Numerical simulations of transverse liquid jet to a supersonic crossflow using a pure two-fluid model

Abstract

A pure two-fluid model was used for investigating transverse liquid jet to a supersonic crossflow. The well-posedness problem of the droplet phase governing equations was solved by applying an equation of state in the kinetic theory. A k-e-k p turbulence model was used to simulate the turbulent compressible multiphase flow. Separation of boundary layer in front of the liquid jet was predicted with a separation shock induced. A bow shock was found to interact with the separation shock in the simulation result, and the adjustment of shock structure caused by the interaction described the whipping phenomena. The predicted penetration height showed good agreement with the empirical correlations. In addition, the turbulent kinetic energies of both the gas and droplet phases were presented for comparison, and effects of the jet-to-air momentum flux ratio and droplet diameter on the penetration height were also examined in this work.

Liquid jet penetration and breakup in a free supersonic gas jet

“…While a number of simulation studies have been performed to study water injection into rocket exhaust including work in [3], [4], [12], [22], and [23], experimental studies are scarce and testament to the difficult test conditions. One study to note is by Liwu et al [6] and later by Zhou et al [7] who investigated water injection into the exhaust plume of a solid rocket motor.…”

“…Figure 5. Left: Jet in crossflow [22], Right: Liquid penetration in a free jet [8] Since the jet in crossflow is traditionally studied as it relates to fuel injection into supersonic combustion chambers, the upstream gas flow is generally uniform and contains no internal shockwave structure. For the injection configuration of interest in this work, the gas phase is expanded to a pressure less than ambient prior to injection into the ambient atmosphere, resulting in an overexpanded flow with an inherent internal shockwave structure.…”

“…Left: Upstream particle detection using holography, Right: Downstream particle detection using holography [21] More recently, detailed numerical simulations have employed computational fluid dynamics (CFD) techniques to gain insight into jet penetration and breakup [3], [4], [12], [22], [23]. [22] CFD simulations have the additional advantage of being able to examine in great detail, the behavior of the primary breakup processes for varied gas phase Mach number and momentum ratio as shown by [23]. The objective of this work was to examine the regime of breakup and the global effects of the solid boundary created by the introduction of the liquid phase.…”

Numerical modeling of atomization in compressible flow

“…The development of liquid fuel supersonic combustion ramjets (scramjets) is a motivating factor for understanding liquid atomization in high speed crossflows. To date, numerical simulations in this flow regime utilized analytical, empirical, or subgrid models for modeling the breakup and atomization of the liquid jet, for example [8,115,116,117,118]. A notable exception is the recent large eddy simulations of Xiao et al [33] In order to demonstrate the capability of the developed numerical approach, a D = 1 liquid jet injected into a supersonic M = 2 crossflow is investigated in two and three dimensions.…”

“…This is especially problematic at high Reynolds and Weber numbers where large numbers of small droplets can be generated. Subgrid droplet models can relax the computational complexity and have been used to simulate liquid jet injection in supersonic crossflows [116,118]. However they generally utilize steady-state empirical relations for the drag coefficient of solid spherical particles as a function of the particle Reynolds number to calculate drop trajectories [124].…”