HIGH SPEED FLOW 1 st Semester 2007 Pawarej CHOMDEJ [email protected] 081 832 7854 05-Jun-071.
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Transcript of HIGH SPEED FLOW 1 st Semester 2007 Pawarej CHOMDEJ [email protected] 081 832 7854 05-Jun-071.
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
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Introduction to compressible flows
• Entropy– Area under T-s diagram = Heat Transfer (Q)
– Reversible process– Specific entropy s , J/(kg K)
T
s
dsTOR
05-Jun-07 8
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.
05-Jun-07 16
Introduction to compressible flows
• Compressible flow– Density changes
05-Jun-07 17
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