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Determination of dynamic pressure and reference pressure in automobile wind tunnels with open test section
Journal of Wind Engineering and Industrial Aerodynamics, 38 ( 1991 ) 11-22
11
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
Determination of dynamic pressure and reference pressure in automobile wind tunnels with open test section P. Mfillenbach and K.-R. Deutenbach Bayerische Motoren Werke AG, Peteulring 130, W-8000 M~nchen 40, German)'
Summary The various procedures for determining dynamic and reference pressure are described and compared. It is shown that the dynamic pressure can be determined accurately from the nozzle pressure difference only, and that a fluid-dynamic equivalent pressure must be used for the reference pressure.
1. Introduction
In automobile wind tunnels with an open test section, there are two methods of determining the reference dynamic pressure q. Depending on the specific drag cDA and the blockage Avehicle/ANozzle, these two procedures can result in different aerodynamic force coefficients. To determine the aerodynamic pressure coefficient %, both the dynamic pressure and the reference pressure must be accurately determined. If the reference pressure does not correspond to the static pressure of the undisturbed flow, the pressure distribution measured at the vehicle is incorrect. The plenum pressure is often used as the reference pressure. However, if there is already a slight difference between the stream static pressure and the plenum pressure for the empty tunnel, and if this difference is increased by operating the tunnel with a vehicle, a fluid-dynamic equivalent pressure must be used as reference pressure. This paper describes and compares the various procedures for determining dynamic and reference pressures. Experiments were carried out in a 10 m 2 tunnel and in a 20 m 2 tunnel. Results show that the dynamic pressure can be accurately determined from the nozzle pressure difference APNozzle only and that in both tunnels a fluid-dynamic equivalent pressure must be used for the reference pressure. If the experiments are evaluated under these conditions, the measured pressure distributions are in good agreement with the reference
0167-6105/91/$03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
12
tunnels described in ref. 1, which use an identical or similar procedure, and to road values. 2. Theoretical consideration o f n o z z l e flow
In order to clarify the problem of the dynamic pressure, a no-loss, two-dimensional nozzle flow will be considered. We denote the inlet plane into the nozzle from the settling chamber with the subscript SC and the nozzle outlet plane with the subscript NO and use the continuity and Bernoulli equations to derive the following relation between nozzle pressure difference APNozzle ----Psc --PNo and the nozzle outlet velocity WNO:
i WNO=
. ~PNozzle -/71/2 (p/2) ( 1 - - A ~ o / A ~ c ) ] =WNoAPN,,zz~e/K
tl)
where ANO is the nozzle outlet cross-section and Asc is the settling chamber cross-section. Non-dimensionalizing the nozzle pressure difference with the dynamic pressure qNO based on WNO, see eqn. ( 1 ), yields PNozzle PSC --
qNO
qNO
PNO = 1
--A
qNO
2
2
No/A sc
2 2 Cp,Nozzle = Cp.SC -- Cp,NO ~- 1 -- A N o / A st;
(2a) (2b)
For a given nozzle: K
dCp,iozzl~ =p/2 -- constant
(3)
V = ANO WNO = ANO (ApNozzle/K) 1/2
(4)
Thus, the volume flow is clearly described by the nozzle pressure difference. 3. D e t e r m i n a t i o n o f d y n a m i c pressure
With the normal blockage ratios it is not possible to take a direct measurement of the dynamic pressure q required for wind-tunnel tests because the entire flow field in the test section can be altered by the vehicle. Therefore, all measuring procedures used up to now have been based on measuring the pressure difference derived from a calibration in the empty tunnel. At present, two procedures are used to determine dynamic pressures (see section 3.1 ), based on different reference pressure: Method 1
£JPRef= ZJPNozzle
Method 2
ApRef APPlenum ~-"
13 Depending on the specific drag of the vehicle CDA and the blockage ratio (either area blockage AVehicle/ANozzle o r volume blockage YVehicle/Vtest section), the two procedures can yield different aerodynamic coefficients. In order to determine which method must be used, extensive pressure and force measurements were taken in a 10 m 2 and a 20 m 2 tunnel. The results given here apply to the B M W reference vehicle, 730i, and were obtained in the 10 m ~ tunnel. Theoretically, the conclusions can be applied to all open wind tunnels although the quantitative results are not directly transferable because of differences in test section configurations. The considerations below assume that the reference pressure corresponds to the static pressure of the undisturbed flow. The physical correlations are described in detail in Section 4.
3.1. Definition of the various methods of measurement Figure 1 shows a schematic drawing of an open throat wind tunnel test section. For the two procedures the relevant dynamic pressures are given by: Method 1
ql
----ZlPNozzleKF1
ql = (Psc --PNo) K F I
Method 2
q2 =PP1. . . . KF2 q2 = P s c -Pvl . . . . KF2
where KF1 and KF2 are wind tunnel specific factors for methods 1 and 2 respectively.
3.2. Comparison of methods in empty tunnel The dynamic pressure q is assigned to a pressure difference by means of the factor KF. In an empty tunnel, the two methods yield the same dynamic pressure
0
PPlenum
* PSflow
PSsc pressure
in
settling
chamber
q ........ d y n a m i c PSflow
-- static
pressure
pressure
undisturbed PSNo pressure nozzle
Fig. 1. Definition of terms.
in
outlet
flow
of
14
q
=ql =q2
q
= (Psc -PNo)KF1 = (Psc -PRef)KF2
KF1 # KF2 For the empty tunnel, the requirements defined in Section 2 are fulfilled:
ANO(APsozzle/KF1)1/2____ANO(APpl. . . . /KF2 ) 1/2 and ~Cp,Nozzle ~ Z~Cp,Plenuin ~
constant
The pressure coefficients depend on the tunnel specific factor: z~Cp,Nozzle =
'~Cp,Pl . . . .
--
1/KF1 = constant
(5)
1 KF2
(6)
PNO --PP~f (Psc -PP~f) KF2 = constant
If both methods are compared for the empty tunnel, eqs. (5) and (6) fulfill the conditions of eqn. (2b). The pressure differences ACp,Nozzleand Acp,plenum are only a function of the given area ratio and must be constant in the empty tunnel (see Section 2 ). The second term of eqn. (6) may be influenced by the presence of the vehicle and A%,pl~nummay not be constant in those cases. Now, it must be determined whether the conditions that are inevitably fulfilled for both methods in the empty tunnel are also fulfilled during test operation with a vehicle.
3.3. Comparison of methods with vehicle In order to arrive at a correct interpretation of the following test results, it must be ensured that the vehicle pressure field does not distort the pressure distribution in the settling chamber (SC) and nozzle outlet (NO) planes of measurement. This was proven for both tunnels and is described in Section 4.5. Figure 2 shows the pressure distribution on the nozzle floor as a function of the vehicle position using the two dynamic pressure methods. In agreement with the discussion of Section 3.2, both methods lead to the same result.
3.3.1. Method 1 As the left-hand graph shows, the pressure coefficients in the nozzle outlet plane (NO) are not influenced by the vehicle and the velocity distribution in this plane of measurement is comparable with that of the empty tunnel, In accordance with the continuity and Bernoulli equations, the change in pressure and velocity of the two planes of measurement is a function o f the area
IO
' ~
th
I 0 PPlenum
+
X
...m--- O---ram.
1
9
SC - P l a n e -
METHOD
15
x
=0
NO
METHOD 2
1 L~
CP
cp
lo
= Pleat
- PRef~
CP Io
(PSC P m A * ' I F I ~ o8
o6
oB
\.
•
qi
\
~ A P~,OZlle
* |Pl
0.4
" ~, Pplenm
" sr~
04
02 730i 13oi l)oi
o
q2
"~ o6
~ ~ : ,,~ '~r~<~oc
x : o. x = I • x : ,1 •
" •
:
o2
cJ
,
.
u tI o
x-O
o~ 9
15
TAP P O S
I
9
15
TAP-POS
Fig. 2. Pressure Distribution on the nozzle floor of the 10 m e tunnel.
ratio only. Thus, the driving pressure difference ZI%,Nozz~eis constant and the mass flow of the nozzle outlet plane (NO) corresponds to that of the settling chamber plane (SC). This is verified by the test results, and the requirements derived in Section 2, eqns. (2b) and (4) are fulfilled. Therefore, the dynamic pressure determined according to Method 1 q] =pNo~zleKF1 is correctly determined in physical terms and is also suitable for test operation with a vehicle. If the vehicle is too close to the nozzle ( x = - 1 m) the velocity profile deformation in the nozzle outlet plane will not have faded fully. The static wall pressure distribution is affected and/l%,Nozzl~is no longer constant. In this case, the dynamic pressure would be incorrectly determined. 3.3.2. Method 2
The right-hand graph shows that, in contrast to Method 1, the vehicle always affects the flow in the nozzle outlet plane (NO). However, this effect has always faded by the time the settling chamber (SC) is reached. Nevertheless, the dynamic pressure determined usingpp] . . . . is incorrect because the selected reference system is always and inevitably a vehicle-independent constant-~ % , s c = l / K F 2 = c o n s t a n t - - w h i c h cannot express any physical correlation.
16 TABLE 1 Drag coefficients determined with dynamic pressures obtained according to Method 1 (cm and Method 2 (cm) Tunnel
A Vehicle/ A Nozzle
(m 2)
('DI
el,::
0.356 0.348
0.325 ().342
(%)
10 20
21 11
Though the driving pressure difference only depends on the area ratio, which remains constant (eqn. (2b)), the values of the "empty tunnel" calibration state are never reached. The mass flow derived from the static wall pressure distribution would be different for the settling chamber and nozzle outlet planes and would not correspond to the continuity equation. According to Method 2, the dynamic pressure qz = APplenum K F 2
is incorrectly determined in physical terms and is not suitable for test operation with a vehicle. The right-hand graph shows that the distortion of the dynamic pressure decreases with decreasing blockage and with increasing distance between nozzle and vehicle. This can also be seen from the drag measurements (Table 1). The values apply to the BMW reference vehicle 730i in its basic configuration. For future correlation measurements, it is best to determine the dynamic pressure in all wind tunnels using the most accurate method in physical terms (Method 1 ) with the nozzle pressure difference APNozzle-When checking blockage, this is the only way to ensure that no dynamic pressure errors: are unintentionally attributed to the "blockage effect". 4. R e f e r e n c e p r e s s u r e s
The calculation of pressure coefficients requires a reference pressure which corresponds to the static pressure of the undisturbed flow Plocal --PRef q
PLots1 -- Pnow
q
Since the open nozzle conditions can be applied to the automobile wind tunnel with open test section, the plenum pressure or atmospheric pressure can :be used as the reference pressure. The particular configuration depends on the test section type (see Section 4.1 ). However, it must be ensured that the conditions applying to the empty tunnel are also accurate for the test operation with a vehicle. If:the plenum pres-
17 atmospher±c pressure
Fig. 3. Schematic view of an open automobile wind tunnel with a plenum.
sure or atmospheric pressure do not correspond to the static pressure of the undisturbed flow, a fluid-dynamic equivalent pressure (see Section 4.3) must be used as the reference pressure. Such a system must be used, for example, in the following cases. When the blockage ratios are high, the outermost stream-lines of the air flow are no longer straight, but describe curves. The static pressure changes laterally with relation to the direction of flow due to centrifugal force (see Section 4.2). When, in the empty tunnel, a difference in pressure exists between the flow static pressure and the plenum pressure. The plenum pressure is reduced by the back flow between the stream periphery and the plenum walls. The difference depends, among other things, on the ratio Apl. . . . /ANo=,o.
4.1. Test section types There are generally two possible arrangements, if the test section is surrounded by a plenum. Figure 3 shows a schematic view of a wind tunnel with open test section. Type A. The open test section is surrounded by the plenum and linked to the atmosphere. The atmospheric pressure affects the static pressure of the flow. Thus, Pnow=PP, . . . .
~---
atmospheric pressure
Type B. The open test section is surrounded by the plenum, but not linked to the atmosphere. The flow static pressure affects the plenum pressure and does not correspond to atmospheric pressure. Thus Pnow =PP1
.....
~ atmospheric pressure
4.2. Flow field Depending on the blockage ratio AVehicle/ANozzle , the main flow influenced by the vehicle is shown in Figs. 4 and 5.
18
~
'
-~-
i
Fig. 4. Principle air flowfor an assumed low blockageratio.
----.l
I
Fig. 5. Principle air flowfor an assumed high blockageratio. W h e n blockage ratios are low (Fig. 4), the outermost stream-line of flow is straight; when blockage ratios are high (Fig. 5), it describes a curve. The curved stream-line requires a pressure gradient perpendicular to the flow direction to equilibrate the centrifugal force: dp
w2
(7)
dr - p r The plenum or atmospheric pressure is balanced by the pressure exerted on the outermost stream-lines. W h e n blockage ratios are high the plenum pressure cannot be used as the reference pressure. The static pressure of t h e undisturbed flow is lower t h a n the plenum pressure owing to the pressure gradient perpendicular to the direction of flow. The cp values determined with the plenum pressure would be too high. W h e n the stream-lines are straight, r = oe and the lateral pressure gradient dp/dr= O.The local pressure of the outermost stream-line is identical with t h a t of the undisturbed flow. The plenum pressure can be used as t h e reference pressure.
4.3. Equivalent system A fluid-dynamic equivalent pressure must be used for the two reference tunnels with ANozzle -----10 m 2 and 20 m 2 for the following reasons. In both tunnels, differences between the flow static pressure and the plenum pressure are already present in the e m p t y tunnel. Owing to the relatively high blockage ratio of 21% in the 10 m 2 tunnel, the
19
outermost stream-lines are curved. According to Section 4.2, the plenum pressure must not be used as the reference pressure. Therefore, taking the plenum pressure as the reference pressure would result in incorrect cv values. Since, in test operation with a vehicle,pnow can no longer be determined directly, it must be related to a flow equivalent pressure--in this case the settling chamber pressure: Plocal - - P s c
% -
KP
ql
(8)
The pressure coefficient factor KP may be obtained in the empty tunnel. It is assumed that the reference dynamic pressure has been accurately determined in physical terms with qi=dpNozzleKF1 (see Section 3). The pressure coefficient factor calibrated in the empty tunnel is a constant in both tunnels.
4.4. Comparison of systems To be able to compare the two reference pressure systems, pressure distribution measurements were carried out in the empty tunnel and with vehicles of various sizes. The results shown here apply to the B M W reference vehicle 730i; they are proportionately transferable to other models. The reference pressure errors occurring in a 10 m 2 and 20 m 2 tunnel can be seen from the body surface pressure distributions shown in Figs. 6 and 7. The comparison is based on the road values measured in ref. 1. Figures 6 and 7 show that higher Cpvalues are measured when the reference pressure is incorrect in physical terms (see Section 4.3). The deviations in the 10 m 2 tunnel with Cp.total + 0.069 are almost constant; in the 20 m 2 tunnel, however, they vary :
04
CP 02
N
02
/:
\
-04
_
.
__
// i ~,"
~--~-,
-I,I
-08
= REF=
PLENUM
= REF=
KP-FACTOR~4
/ ~
301
304
309
315
323
'
-12
:,
i
(,(.
_
:~_
: {,o,
14
301
304
309
315
320
TAP-POS
107
Fig. 6. Reference pressure error in tunnel w i t h ANozzle ----20 m 2 blockage ratio -- 1 1 % .
20 04
CP
•
A/ -02
.
.
.
.
.
.
.,
_
~
/ -04
~
-o6
~
-o s ~ - ~ / = C~:
....
~"
. . . . . . . . . . . .
ROAD
L:~ = R E F = P L E N U M
-1
,/ /
;01
"1
304
309
. . . 3. 1 5. .
323
REF = KP--FACTOR
-12
-14
301
304
309
315
Fig. 7. Reference pressure error in tunnel with
ANozzle
320 =
TAP-PO$
107
10 m 2 blockage ratio --21%.
TABLE 2 Breakdown of
3cp.tota]
Tunnel ( m 2)
AVehiele/ANozzle
Apl. . . . /ANozzle
Cp.t,,tal
Opt
Cp2
10 20
21 11
10.5 2.7
4-0.069 4-0.015-4. 0.025
4.0.012 4.0.017
4-0.057 --0.002-4- 0.008
into %1 and %2
(%)
Cp,total, total difference from reference pressure error (based on physically correct reference pressure); %1 = (Pnow-PPi . . . . )/q, pressure deviation of the empty tunnel; %2-- cp,tot,~- %~, lateral pressure fraction.
between + 0.015 < Cp,tota | -~ "t"0.025. Because of the unfavourable cross-section ratio (Ap1. . . . /ANozzle = 2.7), the back flow in the plenum of the 20 m 2 tunnel is significantly higher than in the 10 m 2 tunnel with Apte..m/ANozzle-'-10.5. The energy exchange of the corresponding boundary flow and the inevitably nonstationary plenum pressure produces the relatively high scatter in the 20 m 2 tunnel. Table 2 shows the breakdown of each total difference Acp,tot~linto fractions of %1 and %2. The results of the systematic comparison test can be interpreted as follows, A fluid-dynamic equivalent system (with KP factor) should be used:t0 determine reference pressures. The pressure distributions are highly comparable with those of other tunnels which use an identical or similar procedure [ 1 ] and to road values.
21
The difference between the flow static pressure and the plenum pressure is approximately the same in the two tunnels. In the case of a blockage ratio of 21%, the proportion of lateral pressure for the pressure coefficient difference c,2 -- 0.057 is very high. Since, in the case of a blockage ratio of 11%, the outermost streamline is almost horizontal, the proportion of lateral pressure is relatively low. 4.5. Necessity of an equivalent system and vehicle influence on the wall pressure The following considerations assume that the dynamic pressure has been accurately determined in physical terms with q~=PNozz]eKF1. By measuring the pressure distribution in the nozzle, it is possible to determine whether a fluid-dynamic equivalent pressure is required to form the reference pressure for a particular tunnel. At the same time, the positions of the wall pressure planes can be checked for possible influence by vehicles. According to Section 2, the difference z~Cp,Nozzle = Cp,SC - - Cp,NOused to determine the dynamic pressure must always be constant. Therefore, the vehicle's effect must not deform the velocity profile in the planes of measurement as compared with the "empty tunnel" calibration beyond the allowable tolerances. In the case of an equivalent system, the velocity distribution is comparable when the static wall pressure distribution is unchanged. Figure 8 shows, as an example of measurements taken from both tunnels, the pressure distribution on the nozzle floor of the 10 m 2 tunnel as a function of reference pressure and vehicle position. A comparison of the two graphs
___o+_~x
1 SC - P l a n e -
9
15
x
=0
NO
1 ? CP ] 0
L:
CJ
.....I
0 q
0 0 0
2
-
1
x
-
9
15
TAP POS
-
T
Fig. 8. Pressure distribution on t h e nozzle floor of the 10 m 2 tunnel.
9
15
IAP-POS
22 demonstrates the effect of a reference pressure error. If the plenum pressure is selected as the reference pressure, the pressure distributions undergo a parallel shift as a function of the vehicle position. The closer the vehicle is to the nozzle, the greater the difference is to the empty tunnel as per Sections 4.2 and 4.3. If, however, the pressures are related to the fluid dynamic reference pressure designated as the K P factor, the curves are identical. Therefore, if there are parallel shifts in a tunnel as shown in the left-hand graph, an equivalent system must be used for the reference pressure. Up to vehicle position x = - 1 m, the driving pressure difference Ac~,,N~,z~o is identical with that of the empty tunnel for both cases. In the position closest to the nozzle, the deformation of the velocity profile in the nozzle-outlet wall pressure plane has not yet faded. Thus, the static wall pressure distribution is affected and dCp,Nozzledeviates from the " e m p t y tunnel" calibration state. This applies not only to the floor distribution, but also to the pressure distribution in the settling chamber and nozzle outlet planes of measurement. At this point, it is possible to check the position of the wall pressure planes for possible influence by the vehicle. 5. C o n c l u s i o n s
The results obtained with t h e B M W reference car show that the forces and pressure distribution measured in a wind tunnel depend on the selected method of determining the dynamic pressure and reference pressure. If a physically correct equivalent method is used the results are i n good agreement with the road values. The equivalent pressure measurement method should be based on the pressure difference ApNozzleand a reference pressure position which is in correlation with the static pressure of the undisturbed flow and independent from the vehicle in the test section. For future correlation measurements, it is best to determine the dynamic pressure in all wind tunnels using the same accurate method, which is the nozzle pressure difference. For checkingblockage, this is the only way to ensure that no dynamic pressure errors are unintentionally attributed to the "blockage effect".
Reference
P. Mfillenbachand K.-R. Deutenbach, Influence of boundary layer control systems on the flow field around passenger cars, 8th Colloq, on Industrial Aerodynamics. Aachen, September 4-7. 1989. J. Wind. Eng. Ind. Aerodyn., 38 (1991) 29-45.
11
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
Determination of dynamic pressure and reference pressure in automobile wind tunnels with open test section P. Mfillenbach and K.-R. Deutenbach Bayerische Motoren Werke AG, Peteulring 130, W-8000 M~nchen 40, German)'
Summary The various procedures for determining dynamic and reference pressure are described and compared. It is shown that the dynamic pressure can be determined accurately from the nozzle pressure difference only, and that a fluid-dynamic equivalent pressure must be used for the reference pressure.
1. Introduction
In automobile wind tunnels with an open test section, there are two methods of determining the reference dynamic pressure q. Depending on the specific drag cDA and the blockage Avehicle/ANozzle, these two procedures can result in different aerodynamic force coefficients. To determine the aerodynamic pressure coefficient %, both the dynamic pressure and the reference pressure must be accurately determined. If the reference pressure does not correspond to the static pressure of the undisturbed flow, the pressure distribution measured at the vehicle is incorrect. The plenum pressure is often used as the reference pressure. However, if there is already a slight difference between the stream static pressure and the plenum pressure for the empty tunnel, and if this difference is increased by operating the tunnel with a vehicle, a fluid-dynamic equivalent pressure must be used as reference pressure. This paper describes and compares the various procedures for determining dynamic and reference pressures. Experiments were carried out in a 10 m 2 tunnel and in a 20 m 2 tunnel. Results show that the dynamic pressure can be accurately determined from the nozzle pressure difference APNozzle only and that in both tunnels a fluid-dynamic equivalent pressure must be used for the reference pressure. If the experiments are evaluated under these conditions, the measured pressure distributions are in good agreement with the reference
0167-6105/91/$03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
12
tunnels described in ref. 1, which use an identical or similar procedure, and to road values. 2. Theoretical consideration o f n o z z l e flow
In order to clarify the problem of the dynamic pressure, a no-loss, two-dimensional nozzle flow will be considered. We denote the inlet plane into the nozzle from the settling chamber with the subscript SC and the nozzle outlet plane with the subscript NO and use the continuity and Bernoulli equations to derive the following relation between nozzle pressure difference APNozzle ----Psc --PNo and the nozzle outlet velocity WNO:
i WNO=
. ~PNozzle -/71/2 (p/2) ( 1 - - A ~ o / A ~ c ) ] =WNoAPN,,zz~e/K
tl)
where ANO is the nozzle outlet cross-section and Asc is the settling chamber cross-section. Non-dimensionalizing the nozzle pressure difference with the dynamic pressure qNO based on WNO, see eqn. ( 1 ), yields PNozzle PSC --
qNO
qNO
PNO = 1
--A
qNO
2
2
No/A sc
2 2 Cp,Nozzle = Cp.SC -- Cp,NO ~- 1 -- A N o / A st;
(2a) (2b)
For a given nozzle: K
dCp,iozzl~ =p/2 -- constant
(3)
V = ANO WNO = ANO (ApNozzle/K) 1/2
(4)
Thus, the volume flow is clearly described by the nozzle pressure difference. 3. D e t e r m i n a t i o n o f d y n a m i c pressure
With the normal blockage ratios it is not possible to take a direct measurement of the dynamic pressure q required for wind-tunnel tests because the entire flow field in the test section can be altered by the vehicle. Therefore, all measuring procedures used up to now have been based on measuring the pressure difference derived from a calibration in the empty tunnel. At present, two procedures are used to determine dynamic pressures (see section 3.1 ), based on different reference pressure: Method 1
£JPRef= ZJPNozzle
Method 2
ApRef APPlenum ~-"
13 Depending on the specific drag of the vehicle CDA and the blockage ratio (either area blockage AVehicle/ANozzle o r volume blockage YVehicle/Vtest section), the two procedures can yield different aerodynamic coefficients. In order to determine which method must be used, extensive pressure and force measurements were taken in a 10 m 2 and a 20 m 2 tunnel. The results given here apply to the B M W reference vehicle, 730i, and were obtained in the 10 m ~ tunnel. Theoretically, the conclusions can be applied to all open wind tunnels although the quantitative results are not directly transferable because of differences in test section configurations. The considerations below assume that the reference pressure corresponds to the static pressure of the undisturbed flow. The physical correlations are described in detail in Section 4.
3.1. Definition of the various methods of measurement Figure 1 shows a schematic drawing of an open throat wind tunnel test section. For the two procedures the relevant dynamic pressures are given by: Method 1
ql
----ZlPNozzleKF1
ql = (Psc --PNo) K F I
Method 2
q2 =PP1. . . . KF2 q2 = P s c -Pvl . . . . KF2
where KF1 and KF2 are wind tunnel specific factors for methods 1 and 2 respectively.
3.2. Comparison of methods in empty tunnel The dynamic pressure q is assigned to a pressure difference by means of the factor KF. In an empty tunnel, the two methods yield the same dynamic pressure
0
PPlenum
* PSflow
PSsc pressure
in
settling
chamber
q ........ d y n a m i c PSflow
-- static
pressure
pressure
undisturbed PSNo pressure nozzle
Fig. 1. Definition of terms.
in
outlet
flow
of
14
q
=ql =q2
q
= (Psc -PNo)KF1 = (Psc -PRef)KF2
KF1 # KF2 For the empty tunnel, the requirements defined in Section 2 are fulfilled:
ANO(APsozzle/KF1)1/2____ANO(APpl. . . . /KF2 ) 1/2 and ~Cp,Nozzle ~ Z~Cp,Plenuin ~
constant
The pressure coefficients depend on the tunnel specific factor: z~Cp,Nozzle =
'~Cp,Pl . . . .
--
1/KF1 = constant
(5)
1 KF2
(6)
PNO --PP~f (Psc -PP~f) KF2 = constant
If both methods are compared for the empty tunnel, eqs. (5) and (6) fulfill the conditions of eqn. (2b). The pressure differences ACp,Nozzleand Acp,plenum are only a function of the given area ratio and must be constant in the empty tunnel (see Section 2 ). The second term of eqn. (6) may be influenced by the presence of the vehicle and A%,pl~nummay not be constant in those cases. Now, it must be determined whether the conditions that are inevitably fulfilled for both methods in the empty tunnel are also fulfilled during test operation with a vehicle.
3.3. Comparison of methods with vehicle In order to arrive at a correct interpretation of the following test results, it must be ensured that the vehicle pressure field does not distort the pressure distribution in the settling chamber (SC) and nozzle outlet (NO) planes of measurement. This was proven for both tunnels and is described in Section 4.5. Figure 2 shows the pressure distribution on the nozzle floor as a function of the vehicle position using the two dynamic pressure methods. In agreement with the discussion of Section 3.2, both methods lead to the same result.
3.3.1. Method 1 As the left-hand graph shows, the pressure coefficients in the nozzle outlet plane (NO) are not influenced by the vehicle and the velocity distribution in this plane of measurement is comparable with that of the empty tunnel, In accordance with the continuity and Bernoulli equations, the change in pressure and velocity of the two planes of measurement is a function o f the area
IO
' ~
th
I 0 PPlenum
+
X
...m--- O---ram.
1
9
SC - P l a n e -
METHOD
15
x
=0
NO
METHOD 2
1 L~
CP
cp
lo
= Pleat
- PRef~
CP Io
(PSC P m A * ' I F I ~ o8
o6
oB
\.
•
qi
\
~ A P~,OZlle
* |Pl
0.4
" ~, Pplenm
" sr~
04
02 730i 13oi l)oi
o
q2
"~ o6
~ ~ : ,,~ '~r~<~oc
x : o. x = I • x : ,1 •
" •
:
o2
cJ
,
.
u tI o
x-O
o~ 9
15
TAP P O S
I
9
15
TAP-POS
Fig. 2. Pressure Distribution on the nozzle floor of the 10 m e tunnel.
ratio only. Thus, the driving pressure difference ZI%,Nozz~eis constant and the mass flow of the nozzle outlet plane (NO) corresponds to that of the settling chamber plane (SC). This is verified by the test results, and the requirements derived in Section 2, eqns. (2b) and (4) are fulfilled. Therefore, the dynamic pressure determined according to Method 1 q] =pNo~zleKF1 is correctly determined in physical terms and is also suitable for test operation with a vehicle. If the vehicle is too close to the nozzle ( x = - 1 m) the velocity profile deformation in the nozzle outlet plane will not have faded fully. The static wall pressure distribution is affected and/l%,Nozzl~is no longer constant. In this case, the dynamic pressure would be incorrectly determined. 3.3.2. Method 2
The right-hand graph shows that, in contrast to Method 1, the vehicle always affects the flow in the nozzle outlet plane (NO). However, this effect has always faded by the time the settling chamber (SC) is reached. Nevertheless, the dynamic pressure determined usingpp] . . . . is incorrect because the selected reference system is always and inevitably a vehicle-independent constant-~ % , s c = l / K F 2 = c o n s t a n t - - w h i c h cannot express any physical correlation.
16 TABLE 1 Drag coefficients determined with dynamic pressures obtained according to Method 1 (cm and Method 2 (cm) Tunnel
A Vehicle/ A Nozzle
(m 2)
('DI
el,::
0.356 0.348
0.325 ().342
(%)
10 20
21 11
Though the driving pressure difference only depends on the area ratio, which remains constant (eqn. (2b)), the values of the "empty tunnel" calibration state are never reached. The mass flow derived from the static wall pressure distribution would be different for the settling chamber and nozzle outlet planes and would not correspond to the continuity equation. According to Method 2, the dynamic pressure qz = APplenum K F 2
is incorrectly determined in physical terms and is not suitable for test operation with a vehicle. The right-hand graph shows that the distortion of the dynamic pressure decreases with decreasing blockage and with increasing distance between nozzle and vehicle. This can also be seen from the drag measurements (Table 1). The values apply to the BMW reference vehicle 730i in its basic configuration. For future correlation measurements, it is best to determine the dynamic pressure in all wind tunnels using the most accurate method in physical terms (Method 1 ) with the nozzle pressure difference APNozzle-When checking blockage, this is the only way to ensure that no dynamic pressure errors: are unintentionally attributed to the "blockage effect". 4. R e f e r e n c e p r e s s u r e s
The calculation of pressure coefficients requires a reference pressure which corresponds to the static pressure of the undisturbed flow Plocal --PRef q
PLots1 -- Pnow
q
Since the open nozzle conditions can be applied to the automobile wind tunnel with open test section, the plenum pressure or atmospheric pressure can :be used as the reference pressure. The particular configuration depends on the test section type (see Section 4.1 ). However, it must be ensured that the conditions applying to the empty tunnel are also accurate for the test operation with a vehicle. If:the plenum pres-
17 atmospher±c pressure
Fig. 3. Schematic view of an open automobile wind tunnel with a plenum.
sure or atmospheric pressure do not correspond to the static pressure of the undisturbed flow, a fluid-dynamic equivalent pressure (see Section 4.3) must be used as the reference pressure. Such a system must be used, for example, in the following cases. When the blockage ratios are high, the outermost stream-lines of the air flow are no longer straight, but describe curves. The static pressure changes laterally with relation to the direction of flow due to centrifugal force (see Section 4.2). When, in the empty tunnel, a difference in pressure exists between the flow static pressure and the plenum pressure. The plenum pressure is reduced by the back flow between the stream periphery and the plenum walls. The difference depends, among other things, on the ratio Apl. . . . /ANo=,o.
4.1. Test section types There are generally two possible arrangements, if the test section is surrounded by a plenum. Figure 3 shows a schematic view of a wind tunnel with open test section. Type A. The open test section is surrounded by the plenum and linked to the atmosphere. The atmospheric pressure affects the static pressure of the flow. Thus, Pnow=PP, . . . .
~---
atmospheric pressure
Type B. The open test section is surrounded by the plenum, but not linked to the atmosphere. The flow static pressure affects the plenum pressure and does not correspond to atmospheric pressure. Thus Pnow =PP1
.....
~ atmospheric pressure
4.2. Flow field Depending on the blockage ratio AVehicle/ANozzle , the main flow influenced by the vehicle is shown in Figs. 4 and 5.
18
~
'
-~-
i
Fig. 4. Principle air flowfor an assumed low blockageratio.
----.l
I
Fig. 5. Principle air flowfor an assumed high blockageratio. W h e n blockage ratios are low (Fig. 4), the outermost stream-line of flow is straight; when blockage ratios are high (Fig. 5), it describes a curve. The curved stream-line requires a pressure gradient perpendicular to the flow direction to equilibrate the centrifugal force: dp
w2
(7)
dr - p r The plenum or atmospheric pressure is balanced by the pressure exerted on the outermost stream-lines. W h e n blockage ratios are high the plenum pressure cannot be used as the reference pressure. The static pressure of t h e undisturbed flow is lower t h a n the plenum pressure owing to the pressure gradient perpendicular to the direction of flow. The cp values determined with the plenum pressure would be too high. W h e n the stream-lines are straight, r = oe and the lateral pressure gradient dp/dr= O.The local pressure of the outermost stream-line is identical with t h a t of the undisturbed flow. The plenum pressure can be used as t h e reference pressure.
4.3. Equivalent system A fluid-dynamic equivalent pressure must be used for the two reference tunnels with ANozzle -----10 m 2 and 20 m 2 for the following reasons. In both tunnels, differences between the flow static pressure and the plenum pressure are already present in the e m p t y tunnel. Owing to the relatively high blockage ratio of 21% in the 10 m 2 tunnel, the
19
outermost stream-lines are curved. According to Section 4.2, the plenum pressure must not be used as the reference pressure. Therefore, taking the plenum pressure as the reference pressure would result in incorrect cv values. Since, in test operation with a vehicle,pnow can no longer be determined directly, it must be related to a flow equivalent pressure--in this case the settling chamber pressure: Plocal - - P s c
% -
KP
ql
(8)
The pressure coefficient factor KP may be obtained in the empty tunnel. It is assumed that the reference dynamic pressure has been accurately determined in physical terms with qi=dpNozzleKF1 (see Section 3). The pressure coefficient factor calibrated in the empty tunnel is a constant in both tunnels.
4.4. Comparison of systems To be able to compare the two reference pressure systems, pressure distribution measurements were carried out in the empty tunnel and with vehicles of various sizes. The results shown here apply to the B M W reference vehicle 730i; they are proportionately transferable to other models. The reference pressure errors occurring in a 10 m 2 and 20 m 2 tunnel can be seen from the body surface pressure distributions shown in Figs. 6 and 7. The comparison is based on the road values measured in ref. 1. Figures 6 and 7 show that higher Cpvalues are measured when the reference pressure is incorrect in physical terms (see Section 4.3). The deviations in the 10 m 2 tunnel with Cp.total + 0.069 are almost constant; in the 20 m 2 tunnel, however, they vary :
04
CP 02
N
02
/:
\
-04
_
.
__
// i ~,"
~--~-,
-I,I
-08
= REF=
PLENUM
= REF=
KP-FACTOR~4
/ ~
301
304
309
315
323
'
-12
:,
i
(,(.
_
:~_
: {,o,
14
301
304
309
315
320
TAP-POS
107
Fig. 6. Reference pressure error in tunnel w i t h ANozzle ----20 m 2 blockage ratio -- 1 1 % .
20 04
CP
•
A/ -02
.
.
.
.
.
.
.,
_
~
/ -04
~
-o6
~
-o s ~ - ~ / = C~:
....
~"
. . . . . . . . . . . .
ROAD
L:~ = R E F = P L E N U M
-1
,/ /
;01
"1
304
309
. . . 3. 1 5. .
323
REF = KP--FACTOR
-12
-14
301
304
309
315
Fig. 7. Reference pressure error in tunnel with
ANozzle
320 =
TAP-PO$
107
10 m 2 blockage ratio --21%.
TABLE 2 Breakdown of
3cp.tota]
Tunnel ( m 2)
AVehiele/ANozzle
Apl. . . . /ANozzle
Cp.t,,tal
Opt
Cp2
10 20
21 11
10.5 2.7
4-0.069 4-0.015-4. 0.025
4.0.012 4.0.017
4-0.057 --0.002-4- 0.008
into %1 and %2
(%)
Cp,total, total difference from reference pressure error (based on physically correct reference pressure); %1 = (Pnow-PPi . . . . )/q, pressure deviation of the empty tunnel; %2-- cp,tot,~- %~, lateral pressure fraction.
between + 0.015 < Cp,tota | -~ "t"0.025. Because of the unfavourable cross-section ratio (Ap1. . . . /ANozzle = 2.7), the back flow in the plenum of the 20 m 2 tunnel is significantly higher than in the 10 m 2 tunnel with Apte..m/ANozzle-'-10.5. The energy exchange of the corresponding boundary flow and the inevitably nonstationary plenum pressure produces the relatively high scatter in the 20 m 2 tunnel. Table 2 shows the breakdown of each total difference Acp,tot~linto fractions of %1 and %2. The results of the systematic comparison test can be interpreted as follows, A fluid-dynamic equivalent system (with KP factor) should be used:t0 determine reference pressures. The pressure distributions are highly comparable with those of other tunnels which use an identical or similar procedure [ 1 ] and to road values.
21
The difference between the flow static pressure and the plenum pressure is approximately the same in the two tunnels. In the case of a blockage ratio of 21%, the proportion of lateral pressure for the pressure coefficient difference c,2 -- 0.057 is very high. Since, in the case of a blockage ratio of 11%, the outermost streamline is almost horizontal, the proportion of lateral pressure is relatively low. 4.5. Necessity of an equivalent system and vehicle influence on the wall pressure The following considerations assume that the dynamic pressure has been accurately determined in physical terms with q~=PNozz]eKF1. By measuring the pressure distribution in the nozzle, it is possible to determine whether a fluid-dynamic equivalent pressure is required to form the reference pressure for a particular tunnel. At the same time, the positions of the wall pressure planes can be checked for possible influence by vehicles. According to Section 2, the difference z~Cp,Nozzle = Cp,SC - - Cp,NOused to determine the dynamic pressure must always be constant. Therefore, the vehicle's effect must not deform the velocity profile in the planes of measurement as compared with the "empty tunnel" calibration beyond the allowable tolerances. In the case of an equivalent system, the velocity distribution is comparable when the static wall pressure distribution is unchanged. Figure 8 shows, as an example of measurements taken from both tunnels, the pressure distribution on the nozzle floor of the 10 m 2 tunnel as a function of reference pressure and vehicle position. A comparison of the two graphs
___o+_~x
1 SC - P l a n e -
9
15
x
=0
NO
1 ? CP ] 0
L:
CJ
.....I
0 q
0 0 0
2
-
1
x
-
9
15
TAP POS
-
T
Fig. 8. Pressure distribution on t h e nozzle floor of the 10 m 2 tunnel.
9
15
IAP-POS
22 demonstrates the effect of a reference pressure error. If the plenum pressure is selected as the reference pressure, the pressure distributions undergo a parallel shift as a function of the vehicle position. The closer the vehicle is to the nozzle, the greater the difference is to the empty tunnel as per Sections 4.2 and 4.3. If, however, the pressures are related to the fluid dynamic reference pressure designated as the K P factor, the curves are identical. Therefore, if there are parallel shifts in a tunnel as shown in the left-hand graph, an equivalent system must be used for the reference pressure. Up to vehicle position x = - 1 m, the driving pressure difference Ac~,,N~,z~o is identical with that of the empty tunnel for both cases. In the position closest to the nozzle, the deformation of the velocity profile in the nozzle-outlet wall pressure plane has not yet faded. Thus, the static wall pressure distribution is affected and dCp,Nozzledeviates from the " e m p t y tunnel" calibration state. This applies not only to the floor distribution, but also to the pressure distribution in the settling chamber and nozzle outlet planes of measurement. At this point, it is possible to check the position of the wall pressure planes for possible influence by the vehicle. 5. C o n c l u s i o n s
The results obtained with t h e B M W reference car show that the forces and pressure distribution measured in a wind tunnel depend on the selected method of determining the dynamic pressure and reference pressure. If a physically correct equivalent method is used the results are i n good agreement with the road values. The equivalent pressure measurement method should be based on the pressure difference ApNozzleand a reference pressure position which is in correlation with the static pressure of the undisturbed flow and independent from the vehicle in the test section. For future correlation measurements, it is best to determine the dynamic pressure in all wind tunnels using the same accurate method, which is the nozzle pressure difference. For checkingblockage, this is the only way to ensure that no dynamic pressure errors are unintentionally attributed to the "blockage effect".
Reference
P. Mfillenbachand K.-R. Deutenbach, Influence of boundary layer control systems on the flow field around passenger cars, 8th Colloq, on Industrial Aerodynamics. Aachen, September 4-7. 1989. J. Wind. Eng. Ind. Aerodyn., 38 (1991) 29-45.