Effect of Inflow Boundary Conditions on the Turbulence Solution in Internal Flows

Abstract

A FULLY implicit numerical method for the solution of threedimensional transport equations of fluid dynamics cast in generalized curvilinear coordinates has been enhanced to demonstrate the effect of inflow conditions on the downstream development of internal flow in a channel. The effect of inlet boundary conditions on turbulence kinetic energy k and the dissipation rate on the downstream developing flow is assessed in terms of local values of k and Reynolds stress profiles. It is shown that the effect of inflow conditions lasts well over tens of channel heights downstream, before the flow eventually attains a fully developed state. This has an important bearing on turbulent flow (especially internal turbulent flow) simulation results where the characteristic dimensions of interest of engineering systems are much shorter. In some simulations, the solution sought may be in serious error if the inflow conditions chosen are not physically realistic. It is therefore important to account for the effect of wind-tunnel inlet turbulence levels when comparing wind-tunnel experimental data with predictions from a given flow simulation. This study serves as a guide in the prescription of inflow boundary conditions on k and in simulating laminar to turbulence transition in such flows. Also, the enhanced fully implicit method presented here is demonstrated to improve the convergence to steady state by 2 orders of magnitude for a fully developed turbulent channelflow at Reynolds numbers (based on the channel height) of 7700 and 12,300 with the Chien kturbulence model over the previous semi-implicit method developed by the author, where the source terms are treated explicitly. For the case of downstream developing flow, 4 orders of magnitude improvement in convergence to steady state has been realized. The solution of transport equations in fluid dynamics involves solving mixed parabolic-hyperbolic systems. Some of these systems can be very stiff and demanding on the computational resources. Thus, they can require long integration times to achieve a steady state. One such stiff system is a two-equation set of partial differential equations governing turbulence kinetic energy, k, and its dissipation rate, . These two quantities define the dynamic turbulence viscosity, t, required for a Reynolds Averaged Navier–Stokes (RANS) computation, according to the relation