Entropy Changes in Nonequilibrium Flows

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Abstract
The entropy increases arising from chemical nonequilibrium in inviscid flows are investigated by the use of an analytical model. After the validity of the model is examined, the irreversibilities in nonequilibrium expansions are studied. The basic approach to the problem is an analytical study of limiting behavior of the entropy integral followed by numerical evaluation of this integral over finite limits. Small perturbation analyses are employed for investigating near‐equilibrium and near‐frozen flow in order to justify truncation of the entropy integral for some cases. The conditions necessary for the existence of freezing and for the existence of entropy bounds are established for large expansions. The results of exact numerical solutions for nonequilibrium nozzle flows are compared with those from isothermal approximations for upper bounds on entropy increments. Irreversibilities are also evaluated for relaxation flows in a constant‐area duct, a shock‐wave reaction zone, and a venturi for a previously frozen flow. It is observed that the entropy rise in the freezing process is practically negligible compared with the total entropy for a wide range of conditions characterizing flows of technical interest. The constant‐area relaxation and venturi relaxation flows also show small entropy rises. The shock wave and its accompanying relaxation zone lead to substantial irreversibilities. The entropy rise in the expansion cases is small permitting constant entropy approximations which may be utilized in numerical computation.

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