lecture7 - MECH 6251/498D Ideal Nozzle Theory The nozzle...

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MECH 6251/498D
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Combustion process was modeled as a heat addition of q R , resulting in a combustion chamber temperature of T o . The nozzle was modeled as, 1-D, steady-state isentropic flow. Ideal Nozzle Theory Combine all these effects to determine the rocket thrust
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Thrust depends on altitude due to P For launch vehicles, pressure thrust can change a large amount over the firing duration due to large atmospheric pressure changes Maximum thrust occurs in vacuum, since P = 0 Specific impulse: e e e A P V m T + = & m A p p V g I c e e e sp & ) ( 0 + = = m g A p p g V m g F I e a e o e sp & & 0 0 ) ( + = = Effective exhaust velocity: This relation indicates that the effective exhaust velocity increases above the exit velocity if the pressure thrust is positive. Thrust Analysis F = m e V e + p e A e p A e ()
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Rocket Thrust Equation • Non-dimensionalize as • For a choked throat m A * P 0 = 1 T 0 γ R g 2 γ+ 1 + 1 1 () Thrust = m V exit + A exit ( p exit p ) Thrust P 0 A throat = m V exit P 0 A throat + A exit A throat ( p exit p ) P 0 Thrust P 0 A * = V exit T 0 R g 2 1 + 1 1 + A e A * ( p exit p ) P 0
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Rocket Thrust Equation • For isentropic flow • Also for isentropic flow V exit = 2 c p T 0 exit T exit = 2 c p T 0 exit 1 T exit T 0 exit 1/2 p 2 p 1 = T 2 T 1 γ 1 Thrust P 0 A * = V exit T 0 R g 2 γ+ 1 + 1 1 () + A e A * ( p exit p ) P 0 T exit T 0 exit = p exit P 0 exit −1 The term 2C p T o is the stagnation enthalpy per unit mass in the combustion chamber (comes from the combustion process for chemical rockets, or heat addition from nuclear rockets). To maximize performance, you would like the term (1 - T e / T o ) to be as close to 1 as possible. This can never be, though, because T e cannot go to zero. Therefore, you can never get complete conversion of thermal energy to kinetic energy in a rocket engine.
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Rocket Thrust Equation • velocity equation becomes • Substituting the above equation into the thrust equation V exit = 2 c p T 0 exit T exit = 2 c p T 0 exit 1 p exit P 0 exit γ −1 1/2 Thrust p 0 A * = 2 c p T 0 exit 1 p exit P 0 exit T 0 R g 2 γ+ 1 + 1 1 () + A exit A * ( p exit p ) P 0 = 1 p exit P 0 exit 2 c p R g 2 1 + 1 1 + A exit A * ( p exit p ) P 0
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Rocket Thrust Equation 2 c p γ R g = 2 c p c p c v = 2 1 1 = 2 2 γ− 1 • Finally, for an isentropic nozzle • Simplifying P 0 exit = P 0 • Non-dimensionalized thrust is a function of Nozzle pressure ratio and back pressure only Thrust P 0 A * = γ 2 1 2 γ+ 1 + 1 1 () 1 p exit P 0 −1 1/2 + A exit A * ( p exit p ) P 0 Eq. 3-29 Sutton & Biblarz
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Ideal I sp
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This note was uploaded on 12/12/2010 for the course MECH 351 taught by Professor Chekhov during the Fall '10 term at Concordia Canada.

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lecture7 - MECH 6251/498D Ideal Nozzle Theory The nozzle...

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