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Turbulent Flow Over a Flat Plate

Turbulent flow over a flat plate is calculated using several turbulent models and compared with analytic models.

Computational Procedure

A Mach number of 0.3 and a Reynolds number of 6.0 x 106 was chosen for the simulation.  The total computational domain extended 1.2 length units in the streamwise direction with a leading edge at 0.2 length units from the start of the domain. The extent of the domain in the normal direction is 1 length units. The simulation type is basic CFD with MUSCL scheme used for spatial differencing and the Beam-Warming scheme used for time differencing. The time step size was chosen as 1.0 x 10-3. The problem was solved as two-dimensional in the i and j directions.

Single Block Calculations

The computational grid employed 65 x 97 x 1 grid points in the i, j, and k directions, which also align with the x, y, and z axes, respectively. The grid is shown in Figure P9.1. At the bottom boundaries (y = 0.0), slip conditions were applied at the first 12 grid points (up till x = 0.0) while no slip conditions were applied at every other grid point. Free-stream conditions were applied at the top boundaries. Subsonic outflow boundary conditions were applied at the x = 1.0 boundary while u = 1.0 was applied at the incoming boundary. The input file included a CGNS file with an initial field for k and e. u = 1.0 was set everywhere for the initial conditions. The calculations were completed for all the turbulence models and compared with the results from the original implementation. The results are shown in Figure P9.1.

Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (a) mesh
Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (a) mesh
Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (b) Launder-Sharma k-e
Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (b) Launder-Sharma k-e
Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (c ) Menteer’s SST k-w
Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (c ) Menteer’s SST k-w
Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (d) DES after 1000 time steps.
Figure P9.1. Comparison of the integrated AEROFLO code with the original implementation (d) DES after 1000 time steps.

Multi-Block Overset Calculations

An overset, two-block version of the flat plate problem described above was set up. Each grid is 65 x 97 but do not have conforming grid points in the overlap region. The flat plate section extended from x = 0.2 to x = 1.2. Overset conditions was set at i = 1 for the second grid block. Outflow boundary conditions are initially imposed at i = End for both grids for about 10,000 iterations after which overset conditions were imposed at i = IE for the first block. This was set to speed up the convergence of the calculations. The grid and results are shown in Figure P9.2. The multi-block and single-block results are compared in Figure P9.2. The multi-block results appear slightly better because of the superior mesh used for the calculations.
Figure P9.2. Multi-block flat plate calculations (a) mesh
Figure P9.2. Multi-block flat plate calculations (a) mesh
Figure P9.2. Multi-block flat plate calculations (b) coefficient of friction, Cf
Figure P9.2. Multi-block flat plate calculations (b) coefficient of friction, Cf
Figure P9.2. Multi-block flat plate calculations (c) u-velocity contours
Figure P9.2. Multi-block flat plate calculations (c) u-velocity contours
Figure P9.2. Multi-block flat plate calculations (d) mt-contours (turbulent viscosity).
Figure P9.2. Multi-block flat plate calculations (d) mt-contours (turbulent viscosity).

Obtain the Files

For single block problem:

Setup file

turbplate.afl

Grid file

turbplate.in

Reference

White, F. M., “Viscous Fluid Flow”, 2nd Ed., McGraw-Hill, 1991. pp 233-237.

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