ch94 - Chapter 9: Compressible Flow 9.1 9.2 9.3 9.4 9.5 9.6...

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Chapter 9: Compressible Flow 9.1 Introduction: Review of Thermodynamics 9.2 The Speed of Sound 9.3 Adiabatic and Isentropic Steady Flow 9.4 Isentropic Flow with Area Changes 9.5 The Normal Shock Wave 9.6 Operation of a Converging and Diverging Nozzles
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Ch.9 – HOW DO FLUID PROPERTIES TO CHANGE IN A 1-D COMPRESSIBLE FLOW? (note if isentropic stagnation properties do not change) (other thermodynamic properties: c v , c p , µ, k)
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Ch.9 - WHAT CAUSES FLUID PROPERTIES TO CHANGE IN A 1-D COMPRESSIBLE FLOW? (note if isentropic stagnation properties do not change) (other thermodynamic properties: c v , c p , µ, k)
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Ch.12 - COMPRESSIBLE FLOW Flow can be affected by: Q Q friction shock shock area change, shock, friction, heat transfer for adiabatic, steady flow T o , h o , a o are constant along streamline for isentropic flow ρ o and p o are constant along a streamline V max = (2c p T o ) 1/2 if no shaft work or heat added
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ASSUMPTIONS ALWAYS ~ Steady Flow Ideal Gas c v and c p are constant Ignore Body Forces No Shaft Work “Quasi - One – Dimensional” MOSTLY ~ Isentropic (adiabatic and reversible: no gradients, no heat tranfer, no shear work, no shaft work) A R E A C H A N G E
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V(s) V(x,y) “quasi-one-dimensional” One - Dimensional Two - Dimensional use one-dimensional theory regrdless because of its simplicity” no viscosity
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“quasi-one-dimensional” Flow properties are uniform across any given cross section of area A(x), and that they represent values that are some kind of mean of the actual flow properties distributed over the cross section. NOTE – equations that we start with are exact representation of conservation laws that are applied to an approximate physical model
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White: pgs 624-625 dV/V = (dA/A)(M 2 -1) -1 = -dp/( ρ V 2 ) (9.40) DERIVED FROM CONTINUITY and FRICTIONLESS MOMENTUM EQUATION Property changes are opposite sign for subsonic and supersonic flow because of the term M 2 -1
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Affect of Change in Area on Pressure and Velocity Isentropic, steady, no body forces, quasi-one-dimensional
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EQ. 9.31 – Cons. of Mom. EQ.9.37 – Cons. of Mass steady & isentropic {d ρ (AV) + dA( ρ V) +dV( ρ A)}/{ ρ AV} = 0
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isentropic, steady Eq. (9.40)
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EQ. (9.40) isentropic, steady EQ. (9.39) EQ. (9.40)
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