On the transition between two-phase and single-phase interface dynamics in multicomponent fluids at supercritical pressures

Abstract

A theory that explains the operating pressures where liquid injection processes transition from exhibiting classical two-phase spray atomization phenomena to single-phase diffusion-dominated mixing is presented. Imaging from a variety of experiments have long shown that under certain conditions, typically when the pressure of the working fluid exceeds the thermodynamic critical pressure of the liquid phase, the presence of discrete two-phase flow processes become diminished. Instead, the classical gas-liquid interface is replaced by diffusion-dominated mixing. When and how this transition occurs, however, is not well understood. Modern theory still lacks a physically based model to quantify this transition and the precise mechanisms that lead to it. In this paper, we derive a new model that explains how the transition occurs in multicomponent fluids and present a detailed analysis to quantify it. The model applies a detailed property evaluation scheme based on a modified 32-term Benedict-Webb-Rubin equation of state that accounts for the relevant real-fluid thermodynamic and transport properties of the multicomponent system. This framework is combined with Linear Gradient Theory, which describes the detailed molecular structure of the vapor-liquid interface region. Our analysis reveals that the two-phase interface breaks down not necessarily due to vanishing surface tension forces, but due to thickened interfaces at high subcritical temperatures coupled with an inherent reduction of the mean free molecular path. At a certain point, the combination of reduced surface tension, the thicker interface, and reduced mean free molecular path enter the continuum length scale regime. When this occurs, inter-molecular forces approach that of the multicomponent continuum where transport processes dominate across the interfacial region. This leads to a continuous phase transition from compressed liquid to supercritical mixture states. Based on this theory, a regime diagram for liquid injection is developed that quantifies the conditions under which classical sprays transition to dense-fluid jets. It is shown that the chamber pressure required to support diffusion-dominated mixing dynamics depends on the composition and temperature of the injected liquid and ambient gas. To illustrate the method and analysis, we use conditions typical of diesel engine injection. We also present a companion set of high-speed images to provide experimental validation of the presented theory. The basic theory is quite general and applies to a wide range of modern propulsion and power systems such as liquid rockets, gas turbines, and reciprocating engines. Interestingly, the regime diagram associated with diesel engine injection suggests that classical spray phenomena at typical injection conditions do not occur.

Autoignition and combustion of n-hexane spray in subcritical and supercritical environments

“…The recent studies done by Dahms and Oefelein [17,18] confirmed findings of previous researchers that in high temperature and pressure environments, the nature of mixing may change. They, however, stated that simply reaching and exceeding supercritical conditions of the injectant may not be sufficient to experience transitional and supercritical mixing.…”

“…The study done by Dahms and Oefelein [17] showed that mixtures of mixture fraction below 0.5 can be described as an ideal gas and the effects of real-fluid behavior do not play a role. It means that for mixtures which are capable of autoignition, the real-fluid effects do not occur.…”

“…They, however, stated that simply reaching and exceeding supercritical conditions of the injectant may not be sufficient to experience transitional and supercritical mixing. In their theoretical study [17], they concluded that enthalpy contained in hot unburnt ambient gases is not sufficient to heat up the gas-liquid interface to its critical temperature and that the transition between two-phase and single-phase interface dynamics is not necessarily induced by diminished surface tension forces alone [17]. They applied Knudsen number criterion in order to determine whether the mixing process is sub-or supercritical.…”

Experimental investigation of Ethane and Propane injection under sub- and super-critical conditions

“…at supercritical pressures [1,2]. At such high-pressure conditions, injection is quite different from classical known behaviors observed at low pressure, and studying these new phenomena is challenging.…”

Experimental Investigation of Droplet Injections in the Vicinity of the Critical Point: A comparison of different model approaches

“…As a first approximation, the adiabatic mixing model is used for estimation of the temperature. Dahms and Oefelein [2], and later Dahms [3] used this assumption for their simulation study of supercritical jets. Qiu and Reitz [4] used an extended adiabatic mixing assumption, which includes phase instabilities and phase separation for their study on high pressure fuel injection.…”