16100lectre37_cj

# 16100lectre37_cj - method Let’s look at what happens...

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Critical Mach Number We can estimate the freestream Mach number at which the flow first accelerates above 1 > M (locally) using the Prandtl-Glauert scaling and isentropic relationships. Recall from P-G: If we have ) 0 ( = M C p say from an incompressible panel solution, we could then find p C anywhere on the airfoil for higher M under the assumptions of P-G (linearized flow, ) 1 < M . We can also use isentropic relationships: + + = = 1 ) 1 ( 2 1 1 ) 1 ( 2 1 1 2 ) 1 ( 2 1 2 2 2 2 γ M M M C p p M C p p The p C for 1 = M at a given M is: This critical freestream M occurs when ). ( ) ( cr p cr p M C M C crit G P = This critical M can be found graphically or can be solved for with a root-finding

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Unformatted text preview: method. Let’s look at what happens graphically: 2 1 ) ( ) ( ∞ ∞ ∞ − = = M M C M C p p On the airfoil surface: ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − + − + = = = − ∞ ∞ ∞ 1 ) 1 ( 2 1 1 ) 1 ( 2 1 1 2 ) , 1 ( 1 2 2 M M M M C C p p crit Critical Mach Number 16.100 2002 2 1. Find minimum p C at = ∞ M 2. Plot G P p C − min vs. ∞ M 3. Plot crit p C from isentropic relationships p C − min p C crit p C cr M ∞ M...
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16100lectre37_cj - method Let’s look at what happens...

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