Hypersonic Flow on the X-34 with Adaptive Mesh Refinement
Emprexx uses the latest version of CD-adapco’s Navier Stokes Solver STAR-CCM+ for Computational Fluid Dynamics (CFD) calculations. Whenever there’s a little down time, we like to keep the solver running on problems which expand both our knowledge and our validation database for the code. One good example of this is the NASA X-34 Vehicle. The X-34 was a technology demonstrator intended to help develop the reusable launch vehicle technology by making frequent hypersonic, sub-orbital hops followed by a fast turn-around. A lot of wind tunnel testing was done on the vehicle, which unfortunately never flew after funding priorities changed.
For this CFD experiment, Emprexx decided to test the CCM+ adaptive mesh refinement capability at a Mach 6, 15° angle of attack re-entry condition for the X-34 and compare the resulting shock angles to the Schlieren images given in AIAA-98-0881.
Initial Mesh Generation
Normally CFD mesh generation provides maximum refinement (smallest size) only at the areas of high curvatures near the vehicle, and then the cell sizes grow with distance into the free stream. For subsonic flows, this works well and the quickly growing cell sizes keep memory and CPU requirements reasonable. This approach provides the initial mesh for the X34 as shown in Figure 1, which is a Cartesian off-body mesh with trimmed cells at the body interface.
However, for hypersonic flow there is a detached shock, like the bow wave of a boat. Since aerodynamics change very quickly across a shock (by definition), and since the propagation of the shock into the far field affects the accuracy of the solution, it will be necessary to refine the off-body mesh to capture the shock in 3D.
Mesh Refinement
In order to place more cells in the location of the shock, a CCM+ “user defined field function” was created, which marked all the grid cells in the volume solution with Mach 5.88 to 5.99 – i.e. just below the free stream Mach number. In the initial very coarse off-body grid, this results in the big blocky blue cells shown in Figure 2, which is a 2D section taken at the centerline of the volume mesh. The mesher was then re-run with a small cell size refinement dictated by the field function, the solution re-started and converged to a sharper shock in the far field. The entire process was repeated a second time to finally arrive at the off-body mesh with localized refinement along the major shocks as shown in Figure 3. Because the solution could be interpolated to the new mesh and restarted each time, the additional run times as the mesh density increased were significantly reduced from a ‘clean start’ condition.
Shock Angles and Experimental Data
The real check on the method comes with comparison to experimental data. This was done by over-laying the CFD side view against the Schlieren images published in AIAA-98-0881, as shown in Figure 4. While the CFD is a 2D slice through a 3D solution, the Schieren is 3D, but the strongest shocks are still going to be the nose in the 2D plane allowing for easy comparison to the CFD solution. The upper shock angle shows a very nice correlation with the computational result, and the lower shock angle is very close, less than two degrees difference, as shown by the red circles. The final image shows the 3D nature of the full solution by putting Mach contours on a series of six cut planes along the body.
