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					    Numerical Investigation of
Supersonic Flow Over a Blunt Body
       RPI Master’s Project Proposal

         Noel A. Modesto-Madera
           September 28, 2010
                        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

For this project, we seek to solve numerically the problem of a cylinder
moving on air at supersonic speeds.
                         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.
                 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.
                       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.
                        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

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