Steady small-disturbance transonic dense gas flow past two-dimensional compression/expansion ramps

Abstract

The behaviour of steady transonic dense gas flow is essentially governed by two non-dimensional parameters characterising the magnitude and sign of the fundamental derivative of gas dynamics ($\unicode[STIX]{x1D6E4}$) and its derivative with respect to the density at constant entropy ($\unicode[STIX]{x1D6EC}$) in the small-disturbance limit. The resulting response to external forcing is surprisingly rich and studied in detail for the canonical problem of two-dimensional flow past compression/expansion ramps.

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

“…Asymptotic analysis of the transonic flow regime has so far concentrated on cases where the unperturbed state with pressure p0, density ρ0 and entropy s0 is close to the transition curve Γ = 0 in the pressure specific volume plane such that |Γ0| 1, Λ0 = ρ ∂Γ ∂ρ s = O(1), Kluwick and Cox [1], [2]. 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.…”

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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. Again an increased wealth of possible solutions is observed.Steady transonic flow past past two-dimensional ramps has recently been considered by Kluwick and Cox [1], [2]. Asymptotic analysis of the transonic flow regime has so far concentrated on cases where the unperturbed state with pressure p0, density ρ0 and entropy s0 is close to the transition curve Γ = 0 in the pressure specific volume plane such that |Γ0| 1, Λ0 = ρ ∂Γ ∂ρ s = O(1), Kluwick and Cox [1], [2].

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“…Asymptotic analysis of the transonic flow regime has so far concentrated on cases where the unperturbed state with pressure p0, density ρ0 and entropy s0 is close to the transition curve Γ = 0 in the pressure specific volume plane such that |Γ0| 1, Λ0 = ρ ∂Γ ∂ρ s = O(1), Kluwick and Cox [1], [2]. Asymptotic analysis of the transonic flow regime has so far concentrated on cases where the unperturbed state with pressure p0, density ρ0 and entropy s0 is close to the transition curve Γ = 0 in the pressure specific volume plane such that |Γ0| 1, Λ0 = ρ ∂Γ ∂ρ s = O(1), Kluwick and Cox [1], [2].…”

“…Such flows have |Γ0| 1, |Λ0| 1, N0 = 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.Steady transonic flow past past two-dimensional ramps has recently been considered by Kluwick and Cox [1], [2]. Most important, the flow medium was taken to be a dense gas of Bethe-Zel'dovich-Thompson type which has the distinguishing property that the so called fundamental derivative Γ = 1 c ∂(ρc) ∂ρ s which is strictly positive for perfect gases may be negative in a region located in the general neighbourhood of the thermodynamic critical point.…”

“…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 p0, density ρ0 and entropy s0 is close to the transition curve Γ = 0 in the pressure specific volume plane such that |Γ0| 1, Λ0 = 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.…”