Numerical Analysis of Thermal and Fluid Behavior Including Phase Change in Container

Abstract

Fluid and thermal behaviors in gas and liquid phase in closed tank were investigated by numerical calculation. In this calculation, mass and energy transfer due to evaporation on free surface was considered. Natural convection in both liquid and gas phase were separately calculated. In gas phase, binary diffusion convection including mixture of vapor component and non condensable gas were additionally considered. In these calculations thermal stratification was obtained in liquid phase by applying heat at side wall. Evaluation tests by using mixture of ethanol and nitrogen gas were also conducted. Pressure history was compared with calculated results, and it was proved that calculated results agreed with experimental ones. Nomenclature mv = Mass flux of vapor [kg/m 2 /s] hv = Latent heat o vapor [J/kg] q = Heat flux through free surface [W/m 2 ] α = Empirical coefficient for calculating mass transfer rate due to phase change Suffix: L:liquid phase, G: gas phase I. Introduction n liquid rocket, cryogen such as liquid hydrogen, liquid oxygen, and liquid methane, is used as propellant and oxidizer. These fluids have very high vaporizing pressure; therefore thermal protection is very important problem to prevent a significant pressure rise. To make an adequate design for thermal protection system, accurate prediction for pressure rise in tank is required. In consideration of suction performance of feed pumps, that is required NPSH, liquids supplied from tanks have to be maintained sub-cooled condition. To attain this situation, tank is pressurized by inert gas, generally helium gas. Helium gas has to be supplied to tanks in order to maintain required pressure in discharging process of liquid during firing of engine. Estimation of consumption weight of helium gas is needed to determine number of helium bottle installed on engine system. This estimation has to be very accurate since number of helium bottle has significant impact on system weight. Numerous numerical estimation tools for temperature in tank, pressure rise, and vaporization amount has been developed. Some tools apply one dimensional analytical model considering only distribution along central axis of tank 1 . The other tools uses axisymmetric 2D model, however these models neglect phase change on the free surface 2,3 . Currently by using commercial CFD codes, fluid and thermal behavior in liquid and gas phase could be easily simulated. However these codes don’t generally possess a standard function to realize evaporation on free surface, boiling and condensation, that is, numerical results hadn’t been evaluated sufficiently. In this study, final target is to establish the technology to analyze thermal and fluid behavior in tank with the phase change. In present study, numerical model were established to calculate fluid and thermal behaviors without liquid discharge and gas supply, but including evaporation only on free surface in closed tank. This calculated system corresponds to the thermal and fluid behavior in rocket tank before launching. As a purpose of evaluation of calculated results, experimental using ethanol as volatile liquid were conducted. In these experiments, temperature distributions and pressure history were measured in closed tank, where heat was applied through tank wall by electrical heater. 1 Senior Researcher, Heat & Fluid Dynamics Dept., 1, Shin-nakahara-cho, Isogo-ku, Yokohama 235-8501, Japan I