1. The mixing region :This isthe regionwhere,the inner region from the incoming turbulent boundary layer interacts with the recirculating region. The productionofTKE inthis regionismainlyduetothe entrainment of the recirculating fluid. The compressibility effects are minimal here. Experimentalobservations24,indicatethatthepeak shearstressvalueincreasesbyabout 4-6timesthe value inthe incoming boundary layer.The increase in shear stress is attributed to an increase in the Reynolds shear stress - u"v". Since, it is also observedthatthere isareduction in|^,agradient transport hypothesis representation for the Reynolds stresses could be erroneous. The standard k-e model is based onthe assumption of equilibrium betweenthe productionanddissipation of TKE. Studies27have shown that this kind of flowfieldischaracterized bystrongnon-equilibrium effects.Thisisthemotivationbehindtheneedtotest the predictive capabilities of the non-equilibrium modifications of Chen and Kirn28.
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3. :ion to I 1.15 + 0.25-1 + 0.25-=M. This modification t tendsto equilibrate the levelsof Production ofTKE and the dissipation rate of TKE.The standard k-e modelwiththismodificationandthemodificationfor the dilatational dissipation term, (proposed by Sarkaret.al.) istermedastheextendedk-e models andisdenotedasEkewhilethestandardk-e model isdenotedbySke.Figures 9through 11,show plots of the velocity components and the TKE magnitudes, (at three representative planes). The figure compares the computations made using the Eke model and the Ske model.Close to the base region, (at x/R = 0.079), there seems to be little differencebetweenthetwomodelsinpredictingthe magnitudes of the velocity components. However, in the recirculating regionthe Ekemodeldoes offer a better prediction incomparisontothe Skemodel. Both models seemto indicateagreater variation in the velocity components inside the recirculating region, than what is measured. The computations failto pick the peak in the measured value ofTKE. This peak is due to the fact that the intensity ofthe longitudinal fluctuations is increased by the rapid expansion while the transverse fluctuations are unchanged from their value in the wall turbulent boundary layer upstream of the base corner. The eddy viscosity models because of their inherent assumptionof isotropymaynot beexpectedtopick up the magnitude of the peak in TKE.Overall it is difficult to conclude which one of these models makesbetter predictions.Further investigationsare being conducted to research into the model deficiencies.The resultsofthese investigationswill becommunicatedatalaterdate.The lowervalueof TKEpredictedbythe Ekecould beduetothe effect of the compressibility corrections which tend to reducethe intensity ofthe fluctuations. Figures 12 and 13 shows plots of the eddy viscosity and dissipation rate predicted by both models at the samethree locations.The Skemodelsconsistently predicts a higher eddy viscosity coefficient as comparedtotheEkemodel.Thiscouldbetheresult of the reduced levels of TKE predicted by the Eke model. The implications of these is the reduced variations, in comparison to Ske, seen in the predicted values of the velocity components. The magnitudesofdissipationratespredictedbythetwo models shows very little difference except at the midpointofx/R=1.26.Thereasonforthisisthatthe non-equilibrium modification reduces the level of the"productionofdissipation"termintheeequation. This results in better agreement of the velocity profiles inthis regionwiththeexperimentaldata.
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