lec34 - Aerodynamics Lecture 34 Subsonic Compressible Flow...

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Aerodynamics Subsonic Compressible Flow: Velocity Potential Equation 34.1 Lecture 34 Aerodynamics Subsonic Compressible Flow AE311 Aerodynamics Manoj T. Nair IIST
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Aerodynamics Subsonic Compressible Flow: Velocity Potential Equation 34.2 Agenda 1 Subsonic Compressible Flow: Velocity Potential Equation
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Aerodynamics Subsonic Compressible Flow: Velocity Potential Equation 34.3 Subsonic Compressible Flow: Velocity Potential Equation I Velocity Potential Equation Consider 2D, steady, irrotational, isentropic flow A velocity potential can be defined φ = φ ( x , y ) V = φ u = ∂φ x ; v = ∂φ y Let us obtain an equation for φ which represents a combination of the continuity, momentum and energy equations
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Aerodynamics Subsonic Compressible Flow: Velocity Potential Equation 34.4 Subsonic Compressible Flow: Velocity Potential Equation II The continuity equation for steady, 2D flow is ( ρ u ) x + ( ρ v ) y = 0 ρ u x + u ∂ρ x + ρ v y + v ∂ρ y = 0 Substituting using definition of φ , we get ρ 2 φ x 2 + ∂φ x ∂ρ x + ∂φ y ∂ρ y + ρ 2 φ y 2 = 0 ρ 2 φ x 2 +
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