Steady transonic dense gas flow past two‐dimensional compression/expansion ramps revisited

Supersonic flow past compression/expansion ramps represents a canonical problem in fluid dynamics which has been studied extensively in the past assuming perfect gas behaviour. More recently real gas effects on such flows have received increasing attention as part of efforts, among others, to increase the efficiency of Organic Rankine Cycles for decentralized power plants. Of special interest in this connection are dense gases of Bethe–Zel'dovich–Thompson fluids which have the distinguishing property that the so called fundamental derivative of gasdynamics Γ takes on negative values in the general neighbourhood of the thermodynamic critical point. Asymptotic analysis of the transonic flow regime has so far concentrated on cases where the unperturbed state with pressure p 0 , density ρ 0 and entropy s 0 is close to the transition curve Γ = 0 in the pressure specific volume plane such that |Γ 0 | ≪ 1, Λ 0 = ρ ∂ Γ ∂ ρ | s = O ( 1 ) , Kluwick and Cox [1], [2]. These studies have revealed a number of new phenomena and a non‐uniqueness of solutions exceeding that known from the theory of perfect gases. Here we extend the analysis to cover flows where the unperturbed state in the p , 1/ρ plane is in the vicinity of the point on the transition line where Γ and Λ vanish simultaneously. Such flows have |Γ 0 | ≪ 1, |Λ 0 | ≪ 1, N 0 = ρ ∂ Λ ∂ ρ | s = O ( 1 ) and are of considerable practical interest as isentropes that can be realized experimentally at present just barely enter the negative Γ region. Again an increased wealth of possible solutions is observed.