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Unformatted text preview: Fluids – Lecture 20 Notes 1. Laval Nozzle Flows Reading: Anderson 10.3 Laval Nozzle Flows Subsonic ﬂow and choking Consider a duct with a throat, connected at its inlet to a very large still air reservoir with total pressure and enthalpy p r , h r . The duct exit is now subjected to an adjustable exit static pressure p e , sometimes also called the back pressure . As p e is gradually reduced from p r , air will ﬂow from the reservoir to the exit with a mass ﬂow ˙ m . We first note that the stagnation conditions are known from the reservoir values all along the duct. γp o γp r 2 p o = p r , a = ( γ − 1) h o = ( γ − 1) h r , ρ o = = o ( γ − 1) h o ( γ − 1) h r If we assume isentropic ﬂow, ˙ m can be computed with the isentropic relations applied at the exit, using the known exit pressure p e and known exit area A e . M γ − 1 2 = ( p o /p e ) γ − 1 2 e γ − 1 γ +1 γp o γ − 1 M 2 2( γ − 1) − ˙ m = ρ e u e A e = M e 1 + 2 e A e (1) ( γ − 1) h o The observed relation between p e and ˙ m is shown on the bottom right in the figure. As p e is reduced, ˙ m will first increase, but at some point it will level off and remain constant even if p e is reduced all the way to zero (vacuum). When ˙ m no longer increases with a reduction in p e , the duct is said to be choked . M u ρ throat ρ * * p p r p r 0 m . choked x x p * 1 p e p h e p < p r r large reservoir m . M a throat 1 1 p e r If we examine the various ﬂow properties along the duct, it is evident that the onset of choking cooincides with the throat reaching M = 1 locally. This also corresponds to the 1 ∗ mass ﬂux...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05