1. HIGH SPEED FLOW 1 st Semester 2007 Pawarej CHOMDEJ fengpac@ku.ac.th 081 832 7854 05-Jun-071

2. Course Outline 1.Introduction to compressible flows 2.Normal Shock Waves 3.Oblique Shock Waves 4.Prandtl - Mayer Flow 5.Application Involving Shocks and Expansion Fans 6.Flow with Friction 7.Flow with Heat Transfer ------------------------ Midterm Examination ------------------------ 8.Linearized Compressible Flow 9.Airfoils in Compressible Flows 05-Jun-072

3. Course Outline 10.Wings and Wing-Fuselage Combinations in Compressible Flows 11.Method of Characteristics 12.Computational Gas Dynamics 13.Hypersonic Flows 05-Jun-073

4. Course assessment Attendance, Presentation, Quiz and Homework 40 points – Attendance 10 points – Presentation10 points – Homework20 points Midterm examination30 points Final examination30 points 05-Jun-074

5. Introduction to compressible flows Compressible flow – Review of thermodynamics – Total (Stagnation) conditions Isentropic flow Supersonic flow Shock waves – Definition – Characteristics 05-Jun-075

6. Introduction to compressible flows Review of thermodynamics – The first law of thermodynamics  q +  w = de – For a reversible process  q - pd  = de – Internal Energy and Enthalpy Internal energy e = C υ T Enthalpy h = e + P υ = C p T Specific heat 05-Jun-076

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 V dV P 05-Jun-077

8. Introduction to compressible flows Entropy – Area under T-s diagram = Heat Transfer (Q) – Reversible process – Specific entropy s, J/(kg K) T s ds T OR 05-Jun-078

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 05-Jun-079

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 s ds = 0 05-Jun-0710

11. Introduction to compressible flows Exercise 1) A perfect gas is expanded adiabatically from 5 to 1 bar by the law PV 1.2 = Constant. The initial temperature is 200°C. Calculate the change in specific entropy. R = 287.15 J/kgK,  =1.4 05-Jun-0711

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 h0T0P0h0T0P0 h0T0P0h0T0P0 05-Jun-0712

13. Introduction to compressible flows Isentropic relation – For and adiabatic, reversible process with so 05-Jun-0713

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 V1V1 V 2 = 0 05-Jun-0714

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 h 0 = const (h 01 = h 02 ) – Steady, inviscid, adiabatic flow T 0 = const – Isentropic flow P 0 = const and ρ 0 = const (Slow down adiabatically and reversibly) For a calorically perfect gas, h 0 = C P T 0 or h = C P T h 01 h 02 h1h1 h2h2 05-Jun-0715

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/m 3 and 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. 05-Jun-0716

17. Introduction to compressible flows Compressible flow – Density changes IncompressibleCompressible ρ constantρ varies 05-Jun-0717

18. Introduction to compressible flows Compressibility – Measure of the relative volume change with pressure P P+dp 05-Jun-0718

19. Introduction to compressible flows Compressibility P+ dp P P Incompressible Flow Compressible Flow 05-Jun-0719

20. Introduction to compressible flows – Entropy – Isentropic Relations – Compressibility M < 0.3 : Incompressible flow M > 0.3 : Compressible flow 05-Jun-0720