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GENERAL RAM CORRELATIONS FOR AUTOMOBILES
by
DEBRA G. VERNER, B.S.M.E.
A THESIS
IN
MECHANICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
MECHANICAL ENGINEERING
Approved
Acceptea
May, 2000
4^^ 1^7/ SoS ACKNOWLEDGEMENTS
p-i-t-o First of all, I would like to thank Dr. Oler, chairman of my committee, for
/[Jo. (f his insight and patience throughout this study. I would also like to express my
CQ~/J,Z^ appreciation to the Ford Motor Company for the generous monetary support that
enabled me to continue my education at a higher level. Most of all, I thank my
husband for his love, encouragement, and support.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii
ABSTRACT v
LIST OF TABLES vi
LIST OF FIGURES viii
LIST OF SYMBOLS ix
CHAPTER
I. INTRODUCTION 1
II. TECHNICAL APPROACH 9
2.1 Introduction 9
2.2 Ram Pressure Coefficient for Individual Grille Openings 13
2.3 Compatible Individual Opening Correlations 14
2.4 Ram Pressure Coefficient for Multiple Grille Openings 15
III. EXPERIMENTAL SETUP 19
3.1 Front-End Modifications 19
3.2 Instmmented Radiator 24
IV. RESULTS AND DISCUSSION 26
4.1 Data Reduction Procedure 26
4.2 Ram Pressure Coefficients for Individual Openings 30
4.3 Ram Pressure Coefficients for Multiple Openings 32
V. CONCLUSIONS AND RECOMMENDATIONS 52
5.1 Conclusions 52
5.2 Recommendations 53
REFERENCES 55
III
APPENDIX
A. FAN AND HEAT EXCHANGER FILES 56
B. WIND TUNNEL DATA FILES 61
C. GRILLE FILES 72
D. INDIVIDUAL GRILLE OPENING KRAM SOLUTION MATLAB PROGRAM 80
E. MULTIPLE GRILLE OPENING KRAM SOLUTION MATLAB PROGRAM 89
IV
ABSTRACT
The driving pressure required for the cooling system airflow comes from
two sources: the pressure due to the forward motion of the vehicle known as ram
pressure, and the radiator fan pressure rise. These internal and external flow
fields interact at the cooling air inlets and at the underside of the engine bay.
These flow fields are closely related and are considered together in this study.
The primary focus of this study is to find general ram pressure correlations for
automobiles. The principal test results consist of a set of correlation equations
which describe the variation of the ram pressure coefficient with respect to the
size and location of the openings, the freestream velocity, and the cooling air flow
rate for individual and combinations of openings. These correlations are in a
format suitable for use with streamtube cooling system models such as
ttu Cool®.
LIST OF TABLES
4.1 Individualized Correlation 30
4.2 Ram Predictions for Top Openings 35
4.3 Ram Predictions for Chin Openings 36
4.4 Ram Predictions for Bottom Openings 37
4.5 Ram Predictions for Top and Chin Openings 41
4.6 Ram Predictions for Chin and Bottom Openings 42
4.7 Ram Predictions for Top and Bottom Openings 43
4.8 Ram Predictions for Combinations of All Openings 44
B. 1 Top Opening A Wind Tunnel File 62
B. 2 Top Opening B Wind Tunnel File 62
B. 3 Top Opening C Wind Tunnel File 63
B. 4 Chin Opening A Wind Tunnel File 63
B. 5 Chin Opening B Wind Tunnel File 64
B. 6 Bottom Opening A Wind Tunnel File 64
B. 7 Bottom Opening B Wind Tunnel File 65
B. 8 Top A and Chin B Combination Wind Tunnel File 65
B. 9 Top B and Chin B Combination Wind Tunnel File 66
B. 10 Top C and Chin B Combination Wind Tunnel File 66
B. 11 Top B and Chin A Combination Wind Tunnel File 67
B. 12 Chin A and Bottom B Combination Wind Tunnel File 67
B. 13 Chin B and Bottom B Combination Wind Tunnel File 68
B. 14 Chin B and Bottom A Combination Wind Tunnel File 68
B. 15 Top A and Bottom B Combination Wind Tunnel File 69
B. 16 Top B and Bottom B Combination Wind Tunnel File 69
B. 17 Top C and Bottom B Combination Wind Tunnel File 70
B. 18 Top A, Chin C, and Bottom A Combination Wind Tunnel File 70
B. 19 Top C, Chin A, and Bottom A Combination Wind Tunnel File 71
C.I Top Opening A Grille File 73
vi
C.2 Top Opening B Grille File 73
C.3 Top Opening C Grille File 73
C.4 Chin Opening A Grille File 74
C.5 Chin Opening B Grille File 74
C.6 Bottom Opening A Grille File 74
C.7 Bottom Opening B Grille File 75
C.8Top Aand Chin B Grille File 75
C.9 Top B and Chin B Grille File 75
CIO Top C and Chin B Grille File 76
0.11 Top B and Chin A Grille File 76
C.12 Chin A and Bottom B Grille File 76
C.13 Chin B and Bottom B Grille File 77
C.14 Chin B and Bottom A Grille File 77
C.15 Top A and Bottom B Grille File 77
C.16 Top B and Bottom B Grille File 78
C.17 Top C and Bottom B Grille File 78
C.18 Top A, Chin C, and Bottom A Grille File 78
C.18 Top C, Chin A, and Bottom A Grille File 79
VII
LIST OF FIGURES
1.1 Cooling Air Streamtube Comparison (Schaub and Charles, 1980) 4
1.2 Block Diagram of the ttu_Cool® Streamtube Model 6
1.3 ttu_Cool® User Interface 6
2.1 Cooling Airflow Streamtube 10
3.1 Modified Taurus Front-End 20
3.2 Modified Taums Front-End With Panels 20
3.3 Location and Identification of Interchangeable Panels 21
3.4 Changing of the Front Panel 23
3.5 Instmmented Radiator 25
4.1 Cooling Package in ttu_Cool® 28
4.2 Streamtube Distribution in ttu_Cool® 28
4.3 Heat Exchanger Pressure Drop Comparison 29
4.4 Heat Exchanger and Fan Pressure Drop Comparison 29
4.5 Isolated Ram Correlation Results 38
4.6 Ram Results for Top and Chin Openings 45
4.7 Ram Results for Chin and Bottom Openings 46
4.8 Ram Results for Top and Bottom Openings 47
4.9 Ram Resultsfor Combinations of All Openings 48
4.10 Ram Pressure Coefficient Spectrum 49
4.11 Calculated Kram versus Predicted Kram 50
4.12 Calculated Flow Rate versus Predicted Flow Rate 51
VIII
LIST OF SYMBOLS
APg grille pressure drop
APc condenser pressure drop
APr radiator pressure drop
APf fan pressure drop
APbay engine bay pressure drop
APu underbody pressure drop
APram ram pressure drop
AHioss head loss
Kbay engine bay pressure drop coefficient
Ku underbody pressure drop coefficient
Kram ram pressure drop coefficient
p air density
Voo freestream velocity
Vr radiator velocity or average air velocity at the radiator
Ar radiator area
Ai inlet area
Ko experimentally determined coefficient - slope of the ram pressure
coefficient curve
KA experimentally determined coefficient -proportionality constant
between the ram coefficient and the an inlet area ratio
Kj experimentally determined coefficient - intercept of the ram pressure
coefficient curve
IX
CHAPTER I
INTRODUCTION
A cooling system of a moving vehicle is subject to the external flow of air
at the front and beneath the vehicle and to the internal flow through the
underhood cooling components. The external flow field is driven primarily by the
motion of the vehicle. The fan, radiator, and condenser influence the interior
airflow path. The internal and external flow fields interact at the cooling air inlets
and at the underside of the engine bay. These flow fields are closely related and
are considered together in this study. The objective of this study is to find
general ram pressure correlations for automobiles. These correlations describe
the variation of the ram pressure coefficient with respect to the size and location
of the openings, the freestream velocity, and the cooling airflow rate for individual
and combinations of openings. The ram pressure correlations can also be
incorporated into streamtube cooling system models such as ttu_Cool® to aid in
the design process of vehicles.
As airflow comes through the cooling air inlets from the freestream to the
front face of the radiator or condenser, a loss in total pressure is associated with
flow through the grille. At high speeds, the flow decelerates from the freestream
velocity to the average velocity through the radiator and condenser. The static
pressure increases as the dynamic pressure of the flow is reduced. This static
pressure rise combined with the static pressure or back pressure reduction at the
engine bay exit associated with the acceleration of the freestream airflow
beneath the vehicle is known as the ram pressure. The ram pressure coefficient
is this ram pressure normalized by the average dynamic pressure at the radiator.
The term ram correlation refers to a set of equations that describe the relation of
the ram pressure coefficient to inlet area, freestream velocity, and cooling flow
rate for both Isolated and combinations of front-end openings. Ram airflow is
defined as the increment In airflow between when a vehicle is in motion and
when a vehicle is stationary with a totally fan driven flow.
1
The cooling air inlets on the front fascia of vehicles are not only
functionally important, but are also a distinctive styling feature of a particular
make or model of a vehicle. With the advancement of vehicle aerodynamics for
reduced drag and improved fuel economy, the hood and fascia of vehicles have
changed over the years. The "nose" of vehicles has moved down, which directly
reduced the size of the cooling air inlets. The previous large inlet area has also
been broken up into several subareas. These changes have resulted in a large
variation of styles with different geometries and locations of the cooling air inlets.
One of the primary steps in the vehicle design process is the development
and evaluation of the engine cooling system. Since the mid-1970s, several
automotive researchers have worked towards more efficient vehicle cooling
systems. Olson's (1976) objective was to replace the "cut and try" method with a
scientific method for designing an optimal vehicle cooling system. By traversing
a rake of multiple vane-anemometers behind the radiator in a full-scale wind
tunnel, he identified the effects of various front-end components. However, the
flow visualization techniques used to determine the total grille airflow only
provided rough estimations and limited the quantifiable results of the study.
Hawes (1976) indicated that engine-cooling designs may be optimized by
implementing the most effective engine-cooling arrangement. He determined
that, as a result of the increased drag, using the freestream dynamic pressure to
increase airflow requires over 30 percent more power than a fan for the same
radiator air-circuit and cooling requirement. An overly large frontal intake
opening increases drag and power requirements that reduce the fuel economy.
Schaub and Charles (1980) investigated the interaction between the ram
airflow and the cooling fan. A streamtube concept was used to study front-end
grille losses. They found that the ratio of the catch flow area to the radiator face
area is infinite when the vehicle is stationary with the fan running and that this
ratio is only 0.26 while the vehicle is moving at high speeds (Figure 1.1). The
enormous change in the boundaries of the entering flow alters the velocity field at
the grille considerably by raising the local velocities, which results in large
increases in front-end losses under ram air conditions. Schaub and Charles
stated that using fan performance data from airflow test stands cannot lead to the
optimum fan design without accounting for the ram air effects and air path
resistance. They listed three reasons why the significance of ram air dependent
loss must not be overlooked during the styling stage of vehicle design.
1. The ram pressure loss is large and well defined.
2. It is highly dependent on front-end body and grille detail, and
consequently will be significantly different for what appears to be minor
changes in stylistic treatment.
3. There is a major dependence of ram air dependent loss on forward
speed.
Williams (1985) questioned the viability of grille open area (GOA), the
amount of grille area that can be frontally projected onto the radiator, as an
Indicator of ram airflow and cooling drag. He analyzed seven different vehicles
with the same physical airflow measurement system. Each vehicle had a
different front-end design. A plot of measured ram airflow, airflow due to the
forward motion of a vehicle, at 35 and 75 mph versus grille open area revealed
that GOA only accounts for 53 percent of the variability in ram airflow and that 47
percent is due to other effects. Therefore, grille open area alone is not a good
predictor of cooling airflow.
Renn and Gilhaus (1986) emphasized the positive effects of ducting
between the air intake and the radiator of vehicles. The ducting improves the
performance of the cooling system by preventing uncontrolled airflow through
open gaps around the radiator and by reducing hot air recirculation. They also
noted that, based on cooling drag data, many cooling systems are not closely
optimized. They concluded that aerodynamic improvements need not
necessarily interfere with cooling requirements.
(a) Stationary Vehicle
(b) Moving Vehicle
Figure 1.1 Cooling Air Streamtube Comparison (Schaub and Charles, 1980)
An inability to accurately predict cooling system performance early in the
design process can result in late and costly design alterations to the cooling
system. Most of the automotive industry currently uses Computational Fluid
Dynamics (CFD) computer modeling. This modeling requires detailed
information of the vehicle's architecture, which is commonly not available early in
the design stages. CFD computer modeling also requires expensive
supercomputers, numerous man-hours, and the process can take weeks.
Building and testing prototype vehicles also takes enormous effort and is not
always possible in early design stages. A more efficient and faster method for
developing the cooling system in a vehicle would reduce time to market for new
products and improve engineering productivity.
To address this problem, a streamtube based computational cooling
system model, ttu_Cool®, was developed at Texas Tech University with the
support of Ford Motor Company (Oler and Jordan, 1988). This model was later
extended to predict heat rejection parameters (Jordan and Oler, 1990). The
model is derived from basic physical principles of conservation of mass,
momentum, energy, and the continuity of pressure changes through the cooling
system. The airflow rate through the engine compartment is calculated with an
iteration process that evaluates pressure changes in the components along the
flow path (Figure 1.2) such that the static pressures in the streamtube upstream
and downstream the vehicle are equal. The pressure changes across the
individual components are determined from correlations based on physical
principles and experimental data. The model uses known component
performance characteristics to predict overall engine-cooling performance under
any vehicle operating conditions.
Figure 1.3 illustrates the customary user interface forttu_Cool® cooling
system performance calculations. The program can determine 20 solutions for
different operating conditions in approximately 2 to 15 seconds.
V ^
Gr
Bypass Region
ille
^
"w
>
:w
Condenser Fan ^
— > — > — >
unaer Douy
^ - >
Engine Bay
>
Shroud Region Radiator
Figure 1.2 Block Diagram of the ttu_Cool® Streamtube Model
Sin^e Operating Point Analysis
•Operating Conditions;
Vehicle Speed
Road Grade
Ambient Temp
Ambient Pres
96.6 'W^:^'^y??yT'-''-
20.0
101.32
km/h
%
C
kPa
Heat Rejectioi^-
Engine Power
Engine Heat ' :'
Trans Heat
Radiator Heat
Coolant Flowrate
Condenser Heat
Refrigerant Flowrate
Trans Cooler Heat
Trans Oil Rowrate
••••••^ft-yi
0.59
L2 .10
•'S \
W kW
kW
i.--: '•
kg/s
kW
kg/s
rSystem Performance:
Rad. Mass Flow "^f 1.296 ^g/s
Rad. Exit Vol. Flow
Top-Water Temp.
Air Exit Temp.
AC Head Pres.
64.65 AC MM
20.9 C \
20.5 0 '
kPa
-Fan Parameters-
Speed Power]
(Watts)
Fan #1
Fantf2
Fan #3
1800.0 236.72
sfea.
• g p c a l c u p t ^ msm:
© Figure 1.3 ttu_Coor User Interface
Oler et al. (1990), studied the relationships between the loss in total
pressure across front-end cooling openings, the cooling airflow rate, and the
freestream velocity. A wind tunnel test was conducted on one-fifth scale models
of automotive front-ends with cooling air inlets 5%, 10%, and 20% of the model
frontal areas. The results of the test demonstrated that the normalized total
pressure loss (defined as the grille coefficient Kg) could be correlated with the
ratio of the velocity at the plane of the inlet with the freestream velocity, i.e..
P - P f ^inlet (1.1)
In 1992, Oler developed a simplified analysis that was successful in
predicting general qualitative features of the grille coefficient variation. He
revealed that the primary source of total pressure loss for airflow through the
cooling inlets Is a negligible static pressure recovery as the airflow decelerates
from the openings to the face of the radiator. He also proposed a procedure for
predicting the net performance of combinations of openings based on the
assumption that the flows through all inlets mix to a common total pressure at the
radiator.
Oler and Crafton (1992) studied the behavior of the grille coefficient for a
full-sized Ford Taurus. They defined the general correlation for isolated grille
openings as
Kg =Kgo+Kg2 ^V^^
^Vw (1.2)
where Vj = velocity in the Inlet
V^ = freestream velocity.
The effect of variations In inlet area were described by
f Kg =Kgo+Kg2
V
vVw (1.3)
where
Kg2 = Kg2 y • (1.4) V^i J
They examined the net influence of the free stream dynamic pressure through
the combined variations of grille and underbody coefficients in a general
parameter they defined as the ram coefficient,
K.am=Kg+K, (1.5)
where the underbody coefficient, Ku, is modeled in ttu_Cool® as
P - P K , = - ^ - i ^ . (1.6)
Oler and Crafton emphasized that the major drawback associated with the
utilization of the ram coefficient for evaluating experimental data and for new
vehicle design is that the effects of inlet configuration cannot be separated from
the underbody effects.
This report continues the study of general ram correlations for
automobiles. The strategy for obtaining these general ram correlations is to
develop correlations for variable sized individual openings at characteristic
locations typical of most sedans. Once obtained, the individual opening
correlations are used to predict the slope and intercept of the ram pressure
coefficient curve for any combination and sizes of those openings.
8
CHAPTER II
TECHNICAL APPROACH
The objective of this study is to find general ram pressure correlations for
automobiles. This chapter shows the derivations of the ram pressure
correlations for individual and combinations of grille openings. The first section
describes the pressure drops in the cooling airflow streamtube that contribute to
the ram pressure rise in order to define the equation for the ram pressure
coefficient. The second section of the chapter introduces experimentally
determined coefficients Ko, KA, and Kbay in the ram pressure coefficient equation
and describes how to find the values for these coefficients for each opening
location. The next section describes an alternative solution process that results
in a single value of Kbay for the opening locations. The final section describes the
prediction of the ram pressure coefficients for combined openings.
2.1 Introduction
Consider a streamtube containing the cooling airflow that originates far
ahead of the vehicle and extends far downstream. Figure 2.1 illustrates the
cooling airflow streamtube with the location and identification of reference states
between components. As the cooling airflow passes through the inlets from the
freestream to the front face of the radiator, a total pressure loss is associated
with flow through the grille and a net static pressure rise occurs between the
freestream and heat exchanger, APg = P2 - Poo. The streamtube then proceeds
through the condenser, radiator, and fan resulting in pressure losses, APc = P2 -
P3, APr = P3 - P4, and APf = P4 - P5, respectively. After leaving the fan, the
streamtube continues through the engine bay to the underbody of the vehicle
causing losses in pressure, APbay = Pe - P5 and APu = Poo - Pe, respectively. The
upstream and downstream air pressures are both equal to the ambient pressure.
Thus, they are equal to each other and the sum of the pressure drops along the
cooling airflow streamtube is zero,
9
0 = APg + AP, + AP, +AP, + AP,3y +AP,.
The ram pressure rise is defined as
AP, ,= - (APg+AP^y+APj
and
(2.1)
(2.2)
AP,,=AP,+AP,-fAP,. (2.3)
Equation (2.2) contains the pressure drops that are evaluated in this chapter for
the basic expression for the predicted ram pressure coefficient. Equation (2.3) is
used as the basis for the experimental evaluation of the ram pressure coefficient.
Grille Condenser Radiator Fan Engine Bay Underbody
Figure 2.1 Cooling Airflow Streamtube
The pressure changes across each component may be evaluated with the
application of the adiabatic, steady flow energy equation. Consider the grille
pressure drop through a single grille opening. Conservation of energy between
the freestream and the face of the heat exchanger is given by
+ V: v 2 • "2 + A H + loss •
pg 2g pg 2g
The head loss is broken into two components: the head loss occurring upstream
of a single cooling inlet or grille opening, and the head loss occurring between
the inlet and the face of the heat exchanger,
AH„33 =H^ - H ^ =(H. - H 0 + ( H , - H J . (2.5)
Assuming that the losses occurring upstream of the inlet are negligible so that
the grille loss is just the change in total head between the grille opening and the
heat exchanger,
10
AH loss ^ " - " ^ = ^ - ^ ( ^ - ^ ^ ^ ) - (2.6)
Additionally, assume that there is a negligible static pressure recovery as the flow
expands abruptly and decelerates from the inlet to the heat exchanger, Pi - P2 s
0,
AH^3 . = ^ ' 2g
(\i y-V, - 1 (2.7)
Substituting Equation (2.7) into Equation (2.4) and rearranging, the grille
pressure drop becomes
AP ,=^pV f - l pV , ^
The engine bay pressure drop is defined as
AP.3y=^pVr 'K,3,
(2.8)
(2.9)
where Kbay is the engine bay pressure drop coefficient and Vr is an arbitrarily
defined internal reference velocity that is defined to be equal to the average
velocity at the radiator. The engine bay pressure drop coefficient remains the
same for a given vehicle, but varies for different vehicles. The pressure drop that
occurs between the underbody region and a location far downstream of the
vehicle is given by
A P u = - ^ p V X (2.10)
where Ku is the underbody pressure drop coefficient.
By substituting the grille, engine bay, and underbody pressure drop
expressions. Equations (2.8, 2.9, and 2.10), into Equation (2.2), the ram pressure
rise becomes
APram = " 1 1 1 1 ^pV,^-;^pV„^+;^pVXay+;^pViK,
The ram pressure coefficient is defined as
(2.11)
11
AP„„ ! • ram ram
2 ^ '
(2.12)
By substituting Equation (2.11) into Equation (2.12), the ram pressure coefficient
IS
Kram = v_
vVry (1 + K j -
vVry - K
bay • (2.13)
The conservation of mass law for a single grille opening is
p V A = p V i A , (2.14)
where Ar is an arbitrarily defined reference area that is taken approximately equal
to the radiator face area. This allows the inlet velocity ratio in Equation (2.13) to
be expressed in terms of the corresponding area ratio.
K_ = ram V,
(1 + K j -r ^ \
\ ^ \ j
- K bay (2.15)
This simplified analysis cannot represent all of the variations associated
with the details of front-end geometry. However, it does identify the primary
source terms contributing to the ram pressure coefficient and their basic
functional forms should be correct. Examination of Equation (2.15) reveals that
the ram pressure coefficient varies linearly with the velocity ratio squared and
that the corresponding intercept is determined by the combination of the inlet
area ratio and engine bay pressure drop coefficient. The first term represents the
positive contribution to ram pressure from the freestream dynamic pressure. The
second term represents the internal total pressure loss due to the unconstrained
expansion and lack of static pressure recovery between the inlet and condenser.
The third term is the pressure loss associated with the engine bay blockage.
The theoretical ram pressure coefficient relationship given by Equation
(2.15) may be generalized to represent a variety of specific vehicle grille
configurations by introducing experimentally determined coefficients for the net
exterior and interior aerodynamic effects.
12
K_ = fy \^
'ram yj
KQ - K j . (2.16)
This form of the ram pressure correlation incorporates the effects of flow rate and
vehicle speed through the slope and intercept, Ko and Kj, of the ram coefficient
curve. The effects of size and location of a single or multiple grille openings is
reflected in variations of the slope and intercept.
The following sections describe methods for predicting the effects of
variations In the size and combination of grille openings on the coefficients in
Equation (2.15).
2.2 Ram Pressure Coefficient for Individual Grille Openings
The expression for the ram pressure coefficient in Equation (2.15) can be
generalized to represent many vehicle configurations by introducing
experimentally determined coefficients for the three terms.
Kram =
ry 2 f\, V
v V r y K,
vVry K A "^bay (2.17)
or
K_ = 'ram
^V ^ ' 00
(ty V
K o -V ^ W
K A K^ay • (2.18)
The values for the three coefficients can be obtained from a least squares fit of
Equation (2.18) to experimental data with N points containing at least two sizes
of a single opening,
(V„.AP„.,V„A,), j = 1.N (2.19)
or
^AP,„ V„ A,^ r2 •
j = 1.N. J apVr ' Vr A,
The least squares fit of Equation (2.18) for the three coefficients becomes,
(2.20)
13
-I / V. A, \
-Z J Vr A,
A.
A^ (t. V
K,
K
l^bayj
J
HI yu
K ram
IK
K ram
ram
(2.21)
Once the coefficients are determined, they may be used to calculate the ram
coefficient for any reasonable size of the opening considered.
2.3 Compatible Individual Opening Correlations
The coefficients Ko and KA are unique to a particular style or location of
grille opening. Other opening locations generally have different values for these
coefficients. The engine bay resistance coefficient should have a single value
representative of the vehicle and independent of the particular grille
configuration. The resulting engine bay pressure coefficients for each opening
location from Equation (2.18) are not always going to be equal. This section
describes the solution process that determines a single Kbay-
The solution process requires that all of the Ko, KA pairs should be
determined simultaneously along with the single Kbay. For example, curve-fitting
data for the four typical grille opening locations requires the solution of nine
simultaneous equations. Through a least squares curve-fitting procedure similar
to Equation (2.21), the simultaneous set of equations required to determine the
nine coefficients are
[C]{K} = {K,3J (2.22)
where
14
-^l^J -£,
-^ *oo"r
^ V r A i
[C] =
Njl^r
^ V r A i
'4Ui
• Z
v ^ i ;
N, 'Bu < *r ^ J - N ^
"Bu VrAi
NflulVr Z 1 ^
[K] =
Ko
KA
Ko
KA
Ko
KA
Ko
KA
•^Bay
Bu . V r A i
y V
"Bu l A . ,
I'. \
"Bu V^^J
zf^r -zf VooAr
VrAi
M
z n^ NcUr
iKRamJ =
N B O ^ V. Z 1 ^
"Bo k^rAi
- Z r, Y
^Ai; 44
Nsol^rj
ZK. NT
ZK. NT
ZK, NB„
Z K R NB„
IK, Nc
IK, Nc
IK. Nee
ZK.
^V ^'
AJ V A/ V
Iv. ^A V
V
lAi.
^A.>^
A / >2
' 4 K
NBul r
- Z
N B U
NclVr
v ^
"Bo V r A ^ ;
"Bo ^^1
- z N B O ^ ^ ;
A J
ZKR + ZKR+ZKR+ZKR
Neol^Vr
- z ^2
'Bo
- N , total
2.4 Ram Pressure Coefficient for Multiple Grille Openings
Prediction of the ram pressure coefficient for combined openings is based
on the assumption that there is a uniform pressure at the front face of the first
heat exchanger. Since the velocity and pressure in the inlets determine this
15
pressure, the assumption implies that the pressures at the inlets are also equal
and that both inlets are operating at the same ram pressure. The correlations
obtained for the isolated openings are used to predict the flow rates through the
two openings required to produce equal pressures at a given freestream velocity.
The development of the ram pressure coefficient for combinations of
openings begins with the ram pressure expression for each of the individual
openings given by Equation (2.15). For No openings, the equation becomes
V K
(\i V ry^V Ram.
vV,y Ko , -
vV,y K A I -Kbay i = 1,No. (2.23)
The mass conservation relation given by Equation (2.14) does not apply for
multiple grille openings. Since Vr represents the internal velocity associated with
the combination of inlet flows, we must use Equation (2.13), which involves the
inlet velocity ratio rather than Equation (2.15), which uses the inlet area ratio.
However, an expression of mass conservation for the multiple inlet configurations
can be written as
pVA=IpVA
or
N V A N
where aj is the fraction of the total flow rate that passes through opening j .
Rewriting Equation (2.23) as
K Rami (y\ y)
' / w . V^A ^ Ko,-
V,A,
v V A y V^ i y KA, -Kbay l = 1,N,
(2.24)
(2.25)
(2.26)
and substituting the mass flow rate fraction from Equation (2.25) for the velocity
and area ratios yields
K ^V . ^ '
Ram. y^ Ko, - a ; KA, -Kbay i = 1.No. (2.27)
16
A single pressure behind the grille requires that all grille openings operate at the
same ram pressure coefficient. For No openings, this requirement leads to No -
1 equations of the form
i = 1,No-1 (2.28) K = K "^ Rami "^ Rami .1
or
y) lA ^^
Ko, - « • vA, ,
K A , - K j g j , = IVrJ
r A A2
KQ;,, -Cti+1 v A i + i y
K A , . , - K , , , i = 1,No-1.(2.29)
This expression may be rewritten as
0 = a; A.f., yAy '
\^\ J K A , -o t j+ i
v ^ i + i y K. -
^i+1 (^J(K.-KJ i = 1,No-1 (2.30)
and simplified to
0 = c a^ - c .a^. - b i = 1.No-1. (2.31)
Arranging the conservation of mass relation (2.25) in a similar format provides
the last equation
No
0 = Iai-1 j=1
(2.32)
The simultaneous nonlinear algebraic equations given by (2.31) and (2.32)
require solution by an iterative procedure. A straightfon^/ard application of the
Newton iteration method requires solution of
F(x) = 0 (2.33)
where
F(x) =
f i ( x ) •
f,(x)
fNo-l(x)
x = a,
a N
0 =
0
0
0
(2.34)
and
fi(x) = Ciai'+Ci,,af,,-bi i = 1,No-1 (2.35)
17
Nr
fNoW=ZcCi-1-j=1
The basic iterative relation becomes
0 = F(X(^))+J[F(X(^))]6X
where J(F) is the Jacobian of the equation set.
(2.36)
(2.37)
J(F) =
^ .
af, N
^a.,
da^
8f,. da Nr
df, N,
da,
(2.38)
and 6x is the change to the vector of inlet mass flow rate fractions between the k
and k+1 iterations,
6x = x(' ) - x ( ' \ (2.39)
The resulting inlet flow rates simultaneously satisfy the requirements given by the
total flow rate and an equality of ram pressures through each of the openings.
Again, the correlations for the individual openings are used as the basis
for predicting the ram correlation for the combined openings. The resulting ram
pressure coefficients for the combined openings can then be compared to the
experimental data for the combined openings.
18
CHAPTER 111
EXPERIMENTAL SETUP
The tests that produced the data used for the current study were
conducted at the Lockheed Aeronautical System Company (LASC) in Marietta,
Georgia during the summer of 1990. Their Low Speed Wind Tunnel has a top
speed of 200 mph. It is a closed-circuit wind tunnel with a center line length of
780.5-feet and test section dimensions of 23.25-feet width by 16.25-feet height
by 43-feet long.
3.1 Front-End Modifications
The original front-end and bumper of the Taurus were replaced with a
fiberglass nose cast from a mold taken from a stock Taurus (Figure 3.1). This
simplified front-end retained major features and contours but eliminated most of
the small details. The openings were cut in the fiberglass nose with four
common inlet locations that will be referred to as the top, the chin, the bottom,
and the bumper. Interchangeable panels with various opening areas and
geometry for each location were used to explore a variety of front-end conditions.
Figure 3.2 is a picture of the front-end with the panels. Figure 3.3 shows the
location, dimensions and identification code for the front-end openings and
interchangeable panels considered in this study, the top, the chin, and the
bottom. The panels were attached to the front-end with high strength duct tape
(Figure 3.4).
Other variations of each opening location were tested individually. They
are not included in this report because the purpose of this study Is to find ram
correlations for multiple grille openings. Details on these other locations can be
found in a technical report by Oler and Crafton (1992).
19
Figure 3.1 Modified Taurus Front-End
Figure 3.2 Modified Taurus Front-end With Panels
20
Top Opening A
24 in. X 4/2 in.
108 square in.
Top Opening B
24 in. X 3 in.
72 square in.
(a) Top Openings
Top Opening C
24 in. X 1/2 in.
36 square in.
Chin Opening A
24 in. X 4/2 in.
108 square in.
Chin Opening B
24 in. X 3 in.
72 square in.
Chin Opening C
24 in. X 1 3/8 in.
72 square In.
(b) Chin Openings
Figure 3.3 Location and Identification of Interchangeable Panels
21
(c) Bottom Openings
Figure 3.3 Continued
Bottom Opening A
24 in. X 4/2 in.
108 square in.
Bottom Opening B
24 in. X 3 in.
72 square in.
Bottom Opening C
24 in. X 1.4 in.
72 square in.
22
Figure 3.4 Changing of the Front Panel
23
3.2 Instrumented Radiator
Emprise Corporation of Atlanta, Georgia prepared the instrumented
radiator. They also developed and provided operational support for a
microcomputer-based data acquisition system used in conjunction the
instmmented radiator in the wind tunnel and the flow stand tests.
The back face of the radiator was divided into nine equal areas with a
four-inch diameter turbine anemometer centered in each (Figure 3.5). The
anemometers give an indication of air velocity through each area from which the
incremental contribution to the total volumetric flow rate can be estimated. The
actual flow rate is determined by summing the contributions and applying a
correction from a flow stand calibration of the instrumented radiator.
Other modifications were tested such as an inclined radiator and two
different air dams. Leakage flow rates were also studied. These are not relevant
to the research described in this thesis. Further details on these studies can be
found in technical report by Oler and Crafton (1992).
Data taken during each mn of the test included lift, drag, temperature,
pressure, and mass flow measurements. The major data needed for the ram
correlation is the mass flow through the radiator and the pressure change from
the freestream to the radiator back plane. This data was organized into a
spreadsheet with corresponding operating conditions for evaluation purposes.
24
Pressure Taps Turbine Anemometer
Figure 3.5 Instrumented Radiator
25
CHAPTER IV
RESULTS AND DISCUSSION
The objective of this study is the determination of general ram pressure
correlations for automobiles. The correlations will be incorporated into the
cooling system model ttu_Cool®.
The magnitude of the ram pressure depends on the size and location of
the opening or openings, the vehicle speed, and the cooling airflow rate. The
basic form of the ram pressure correlation incorporates the effects of flow rate
and vehicle speed through the slope and intercept, Ko and Kj, of the ram
coefficient curve. The effects of size and location of single or multiple grille
openings is reflected in variations of the slope and intercept. A general
correlation that can be used to predict these variations is the primary objective of
this study. The strategy for obtaining the general correlation is to develop
correlations for variable sized individual openings at characteristic locations
typical of most sedans. Once obtained, the individual opening correlations are
used to predict the slope and intercept of the ram coefficient curve for any
combination and sizes of those openings.
This chapter contains the evaluation of ram coefficients for individual and
multiple grille openings of the Ford Taums. The correlations for individual
openings are determined first and then used as the basis for predicting the ram
correlation for the combined openings. The experimental data for the combined
openings are used for comparison purposes only, i.e., they are not used in the
generation of the correlations.
4.1 Data Reduction Procedure
All of the experimental data from the wind tunnel tests and flowstand tests
of 1989 were collected and organized. The fan and heat exchanger performance
files were developed in ttu_Cool® using the flowstand test data and the
parameters of the fan and the heat exchanger. These files contain the
26
correlation data necessary to calculate the pressure drop and heat transfer
characteristics of the heat exchanger and the pressure jump and power
consumption characteristics of the fan. Figures 4.1 and 4.2 illustrate the resulting
cooling package and streamtube distribution of the radiator and heat exchanger
of the Taurus generated by ttu_Cool®, respectively. A listing of these files is
included in Appendix A. A comparison of the calculated heat exchanger
pressure drop with the experimental flowstand data is presented in Figure 4.3.
Similarly, a comparison of the calculated and experimental flowstand based
pressure drop across the complete cooling package consisting of heat exchanger
and fan is presented in Figure 4.4.
Wind tunnel data files are necessary to find ram coefficients in ttu_Cool®.
The following experimental data from the wind tunnel tests are included in the
wind tunnel data files: wind tunnel speed, fan speed, flowrate, ambient pressure,
and ambient temperature. An example of the wind tunnel data files for the
individual openings and multiple openings are included in Appendix B.
The fan, heat exchanger, and wind tunnel file are provided as input to
ttu_Cool® to solve for the measured ram pressure coefficients. ttu_Cool®
currently contains a built-in capability for finding the slope and intercept of the
ram pressure coefficient curve for a single front-end geometry and set of
operating conditions. This capability has not been used in the current study.
Instead, the coefficients KA, KO, and Kbay for the individual grille openings are
found for the ram pressure coefficient results by applying Equation (2.18). The
values of Kj and Ko for the individual and multiple grille openings are then
entered into grille files (Appendix C). The fan, heat exchanger, and grille file are
provided as input to ttu_Cool® to solve for the predicted ram pressure coefficients
and the predicted flowrates.
27
S Coolmg Package
** Component Models ** grL DN5_160.GRL htx: DN5_R.HTX fen; DN5.FAN
Figure 4.1 Cooling Package in ttu_Cool ©
1 B Streamtube Distiibution H @ 0 | |
i^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^H^^^^^^^^&l^^^^^^^^^^^^^^^^^^^^^^^^^^^^l
** Component Models ** grl: DN5_160.GRL htx: DN5_R.HTX fen: DN5.FAN
Figure 4.2 Streamtube Distribution in ttu_Coor
28
Plenum Pressure
Mass Flowrate (SCMM)
Figure 4.3 Heat Exchanger Pressure Drop Comparison
Plenum Pressure
08
PU
yIass Flowrate (SCMM)
Figure 4.4 Heat Exchanger and Fan Pressure Drop Comparison
29
4.2 Ram Pressure Coefficients for Individual Openings
The correlations for individual openings are determined first since they are
used as the basis for predicting the ram pressure correlation for the combined
openings. This section describes the ram pressure correlation results for the
individual top, chin, and bottom openings. These correlation results are
presented in tabular and graphical formats and are discussed below.
A least squares fit of Equation (2.18) is first applied to each opening
location. The results for the engine bay pressure coefficient for each opening is
shown in Table 4.1. The range of Kbay values is from about four to over twenty-
eight. The engine bay pressure coefficient should have a single value for each
vehicle and be independent of the particular grille configuration. A single engine
bay pressure coefficient eases the process of evaluating the ram pressure
coefficient results by limiting the variations to the first two terms in Equation
(2.18).
Since the engine bay pressure coefficient should have a single value
representative of the vehicle, all of the Ko, KA pairs for the three opening
locations are determined simultaneously along with a single Kbay in Equation
(2.22). The result is a single Kbay value of 7.59. The Matlab program developed
to solve this equation is in Appendix D. Figure 4.5 shows the accuracy of the
unified ram correlation results when compared to the individualized ram
correlation for the top, chin, and bottom openings. Tables 4.2, 4.3, and 4.4 show
the values for the measured and predicted ram pressure coefficients and the
measured and predicted flow rates for the top, chin, and bottom opening
locations based on the unified correlation.
Table 4.1 Individualized Correlation
Opening Top Chin Bottom
Kbay 4.0703 5.3520
28.1883
30
For each opening location, the ram pressure coefficient is greater with the
fan off than with the fan on for the same size opening at the same vehicle speed.
This is due to the decrease of the ratio of the freestream velocity to the radiator
velocity when the fan is on. As the fiow rate increases at constant vehicle speed,
the pressure in the inlet decreases causing the losses due to unrecovered static
pressure to Increase. As the size of the openings decreases, the ram pressure
coefficient decreases with the fan on due to the decrease in total pressure loss.
Also with the fan on, the ram pressure coefficient increases as the vehicle
velocity increases due to the increase in static pressure. The ram pressure
coefficient also decreases the further down the opening is on the face of the
vehicle. This may be due to an opening's location relative to the stagnation point
of the local static pressure on the front of the vehicle. As the opening is moved
away from the stagnation point, the local static pressure on the front of the
vehicle decreases, which results in a lower ram pressure coefficient. The
predicted flow rates using the ram pressure coefficient correlation results for all of
the openings remained within about 10% of the measured flow rate.
All of the top openings had the same value for the coefficient Ko, 0.7714.
The same is tme for the chin openings, Ko = 0.6748, and for the bottom
openings, Ko = 0.7769. The coefficient Ko represents the slope of the ram
pressure coefficient lines in the Figure 4.5. The coefficient Kj decreases with
decreasing sizes of the grille opening. It represents the intercept of the Kram axis.
As evident in the plot of the top openings, the ram pressure coefficient is slightly
underestimated by the correlation. In the plot of the chin openings, the ram
pressure coefficient results represent a good average of the experimental data.
The plot for the isolated bottom openings reveals an overestimation of the ram
pressure coefficient for opening A and an underestimation of the ram pressure
coefficient for opening B.
Some of the smaller openings of the lower grille locations are not included
in Figure 4.5. Chin C and Bottom C are the two openings not shown in the figure
because their experimental data deviated too far from the ram pressure
31
correlation. As seen when comparing the isolated bottom plot with the other
openings with larger opening size, the data points that deviate the most from the
ram pressure correlation are for the smallest and lowest inlet areas. It is not
known at this time whether the deviations Indicate tme physical differences in the
flows or a breakdown in the experimental procedures used to determine the flow
rate and an average pressure on the back face of the radiator.
4.3 Ram Pressure Coefficients for Multiple Openings
Many vehicles have more than one inlet opening on their grilles. Thus, the
need for determining ram pressure correlations for mulfiple grille openings is
evident. For the multiple grille opening correlation. Equation (2.37) is applied
using the correlation results from the individual openings. The Matlab program
developed to solve this equafion is in Appendix E. This section presents the ram
pressure correlation results for combinations of the top, chin, and bottom
openings. Again, the experimental data in this section are not used in the
generation of the correlations.
Tables 4.5 through 4.8 show the measured and predicted flow rates and
ram pressure coefficients for combinations of multiple openings. Figure 4.6
shows the ram pressure coefficient versus the velocity rafio squared for
combinations of the top and chin openings. The plot reveals an underestimation
of the ram pressure coefficient. The ram pressure correlation for the chin
openings combined with tops A and B produces too small of a slope (Ko value)
when comparing it to the experimental data. The experimental data from the
combination of top C and chin B is the closest to the ram pressure correlation.
The ram pressure coefficient for combinations of chin and bottom
openings is plotted against the velocity ratio squared in Figure 4.7. In this plot,
the ram pressure coefficient is overestimated. In general, the slopes are fairly
accurate. However, the Kj value is too high for the experimental data. The chin
A and bottom B combination provides the best correlation result compared to the
experimental data.
32
Figure 4.8 shows the ram pressure coefficient results for combinations of
the top and bottom openings versus the velocity ratio squared. The plot reveals
an underestimation of the ram pressure coefficient. The slope (Ko value) is also
too small compared to the experimental data.
The ram pressure coefficient versus velocity squared for combinations of
the top, chin, and bottom openings is shown in Figure 4.9. The ram pressure
correlation is underestimated for both combinations. The slope (Ko value) is
again too small for the experimental data. The intercept is also overestimated.
The consistent underestimation of the flow rate for the top combinations
may provide the underlying reason for the underestimation of the ram pressure
correlation. The chin and bottom combination reveals an overestimation of the
ram pressure coefficient possibly due to the flow rates also being overestimated.
The discrepancies may also be a result of the way the actual projected area ratio
influences the ram pressure coefficient. Again, it Is also not known at this time
whether the deviations indicate true physical differences in the flows or a
breakdown in the experimental procedures used to determine the flow rate and
the average pressure on the back face of the radiator.
The flow rate results for the combinations of openings are also better than
expected based on the individual opening ram pressure coefficient results. This
may be explained with the reasoning that two openings together have a higher
net projected area than they would alone and consequently work better.
Another application of the ram correlation for multiple openings provides a
range of possible ram pressure coefficients for two or more inlets. If 100% of the
airflow was through either of the respective openings, then a = 1. Equation
(2.27) becomes
•^Ram,
ry \^ AA ^ 0 Ko,-
\ ^ \ j
K , - K ^ „ i = 1.N. (4.1) ' A| ' ^ bay
The opposite is true if the airflow through the inlet is zero. With a = 0 for the
openings , Equation (4.1) becomes
33
•^Ram,
ryy vVry
Ko,-Kbay i = 1.N. (4.2)
Figure 4.10 illustrates the spectrum of possible ram pressure coefficients
for the Top A Chin B combination of openings. The lower dashed and dotted
lines represent the ram pressure coefficient that would result if 100% of the
airflow were through either opening. The upper dashed and dotted lines
represent the ram pressures that the openings would produce if the airflow
through the inlet was zero. The solid line shows the ram pressure coefficient for
the corresponding combination of openings.
Note that the intercepts for the upper dashed and dotted lines are both
equal to the engine bay pressure drop coefficient. This situation occurs when the
flow through a dominant opening with a high Ko produces a ram pressure that
causes a back pressure in the weaker opening preventing any flow from entering.
A higher value of the freestream velocity ratio from the intercept would result in
the forcing of flow out of the weaker opening. The ram pressure coefficient
values below this extreme, a < 1, is where the total airflow rate is split between
the openings. This analysis can help guide engineers in the placing and sizing of
inlet openings.
Finally, Figure 4.11 compares the results of the calculations of the ram
pressure coefficient for the individual and combination of openings with the
measured ram pressure coefficient values. When these calculated ram pressure
coefficient values are used in ttu_Cool®, for flow rate predictions, the results in
Figure 4.12 are produced.
34
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experimental individualized correlation, A1/Ar = 0.264 individualized con-elation, A1/Ar =0.167 individualized con-elation, A1/Ar = 0.083 unified con-elation, A1/Ar = 0.264 unified con-elation, A1/Ar =0.167
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Figure 4.5 Isolated Ram Correlation Results
38
200
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(b) Chin Openings
Figure 4.5 Continued
39
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2
experimental individualized con-elation, A1/Ar = 0.244 indi\^dualized correlation, Al/Ar =0.167
- unified con-elation, Al/Ar = 0.244 - unified con-elation, Al/Ar =0.167
-100 50 100 150 200 250 300
(VoA/rr
(c) Bottom Openings
Figure 4.5 Continued
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100
80
60
40
20
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-20
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- - top A, chin B: Ko = 0.7317, Ki = -11.5697 — top B. chin B: Ko = 0.7252. Ki = -14.9347
_ _ top C, chin B: Ko = 0.7140, Ki = -22.8942 top B, chin A: Ko = 0.7071, Ki = -11.8226
X top A, chin B + top B, chin B j top C, chin B
O top B. chin A
_ _ L 1 J. J _ J 1 1 1 1
1 1 1 1
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10 20 30 40 50
(VoA/r)
60 70 80 90 100
Figure 4.6 Ram Results for Top and Chin Openings
45
100
80
E 2
60-
40
20
-20
-40
chin A. bottom B: Ko = 0.6973, Ki = -15.5216 — chin B. bottom B: Ko = 0.7125, Ki = -25.2439
chin B, bottom A: Ko = 0.7203, Ki = -20.1041 X chin A, bottom B + chin B, bottom B
_ + chin B, bottom A 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L X -L J J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \ j^ y 1 1 1 1 1 1 ^ >-1 1 1 1 1 J ' ' - - 1 - ^ 1 1 1 1 ^ -^ y ^ ^ ^
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10 20 30 40 50 60 2
70 80 90 100
(VoA/r)
Figure 4.7 Ram Results for Chin and Bottom Openings
46
100
80- —
E 03
60
40
20
-20
-40
~-~
top A, bottom B: Ko = top B, bottom B: Ko = top C, bottom B: Ko =
0.7725, Ki = -0.7730, Ki = -0.7739. Ki = -
12.4255 17.2065 30.4602
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- 1 1
1 1
1 1
1 1
1 1
1 1
1 1
t 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1 1
1
10 20 30 40 50
(VoA/r)
60 70 80 90 100
Figure 4.8 Ram Results for Top and Bottom Openings
47
E
100
80-
60
40
20
-20
-40
top A, chin C, bottom A: Ko = 0.7218, Ki = -9.3266 _ top C, chin A, bottom A: Ko = 0.7080. Ki = -11.3878
X top A, chin C, bottom A + top C, chin A, bottom A
1 1 1 1 1 1 1 1 1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1
1 X ^ -
' yy -£ -y
y 1 1
1
1
1
1
1
1
1
1
1
1
1
J
1 >^
+ y -1 y r'
-^ --r 1
+ ^
_
. - 1 ' ' ^ 1
10 20 30 40 50 60
(VoA/r)2
70 80 90 100
Figure 4.9 Ram Results for Combinations of All Openings
48
03
100
80
60
40
20
-20
-40
-60
"- -'• X J ^ -^i_^,yy^A \ 1 1 yyy -yyy > i
1 ^ - J j > ^ < ^ . I I I \^,iC'^h,-cy\x. ' ^ X X -J 1
^ y y y - 1 1 1 1 1 -y-^yy^^ 1 1 1 1 1
- " I I 1 1 t y _ L X X X J y 1
1 1 1 1 .- r ' 1
1 1 1 ..- 1 ' 1 1
L X ^ ' X L _l 1 1 _\'" \ 1 1 1 1 ^ - ' 1 1 1 1 1
^ ^ -T ' 1 1 1 1 1 -• ' ' 1 1 1 1 1 1
1 1 I 1 1 1
^ •
— -
X
o
1 ^
combined openings . 1 top. alpha = 1 I top. alpha = 0 I
chin, alpha = 1 j chin, alpha = 0 ; isolated top isolated chin ' combination i
1 1 1 1
10 20 30 40 50 60 70 80 90 100
(VoA/r)2
Figure 4.10 Ram Pressure Coefficient Spectrum
49
\
< -4 o \
^ 9: r <
A*
sola
ted
top
ope
ning
s
sola
ted c
hin
ope
ning
s
sola
ted
botto
m o
peni
ngs
com
bine
d to
p, c
hin,
and
bot
tom
ope
ning
s
com
bine
d t
op a
nd c
hin
ope
ning
s
com
bine
d c
hin
and
tso
ttom
ope
ning
s
com
bine
d to
p a
nd b
otto
m o
peni
ngs
idea
l
o < o • • << •
O
1
M
o o
o 00
o CD
O
o 1>J
o
-20
o ^
o CD
E ra ^
red
3 (A
ra S
E OJ 1 -
cte
dK
us
Pre
d
CO 1 _
0 > F 2
^ • o 0 CO
11 C
alcu
,
gu
re4
u_
o CO
o o
o o o 00
o CO
o o CN
o o CO
o 00
o o
uiejx ps^einojeo
50
</) O)
c c 0) a. o Q. O
•u Qi
ro o (/)
(0 O) c c 0) CI.
o c o u 0) CO
u (/)
O) c c 0)
O
E o
bott
• o 0) (0
u (/)
5. o
1-o o
c CO
c" !c o ri o
T3 (1) c 'n F o o
M U> c 'c 0) Q. O
c .c CJ
c (0 Q. O
T3 4) C n F o u
O) c 0) CI.
o
torn
o n
• o c m
chin
.
•o 0) r f )
F o o
c/> o> c c
ope
E o c o
• o c CO
o. o •o 0) c n F o o
0 ^-> CO
u_ • D
B "o 0
CO
CO i _ 0 > 0 CO
CC
Ol
u_ • D 0 * ->
i5 _o CO
O Csi
0 k_
D D)
L J .
— I —
CO
(s/B)i) ejBJMOjj peiB|no|BO
51
CHAPTER V
CONCLUSIONS AND RECOIVIMENDATIONS
The driving pressure required for the cooling system airflow comes from
two sources: the pressure due to the forward motion of the vehicle known as ram
pressure, and the radiator fan pressure rise. These internal and external flow
fields interact at the cooling air inlets and at the underside of the engine bay.
The flow fields are closely related and were considered together in this study.
The primary focus of this study has been to find general ram pressure
correlations for automobiles. The principle test results consist of a set of
correlation equations which describe the variation of the ram pressure coefficient
with respect to the size and location of the openings, the freestream velocity, and
the cooling airflow rate for individual and combinations of openings. These
correlations are in a format suitable for use with streamtube cooling system
models such as ttu_Cool®.
5.1 Conclusions
The general correlation for the top, chin, and bottom individual openings
was first evaluated by performing a least squares fit of Equation (2.18). This
resulted in large variations of the engine bay coefficient for each opening. Since
the engine bay coefficient should have a single value representative of the
vehicle, all of the Ko, KA pairs for the three opening locations were determined
simultaneously along with a single Kbay by applying Equation (2.22). The
resulting engine bay coefficient was 7.59. The effects of the opening sizes and
locations were reflected in variations of the slope, Ko, and intercept, Kj. The
correlation for the individual openings can be applied over a broad range of areas
for each opening location. However, there is a breakdown of the correlation at
high velocity ratios associated with small, low openings.
The general correlations for multiple openings were determined by using
the correlation results from the individual openings in Equation (2.37). This
52
correlation underestimated the ram pressure coefficient for combinations that
include the top opening and overestimated the ram pressure coefficient for the
chin and bottom opening combination. The basis of these errors may come from
the influence of the actual projected area ration on the ram pressure coefficient,
differences in the flows, or a breakdown in the experimental procedures used to
determine the flow rate and the average pressure on the back face of the
radiator.
5.2 Recommendations
The correlation of the ram pressure coefficient for individual and
combinations of openings is a well-developed process that produces results that
compare well to experimental data. However, further studies and modifications
of the ram pressure correlation could produce even more accurate results.
Further studies that would quantify the effect of the face velocity
distribution on the radiator pressure drop may help to explain some of the
variations between the ram pressure correlation results and the experimental
data. The radiator calibrations were performed on a flow stand, which produces
a rather uniform velocity distribution over the radiator face. Small openings, fan
effects, and engine blockage in the wind tunnel testing cause the velocity
distribution over the radiator face to vary from the flow stand conditions. Since
the flow resistance is a function of velocity, the average velocity currently used by
the radiator correlation could produce a flawed radiator pressure drop. Also,
studies to help understand the influence of the actual projected area ratio on the
ram pressure coefficient could explain why the ram pressure correlation for
multiple openings works better than expected based on the individual ram
pressure correlation results.
The ram pressure correlation process could be simplified by making
modifications to the equations. The definition of the engine bay pressure drop
requires a different value for Kbay for each vehicle. This equation could be
modified to make Kbay constant for all vehicles such that for a given engine bay
53
volume, the effects of changes in the blockage parameter can be directly
evaluated in ttu_Cool®. If Ko and Kj were independent of the projected area ratio,
then the ttu_Cool® user would not have to make grille data file adjustments due
to a radiator change. These changes would simplify and shorten the ram
pressure correlation process.
54
REFERENCES
Hawes, S.P. "Improved Passenger Car Cooling Systems." SAE Paper 760112. February, 1976.
Oler, J.W.and J.W. Crafton. "Grille Coefficient Measurements for a Ford Taurus." Technical Report TR-FMC-92-3. September, 1992.
Oler, J.W., Roseberry, CM., Jordan, D.P. and T.E. Maxwell. "Ram Recovery Coefficient Correlations." Technical Report TR-FMC-90-1. December, 1991.
Olson, M.E. "Aerodynamic Effects of Front-end Design on Automobile Engine Cooling Systems." SAE Paper 760188. February, 1976.
Renn, V. and A. Gilhaus. "Aerodynamics of Vehicle Cooling Systems." Journal of Wind Engineering and Industrial Aerodynamics. Vol 22:339-346. 1986.
Schaub, U.W. and H.N. Charles. "Ram Air Effects on the Air Side Cooling System Performance of a Typical North American Passenger Car." SAE Paper 800032. February, 1980.
Williams, J. "An Automotive Front-End Design Approach for Improved Aerodynamics and Cooling." SAE Paper 850281. 1985.
55
APPENDIX A
FAN AND HEAT EXCHANGER FILES
56
FAN DATA FILE
* ?an daCa for ttu_Cool and UH3D * Save as "rad_lD.fan" for use in ttu_Cool * or incorporate into a "run" file for use * for ttu_Cool and UH3I>
** Calculation Source Data ** * Component Data * htx: DNS_R.HTX * fan: DHS.FAH ( m o d i f i e d ) * E x p e r i m e n t a l D a t a * DNS_RF.FS
* This file is compatible with UH3D v3.0 ^version 3.0
ffan_data ^ ; # of fans
* speeds (rpm) 1800.0 ; fan fl
$fan_locations * fancenter-x fancenter-y fancenter-z
1.0760 0.S684 0.0S89 ; fan «1
tfan_info * Fan type: 'radial' or 'axial' •axial' ; fan #1
* Fan diameter hub diameter thickness (m), Rotation angle about axis x,y,2 (degrees) 0.4064 0.1166 0.02S4 0.0000 0.0000 -S.OOOO ; fan #1
* Turbulence generation fraction 0.0000 ; fan #1
* Use fan pre-swirl effects CY' or 'H') 'N' ; fan Jl
$fan_shroud_info ; HOTS: this section utilized in ttu_Cool only 1 ;$ of fan shrouds
* lower left corner coordinates (m) X Y Z height width thickness (m)
I.OSIO 0.3810 0.3161 0.3747 0.5144 0.02S4 ; shroud #1
57
f fan_performance
•fan #1
10 5
0.3582
0.5008
0.6435
0.7861
0.9287
*fan il
10 5
0.3582
0.5008
0.6435
0.7861
0.9287
•fan #1
10 5 1
0.3582
0.5008
0.6435
0.7861
0.9287
performance tabl
; COLUMNS f
; ROWS for
0.1435
0.1017
0.1017
0.1017
0.1017
0.1017
0.2023
0.1596
0.0894
0.0894
0.0894
0.0894
0.0894
0.1951
performance tabl
; COLUimS f
; ROUS for
0.1435
0.0000
0.0000
0.0000
0.0000
0.0000
0.1596
0.0000
0.0000
0.0000
0.0000
0.0000
performance tabl
; COLUMNS f
; ROWS for
; Option sp
0.1435
0.0000
0.0000
0.0000
0.0000
0.0000
0.1596
0.0000
0.0000
0.0000
0.0000
0.0000
e axial
or phi 1
radius i
0.1756
0.0710
0.0710
0.0710
0.0710
0.0710
0.1716
direction
tdimensionless)
tdimensionless)
0.1917
0.0466
0.0466
0.0466
0.0466
0.0466
0.1259
0.2078
0.0161
0.0161
0.0161
0.0161
0.0161
0.0495
e tangential direction
or phi
radius
0.1756
0.0000
0.0000
0.0000
0.0000
0.0000
(dimezis i onl e s s)
(dimensionless)
0.1917
0.0000
0.0000
0.0000
0.0000
0.0000
0.2078
0.0000
0.0000
0.0000
0.0000
0.0000
e radial direction
or phi
radius
ecifier
0.1756
0.0000
0.0000
0.0000
0.0000
0.0000
(dimensionless)
(dimensionless)
0.1917
0.0000
0.0000
0.0000
0.0000
0.0000
0.2078
0.0000
0.0000
0.0000
0.0000
0.0000
0. -0. -0. -0. -0. -0. -0.
0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0.
.2239
.0203
.0203
.0203
.0203
.0203
.0719
.2239
.0000
.0000
.0000
.0000
.0000
.2239
.0000
.0000
.0000
.0000
.0000
0.2399
-0.0629
-0.0629
-0.0629
-0.0629
-0.0629
-0.2621
0.2399
0.0000
0.0000
0.0000
0.0000
0.0000
0.2399
0.0000
0.0000
0.0000
0.0000
0.0000
0. -0. -0. -0. -0. -0. -0.
0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0.
.2560
.1114
.1114
.1114
.1114
.1114
.5663
2560
.0000
.0000
,0000
.0000
0000
2560
.0000
.0000
.0000
.0000
.0000
0, -0. -0. -0. -0. -0. -1.
0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0.
.2721
.1660
.1660
.1660
.1660
.1660
.0794
.2721
.0000
.0000
.0000
.0000
.0000
.2721
.0000
.0000
.0000
.0000
.0000
0. -0. -0. -0. -0. -0. -2.
0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0.
.2881
.2267
.2267
.2267
.2267
.2267
.0429 efficiency
2881
0000
0000
0000
0000
0000
2881
0000
0000
0000
0000
0000
ffan off_resistance ; NOTE: this section only utilized in ttu_Cool
*fan Jdl
7 5
0.3582
0.5008
0.6435
0.7861
0.9287
1. 8. 8. 8. 8. 8.
; COLUMNS 1
; ROWS for
.7491
.0850
.0850
.0850
.0850
.0850
2.4941
8.4851
8.4851
8.4851
8.4851
8.4851
!or average veloc
radius i
3.8707
6.8411
6.8411
6.8411
6.8411
6.8411
:ity (m/s
t dimens i onle s s)
5.1478
5.7191
5.7191
5.7191
5.7191
5.7191
6.2373
5.1230
5.1230
5.1230
5.1230
5.1230
)
8. 4. 4. 4. 4. 4.
.0732
.6212
.6212
.6212
.6212
.6212
9. 4. 4. 4. 4. 4.
.6010
.4343
.4343
.4343
.4343
.4343
58
HEAT EXCHANGER FILE
* Heat: exchanger component data f i l e * Save as "ComponentNaaie.htx" for use i n ttu_Cool * or incorporate i n t o a "rvm" f i l e for ttu_Cool and UH3D
** C a l c u l a t i o n Source Data ** * Component Data * htx: DNS_R.HTX (modified) * Experimental Data * DNS_R.FS
* This file is compatible with UH3D v3.0 ^version 3.0
$c omp onent_dat a 1 if ot heat exchangers
* heat rejection units ("btu/hr" or 'watts') 'watts•
* heat * rejection *
586
flow rate (kg/s) 2.10 ; radiator
$ component_names ^component nvmber component name
1 'radiator'
$ c omp onent_lo c at i ons * heat exchanger coordinates * lower left corner point (m) * X y z
1.0000 0.3810 0.3161 ; radiator
$component_info * height width thickness. Rotation angle about axis x,y,z (degrees)
0.3747 0.5144 0.0260 0.0000 0.0000 0.0000 ; radiator
$component_friction AREA RATIO TOT/ FACE
34.440
AREA RATIO HIH/ FACE
0.7720
CHST FOR ReNo EQN
3.7770
EXP FOR ReHo EQN
-0.4836 ; radiator
59
$ l o s s _ c o e f f i c i e n t s * Kc *
l i n e a r 0 .0
* squared - 0 . 4
constant 0 .4
squared 1.0
Ke
l i n e a r - 2 . 0
constant 1.0 rad ia tor
$component_eff_table
* radiat 9 9
0.2500 0.5000 1.0000 l.SOOO 2.0000 2.5000 3.0000 3.7500 4.5000
or
0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
w
0
5000 8514 9320 .9682 .9784 .9830 .9856 .9873 .9889 .9899
COLUMNS FOR VELOCITY (m/s) ROUS FOR COOLANT RATE (kg/s)
1.0000 0.6426 0.7844 0.8746 0.9069 0.9232 0.9329 0.9394 0.9459 0.9503
2.0000 0.4163 0.5716 0.7027 0.7607 0.7934 0.8143 0.8290 0.8442 0.8547
3.0000 0.3049 0.4458 0.5823 0.6496 0.6899 0.7169 0.7362 0.7569 0.7715
4.0000 0.2396 0.3647 0.4967 0.5666 0.6103 0.6403 0.6623 0.6862 0.7034
5. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0000 1968 .3083 .4331 .5027 .5476 .5792 .6026 .6285 .6473
7. 0. 0. 0. 0. 0. 0. 0. 0. 0.
.0000
.1443
.2350
.3452
.4111
.4556
.4879
.5125
.5401
.5607
9. 0. 0. 0. 0. 0. 0. 0. 0. 0,
0000 .1134 .1896 .2871 .3485 .3911 .4228 .4474 .4754 .4966
12. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0000 .0853 .1466 .2294 .2842 .3236 .3536 .3774 .4050 .4262
% non\uii f o rmi t y _ f a c t o r s
1.0000 ; rad ia tor
60
APPENDIX B
WIND TUNNEL DATA FILES
61
Table B. 1 Top Opening A Wind Tunnel File
Aiabient P r e s s u r e (kPa) : 9 8 . 1 1 Aiabient Temperature (C) : 2 5 . 3
Number o£ d a t a p t s : 6
Turmel Speed (km/h)
4 8 . 8 7 2 . 4 7 2 . 4 9 6 . 6 9 6 . 7
1 2 0 . 7
Fan#l Speed (rpm)
2393 2400
0 2400
0 0
Fan#2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flovrat^e ( k g / s )
1 . 0 8 6 1 . 2 2 6 0 . 6 7 7 1 . 3 9 5 0 . 9 6 6 1 . 2 S 3
Table B. 2 Top Opening B Wind Tunnel File
Ambient: Pressure (kPa) : 98.1 Ambient: Temperat^ure (C) : 25.9
Number of daca pt:s: 6
Ttxnnel Speed (km/h)
4 8 . 4 7 2 . 4 7 2 . 4 9 6 . 6 9 6 . 6
1 2 0 . 9
Fan$ l Speed (rpm)
2 3 9 3 2407
0 2407
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrat:e ( k g / s )
0 . 9 6 7 1 . 1 4 3 0 . 5 9 7 1 . 2 7 1 0 . 8 5 0 1 . 1 3 8
62
Table B. 3 Top Opening C Wind Tunnel File
Ambient: P r e s s u r e (kPa) : 9 8 . 1 Ambient: Temperature (C) : 2 5 . 9
Number o f dat:a p t s : 6
Tunnel Speed (km/h)
4 8 . 4 7 2 . 4 7 2 . 4 9 6 . 6 9 6 . 6
1 2 0 . 9
Fan$l Speed (rpm)
2393 2407
0 2407
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
F l o w r a t e ( k g / s )
0 . 9 6 7 1 . 1 4 3 0 . 5 9 7 1 . 2 7 1 0 . 8 5 0 1 . 1 3 8
Table B. 4 Chin Opening A Wind Tunnel File
Ambient Pressure (kPa): 97.90 Ambient Temperature (C): 26.4
Number of data pts: 6
Tunnel Speed (km/h)
Fan$l Speed (rpm)
Fan$2 Speed (rpm)
Fan$3 Speed (rpm)
0 0 0 0 0 0
F lo t j ra te ( k g / s )
0 . 9 2 8 1 . 0 8 4 0 . 5 9 1 1 . 2 1 7 0 . 8 5 1 1 . 1 1 1
48.3 72.6 72.6 9S.6 96.6 120.7
2400 2400
0 2393
0 0
0 0 0 0 0 0
63
Table B. 5 Chin Opening B Wind Tunnel File
Ambient Pressure (kPa): 97.89 Ambient Temperature (C): 25.9
Number of data pts: 6
Tvtnnel Speed (km/h)
Fan#l Speed (rpm)
Fan#2 Speed (rpm)
Fan#3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
0.781 0.863 0.442 0.996 0.649 0.850
48. 72. 72. 96. 96.
120.
2407 2407
0 2393
0 0
0 0 0 0 0 0
Table B. 6 Bottom Opening A Wind Tunnel File
Ambient Pressure (kPa): 97.81 Ambient Temperature (C): 24.3
Number of data pts: 6
Tunnel Speed (km/h)
48.3 72.6 72.4 96.4 96.6
120.7
Fan#l Speed (rpm)
2400 2400
0 2407
0 0
Fan#2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
0.762 0.863 0.491 0.920 0.687 0.876
64
Table B. 7 Bottom Opening B Wind Tunnel File
Ambient Pressure (kPa): 97.81 Ambient Temperature (C): 24.4
Number of data pts: 3
Tunnel Fan#l Fan#2 Fan#3 Speed Speed Speed Speed Flowrate (km/h) (rpm) (rpm) (rpm) (kg/s)
72.6 0 0 0 0.426 96.6 0 0 0 0.570 120.7 0 0 0 0.721
Table B. 8 Top A and Chin B Combination Wind Tunnel File
Ambient Pressure (kPa): 97.79 Ambient Temperature (C): 24.2
Number of data pts: 6
Tunnel Speed (km/h)
48.3 72.6 72.4 96.7 96.6 120.7
Fan$l Speed (rpm)
2400 2400
0 2407
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan#3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
1.154 1.325 0.734 1.518 1.048 1.362
65
Table B. 9 Top B and Chin B Combination Wind Tunnel File
Ambient Pressure (kPa): 97.79 Ambient Temperature (C): 24.2
Number of data pts: 6
Tunnel Speed (km/h)
48.3 72.4 72.4 96.6 96.7
120.7
Fan$l Speed (rpm)
2400 2393
0 2407
0 0
Fan#2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
1.109 1.231 0.679 1.425 0.966 1.263
Table B. 10 Top C and Chin B Combination Wind Tunnel File
Ambient Pressure (kPa): 97.89 Ambient Temperature (C): 23.9
Number of data pts: 6
Ttxnnel Speed (km/h)
48.3 72.4 72.6 96.6 96.6 120.7
Fan#l Speed (rpm)
2407 2407
0 2407
0 0
Fan#2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
0.980 1.122 0.611 1.239 0.852 1.105
66
Table B. 11 Top B and Chin A Combination Wind Tunnel File
Ambient P r e s s u r e (kPa ) : 98 .03 Ambient Tempera ture (C): 2 4 . 3
Nuiober of d a t a p t s : 6
Tvmnel Speed (km/h)
48.4 72.6 72.4 96.7 96.6
120.7
Fan#l Speed (rpm)
2407 2400
0 2393
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
1.158 1.305 0.719 1.488 1.021 1.329
Table B. 12 Chin A and Bottom B Combination Wind Tunnel File
Ambient Pressure (kPa): 98.00 Ambient Temperature (C): 24.3
Number of data pts: 6
Tvinnel Speed (km/h)
48.3 72.6 72.6 96.6 96.6
120.5
Fan$l Speed (rpm)
2400 2400
0 2400
0 0
Fan#2 Speed (rpm)
0 0 0 0 0 0
Fan#3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
1.011 1.152 0.640 1.315 0.897 1.162
67
Table B. 13 Chin B and Bottom B Combination Wind Tunnel File
Ambient Pressure (kPa): 98.04 Ambient Temperature (C) : 24.4
Number of data pts: 6
Tunnel Speed (km/h)
48.4 72.6 72.6 96.6 96.6
120.5
Fan#l Speed (rpm)
2407 2407
0 2393
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan#3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
0.920 1.025 0.548 1.174 0.766 0.991
Table B. 14 Chin B and Bottom A Combination Wind Tunnel File
Ambient Pressure (kPa): 98.04 Ambient Temperature (C) : 24.4
Number of data pts: 6
Tunnel Speed (km/h)
48.4 72.6 72.6 96.6 96.6 120.5
Fan#l Speed (rpm)
2407 2407
0 2393
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
0.920 1.025 0.548 1.174 0.766 0.991
68
Table B. 15 Top A and Bottom B Combination Wind Tunnel File
Ambient P r e s s u r e ( k P a ) : 9 7 . 9 3 Ambient Temperature (C): 2 4 . 0
Ntomber of d a t a p t s : 6
Ttinnel Speed (km/h)
4 8 . 3 7 3 . 2 7 2 . 4 9 6 . 6 9 6 . 6
1 2 0 . 7
Fan$l Speed (rpm)
2400 2393
0 2400
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan#3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
1.175 1.358 0.774 1.571 1.099 1.438
Table B. 16 Top B and Bottom B Combination Wind Tunnel File
Ambient Pressure (kPa): 97.96 Ambient Temperature (C): 24.2
Number of data pts: 6
Tunnel Speed (km/h)
48.3 72.4 72.4 96.6 96.7 120.7
Fan$l Speed (rpm)
2400 2400
0 2407
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
1.139 1.301 0.722 1.490 1.026 1.340
69
Table B. 17 Top C and Bottom B Combination Wind Tunnel File
Ambient Pressure (kPa): 97.97 Ambient Temperature (C): 24.4
Number of data pts: 7
Tunnel Speed (km/h)
48.3 72.6 72.4 96.7
120.9 120.7 96.7
Fan$l Speed (rpm)
2400 2400
0 2400
0 0 0
Fan|f2 Speed (rpm)
0 0 0 0 0 0 0
Fan#3 Speed (rpm)
0 0 0 0 0 0 0
Flowrate (kg/s)
0.936 1.122 0.632 1.301 1.169 1.162 0.887
Table B. 18 Top A, Chin C, and Bottom A Combination Wind Tunnel File
Ambient Pressure (kPa): 98.16 Ambient Temperature (C): 24.1
Number of data pts: 6
Tunnel Speed (km/h)
48.4 72.6 72.4 96.7 96.6 120.7
Fan$l Speed (rpm)
2407 2400
0 2400
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Speed (rpm)
0 0 0 0 0 0
Flowrat( (kg/s)
1.191 1.377 0.772 1.587 1.107 1.456
70
Table B. 19 Top C, Chin A, and Bottom A Combination Wind Tunnel File
Ambient P r e s s u r e (kPa) : 98 .14 Ambient Tempera ture (C): 24 .6
Nvunber of d a t a p t s : 6
Tunnel Speed (km/h)
48.4 72.6 72.4 96.6 96.7
120.7
Fan#l Speed (rpm)
2393 2393
0 2400
0 0
Fan$2 Speed (rpm)
0 0 0 0 0 0
Fan$3 Speed (rpm)
0 0 0 0 0 0
Flowrate (kg/s)
1.099 1.259 0.699 1.451 0.992 1.300
71
APPENDIX C
GRILLE FILES
72
Table C.I Top Opening A Grille File ** DN5_88 Grille File * Coefficients obtained from generalized correlation
?grille_data * (Grille Coefficients: * KO Ki
0.7714 -15.3491
I
Table C.2 Top Opening B Grille File
** DN5_94 Grille File '* Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7714 -27.0439
Table C.3 Top Opening C Grille File
** DN5_100 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7714 -85.4071
73
Table C.4 Chin Opening A Grille File
** DN5_124 Grille File '*' Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.6748 -22.4600
Table C.5 Chin Opening B Grille File
** DN5_130 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.6748 -57.0051
Table C.6 Bottom Opening A Grille File
** DN5_142 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7769 -58.3037
74
Table C.7 Bottom Opening B Grille File ** DN5_150 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients:
KO Ki 0.7769 -116.6803
Table C.8 Top A and Chin B Grille File
** DN5_160 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7317 -11.5697
Table C.9 Top B and Chin B Grille File
** DN5_166 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7252 -14.9347
75
Table CIO Top C and Chin B Grille File
** DN5_172 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7140 -22.8942
Table C.11 Top B and Chin A Grille File
** DN5_21S Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7071 -11.8226
Table C.12 Chin A and Bottom B Grille File
** DN5_197 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.6973 -15.5216
76
Table C.13 Chin B and Bottom B Grille File ** DNS_203 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7125 -25.2439
Table C.14 Chin B and Bottom A Grille File
** DN5_230 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7203 -20.1041
Table C.I5 Top A and Bottom B Grille File
** DN5_178 Grille File * Coefficients obtained from generalized correlation
?grille_data * Grille Coefficients: * KO Ki
0.7725 -12.4255
77
Table C.16 Top B and Bottom B Grille File
** DN5_184 Grille File * Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7730 -17.2065
Table C.17 Top C and Bottom B Grille File
** DN5_190 Grille File •*• Coefficients obtained from generalized correlation
$grille_data * Grille Coefficients: * KO Ki
0.7739 -30.4602
Table C.18 Top A, Chin C, and Bottom A Grille File
** DN5_242 Grille File * Coefficients obtained from generalized correlation
$grille_data * G r i l l e C o e f f i c i e n t s : * KO Ki
0 . 7 5 1 7 - 1 0 . 5 5 2 8
78
Table C.18 Top C, Chin A, and Bottom A Grille File
** DN5_248 G r i l l e F i l e * C o e f f i c i e n t s obta ined from genera l i zed c o r r e l a t i o n
$ g r i l l e _ d a t a * G r i l l e C o e f f i c i e n t s : * KO Ki
0 . 7 0 8 0 - 1 1 . 3 8 7 8
79
APPENDIX D
INDIVIDUAL GRILLE OPENING KRAM
SOLUTION MATLAB PROGRAM
80
clear; close all;
a = zeros(7,7); r = zeros(7,1);
top_calcs2; chin_calcs2; bottom_calcs2;
k = a\r; disp('unified correlation results'); disp(k);
tabularResults2; top_plot2; chin_plot2; bottom_plot2;
top calcs2:
atl =0.7917/3; at2 = 0.5 / 3; at3 = 0.25 / 3;
% Ai/ArVoA/r Kram top = [atl 3.985 -2.505;
atl 5.237 6.823; atl 9.485 58.189; atl 6.141 13.728; atl 8.878 48.445; atl 8.543 43.453; at2 4.430-10.770; at2 5.606 2.793; at2 10.733 62.715; at2 6.726 8.765; at2 10.058 51.197; at2 9.402 44.999; at3 6.226-53.215; at3 8.170-28.860; at3 14.318 73.320; at3 9.668-16.260; at3 13.744 61.296; at3 13.941 54.294];
81
ntop = size(top, 1); t = zeros(3, 3); tr = zeros(3, 1);
fori = 1:ntop t(1,1) = t(1.1) + top(i.2)M; t(1.2) = t(1.2)-(top(i.2)/top(i.1)r2; t(1,3) = t(1,3)-top(i.2r2; t(2,1) = t(2,1) + (top(i,2)/top(i,1)r2; t{2.2) = t(2.2)-(1/top(i.1))M; t(2,3) = t(2,3)-(1/top(i.1)r2; t(3,1) = t(3.1) + top(i.2r2; t(3,2) = t(3.2)-{1/top(i.1)r2; t(3,3) = -ntop;
tr(1,1) = tr(1.1) + top(i.2r2*top(i,3); tr(2.1) = tr(2,1) + (1/top(i,1)r2 * top(i,3); tr(3,1) = tr(3,1) + top(i.3);
end
tk = t\tr; disp('top opening individualized correlation results'); disp(tk);
a(1:2,1:2) = t(1:2,1:2); a(7,1:2) =t(3,1:2); a(1:2,7) =t(1:2,3); a(7,7) = a(7,7) + t(3.3); r(1:2) =tr(1:2); r(7) = r(7) + tr(3);
chin calcs2:
a d =0.72916667/3; ac2 = 0.40 / 3; %ac2 = 0.50 / 3; ac3 = 0.22917/3;
% Ai/Ar VoA/r Kram chin = [ad 4.589-14.481;
a d 5.905 0.029; a d 10.831 63.009; a d 6.999 6.887; a d 10.009 51.155;
82
a d 9.579 45.373; ac2 5.462-34.471; ac2 7.429-18.099; ac2 14.466 73.798; ac2 8.565 -5.415; ac2 13.145 59.617; ac2 12.540 51.153;
%ac3 16.076 77.517; %ac3 15.306 64.994;
%ac3 14.709 55.866 ];
nchin = size(chin, 1); c = zeros(3, 3); cr = zeros(3, 1);
for i = 1:nchin c(1.1) = c(1,1) + chin(i,2)M; c(1,2) = c(1,2) - (chin(i.2)/chin(i,1))'^2; c(1,3) = c(1,3)-chin(i.2)'^2; c(2,1) = c(2,1) + (chin(i,2)/chin(i,1))^2; c(2,2) = c(2.2)-(1/chin(i.1))M; c(2,3) = c(2,3)-(1/chin(i.1))^2; c(3,1) = c(3,1) + chin(i,2)'^2; c(3.2) = c(3.2)-(1/chin(i,1))'^2; c(3,3) = -nchin;
cr( l . l ) cr(2,1) cr(3.1)
cr(1,1) + chin(i,2)^2*chin(i,3); cr(2.1) + (1/chin(i,1))^2 * chin(i,3); cr(3,1) + chin(i,3);
end
ck = c\cr; disp('chin opening individualized correlation results'); disp(ck);
2); 3(3:4,3:4) = c(1:2.1 a(7,3:4) =c(3,1:2); a(3:4,7) =c(1:2,3); a(7.7) = a(7,7) + c(3,3); r(3:4) =cr(1:2); r(7) = r(7) + cr(3);
83
bottom calcs2:
abol = 0.7333333333 / 3; abo2 = 0.5 / 3; abo3 = 0.2333333333 / 3;
% Ai/Ar VoA/r Kram bottom = [abol 5.623 -37.844;
abol 7.463-18.319; abol 13.081 69.812; abol 9.296-12.731; abol 12.474 57.622; abol 12.224 50.506; %abo2 5.696-40.250; %abo2 8.016-26.601; abo2 15.114 75.212; %abo2 9.723-15.972; abo2 15.030 64.326; abo2 14.846 56.018; %abo3 5.736-41.020; %abo3 9.917-59.430; %abo3 31.242 112.349; %abo3 12.781 -53.633; %abo3 28.574 84.851; %abo3 28.382 79.591
];
nbottom = size(bottom, 1); bo = zeros(3, 3); bor = zeros(3,1);
fori = 1:nbottom bo(1,1) = bo(1,1) + bottom(i,2)M; bo(1,2) = bo(1,2) - (bottom(i,2)/bottom(i,1))'^2; bo(1,3) = bo(1,3) - bottom(i,2)'^2; bo(2.1) = bo(2,1) + (bottom(i,2)/bottom(i,1))'^2; bo(2,2) = bo(2.2) - (1/bottom(i.1))M; bo(2,3) = bo(2,3) - (1/bottom(i,1))'^2; bo(3,1) = bo(3,1) + bottom(i,2)'^2; bo(3,2) = bo(3,2) - (1/bottom(i,1))'^2; bo(3,3) = -nbottom;
bor(1,1) = bor(1,1) + bottom(i,2)'^2 * bottom(i,3); bor(2,1) = bor(2.1) + (1/bottom(i,1))'^2 * bottom(i,3); bor(3,1) = bor(3,1) + bottom(i,3);
84
end bok = bo\bor; disp('bottom opening individualized correlation results'); disp(bok);
a(5:6,5:6) = bo(1:2,1:2); a(7,5:6) =bo(3,1:2); a(5:6,7) =bo(1:2,3); a(7.7) = a(7.7) + bo(3.3); r(5:6) =bor(1:2); r(7) = r(7) + bor(3);
tabularResults2:
Ko = k(1); Ka = k(2); Kbay = k(7); top(:,4) = top(:,2).'^2*Ko - (1./top(:.1)).'^2*Ka - Kbay; disp (''); disp ('top comparison') disp (' Ai/Ar Vo/Vr Kr meas Kr corr') disp ([top(:.1) top(:,2) top(:,3) top(:,4)])
Ko = k(3); Ka = k(4); chin(:,4) = chin(:,2).'^2*Ko - (1./chin(:,1)).^2*Ka - Kbay; disp (•'); disp ('chin comparison') disp (• Ai/Ar Vo/Vr Kr meas Kr corr') disp ([chin(:,1) chin(:,2) chin(:,3) chin(:,4)])
Ko = k(5); Ka = k(6); bottom(:,4) = bottom(:,2).'^2*Ko - (1./bottom(:,1)).'^2*Ka - Kbay; disp (•'); disp ('bottom comparison') dispf Ai/Ar Vo/Vr Kr meas Krcorr') disp ([bottom(:,1) bottom(:,2) bottom(:,3) bottom(:,4)])
top plot2:
xmin = 0; xmax = 300;
85
xtic = [0:50:300]; ymin = -100; ymax = 200; ytic = [-100:50:200]; vrange = [0,300];
Ko = tk(1); Ka = tk(2); Kbay = tk(3); Kram(1,1) = -(1/at1)^2*Ka - Kbay: Kram(1,2) = 300*Ko - (1/at1)^2*Ka - Kbay; Kram(2,1) = -(1/at2)' 2*Ka - Kbay; Kram(2,2) = 300*Ko - (1/at2)' 2*Ka - Kbay; Kram(3,1) = -(1/at3)^2*Ka - Kbay; Kram(3,2) = 300*Ko - (1/at3)^2*Ka - Kbay;
Ko = k(1); Ka = k(2); Kbay = k(7); Kram(4,1) = -(1/at1)' 2*Ka - Kbay; Kram(4,2) = 300*Ko - (1/at1)' 2*Ka - Kbay: Kram(5,1) = -(1/at2)' 2*Ka - Kbay; Kram(5,2) = 300*Ko - (1/at2)' 2*Ka - Kbay; Kram(6.1) = -(1/at3)' 2*Ka - Kbay; Kram(6,2) = 300*Ko - (1/at3)' 2*Ka - Kbay;
hold on; plot(top(:,2).^2, top(:,3),' xk'); plot(vrange, Kram(1,1:2),'- k'); plot(vrange, Kram(2,1:2),'- k'); plot(vrange, Kram(3,1:2),'- k'); plot(vrange, Kram(4,1:2),'- k') plot(vrange, Kram(5,1:2),'- k') plot(vrange, Kram(6,1:2),'-- k') legend('experimentar, ...
'individualized corelation, Ai/Ar = 0.264', 'individualized correlation, Ai/Ar = 0.167', 'individualized con-elation, Ai/Ar = 0.083', 'unified correlation, Ai/Ar = 0.264',... 'unified correlation, Ai/Ar = 0.167',... 'unified correlation, Ai/Ar = 0.083', 4);
axis([xmin, xmax, ymin, ymax]); set (gca,'XTick', xtic); set (gca.'YTick', ytic);
86
grid on; xlabel('(VoA/r)'^2'); ylabel('Kram'); hold off;
chin plot2:
Ko = ck(1); Ka = ck(2); Kbay = ck(3); Kram(1,1) = -(1/ac1 )' 2*Ka - Kbay; Kram(1,2) = 300*Ko - (1/ac1 )' 2*Ka - Kbay; Kram(2,1) = -(1/ac2)'^2*Ka - Kbay; Kram(2,2) = 300*Ko - (1/ac2)' 2*Ka - Kbay; Kram(3,1) = -(1/ac3)'^2*Ka - Kbay; Kram(3,2) = 300*Ko - (1/ac3)' 2*Ka - Kbay;
Ko = k(3); Ka = k(4); Kbay = k(7); Kram(4,1) = -(1/ac1)'^2*Ka - Kbay; Kram(4,2) = 300*Ko - (1/ac1)'^2*Ka - Kbay; Kram(5,1) = -(1/ac2)'^2*Ka - Kbay; Kram(5,2) = 300*Ko - (1/ac2)'^2*Ka - Kbay; Kram(6,1) = -(1/ac3)'^2*Ka - Kbay; Kram(6,2) = 300*Ko - (1/ac3)'^2*Ka - Kbay;
figure(3); hold on; plot(chin(:,2).' 2, chin(:,3),'xk'); plot(vrange, Kram(1,1:2),'- k'); plot(vrange, Kram(2,1:2),'- k'); plot(vrange, Kram(3,1:2),'- k'); plot(vrange, Kram(4,1:2),'-- k'); plot(vrange, Kram(5,1:2),'-- k'); plot(vrange, Kram(6,1:2),'-- k'); legend('experimentar,...
•individualized correlation, Ai/Ar = 0.243',. •individualized correlation, Ai/Ar = 0.167',. 'individualized correlation, Ai/Ar = 0.076',. •unified correlation, Ai/Ar = 0.243',... "unified correlation, Ai/Ar = 0.167',...); 'unified correlation, Ai/Ar = 0.076', 4);
axis([xmin, xmax, ymin, ymax]);
87
set (gca,"XTick', xtic); set (gca,'YTick', ytic); grid on; xlabel('(VoA/r)'^2'); ylabel('Kram'); hold off;
bottom plot2:
Ko = bok(1); Ka = bok(2); Kbay = bok(3); Kram(1,1) = -(1/abo1 )' 2*Ka - Kbay; Kram(1,2) = 300*Ko - (1/abo1)' 2*Ka - Kbay; Kram(2,1) = -(1/abo2)'^2*Ka - Kbay; Kram(2,2) = 300*Ko - (1/abo2)^2*Ka - Kbay;
Ko = k(5); Ka = k(6); Kbay = k(7); Kram(4,1) = -(1/abo1)'^2*Ka - Kbay; Kram(4,2) = 300*Ko - (1/abo1)' 2*Ka - Kbay; Kram(5,1) = -(1/abo2)'^2*Ka - Kbay; Kram(5,2) = 300*Ko - (1/abo2)^2*Ka - Kbay:
figure(4); hold on; plot(bottom(:,2).' 2, bottom(:,3),' xk'); plot(vrange, Kram(1,1:2),'- k ); plot(vrange, Kram(2,1:2),'- k'); plot(vrange, Kram(4,1:2), •-- k ); plot(vrange, Kram(5,1:2),'-- k'); iegendCexperimentar, ...
'individualized correlation, Ai/Ar = 0.244',... 'individualized correlation, Ai/Ar = 0.167',... 'unified correlation, Ai/Ar = 0.244',... 'unified correlation, Ai/Ar = 0.167', 4);
axis([xmin, xmax, ymin, ymax]); set (gca.'XTick', xtic); set (gca.'YTick', ytic); grid on; xlabel('(VoA/r)'^2'); ylabel('Kram');
88
APPENDIX E
MULTIPLE GRILLE OPENING KRAM SOLUTION
MATLAB PROGRAM
89
% Ko Ka A d1 =[0.7714 0.5404 0.7917;
0.7769 3.0303 0.5]; d2 = [0.7714 0.5404 0.5;
0.7769 3.0303 0.5]; d3 = [0.7714 0.5404 0.25;
0.7769 3.0303 0.5];
% VoA/r Kram TaBb = [3.655 1.734;
4.793 12.450; 8.317 54.027; 5.467 19.294; 7.815 45.600; 7.463 41.079 ];
TbBb = [3.769 0.026; 4.946 10.037; 8.913 56.048; 5.762 16.694; 8.377 47.135; 8.006 42.251 ];
TcBb = [4.584-14.039; 5.748 1.526; 10.176 60.724; 6.602 9.957; 9.187 44.609; 9.227 44.656; 9.684 50.252 ];
%top A % bottom B
%top B % bottom B
%top C % bottom B
Kbay = 7.5895;
close all; Vo = [0:16]; hold on [Ko, Ki] = Kram(d1,Kbay); s i = sprintf('top A, bottom B: Ko plot(Vo.'^2, Ko*Vo.'^2 + K I , ' - k');
[Ko, Ki] = Kram(d2, Kbay); s2 = sprintf('top B, bottom B: Ko plot(Vo.'^2, Ko*Vo.'^2 + Ki,'-. k');
= %8.4f, Ki = %8.4f , Ko, Ki);
= %8.4f, Ki = %8.4f , Ko, Ki);
90
[Ko, Ki] = Kram(d3, Kbay); s3 = sprintf('top C, bottom B: Ko = %8.4f, Ki = %8.4f , Ko, Ki); plot(Vo.' 2, Ko*Vo.' 2 + Ki,'-. k');
plot(TaBb(:,1).'^2, TaBb(:,2),' xk'); plot(TbBb(:,1).' 2, TbBb(:.2),' +k'); plot(TcBb(:,1).' 2, TcBb(:,2),' *k');
grid on axis([0, 150,-50. 100]); xlabel('(VoA/r)' 2') ylabel('Kram') Iegend(s1, s2, s3, 3)
function [Ko, Ki] = Kram(d. Kbay) Ar = 3; N = size(d,1);
if N == 1 Ko = d(1.1); Ki = -((Ar/d(1.3))'^2*d(1.2) + Kbay); return
end
fori = 1:N c(i) = d(i.2)*(Ar/d(i,3))'^2; a(l,1)=1/N;
end
Vo = 0; isoln = 0; allPositive = 1; while Vo<11 & allPositive
J = zeros(N,N); iter = 1; del = 1; while (del>0.000001 & iter<20 & allPositive)
fori = 1:N-1 F(i.1) = -( c(l)*a(i)' 2 - c(i+1)*a(i+1)'^2 - Vo'^2*(d(i,1)-d(i+1,1))); J(i.i) = 2*a(i)*c(i); J(i.i+1) = -2*a(i+1)*c(i+1);
end F(N.1) = -(sum(a)-1 ); J(N,:) = J(N,:) + ones(1,N);
91
da = J\F; a = a + da; allPositive = 1; fori = 1:N
allPositive = allPositive & (a(i)>=0); end del = norm(da); iter = iter+1;
end if allPositive
isoln = isoln + 1; Kr(isoln) = Vo'^2*d(1,1) - d(1,2)*(a(1)*Ar/d(1,3))^2 - Kbay;
end Vo = Vo + 1;
end
Ko = (Kr(isoln)-Kr(1))/(isoln-1)'^2; Ki = Kr(1);
92
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