cff - Puneet Kumar Department of Chemical Engineering IIT...

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Unformatted text preview: 3/8/2007 Puneet Kumar, Department of Chemical Engineering, IIT Madras 1 Compressible Fluid Flow Presented By : Puneet Kumar Department of Chemical Engineering Indian Institute of Technology Madras Tutor : Dr. Sanjay Mittal Indo ‐ German Winter Academy 2006 3/8/2007 Puneet Kumar, Department of Chemical Engineering, IIT Madras 2 Contents • Compressible flow – History • Basics of Compressible flow • Speed of Sound • A Brief Review of Thermodynamics • Propagation of sound source • Shock waves and Normal shock • Oblique Shock • Summary 3/8/2007 Puneet Kumar, Department of Chemical Engineering, IIT Madras 3 Historical Prospective • Convergent – divergent steam nozzles of ‘ de-Laval ’ • Advent of jet propulsion and high speed flights as ‘ Bell XS-1 ’ • Dealing with high temperature, chemical reactive gases associated with rocket engines 3/8/2007 Puneet Kumar, Department of Chemical Engineering, IIT Madras 4 Compressible flow • Compressible flow – Variable density flow • Compressibility of fluid • Gas velocities less than 0.3 of the speed of sound are considered as incompressible flow • Compressible flows are high energy flow • Shock waves in all disturbed supersonic flows • Examples : High speed airplanes and jet engines 1 1 dv d v dp dp ρ τ ρ = − = − 3/8/2007 Puneet Kumar, Department of Chemical Engineering, IIT Madras 5 Flow Regimes • Subsonic Flow – Flow velocity everywhere less than the speed of sound • Transonic Flow – Flow velocity is close to the speed of sound • Supersonic Flow – Flow velocity is everywhere greater than the speed of sound • H y p e r s o n i c F l o w – Properties of flow increases explosively across the shock wave 3/8/2007 Puneet Kumar, Department of Chemical Engineering, IIT Madras 6 Basic Conservation Equations Conservation Equations Three Fundamental Principles Models of Flow Continuity equation Momentum equation Energy equation Some Applications 3/8/2007 Puneet Kumar, Department of Chemical Engineering, IIT Madras 7 Balance Equations • Continuity equation • Momentum equation • Energy equation V. S V dS dV t ρ ρ ∂ − = ∂ ∫∫ ∫∫∫ u r u r   ( V ) (V. ) V vis S V V S dS dV f dV pdS F t ρ ρ ρ ∂ + = − + ∂ ∫∫ ∫∫∫ ∫∫∫ ∫∫ ur ur uur ur ur ur     2 2 (V. ) ( .V) V V ....
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cff - Puneet Kumar Department of Chemical Engineering IIT...

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