# chap4_65_70 - AAE 439 Exhaust Plume Pattern Perfectly...

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Unformatted text preview: AAE 439 Exhaust Plume Pattern Perfectly Expanded Flow: pe = pa Underexpanded Flow: pe > pa We obtain no pressure thrust. We obtain positive pressure thrust. Overexpanded Flow: pe < pa We obtain negative pressure thrust. Vulcain engine, hot-firing at DLR P5 ground test facility RL-10 engine w/o NE Saturn 1B with 8 H1 engines, Apollo 7 mission Ch4 65 AAE 439 Effect of Back Pressure Ch4 66 AAE 439 NOZZLE FLOW SEPERATION T = m v e + pe - pa A e Thrust Equation ( ) Qualitative Analysis: Momentum-thrust (MT) term increases for increasing altitude (i.e. decreasing pa) Momentum-thrust (MT) term maximum for pe=0 Pressure-thrust (PT) term largest for pa=0 Practical Considerations: pe=0 requires nozzle of Infinite Expansion Ratio (maximizing MT in vacuum), Rocket propulsion of launch vehicles is performed in atmosphere ( pa 0). Condition for Maximum Thrust: ! dT =0 d p e p0 ( ) pe = pa Thus, max. thrust for a given altitude is achieved by a nozzle that expands flow to ambient pressure at that altitude. T = A * p0 2 2 - 1 + 1 +1 -1 -1 pe 1 - + pe - pa A e p 0 Ch4 67 ( ) AAE 439 NOZZLE FLOW SEPERATION T = m v e + pe - pa A e Thrust Equation ( ) Overexpansion can cause and lead to flow separation. Nozzle separation results from flow in the boundary layer not having sufficient energy to overcome adverse pressure gradients. Transient Phenomenon: Engine ignition, Typically occurs on one side of nozzle creating azimuthal pressure distribution. Summerfield/Oates (1954) developed estimation for altitude at which flow separation will occur for given nozzle. Ch4 68 AAE 439 NOZZLE FLOW SEPERATION Flow Separation according to Experimental Observations: Kalt-Bendall Separation Criteria: p sep p = 0.667 0 pa pa - 0.2 MorrisetteGoldberg Condition: Valid for Axisymmetric Contoured Nozzles!! p sep = 1.082 - 0.363 Msep + 0.0386 M2 2.4 < Msep < 4.5 sep pa Altitude Estimation for Flow Separation Atmospheric pressure as a Function of Altitude: hscale= scale height for model = 7,010.4 m h p = exp - pSL h scale p h = -h scale ln pSL Altitude as a Function of Pressure Ratio: Design Altitude (pe=pa=pd): p h d = -h scale ln d pSL h sep p sep = -h scale ln pSL p sep pd =K = pa p shock Separation Altitude: At separation altitude psep=pa for that altitude, while pdesign=pshock because shock is at nozzle exit plane. Altitude above SL at which Flow Separation occurs: h sep = h d - h scale ln K Ch4 69 AAE 439 EXAMPLE Ch4 70 ...
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## This document was uploaded on 01/15/2012.

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