Numerical analysis of gaseous hydrogen/liquid oxygen flamelet at supercritical pressures

Supercritical conditions are typically encountered in high-pressure combustion devices such as liquid propellant rockets and gas turbine engines. Significant real fluid behaviors including steep property variations occur when the fluid mixtures pass through the thermodynamic transcritical regime. The laminar flamelet concept is a robust and reliable approach that correctly accounts for real fluid effects, the large variation in thermophysical properties, and the detailed chemical kinetics for turbulent flames at transcritical and supercritical conditions. In the present study, the flamelet equations in the mixture fraction space are extended to treat the flame field of general fluids over transcritical and supercritical states. Flamelet computations are carried out for gaseous hydrogen and cryogenic liquid oxygen flames under a wide range of thermodynamic conditions. Based on numerical results, the detailed discussions are made for the effects of real fluid, pressure, and differential diffusion on the local flame structure and the characteristics encountered in liquid propellant rocket engines.     

A non-premixed combustion model based on flame structure analysis at supercritical pressures

This work presents a study of non-premixed flames at supercritical-pressure conditions. Emphasis is placed on flame stability in liquid rocket engines fueled with liquid oxygen and gaseous hydrogen. The flame structure sensitivity to strain, pressure, temperature and real-fluid effects was investigated in detailed opposed-jet flames calculations. It is shown that the flame is very robust to strain, that the flamelet assumption is valid for the conditions of interest, and that real-fluid phenomena can have a significant impact on flame topology. At high-pressure supercritical conditions, small pressure or temperature variations can induce strong changes of thermodynamic properties across the flame. A substantial finding was also that the presence of water from combustion significantly increases the critical pressure of the mixture, but this does not lead to a saturated state where two-phase flow may be observed. The present study then shows that a single-phase real-fluid approach is relevant for supercritical hydrogen–oxygen combustion. Resultant observations are used to develop a flamelet model framework that combines detailed real-fluid thermodynamics with a tabulated chemistry approach. The governing equation for energy contains a compressible source term that models the flame. Through this approach, the solver is capable of capturing compressibility and strain-rate effects. Good agreements have been obtained with respect to detailed computations. Heat release sensitivity to strain and pressure variations is also recovered. Consequently, this approach can be used to study combustion stability in actual burners. The approach preserves the density gradient in the high-shear region between the liquid-oxygen jet and product rich flame region. The latter is a key requirement to properly simulate dense-fluid jet destabilization and mixing in practical devices.     

Equation of state for fluid mixtures based on the principle of corresponding states with a two‐fluid model: Application to fluid mixtures of water + ammonia

We propose an equation of state for fluid mixtures of water + ammonia which is expressed in Helmholtz free energy as a function of temperature, molar volume, and mole fraction. IAPWS Formulation 1995 for water and the equation of state by Tillner‐Roth and colleagues for ammonia should be used for each pure component with the present equation. We applied the principle of corresponding states with a two‐fluid model to the present equation for fluid mixtures. On comparison with experimental data, the uncertainty in property calculations by the present equation was evaluated: within ±0.03 · x for bubble point curve, within ±0.04 · x for dew point curve, within ±0.02 · ρ^L for saturated liquid density, and within ±0.02 · ρ for PVTX properties. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 131(4): 320–330, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10023     

ACCURATE SURFACE TEMPERATURE PREDICTION AT HIGH SPEEDS

Computational tools of turbulent combustion have practical applications for various fields including liquid rocket engines, but some numerical issues are still presented for solving supercritical combustion. In the present study, several of these numerical issues are studied and discussed. Turbulent flow and thermal fields of gaseous hydrogen/cryogenic liquid oxygen flame at supercritical pressure are simulated by a turbulence model. To realize real-fluid combustions, the modified Soave-Redlich-Kwong (SRK) equations of state (EOS) are implemented into the flamelet model with a look-up table as functions of mean and variance of mixture fraction, scalar dissipation rate, enthalpy, and pressure. For supercritical combustion flows, modified forms of the pressure implicit with splitting of operator (PISO) algorithm for solving the pressure-velocity linked equation are introduced. From a comparison of instantaneous temperature distributions for gaseous hydrogen/cryogenic liquid oxygen flame at supercritical pressure, the capability of each method based on the different solution sequence is examined and the effective sequence is explored. The results show that the updated mixture fraction reflected in the pressure correction loop is a critical factor for numerical stability. Also, the relative performance of six convection schemes for supercritical combustion is discussed.     

Phase equilibria of benzene–cyclohexane binary mixtures using a solid–liquid–vapor equation-of-state

Based on our previously developed solid–liquid–vapor equation of state (EOS), we have calculated phase equilibria of benzene, cyclohexane, and their mixtures. The model predictions for phase behaviors of pure compounds and vapor–liquid phase equilibria of the binary system have been straightforward and agreed well with the reported data. However, solid–liquid phase equilibria of the binary system are not well correlated to the experimental data with the present unified EOS model. Then, from this fact, we have found that the coexisting solid phases in the present binary system exist in two different solid structures (or two different Gibbs free-energy curves). We have developed a model to overcome such a problem within the present unified EOS model and successfully correlated the experimental data for wide ranges of temperatures and pressures.     

Thermodynamic modeling of carbon dioxide adsorption in aqueous methyl diethanolamine using cubic plus association equation of state (CPA)

The vapor liquid equilibrium of the 3-component system composed of carbon dioxide, water, and methyl diethanolamine has been modeled by the cubic plus association equation of state in a wide range of temperatures (313–433 K), pressures (0.775–4,930 kPa), and methyl diethanolamine wt% (5–75). Carbon dioxide has been considered in two states in this approach: (1) an accumulative molecule bearing the structural shape of 4C and 3B, and (2) a noncumulative molecule. The results obtained from the cubic plus association equation of state showed a good compatibility with the experimental data for the 3-component system. Comparing the results gathered from the Clegg-Pitzer and N-Wilson-NRF models reveals that the cubic plus association model leads to more convincing results than both of them. Furthermore, results obtained from the 4C cumulative design for carbon dioxide in the cubic plus association equation of state shows a lesser error compared to 3B cumulative design and to no designs.     

Temperature variations in the simulation of high-pressure injection-system transient flows under cavitation

Temperature variations and their effects on the simulation of unsteady pipe flows, in the presence of pressure-wave induced cavitation, were investigated with reference to high-pressure fuel injection systems. The thermal effects due to the compressibility of the liquid and to the thermodynamic process in the cavitating flow mixture were analyzed. To that end, the energy conservation equation was applied, in addition to the mass-continuity and momentum-balance equations, along with the constitutive state equation of the fluid. In particular, for the liquid, the physical properties (i.e., bulk modulus of elasticity, density, isothermal speed of sound, thermal expansivity, kinematic viscosity, specific heat at constant pressure) were implemented as functions of pressure and temperature in a closed analytical form matching carefully determined experimental data. Consistent with virtually negligible combined effects of heat transfer and viscous power losses involved in the flow process, the equation of energy was reduced to a state relation among the fluid thermodynamic properties, leading to a barotropic flow model. A comparison between isentropic and isothermal evolutions in the pure liquid regions was carried out for evaluating the influence of the temperature variation simulation on the macroscopic results given by local pressure time-histories. Besides, for cavitation analysis, different thermodynamic transformations of the vapor–liquid mixture were considered and compared.A recently developed conservative numerical model of general application, based on a barotropic flow model, was applied and further assessed through the comparison of prediction and measurement results on injection-system performance.A conventional pump-line-nozzle system was considered for this purpose, being relevant to model evaluation for its pressure-wave dynamics and also because it was subject to severely cavitating flow conditions at part loads. Predicted time-histories of injector-needle lift and pressure at two pipe locations were compared to experimental results. This substantiated the validity and robustness of the conservative model taking temperature variation effects into account, in the simulation of high-pressure injection-system transient flows with great degree of accuracy, even in the presence of cavitation induced discontinuities. The thermal effects due to the temperature variations in the liquid fuel and in the cavitating mixture were analyzed and discussed.     

A model for high-pressure vaporization of droplets of complex liquid mixtures using continuous thermodynamics

This paper presents a comprehensive model for the transient high-pressure vaporization process of droplets of complex liquid mixtures with large number of components in which the mixture composition, the mixture properties, and the vapor-liquid equilibrium (VLE) are described by using the theory of continuous thermodynamics. Transport equations, which are general for the moments and independent of the distribution functions, are derived for the semi-continuous systems of both gas and liquid phases. A general treatment of the VLE is conducted which can be applied with any cubic equation of state (EOS). Relations for the properties of the continuous species are formulated. The model was further applied to calculate the sub- and super-critical vaporization processes of droplets of a representative petroleum fuel mixture - diesel fuel. The results show that the liquid mixture droplet exhibits an intrinsic transient vaporization behavior regardless of whether the pressure is sub- or super-critical. The regression rate of the liquid mixture droplet is reduced significantly during the late vaporization period. The comparison with the results of a single-component substitute fuel case emphasizes the importance of considering the multi-component nature of practical mixture fuel and the critical vaporization effects in practical applications. This paper provides a practical means for more realistically describing the high-pressure vaporization processes of practical fuels.     

Extended compressible thermal cavitation model for the numerical simulation of cryogenic cavitating flow

The compressibility of the vapour–liquid phase is indispensable in simulating liquid hydrogen or liquid nitrogen cavitating flow. In this paper, a numerical simulation method considering compressibility and combining the thermal effects of cryogenic fluids was developed. The method consisted of the compressible thermal cavitation model and RNG k–ε turbulence model with modified turbulent eddy viscosity. The cavitation model was based on the Zwart–Gerber–Belamri (ZGB) model and coupled the heat transfer and vapour–liquid two-phase state equations. The model was validated on cavitating hydrofoil and ogive, and the results agreed well with the experimental data of Hord in NASA. The compressibility and thermal effects were correlated during the phase change process and compressibility improved the accuracy of the numerical simulation of cryogenic cavitating flow based on thermal effects. Moreover, the thermal effects delayed or suppressed the occurrence and development of cavitation behaviour. The proposed modified compressible ZGB (MCZGB) model can predict compressible cryogenic cavitating flow at various conditions.     

发动机氧涡轮喷嘴叶栅气动特性的试验研究

对一个用于大推力液体火箭发动机氧涡轮泵的复速级涡轮的喷嘴叶栅进行了试验研究，以考察喷嘴叶栅的气动特性，验证喷嘴叶栅的气体设计。该复速级喷嘴叶栅采用先进的后加载流动控制技术，以减弱叶机的二次流损失，对喷嘴叶栅进行了四个进气口流角，三个出口等熵马赫数条件下的平面叶栅吹风试验，测取了型面压力分布，出口气流角以及叶栅损失等重要气动特性参数，试验研究表明氧涡轮的喷嘴叶栅的设计是成功的，具有良好的气动特性，可以有效地应用于液体火箭发动机的涡轮中，本研究也为该类喷雾叶栅的设计提供了有用的实验数据和指导意义的结论。