Normal shock-wave structure in two-phase vapour-droplet flows

Abstract

A study of the structure of stationary, fully and partly dispersed, normal shock waves in steady vapour–droplet, two-phase flow is presented. Pure substances only are considered, but, unlike most previous work, the droplet population is allowed to be polydispersed. It is shown how the effects of thermal relaxation for such a mixture can be elegantly incorporated into the analysis.Three types of fully dispersed wave are identified. Type I waves are dominated by thermal relaxation and an approximate analytical solution is presented which gives results in close agreement with accurate numerical solutions of the governing equations. The analysis predicts some unexpected behaviour of the thermodynamic variables and demonstrates the correct scaling parameters for such flows. An approximate analysis is also presented for Type II waves, dominated by both velocity and thermal relaxation. Type III waves, where all three relaxation processes are important, are of little practical significance and are only briefly discussed. Partly dispersed waves are also considered and the results of a numerical simulation of the relaxation zone are presented. A linearized solution of this problem is possible but, unlike other relaxing gas flows, does not give good agreement with the more exact numerical calculations.The apparent discontinuity in the speed of sound in a vapour–droplet mixture as the wetness fraction tends to zero has been responsible for some confusion in the literature. This problem is reconsidered and it is shown that the transition from the two-phase equilibrium to the single-phase frozen shock wave speed is continuous.

AEROFROSH: a shock condition calculator for multi-component fuel aerosol-laden flows

“…Therefore, Dalton and Raoult's Laws are used to compute the average vapor pressure of the fuel P vap,fuel,avg using the saturated vapor pressures of each fuel component P sat,fuel,j and the liquidphase mole fractions y j . The result is shown in (26).…”

“…In Reference [25] they introduced several governing equations applicable to two-phase flows (specifically, wet steam), and set forth three expressions for sound speed in two-phase mixtures. They also presented analytical expressions to describe the structure of normal shock waves in steady vapor-droplet flows [26]. Guha applied the Rankine-Hugoniot relationships to shocks in aerosols and examined the internal structures of these waves using analytical and numerical approaches [27].…”

“…This is because the droplet size and yield from ultrasonic nebulizers depend largely on the liquid surface tension and viscosity [79], which, in ideal solutions, are properties of the liquid mixture rather than the individual fuel components. Note that the use of Raoult's Law in determining the partial vapor pressures of each fuel component (26) implies that preferential evaporation is taking place. This does not significantly alter the mole fractions of fuel components in the drops, however, because most fuel vapor is generated via evaporation from the 25-ml liquid pools in the AGT rather than from the droplets themselves (this can be verified by pumping down the AGT and measuring the residual vapor pressure).…”

Numerical modeling of two-phase supersonic ejectors for work-recovery applications

“…Therefore, for the sound speed to be ''intrinsically'' derived from the transport equations, one needs to accurately calculate the local interphasial area, which in turns, requires a precise tracking of the liquid/vapor interface, a problem still not trivial even in moderate speed gas-liquid flows. An extensive number of publications (e.g., [20][21][22]8]) have studied supersonic two-phase flow regimes where they impose a homogeneous frozen expression for the speed of sound with a critical assumption of no mass exchange between the two phases,…”

Development of an Aerosol Loading Technique for Ignition Time Measurements in Shock Tubes

“…The interaction of a shock wave and an aerosol has been studied by numerous researchers. 11,12,13 In the following section, we describe some theoretical and experimental aspects of the operation of the aerosol shock tube.…”