lecture_26

lecture_26 - 16.512, Rocket Propulsion Prof. Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 26: Turbopumps Turbopump Components The mechanical components of the pressurization cycle (pumps and turbines) are next to be considered. An excellent recent survey of this area is given in Ref.40. A more comprehensive, but older survey is contained in a series of NASA SP reports [41-43]. Pumps and turbines will first be discussed separately, and their integration will then be examined. (a) Pumps Almost all existing rockets have centrifugal turbopumps. These deliver more P per stage than axial flow pumps, with only slightly less efficiency. Only if multistaging becomes necessary is there a possible incentive to go to axial pumps; this happens with LH 2 fuel, where, due to the low density, the P per stage is limited by the attainable rim speeds. In general, the design attempts to maximize operating speed, since this reduces the pump size, and hence the weight. Pump speed is limited by several effects, most importantly cavitation at inlet. Others are centrifugal stresses (either at the impeller or in the driving turbine), limiting peripheral speeds for bearing and seals, and avoidance of critical speeds. “Head rise” is used commonly instead of pressure rise to express the performance of pumps. We can define head rise as the height to which one could raise one Kg of fluid with the amount of ideal work per Kg done by the pump: H = 2 1 P sP dp h/g g ∆= ρ (1) The rise is directly related to the pump work, even if the fluid has significant compressibility: Work/mass= p gH h η (2) and this is one of the advantages of its use. Obviously, if ρ = const., P H, g = ρ p Work P mass = ρη (3) 16.512, Rocket Propulsion Lecture 26 Prof. Manuel Martinez-Sanchez Page 1 of 8
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The head rise is directly to the peripheral speed of the impeller disk. The fluid enters axially near they impeller hub, with no angular momentum; it leaves the impeller with absolute tangential speed ω R 2 – V r2 tan β 2 , where β 2 is the back-leaning blade angle at the rim Fig 1, and V r2 is the fluid radial exit velocity, related to the volume flow rate as Q = 2 π R 2 b 2 V r2 ( 4 ) The torque needed to drive the impeller is the net outflow rate of angular momentum, and the work rate is this, times ω . Thus, Power = () 2 r2 2 2 V mR 1 t a n R ⎛⎞ ω− 2 β ω ⎝⎠ i (5) and since we also have Power = p gH m η i , the head rise is 2 2 p 2 R V H1 t gR ω β ω 2 a n ( 6 ) 16.512, Rocket Propulsion Lecture 26 Prof. Manuel Martinez-Sanchez Page 2 of 8
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The quantity r2 p 2 V 1t a n R ⎛⎞ 2 ψ = η β
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This note was uploaded on 11/07/2011 for the course AERO 16.512 taught by Professor Manuelmartinez-sanchez during the Fall '05 term at MIT.

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lecture_26 - 16.512, Rocket Propulsion Prof. Manuel...

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