsor to

calculate the volume and mass to compare with current technologies. This comparison provides

our sponsor important insights about using alternative braking systems.

The first stage of this project is to conduct extensive background research; to understand

the capabilities and limitations of current carbon-carbon frictional wheel brakes. This background

research explains that the purpose of carbon brakes is to act as a heat sink, capturing and holding

all thermal energy generated when bringing the aircraft to a stop. In the case of a rejected takeoff,

these brakes can heat to temperatures of 1500 °C, damaging brake and surrounding aircraft

components. Although cooling systems exist to try to alleviate extreme temperatures, they are not

widely used in order to save weight, complexity, and costs. To improve the current braking system,

a fluidic braking system that utilizes MRF is explored. The primary focus is to reduce the

maximum brake temperature through the use of active heat rejection. However, in order for this

braking system to be considered for commercial airlines, it must be able to trade in both mass and

volume, so that it can be easily integrated onto existing aircraft.

In order to obtain the parameters of the fluidic braking components, a thermodynamic

model is created to determine the initial thermodynamic feasibility of this concept. One of the

major discoveries of this model is that the efficiency of the pump must be approximately 0.1%

efficient in order to effectively add the required heat to the fluid. Once this thermodynamic cycle

is completed, the inlet and outlet pressures of the major components, such as the heat exchanger,

are obtained for the heat exchanger sizing tool, owned by the sponsor. Using this sizing tool, it is

87

determined that the mass of the heat exchanger needed for a rejected takeoff is approximately

350kg, which is three times the mass of a current carbon-carbon braking system.

This project leaves several unanswered questions, allowing room for future project work.

1. What is the possibility of degrading pump performance to low levels such as 0.1% solely

by modulating the viscosity of the MRF? An experimental test procedure is included on

page 91 to test this feasibility.

2. What is the possibility of creating a heat exchanger that is the optimal size, however will

remain within the weight requirements?

3. Will 20 kg of magnetorheological fluid be and adequate enough to withstand the heat and

work in the entire system?

4. Does adding a clutch to the system increase complexity and make this idea unachievable?

5. Would this system be equally or more reliable than any current existing braking system?

6. Is there enough space in the landing gear of the aircraft to safely contain all the equipment

for this system?

This project has a wide range of continuous opportunity for future work and research to better

understand the feasibility of using MRF for a fluidic break. More extensive experimentation and

modeling will be required in order to prove or disprove these questions.

88

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91

APPENDICES

EXPERIMENTAL PROCEDURE OF PUMP PERFORMANCE WITH MRF

Pump Performance of Induced Magnetorheological Fluid

Matthew Dunster Thomas Nuthmann Gregory Stockman Nathan Varney

Goals:

To generate a range of magnetic fields in a centrifugal pump using an electromagnet

To examine various viscosities of magnetorheological fluids within the centrifugal pump

To measure and determine pump head VS flow rate across various viscosities

To measure and determine pump head VS flow rate across various RPM

To confirm pump efficiency by through a fluid temperature relationship

Materials:

1 Non-ferrous centrifugal or lateral ring pump

1 liter of magnetorheological fluid

1 Pressure Transducer

2 Flow meters (1 Paddle, 1 Venturi)

0.5” tubing (5 feet)

Container with minimum volume of 2 L

Thermocouple

Power Supply

DAQ

Computer

Valve (Optional)

Experimental Set Up:

Secure the pump to the test table and ensure it is steady

Connect the hand drill to the pump so that it can be easily operated by hand

Connect the Rotational Torque sensor to the drill so that the output torque of the pump

can be measured

Connect the tubing from the reservoir to the inlet of the pump

Connect the outlet of the pump to the pressure transducer, flow meter, and thermocouple,

before returning back to the reservoir / container

Connect the rotational torque sensor, pressure transducer, flow meter, and thermocouple

to the DAQ

Run the pump at 0.25 the normal operating

92

Experiment:

1. Determine three points of magnetic field to be tested for the fluid. Due to the reactive

nature of magnetorheological fluid the difference in magnetic field needed will only

range between 8-12 mili-tesla.

2. Run the drill pump at one-third the maximum operating rotational speed and at the lowest

magnetic field point. Measure the output pressure, flow rate, and temperature using

Labview software.

3. Repeat step two for two-thirds operating rotational speed and for maximum operating

speed. Compare results.

4. Repeat step three for three different magnetic fields. At the end of this step, there should

be nine different experiments run, with three different magnetic fields and three different

rotational speeds.

5. Compare the graphs of the various results.

Focus Questions:

What is the relationship between pump outlet pressure and flow rate in terms of rotational

speed of the pump and magnetic field upon the fluid?

Does pumping magnetorheological fluid prove to be a feasible method of adjusting pump

performance?

93

BOEING 777 STANDARD LANDING ENERGY AND FORCES

Figure 56: Boeing 777 Standard Landing Forces

Figure 57: Boeing 777 Standard Landing Power Dissipation

94

Figure 58: Boeing 777 Standard Landing Velocity

95

BOEING 777 LOW POWER Standard Landing Energy And Forces

Figure 59: Boeing 777 Low Power Standard Landing Forces

Figure 60: Boeing 777 Low Power Standard Landing Power Dissipation

96

Figure 61: Boeing 777 Low Power Standard Landing Velocity

97

BOEING 777 STANDARD REJECTED TAKEOFF ENERGY AND FORCES

Figure 62: Boeing 777 Standard Rejected Takeoff Forces

Figure 63: Boeing 777 Standard Rejected Takeoff Power Dissipation

98

Figure 64: Boeing 777 Standard Rejected Takeoff Velocity

99

BOEING 777 LOW POWER REJECTED TAKEOFF ENERGY AND FORCES

Figure 65: Boeing 777 Low Power Rejected Takeoff Forces

Figure 66: Boeing 777 Low Power Rejected Takeoff Power Dissipation

100

Figure 67: Boeing 777 Low Power Rejected Takeoff Velocity

101

BOEING 777 STANDARD EMERGENCY LANDING ENERGY AND FORCES

Figure 68: Boeing 777 Standard Emergency Landing Forces

Figure 69: Boeing 777 Standard Emergency Landing Power Dissipation

102

Figure 70: Boeing 777 Standard Emergency Landing Velocity

103

BOEING 777 LOW POWER EMERGENCY LANDING ENERGY AND FORCES

Figure 71: Boeing 777 Low Power Emergency Landing Forces

Figure 72: Boeing 777 Low Power Emergency Landing Power Dissipation

104

Figure 73: Boeing 777 Low Power Emergency Landing Velocity

105

EMBRAER 175 STANDARD LANDING ENERGY AND FORCES

Figure 74: Embraer 175 Standard Landing Forces

Figure 75: Embraer 175 Standard Landing Power Dissipation

106

Figure 76: Embraer 175 Standard Landing Velocity

107

EMBRAER 175 LOW POWER STANDARD LANDING ENERGY AND FORCES

Figure 77: Embraer 175 Low Power Standard Landing Forces

Figure 78: Embraer 175 Low Power Standard Landing Power Dissipation

108

Figure 79: Embraer 175 Low Power Standard Landing Velocity

109

EMBRAER 175 STANDARD REJECTED TAKEOFF ENERGY AND FORCES

Figure 80: Embraer 175 Standard Rejected Takeoff Forces

Figure 81: Embraer 175 Standard Rejected Takeoff Power Dissipation

110

Figure 82: Embraer 175 Standard Rejected Takeoff Velocity

111

EMBRAER 175 LOW POWER REJECTED TAKEOFF ENERGY AND FORCES

Figure 83: Embraer 175 Low Power Rejected Takeoff Forces

Figure 84: Embraer 175 Low Power Rejected Takeoff Power Dissipation

112

Figure 85: Embraer 175 Low Power Rejected Takeoff Velocity

113

EMBRAER 175 STANDARD EMERGENCY LANDING ENERGY AND FORCES

Figure 86: Embraer 175 Standard Emergency Landing Forces

Figure 87: Embraer 175 Standard Emergency Landing Power Dissipation

114

Figure 88: Embraer 175 Standard Emergency Landing Velocity

115

EMBRAER 175 LOW POWER EMERGENCY LANDING ENERGY AND FORCES

Figure 89: Embraer 175 Low Power Emergency Landing Forces

Figure 90: Embraer 175 Low Power Emergency Landing Power Dissipation

116

Figure 91: Embraer 175 Low Power Emergency Landing Velocity

117

MAIN FILE FOR THE FLUIDIC BRAKING SYSTEM MODEL

This section examines each component of the fluidic braking system in a closed loop through the

entirety of a braking event.

clear all;

Plane_Template;

Plane = B737;

% Fluid_Water;

% Fluid_Glycerol;

% Fluid_Oil;

if ~exist('brakePower.mat','file')

disp('Brake power not found: Calculating brake power')

RTO = GetEventParameters(B737, 'RTO Certification','Minimize Power');

RTO = StopEnergy(RTO);

velocity = RTO.velocity;

brakePower = RTO.brakePower./Plane.NumBrakes;

save brakePower;

disp('Brake power calculated')

else

load('brakePower.mat')

end

global effectivenessFit;

effectivenessFit = EffectivenessFit('HX Size.xlsx','C3:X16');

global dt;

dt = RTO.t(2)-RTO.t(1);

global omega_knot;

omega_knot = RTO.RPM(1);

global pump_eff_temp;

Fluid_MRF132DG;

%state1(1:length(brakePower));

init_Temp = 20;

init_Pressure = 101.3e3;

A = 1; %m^2

m = 20; %kg

m_solid = 100-m;

%percent volume of each component

f_pump = .3;

f_shex = .3;

f_hex = .3;

118

f_valve = .1;

%initial conditions

state1(1).Fluid = MRF; state1(1).T = init_Temp; state1(1).P = init_Pressure;






tic

for I = 2:length(brakePower)

if brakePower(I) < 0, brakePower(I) = 0; end

%Pump

[state2(I), m_dot(I)] = Pump_broken(state1(I), state2(I-1), brakePower(I),

RTO.RPM(I), f_pump*m);

pump_eff(I) = pump_eff_temp;

%Heat Sink

state3(I) = SolidMassHEX(state2(I), state3(I-1), m_dot(I), brakePower(I),

.1,f_shex*m);

%HEX

[state4(I), q_dot(I)] = HEX(state3(I), state4(I-1), m_dot(I), f_hex*m,

velocity(I),A);

%Valve

pressureDrop = state4(I).P-state1(1).P;

state5(I) = Valve(state4(I), state5(I-1), m_dot(I), f_valve*m, pressureDrop);

if ~(I >= length(brakePower))

state1(I+1) = state5(I);

end

if rem(I,length(brakePower)/100) <= 1

disp(strcat(num2str(round(I/length(brakePower)*100)),'%'))

end

end

toc

PlotState(state1, RTO.t, 'State 1: Pump Inlet')

PlotState(state2, RTO.t, 'State 2: Pump Outlet')

PlotState(state3, RTO.t, 'State 3: Heat Sink Outlet')

PlotState(state4, RTO.t, 'State 4: HEX Outlet')

119

figure

plot(RTO.t(2:length(RTO.t)), m_dot(2:length(m_dot)))

xlabel('Time [s]')

ylabel('Mass Flow Rate [kg/s]')

title('System Mass Flow Rate over time')

figure

plot(RTO.t(2:length(RTO.t)), q_dot(2:length(q_dot)))

xlabel('Time [s]')

ylabel('Heat Exchanger Heat Rejection [J/s]')

title('Heat Exchanger Heat Rejection')

figure

plot(RTO.t(2:length(RTO.t)), pump_eff(2:length(pump_eff))*100)

xlabel('Time [s]')

ylabel('Pump Efficiency [%]')

title('Pump Efficiency')

120

PUMP MODEL

From a given input state, brake power, and rotational speed the output state of the pump is

calculated.

function [ output_state , m_dot ] = Pump(input_state, current_state, BrakePower, omega,

fluid_mass )

% from a given input state , brake power, and rotational speed the output

% state of the pump

% input_state and output_state contain:

% .Fluid

% .T

% .P

% The pump increases the temperate and pressure of the fluid. The thermal

% mass of the system is model acording to the ThermalReservoir function

global g;

global pump_eff_temp;

g = 9.81;

if isnan(input_state.T)

error('help')

end

output_state.Fluid = input_state.Fluid;

Fluid = input_state.Fluid;

options = optimoptions('fsolve','Display','none');

Q = fsolve(@(x) (T_out(x,input_state, BrakePower, omega)-Fluid.maxTemp),1e-7,options);

if H(Q,omega)<0

Qmax = fsolve(@(x) H(x,omega),0,options);

Q = Qmax;

end

m_dot = Q*Fluid.rho;

mid_state.T = T_out(Q, input_state, BrakePower,omega);

mid_state.P = H(Q,omega)*Fluid.rho*g+input_state.P;

mid_state.Fluid = input_state.Fluid;

if mid_state.P < 0

plot(Q,H(Q,omega));

plot(Q, T_out(Q,input_state,BrakePower));

error('pump curve not compatible with required delta T, negative head')

end

if Q < 0

plot(Q,H(Q,omega));

plot(Q, T_out(Q,input_state,BrakePower));

P error('pump curve not compatible with required delta T, negative flow')

121

end

output_state = ThermalMass(mid_state, current_state, m_dot, fluid_mass);

if BrakePower<= 0

output_state.T = current_state.T;

output_state.P = current_state.P;

m_dot = 0;

end

pump_eff_temp = 1/(1+(mid_state.T-

input_state.T)*input_state.Fluid.rho*input_state.Fluid.Cp/(mid_state.P-

input_state.P));

end

function [H] = H(Q,omega)

global omega_knot;

Y0 = 191.4311512;

V0 = 0.02674332;

K = -0.006747174;

alpha = .5/6.30902e-5; %convert m^3/s to gpm and adjust

beta = .3048*.13; %convert ft to m and adjust

V = Q*alpha/(omega/omega_knot);

H = (omega/omega_knot)^2*beta*(Y0 - (V0/K)*(1-exp(-(K*V))));

end

function [T_out] = T_out(Q, input_state, BrakePower,omega)

global g;


T_out = input_state.T + (BrakePower-Fluid.rho*g*Q*H(Q,omega))/(Fluid.rho*Q*Fluid.Cp);

end

Published with MATLAB® R2015b

http://www.mathworks.com/products/matlab/

122

HEAT EXCHANGER MODEL

%determines the outlet conditions based on given inlet conditions by

%evaluating the performance of the heat exchanger.

function [ output_state, heat_out ] = HEX( input_state , current_state, m_dot,

fluid_mass, velocity, A)

%Heat Exchanger Model evaluates the performance of the heat exchanger and

%determines the outlet conditions based on given inlet conditions

% input_state and output_state contain:

% .Fluid

% .T

% .P

% The heat exchanger reduces the temperature and pressure of the system

% The thermal mass of the system is model acording to the ThermalReservoir

% function

pressure_drop = .4*(input_state.P-101.3e3);

if input_state.P - pressure_drop < 101.3e3

error('Pressure not high enough to pass through HEX')

end

Air.C_p = 1; %kJ/kg

Air.rho = 1.225; %kg/m^3

Fluid.C_p = input_state.Fluid.Cp/1000; %kj/kg

Inlet.coldside_mdot = Air.rho*velocity*A; %kg/s

Inlet.hotside_mdot = m_dot;

Inlet.T_c1 = 298; %K

Inlet.T_h1 = input_state.T+273; %K

eff = effectiveness(Inlet);

C_p_min = min(Air.C_p*Inlet.coldside_mdot, Fluid.C_p*Inlet.hotside_mdot);

Q = eff*C_p_min*(Inlet.T_h1-Inlet.T_c1);

if (C_p_min == Air.C_p*Inlet.coldside_mdot)

error('HEX Map Invalid, Cmin is air')

end


mid_state.P = input_state.P - pressure_drop;

mid_state.T = -Q/(m_dot*Fluid.C_p) + Inlet.T_h1 - 273;

output_state = ThermalMass(mid_state, current_state, m_dot, fluid_mass);

heat_out = Q*1000;

end

function [e] = effectiveness(Inlet)

global effectivenessFit;

123

beta =.8;

e = .8*effectivenessFit(Inlet.hotside_mdot,Inlet.coldside_mdot);

if isnan(e)

error('what the fuck');

end

% e = 0.5996 - 0.006173*Inlet.hotside_mdot + 0.004988*Inlet.coldside_mdot;

end



124

HEAT SINK MODEL

This Section of Matlab evaluates the amount of heat that can be stored in the landing structure

and the thermal mass of the system.

function [ output_state ] = SolidMassHEX( input_state, current_state, m_dot, BrakePower,

f_q,m )

%SolidMassHEX models the amount of energy that is stored within the landing

%struture and other available thermal mass

% Detailed explanation goes here

C = 0.49;%kj/kg*k


mid_state.T = input_state.T - BrakePower*f_q/(m_dot*input_state.Fluid.Cp);

mid_state.P = input_state.P-(input_state.P-101.3e3)*.15;

output_state = ThermalMass(mid_state,current_state,m_dot,m);

end



125

PUMP MODEL

This section of Matlab code evaluates the pressure drop and temperature change across the valve.

function [ output_state ] = Valve( input_state , current_state, m_dot, fluid_mass,

pressureDrop )

%Valve evaluates the required change and pressure to bring the pressure of

%system back to the pump inlet conditions and the resulting change in

%temperature for a given input state



mid_state.T = pressureDrop/(Fluid.rho*Fluid.Cp) + input_state.T;

mid_state.P = input_state.P-pressureDrop;

output_state = ThermalMass(mid_state,current_state,m_dot, fluid_mass);

end



126

BOEING 737 PARAMETERS DEFINITION

%Plane Parameters

B737.Name = 'Boeing 737 ';

B737.MTOW = 79010; %kg

B737.MaxLandWeight = 66361; %kg

B737.EndMissionWeight = 57735.5+1854; %kg

B737.WingArea = 124.58; %m^2

B737.WingHeight = 3.05; %m

B737.WingSpan = 35.32; %m

B737.WheelDiam = 1.13; %m

B737.MaxThrust = 121.4e3*2; %N

B737.PercentN2TR = .3;

%Brake Parameters

B737.NumBrakes = 4;

B737.RTOBrakeTemp = 1000; %C

B737.MaxUseableBrakeTemp= 750; %C

B737.BrakeCp = 760; %j/kg*K

B737.BrakeWearLimit = .3;

%Thrust Reverser Parameters

B737.MaxThrust = 121.4e3*2; %N

B737.PercentN2TR = .3;

B737.TRAngle = 35*pi/180; %radians

%Drag Parameters

B737.Cd0 = 0.0159;

B737.Kuc = 3.16e-5;

%Velocities

B737.V1 = 79.2; %m/s

B737.LandingVelocity = 79.7; %m/s

B737.MaxTaxi = 10.2889; %m/s

%Acceleratoin

B737.MaxAccel = 3.92; %m/s2

%Runway

B737.FARLandingFieldLength = 1767.84; %m

B737.FARTakeoffFieldLength = 2377; %m



127

EVENT ENERGY

This section of Matlab code determines the forces, velocity and kinetic to thermal energy

conversion requirements on an airplane for a given braking event.

function [ Event ] = EventEnergy( Event )

%EventEnergy determins the power, force, and velocity requirements for a

%given braking event.

% Utilizes ode45 to solve the differential equation associated with

% stopping an airplane to determine the instantenous heat dissipation,

% forces, and velocities.

% Define Global Variables

global rho Plane brakeForce; %Need to figure out how to remove global variables and

add thrust reverser force

Plane = Event.Plane;

rho = AirDensity(Event.Altitude);

%Initial guess of brake force

brakeForce = 1.5e5;

%%Define local variables

stopIndex = 0;

%Reset event parameters

Event.x = NaN; Event.t = NaN; Event.velocity = NaN; Event.brakeEnergy = NaN;

Event.dragForce = NaN; Event.trForce = NaN; Event.netForce = NaN; Event.accel = NaN;

Event.RPM = NaN; Event.brakeForce = NaN;

% Solve Braking Event

% Guess a brake force and iterate calculation changing the brake force until

% the stopping distance is within .1% of required distance. Solves for the

% velocity and position over time.

while ~(Event.x(end) > Event.StopDistance*.999 && Event.x(end) <

Event.StopDistance*1.0001)

%Reset event parameters

Event.x = NaN; Event.t = NaN; Event.velocity = NaN; Event.brakeEnergy = NaN;

Event.dragForce = NaN; Event.trForce = NaN; Event.netForce = NaN; Event.accel =

NaN;

Event.RPM = NaN; Event.brakeForce = NaN;

%Define timespan and timesteps for ode45

dt = .1;

tstop = 120;

tspan = 0:dt:tstop;

%Define inital parameters: initial velocity = Plane.LandingVelocity

v0 = [Event.V0];

%Solve differential equation where x_doubledot = sum(Forces)/m for velocity

128

[Event.t,Event.velocity]=ode45(@Acceleration,tspan,v0);

Event.velocity = transpose(Event.velocity);

Event.x = cumsum(Event.velocity.*dt); %Integrate velocity to get position function

%Truncate arrays to only include time when the plane is moving

stopIndex = find(Event.velocity < .005,1);

Event.velocity = Event.velocity(1:stopIndex);

Event.t = Event.t(1:stopIndex);

Event.x = Event.x(1:stopIndex);

%Guess a new brake force proportional to the error in stopping distance

brakeForce = brakeForce + (Event.x(end)-Event.StopDistance)*100;

end

% Calculate Event Parameters

%Fill the dragForce and brakeForce arrays. Calculate drag force based

%on the velocity curve

for I = 1:stopIndex

Event.dragForce(I) = DragForce(Plane,Event.velocity(I),rho);

Event.brakeForce(I) = brakeForce;

end

Event.brakeEnergy = Event.brakeForce.*Event.x;

Event.brakePower = Event.brakeForce.*Event.velocity;

Event.dragPower = Event.dragForce.*Event.velocity;

Event.RPM = Event.velocity ./ (Plane.WheelDiam*2*pi)*60;

end



129

GET EVENT PARAMETERS

%gets the initial conditions and parameters required for

%the EventEnergy function to evaluate the requirements

function [ Event ] = GetEventParameters( Plane, EventType, forceCalcType )

%GetEventParameters gets the initial conditions and parameters required for

%the EventEnergy function to evaluate the requirements

% Detailed explanation goes here

Plane_Template;

Event.Plane = Plane;

Event.Name = EventType;

if ~strcmp(forceCalcType,'')

if IsValidForceCalc(forceCalcType)

Event.forceCalcType = forceCalcType;

end

else

Event.forceCalcType = 'Minimize Acceleration';

disp('Mimizing acceleration for brake force calculation');

end

if strcmp(EventType, 'RTO Certification') == 1

Event.Weight = Plane.MTOW;

Event.V0 = Plane.V1;

Event.StopDistance = Plane.FARTakeoffFieldLength*.4;

Event.TREngaged = false;

Event.TRLevel = 0;

Event.Altitude = 0;

Event.AmbientTemp = 20; %c

Event.MaxBrakeTemp = Plane.RTOBrakeTemp;

Event.WearAmount = Plane.BrakeWearLimit;

elseif strcmp(EventType, 'Emergency Landing Certification') == 1

Event.Weight = Plane.MaxLandWeight;

Event.V0 = Plane.LandingVelocity;

Event.StopDistance = Plane.FARLandingFieldLength*.6;


Event.TRLevel = 0;

Event.Altitude = 0;


Event.MaxBrakeTemp = Plane.RTOBrakeTemp;


elseif strcmp(EventType, 'Landing no Thrust Rev') == 1

Event.Weight = Plane.EndMissionWeight;




130

Event.TRLevel = 0;

Event.TROffVelocity = Plane.LandingVelocity*.3;

Event.Altitude = 0;


Event.MaxBrakeTemp = Plane.MaxUseableBrakeTemp;


elseif strcmp(EventType, 'Standard Landing') == 1

Event.Weight = Plane.EndMissionWeight;



Event.TREngaged = true;

Event.TRLevel = .05;

Event.TROffVelocity = Plane.LandingVelocity*.3;

Event.Altitude = 0;


Event.MaxBrakeTemp = Plane.MaxUseableBrakeTemp;


else

error('Unknown Mission Type. Please enter valid mission:\n')

end

end

function [isValid] = IsValidForceCalc(forceCalcType)

isValid = false;

if strcmp(forceCalcType,'Minimize Acceleration') || strcmp(forceCalcType,

'Minimize Power')

isValid = true;

end

if isValid == false

error(strcat('Invalid brake force calculation type'))

end

end



131

DRAG FORCE CALCULATION

%calculates the drag force on a plane at a given velocity

function dragF = DragForce(Plane,velocity, rho)

%DragForce calculates the drag force on a plane at a given velocity

g = 9.81;

WingLoading = Plane.MTOW*g/Plane.WingArea;

hdb = Plane.WingHeight/Plane.WingSpan;

G = (16*hdb)^2/(1+(16*hdb)^2);

DeltaCd0 = 2.42*WingLoading*Plane.Kuc*Plane.MTOW^-.215;

AR = Plane.WingSpan^2/Plane.WingArea;

Cl = 2*Plane.MTOW*g/(rho*Plane.V1^2*Plane.WingArea);

eff = .9;

Cd = Plane.Cd0+DeltaCd0+(.02+(G/(pi*eff*AR)))*Cl^2;

dragF = rho*(velocity^2)*Cd*Plane.WingArea/2;

end



132

BRAKEFORCE

This Matlab code outputs the brake force for a given braking event depending on the desired

calculation type: minimized power or minimized acceleration.

function brakeF = BrakeForce(b,velocity,Event)

if strcmp(Event.forceCalcType, 'Minimize Power')

if Event.accelFlag

if velocity > 0

brakeF = Event.Weight*Event.Plane.MaxAccel-Event.dragForce(end)-

Event.trForce(end);

else

brakeF = 0;

end

else

if velocity > 0

brakeF = b/velocity;

else

brakeF = 0;

end

end

elseif strcmp(Event.forceCalcType, 'Minimize Acceleration')

if velocity > 0

brakeF = b;

else

brakeF = 0;

end

else

error('invalid brake force calculation')

end

end



Documents

Alternative Methods of Aircraft Braking · 2016. 4. 28. · 1 ABSTRACT Aircraft braking systems are required to convert large amounts of kinetic energy into thermal energy produced