AlAA 98-0164 Heat and Mass Transfer for Isolated and Interacting Fluid Drops Under Quiescent Supercritical Conditions

A model has been developed for the behavior of all isolated fluid drop of a single component species inlrnersed into another single component species in finite, quiescent surroundings at supercritical conditions. ‘1’he model is based upon fluctuation theory which accounts for both Soret and Dufour effects in the calculation of the transport matrix relating molar and heat fluxes to the transport properties and the thermodynamic variables. The contribution of the chemical potentials to the fluxes is fully included and accounts for potentially non-unity mass diffusion factors and transport effects of enthalpy and molar volumes with temperature gradients and pressure gradients, respectively. This model has been used as a building block in a fornnrlatiol~ describing interactions of fluid drops inducecl by drop proximity. Heat and mass transfer to the cluster are modeled using the hTusselt number concept. Calculations were performed for the 1,0= -H2 systeIn; the transport properties have been mocleled over a wide range of pressure and temperature variation applicable to L O= -Hz conditions in rocket engine combustion chambers, and the equations of state have becx) calculated using a previously-derived, conlputationallyefflcient and accurate protocol. The results show that the supercritical behavior is essentially one of diffusion. The temperature profile relaxes fastest followed by the density and lastly by the mass fraction profile. To understand heat and mass transfer, an effective Lewis number was calculated for situations where tenlperature and mass fractions gradients are very large. Results show that the effective Lewis number can be 2 to 40 times larger than the traditional Lewis number and that the spatial variation of the two numbers is different; the reason for these Lewis number effects is discussed. Parametric simulations as a function of pressure show that length scales decreasse with increasing pressure. This hinders interdiffusion for isolated fluid clrops, but enhances it for clusters of drops due to the additional effect of increasing cluster volume. Introduction Licluicl rocket engine design is not a mature technology in that the issues of reliability and efhciency are unresolved. Current designs are still based upon enlpirical knowledge and theory that does not portray the complexities of the physical processes and of the environment in the combustion chambers. The extensive review on liquid propellant rocket instabilities compiled by Harrje and Reardon [I] more than twenty years ago remains the base of rocket design despite the increased understanding that many of the approximations made in perforlniug the calculations compromise the validity of the results. One of the foundations of liquid rocket instabilities is the theory of isolated drop evaporation and combustion in an infinite meclium [I], [2]. The early version of that theory was based on the assumption of quasi-steady gas behavior with respect to the liquid phase, an assumption strictly valid only at low pressures where the liquid density is three orders of magnitude larger than that of the gas. Recognizing that at the elevated pressures c)f liquid rocket chambers the liquid density approaches that of the gas, the quasi-steady assumption was relaxed in other investigations [3], [4], [5], [6], [7]. However, it is only recently that the description of the full complexity of combustion chambers processes was sought; this includes not only the complete unsteady treatnlellt of the conservation equations but also appropriate equations of state with consistent mixing rules and transport properties valid over transcritical/supercritical conditions. Recent studies related to these aspects are those of Yang et al. [8], Hsiao et al. [9], Dclplanclue and Sirignano [10] and Haldenw’ang et al. [11]. Isolated drop behavior, although very relevant to understanding phenolnena in rocket engine motors, is by itself insutlcient for deriving the necessary insight into controlling licluicl rocket combustion operation. Experimental observations of atomization of coaxial jets (SUC1l as those used in liquid rocket engines) by Harclalupas et al. [12] and Engelbert et al. [13] reveal tile initial formation of ligaments, each ligament quickly disintegrating into a cluster of clrops. Similarly, visualizations of impinging licluicl jets [I] have shown that un-