1. HighMachnumbercompressibilityeffectsstronglyinfluencethe mixing in the developingshear layer but do influence the mixingbeyondthetransitionalregion. Thetransitionfromshear layer to axisymmetricjet involves dealing with the effects of mean vortex stretching on the turbulent dissipation as the flow becomesmorejet like. For asymptotichigh-speed shearlayers, significantwork has been doneover the years to deal with the compressibilityproblem. In 1975,DashetaL8characterizedthe turbulentcompressibilityasa measureofvelocity fluctuationsto localsoundspeed(i.e., by M7= \/2k/a wherekistheturbulent kinetic energy). A compressibility-correctedversion of the ke model (thekcCC model) resulted from this research which was calibrated to match the high-speed isoenergeticshear layer data by making the viscosity coefficient dependent on M, (Le., v, = C, (M,)pk 2/E). Morerecently,Sarkaretal.9andZemanio have formulated compressible-dissipationmodels which supplement the "incompressible" dissipation, cs, by an additive compressible term, cc, which is calibrated in terms of M, (Le., c = c8 +cc(M,)). Theinclusionofcompressible-dissi ation models into the ke framework had been initiatedby Dashri and ViegasandRubein.
2. Whilevariedextensionstotwo-eqnationandReynolds-stress turbulence models have been formulated to deal with both asymptotic high-speed shear layers and axisymmetric jets, combiningthese extensions to provide a unifiedmodel which analyzesall regions of the jet has not proven straightforward. Given the heuristic nature of turbulence modeling, this work requires consideringmany sets of data in a systematicmanner. In the period 1975-1985,significant work was performed to establisha turbulencemodel forhigh-speed straightbackaxisymmetricjets which wascapableofanalyzing subsetsof the full jet problem as listed in Table IV.A hybridzonal turbulence modeli 6resulted fromthiswork whosefeaturesareschematized inFigure 4. This hybrid model implemented the compressibility-correctedkcCC model for thedevelopingshear layer' and the kW modeli 3 for the downstreamjet. A switch from keCC to kW wasbased on the parameterf = 6/r, (shear layerwidthto jet half-radius)with values of .3 < f <5fortheswitchpoint providingbest overallagreementwithdata. Theperformance of thismodelagainstthebuilding-blockdataavailableprior to 1985 is summarized in Refs. 11and 16. For later reference, Figure 5 exhibits the performance of the ke, kW and keCC models versusthe high-speed/single-streamisoenergeticshearlayerdata correlation of the 1972NASA Free Shear Flow Conference." The ke model does not reproduce the decrease in spread rates associatedwithincreasingMachnumbers overunity(thespread