EML 5725 Computational Fluid Dynamics Spring 2003
Final Project

There is no working together on this project. Upon suspicious similarities between projects, the F grade will be assigned to all parties involved. See the instructor with questions.

Due: Noon, Wednesday, April 30

Write a program that solves the supersonic flow around a cone of semi-apex angle degrees moving through air at standard conditions with Mach number (cone velocity divided by speed of sound) equal to three. Use SI units.

• The input file to start with is available on the web
• Use computational coordinates , if is the cylindrical coordinate system with origin at the cone apex and positive z-axis along the cone axis.
• Initialize the mesh points at z=1 with the incoming flow values of velocity, density, and pressure. Correct the wall velocity by eliminating its component normal to the wall. Compute toward larger z until the flow becomes conical. In the predictor step, use backward differences, and forward in the corrector step.
• My data show that the shock angle should be a couple of degrees more than the Mach angle of the incoming flow. The pressure on the wall should be about 34.3% more than ambient, and the Mach number on the wall 2.80.
• Program and results must be very neat, easy to read by anyone normally knowledgeable, well commented, complete, use an input file to set all variables, instead of recompilation, check all input variables, good variable names, well indented, lines broken if more than 70 characters long, use blank lines to logically group things, everything explained in clear comments, no typos, etc, or significant credit will be lost.
• Use the in class symbols and names for all variables whenever possible. Use the class ordering (continuity, z-momentum, r-momentum for the equations, z, r for the independent variables.)
• I found it useful to store the vectors as well as the transformed vectors .
• Wasting storage or operations (more than a finite factor above that really required) will significantly reduce credit.
• Attach a neat complete set of formulae implemented in your program and a discussion of the results obtained.
• Output file should show all input variables and all meaningful results. No dumps of raw numbers in output file! Every number should be worthwhile to read, and no important data should be missing.
• Plot the nondimensional presssure (ratio of pressure over incoming pressure), the Mach number, the nondimensional temperature, and the nondimensional density as a function of the angle from the axis for the final conical flow.

Speed of sound, enthalpy, and ideal gas law are:

The Mach lines make an angle with the z-axis equal to , where is the angle of the local velocity with the z-axis and the local Mach angle: