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lecture_30 - 16.512 Rocket Propulsion Prof Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 30: Dynamics of Turbopump Systems: The Shuttle Engine Dynamics of the Space Shuttle Main Engine Oxidizer Pressurization Subsystems Selected Sub-Model In the complete SSME engine, all variables affect each other in complex ways. In order to test our fault detection algorithms, a dynamic subsystem is desired, with reduced order, but with the unmodelled states interacting as weakly as possible with those modelled. Attention was focused on the liquid oxygen subsystem for two main reasons: (a) The O/F ratio at rated power is 6, so that the LOX dynamics should dominate over the LH effects wherever they interact, and (b) The turbopump pre-burners are run very fuel-rich in order to limit the turbine inlet temperatures below the metallurgical limits of the uncooled blades; small excursions of the LOX flow to the pre-burners are then immediately translated into large and potentially critical turbine temperature excursions. In our submodel we therefore focus attention on the LOX turbopump, which feeds both, the main LOX injectors, and (after the boost stage) the two turbine pre- burners. Also modeled are the dynamics of the LOX feeding line to the pre-burners, as well as to the main LOX valve and main injector, plus the LOX pre-burner itself and the main chamber pressure. Variations of the LH-related states should indeed couple weakly to the LOX system, mainly through LH flow variations onto the pre- burners (insensitive, since they are fuel-rich), and into the main chamber (choked flow, no feedback). The Dynamic Equations There are three types of dynamic equations to be considered: (1) Rotational dynamics of the LOX turbopumps. (2) Equations expressing the liquid inertia under pressure difference variations (analogous to inductance in electric circuits). (3) Equations expressing the ability of cavities to store fluid due to its compressibility under pressure fluctuations (analogous to capacitive effects). (1) Rotational Dynamics If I OTP is the moment of the inertia of the Oxidizer Turbo Pump (OTP) rotor, its angular velocity, 02 2 OT τ the torque delivered by the OTP turbine, 2 OP the torque absorbed by the main oxidizer pump stage, and 3 OP the torque absorbed by the oxidizer booster pump, then 16.512, Rocket Propulsion Lecture 30 Prof. Manuel Martinez-Sanchez Page 1 of 11
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223 02 =−− OTP OT OP OP d I dt τ ( 1 ) In a hybrid system where 02 is in rad/sec, t in seconds, and the torque in lb- in, the constant I OTP has a value 1 0.916 (which implies I OTP = 422 lb m in 2 ).
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