Entropy-constrained closure for steady, quasi-one-dimensional flow of ideal gases

An entropy-constrained closure is developed for steady quasi-one-dimensional flow of a calorically perfect ideal gas. Net irreversibility is represented by a prescribed entropy change between the inlet and outlet or, equivalently, by a stagnation pressure ratio together with the stagnation temperature ratio implied by the energy balance equation. The thermodynamic constraint, enforced through Gibbs relation together with conservation of mass and energy, yields an algebraic mapping from the inlet flow state, area ratio and prescribed stagnation property ratios to the outlet flow state. The momentum balance is retained only as an auxiliary post-processing relation and may be used to infer integral quantities such as a net wall force or an equivalent mean wall pressure. For an ideal gas with integer number of molecular degrees of freedom $f$ , the resulting equation reduces to a polynomial of degree $f+1$ in the squared outlet Mach number. The $f=3$ case reduces to a quartic, and the $f\to \infty$ limit admits an explicit Lambert- $W$ solution; existence, multiplicity, choking and admissibility conditions consistent with the second law of thermodynamics are obtained for general $f$ . Classical isentropic nozzle, Rayleigh and Fanno flows, normal shocks, and simultaneous friction and heat transfer in a constant-area duct are recovered in the respective limiting cases. Comparisons with experimental measurements of nozzle wall pressures, sudden expansion outlet Mach numbers and sudden contraction stagnation pressure ratios show good agreement with predictions across a wide range of inlet Mach numbers and area ratios.