Simulation of flow over a backward-facing step.
The mean velocity profile obtained from a boundary layer simulation by Spalart (1986) is imposed at the inlet at = 667. Random velocity fluctuations u', v', and w' are superimposed on this profile according to a variant of the method of Lee et al. (1992). The fluctuations are prescribed such that, at the inlet, the turbulence intensities and Reynolds shear stress of Spalart's data are also duplicated. A convective boundary condition (Pauley et al., 1988) is imposed at the exit. The streamwise domain consists of an entry section of length l0h prior to the step and a 20h post-expansion section, where h is the step height. The vertical dimensions before and after the expansion are W1 = 5h and W2 = 6h which give an expansion ratio ER of 1.20.
The Reynolds number, based on h and the mean inlet free stream velocity U0, is Reh = 5100.
The above figure shows contour plots of the instantaneous spanwise vorticity on a typical vertical plane. The vorticity is normalised by U0/h. A free-shear layer spreading from the step and interacting with the lower wall near the mean reattachment location, xR = 6h, is discernible.
The basic statistical quantities are compared to results from concurrent experiments by Jovic and Driver. In 1991, they conducted a backward facing step experiment at Reh = 6800 and ER = 1.09, herein referred as "JD1". However, the results indicated that these parameters are not sufficiently close to those used in simulations. Thus, Jovic and Driver in 1992 conducted a second experiment with Reh = 4950 and ER = 1.20 ("JD2").
The Navier-Stokes equations are discretized using a finite difference method on a staggered mesh. Uniform mesh spacing is applied in the streamwise (x) and spanwise (z) directions. In the vertical (y) direction, non-uniform mesh is employed with mesh refinement at the wall and near the step. The fractional step method from Le and Mom (1990) is used for time advancement. The Navier-Stokes equations are first advanced using a second-order semi-implicit method without the pressure terms. The pressure is calculated by solving the Poisson equation, and the velocities are then corrected to satisfy the continuity equation.
The spanwise dimension is 4h where periodic boundary conditions are imposed. i The simulation uses 770 × 194 × 66 grid points in the streamwise, wall normal, and spanwise directions, respectively.
The computation uses 13 megawords of memory and requires approximately 55 CPU seconds per time step on a single processor CRAY Y-MP at a rate of 186 mflops. Statistical quantities are averaged over the spanwise direction and time. About 1100 CPU hours were required to obtain an adequate statistical sample. The total computational time corresponds to approximately 4.5 flow-through times.
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