Drew Rosecrans
Lab 3
Abstract
Pressure measurements and schlieren images were taken on a diamond airfoil
with a 10° half angle, in flows between Mach 2 and 3, with angles of attack between 0
and 8. The differences from the pressure measurements were greater than expected
and can be attributed to the carryover of the error between the two top or bottom
surfaces. Also there is certainly experimental error. The schlieren images showed
important characteristics of the flow at different Mach numbers and angles of attack.
Introduction
The diamond airfoil is a very simple airfoil and thus it can be the basis of future
studies to compare. It is important to understand how this simple airfoil behaves in
supersonic flow at different Mach numbers and different angles of attack. It might be
counter intuitive on what is going on in the flow, so it is useful to take images and
measurements of the flow to make sure it is known what is happening in it. Also the
comparing the measured values to the calculated values will give some insight on how
accurate our assumptions can be in the real world.
Theory
To find the pressure drop over the bow shock on the diamond airfoil, the oblique
shock theory is used. This theory depends on the turning angle, theta, that the flow
must turn and the Mach number, M, of the freestream. Here is a diagram explaining the
oblique shock.
The diamond airfoil used here is has a half angle of 10°. Theta is related to the angle of
attack of the airfoil.
1
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Drew Rosecrans
Lab 3
With theta and the freestream Mach number known, beta, the oblique shock angel, can
be found using the thetabetaM chart. Once beta is known, geometry is used to find the
portion of the Mach number that is normal to the oblique shock
=
∞
M1n
M
sinβ
Now with M1n, the normal shock table can be used to find the Mach number after the
shock, M2n, and the static pressure ratio over the shock, P2/P1. Using the static
pressure before the shock the pressure after the shock, P2, can be found, which is the
pressure at the surface of the airfoil. Now M2 can be found using this equation.
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 Fall '10
 Staff
 Fluid Dynamics, Aerodynamics, Mach number, Shock wave, rew Rosecrans, schlieren images

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