16.512, Rocket Propulsion
Prof. Manuel Martinez-Sanchez
Lecture 14: Non-Equilibrium Flows
Reacting Nozzle Flow
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
(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
” results belong in this category, and can be used as a first
approximation for nozzle flow calculations (using for instance the value of
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
CC C C R
a constant, since
, the gas constant, does not vary
due to the constancy of the molecular mass.