Numerical Investigation of Transonic Supercritical CO2 Flows with Nonequilibrium Condensation in a Laval Nozzle

In this paper, we numerically investigate the nonequilibrium condensation of supercritical CO2 flows in an axisymmetric Laval nozzle. Our numerical method was originally developed for moist-air flows over an airfoil and wet-steam flows in steam turbines. This method was coupled with the thermophysical database, REFPROP, and applied to the simulation of the transonic supercritical CO2 flows with nonequilibrium condensation. In the results, nonequilibrium condensation started near the throat, and the pressure and temperature were increased at the diverging area by the release of the latent heat. The position of the maximum nucleation rate of CO2 liquid particles was moved by changing the inlet temperature, resulting in the pressure difference at the diverging area. The results indicate that the condensation certainly affects the performance of the Laval nozzle. INTRODUCTION Supercritical CO2 Brayton cycles have been studied for developing a compact and efficient power generation with solar power, fossil fuel, geothermal energy, exhaust heat, and other many heat sources. Since a radial compressor working along the cycle is considered to compress the supercritical CO2 near the critical point, the accurate prediction of the performance is a primary issue to design the compressors. Changing the impeller shape to decrease secondary vortices may be one of the standard approaches to improve the performance. Pressure and temperature in the compressor working in the supercritical state may conditionally decrease in the flow passage as crossing the saturated values. A strong supercooled condition may induce nonequilibrium condensation of CO2 gas, forming CO2 liquid particles in the flow passage. Therefore, the condensation of CO2 is another issue to be predicted for designing the supercritical CO2 compressor. Recently, supercritical and high-pressure CO2 flows with nonequilibrium condensation were numerically and experimentally investigated by some researchers. Rinaldi et al. [1] and Ameli et al. [2] numerically studied a supercritical CO2 flow in a radial compressor and predicted the saturation condition in the flow path. Lettieri et al. [3] and Paxson et al. [4] 2 experimentally investigated supercritical and high pressure CO2 flows with condensation in a Laval nozzle. Nonetheless, the fundamental investigation of supercritical CO2 flows is still not sufficient for understanding condensate phenomena in supercritical conditions. Our group has developed a numerical method for supercritical-fluid flows in which a preconditioning method [5] and the thermophysical database, PROPATH [6], was employed. The method was applied to several supercritical CO2 problems [7][8]. We also developed another numerical method [9] to simulate transonic moist-air flows over an airfoil and transonic wet-steam flows in a steam turbine with nonequilibrium condensation and applied the method to several flow problems [9][10]. The obtained results indicate that nonequilibrium condensation certainly affects the performance of the airfoil and the steam turbine. In this study, we coupled our numerical method [9] with the Reference Fluid Thermodynamic and Transport Properties Database (REFPROP) developed by National Institute for Standards and Technology (NIST) to simulate supercritical CO2 flows with the accurate thermophysical properties. In this paper, we applied the method to supercritical CO2 flows in a Laval nozzle to understand the basis of nonequilibrium condensation in transonic supercritical CO2 flows. The flows while changing the inlet temperature are calculated and the results are compared with each other. NUMERICAL METHODS Fundamental equations Two-dimensional compressible Navier-Stokes equations, which comprise of the conservation laws for total density, momentum, total energy, are solved with conservation equations for density of CO2 liquid particles and the number density. These equations are coupled with SST turbulence model [11]. Flows are assumed as a homogeneous flow without any slippage between the gas phase and the liquid particles since the particles are sufficiently small. The set of equations is written as   , ) 2 , 1 ( 0               i H H F E t Q Q L t Q axi v i i  (1) where Q, Ei (i = 1, 2), Fv, H, and Haxi are the vectors of unknown variables, the flux, the viscous term, the source term, and the axisymmetric term, respectively, and are defined by