HIGH SPEED FLOW

1st Semester 2007 Pawarej CHOMDEJfengpac@ku.ac.th

081 832 7854

05-Jun-07 1

Course Outline

1. Introduction to compressible flows2. Normal Shock Waves3. Oblique Shock Waves4. Prandtl - Mayer Flow5. Application Involving Shocks and Expansion Fans6. Flow with Friction7. Flow with Heat Transfer ------------------------ Midterm Examination ------------------------8. Linearized Compressible Flow9. Airfoils in Compressible Flows

05-Jun-07 2

Course Outline

10. Wings and Wing-Fuselage Combinations in Compressible Flows

11. Method of Characteristics12. Computational Gas Dynamics13. Hypersonic Flows

05-Jun-07 3

Course assessment

• Attendance, Presentation, Quiz and Homework 40 points– Attendance 10 points– Presentation 10 points– Homework 20 points

• Midterm examination 30 points• Final examination 30 points

05-Jun-07 4

Introduction to compressible flows

• Compressible flow– Review of thermodynamics– Total (Stagnation) conditions

• Isentropic flow• Supersonic flow• Shock waves– Definition– Characteristics

05-Jun-07 5

Introduction to compressible flows

05-Jun-07 6

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

dVP

05-Jun-07 7

Introduction to compressible flows

• Entropy– Area under T-s diagram = Heat Transfer (Q)

– Reversible process– Specific entropy s , J/(kg K)

T

s

dsTOR

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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-07 9

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-07 10

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

05-Jun-07 11

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

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Introduction to compressible flows

• Isentropic relation– For and adiabatic, reversible process

with

so

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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

05-Jun-07 14

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 = CPT0 or h = CP T

h01 h02

h1 h2

05-Jun-07 15

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/m3 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.

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Introduction to compressible flows

• Compressible flow– Density changes

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Introduction to compressible flows

• Compressibility– Measure of the relative volume change with

pressureP

P+dp

05-Jun-07 18

Introduction to compressible flows

• Compressibility

P+ dp

P

P+dp

P

Incompressible Flow

Compressible Flow

05-Jun-07 19

Introduction to compressible flows

– Entropy

– Isentropic Relations

– Compressibility

• M < 0.3 : Incompressible flow• M > 0.3 : Compressible flow

05-Jun-07 20