650:433 Mechanical Engineering Laboratory – Aerospace Option
Lab 5 – Supersonic Wind Tunnel
Data Analysis
DATA ANALYSIS TOOLS
Sphere in Supersonic Flow
Instructions for Sphere: A MATLAB code has already been used to extract the shock
shape from an image. That data has been entered in the EXCEL spreadsheet. Change the
Mach number on the comparison worksheet to determine the best fit Mach number. The
two parameter model allows for two estimates of the Mach number. The two parameters
are shock standoff distance (distance from shock to front of sphere, /R) and the local
radius of curvature of the shock (related to the far-field Mach angle, Rc/R). Compare the
accuracies of determining the Mach number from the shock standoff distance and radius
of curvature (overall fit of the experimental data to the theoretical curve). Which method
provides better sensitivity to the Mach number? Can you quantify this sensitivity?
Billig, F. S., "Shock Wave Shapes Around Spherical and Cylindrical Nosed Bodies," Journal of
Spacecraft and Rocketry, Vol. 4, No. 6, June 1967, pp. 822-823.
Wedges in Supersonic Flow
Instructions for Wedge: The spreadsheet file has the reduced data from the experiment.
Twenty-nine image files were analyzed to extract the angle of attack (theta), angle of
shock wave on wedge upper surface (beta_upper), and the angle of the shock wave on the
lower surface (beta_lower). A MATLAB file is used to compute the theoretical angles of
the shock/expansion waves on the surface of your wedge. The wedge half angle ()
should be 15 degrees. You should run the MATLAB file and copy its output into the
EXCEL Spreadsheet. The easiest way is to open the file that the MATLAB program
creates (wedgeangle.txt, the column are theta, beta_lower, and beta_upper respectively)
with Wordpad or Microsoft Word and then copy the data in the EXCEL Spreadsheet.
You will need to find the Mach number which fits your data the best. Can you fit both the
all portions of the curve simultaneously? How sensitive is this measurement of the Mach
number?
Pressure Ratio Analysis
Use the spreadsheet given, which has the stagnation and static pressures recorded as a
function of time, to calculate the theoretical Mach number in the test section.
Mach Wave Analysis
Take any of the images given and measure the angle of the Mach waves with respect to
the oncoming flow. Use the simple relation for Mach angle give in the handout to
determine the Mach number.