to LANGTRY ROBIN :help, hypersonic transition SST

ben akih

hi Robin and all folks out there! i have a problem simulatiing hypersonic boundary layer transition (first of all for flat plate at mach 7.5).

i first had a lot of problems with convergence using a high resolution scheme. switching to upwind scheme, i obtained a converged solution for FSTI 1% and viscosity ratio of 10 (default) but the transition point was very far downstream. due to the decay of tke (as a result of zero production in free stream), the prescribed fSTI decayed to 0.65% before reaching the leading edge. to avoid this i set the viscosity ratio at 50 and later at 75, solutions do not reach convergence target of 1e-6 but fluctuate at about e-4.

my observation is that once the conti, mom and turbulence equations reach convergence target, solution converges irrespective of the high residual levels of gamma and retheta. -although the solutions referred to above do not converge they show the stanton number shows the expected tendency, that is the transition point moves upstream as viscosity ratio is increased (higher viscosity ratio leads to lower FSTI decay).

-an investigation of the effect of cell expansion ratio near the wall shows that there is a variation of the transition ppoint but no clear tendency can be seen and the discrepancy is more than reported by others.

-IMPORTANT observation is made: the langtry-menter correlation uses the vorticity reynolds number to determine the momentum based reynolds number assuming Rev/2.193=Retheta. In hypersonics (in fact in compressible flows): theta =Integral(rho*u/rho_e*u_e(1-u/u_e)dy as opposed to the incompressible definition theta =Integral(u/u_e(1-u/u_e)dy. using the compressible definition i arrive at a fairly constant relation with Rev/6.3=retheta; using the empirical correlation employed in the model with FSTI of 0.65 i get retheta_transition of about 665 this is almost comparable with abu ghannam-shaw correlation (about 681). according to these values and my computed compressible retheta, transition should set in at 150 mm downstream which agreés well with experiment.

sorry for the long story. i thought it necessary to give a view of what i am doing. now questions: any tips on how i can get round these problems with convergence? is a convergence target of e-4 permissible? is the SST model well suited at all for hypersonic transition.or are the results i am getting just coincidental. would be grateful for any help. i have been too long on this problem and i want to graduate soon .

regards, ben

p.s. Robin in case you want to get details of the problem could you please give me your email contact?