An Efficient Way of Specifying Profile Inflow Boundary Conditions

Abstract

An efficient way to systematically reproduce inflow profiles across a compressible, turbulent boundary layer for the mean flow variables, as well as the turbulent quantities in one-equation and two-equation turbulence-models, from given external flow conditions and one boundary layer parameter, is described. The reproduced profiles are checked against both experimental results and numerical solution of boundary layer equations. Theoretical analysis shows that a new form of density-weighted velocity, rather the Van Driest density-weighted velocity, obeys the linear-law at the viscous sublayer in a compressible turbulent boundary layer. Especially for non-adiabatic wall at hypersonic Mach numbers, where there are large density gradients, these two kinds of density-weighted velocity could differ considerably. Therefore, the new form of density-weighted velocity proposed in this paper should be employed for the viscous sublayer. It is also shown that power-law fitting for the streamwise velocity gives an unacceptable profile in the viscous sublayer. An efficient way to specify the normal velocity profile is also proposed and tested. The reproduced normal velocity at the boundary layer edge is found to agree remarkably well with the numerical solution of boundary layer equations.

Turbulent Navier-Stokes Simulations of Heat Transfer with Complex Wall Temperature Variations

“…When trying to match experimental results using numerical simulations, great care must be taken into accurately reproducing the experimental conditions. 21,22 For the considered problem this translates into making sure that the initial boundary layer profile used for the computation matches the one found in the wind tunnel. To perform the simulation, the profiles of ρ, u, v, w, p, k, ω must be specified at the inlet.…”

“…Another approach consist in using the measured u-velocity profile to compute the turbulence quantities. 21 This was accomplished by using the Cebeci-Smith 23 algebraic turbulence model. The approach used is described as follows.…”

“…When θ (or δ) and [T w , T e , U e , ρ e , ρ w , y i ] are known we can compute δ (or θ) and [u(y i ), T (y i ), C f , q w ] using the following algorithm first developed by Huang et al 27 and improved by Zhang and Morishita. 21 1. Guess the value of δ (or θ) and u τ .…”

“…For higher Mach number, a scaling of y + was done by Zhang and Morishita. 21 This was implemented but wasn't significant for the Mach number considered herein. The following steps are used to compute the v-velocity profile.…”