A boundary layer computational model for predicting the flow and heat transfer in sudden expansions

Fully developed turbulent and laminar flows through symmetric planar and axisymmetric expansions with heat transfer were modeled using a finite-difference discretization of the boundary-layer equations. By using the boundary-layer equations to model separated flow in place of the Navier-Stokes equations, computational effort was reduced permitting turbulence modeling studies to be economically carried out. The continuity and momentum equations were solved in a coupled manner. The validity of the once-through calculation scheme utilizing the FLARE approximation was studied by using a multiple sweep procedure in which the FLARE approximation is removed after the first sweep. For laminar constant property flow, the equations were nodimensionalized so that the solution was independent of Reynolds number. Two different dependent hydrodynamic variable sets were tried: the primitive variable set (u-v), and the streamwise velocity stream function variable set (u-rp). The predictions of the boundary-layer equations were identical regardless of the variable set used. The predictions of the boundary-layer equations for parameters associated with the trapped eddy compared well with the predictions of the NavierStokes equations and experimental measurements for laminar isothermal flow when the Reynolds number was above 200 and the ratio of inlet to outlet channel diameter(width) was less than 1/3. The reattachment length and the flow field outside of the trapped eddy were well predicted for Reynolds numbers as low as twenty for laminar flow. The Boussinesq assumption was used to express the Reynolds stresses in terms of a turbulent viscosity. Near-wall algebraic turbulence models based on Prandtl's-mixing-length model and the maximum Reynolds shear stress were compared. The near-wall models were used with the standard high-Reynolds-number k-e turbulence model. A low-turbulentReynolds -number k-e model was also investigated but found to be unsuitable for separated flow. The maximum-shear-stress near-wall model gave better predictions than the Prandtl-mixing-length models, especially for heat transfer. The predicted turbulent heat transfer is primarily dependent on the turbulence model used in the near-wall region. Globally iterating over the flow field had a more pronounced effect on the heat transfer solution than on the hydrodynamic solution.