Bullet Parametric Optimization

The motivation behind this project was to begin familiarizing myself with supersonic flows and parametric optimization in ANSYS fluent CFD. Because this is a purely academic project, I greatly simplified the analysis and relaxed constraints so that the calculation didn't take too long (the solution will need to be evaluated 18 times for the parametric optimizations). This project will be consist of an radially symmetric flow so the analysis can be simplified to a 2D cross-section, this cross-section can be further simplified by assuming that that the flow is symmetric across the cross section. The geometry used can be seen in Figure 1, the dimensions are not specified because I somewhat arbitrarily assigned them; the purpose here is to get a general feel for the behavior of the software and not to actually design a final part.

After creating the initial geometry, the process of meshing began. I am familiar using the Fluid flow feature of SolidWorks which largely takes care of the meshing for the user, this is where the real advantages of using a more professional level software are apparent; in ANSYS one can get extreme control over the meshing, it is worth spending the extra time here so that the results converge properly. As you can see from Figure 2, the elements of the mesh I generated are all fairly un-deformed (the max skewness is 0.49517 and the standard deviation is 6.6157e-2), this was accomplished by applying several edge sizing constraints with a variety of specified number of divisions, behavior and bias. Overall the mesh seems good, it is fairly uniform in shape and quite dense around the areas of interest.

The results from the first analysis can be seen in Figure 3, the contour plot helps verify that the results appear to be valid compared to documented behavior. In the figure one can see the behavior of the detached shock front, although the angle is difficult to determine due to the curved geometry of the surface. I see strange behavior near the top of the wall and at the back along the center line, this is probably due to a incorrectly expressed boundary condition, although it is difficult to determine.

The next few diagrams show the setup for the parametric optimization, I chose this example on purpose because it is easy to visualize the relation between the changing geometry and drag force. As you can see, 18 different cases were tested with case 3 reaching a minimum value. The contour plots of case 3 can be seen in Figure 4. The drag force seemed to follow an order 2 polynomial trendline, but further cases would need to be evaluated to verify this. If this were a real world scenario, the next steps would be to chose some more points near this optimal point to increase the resolution of the cost function around those values, that way a truly optimal solution could be arrived at quickly.