NPARC Alliance Validation Archive
Validation Home   >   Archive   >   Driven Cavity

Driven Cavity

Figure 1 is described in the surrounding text
Figure 1. The Mach number contours for the driven
cavity run C with Reynolds number of 3200.

Introduction

This validation case computes the laminar incompressible flow for a 2D driven cavity at various Reynolds numbers. Because WIND models only compressible flow for a gas, we approximate incompressible flow by choosing a small Mach number. The domain is a 1 inch by 1 inch square. The cavity is driven by a translating plate at the top of the cavity.

Download tar File

All of the archive files of this validation case are available in the Unix compressed tar file cavity.tar.Z. The files can then be accessed by the commands

uncompress cavity.tar.Z
tar -xvof cavity.tar

Grid

The grid used was a simple non-clustered rectangular grid with 65x65 points for Re = 100 (run A) and 128x128 for runs B and C.

Topology: Structured, multi-block
Number of Blocks: 1

Figure 2 is described in the surrounding text
Figure 2. A plot of the example grid for the driven cavity case.

Table 1 lists the names of the common grid files (*.cgd) and the PLOT3D grid files for the grids. The PLOT3D files are three-dimensional, whole, single-block and unformatted.

Table 1. The grids used for the driven cavity case.
Run Reynolds Number Grid Size CGD File PLOT3D Grid File
A 100 65 x 65 cavity.A.cgd cavity.A.x.bin
B 400 128 x 128 cavity.B.cgd cavity.B.x.bin
C 3200 128 x 128 cavity.C.cgd cavity.C.x.bin

Boundary Conditions

The boundary conditions were set using GMAN. The I1, IMAX, and J1 boundaries were set as VISCOUS WALL boundary conditions. The JMAX boundary is the translating wall. Within GMAN, a moving wall requires that the boundary be specified as a BLEED boundary condition. Then in the input data file, the MOVING WALL keyword is used with the velocity of the upper wall to 52.56 ft/s in the positive x-direction.

GMAN is executed for each run in following manner,

gman < gman.A.com
gman < gman.B.com
gman < gman.C.com

Initial Conditions

The flowfields for the runs are intialized according to the conditions specified in the FREESTREAM keyword in the input data files (*.dat). These conditions are listed in Table 2. The static pressure varies for each run to achieve the desired Reynolds number. How the pressure is computed is discussed below.

Table 2. Freestream conditions. 
Mach number Temperature(R) Angle-of-Attack (deg)
0.05 460.0 0.0

Computation Strategy

The computations were performed using the time-marching capabilities of WIND to approach the steady-state flow starting from the freestream conditions.

Input Files and Computations

Table 3 below lists the name of the input data files for the three runs. The runs used the default input values for WIND. The computations were performed for a set number of iterations until that the convergence histories leveled out.

For all of the runs, we assume the gas in the box is ideal air (R = 1714.48 ft^2/(s^2*deg R) and ratio of specific heats = 1.4). The freestream conditions involved a Mach number of 0.05 and a static temperature 460 degrees Rankine. These (arbitrary) choices resulted in a freestream velocity of 52.56 ft/s, which was used as the velocity of the upper boundary wall in order for the freestream Reynolds number to be the same as the Reynolds number based on the wall velocity.

Assuming a viscosity determined by Sutherland's law and using a reference length of 1 inch, we get the following relation between Re and freestream pressure:

p_infty = (4.250e-04 lbf/in^2)*Re_infty

Thus the freestream pressure is used as a parameter which is chosen to reflect a desired Reynolds number (other parameters listed as well).

Table 3. Freestream static pressures. 
Run Static pressure (psia)
A 0.0425
B 0.17
C 1.3

Table 4. The input data files, CFL number, and number of iterations for each computation.
Run Reynolds Number Input Data File CFL Number Iterations CPU Time (sec)
A 100 cavity.A.dat 0.5 25000 29677.96
B 400 cavity.B.dat 1.5 11193 -
C 3200 cavity.C.dat 1.5 30000 162186.06

For each of the runs, WIND produces a listing file (.lis) and a solution file (.cfl). Note the list file for run B end prematurely, and so, the CPU times are not available. The files are listed below in Table 5.

Table 5. The output data files from the computations.
Run Reynolds Number List File L2 Residual CFL File PLOT3D Solution
A 100 cavity.A.lis cavity.A.resl2.gen cavity.A.cfl cavity.A.q.bin
B 400 cavity.B.lis cavity.B.resl2.gen cavity.B.cfl cavity.B.q.bin
C 3200 cavity.C.lis cavity.C.resl2.gen cavity.C.cfl cavity.C.q.bin

Convergence

The convergence histories of the L2 residual for each run can be obtained from the list files (*.lis), listed in Table 5 above, using the utility RESPLT. The GENPLOT files created can be viewed with CFPOST using the command

plot data cavity.A.resl2.gen

These GENPLOT files are listed in Table 5 above. Figure 3 below shows these convergence histories.

Figure 3 is described in the surrounding text
Figure 3. The plot of the convergence history for the
WIND computations of flow in the driven cavity.

Post-Processing

The CFPOST utility was used to generate the PLOT3D grid and solution files for each run. The PLOT3D grid and solution files are listed in Tables 1 and 5, respectively.,

cfpost < cfpost.A.com
cfpost < cfpost.B.com
cfpost < cfpost.C.com

Comparisons of the Results

A cursory comparison of these results was made with results from Ghia, Ghia, and Shin (Journal of Computational Physics, Vol. 48, pp. 387-411, 1982). Using an eyeball comparison, WIND appears to produce very similar solution results.

Figure 4 is described in the surrounding text
Figure 4. The plot of the mach number contours for the
driven cavity with a Reynolds number of 100.

Figure 5 is described in the surrounding text
Figure 5. The plot of the velocity vectors colored by
the Mach number near the upper right corner for the
driven cavity with a Reynolds number of 100.

Figure 6 is described in the surrounding text
Figure 6. The plot of the mach number contours for the
driven cavity with a Reynolds number of 400.

Performance

These runs were performed on a Silicon Graphics Indigo-2 with a IP22 processor running IRIX 5.3. The CPU times are listed above in Table 4. Note that the CPU time for run B was not available because the list file is incomplete.

References

Ghia, Ghia, and Shin, Journal of Computational Physics, Vol. 48, pp. 387-411, 1982.

Contact Information

This case was run on June 30, 1997 by Scott Dudek, a former NRC Research Associate at NASA Lewis who is no longer at NASA. Questions or comments about this case can be sent via email to Julianne Dudek at the NASA Lewis Research Center.
Last Updated: Tuesday, 08-Jul-2008 13:44:19 EDT