lecture_14 - 16.512, Rocket Propulsion Prof. Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 14: Non-Equilibrium Flows Reacting Nozzle Flow 14.1 Introduction As indicated in the introductory discussion of section 12.1, the actual expansion process in a rocket or ramjet nozzle is intermediate between the extremes of “frozen” and “equilibrium” flow, with the latter producing higher performance due to recovery of some of the chemical energy tied up in the decomposition of complex molecular species in the chamber - a kind of afterburning effect. The two limits, “frozen” and “equilibrium” flow share an important property: both are isentropic flows (if we ignore friction or heat losses). This is because, in the frozen case no chemical change during expansion), there are no rate processes at all occurring, the molecules preserving their identity all the way, while in the equilibrium case, in which reactions do occur, their rate is so high (compared to the expansion rate) that conditions adjust continuously to maintain equilibrium at the local pressure and enthalpy level, with the result that the whole process can be regarded as reversible (and hence isentropic). For any more realistic intermediate conditions, in which reactions may proceed at rates comparable to that of the expansion, these finite rate reactions produce an irreversibility, and a consequent entropy increase. In this Section we will discuss in detail an example of each, frozen and equilibrium expansion. We will use for this purpose the results of the equilibrium chamber calculations of Sec. 13.1, relative to the space Shuttle Main Engine. 14.2 Frozen Flow Calculation The simple ideal gas model we have used throughout most of this course (constant molecular mass, constant specific heats) is an example of a frozen flow model, since it is implied by these assumptions that no chemical change takes place. Thus all of our “constant γ ” results belong in this category, and can be used as a first approximation for nozzle flow calculations (using for instance the value of and M computed for the combustor). However, even with no chemical changes, the specific heats of the various molecules do change with temperature, generally decreasing as temperature decreases in the range encountered in nozzles. This means that () pv p p g CC C C R γ= = is not a constant, since , the gas constant, does not vary due to the constancy of the molecular mass.
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lecture_14 - 16.512, Rocket Propulsion Prof. Manuel...

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