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HIGH SPEED FLOW

HIGH SPEED FLOW. 1 st Semester 2007 Pawarej CHOMDEJ fengpac@ku.ac.th 081 832 7854. Course Outline. Introduction to compressible flows Normal Shock Waves Oblique Shock Waves Prandtl - Mayer Flow Application Involving Shocks and Expansion Fans Flow with Friction Flow with Heat Transfer

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HIGH SPEED FLOW

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  1. HIGH SPEED FLOW 1st Semester2007 Pawarej CHOMDEJ fengpac@ku.ac.th 081 832 7854

  2. Course Outline • Introduction to compressible flows • Normal Shock Waves • Oblique Shock Waves • Prandtl - Mayer Flow • Application Involving Shocks and Expansion Fans • Flow with Friction • Flow with Heat Transfer ------------------------ Midterm Examination ------------------------ • Linearized Compressible Flow • Airfoils in Compressible Flows

  3. Course Outline • Wings and Wing-Fuselage Combinations in Compressible Flows • Method of Characteristics • Computational Gas Dynamics • Hypersonic Flows

  4. Course assessment • Attendance, Presentation, Quiz and Homework 40 points • Attendance 10 points • Presentation 10 points • Homework 20 points • Midterm examination 30 points • Finalexamination 30 points

  5. Introduction to compressible flows • Compressible flow • Review of thermodynamics • Total (Stagnation) conditions • Isentropic flow • Supersonic flow • Shock waves • Definition • Characteristics

  6. Introduction to compressible flows • Review of thermodynamics • The first law of thermodynamics q + w = de • For a reversible process q - pd = de • InternalEnergy and Enthalpy • Internal energy e = CυT • Enthalpy h = e + P υ = CpT • Specificheat

  7. Introduction to compressible flows • Entropy • Theory of work laws in closed system • 2 Forms of energy transfer : Work and Heat • Area under Pressure-Volume diagram = Work (W) • Reversible expansion or compression P P dV V

  8. Introduction to compressible flows • Entropy • Area under T-s diagram = Heat Transfer (Q) • Reversible process • Specific entropy s , J/(kg K) T T ds s OR

  9. Introduction to compressible flows • The second law of thermodynamic (Irreversible process) • From the first law Tds = dh - dP = de +pd • Entropy change of a calorically perfect gas between two states or

  10. Introduction to compressible flows • Isentropic Processes • Isentropic → Constant Entropy • Reversible and Adiabatic process • No heat transfer to or from fluid dQ = 0 • Application in steady systems for gasses and vapors T ds = 0 s

  11. Introduction to compressible flows • Exercise • 1) A perfect gas is expanded adiabatically from 5 to 1 bar by the law PV1.2 = Constant. The initial temperature is 200°C. Calculate the change in specific entropy. R = 287.15 J/kgK,  =1.4

  12. Introduction to compressible flows • Isentropic Flow • Adiabatic and Reversible • No energy added, No energy losses • Small an gradual change in flow variables • ds = 0 h0 T0 P0 h0 T0 P0

  13. Introduction to compressible flows • Isentropic relation • For and adiabatic, reversible process with so

  14. Introduction to compressible flows • Total (Stagnation) conditions : • A point (or points) in the flow where V = 0. • Fluid element adiabatically slow down • A flow impinges on a solid object V1 V2 = 0

  15. Introduction to compressible flows • From Energy Equation and the first law of thermodynamics • Total enthalpy = Static enthalpy + Kinetic energy (per unit mass) • Steady and adiabatic flow h0 = const (h01 = h02) • Steady, inviscid, adiabatic flow T0 = const • Isentropic flow P0 = const and ρ0 = const (Slow down adiabatically and reversibly) • For a calorically perfect gas , h0 = CPT0or h = CP T h01 h02 h1 h2

  16. Introduction to compressible flows • Question • 2) Consider a point in a flow where the velocity and temperature are 230m/s and 375K respectively. Calculate the total enthalpy at this point. • 3) An airfoil is in a freestream where P∞ = 0.75 atm, ρ∞ = 0.942 kg/m3and V∞ = 325 m/s. At a point on the airfoil surface, the pressure is 0.62 atm. Assuming isentropic flow, calculate the velocity at the point.

  17. Introduction to compressible flows • Compressible flow • Density changes FLUIDS Incompressible Compressible ρ constant ρ varies

  18. Introduction to compressible flows • Compressibility • Measure of the relative volume change with pressure P+dp P υ υ+dυ

  19. Introduction to compressible flows • Compressibility Incompressible Flow P P P+ dp υ υ υ Compressible Flow P+dp υ

  20. Introduction to compressible flows • Entropy • Isentropic Relations • Compressibility • M < 0.3 : Incompressible flow • M > 0.3 : Compressible flow

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