J.fluids.engineering.1981.Vol.103.N1

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J . Cervantes de GortariProfessor,School of Engineering,National University of Mexico,Mexico, D.F., Mexico

V. W. GoldschmidtProfessor,School of Mech anical Engineering,Purdue U niversity,W. Lafayette, Ind.Mem.ASME

The A pparent F lapping M otion ofa Turbu lent P lane JetF urtherE xperimental ResultsMeasurements of four types of correlations in the self preserving region of a turbulent plane jet are presented. Negative correlations are noted between the twohalves of the jet, exhibiting an apparen t flapping like motion. That motion is notedto be self-preserving and most likely attributed to the presence of large scaleorganized structures.

IntroductionTurbulent plane jets may exhibit an apparent sideways,flapping type motion. This motion may be attributed either toconservation, along the length of the jet , of the lateralcomponent of momentum due to asymmetric effects at theexit (leading to an overall sideways motion of the flow field)or to the presence of organized coherent structures withoscillations of finite extent. The apparent flapping motion, atone particular downstream station only, was reported in (1).The apparent flapping, attributed either to a lateraloscillatory-like motion of the entire flow field or to anasymmetric coherent structure within the jet , is hidden in therandomness of the turbulent field and can be found only afterlong-time statistical averages. It is exhibited by the negative

long-time averaged correlation of the longitudinal components of the velocity detected at two points, each one atopposite sides of the jet center line. When the velocity at onepoint increases, the velocity at the opposite point generallydecreases. This could be explained by an overall lateraloscillatory motion of the flow field or by the passage of anorganized vortex-street l ike structure. The time dependentcross correlation, taken with the velocity signal from onepoint delayed in time with respect to the other, gives furtherevidence to a flapping like motion by the distinctive negativevalue at zero time delay as well as by the ensuing quasi-periodic signal.In the work now repor ted , s tandard hot -wire anemometryand on line digital processing instrumentation were used infour types of measurements: (a ) two normal hot-wires

symmetrically positioned with respect to the centerline of thejet; (>) two nor ma l hot-w ires pos itioned at op posite sides ofthe jet but with different lateral coordina tes, (c) two n orma lwires, positioned on opposite sides of the jet, with equivalentdistances from the centerline but at different x locations (x ismeasured along the jet axis); and (d ) a single x-wire at thecenterline of the jet , sensitive to the lateral component, v, inorder to determine its autocorrelation. Longitudinal stationsranging from 10 to 100 times the slot width were in vestiga ted.Contributed by the Fluids Engineering Division of The American Society ofMechanical Engineers and presented at the Winter Annual Meeting, November16-21, 1980, Chicago, Illinois. Manuscript received by the Fluids EngineeringDivision, A ugust 3, 1979. Paper No. 80-WA/FE-l3.

These experiments were planned to:1) Clea rly establish the existence of the flapping-like mo tionas opposed to a puffing effect, i.e., longitudinal oscillationsof the flow field. (A puffing-like motion could be originatedby artificial instabili t ies somewhere upstream of the nozzleexit or by symmetric coherent structures near the mouth of thejet . It would be characterized by periodic cross-correlationfunctions w ith positive values at zero t ime delay.)2) Look for any dependence of the apparent flappingfrequency on the longitudinal and lateral coordinates.3) Study the characteristics of the apparent flappingbehavior in the downstream direction, and4) Investigate the Reynolds number independence and self-preservation of the apparent flapping motion.Experimental Setup

The facility consisted of a vertical rectangular nozzle of0.635 X 30.48 cm (aspect ratio 48) supplied with air by a 1/4HP squirrel-cage blower. A flexible duct connector betweenthe blower outlet and the plenum chamber was employed inorder to avoid the transmission of vibrations from the blower.The plenum c hamb er of dimensions 10.25 cm width, 3 0.48 cmheight, and 67.5 cm long, was provided with a series ofhoneycombs and screens to insure uniform flow. The testsection downstream of the nozzle exit was confined betweentwo 90.2 x 122 cm plywood horizo ntal plates. In this way, aturbulent jet with Reynolds number based on the slot width(0.635 cm) and exit velocity (2.43 x 103 cm/s) of approximately 104 was obtained. (No unusual precautions weretaken to reduce room draft effects. However, measurementsin three different setups, and in different rooms werefavorably compared .)

The usual checks for self-preservation, equivalence to otherreported data for turbulent plane jets, etc. were made. Thisparticular flow satisfied, for x/D > 20, the relationships( ) = 0.24 (x/D-4.53)

D = 0.083(x/Z> + 6 .62)

(1)

(2)

Journal of Fluids Engineering MARCH 1981 , Vol . 1 03 / 1 1 9Copyright 1981 by ASME

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Table 1 Probe configurationsMeasurementstype x/D >> i lb

I 1 0 , 2 0 , 3 0 , 4 0 , 6 0 , 8 0 , 1 0 0 oT5~~V 0 . 7 5V l . oV 1.25U 40 0 2 TV 0.5V 0 . 7 5V 1.0V 1.25m 20,30A) 065~10,20,30,40 1.0T V 1 0 , 2 0 , 3 0 , 4 0 , 6 0 , 8 0 0 ~ ~

i t a second f re que ncy / 2 , as also i l lustrated in Figure 3 can bedetermined. These two frequencies are not exactly the same invalue for reason s not yet fully unde rstood .Type 1 Measurements. Type I cross correlation functionswere determined for the probes equally distant from the axisof the jet and at varying locations. The app arent flappingfrequencies measured are plotted as a Strouhal number,

fd/U0 on Figs. 4(a) and 4(b).The apparent flapping frequency decreases with x but doesnot strongly depend on the lateral coordinate, y, at least forx /d > 30 where the jet becomes self-preserving in terms ofmean velocity and turbulence intensity [3 , 4]. The data pointscorresponding to x/d values of 10 and 20 show a large a mo untof scatter. The reason for this could be the lack of self-preservation or simply error in positioning the probes at thesesmall x/d s tat ions.The decrease of / , a n d / 2 along x demonstrates a dependence on local scaling properties. The results of Fig. 4()satisfy, quite closely, a "universal" value

7 T = 0 . l l (4)The proper scaling parameter can now be applied to nor

malize the time delay T. The c harac terizin g time scale is thenbl U , , and varies along x/d. The measured cross correlationsnow replotted in terms of rU m/b are plotted in Fig. 5,showing commonality in their shape. The magnitude, particularly the correlation at zero time delay is still dependent onlateral location, as exhibited in Fig. 6. An equation of theform# ( 0 ) = ( 1 - 2 . 5 y/b)(exp ( - 2 . 9 y/b) (5)

appears to satisfy the data. For small y/b values (within thelateral spatial macroscale) the correlation has to obviouslyapproach the classical lateral correlation functions noted inturbulent flows.The amplitude of the apparent flapping can be determinedfrom the correlations at zero t ime delay. If the apparentflapping were locally sinusoidal then its displacement wouldbe given bye = e, sin lirft (6)

where e , is the amplitude to be estimated. As shown in [1],the amplitude of the cross correlation at zero t ime delay isrelated to the amplitude of apparent flapping and dependenton the mean velocity gradient and hot-wire response. Theamplitudes e, are seen to vary from 0.15b to 0.23b as noted inTable 2.Data were also taken at exit Reynolds numbers of 7900 and15100 to investigate the dependence on Reynolds number.Figure 7 presents the results. The Reynolds num ber similarity,at least for the tested range, is confirmed. The apparent

y 2 /b Ax/D_ _-0 .75- 1 . 0-1 .25- 0 . 5 , - 0 . 7 5 , ~1.0 ,-L~25- 0 . 2 5 , - 0 . 7 5 , - 1 . 0 , - 1 . 2 5- 0 . 2 5 , - 0 . 5 , - 1 . 0 , - 1 . 2 5- 0 . 2 5 , - 0 . 5 , - 0 . 7 5 , - 1 . 2 5- 0 . 2 5 , - 0 . 5 , - 0 . 7 5 , - 1 . 0

^^65 2,4,6,8,K)-1 .0 Vo ZZ

flapping behavior characterized by relatively low frequenciesshould be related to the large-scale components of the flowfield, and therefore independe nt of the viscosity.Type II Measurements. One speculation is that the jetappears to flap while i t actually "weaves" through a standingvortex type structure. A train of large scale vortices if presentnear the edges of the jet would have to give further changes inthe sign of the cross correlation function at zero t ime delay.

The type II measurements were performed to diagnose thepossible existence of a weaving type motion. The data confirmed (a ) a constancy of / , blUm = 0 .1 1 , (b ) a correlation atzero time delay, see Fig. 8, always positive whenever 1/2[Y\/b + Y2/b ) > 0 hence not exhibiting, by itself, a vortexstreet near the edges of the jet capable of inducing a weavingmotion. However i t does not suffice to dispose the existenceof a vortex short l ike structure smeared across most of theflow field.Type H I Measurements. The type III measurements wereintended to further investigate the uniformity of the apparentflapping motion. Locating both probes on either side of thejet, but one slightly upstream of the other, gives insight as tothe propagation of the apparent flapping type behavior. Thecross correlations were measured as one probe was fixed at acertain x/d and the other alternatively moved in steps of 2ddownstream. Figure 9 presents one set of the many measuredcross correlations. It exhibits a convected pattern where thetime delay for a maximum negative correlation shifts by atime AT as the probes are Ax apart . This indicates that theapparent flapping like behavior as detected at a givenlongitudinal station can sti l l be sensed with considerablecoherence some time later at a downstream location.A convection velocity for the apparent flapping can bedefined by the limit

Ax and AT can be plotted for each set of curves; an extrapolation to a zero separation distance would permit ameasure of U cf. Table 3 presents the results and comparesthem to the data in [5] who, in the same setup, measured theturbulent convective velocity U c (defining the apparentmotion of the turbulent structure). These two velocities arenoted to be different, with a lower value for the apparentflapping motion.

Type IV Measurements. Autocorrelation functions of the.y-component of the velocity were determined along the jetcenterline at x/d stations of 20, 30, 40, 60, and 80. The datashould obviously give the normal auto corre lation function forsmall delay times, with a maximum (equal to the mean squareJou rna l o f F l u ids E ng ineer ing MARCH 1981, Vol . 10 3/ 12 1



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Measurements Type Ix/d - 40 , y/b = 0.5 y/ b

-y/bMeasurements Type IIx/d = 40, y / b = 0 . 7 5

y 2 / b = 0 . 2 5

0 . 3 3 5 v , / e _ = 0 . 2 8 v

T 2 -/ b

Time Delay T [sec] Time Delay T [sec]Fig. 2(a) Cross correlation function for x/d = 40, y/b = 0.5 (Type I) Fig. 2(c) Cross correlation function for x/d -0 .2 5 (Type I I) 4 0, y^b = 0 .75 , y2/b =

O - 0 . 0 0 4

g - 0 . 0 0 8

Measurements Type Ix/d = 100, y/b ^

e, = 0.37v, /e, = 0.31Z v

0 . 1 0 . 1 5Time Delay T [sec ]Fig. 2(b) Cross correlation function for x/d = 100, y/b = 1. (Type I)

Measurements Type IIx / d = 4 0 , y j / b = 1 - 2 5

y 2 / b = - 0 . 5

Time Delay T [sFig. 2(d) Cross correlation function for x/ d =-0.5 (Type I I ) 40 , y-j/b = 1.25, y2/b

value of the signal) at T = 0. However, for large delay times, Figure 10 shows a sample plot at x/d = 40. Data were takenthe appa rent flapping motion (if at all present) should be at x/d = 20 and 80 as well .accom panied by alternatively positive and negative values of The plots are pseudo-oscillatory as the t ime delay increases,the autoc orrela tion. The results, with a single x-wire suffered consistent with the previously described cross correlationin signal resolution but did indeed show the expected trends . functions of the x-comp onent of the velocity. The dimen-

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i_ . . -1, .

Fig. 3 Definition of apparent flapping frequency

sionless apparent flapping frequency can be determined asbefore and compared wi th the results of Type I and II d a t a ,Fig. 11, favourably confirming the trends noted earlier. (Dataof the type I, II or III but based on correlations of the lateralvelocity component would have been desirable but was nottaken. It would have required four hot wire anemometers . )C onc lus ions and Obse r va t ions

The following conclusions and observations can beestablished, based on the experimental results:1 The apparent flapping motion of a turbulent plane jet is adistinctive and measurable natural phenomenon. This wasconfirmed by the reported data, spot-checks at two other jetset-ups (not reported herein) and by a previous preliminaryinvestigation, [1].2 The frequency of the apparent flapping motion decreasesin the longitudinal direction and remains unchanged in thelateral direction (within the regions tested).3 Approximate self-preservation is obtained for the apparent flapping frequency (for x/d > 30), if scaled with thecenterline mean velocity and the half-width of the jet, giving

fb/U, = 0 . 1 1 .4 An est imate of the ampl i tude of apparent flapping gavevalues in order of 20 percent of th e jet half-width.5 The dimensionless frequency of apparent flapping isindependent of the Reynolds number in the range 7900 < Re< 15100.6 Were the apparent flapping motion to be caused by someoverall flapping behavior of the jet then it would be expectedto satisfy a travelling wave solution which in turn would notexhibit self-preservation. The fact that the results exhibit self-preservation suggest then that the apparent flapping motion isno t due to an overall sideways motion of the jet.7 Comparing the measured apparent flapping frequencieswith the frequency of the structures responsible for in-termittency (see for instance ([3,6, and 7]) shows these to be ofthe same order. This suggests that the apparent flappingmotion is at t r ibu ted to a local large scale motion resultingfrom an organized coherent structure within the je t ' s tu rbulent field.8 Noting that: (a) the apparent flapping frequenciescorrespond to those of the intermittency (driven by large scalestructures), (b) the convective velocity of the apparentflapping motion can be seen to correspond to the wave speedof a travelling wave solution, and (c) the motions noted areself-preserving, suggests that large scale motions exist whichon occasion develop in such a way that the scales are appropriate to a travelling wave solution. However due to thenature of turbulence, this travelling wave would not exist forvery long. It could be co m p ared to a suitable large structure

0 10 20 30 40 50 60 70 HO


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S.OO 10 .00 15 .0 0 20 .00 aS.J O 3J .Q 0 3 5 .00 40 . 00 4S.0O SO.OODim ension less Time Delay u / bm/

Fig. 5 Normalized cross correlation functions


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Fig. 8 Normalized lateral correlation (y now equals (y 1 + y 2 ) '2 ) (uncertainty in the order of 10 percen t)

-125.0 -75.0

x/d = 20y/b = 0.65

-25.0 o 25.0_l I IAx/d = 4

75.0 125.0Time Delay T [msec]

Fig. 9 Type III Cross correlation functions, x/d = 20, y/b = 0.65

V^nAA.

0 . 0 5T ime Delay T [ s ec ]

Fig. 10 Auto correlation of the y-component {x/d = 40, y = 0)

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0 10 20 30 40 50 hO 7Dimensi onloss Longi tudinal Coordinate x/d

Fig. 11 Strouhal number 1-\ d/U0 versusx/ d

D I S C U S S I O N

P . Bradshaw 1This work seems to be an admirably conclusive demonstration that a distinct "flapping" correlation exits betweenthe two sides of a jet, and that, at least in a jet with uniform

exit flow, the flapping is a real part of the turbulence structurerather than an effective disturbed boundary condition. Onenow asks whether the correlation is entirely the result ofpressure fluctuations ("irrotational motion") or whether thelarge eddies (i.e. vortical motions) extend significantly acrossthe jet center line. In the former case one could still argue tha tthe interaction between the two sides was weak enough to beignored in turbulence m odelling. The p oint might be settled bypressure-velocity correlations, or, better, by velocity correla-1 Professor of Experimental Aerodynamics, Imperial College, London,England.

tions in and near a jet in a slow external stream, so that theirrorational field could be deduced from velocity fluctuations just outside the turbulent zone.

Authors ' C losureWe are grateful for Professor Bradshaw's comments. Onlyfuture and further research will authoritatively answerwhether or not the correlation is due to pressure fluctuationsor to large eddies. Recent photographs taken by K. Moallemi(M.S. thesis, Purdue University, 1980) tend to support thelatter. "Smoke wire" visualization in the outer flow showslarge scale structures extending well beyond the jet centerlineeven at positions as far asX/ D = 60 .

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0 10 20 30 40 50 hO 7Dimensi onloss Longi tudinal Coordinate x/d

Fig. 11 Strouhal number 1-\ d/U0 versusx/d

D I S C U S S I O N

P . Bradshaw1This work seems to be an admirably conclusive demonstration that a distinct "flapping" correlation exits betweenthe two sides of a jet, and that, at least in a jet with uniform

exit flow, the flapping is a real part of the turbulence structurerather than an effective disturbed boundary condition. Onenow asks whether the correlation is entirely the result ofpressure fluctuations ("irrotational motion") or whether thelarge eddies (i.e. vortical motions) extend significantly acrossthe jet center line. In the former case one could still argue thatthe interaction between the two sides was weak enough to beignored in turbulence modelling. The point might be settled bypressure-velocity correlations, or, better, by velocity correla-1 Professor of Experimental Aerodynamics, Imperial College, London,England.

tions in and near a jet in a slow external stream, so that theirrorational field could be deduced from velocity fluctuations just outside the turbulent zone.

Authors ' ClosureWe are grateful for Professor B radshaw's com ments. Onlyfuture and further research will authoritatively answerwhether or not the correlation is due to pressure fluctuationsor to large eddies. Recent photograph s taken by K. Moallemi(M.S. thesis, Purdue University, 1980) tend to support thelatter. "Smoke wire" visualization in the outer flow showslarge scale structures extending well beyond the jet centerlineeven at positions as far asX/D = 60.

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S. E. ElghobashiAssistant Professor.

Mem. ASME

G. S. Sam uelsenAssociate Professor.

Mem. ASMEM echanical Engineering,

University of California,Irvine, Calif.

J . E. WuererSenior Scientist,

Spectron Development Labo ratories, Inc.,Costa M esa, Calif.

J . C. LaRueAssistant Research Engineer and Lecturer,

University of California,San Diego, Calif.

Prediction and M easurem ent ofM ass, Heat, and M om entumTransport in a NonreactingTurbulent Flow of a Jet in anOpposing StreamThe paper addresses the measurement and prediction of heat, mass, and momentumtransport in a confined axisymmetric turbulent nonreacting flow of a jet in anopposing stream. The predictions are obtained by solving numerically the conservation equations of the mean flow and the transport equations of the kineticenergy of turbulence and its dissipation rate and the mean square temperaturefluctuations. The predicted velocity field is in agreement with the experiment, bu tthe predicted scalar fields p oint to the need of examining the employed model of ascalar turbulent diffusion.

IntroductionThe present capabilities of methods available to predictturbulent, reacting flows with recirculation have beendemonstrated in studies directed to the evaluation of com-bustor performance (e.g., [1-3]). The results, though en

couraging, suggest that systematic testing is needed to validatethe mathematical models employed by such methods. Forexample, well controlled experiments need to be conducted,and complexities need to be introduced one at a time. A majorrequirement of such an approach is to first test the performance of the models against the experiment in the absenceof reaction and heat release.In earlier work, tests for the description of mass andmomentum transport have been conducted in the absence ofreaction and heat release [4, 5]. The present investigationextends the tests to include the transp ort of heat.The flow configuration consists of a turbulent pipe flowwith an on-axis jet opposing the main flow (Fig. 1). A highlyturbulent recirculation zone results from the interaction of thetwo flows. The flowfield has distinctive features that make itparticularly attractive from both experimental and analyticalviewpoints. First, the recirculation zone is not attached tosolid walls. Secondly, the range of velocity gradients, turbulence levels, and mixing lengths is increased over thatoffered by bluff bodies. The isolation of the recirculationzone from solid boundaries frees the analysis from complicated questions associated with the boundary conditionspecifications, while the extension of the range of turbulence

= 7 / ^mr

R e s i st o n r. s t h e r m o m e t e r . ,a n d t h e r m i s t e r

The rm is te r DCWhea ts tone Br idge

Resis tdnce the rmom e te rAC Whed ts tone Br idge

Ave rog inOV M

Av e r a g i n gR M S m e t e r

not to scaleFig . 1 Schematic of experimental apparatus

phenomena provides a broad test of the mathematical modelsinvolved in the flowfield predictions.In the present case, the accuracy of the predicted masstransport was assessed by comparing the predicted andmeasured axial and radial transport of a tracer species,carbon monoxide, which was introduced through the jet withexperimental data. Momentum transport was assessed bycomparing predicted values of velocity and turbulence intensity with their measured values. Heat transport wasassessed by heating the jet and com paring predicted values ofmean and RMS temperature with experimentally measuredvalues.

Contributed by the Fluids Engineering Division for publication in theJOURNAL O F FL UID S E NGINE E R ING . Manuscript received by the FluidsEngineer ing Divis ion, N ovember 27 ,1979.

ExperimentGeometry. The experimental apparatus (Fig. 1) consisted ofa 51 mm inside diameter (3 mm wall) by 240 mm longcylindrical Vycor (transparent quartz) tube containing an

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Table 1 Operating conditionsVariable Cold flow Heated flow

,mJ(m/s)U,j ( m / s )Mach N o.Re,Mach,,/Re,-Tj(K)T: (K)Main flow fluidJet flow fluid

7.50.02525000 1350.411000295295ai rC O

150.05500007.50.02525000 1530.412500295327ai rai r

150.0550000

opposing axisymmetric jet . The diameter of the jet was 1.3mm and the jet exit was located at xld = 3.54 (i.e., 180 mmfrom the inlet plane). The jet tube was a circular cylinder withan outside diameter of 6.4 mm. The exit plane of the tube waslocated at xld = 4 .7 1 .Operating Conditions. Table 1 summ arizes the four experimental operating conditions considered in this study.Velocity Measurements. Velocity measurements were madeusing a laser anemom eter system. O ne thousa nd sam ples ofinstantaneous velocity were taken at each measurement pointwithin the flowfield. These measurements allowed the subsequent determination of the t ime-mean and root mean squarevalues of the axial velocity.The laser anemometer system was operated in a differentialdoppler mode using forward scattered light collection. Twobeam s, split from a 15 mw helium-neon laser (Spectra-PhysicsModel 124B), were focused through a 250 mm lens to form afringe spacing of 1.69 /j,m. A 40 MH frequency shift (TSIModel 915 Bragg Cell) was applied to one beam to resolveambiguity of velocity direction over the wide dynamic rangeobserved in the highly turbulent flow. Signal validation wasobtained using a counter processor (Macrodyne Model 2098).The data were reduced by a min icomputer (DEC Model PDP11/10). The m ain flow w as seeded with approxim ately 1 /xmsodium chloride particles. The jet was not seeded in thepresent experiment. Velocity measurements in the recir

culation zone are therefore biased to the main flow within aregion bounded by approximately r/R < 0.3 and xld > 2.5.Concentration Measurements. The local concentration ofthe CO tracer species was measured using a continuous probesampling system in conjunction with a nondispersive infraredanalyzer (Beckman M odel 915BL ). The probe was constructedof capillary tubing (1.25 mm O .D.) to minimize prob e perturbation effects. This technique provided local t ime-averaged concentration measurements. The use of a tracerspecies having essentially the same molecular mass as that ofthe main flow avoided biasing errors associated with density

fluctuations. Repeated measurements at the same nominalposition in the flow indicated that the variation in COmeasurement is less that 10%. The repeated measurementsincluded the evaluation of probe perturbation by using independently three probes, each with a unique angle of approac h to the sampling point (straight - 0 deg, angle -9 0deg, hook - 180 deg).Temperature Measurements. The temperature signals wereobtained by means of 0.125 mm diameter glass coatedthermisters and a 1.25 /tm diameter resistance ("cold wire")thermometer. The cold wire were platinum and 0.48 mm inlength for Umi = 7.5 m /s , and platinum - 10 percentrhodium and 0.66 mm in length for U m 15.0 m/s. Thecold wires were operated with a root mean square current of255 microam peres .

N o m e n c l a tu r e

C-nC ] , C2< C 7 2 dDfF

FGhHkPrRT

T,Ui,u t

Xire

= constants in the turbulence model= diameter of the large tube= molecular diffusivity= fluctuation of F= mass fraction of carbon monoxide= volume fraction of carbon mon oxide= produ ction of the turbulence kinetic energy= enthalpy fluctuation= stagna tion enthalpy= kinetic energy of turbulence = ViUjU,= mean static pressure= radial distance= radius of the large tube= t ime-mean temperature= RMS temp erature fluctuation= mean and fluctuating velocities (tensornotatio n) in direction x- ,= distance coordinate= ther ma l diffusivity of the fluid= Kronecke r delta= rate of dissipation of turbulence kineticenergy, k

A'cffvP

T iiSubscripts

C . L .

m -max =Superscripts

9 = time-mean temp erature difference = T T,Ilax = max time-mean tem peratu re difference = 7",- T- ,effective eddy viscositykinematic viscosity of the fluidfluid densityturbulen t Prandt l /Schmidt numbers

stress tensor

center linecondition at the inlet of the large tube, exceptwhen used in tensor no tationcondition at the jet exit, except when used intensor notationaverage axial velocity at a given axial locationmaximum value

fluctuating componenttime-averaged value

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Table 2c .0.09 c,1.43 c21.92 "*1.0 "c1.09 C-n2.8 C n1.4 Oj0.9

The set of constants used in the turbulence m odels are givenin Table 2.The values of the first five constants are adopted fromL aunder and Sp alding [11]. The value of Cn was first obtained from comparisons with experimental data of concentration fluctuations in isotherma l flows [12]. The value ofCj ^ adopted in [13] was 2; however, the value used here, 1.4,is consistent with the experimental data of the decay of scalarfluctuations in grid turbulence [14], [15].

The Boundary Conditions. To complete the mathemat icalformulation, boundary conditions must be specified along theboundaries of the integration domain. Along the symmetryaxis, the radial gradient vanishes for all variables except theradial velocity which equals zero. The inlet velocity profilesfor the main flow are specified from the experimental data;for the jet the profile is assumed to be of the plug type. Thevalues of k and e at the inlet planes are prescribed byspecifying the intensity and the scale of turbulence at the inlet.At the exit plane, i t is assumed that the axial gradients forall variables are zero. A long the top cylindrical wa ll , the axialand radial velocities equal zero. The wall functions [1] areused to calculate the values of the generation and dissipationof k and e at the near wall node based on the assumption ofCouette flow.

The Numerical Solution Procedure. The set of equations(1-4), (7), (8), (10) described above, together with theirboundary conditions, was solved by an iterative finite difference procedure based on the Simple algorithm of Patankarand Spalding [16], but modified for elliptic flows. The gridrefinement tests were carried out using three nonuniformgrids: 1 6x 12 , 25 x 12, and 25 x 20, where the larger num berof nodes was in the axial direction. The 25 x 20 grid w asemployed for the computations presented here.A typical CP U time required for achieving a converged

solution (300 iterations) was 5 minutes on a DEC 10 comp uter(equivalent to CDC 6400). The convergence criterion employed is that the maximum residual R$ is less than 10~ 4 ,where R^ = (convection + diffusion + source)/ reference, and is the dependent va riable solved for.R e s u l t s and D isc uss ions

The experimental and predicted results are presented for thecold and heate d flows at 15 m /s a nd 7.5 m/ s inlet velocities inFigs. 2 through 8. These include radial profiles of the t ime-mean axial velocity, the distribution of kinetic energy ofturbulence along the center l ine of the tube, the radial profilesof the t ime-mean and the RMS temperature, and rad ialprofiles of CO volume -fraction.The Time-Mean Axial Velocity. Figure 2 shows the radialdistributions of (U/UCL J) at two axial locations (xld =2.95, 3.15) for both the cold and heated flows with UmJ = 15m/s. At these stations velocity measurements were obtained atradial locations of r/R equal to or greater that 0.2 due to thebiasing adjacent to the center l ine that was caused by theabsence of seeding in the jet . At these radial locations, thepredicted velocities are in fair agreement with their experimental values.The two velocity profiles of the cold flow indicate that thestagnation point along the centerline of the jet l ies between thetwo stations of xld = 2.95 and xld = 3.15 where the normalized center-line velocity drops from 0.4 .to 1.0. The

O 0.2 0.4 0.6 0.8 1.0r / RF i g . 2 Radia l profiles of time-m ean velocity (15 m/s)

E x p e r i m e n t a l P r e d i c t i o nsx / dheated 1 -z ic /heatedA c o l d / - l: > / c o l d" heo ted l o Q e /healedO c o l d / ^ ' M :> \ c o l d

0 . 2 0 . 4 0 . 6 0 . 8 1 . 0r / R

F i g . 3 Radi al profiles of time-m ean velocity (7.5 m/s)

respective profiles for the heated jet demonstrate that i tsstagnation point is located upstream the station of xld =2.95 , i .e. the recirculation zone is longer for the heated thanfor the cold jet .The predicted center line velocities for the heated flowattain larger negative values compared to their values in thecold flow. This is because the velocity of the heated jet isapprox imately 11 percent higher than that of the cold jet . Themomentum of the jet is 21 percent and 27 percent, respectively, of that of the main flow for the cold and heated cases.Figure 3 shows that radial distributions UIUCL ,- at thesame axial stations for U,_,- = 7.5m/s. The experiments andpredictions depict similar behavior to that of the high velocitycase, except that the magnitudes of the negative velocities atthe centerline are much larger (almost twice as large) than

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Predictions x/d2.751O W A 2 9 5 t u m i i = 7 . 5 m / s

3.15 U m i = l 5 m / s

F i g . 8 Radial profiles of t ime-mean CO volume fractionbut an exam ination of Fig. 5 would run contra ry to thatsuggestion.It should be mentioned here that the transport equation forthe mean square fluctuation of a scalar quantity (10) has beenvalidated for turbulent free jets [17] and for confined turbulent recirculating flows [18]. The same equ ation (with boththe values of Cn of 2. and 1.4) did not predict accurately themeasured values of RMS temperature fluctuations under theexperimental conditions of this study. This stresses the need tosolve a transport equation for the dissipation of the temperature f luctuat ion .

The Time-Mean CO Concentration. Figure 8 exhibits themeasured and predicted radial profiles of CO volume-fraction(F ) at three stations for the 7/5 m/s flow and at one stationfor the 15 m /s flow.For the 7.5 m/s flow, Fv is overpredicted near the axis andunderpredicted in the outer region (r/R > .5 ) . However , F isunderpred icted for the 15 m /s flow. Again, this points out theneed for a closer look at the e equation and for a distributionof o> instead of the constant value used in the presentpredictions.

C o n c l u s i o n sThe present contribution provides detailed measurementsof velocity, temperature, and concentration in a turbulentinert recirculating confined flow with the objective ofvalidating current mathematical models of turbulence.Althoug h fair agreement is obtained between the measu redand predicted mean velocity field, discrepancies occur between the experimental data and the predicted time-meantemperature, t ime-mean concentrat ion and RMS temperaturefluctuation.The need exists for a closer examination of the e equation

and the assumption of the constant turbulent Prandtl andSchmidt nu mb ers. O ne such example is a recent developmentof the k- t model [19].In order to improve the predicted distribution of thetemperature fluctuation a transport equation for thedissipation rate of this fluctuation m ust be solved.A c k n o w l e d g m e n t s

This study was performed at the U CI Com bustionL abo rator y and sponso red by the Air Force O ffice ofScien ti fic Research (G ran t N o . AFO SR-78-3586) . The U . S .G overnm ent is authorized to reprodu ce and distribute reprintsfor government purposes notwithstanding any copyrightnotation hereon. Support for one of the authors (J . C. LaRue)was obtained f rom a N SF gran t , EN G -78-15712 and NASAg ran t , L -N SG -3 21 9 .R e fe r e nc e s

1 Elghobashi , S . C , Studies in Convection, Vol. 2, edited by B. E.L aunder , Academic Press , 1977, p . 141.2 Peck , R. E., and G. S. Samuelsen, "An alytical an d Experimental Studyof Turbulent Methane F ired Backmixed Combus t ion, " AIAA Journal, Vol. 15,N o. 5, 1977, p. 730.3 Khalil, E. E., D. B. Spalding, and J . H. Whitelaw, "The Calculation ofL oca l F low Proper t ies in 2-D Furnaces ," Int. Journa l of Heat an d MassTransfer, Vol. 18,19 75, p . 775.4 W uerer, J . , and G . S. Samuelsen, "P redictiv e Modeling of Back-mixedCombustor F lows: Mass and Momentum Transpor t , " AIAA 79-0215,presented at the 17th Aerosp ace Sciences Meeting, N ew Orlean s, Jan , 1979.5 Peck, R. E., and G . S. Samuelsen, "Ed dy V iscosity Modeling in thePrediction of Turbulent, Backmixed Combustion Performance," SixteenthSymposium (International) on Combustion, The Combustion Institute, 1977,p . 1 6 7 5 .6 Wyngaard, J. C , "Spa tial Resolution of a Resistance Wire TemperatureS e nso r , " Phy. Fluids, Vol. 14 ,1971 , p. 2052.7 Brem horst, K. and D. B. G ilmore, "In fluence of End Condu ction on theSensitivity & Stream Temp erature Fluctua tions of a Hot-W ire Anem ometer,"Int. J. Heat Mass Transfer, Vol. 21,1978 , p . 145.8 Millon, F., P. Paranthoen, and M. Trinite, "Influence des EchangesThermiq ues E ndre le Capteur et ses Supports sur la Mea sure des Fluctuations deTempera tures dans un Ecoulement Turbulent ," Int. J. Heat Mass Transfer,Vol. 21,1978, p . 1 .9 L arsen, S. E., and J . H0js trup, "Spa tial and Tempo ral Resolution of aResis tance Wire Sens or ," J. Atmos. Sci, (submitted for possible publication).10 L aRue , J . C , T. Dea ton, and C. H. G ibson, "M easurements of High

Frequency Turbulent Tempera ture ," Rev. Sci. Instrum., Vol. 46, N o. 5, 1975,p p . 7 5 7 - 7 6 4 .11 Lau nder , B . E. , and D. B . Spa lding, "Th e N umer ical Computa t ion ofTur bu len t F low s , " Computer Methods in Applied M echanics and Engineering,Vol. 3 ,1974, p . 269.12 Spalding, D. B., "Concentration Fluctuations in a Round Turbulent FreeJ e t , " Chem. Eng. Sc, Vol. 2 6 , 1 9 7 1 , p. 95.13 L aund er, B. E., and D. B. Spalding, " Turb ulenc e Models and theirExperim ental Veri fication ," L ectures for Post Experience Course held atImperial College, Apr. 1973, p. 11.5.14 G ibson, C. H., and W. H. Schwarz, "Th e Un iversal Equilibrium Spectraof Turbulent Velocity and Scalar Fields," Journal of Fluid Mechanics, Vol. 16,1963, p. 365.15 Lau nder , B .E . , Pr iva te Comm unica t ion, N ov. 1973.16 Pa tan kar , S. V., and D. B. Spalding , "A Calculatio n Procedu re for Heat,Mass and Momen tum Transfe r in Three Dimensiona l Parabol ic F low s," Int. J.Heat Mass Transfer, Vol. 15,1972, p. 1787.17 L ockw ood, F. C. and A. S. N aguib , "Th e Prediction of the Fluctuationsin the Properties of Free Round Jet, Turbulent Diffusion Flames, Combustionand Flame, Vol. 24,197 5, p . 109.18 Elgho bashi, S. E., W . M. Pun, and D. B. Spalding, "Concen trationFluc tua t ions in I sothermal Turbulent Conf ined J e ts , " Chem. Eng. Sc, Vol. 32,1977, p. 161.19 Hanjalic -, K., B. E. L aunder, an d R. Schiestel, "Multiple-Time-ScaleConcepts in Turbulent Transpor t Model ing," Proceedings of Second Symposium on Turbulent Shear F lows ," July 1979, L ondon.

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H . H . Kors tProfessor of Mechanical Engineering.

Fellow ASME

R. A. W h i t eProfessor of Mechanical Engineering.

Department of Mechanical andIndustrial Engineering,University of Illinois atUrbana-Champaign,Urbana, III. 61801

Evaluation of Vehicle DragParameters From CoastdownExperiments Conducted UnderNonideal Environmental ConditionsParameter identification by optimization forms the analytical basis for extractingroad load information from well controlled coastdown tests. Specific attention isgiven to the effects of both biased and rando m errors as may be caused by environmental disturbances, road conditions, inaccurate parameteric input, or signaland instrument noise. As a consequence, experimental conditions can be identifiedand quantitative criteria established for either avoiding or correcting such errors.Test results are presented which support the methodology and conclusions.

IntroductionFuel economy and emission testing as required by federalagencies specify the use of chassis dynamometers but allow todetermine road load power settings by "procedures requestedby the manufacturer and approved in advance by the administrator" [1]. Thus, efforts have been made to identify,document, and seek approval for methods of realisticallyassessing road load power.Coastdown testing with full scale vehicles on level and

inclined roads affords such opportunities, provided thatexperimental methods, procedures, and data processing canbe devised which produce acceptable (i.e., accurate) information. While coastdown testing is not a new experimentalapproach for determining vehicle drag, introduction ofcontrol theory related data processing methods, based onparameter identification by optimizing techniques, has improved the accuracy with which drag components can beseparated and quantitatively extracted.Earlier work by the authors has directed attention to thepotential of this method [2,3] which, in its original version ofa two-parameter drag component formulation, forms thebasis for EP A approved procedures now used routinely by thelarge car manufacturers. Closer examination of the restrictions imposed [3,4,5] and possible errors in componentevaluation caused by the use of only two performanceparameters led to the present investigation.The overall objective is to give a critical appraisal of dragcomponent evaluation by coastdown experiments with fullattention given to all significant variables and parameters insuch tests, including study of the effects of biased and randomdisturbances. It is significant that capabilities can bedeveloped for correcting effects of environmental disturb-Contributed by the Fluids Engineering Division of THE AM ERICAN S OCIETY OF

MECHANICAL ENGINEERS and presented a t the Joint AS M E/CS M E AppliedM echanics, Fluids Engineering, and Bioengineering, N iagara Falls, N . Y., Jun e18-20, 1979. M anuscript received by the Fluids Engineering Division, S eptember 17, 1979.

ances during coastdown experiments. This holds the promiseof sizable cost reductions in fleet testing.H owever, the study shows that even while accounting fullyfor the overall energy dissipation due to aerodynamic dragand road-tire-suspension interactions, coastdown tests cannotcleanly separate these individual component losses withoutsome laboratory testing of the tires. Efforts to improve theoverall fuel economy of road vehicles must, therefore, dependon close cooperation and exchange of information betweencar and tire manufacturers.Analysis

Equation of Motion for Coastdown. The analysis proceedsfrom the equation of motion for the vehicle under coastingconditions [3] with the drag contributions distinguishingbetween "correct performance coefficients," a, , and"disturban ce co efficients," c,, in the form of the polynomial-dV/dt[(m fi + A/w,0)/g0] = Ej;g (a, + c,)V (1)

where the limitation to ; = 2 is imposed by our chosen formof parameter identification procedure and must be complemented by certain restrictions in experimental conditions.We identify a, as the correct performan ce coefficientso=r0,o;i =r\fi\a1=r 2fi + (p fi/2g0)A CD (2a,b,c)where r0Q , r[0 , and r2,o relate to the tire rolling resistanceparameters

^o.o = K ' o . o l 0 0 0g 0 ) / ! ,o * ) ] (3)Si.o = WofiruoVfofi]Si.o - (r2,o/ro,a)Fo,a

Ob)(3c)

and the aerodynam ic drag is accounted for by the parameterJournal of Fluids Engineering M A R C H 1 9 81 , V o l . 1 0 3 / 1 3 3

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B M =A CD (p,0/2g0)[( ô,o)2//-o,ol (4)The disturbance terms, due to wind and road slope effects canbe identified as follows: An instantaneous vector diagram(Fig. 1 (a )) relates the relative flow past the vehicle V (0 tothe vehicle velocity V{t) and the wind speed and direction(U,a) in the form

V'(t)=[(V+Ucosa)2+(Usma)2]U2 ' (5)Introducing CD, the effective drag coefficient in the directionof the car trajectory, the aerodynamic drag can be written asD,D = l(V+ [/cos a)2 + U2 sin2 a] (p$/2g0)A c'D

= ^(pp/lgÂ CD+2VUcos a (p,0/2ga)A C'o + lflp^ c'D/2g0

The contribution due to road slope will be(m,0 g/g0) sin 6 = (mfi g/g0) H?o/\00.

Accordingly, the disturbance terms are now3c0 = U2 AC 'DH P,0g)/g0] + (mfig/gt))mo/l00c, = 2Ucos a(pt0/2gn)A C'D; c 2 =0.

(6)

(7)

( 8 f l )

(86,c)

Discussion of road roughness effects on tire and suspension losses have beentreated in reference [8].

The force terms in equation (3) are now identified accordingto their causes-dV/dt[(m.0 + AmiQ)/g0] = /,

+ i(mfig)/goy\(m/ioo)+ U2AC'D(p,0/2g0) + [rh0+ 2Ucosa(p0/2g0)AC'D] V+ [r2,0 + (p,0/2g0)AC'D] V2. (9)

Using the initial velocity K00 as reference, we introduce adimensionless velocity=V/V0,o (10)

and define a dimensionless timeT=t/T,D (11)

where T,D is a characteristic timeT,D = [(/72i0 + A/w,0) V0t0]/lg0 r0fiV

+ (U/Vafi)2AC'Dp,0Vl,0+ (mfigim)/{g0r0t0W)]) (12)Contracting the terms according to powers of v, one arrives,

after separation of variables, at-dr=dv/(\+2Fv+Bv2) (13)

Nomenc l a t u r e

Dimensional Variables't f o . c0" i . c ,

AA\\,\] = Vj /coastdown

. = coefficients in fIN]equations (1), (8) y N g / ^ - i jfrontal area of test car

A[\,2]=t; matrix rsiD = aerodynamic drag force [N]g = local gravitational acceleration

[ms" 2]ô = gravitational constant = 1 [kg

m s - 2 N - ' ]H = road slope [%]in = mass of vehicle [kg]

Am = additive mass accounting forrotational inertia [kg]

p = air density [kg m~ 3]p = tire pressure [ Nm - 2 ] [psig]r0,rur2 = tire rolling resistance coef

ficients [N], [N s m _ 1 ] , and [Ns2 m~ 2], respectivelyR = tire rolling resistance [N/1000

N]Si.o^.o^b.o = t i r e r o l l i n g r e s i s t a n c e

parameters. [N s/1000 Nm], [Ns2/1000 Nm2], and [N/1000 N]respectively.t = time [s]

' Utilization of some English units is necessitated by the present specificationsof the Environmental Protection Agency for vehicle chasis dynamometertesting.

T D = reference time [s], see equation(12)U = wind velocity [ m s - 1 ] ; [ft s~']V = vehicle velocity [m s~ ']; [fts - 1 ] ; [mph]

V0 = initial vehicle velocity at / = 0[ m s - ' M f t s - 1 ]6 = road slope [rad]

a = wind direction [rad]A = yaw angle [rad]

Dimensionless ParametersB = see equations (4) and (15)

CD = aerodynamic drag coefficient atzero yaw angleC D = aerodynamic drag coefficient atyaw angle

F = see equations (3a) and (14)Dimensionless Variables

Subscripts

v = VIVQ dimensionless velocity[- ]r = t/T,D dimensionless time [-]

,0 = smooth road and undisturbedconditions2

,D = disturbed (biased) conditions/ = index for test points

U se of this subscript reflects the need for distinguishing rough road conditionsas treated in reference [8].

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A

V ( t )

, -*\

V ' ( t )

'A

V ' ( t ) = U -V(t)Fig, 1(a) Vecto r diagram of wind-car spe ed rela t ion

Yaw Angle,AFig. 1(b) Typical normalized wind tunnel data on drag yaw dependenceFig. 1 Vecto r d iagram of instantaneous wind-car speed rela t ion andnormalized drag co ef f ic ient yaw depe ndence

whereF=F.n = [(SifiV0.0)/2FM ]

+ (Ul Vw) co s a B 0i0 ]/[1 + (U/ VM)2BM+ ( 1 0 # % / F , o ) ]an d

B=B.D = [B OJ B+ SM (V M )/F 0fl]/ll(15)(U/VQf i)2B Q,n+ (\Omo/Fofi)}

will ultimately have to be determined by parameter identification through optimization in comparing to experimentalcoastdown data.Theoretical Coastdown Function. Integrals of equation (13)ta n be obtained in three distinctively different formsdepending on the discrim inant

(16)

(17)

B -F 2>0results in a finite coastdo wn time while

B -F 2 0. (For level coastdown, this imposes physical l imits ontailwind strength and road slope so that their combined effects do not lead to a finite terminal coastdown speed.) Uponintegration, one obtains for r = 0 as v = 1T=[U(B-F2)]/2 ] ( t a n -1 [(B + F)/(B-F2)W2

- t a n " 1 [(Bv+ F)/(B-F 2)]/2 ]} (19)and a finite dimensionless coa stdown time results for v = 0TF = [\/(B-F 2)W2 ] [tan-][(B + F)/(B-F2)W2]

- t a n - ' [ / ? / ( B - F 2 ) l / 2 ] ] (20)Inspection of equat ions (2a,b,c) and (ia,b,c), together withequation (4) shows that four performance parameters are ofinterest . O bviously, separation of S 2,o and B00 is not possibleso that S2 a m u st be extracted from tire testing or its effectsexcluded either by proper tire selection or by an appropr iate(linear) approximation of t ire speed dependency. This leavesthree parameters to be determined; however, separation ofeven three parameters under generally noisy experimentalconditions is not possible4 so that it is deemed necessary tointroduce some experimental information on the tire speeddependency, e.g. in the form of values of S ( 0 or both S]0 an dS 2,o. We shall assume that such data are either available fromtire laboratory tests or can be reduced to insignificance (atleast for the purpose of establishing aerodynamic dragcoefficients) by proper selection of tires, high inflationpressure, and coastdown speed ranges. The remaining twoperformance parameters are determined by the optimizationrequirements

(d/dT M )L N[T M T(v i)- ti]2=0 (21)(d/dB tB )L N[T M T(u i)- ti]2=0 (22)

with th e errors summed for N experimental point pairs, V,and ThWe now introduce the following abbreviations with A (1,1)= v, and .4(7,2) = ?,:Ax = \+(B + F) 2/A};A2 = t a n - ' ( B + F A 4 3 ) ;

(14) A, = (B-F2)*[ l - ( B + F ) / (2 / l3 2 ) ] [^3 /^ i ] -

C 0 = B-A(l,l) + F; C, = 1 + C M 3 ;

(23a,b)

(23c,d)(24a,b)

C2 = t a n - ' ( C 0 / 4 3 ) ; C 3 =A(I,\)- Ca/(2A2); (24c,d)

This is borne out in Fig. 5 where the dependency for the SliQshown to be submerged in the rms data scatter. residual is

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an dS 0 = E f C 2 ; S,=L?Cl; S2 = L? A(I,2) C 2 ; (25a,b,c)S 3 = Z?A(I,2) S 4 = E f l / C , ; S 5 = E f C 3 /C , ; (2 5 t f , e / )S 6 = E f ( C 2 / C , ; S 7 = E { M ( / ,2 ) ( C 3 / C , ) ; (25*, A)

The optimizing con dition, e quation (21), yields7",D, =[AMi S3-S 2)]/(NAj-2A2 S 0 + S , ) . (2 6)

and equation (22) producesr D = f ^ 3 [ ( / 4 4 - / l 2 / 2 ) S 3 + S 2 / 2 - / l 3 S 7 ] | /

[ T V T/ M i -Ai/2] + (4 2 ~A4)S0 -A 2A3S5- S , / 2 + ^ 3 S 6 ) . (27)

Using F D as a variable and expressing TD = TD (F D) andB D = B d (F D), a numerical i teration can be carried out withthe help of digital computers to determine, for N point pairsVj, T,, a solution for which

TD.I = TDin (28)

thus determining the optimized values for FD, S D , and TD.SinceB0,0 = lB %D [l+(lOm>/F0fi)]

-S 2,oKV 0fiy/F ofi ]}/[\-(U/V o^B M ]and^0,0 = [(". + Am / g m,0) 1000 K0,0 - T D 10 / / % ] /

iGenerating Function L&J Data Fi le L V eh ic le Test Data, see Fig.^ E Z

(29)

( r D [ l + ( t / / K 0 , 0 ) 2 5 0 , 0 ]i (30)a unique solution will be obtained for JB 00 and Fofi. S u b sequently, one finds from equation (4)

AC 'D={ B 0fi F0J0 m fig)/[p fi(V Of i)25O0] (31)O ne recalls that c'D is the drag coefficient experienced by thevehicle under v arying conditions of yaw angle due to the crosswind component. While yaw angle dependency will vary fordifferent vehicle configurations, the increase in CD for smallyaw angles can be approximated by

c' D/cD = cD(d)/[cD\^ Q] = i + C A 2where C is of the order of 2.53 or less (for A in rads) [6,7], seeF ig . 1 (6 ) .During a typical coastdown run as the car speed decreasesfrom ab out 110 to 55 km h, yaw angle effects will genera lly besmall in the higher speed range where the present testevaluat ion procedure pu ts emphasis on the aerodynamic dragcontr ibu t ion ; hence, CD = c' D. Crosswinds can, however,exhibit more noticeable influence on the rolling resistance ifcoastdown records are processed to extend the lower endspeed range.

Hill Coasting or Rolling. Starting again from equation(13), i .e.,

~dT=dv/(Bv2+2Fv +l ) (32)with

F=F DandB=B D (33,34)as before but

B -F 2 = A < 0 ( 3 5 )(fogncg = A is pqsjf jve) sg that tfl? integrgj gf equ atio n (32) is

ReductionProgramsSR0LLHR0LLGR0LL

-Known Parameters

Fig. 2 Schematic showing use of generating function

Table 1M ass, m i0 1,814kg [4 ,000IbJEffective mass ratio ( m 0 + Am 0)/ m io = 1.035Frontal area A 2.09m 2(ff)Drag coefficient CD 0.5Tire Rolling ResistanceG 0 0 12 [N/1 ,000N]5 , 0 0 .1 64 N s / l,000NMS la O N s2/ l , O O O N m2Atmospheric ConditionsAir density, pa 1.2kg/m3Wind speed, U variable, m /sWind direction, a degrees, variableY aw angle coefficient, C 2.53, dimensionless

(n ) N ote that only the product A CD is of real significance for dragevaluation and dynamometer setting.

T = l / [ 2 ( - A ) l / 2 ] ( l n [ ( - A ) '+ F+ Bv]/[(-Ay/2-F-Bv]

(36)l n [ ( - A ) 1 / 2 + . F + 5 ] / [ ( - A ) 1 / 2 - . F - . B ] )A terminal velocity is reached as r oo

ur = [(-Ay/2-F]/B (37)This terminal velocity can be approached in both acceleratingruns (v \T= 0 vT). L owvelocity experiments, starting with v(t = 0) = 0 will bereferred to as hill roll ing. O ptimization procedures and extraction of the correct performance parameters follow thescheme outlined for level roads.

Generating Functions. Parameter identification by optimization has to be carried out in the presence of disturbances which are either random or biased. To study parameterobservabili ty, separabili ty, and resulting errors for performance coefficients, it is convenient and instructive toconstruct generating functions with well defined noise inputs.R ando m disturba nces such as scatter of data points mayresult from noisy signals (analog), truncated signals (digital)

as received or recorded, or from random processing errors(digitizer). Such disturbances can be modeled and subsequently studied by (i) first establishing a theoretical(smoo th) generating function and (ii) subsequently subjectingit to digital randomization (this can easily be achieved byrounding the V(t) curve to any prescribed number of G"de cim als" ) . I t is no teworthy that , in th is contex t " dec ima ls"can also be assigned fractional values so that a continuousrelation between G and rms is accom plished. This facili tatesthe discussion of random noise influences on parameterobservabili ty and on parameter accuracy.For biased disturbances, one may consider the followingcases as representative: (i) changes in road slope as a function

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oo5 -

>*oooo4 and provided profiles of concentration flux whichallowed the identification of jet fluid. The open circuit wind tunnel used for these experiments was

. N o m e n c l a t u r eD = diameterE = voltage of hot-wireanemometer signalU,V,W = instantaneous velocitiesin X, Y, and Z directionsU,V,W = time-average velocity inX, Y, and Z directionsU = freestream time-averagevelocity

u,v,w = fluctuating component ofvelocity in X, Y, and Zdirections ({/= U+u etc.)rms of velocity fluctuations ( = Vi?)jet velocity, averagedacross DX = coordinate measured

u =V, =

from hole center-line indownstream directionY = coordinate measuredfrom floor of wind tunnelZ = coordinate measuredfrom line of hole centreline across wind tunneld = mean concentrationa = standard deviationJournal of F luid s En gineer ing M A R C H 1981, Vol . 103 /143



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Table 1 Previous experimental investigations of round jets in crossf low

jet jet cross-flowdiameter incident velocity velocity velocityref. (mm) angle profile (m/s) ratio measured123

456

78

9

10

11

12

6.35,9.512.7,15.96.35,9.512.7,15.9

12.725.4

9.525.46.35

25.450.8

8.4

50.8

23.5

25.4

9030 ,4560 ,90

90

9090

1 5 , 30, 4 5 , 90,- 1 8 0 , 3 0 ,60 , 90, 120,150, 180

90

90

90

35 ,90

90

orificeorificeorifice

pipepipepipe

nozzlepipe

nozzle

nozzle

pipe

nozzle

_72122-1.5

18.3,36.61.6

7.615.2M A C H0.1,0.20.4,0.6

15.230.561

12.2

-2-8

4 , 6 , 8

4,-6, 82 , 4 , 8 ,11.34 , 6 , 8

1.18-104.12

1.4

8,12

0.1-22 , 4 , 8 ,12, 16,20

penetrationparameterscorrelation between parameterstotal pressures,flow directionsvelocity, turbulence intensity,entrainmentstatic pressuredistributionsjet trajectory,entrainmenttrajectory bypho tographswall staticpressureswall staticpressuresturbulence measurements in wakeregiontemperature,velocity, turbulenceintensity contourswall static pressures, turbulenceintensity vorticity

jet jet cross-flowdiameter incident velocity velocity velocityref. (mn) angle profile (m/s) ratio measured

1314

15

16

17181920

21222324

23.511.86.35

23.538.176.2

8.440

101.6101.6

19.0523.6

varied

35 ,9090

35 ,90

90

909090

45 , 60, 7590 , 105

9090

90

pipepipe

pipe

orifice

nozzlepipe

orificenozzle

pipepipe

orifice

30.5616-9

30.561

-M A C H0.1,0.20.4,0.6

3.430.430.555.3

268.5

pipe flow15

0.1-2.182.8-8.5

0.1-2.02 , 4 , 6 , 8 ,12

adiabatic wall temperature, film cooling effectivenessvelocity and tem perature distributionsadiabatic walltemperatures, p itotand static pressureswall static pressuredistribution

dynamic pressure ratio floor static0-1000 pressures2.37,3.956.35

53.38

0.046-0.13.48

. 2-5-12.32.45-7.75

velocitydistributionsvelocity andvorticityvelocitystatic pressure, velocity, film coolingeffectivenessvelocity,vorticitytemperatureprofiles

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previously discussed in references [26 and 27], The carefullyestablished two-dimensional flow is produced through a 7:1contraction ratio section and the free stream turbulence is lessthan 0.6 percent in the range 6-20 m/s. A free stream velocityof 12 m /s w as used for these experiments. The dime nsions ofthe working section of the wind tunnel are 0.46 m wide, 0.300i high and 1.8 m long. The wind tunnel, without the jet flow,had a zero static pressure gradient over the working length.A single tube, 25.4 mm inside diameter an d 0.75 m long wasused to inject the jet normal to the freestream. The jet waslocated at a distance 0.15 m downstream of a 25x460 mmemery paper trip. The resulting boundary layer thickness atthe leading edge of the jet was, at the 99 percent value, approximately 6 mm with no jet flow. The jet was supplied froma centrifugal fan through a screened plenum chamber andresulted in a fully developed turbulent pipe flow profile, in theabsence of cross-stream flow.

The tunnel floor was made from a high surface qualityaluminum block with a flatness tolerance of 0.05 mm. Thejet tube was stainless steel honed to 0.05 mm over the final0.25 m. The velocity profile at the exit plane of the jet, whichwas flush with the tunnel floor, was measured on two orthogonal planes, without the cross-flow, and found to besymmetric to better than 1 % of the center-line mean velocity.Hot-wire measurements were made laterally across the jet andcross-flow at a dow nstream p lane corresponding to X / D = 10and showed symmetry to within 2 percent of the undisturbedfree-stream velocity. The maximum temperature differencebetween jet and free stream was 1 C .

The LDA optical system was traversed in three orthogonalplanes and the measurement location was known to an accuracy of better than 0.1 mm. Hot-wires and other probeswere traversed with a mechanism located on the roof of thetunnel and providing movement in three orthogonal planes towithin 0.1 mm. The hot-wire probe holder had three furthermovements, allowing pitch, yaw and rotation of the sensor.R otation was limited to eight equi-spaced positions by mean sof a locating dowel. Positioning of the sensors, both LDA andhot-wire, was achieved with slip gauges, a pointer locatedwithin the jet and a grid of 0.3 mm holes arranged across thefloor of the tunnel.

M e asur e me nt Syste msL ase r -D opple r A ne mome tr y . T h e l a s e r - D o p p l e ranemometer made use of an Argon ion laser (Spectra Physics164) operating at 488 nm and approximately 800 mW. Anacousto-optic water fi l led cell , based on the arrangement ofreference [28], ope rate d with a frequency shift of 21.00 M H zand divided the beam into zero and + 1 order beams of approximately equal intensity. The two beams, after separationand parallel alignment, were focussed to an intersection zoneand backward scattered light collected through the same lens.The collected light was focused by another lens, via a mirror,Onto a pinhole located immediately in front of the cath ode ofa photomultiplier (E MI 9815B). The resulting control volume

had a calculated diameter of approximately 0.12 mm andlength 0.85 m m. T he distance betwee n consecutive fringes was2.05 fim and the zero frequency correspo nded to - 43.05 m/ s.The resulting Doppler signal was processed by a spectrumanalyzer, Hew lett Pack ard R F stage (model 8553B) and IFstage (model 8552A) and c ounter unit similar to that describedby Du rao, L aker , and W hitelaw [29]. At central l inearlyspaced frequencies, the number of signals in a predeterminedtime (usually 30 seconds) and with constant bandwidth(usually 100 kH z), were counted over the range of Dopp lersignal frequencies and yielded a probability distribution ofsignal frequencies. Each probabili ty distribution consisted ofmore than 103 signal counts. The effective control volume

dimensions were slightly smaller than the quo ted values due tothe instrumentation electronic discrimination.To provide a measurable particle arrival rate, the windtunnel and jet were seeded with kerosene smoke generatedfrom an evaporat ion /condensat ion arrangement . The twoflows were seeded from a common reservoir at a rateproportional to the respective volume flow rates causinguniform seeding thus avoiding bias due to different seedinglevels. The resulting droplets were smaller than 5 /xm indiameter and allowed construction of a velocity probabili tydistribution in less than 15 minute s.The average quality of the signals processed correspondedto a signal to noise ratio of approximately 20 dB whichallowed easy discrimination and processing. Limitations onthe precision of the measurements were imposed by thenumber of observed signals and the histogram intervalsresulting in an estimated accuracy of 2 and 5 percent of thelocal mean and rms frequency, respectively. In addition, thecombination of photomultiplier and particle-velocitycorrelation bias can contribute to uncertainty but, as shownby Du rao , La ker, and W hitelaw [30] the overall effect is l ikelyto be small . The overall uncertainty in measured values ofmean velocity is of order 3 percent and of the rms frequency 7percent.When measuring the vertical velocity component, close tothe wind tunnel floor, the complete optical system was in

clined to a maximum 5 deg to avoid the lower beam intersecting the tunnel floor. The maximum possible errorassociated with this procedure was 0.8 percent assumingI V\ = I W\; however these profiles were only taken over thejet area where V> Wand the probable error is less than 0.4%.Hot-Wire Anemometry. The constan t temperatureanemometers , DISA 55D01 or 55M01, were operated at anoverheat ratio of 0.8 and, with a bridge ratio of 20 and cablecompensat ion ad justments , a bandwidth of approximately 40kHz was obtained . The probe types were DISA 55P11 and55P12, normal and slanting, respectively, and DISA 55P61crosswire. The holders , DISA 55H20 and 55H24 were bo thlocated within stainless steel tubing to maintain constantsensor position when the probes were rotated.Static calibration was perform ed using the potential core ofa 50 mm diameter jet with a turbulence intensity of less than0.3 percent. The reference velocities were from a standardNPL pitot static tube and input to a minicomputer forcomparison via a Furness Controls electronic transducer. Theprobes were calibrated before every run and checked atvarious stages during the mea suremen ts to insure the effect ofaccum ulated dirt and drift were negligible.Exponential type linearisers, DISA 55D10, were preferredto digital l inearisation, transfer function or curve storage,since both digital procedures were found to be lacking ineither efficiency (curve storage) or accu racy (transfer functionbased upon a King's law relationship). The linearisers accurately reproduced the relationship EaU+b and the incorporation of two external operational amplifiers allowed"b" to be removed.All hot-wire signals, for calibration or measurement, wereprocessed with a DEC PDP 8E minicomputer and peripherals. The minicomputer, with 12k of random access memory,ope rate d w ith a 1.2 /xs cycle time using 12 bit wor ds. Co mmun ication w as throug h an ASR 33 teletype with paper tapereader and punch. The anemometer signals were input to amultiplexer (DEC A124) either directly or through the sampleand hold modules (Burr Brown SH40) when the crosswireswere sampled. The signal from the multiplexer was thenpassed, via a programmable gain amplifier and sample andhold module, to an A/ D converter. The converter (DECA862) produc ed a 10 bit word plus two sign bits thus the totalinput v oltage range was resolved into 2047 divisions. A digital

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tape system, R AC AL T7000, was used to facili tate datat ransfer between the PD P 8E and a CD C 6500.The method of data processing was dependent on the degreeof complexity required; for standard hot-wire measurementsinvolving only mean and rms quantit ies, all the processingwas done by the PDP 8E but for more complicated analysisthe data was transferred to a CDC 6500. To produce meanand rms quantit ies at least 150,000 samples were takendepending on the fluctuation magnitude and for probabili tydensity distributions 400,000 samples were recorded. Energyspectra were obtained w ith a G eneral R adio (Model 1564-A)frequency analyzer with a 1/10 octave filter.The interpretation of the hot-wire signals was based on theevaluation method of Champagne and Sleicher [31].The accuracy of the signals recorded by the hot-wire wasdependent on the accuracy of the calibration andlinearisation. A single wire was l inearised to w ithin 1 % of thevelocity recorded on the manometer over the range 3-30 m/sand a pair of cross wires were similarly linearised to within 3percent. The total system was dependent upon the accuracy ofthe manometer used for calibration and for thesemeasurements the maximum manometer error was around 0 .6percent which occurred in the low velocity range. It can beanticipated that the precision of the measurements, due to thetransform equation, will diminish for values of turbulenceintensity above around 0.20. Where negative velocities occur,additional errors will occur; in general the laser-Doppleranemometer was used in these flow regions. The summationof the total errors for the hot-wire system at a turbulenceintensity of 15% gave probable uncertainties of U/Ux2percent; u/U, v/U, w/Ul percent; and iiv/U2, uw/U2,uw/U2 15 percent .

Hel ium t race measurements were recorded using a probewith external and internal diameters of 0.87 mm and 0.26mm, respectively. The air sample was passed to a Servomexthermal conductivity cell , located in a constant-temperatureoven. This allowed the measurement of helium concentrationto within 2 percen t of the 1 percent concentra tion level atthe jet exit . In the range of measurements, the calibrationindicated that the relationship between the output voltage ofthe thermal conductivity cell and helium concentration waslinear.A more detailed discussion of this method and analysis ofthe optimum operating condition is found in reference [32].

R e s u l tsThe results are discussed in three sections which relate tothe init ial mixing region where the measurements were obtained by laser Doppler anemometry, the downstream zonewhere hot-wire anemometry was used; and finally the heliumtrace concentration results obtained throughout the flow.In i t i a l R eg io n . Th e l ase r Do p p le r an e m o m ete rmeasurements were extended to cover the range of the flow,x/D=l to 6, where hot-wire measurements would besubject to imprecision from directional ambiguity for tur

bulence levels greater tha n a round 30 percent. Figures 1 to 4present results showing V/Vj, v/Vj, UIUX and u/U fo rvertical planes corresponding to Y/D of 0.25, 0.75, 1.35, and2.5 .The jet development in the vicinity of the pipe exit is shownin figure la with the profile of the undisturbed jet velocity,which has the characteristics of a fully developed turbulentpipe flow. When subjected to the cross-flow, distortion of thejet potential core has begun even by a height of 0.25D and by0.75D is well pronounced. The measurements recorded at alower velocity ratio (1.15) show greater distortion of the outletprofile than in the higher velocity case and suggest that theprofile is modified at the outlet plane. For both ratios the

front half of the jet has a decreased velocity and the rear halfis forced to accelerate, and probably widen, to compensatefor the extra flow of jet fluid. This rear-edge acceleration ismo re noticeable in the lower velocity case.As indicated on Fig. 1(c), the mainstream flow in thesymm etry plane and in front of the jet shows a minimum of0.42 U but the reduction in the vertical velocity in the upstream part of the jet is accompanied by an increase in thehorizontal component up to a value of 0.61 U. At the rear ofthe jet the minimum value of U is 0.23 U and no recircula tion is show n, indicatin g that the flow is very differentfrom that associated with the wake from a solid body. Theregion immediately behind the jet is fi l led with mainstreamflow that has mixed with low momentum boundary-layerfluid from the jet which is easily transformed into horizontalm o m e n t u m .

Figure 2(a), at Y/D = 0J5, shows two important characteristics of the jet in the initial stages. First, the twin vortexpair starts to develop as indicated by negative values of V atZ/D = 1.0, ~0.5


148/182

vov/v.

0-5

o1-

2 0U/U,

0-3v7Vj

0-2

0-1

o i -

0-75a/Uoo

0-5

0-25

Fig. 2(a,b,c,d) Mean velocity and normal stress profi lesY ZD

0.750.750.7500.51.0

consistently larger than the upstream while the downstreampeak of v tends to disappear with increasing Y/D; thestructure is largely anisotropic. The normal stresses in theinner core of the jet increase in amplitude with height until\ID= 1.35 after which the inner core is destroyed leaving, forv, a single m aximum in the Y/D = 2.5 plane which is furtherhalved by Y/D =3 .5 . Immediately downstream of the jet thenormal stresses are high, on all planes, and decrease slowlywith increasing downstream distance.Figure 5 presents profiles of Ul U and ill U^, interpolatedfrom Figs. 1 to 4, for center-plane locations in the regionX/D= - 1 to 4. The mean velocity profiles show a peakbeginning at X/ D = 0 and continuing at X/ D = 0.5 and 0.75with a wake region developing between it and th e floor of thetunnel. This peak is the result of jet fluid that has beentransformed from vertical to horizontal momentum. ThePeak is reduced in size at X/D = 0J 5 and is destroyed byX/D=l,o when the recirculation zone commences. TheProfile at XID = 1 shows the end of the high velocity regionwhich stems from the jet. Further downstream , at X/D = 1.5,

there is a strong recirculation zone in the region of the formerpeak and a new maximum has developed above it composedmainly of cross-flow fluid as is confirmed by the later heliumtrace concentration measurements. The second peak increasesat X/D = 2, with a small reduction in recirculation strength;by X/ D = 4 the peak has reduced and the gradients can beexpected to diminish with further downstream distance. Thenormal stress profiles between X/D = 0.S and 1.0 exhibit apeak in the region under the mean velocity peak but atX/D=\.5 and 2, with regions of strong recirculation, thenormal stress profile is fairly uniform. At X/D = 4 a normalstress peak is again developing under the second mean velocitypeak.Downstream Region. The results presented on Fig. 6 andappropriate to the downstream region from X/ D = 6 to 20,were obtained by hot-wire anemometry. The results representa continuation of the centre-line values of figure 5, measuredby LDA, although it should be noted that the normalisingconstant of the rms value is now the local mean velocity since

Journal of F luids Enginee r ing M A R C H 1981, Vol . 103 /147Downloaded 02 Jun 2010 to 171.66.16.86. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm


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0-5V / V j

0 L "0

0-3

v / V ,

0-2

0 - 1 -

~"l~Nw>frff l-t i% I M ^ i i UI A l _ 2 3 N T-

2 3Fig . 4(a)

_ Jx / D '

2 0

U / U

1 0

0 i _

0-5

0-25

2 3Fig . 4(c)

l> 5x / D

Fig . 4(a,b,c,d) Mean veloc ity and norm al stress prof i lesY

2.52.53.52.5

01.500.5

X / D - l X / D - O X / D - - 5 X / D - 7 5 X / D - l- O X / D - l ' 5 X / D - 2 ' O X / D - 4 - OFig . 5 Centerp lane mean ve loc i t y and normal s t ress p rof i les

8(c) shows significant bimodality though both U and V have behind the obstacle imposed by the jet . A single hot-wire,near G aussian distribution s. The mean velocity profiles of sensitive to all three velocity com ponen ts, was used toFig. 6 indicate that the l ine Y/D=l, Z/D = 0, is the ap- mea sure the correspo nding energy spectrum and showed aProximate locus of the maxim um wake mean velocity, very small peak at a frequency of 25 H z, abou t four timessuggesting that the b imo dal shape stems from the wake lower than that correspo nding to a Strouha l numb er based on

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W D - 6 X / D - 8 X / D - I O X / D - 12 X / D - 1 4 X / D - 1 7 X / D - S OFig. 6 Cente rplane mean velocity and intensity profiles

u /u1-2J ^ y | > ' 0 x > ^ c > ^ o < ^ ^ K > n < )

u/U0-_2

v / UOJw/ u : f * N -

z /DFig.7(a,b)

z /D

Fig. 7 Mean velocity and Reynolds stress profiles at X/D = 8.a. y/ D = 1, b. y/ D = 2, c. y/ o = 3 d. y/D = 4 .o u/Wo V /u+ w/ 0e u v / 0 2e Vw/02

1 5 0 / V o l . 103, MA R CH 1981 Transac t ions o f the ASMEDownloaded 02 Jun 2010 to 171.66.16.86. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm


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-3 -2 1 u/crFig. 8(a) Fig. 8(6)

r\ \ \

0"P(w)

tJPIv)- i -5"(IP(ki)

5 -

A L_XJ iSs**,-


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X/ D =Fig . 9 Centerp lane he l ium t race concent rat ionso 0?flj+ U/Ua

Q / 9 ,X / D - I O

0/Uoo/O 978 j

C onc lud ing D i s c u s s i o nThe present results confirm the general trends of previousinvestigations and provide further information which adds toknowledge of the flow structure. The double vortex structureof the downstream region, for example, is observed andquantified for the present configurations: the upstreammeasurements allow its formation to be recognized atx/D=-0.25, Y/D = 0J5 and between Z/D = 0.5 and 1.0.Similarly, the contour plots of mean velocity and heliumconcentration confirm that the locus of maximum velocitydoes not correspond to fluid from the jet exit; indeed, thedownstream regions of high velocity are shown to be composed mainly of free-stream fluid.In i ts mean-flow characteristics, the jet in cross-flow iscontrolled mainly by pressure forces which cause the bendingof the jet and the double-vortex structure. In principle,

therefore, and provided the considerable curvature of theflow can be adequ ately represen ted, the flow shoul

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