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Supercritical (And Subcritical) Fluid Behavior and Modeling Supercritical (and Subcritical) Fluid Behavior and Modeling: Drops, Streams, Shear and Mixing Layers, Jets and Sprays Josette Bellan Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Drive MS125-109 Pasadena, CA 91109 josette.bellanQjpl.nasa.edu Tel: (818) 354 6959 Fax: (818) 393 5011 October 20, 1999 Abstract A critical review of recent investigations in the realm of supercritical ( and subcritical) fluid behavior is presented with the goalof obtaining a perspective on.the peculiarities of high pressure observations. Experiments with drops, isolatedor in groups, streams, shear and mix- 1 ing layers, jets and sprays are tabulated and discussed as a precursor t,o €orming a conceptual picture of fluid comportment. The physics of fluid behavior in the supercritical and subcritical regimes is discussed, and major differences between the observations in these two regimes are identified and explained. A variety of supercritical fluid models is then examined in the con- text of drop studies, and salient aspects of fluid behavior are identified. In particular, a model that has been validated with microgravity drop experiments is described and summarized; in this validated model, the differences in subcritical/supercritical comportment are interpreted in terms of lengths scales and it is this difference that is responsible for the traditional Lewis number expression no longer portraying the ratio of heat to mass transfer in supercritical fluids; instead, an effective Lewis number is recommended that gives a realistic estimate of the ratio of these length scales. Furthermore, the application of various fluid models to the description of supercritical fluid in various geometric configurations is discussed for conditions relevant to liquid rocket, Diesel and gas turbine engines. Such preliminary simulations per- formed with the validated fluid model have already reproduced some specific experimental features of supercritical fluid jet disintegration. Finally, comments are offered regarding future areas of research. Contents 1 Introduction. .......................................... 3 2 Experimental observations ................................... 6 2.1 Fluiddrops ........................................ 8 2.1.1 Microgravity emission/evaporation observations ................ 9 2.1.2 Normal gravity emission/evaporation observations ............... 10 2.1.3 Microgravity combustion observations ...................... 14 2.1.4 Normal gravity combustion observations .................... 20 2 2.2 Fluid shear layers. jets andsprays ............................ 25 2.2.1 Shear and mixinglayer evolution ........................ 25 2.2.2 Disintegration and emission/evaporation experiments ............. 26 2.2.3 Burningsprays and jets ............................. 29 3 Modeling of subcritical/supercritical fluids .......................... 32 3.1 Salient physics of subcritical/supercritical behavior .................. 32 3.2 Modeling of drops ..................................... 34 3.2.1 Drops instagnant surroundings ......................... 35 3.2.2 Drops in convective surroundings ........................ 51 3.2.3 Conclusions from drop models .......................... 54 3.3 Modeling of groups of drops(arrays, clouds and clusters) ............... 57 ~ 3.4 Modeling of streams,shear and mixing layers. jets and sprays ............ 61 3.4.1 Streams ...................................... 62 3.4.2 Shear and mixing layers ............................. 62 3.4.3 Jets ........................................ 64 3.4.4 Sprays ........................................ 65 4 Conclusions ........................................... 68 1 Introduction Supercritical fluids are involved in numerous aspects of natural or industrial situations related to energy production or transfer . According to classical thermodynamic theory [l].a fluid is in a supercritical state when it is at a pressure or temperature exceeding its critical value; the value of the pressure. p. temperature. 2’. or molar volume. 21. divided by its corresponding critical value (subscript c) is called the ‘reduced’ (subscript T) value . When p, > 1 or T. > 1. in the (p. T)plane there is no longer the possibility of a two phase (i.e. gas/liquid) region and instead there is only a single-phase region [2]. The general term for the substance is fluid (neither a gas nor a liquid) and it is in a supercritical state. In the realm of natural situations, oil in underground reservoirs or volcanic lava are both supercritical fluids. In the realm of industrial processes, liquid rocket, Diesel or the new generation of gas turbine engines, all operate at supercritical conditions for the injected fuel. Although in all above examples the fluids are at supercritical conditions, the oil and lava have very different behavior than fuels in engines; this is because the natural and industrial examples above represent two extremes of supercritical fluids, the former having a high and the latterhaving a small molar volume. In this paper we will address only the behavior of fluids having small molar volume under supercritical conditions, although from the modeling point of view, providing that the equation of state (EOS) is correct, the same conservation equations can be used independently of the value of the molar volume. Since most human experience is with atmospheric conditions phenomena, the physics of super- critical fluids is not intuitive. These fluids exhibit characteristics resembling both liquids and gases [3] in that they may have liquid-like densities but gas-like properties. The importance of using correct fluid properties is shown in Table 1 listing the percent difference in the thermal conduc- tivity of fluid propane compared to that of the liquid at the same temperature. The calculations were performed using the plotted values of Reid et al. [3] (Fig. 10-5). Following the procedure for calculating conductivities at large p,’s knowing the conductivity at the same T, but at a lower p,. (American Petroleum Institute [4], procedure 12A4.1), one can see that the difference increases with increasing p, and T,, that is with increased pressure and fluid heating. Previous extensive reviews of supercritical studies (e.g. [5]) focussed primarily on experimental observations of hydrocarbon drops, and few details of modeling aspects were discussed; moreover, since no validated first-principles models of supercritical fluids were available, the reviews tended to be non-judgemental as to the effectiveness of the models in portraying reality, and therefore of 4 limited usehlnws to the novice reader. The present review has a diffcrcmt cmphasis in that both experiments (that are not necessarily restricted to drops) and theory are discussed to a similar extent, and a variety of species combinations including the LOx/H2 system (which is of practical importance in rocket propulsion) are analyzed. It turns out that because of the special therm- physical properties of the LOX/H2combination, supercritical phenomena in this system tend to be enhanced, and the reason for it will be explained. Furthermore, given the recent success in first- principles modeling of both supercritical and subcritical fluids with the same formulation,one isnow in a position to evaluate the necessary ingredients for obtaining an accurate theory of supercritical fluids, and thus to provide guidance to the novice reader. This paper is organized as follows: First, the phenomenology of supercritical versus subcritical behavior is presented by examining observations of drops, shear layers, jets and sprays. Then, an extensive review of models from the last decade is performed with the goal of extracting the essence of the physics in each of the two regimes. A promising model is identified that has been validated with data over a significant range of (p,T), and its success is traced to thecorrect transport matrix, as well as to accurate EOS and transport properties. The implications of this model are discussed, and its preliminary application to the modeling of fluid disintegration is examined. Finally, in the concluding section the progress in the understanding of supercritical fluid behavior is summarized and comments on new avenues of research are offered. Owing to thefact that the critical locus is a function of (p,T, yZ) where yZ is the mass fraction of species i, in this entire paper “subcritical” and “supercritical” refers to the situationwith respect to the critical point (primarily the pressure) of an individual fuel species, and in the case of mixtures the reference is the fuel with the lowest critical pressure. 2 Experimentalobservations Classical thermodynamics provides guiding rules (that are a consequence of the definition based on p, and TT)to differentiate between the subcritical and supercritical states. For example, it is well known that both the surface tension and the latent heat, being manifestations of the two phase regime, become null at and past the critical point [l].In the supercritical regime, solubility effects become important and the heatof solvation becomes the relevant thermodynamic quantity for fluid interpenetration [l].For this reason, a very precise semantics will be used in this entire review to remedy some of the inappropriate terminology used by habit in the literature. A special case is the appellation of “evaporation constant” or “evaporation rate” used indiscriminately under subcritical and supercritical conditions. )Under true supercritical conditions there cannot be evaporation since the
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