Modeling of turbulence for compression corner flows and internal flows

A compressible Reynolds averaged NaYler-Stokes code is applied to examine the performances of basic tuIbulence models for ""separated and separated flows. The turbulence models Considered are a zero-equation model and several two-equation models. including a new k-r model With an eddy viscosity damping function depending upon the Reynolds number and the distance from the wall. The turbulence models are a86eQsed using experimental flows: a channel flow, a backward facing step. and a two-dimensional compression comer at Mach 2.8. Discussions and comparisans of the experlmental and numerical results are given. Mesh refinement is shown to have a slgnificant beneficial effect on free shear layer flaw results obtained with two-equation turbulence models. The results illuatrats the usefulness of several turbulence models 8s a design Loo1 Lor fluid engineering eyetems. Nomenclature 2 Cf Skin-friction coefficient, 7J(1/2precUref] 2 pressure coefficient, ( p p ~ ~ f ] / ( l / z p ~ ~ f " ~ ~ ~ ' cP c constant in Viscosity model (usually= 0.091 P C1, C 2 Con5tantS in the 6 or Y equation e = CVT specific internal energy = e t ( 1 / 2 ) UiUi specific total energy E h o r H etep height IE, JE number Of cells In xand ydirections k I I , , , = ( p + p Iu u /2p. mass-averaged turbulent i i kinetic energy P pressure, p = (I-lIpe (equation of state1 PI PIT = cp P/K Prandtl number (0.72 for air) = CPPlr/ x turbulent Prandtl number (0 .91 Prk, PrL, Prq, Pru model constants pressure at the wall P W q c k1/2 9 heat flux vector s1,e2 turbulent field variables: k, 6 or 9, w T temperature "," ~ ul, u2 velocity components in x and y ~ shear (or friction) velocity directions u, Y+ = U,Y/" = c /c ratio of apeclfic heats dissipation rate of k P V 7 x molecular thermal conductivity Of the fluid X T turbulent thermal conductivity molecular and turbulent vlacoaitles P , pT +Principal Scientist. Member A I M . This work was supported by the Small Business Innovative Research Phase I program to Applied h Theoretical Mechanics, 1°C.. under NASA contract NAS2-12778. Copyright @ American lns!iiuie of Aeronautics and Astionautic~. Inc.. 1989. All rights reserved. y , yT molecular and turbulent kinematic viscosities y' P density total stress tensor turbulent Reynolds Stress mi j QT, w = E/L subscripts i,j indicate direction 1.j w value at the wall free-strean condition upstream of lntcraction X.Y indicate direction x,y j ( 1 or ,j = e/sx j