Program EDDYBL

(1_k_424 APPENDIX D. PROGRAM EDDYBLD.11 .2 k-w and Multiscale Model EquationsFor both the k-w and multiscale models the dissipation, e, is given byc = (j*wk (D .7)where k is turbulence kinetic energy and w is specific dissipation rate . Theequations for k and w applicable to compressible boundary layers are asfollows .Pn as +Pv On - PT an -'a*P,k + r an [rj (P + 0'*ILT) an](D .8)_awTsw-.P7 _ au _au _1 _a _awPu as +Pv an = a k On - I3pw [c.' +f an] + r3 an [~ (P + 0/1T) an(D .9)For the k-w model, the Reynolds shear stress is given byaiipr = a* FATan(D .10)For the multiscale model, the Reynolds stresses are computed from thefollowing equations :_197 07 _ [a)Qy-~o,x+3(1-&-,l32 3 auPn as +Pv_ an+4fk -Ci,Q * PWTp8n(D .11)_aux _ao-x _ 2_auP'u - Cas +Pv (D [2(1 a) an 3 - +'~~ PT ani 'Q'pwQx.12)pu OQy + pv OQy - -2 - +[(1 &) 2a1 pr aii - * CIO PwO-y (D .13)as an 3 anwhere C1 is defined in terms of the ratio of large eddy energy (k - e) toturbulence kinetic energy according to3/2C 1 =1+4( k ek )and (k - c) satisfies the following equation .(D .14)a_aiikPu as (k-e)+Pv an(k-e)Pran-a*jowk~e3/2l(D .15)