1. RPI Master’s Project Proposal Noel A. Modesto-Madera September 28, 2010 Numerical Investigation of Supersonic Flow Over a Blunt Body

2. Project Overview One of the most studied problems in fluid dynamics is that of a supersonic flow over a blunt body. The reasons for this collective interest may be that this problem is related very closely to the NASA space program in the 1950’s and 1960’s. The shape of the return capsules resemble that of a blunt body. For this project, we seek to solve numerically the problem of a cylinder moving on air at supersonic speeds.

3. Problem Statement An infinite cylinder moves through air at supersonic speeds. A bow shock develops at the front of the cylinder. Find: 1- The shape of the bow shock 2- The standoff distance of the bow shock 3- The static pressure distribution at the surface of the cylinder. 4- The relationship between upstream Mach number and shape of the bow shock, standoff distance and static pressure distribution at the surface of the cylinder. 5- The effects of using a different gas instead of air.

4. Methodology and Approach The geometry (physical bounds) of the problem is defined. The volume occupied by the fluid is divided into discrete cells. Boundary conditions are specified at the volume boundaries. The simulation is carried out in a computer for several different upstream Mach numbers. The results of the simulations are compared to experimental data found in the literature.

5. Expected Outcomes A working two dimensional Euler equation solver capable of resolving the bow shock wave location and geometry. The solver has to be validated using experimental data. It would be desirable for the solver to be written in a general way so that it can be used for other two dimensional problems of compressible flow. Post-processing tools written in Matlab to visualize the results.

6. Project Schedule 09/28/2010: Project Proposal Due 10/ 05/2010: Finish literature search and have LaTex environment working 10/ 12/2010: Digitize data and finish implementation of the grid generator 10/19/2010: First Progress Report 10/ 26/2010: Computer Program Implementation of Solver Completed 11/ 02/2010: Validate Computer Program with Data 11/09/2010: Second Progress Report & Brief Presentation of Progress 11/16/2010: First draft of document in LaTex 11/23/2010: Second draft of document in LaTex 11/30/2010: Final Draft Due 12/07/2010: Final draft of document in LaTex 12/14/2010: Final Report Due & Comprehensive Presentation of Work