Wind tunnel techniques

Module 1

Buckingham Pi theorem

The application of this theorem provides afairly easy method to identify dimensionless

parameters (numbers).

However identification of the influencingparameters is the job of an expert rather than

that of a novice.

THE PRINCIPLE OF DIMENSIONAL HOMOGENEITY

The principle is basic for the correctness ofany equation.

It states If an equation truly expresses aproper relationship between variables in a

physical phenomenon, then each of the

additive terms will have the same

dimensions or these should be dimensionally

homogeneous.

Model & prototype In the engineering point of view model can be

defined as the representation of physical

system that may be used to predict the

behavior of the system in the desired aspect

The system whose behavior is to be predictedby the model is called the prototype.

Similarity Geometric Similarity :Some of the PI terms involve the

ratio of length parameters. All the similar linear dimension of themodel and prototype should have the same ratio. This I calledgeometric similarity. The ratio is generally denoted by the scale orscale factor

Dynamic Similarity: PI terms like Reynolds number, Froudenumber, Weber number etc. be equal for the model and prototype. Thesenumbers are ratios of inertia, viscous gravity and surface tension forces.This condition implies that the ratio of forces on fluid elements atcorresponding points (homologous) in the model and prototype should bethe same. This requirement is called dynamic similarity

Kinematic Similarity: When both geometric and dynamicsimilarities exist, then velocity ratios and acceleration ratios will be thesame throughout the flow field. This will mean that the streamline patternswill be the same in both cases of model and prototype. This is calledkinematic similarly

Non- Dimensional Numbers

Reynolds number (Re) = Inertia force/Viscous force

Mach number = Inertia force/Elastic force

Froude number = Inertia force/Gravity force

Weber number : It is defined as the ratio of the inertia force to surface tension force

Model or similarity Law

For the dynamic similarities between the modeland prototype, the ratios of corresponding forceacting on the corresponding points should beequal.

The ratio of the forces of non-dimensionalnumbers it means that for the dynamic similaritybetween model and prototype , the dimensionlessnumber should be same for model and prototype.

The law on which the model are designed fordynamic similarity are called model laws orsimilarity laws

Reynoldss model law

It states that the Reynolds number for themodel and prototype must be equal where the

viscous force is predominant in addition to the

inertia force

Types of Models Undistorted model: An undistorted model is one which is

geometrically similar with its prototype. The condition ofsimilarities are completely satisfied for such models hence theresults obtained from the model test are easily used

Distorted model: geometrically not similar with its prototype.In such model, the different scale ratios for linear dimensions are

adopted. Distortion of dimension- adoption of different scale for

vertical and horizontal

Distortion of Configuration Model does not be an resemblance of its Prototype.

Material Distortion - Adoption of different material for model and prototype

Scale Effect

The behaviour of the prototype as predicted by two models with different scale ratio is generally not the same. Such an

difference in the prediction of behaviour prototype is known as

Scale Effect.

Introduction Need of experiments :

(i)Theory is incomplete and needs to be supplemented.

(ii) Information of fundamental nature needed in many

areas.

Experimental information towards solving aerodynamic

problems could be obtained in a number of ways. Flight

tests, rocket flights, drop tests water tunnels, ballistic

ranges and wind tunnels are some of the ways by which

aerodynamic data can be generated. With the help of well

performed experiments even information of fundamental

nature could be derived

Wind tunnel

Majority of experimental data needed inaerodynamics is generated using wind tunnels. Wind

Tunnel is a device for producing airflow relative to

the body under test. Wind tunnels provide uniform

flow conditions in their test section.

Applications of wind tunnels

1. Aerodynamic applications

2. Non-Aero applications in

Civil Engineering

Automobile Engineering

Calibration of instruments

Classifications of wind tunnels

Operational point of view

Low speed tunnels

High speed tunnels

Intermittent

Blow down M > 0.5 < 5.0

Indraft

Intermittent pressure vacuum tunnel for M>5

Special purpose tunnels

Wind tunnels may be classified based on

Speed, Mach no :

(a) subsonic,

(b) transonic,

(c) supersonic

(d) hypersonic wind tunnels.

(b) Mode of operation (Pressure storage, in-draftor Pressure vacuum type.)

(c) Kind of test section (T.S) - Open, Closed or Semienclosed

Low speed wind tunnel (continuous type; up to 40 m/s)

High speed wind tunnel (intermittent/blow down Mach 3, 600m/s)

Shock tunnel (impulse type; Mach 7, 2km/s)

Free piston shock tunnel (impulse type, Mach 4-10, 5km/s)

Expansion tube (impulse type, Mach 10, 10km/s)

Open ReturnClosed Test Sectionlow speed tunnels

effuser

Honey comb

Suction type Fan & motor Unit

Honey combs: its used to improve the flow qualities in the testsection. Are made of octagonal, hexagonal, square or cylindricalcells.

Effuser : basically a contraction cone, which bring down theturbulence level and increases the velocity of the flow thecontraction ratio n is the ratio between entry and exit of thecone . Normally the ratio varies from 4 to 20 for low speedtunnels

n = area at entry of contraction cone

area at exit of contraction cone

Test section : the portion which have constant flow patterns . Because the boundary layer is formed along the

test section walls , the walls are given suitable divergence

. So that the net C/S area of the flow is constant along the

length of the test section

Test section wall Boundary layer

Constant flow Constant flow

Divergence angle

Diffuser : is to convert the KE of the flow coming outof the test section in to PE. Before it leaves the diffuser as

efficiently as possible. Normally smaller the divergence

angle of diffuser will give more efficiency . Near to the

exit it will be circular to accommodate the fan .

Driving unit : generally it consist of motor and propelleror a fan combination . Speed adjustment has to be done by

varying the RPM. (many larger tunnel tat are equipped

with both RPM and pitch change mechanisms )

Closed circuit low speed tunnel

Tunnel at MSN

High speed tunnels Test section flow velocity more than 650km/hr

High speed tunnel are normally intermittent (discontinuous) type

Energy is stored in the in the form of pressure or vacuum or both and is allowed to drive the tunnel only for few seconds

Intermittent tunnel

Blow down tunnel

Induction tunnel

Continuous operation tunnel

Blow down type wind tunnel (High speed tunnel)

Blow down type wind tunnel

Advantages

The most economical typeof super sonic tunnel

Can have larger test sectionand high mach number

(M=4 can obtained)

Constant blowing pressurecan be maintained

Running time considerableduration can be achieved

Single drive may easily runseveral tunnels of different

range

Dis advantages

Charging time to running timeratio will be very high for

larger size tunnel

Stagnation temperature in thereservoir drops during the run

and changes the Reynolds

number

And adjustable throttlingvalve is necessary for constant

stagnation pressure

Starting load is high

Pressure range of reservoir100 to 2000 psi.

Induction type tunnel

Vacuum created at the down stream end of the tunnelis used to establish the flow in the test section .

Advantages

To Po are constant

No oil contamination , because pump at the down stream end

Disadvantages

Drier size should be large because it has to handle a large massflow in a short duration

Vacuum tank size required is too large

M > 2 is not possible

Continuous super sonic wind tunnels(closed circuit super sonic wind tunnel)

A small drier is sufficient

Testing condition can be maintained over a long period of time

The test section can be designed for M>4 and large size models

Starting condition can be reduced by starting at low pressure in the tunnel shell

Supersonic tunnel basic note(common to all tunnel )

Axial flow compressor isbetter suited for largepressure ratio and massflow rate

Proper nozzle geometry isvery important to obtaingood distribution of Machnumber & freedom fromfloe angularity in the testsection

Subsonic portion of thediffuser must have anoptimum angle, tominimize the frictional andseparation losses

Model size is determined fromtest rhombus. The model

must be accommodated in side

the rhombus formed by the

incident and reflected shock for

proper measurements

Disadvantages

Power required is very high

Requires large size cooler

Tunnel design and operation are more complicated

Power losses in a wind tunnel

Losses in the cylinder part

Losses in the guide vane at the corners(CCT)

Losses in the diffuser

Losses in the contraction cone

Losses in the honey comb

Losses in test section (jet loss in case of open jet)

Losses in the exit (OCT)

Generally losses is expressed in terms of pressure drop p ,In dimension less form called pressure drop coefficient K

K= (p/q)

q- is the dynamic pressure of the flow given by

p

K= -------------------

V2

Compressor tunnel matching 1. Chose a compressor for specified test section size, mach number

& pressure level

2. Determine the best utilization of already available compressor

In both case the characteristics to be matched are over all pressure ratio and mass flow rate.

Usually the compressor are measured in terms of

volumetric Flow V

Because the density varies through out the circuit , the V also varies through out the tunnel.

- operating pressure ratio

V- volumetric flow rate

Matching of Wind tunnel & compressor characteristics (one test section condition )

By increasing the stagehigh pressure ratio canbe obtained

Leads to large machnumber flow

Operation over a range of Mach n- matching point

b- matching point withbypass

0 matching point atminimum operating ratio

The plot Vs V is a straight line through the origin with a

slope 1/ V0

Power requirement for a multi stage compressor is given by

- mass flow rate

P03 & P0c- total pressure at the inlet and out let of compressor

N- no of stages

Ts- stagnation temp

Basic formula for wind tunnel calculation

Pt & t stagnation pressure and density

P , , T - local pressure density and temperature

P1 & P2 pressure at up stream and down stream of shock

Mass flow rate One of the primary

consideration in sizing a windtunnel test section andassociated equipments such as ,compressor diffuser .

This equation is applicable bothfor subsonic and super sonictunnel

for sub sonic flow testsection mach number isevaluated

For super sonic flow nozzlethroat of mach number isevaluated for predicting themass flow rate

Blow down tunnel usuallyoperated at constantpressure

Objective of constantpressure is to obtain a steadyflow at the time of databeing recorded

Blow down tunnel operation The pressure and temperature at the storage tank

changes during the operation . This pressure

changes causes the following effect

Tunnel stagnation and settling chamber pressure fall

Force acting on the model changes during test

Reynolds no of the flow changes during tunnel run

3 methods are followed blow down tunnel run

constant Reynolds number operation

Constant pressure operation

Constant throttle operation

Pbi settling chamber pressure

P0i - storage tank inletpressure

From the graph its clearReynolds number decreaseswith running time for aconstant throttle operation

Reynolds increases with runningtime for a constant pressureoperation

Reynolds change result inboundary layer thinness and thataffects the area and mach numberat the test section

But the M changes due to theabove causes will be normallyless

Reynolds number control m viscosity index

n- polytropic index

Its clear that Re decreases withtime t for a throttling processes

For a given P & T the running timet will be Shortest for constant throttle

operation

Longest for Reynolds no operation

In between above 2 for constantpressure operation