lectures-chapter8

# lectures-chapter8 - 650:460 Aerodynamics Chapter 8 Prof...

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Unformatted text preview: 650:460 Aerodynamics Chapter 8 Prof. Doyle Knight Tel: 732 445 4464, Email: [email protected] Office hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment Fall 2009 1 Thermodynamic Concepts Specific Heats • The internal energy of a perfect gas is defined by u e = c v T where c v is the specific heat at constant volume • The static enthalpy of a perfect gas is defined by h = c p T where c p is the specific heat at constant pressure 2 Second Law of Thermodynamics Entropy • The Second Law of Thermodynamics applied to an adiabatic process is ds ≥ where s is the entropy per unit mass of the fluid • For a perfect gas, the change in entropy between two states s 2- s 1 = c v log braceleftbiggbracketleftbiggparenleftbigg ρ 1 ρ 2 parenrightbigg γ bracketrightbigg p 2 p 1 bracerightbigg • For an isentropic flow p 2 p 1 = parenleftbigg ρ 2 ρ 1 parenrightbigg γ 3 Speed of Sound Fig. 8.1 4 Speed of Sound Mach Cone • In supersonic flow, the disturbance is restricted to the Mach cone defined by sin μ = 1 M where M is the Mach number M = U a and a = radicalbigg γ p ρ = radicalbig γ RT where R is the gas constant for the specific fluid 5 Adiabatic Flow in Variable Area Streamtube Conservation of energy p 1 U 1 A 1- p 2 U 2 A 2 =- ( u e 1 ρ 1 U 1 A 1 + 1 2 U 2 1 ρ 1 U 1 A 1 ) + ( u e 2 ρ 2 U 2 A 2 + 1 2 U 2 2 ρ 2 U 2 A 2 ) Fig. 8.3 6 Adiabatic Flow in Variable Area Streamtube The static enthalpy h and total enthalpy H are defined as h = u e + p ρ H = h + 1 2 U 2 The conservation of energy becomes ρ 1 U 1 A 1 ( h 1 + 1 2 U 2 1 ) = ρ 2 U 2 A 2 ( h 2 + 1 2 U 2 2 ) Fig. 8.3 7 Adiabatic Flow in Variable Area Streamtube The conservation of mass is ρ 1 U 1 A 1 = ρ 2 U 2 A 2 and therefore the conservation of energy becomes h 1 + 1 2 U 2 1 bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright H 1 = h 2 + 1 2 U 2 2 bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright H 2 Fig. 8.3 8 Adiabatic Flow in Variable Area Streamtube For a perfect gas c p T 1 + 1 2 U 2 1 = c p T 2 + 1 2 U...
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lectures-chapter8 - 650:460 Aerodynamics Chapter 8 Prof...

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