The Determination of the Reference DynamicPressure in Automotive Wind Tunnels

B. Nijhof, G. WickernAudi AG, Ingolstadt, Germany

ABSTRACT

Usually the reference dynamic pressure in wind tunnels is determined bymeasurements of pressure differences at upstream positions at the wind tunnelnozzle. For closed wall wind tunnels usually the so called nozzle method is used,where the volume flux is calculated from a pressure difference measured at thenozzle contour and a calibration factor determined in the empty test section. Foropen jet wind tunnels a choice is available between nozzle and plenum method. Forthe latter method, the second measuring position at the nozzle is replaced by ameasuring position in the plenum chamber. Again, an additional calibration factor isnecessary. A third possibility, which is typically used only in thermal wind tunnels, isthe measurement of a reference wind speed instead of a reference pressuredifference by a probe positioned in the nozzle exit.In this paper, the definitions and the differences between the different methods arediscussed in detail. Possible sources of errors, such as velocity-dependentcalibration factors, interference with boundary layer suction and empty test sectionvelocity distribution are discussed. Special focus will be laid on the investigation ofthe interference of model displacement (blockage) on measured dynamic pressure. Itwill be shown, that local effects of the pressure build up in front of the model usuallydo not affect the accuracy of the measured dynamic pressure.Nevertheless model blockage does affect the measured aerodynamic forces as wellas the pressure distributions. A short discussion of the sources of errors and ofpossible theoretical corrections to force coefficients and pressure distributions will begiven. In this case special focus will be laid on the influence of the distance betweenmodel and nozzle in an open jet wind tunnel. The measured effect on the pressuredistribution of a vehicle will be analysed and it will be shown, that, without additionalcorrections, neither nozzle nor plenum method deliver correct pressure distributions,if the blockage level is high.

INTRODUCTION

In the literature known to the authors the determination of the reference dynamicpressure is not treated in much detail. A possible reason is that the procedure todetermine the dynamic pressure is considered to be straight forward. In the standardbooks on subsonic wind tunnels by Barlow, Rae and Pope [1] and Pankhurst andHolder [2] the procedure is described primarily for closed wind tunnels. In the largelyreferenced book on vehicle aerodynamics by Hucho [3] an alternate procedure forthe determination of the dynamic pressure in an open jet wind tunnel is described,the so called plenum method. The method used in closed wall tunnels is callednozzle method. Hucho refers to an SAE paper by Knstner et al. [4], where thedefinitions and the differences between nozzle and plenum method are described indetail.An important additional feature of both methods is highlighted in the paper byKnstner et al.. In the determination of the dynamic pressure the zero level of thestatic pressure in the test section is also determined. This is especially true for thenozzle method, where all pressures are referenced to the pressure in the settlingchamber. Only for the plenum method the pressure in the plenum chamber aroundthe test section is by definition the zero level for the static pressure.In an ideal zero blockage wind tunnel both nozzle and plenum method will yield thesame results. Only in wind tunnels with significant blockage levels differences occur.Therefore the discussion of blockage effects is an inherent feature of investigationson the differences between nozzle and plenum method. The investigation iscomplicated by the fact, that the treatment of blockage effects in automotiveapplications is not completely settled (see Cooper [5], Lindener [6] and Wickern [7]).A blockage correction applicable to results obtained using either the nozzle orplenum method is offered by Mercker et al. [8]. An extension of the theory to includethe correction of measured pressure distributions seems possible, but has not yetbeen proposed. The difference in the correction for the dynamic pressure betweenthe two methods can also be calculated by the theoretical approach proposed byWickern [7]. In this paper predictions calculated using Merckers proposal and usingWickerns proposal will be compared to experimental results.A major conclusion in the paper by Knstner et al. [4] is, that based on experimentalresults, the pressure distribution in an open jet wind tunnel is only measured correctlywhen using the nozzle method. This finding has to be revisited in the light of thediscussion on the different contributions to the blockage effect in open jet tunnels.Mercker and Wiedemann [9] showed that there are at least four distinct parts in thetotal blockage effect. All four parts can contribute to a local change in the staticpressure. Therefore it is expected, that both methods do not yield the same resultunless a correction is applied. Whether one method has an advantage over the otherand under which circumstances, has to be verified.The effect of the pressure build-up in front of the model on the pressure taps used forthe measurement of the dynamic pressure in an open jet wind tunnel wasinvestigated by Kopp [10]. A significant influence dependent on model blockage andon the distance between model and nozzle exit was found. It was not discussed in[10], whether this is a general blockage effect or a local effect on single pressuretaps. In the second case, the measurement of the dynamic pressure would beinvalid. Therefore this question will be investigated in this paper using newexperimental data.

BASIC DEFINITIONS FOR NOZZLE AND PLENUM METHOD

Air speed determination in a wind tunnel test section is of great importance,especially since it is used to non-dimensionalise forces, moments and pressuresacting on the model in the test section. A method for measuring the air velocity in anempty test section would be to place a Pitot-static tube in the test section. Thedifference in total and static pressure would yield the dynamic pressure from whichthe velocity could be calculated:

-= ppq tot (1)

2

2 r= Uq (2)

However, with a model present in the test section this method cannot be used sincethe model induces changes into the air flow and therefore the local air velocity in thetest section.

A solution to this problem is to measure a pressure difference elsewhere in the tunnelthat would remain unaffected even with a model placed in the test section.Commonly, the static pressure difference between two different positions in the windtunnel with varying cross sectional areas is measured. This pressure differencewould be related to the dynamic pressure in the empty test section by a tunnel factork. The dynamic pressure in the test section could then be calculated from thepressure difference and the tunnel factor k, regardless whether a model is in the testsection or not.

( ) kppq -= 21 (3)

Ideally, the two positions in the tunnel where the static pressures are obtained shouldnot have any meshes or other obstructions in between them, which could causepressure losses.Secondly, it would be preferable if the pressure difference would be of the sameorder as the dynamic pressure.

Closed test sections

For closed test section wind tunnels the dynamic pressure is determined bymeasuring the static pressure difference between the settling chamber A (Figure 1)and a position near the nozzle end, i.e. somewhere between B and C. The staticpressure measured at A would be similar to the flows total pressure because of thelow flow velocity in the settling chamber. The static pressure at B or C wouldapproximately be the same as the static pressure of the flow in the test section.This method of determining the wind velocity in the test section is called the nozzlemethod.

( ) =- qkpp NNSC (4)

A CB

Velocity closeto the wall

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eter

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l/U

Figure 1: Velocity distribution in the nozzle

In Figure 1 the velocity profile is sketched and it can be seen that between B and Can overshoot occurs. If possible the pressure should be measured in a plane wherethe velocity is approximately equal to the velocity in the test section. This could beeither at B or C. However, since B is further away from the test object, the pressurethere is less prone to interference from the model. Therefore it would make moresense to measure the static pressure at B.For the nozzle method the tunnel factor kN strongly depends on the tap location. Thetunnel factor is often velocity dependent as well. This means that the static pressuredifference obtained between settling chamber and nozzle tap must be correlated tothe reference dynamic pressure over a range of different wind velocities to yield avelocity dependent tunnel factor curve. This is usually done by a least square fit of ahigher order polynomial.

Open jet test sections

In wind tunnels with an open test section the nozzle method can also be used butthere is another method available. Instead of measuring the static pressuredifference between the settling chamber and the nozzle exit, the static pressuredifference between the settling chamber and the plenum chamber could bemeasured. The static pressure in the settling chamber would be similar to the flowstotal pressure and the static pressure in the plenum chamber would be the same asthe static pressure of the flow in the test section.This method of determining the wind velocity in the test section is called the plenummethod.

( ) =- qkpp PPSC (5)

For the plenum method the tunnel factor depends mainly on the contraction ratio.Using the continuity equation

NSCSC AuAu = (6)

and the energy equation

+r=+r pupu SCSC

22

22 (7)

yields

-r=-

2

2 12SC

NSC A

Aupp (8)

Combining Eqn. (8) with Eqn. (5) shows the dependency of kP on the contractionratio of the nozzle:

2

1

1

-

=

SC

N

P

AA

k (9)

This theoretical tunnel factor is slightly modified by boundary layer effects in thenozzle. To obtain exact values it is recommended to determine the tunnel factorexperimentally by a similar approach as for the nozzle method.

Another method to determine the velocity in the wind tunnel is not through a pressuredifference between two different locations in the tunnel but to directly measure thevelocity at a certain point in the test section. This can be done with various types ofprobes like turning vane anemometers, Pitot-static tubes or hot wire anemometers.The chosen position in which they are placed can have a large effect on the velocity,especially when blockage is large.For closed test sections, placing the probe near the nozzle end will result in abehaviour similar to that of the nozzle method. The probe can also be placed nearthe model to obtain a different flow velocity behaviour. However, near the model thepressure gradient is usually large and a small change in the lateral position of themodel or the model size could cause large changes in wind velocity.For example, a probe in the roof of the test section near the model might produce thedesired velocity for a particular size of model. However, if a model of different sizewas introduced into the tunnel or large changes were made to the model, thepressure distribution might change resulting in a different velocity. It is clear howsusceptible to errors this method is.In an open test section, placing the probe near the jet boundary will result inbehaviour similar to the plenum method and placing the probe in the nozzle willcause the same effects as the nozzle method. A position could be found in the testsection so that the result would be something between the plenum and the nozzlemethod, but again the behaviour at this position would be very dependant on modelposition.

NOZZLE METHOD vs. PLENUM METHOD

Many discussions and papers have been written which of the two methods is thecorrect one. In fact, neither of them is more correct than the other, they both havetheir individual disadvantages.

As explained in the section above, both methods use a pressure difference todetermine the wind velocity. However, the nozzle method uses the pressuredifference between two points in the tunnel whereas the plenum method uses thepressure difference between a point in the tunnel and a point in the plenum chamber(i.e. outside the tunnel). This difference results in different flow characteristics thatare kept constant. In case of the nozzle method the volume flux or the average flowvelocity is kept constant. For the plenum method the flow velocity at the jet boundaryis kept constant. As long as the test section is empty, both methods should producethe same velocity in the test section, i.e. the air velocity at the jet boundary is equal tothe average flow velocity.

With a model in the test section, the two methods produce different results. Twothings occur when a model is inserted into the test section. Due to the blockage thevolume flux is decreased and the pressure is increased.The following example will be used to explain what occurs to the static pressure in aGttingen type wind tunnel when a model is inserted into the open test section. Inthis example the plenum chamber is connected to the atmosphere. Also thedifference between the nozzle and plenum methods will be explained. Bar graphs willbe used to show the static pressure at different positions in the tunnel.

The nozzle method

Figure 2 shows the static pressures at the settling chamber and the nozzle exit,which are used to determine the dynamic pressure using the nozzle method. Thegrey areas indicate the static pressures at these two locations for a certain windvelocity when the test section is empty. This pressure difference between these twopositions in the tunnel together with the tunnel factor is then used to obtain thereference dynamic pressure.

( ) =- qkpp NNSC 1,1, (10)

When a model is then inserted into the tunnel at constant fan speed the overallpressure in the wind tunnel rises as indicated by the white areas.The pressure in the settling chamber rises from psc,1 to psc,2 and the static pressure inat the nozzle exit rises from pN,1 to pN,2.However, due to the reduced volume flux the pressure difference is now smaller thanwhen the test section was empty (the static pressure in the settling chamber hasrisen less than the static pressure at the nozzle exit as indicated by the smaller whitearea).

1,1,2,2, NSCNSC pppp -

PN,1

PSC,1

PN,2

PSC,2

PN,3

PSC,3

Settling Nozzle

Figure 2: Static pressure in the settling chamber and nozzle exit

This smaller pressure difference results in a smaller dynamic pressure q,2.

( ) 1,2,2,2,

PSC,1

PP

PSC,2

Settling Plenum

Figure 3: Static pressure in the settling chamber and plenum chamber

to obtain the reference dynamic pressure.

( ) 1,1, =- qkpp PPSC (15)

When a model is then inserted into the tunnel at constant fan speed the overallpressure in the wind tunnel rises as indicated by the white area. In the plenumchamber this rise in pressure is not noticed because the static pressure is alwaysequal to the atmospheric pressure if it is connected to the atmosphere.

The pressure difference has therefore increased resulting in a larger dynamicpressure.

( ) 1,2,1,2, >=- qqkpp PPSC (16)

To obtain the same dynamic pressure as in the empty test section the static pressurein the settling chamber has to be decreased to equal the static pressure when thetunnel was empty. The pressure decrease can be obtained by decreasing the windvelocity in the wind tunnel.

Even though in the above example the plenum is connected to the atmosphere, thisdoes not necessarily need to be so for the plenum method to be correct. Windtunnels exist where there is no connection to the atmosphere or the connection iselsewhere in the tunnel. The point is that when using the plenum method, thepressure difference between the plenum and the settling chamber is kept constant,no matter what the absolute values of the pressure at these two positions.

What happens to the flow at the nozzle exit? When the test section is empty the flowvelocity equals U and the velocity profile is relatively straight (Figure 4). When a

model is inserted into the test section the flow velocity in front of the model isdecreased. This is shown in the Figure 4 as a curved velocity profile.

plenum methodnozzle methodempty test section

nozzle

nozzleexit plane

U

Figure 4: Velocity profile at nozzle exit seen from above

The nozzle method keeps the average flow velocity constant leading to a flowvelocity that is less than U in front of the vehicle but greater than U at the jetboundary.This is not the case for the plenum method where the flow velocity at the jetboundary is kept constant, i.e. U. The average flow velocity in this case is less thanU.

Using the plenum method instead of the nozzle method results in a lower truevelocity in the test section. This in turn results in lower forces and higher pressuresmeasured on the model from which follows that force coefficients measured using theplenum method will have lower values and pressure coefficients will have highervalues than those measured using the nozzle method.

REFERENCE STATIC PRESSURE

To determine the pressure coefficient not only the dynamic pressure q in the testsection but also the static pressure of the undisturbed flow p in the test section isrequired.

-=q

ppcp (17)

Again a Pitot-static tube could be used to obtain the static pressure in the empty testsection but when a model is inserted into the test section the measured staticpressure would be incorrect due to the changes in the flow induced by the model. Areference pressure is required that is related to the static pressure in the undisturbedflow.

The nozzle method

The first possibility is to measure the total pressure in front of the model, subtract thereference dynamic pressure obtained from either the plenum or nozzle method andthe result is the reference static pressure in the test section. However, this is notalways practical, especially if the model is not equipped with a total pressure probe.

The total pressure can equally well be determined upstream of the model in thesettling chamber. This is possible since the nozzle accelerates the flow ideallywithout any friction losses. The measurement of the total pressure in the settlingchamber is usually replaced by a measurement of the static pressure in the settlingchamber. The measurement instrumentation is much easier in this case and errorsdue to local flows in the settling chamber can be avoided. This method is typicallyused in closed test section wind tunnels. The static pressure in the settling chamberis used as the reference pressure. However, this static pressure is not exactly thesame as the total pressure. Consequently an offset is required which can becalculated using the dynamic pressure in the test section. The dynamic pressures inthe settling chamber and in the test section are related through the contraction of thenozzle. The static pressure in the empty test section can be determined using thestatic pressure in the settling chamber.

1+-

=-

=

qpp

qpp

c totp (18)

-+

-=+

+-=

qqq

qpp

qq

q)qp(p SCSCSCSC

-+

-=

qpp

qpp SCSC (19)

Substituting (5) into the last term, where pP equals p8 , results in

P

SCp kq

ppc

1+

-=

(20)

At first sight it is confusing, that the tunnel factor for the plenum method now occursin the determination of the reference pressure level for the nozzle method. But kP isjust a quantity relating dynamic and static pressures in a duct with changing crosssection.In closed wall wind tunnels q has to be corrected for blockage effects of the model.By using this correction the zero level for the static pressure in the test section canbe significantly lowered. Thus the zero level depends on the type and quality of theblockage correction used.

The plenum method

The second possibility is to use the pressure in the plenum chamber as the referencepressure. Ideally this pressure is the same as the static pressure in the undisturbed

low. The plenum pressure is usually also the same as the atmospheric pressuresince often the plenum chamber is connected to the air outside the building.

atmPref ppp == , (21)

To avoid errors when calculating pressure coefficients the respective reference staticpressures should be used with either the nozzle or plenum methods.This is not critical when using the plenum method. Regardless of blockage the flowvelocity at the jet boundary remains constant. This is also true for the flows staticpressure, which equals the static pressure in the plenum chamber. The flow velocityobtained when using the plenum method is related to the static pressure in theplenum.This is not the case for the nozzle method. With increasing blockage the flows staticpressure increases. This is indicated by Figure 2 where it can be seen that the staticpressure at the nozzle exit increases from PN,1 to PN,3 when a model is inserted intothe test section. The plenum chamber pressure cannot be used as the referencestatic pressure because it remains the same regardless of blockage. The referencestatic pressure given would be too low. However, the pressure in the settlingchamber does notice any rise in pressure and would therefore be suitable as areference static pressure. Figure 2 shows that when inserting a model in the testsection the pressure in the settling chamber rises accordingly from PSC,1 to PSC,3. Thestatic pressure in the settling chamber is related to the flow velocity obtained whenusing the nozzle method. Therefore, when using the nozzle method to determinewind velocity, the reference static pressure must be obtained using the staticpressure in the settling chamber.

When probes are used that do not use pressure to determine wind speed, thereference static pressure must be obtained elsewhere. Either the plenum or settlingchamber static pressure could be used. Whether one or the other should bepreferred will discussed in a later section at hand of experimental results for thepressure distribution of a vehicle.

POSSIBLE SOURCES FOR ERRORS IN THE DETERMINATION OF THEREFERENCE DYNAMIC AND STATIC PRESSURE

The determination of the two reference pressures is generally influenced by blockageeffects, which are of course dependent on the details of the individual tunnel design.In addition there are a number of possible errors not related to tunnel blockage. Inthe first section these errors will be treated and in a second section some results onthe influence of blockage will be discussed.

Non-blockage-related errors

The determination of q from measurements in the settling chamber and the nozzle isa comparably simple measurement task. Nonetheless a number of errors arepossible.To obtain proper basic data, of course the pressure taps in the walls of settlingchamber and nozzle should be manufactured properly and according to the commondesign rules (see for example Barlow, Rae and Pope [1]). Usually a large number of

pressure taps are connected to become independent from local flow disturbances.For practical reasons they are linked to a single pressure transducer. The tubingbetween the taps and the transducer should be properly sealed and checked byincreasing the pressure in the tubing and inspecting for leaks.The taps are usually located on a plane intersecting the settling chamber or nozzlenormal to the flow direction in order to have approximately the same pressure level ateach tap. In wind tunnels for aircraft, the taps can be distributed on all four tunnelsides. In tunnels used for ground vehicles, only the ceiling and the side walls shouldbe used. In this case the pressure build up in front of the model protrudes furtherforwards along the bottom. Pressure taps in the floor should not be used in this case.A potential error could occur when one of the pressure taps in the rings in the nozzleor settling chamber is blocked. If the nozzles height and width differ, then thepressure measured at the pressure taps on the ceiling and floor are not the same ason the walls. If the pressure tap is blocked before obtaining the tunnel factor this isusually not a problem because the nozzle and plenum methods are based onreproducing the pressure difference and multiplying it by the tunnel factor to obtainthe reference dynamic pressure. If one of the pressure taps is blocked after obtainingthe tunnel factor however, then the pressure in the ring is changed and a falsedynamic pressure would be reproduced.

Having measured the static pressures correctly, the remaining task is to determine acorrect calibration factor to calculate the dynamic pressure from this.

Velocity dependence of the tunnel factor

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0 1000 2000 3000 4000 5000 6000Pressure difference [Pa]

Dyn

amic

pre

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e [P

a]

Nozzle ring 1Nozzle ring 2Nozzle ring 3Plenum

Figure 5: Tunnel factors for nozzle rings 1 to 3 and plenum ring

A common problem to both the plenum and nozzle methods involves the tunnelfactor and the manner in which this factor is acquired. To determine this factor therelation between the dynamic pressure in the empty test section and the staticpressure difference must be compared over a range of different wind speeds (Figure5).The result is a set of points through which a curve can be drawn. Although the curveat a first look appears to be a straight line, there are some effects of boundary layergrowth. The effects become obvious, if the tunnel factor versus the tunnel speed isplotted (see Figure 6). To obtain the required accuracy a polynomial fit of the curve isnecessary.

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50 100 150 200 250 300Velocity [km/h]

q/D

elta

P

Nozzle polynomial

Nozzle exp. data points

Plenum polynomial

Plenum exp. data points

Figure 6: Tunnel factors for nozzle and plenum methods

Influence of boundary layer control on the tunnel factor

If boundary layer control by suction or blowing is used, this usually affects the tunnelcalibration. Especially when using the nozzle method this can result in significanterrors. The nozzle method tries to keep the volume flux constant. If the volume flux ismodified by additional in- or outlets close to the nozzle exit, this is no longer the case.Therefore an independent calibration is necessary for the cases with and withoutboundary layer control. For every modification on the boundary layer control systema new calibration is necessary.In Figure 7 the calibration data from the Audi aeroacoustic wind tunnel is shown. Inthe case with boundary layer suction for every wind speed the appropriate suctionrate was applied. It can be seen, that by the boundary layer suction, the tunnel factoris reduced. This corresponds to the reduced volume flux in the test section.

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elta

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No BLS polynomial

No BLS exp. data points

BLS polynomial

BLS exp. data points

Figure 7: Tunnel factors with and without boundary layer suction

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Model exp. data points

Figure 8: Influence of calibration position on tunnel factor

Influence of the calibration position on the tunnel factor

In case of a closed test section the position of the Pitot-static tube in the empty testsection is important when determining the tunnel factor. Boundary layer growth alongthe walls of the test section cause a reduction in the effective cross section of the testsection resulting in an acceleration of air velocity from the nozzle towards thecollector. Thus the Pitot-static tube is sensitive to its position in the test section.Theeffect of the calibration position is much less important in open jet wind tunnels.Nevertheless some minor effects of the position in the jet are possible. In the Audiaeroacoustic wind tunnel there is a second model position for the testing of scalemodels. This model position is significantly closer to the nozzle and to the boundarylayer control. Therefore an independent calibration was carried out. The results(given in Figure 8) show some minor differences for smaller velocities and for veryhigh velocities). In the usual testing range for scale model from 100 km/h to 270 km/hpractical no difference exists.

Blockage-related errors

The blockage related errors can not be avoided by performing a carefulmeasurement, they can however be minimized by choosing a suitable wind tunneldesign. In certain cases a theoretical (or experimentally derived) blockage correctionis necessary in order to make reliable wind tunnel measurements without the need ofwind tunnels with extremely large dimensions. For example, closed wall wind tunnelspractically can not be operated without such a correction to the measured dynamicpressure. For open jet wind tunnels such blockage corrections are typically notapplied. One reason for this is that open jet tunnels are less sensitive to blockagethan closed wall tunnels. The other, more important reason is that open jet tunnelsare typically tuned to measure comparable data to other wind tunnels. This can bedone by suitable selection of nozzle and collector dimensions, test section length andposition of the model in the test section.In order not to revisit all the literature written on blockage in closed test sections, thispaper will concentrate on blockage effects in open jet tunnels. The focus will be onproblems, where it was unclear, whether it is a blockage problem or a problem ofproper measurement.

Nozzle blockage effect on determination of dynamic pressure

The first of these could be the influence of the model on the pressure ring or taps atthe nozzle exit. If the model is too close to the nozzle exit or to be more specific, thepressure taps, the pressure build up in front of the model could influence thepressure measured by these pressure taps. This is of course more of a problemwhen using the nozzle method. The plenum method uses only a pressure ring in thesettling chamber, which should not be influenced by any type of blockage.

If the model is large enough or near enough to the nozzle exit plane, the stagnationarea in front of the model will reach into the nozzle. This causes the flow at the wallsand the roof of the nozzle to accelerate. The larger this effect, the larger thedifference between the plenum and nozzle method.

Also, if this effect reaches into the plane where the pressure taps used for the nozzlemethod are, then the flow velocity past the pressure taps, which are typically only onthe walls and the ceiling of the tunnel, will also be higher, resulting in a lowerpressure measured at the taps. This in turn increases the measured pressuredifference. To keep the flow velocity in the test section constant, the pressuredifference must be reduced, resulting in a reduced true flow velocity in the testsection. The whole measurement would be invalid in this case, because aninfluenced pressure tap can not be corrected for. Therefore it is important todifferentiate between blockage effects and influenced pressure tap or pressure ring.To do this, an experiment was carried out in the Audi aeroacoustic wind tunnel. Inthis tunnel three different pressure rings at different distances from the nozzle exitare available for the nozzle method. Parallel to these, measurements with the plenummethod can be done. Two sets of test were done using a small sedan and a van(Figure 9). They were moved towards the nozzle to induce blockage effect. The windvelocity was determined using both the nozzle and plenum method. In case of thenozzle method, all three pressure rings were used simultaneously to measure thewind speed. The graph shows the ratio between the two methods against thedistance of the vehicle from the nozzle exit.First, it can be seen that qN/qP increases as the vehicles are moved towards thenozzle. This effect is larger with the van. This confirms that as blockage increases,the difference between the plenum and nozzle method increases due to the differentmethods in determining wind velocity.

Figure 9: Influence of model position on nozzle blockage

Secondly, it can be seen that the three pressure rings give the same result andcontinue to do so even when the vehicles distance to the nozzle decreases. In the

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2 2.5 3 3.5 4 4.5 5 5.5Distance to nozzle [m]

q N/q

P

sedan; ring 1sedan; ring 2sedan; ring 3van; ring 1van; ring 2van; ring 3

forward most position the vehicles were already entering the nozzle exit plane. Thisindicates that the vehicles do not influence the pressure rings. If local effects at thepressure rings would be important, the ring closest to the nozzle exit should beinfluenced first and the ring with the largest distance last. Since there is nodifference between the three rings, it can be concluded that all three rings are stillable to deliver a pressure difference proportional to the volume flux. The measureddifferences between qP and qN are entirely due to blockage effects at the nozzle.

For the correction of nozzle blockage two different theoretical models were proposedby Mercker et al. [8] and by Wickern [7]. The blockage models will not be discussedin detail here. Both models are able to predict the difference between nozzle andplenum method as a function of blockage ratio, geometry of the model and position ofthe model in the test section. The results of the predicted difference are compared tothe experimental results in Figure 10. Both methods describe the rising differencebetween the two approaches for decreasing distance to the nozzle reasonably well. Ageneral blockage correction therefore seems not completely hopeless.

Figure 10: Experimental and theoretical nozzle blockage

Reference Static Pressure

The reference static pressure is of primary importance for the measurement of thepressure distribution at the model. In closed wind tunnels the reference staticpressure is highly blockage dependent. The blockage corrected dynamic pressure issubtracted from the measured total pressure to obtain the reference static pressure.The only blockage independent pressure at the model is at the stagnation point,where the pressure is identical to the total pressure. Only with a valid blockage

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q N/q

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Exp. sedan

Exp. van

Wickern correction; sedan

Wickern correction; van

Mercker et al. correction; sedan

Mercker et al. correction; van

correction a blockage independent zero level is obtained. Thus only then a blockageindependent CP-distribution at the model can be measured. For the discussion ofblockage correction in closed wind tunnels the reader is again referred to thestandard books on the topic [1,2, 5].In open jet wind tunnels a similar strong influence of blockage is to be expected. Ifthe nozzle method is used, the only blockage independent pressure is again in thestagnation point. If the plenum method is used, the reference static pressure doesnot depend on model blockage, since the plenum pressure is used. Nevertheless thisdoes not mean that there is no blockage effect for the pressures measured at themodel surface. As discussed by Mercker and Wiedemann [9], the drag of a vehicle inan open jet wind tunnel is affected by at least four different contributions, namelynozzle blockage, jet blockage, collector blockage and horizontal buoyancy. All fourare to be expected to influence the pressure distribution as well. This is of coursetrue for both methods available, nozzle and plenum method.In order to provide experimental basic data for a first judgement on possible blockageeffects, the pressure distribution of the calibration car (geometry see Fig. 11) wasmeasured in the Audi Aeroacoustic wind tunnel. To vary the influence of blockage,the car was moved longitudinally along the test section. In the most forward positionthe bumper of the car was in the nozzle exit plane, the rearmost position was at thestandard measurement position (middle of the turntable, see also Fig. 12).In Fig. 13 the results are plotted for the nozzle method and in Fig. 14 for the plenummethod. Pressure tap #1 is on the hood, tap #59 on the rear bumper and tap #60 to#64 on the front bumper. When the model is moved towards the nozzle, itincreasingly blocks the flow coming out of the nozzle. The nozzle method keeps theaverage flow constant causing the flow over the model to increase as the modelnears the nozzle. The plenum method on the other hand keeps the flow at the jetboundary constant. This results in a more constant flow over the model. This effectwas mentioned in the experiment above, i.e. the increasing qN/qP.

Figure 13 clearly shows that when using the nozzle method, moving the car closer tothe nozzle causes the Cp-values to drop. A linear tendency can be detected wherebythe difference becomes less at Cp-highs and the difference becomes exaggerated atCp-lows. The decrease in Cp-values is also greater at the centre of the model than atthe front or the rear. This is because of the larger increase in local velocity at thecentre of the car compared to the smaller increase in local velocity at the front or rearof the car.Two effects take place as the car is moved closer to the nozzle.Firstly, the true flow velocity over the car increases resulting in higher forces andlower pressures acting on the model. This results in higher force coefficients andlower pressure coefficients. This effect is explained in the section Nozzle method vs.Plenum method.However, when determining the pressure coefficient another variable is ofimportance, the reference static pressure. When using the nozzle method, thisreference static pressure is calculated from the static pressure in the settlingchamber (Eq. 20). When the car is moved towards the nozzle, blockage is increasedand so is the static pressure in the settling chamber, resulting in a higher referencestatic pressure. This is the second effect.

This means that when the car is moved towards the nozzle, the pressure coefficientis reduced due to lower measured pressures and an increased reference staticpressure.Figure 14 shows what happens to the Cp-values when the car is moved towards thenozzle in case the plenum method is used. Only when the car comes very near to thenozzle, is there a detectable change in the Cp-values. Instead of decreasing however,the Cp-values increase. An exponential tendency can be detected whereby again thedifference becomes less at Cp-highs and the difference becomes exaggerated at Cp-lows. As the car is moved towards the nozzle, the greatest change in Cp-valuesoccurs at the front of the car, contrary to when using the nozzle method. This isbecause the greatest change (decrease) in local flow velocity, when using theplenum method, happens at the front of the model whereas the flow at the centre ofthe car is kept relatively constant as the car is moved towards the nozzle.The plenum method causes a much smaller change in Cp-value because the flowvelocity over the model is kept more constant. Also the reference pressure used tocalculate the Cp-value remains the same, regardless of the position of the model inthe test section. This because the reference pressure is the static pressure in theplenum chamber and remains constant at all times. Therefore the only effect thatcauses the increase in Cp-values is the first effect which occurs in the opposite senseand not as strongly as with the nozzle method.

What can be concluded from the above is that the plenum method is less sensitive toplacement of the model in the test section.

In order to show the dependency of cp at certain positions in more detail, the resultsof Fig. 13 and 14 can be plotted in a different way. In Fig. 15 cp at the end of the trunklid (tap #53), which is essentially the base pressure, is plotted versus the vehicleposition relative to the nozzle. The plenum method results show only a weakdependency, whereas the nozzle method results show a stronger influence. For thenozzle method the effect has not completely decayed at the standard measuringposition of the Audi wind tunnel. A similar result is found for cp on the front hood,close to the position where cp crosses the zero level (tap #9, plotted in Fig. 16). Againthe plenum results are less affected by the distance to the nozzle, and the effectseems to have decayed completely at the standard position.

When using probes, such as hot wire anemometers or turning vane anemometers todetermine the wind velocity, the reference static pressure cannot be obtained bythese probes. The static reference pressure could be obtained from the settlingchamber or the plenum chamber. The latter would be the preferable option since thepressure in the plenum chamber remains constant and the Cp-values would be lesssensitive to placement of the model in the test section.

1

2 34 5 6

7 8 9 1 01 112 1 3

1415

1617

1 819

2 0

232 42 52 627 282 9 303 13 23 33 43 53 63 73 839

5 455

5 6

5 75859

606 16 26 36 4

21 22

4 041

4 243

4445

4 647

4 849

5051

5 253

Figure 11: Pressure tap distribution on the calibration car

Figure 12: Front- and rearmost vehicle position in the test section

Nozzle

Collector

-2 m

4 m

Nozzle Method

-2.0

-1.5

-1.0

-0.5

0.0

0.5

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63

Pressure tap

Cp

0.0 m-0.4 m-0.8 m-1.2 m-1.6 m-2.0 m

Figure 13: Pressure distribution along the surface of a car

Plenum Method

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63

Pressure tap

Cp

0.0 m-0.4 m-0.8 m-1.2 m-1.6 m-2.0 m

Figure 14: Pressure distribution along the surface of a car

-0.2

-0.15

-0.1

-0.05

0

0.05

-2.5 -2.0 -1.5 -1.0 -0.5 0.0

Distance from centre turn table [m]

Cp

Plenum methodNozzle method

Figure 15: Pressure at the boot lid of the car (tap # 53) as a function of thedistance to the nozzle (origin at centre of turn table, 4 m from nozzle exit)

-0.2

-0.15

-0.1

-0.05

0

0.05

-2.5 -2.0 -1.5 -1.0 -0.5 0.0Distance from centre turn table [m]

Cp

Plenum methodNozzle method

Figure 16: Pressure on the front hood of the car (tap # 9) as a function of thedistance to the nozzle (origin at centre of turn table, 4 m from nozzle exit)

The results discussed above allow of course only a judgement on the effect ofnozzle blockage. The influence of jet blockage, collector blockage andhorizontal buoyancy are also always present. Collector blockage andhorizontal buoyancy could be investigated by more rearward positions in thetest section, whereas jet blockage can be influenced by different model or testsection sizes. The effects of the three other contributions possibly biased thejudgement in Knstner et al. [4] towards the nozzle method. As can be seen inFig. 15, the base pressure is approximately linearly dependent on the distanceto the nozzle, at least for the range in question. If the base pressure isincreased due to other blockage effects, as expected from jet blockage andhorizontal buoyancy, the effect of nozzle blockage can be used to tune thebase pressure back to the correct level. A similar approach is used to tunesmall open jet tunnel drag coefficients to the correct level, as discussed inWickern and Lindener [11]. Therefore the better match between on road dataand large and small wind tunnel data partly was by coincidence.At this point a comment on road data seems necessary. For on road data thequestion of a proper reference static pressure is a question as unresolved asthe blockage problem. Any reference determined by a wind tunnel testcontains all the errors of the specific wind tunnel as discussed in the paper.Any attempt to position a probe outside the pressure field of the vehicle cannot achieve a level better then the usual wind tunnel simulation without usingadditional corrections (theoretical or experimentally derived). Even 10 mabove the vehicle the reference pressure is not free of the influence of thevehicle to the required accuracy. Already at this distance significant effects ofchanging ambient conditions are expected due to natural wind. On roadmeasurements of the correct base pressure is expected to be as difficult asthe on road measurement of the correct drag coefficient.The pressure distribution for on road measurements of course also containthe influence of the moving ground, which is typically only partially simulatedin a wind tunnel. This makes the comparison between wind tunnel and onroad results even more complicated.

CONCLUSIONS

The focus of the paper was to revisit the basic definitions for the differentreference pressures used in automotive wind tunnels. Basically, two differentways to define the dynamic pressure in the test section (and the adjacentstatic pressure) are available: the nozzle method, where all conditions arerelated to the situation in the settling chamber, and the plenum method, wherethe reference conditions are defined in the plenum chamber. In ideal zeroblockage situations both methods deliver identical results, but majordifferences emerge under high blockage conditions. Therefore sources oferror are qualified whether they are blockage related or not.A number of non-blockage related sources of error are discussed, such as thevelocity dependence of tunnel factors, the interaction with boundary layerconditioning systems and local empty tunnel velocity differences. Usuallythese errors can be ruled out by reasonable technical efforts. The oftendiscussed effect of the pressure build up in front of the model on localpressure taps is shown to be a general blockage effect, which does notdepend on the position of the pressure taps.

The second, blockage related class of errors is far less under control. At handof new experimental data it is shown, that both nozzle and plenum methoddefine reference conditions, which at high blockage need additional windtunnel corrections to make the results comparable to results in infinite flow.In contradiction to older investigations, the plenum method seems to be lessliable to nozzle blockage effects than the nozzle method. It is less sensitive tothe position of the vehicle relative to the nozzle and should therefore bepreferred for measurements of practical interest, as for example pressuredistributions at cooling air inlets or measurements of wind loads on vehicleparts.If it is intended to judge the validity of force measurements in a wind tunnel,cP-measurements are not well suited, independent of the method used. Themeasured cP-values are blockage dependent to a similar extend as themeasured forces are.Blockage corrections are not treated in the paper. Although considerable efforthas been spent in the past on working out correction schemes for automotiveapplications, this remains at least from the viewpoint of the authors anunresolved item, especially for open jet wind tunnels.

LITERATURE

1. BARLOW, J.B., RAE, W.H. and POPE, A.: Low-Speed Wind TunnelTesting, John Wiley & Sons, New York, (1999)

2. PANKHURST, R.C. and HOLDER, D. W.: Wind tunnel technique, Pitman,London (1965)

3. HUCHO, W.-H.: Aerodynamics of Road Vehicles, 4th Edition, SAE, Detroit,(1998)

4. KNSTNER, R., DEUTENBACH, K.-R. and VAGT, J.-D.: Measurement ofReference Dynamic Pressure in Open-Jet Automotive Wind Tunnels. SAETechnical Paper 920344, (1992)

5. COOPER, K.R. (ed.): Closed-test-section wind tunnel blockage correctionsfor road vehicles, SAE SP-1176, Warrendale, (1996)

6. LINDENER, N. (ed.): open jet-test-section wind tunnel blockagecorrections for road vehicles, SAE SP-1176, Warrendale, (1996)

7. WICKERN, G.: On the Application of Classical Wind Tunnel Correctionsfor Automotive Bodies, SAE Technical Paper 2001-01-0633, Detroit,(2000)

8. MERCKER, E., WICKERN, G. and WIEDEMANN, J.: Contemplation ofnozzle blockage in open jet wind tunnel in view of different qdetermination techniques, SAE Technical Paper 970136, Detroit, (1997)

9. MERCKER, E. and WIEDEMANN, J.: On the Correction of InterferenceEffects in Open Jet Wind Tunnel, SAE Technical Paper 960671, Detroit,(1996)

10. KOPP, S.: Experimentelle und theoretische Untersuchungen im Hinblickauf eine Blockierungskorrektur fr Automobilwindkanle mitFreistrahlmestrecke. Diplomarbeit am Lehrstuhl fr Fluidmechanik(Experimental and Theoretical Investigations with Respect to a BlockageCorrection for Automotive Wind Tunnels with Open Jet Test Section)), TUMnchen, (1997)

11. Wickern, G. and Lindener, N.: The Audi Aeroacoustic Wind Tunnel: FinalDesign and First Operational Experience, SAE 2000-01-0868, (2000)

NOMENCLATURE

AN nozzle exit cross sectionASC settling chamber cross sectionCP pressure coefficientk tunnel factorkN tunnel factor when using the nozzle methodkP tunnel factor when using the plenum methodp pressurepatm atmospheric pressurepN static pressure at the nozzle exitpP static pressure in the plenum chamberpSC static pressure in the settling chamberptot total pressurep undisturbed static pressureq undisturbed dynamic pressureuSC wind velocity in the settling chamberU undisturbed wind velocityr air density