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1. Multi-component transcritical flow simulation using in situ adaptive tabulation of vapor-liquid equilibrium solutions

   Zhang, Hongyuan; Yang, Suo. (May 2021, ILASS-Americas 31st Annual Conference on Liquid Atomization and Spray Systems)

   null (Ed.)

   The studies of transcritical and supercritical injection have attracted much interest in the past 30 years. However, most of them were mainly concentrated on the single-component system, whose critical point is a constant value. To capture the thermophysical properties of multicomponent, a phase equilibrium solver is needed, which is also called a vapor-liquid equilibrium (VLE) solver. But VLE solver increases the computation cost significantly. Tabulation methods can be used to store the solution to avoids a mass of redundant computation. However, the size of a table increases exponentially with respect to the number of components. When the number of species is greater than 3, the size of a table far exceeds the limit of RAM in today's computers. In this research, an online tabulation method based on In Situ Adaptive Tabulation (ISAT) is developed to accelerate the computation of multicomponent fluid. Accuracy and efficiency are analyzed and discussed. The CFD solver used in this research is based on the Pressure-Implicit with Splitting of Operators (PISO) method. Peng-Robinson equation of state is used in phase equilibrium. 

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2. An in situ adaptive tabulation based approach to multi-component transcritical flow simulation

   Zhang, Hongyuan; Yang, Suo. (May 2021, 12th U.S. National Combustion Meeting)

   null (Ed.)

   The studies of transcritical and supercritical flow have attracted much interest in the past 30 years. However, most of them mainly focus on the single-component system, whose critical point is constant. We use the vapor-liquid equilibrium (VLE) theory to capture the thermodynamic properties of the mixture and investigate transcritical flows (i.e., supercritical CO2 oxy-combustion systems). In sCO2 oxy-combustion systems, due to the presence of water from the previous cycles, the mixture critical point increases significantly, such that the phase separation could occur in both the compressor and combustor. However, the VLE solver increases the computation cost of fluid simulation significantly, which limited the size of simulations we can conduct. Naturally, tabulation methods can be used to store the VLE solutions to avoids redundant computation. However, the size of the VLE table increases exponentially with respect to the number of components. When the number of species components is greater than three, the size of the VLE table far exceeds the RAM’s limit in today’s standard computers. In this research, an online tabulation method based on In Situ Adaptive Tabulation (ISAT) is developed to accelerate the computation of multicomponent fluids based on VLE theory. Accuracy and efficiency are analyzed and discussed. The CFD solver used in this research is based on the Pressure-Implicit with Splitting of Operators (PISO) method. Peng-Robinson equation of state (EOS) is used in the calculations of phase equilibrium. 

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3. Investigation of transcritical shock-droplet interaction using vapor-liquid equilibrium (VLE)-based CFD simulation

   Zhang, Hongyuan; Yang, Suo (May 2022, ILASS-Americas 32nd Annual Conference on Liquid Atomization and Spray Systems)

   To achieve high performance, the working pressure of liquid-fueled rocket engines, diesel engines, and gas turbines (based on deflagration or detonation) is continuously increasing, which could reach the thermodynamic critical pressure of the liquid fuel. For this reason, the studies of trans- and super-critical injection are getting more attention. However, most of the multiphase researches were mainly concentrated on single- or two-component systems, which cannot capture the multicomponent phase change in real high-pressure engines and gas turbines. The phase boundary, especially near the critical points, needs to be accurately determined to investigate the multicomponent effects in transcritical flow. This work used our previously developed thermodynamic model based on the vapor-liquid equilibrium (VLE) theory, which can predict the phase separation near the critical points. An in situ adaptive tabulation (ISAT) method was developed to accelerate the computation of the VLE model such that the expensive multicomponent VLE calculation can be cheap enough for CFD. The new thermodynamic model was integrated into OpenFOAM to build a VLE-based CFD solver. In this work, simulations are conducted using our new VLE-based CFD solver to reveal the phase change effects in transcritical flow. Specifically, shock-droplet interaction are investigated to reveal the shock-driven high pressure phase change. 

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4. Numerical investigation of high-pressure transcritical shock-droplet interaction and mixing layer using VLE-based CFD accelerated by ISAT

   https://doi.org/10.2514/6.2023-1857  

   Zhang, Hongyuan; Yang, Suo (January 2023, AIAA SCITECH 2023 Forum)

   To achieve high power density and thermodynamic cycle efficiency, the working pressures of liquid-propellant rocket engines, diesel engines, and gas turbines (based on deflagration or detonation) are continuously increasing, which could reach or go beyond the thermodynamic critical pressure of the liquid propellant. For this reason, the studies of trans- and super-critical injection are getting more and more attention. However, the simulation of transcritical phase change is still a challenging topic. The phase boundary, especially near the mixture critical point, needs to be accurately determined to investigate the multicomponent effects on transcritical injection and atomization. This work used our previously developed thermodynamic model based on the vapor-liquid equilibrium (VLE) theory, which can predict the phase separation near the mixture critical point. An \textit{in situ} adaptive tabulation (ISAT) method was developed to accelerate the computationally expensive multicomponent VLE computation such that it can be cheap enough for CFD. The new thermodynamic model was integrated into OpenFOAM to develop a VLE-based CFD solver. In this work, shock-droplet interaction and two-phase mixing simulations are conducted using our new VLE-based CFD solver. The shock-droplet interaction simulation results capture the thermodynamic condition of the surface entering the supercritical state after shock passes through. The atomization of droplets could be triggered by vorticity formed at the droplets' surface. 2D temporal mixing layer simulations show the evolution of the transcritical mixing layer and capture the phase split effect at the mixing layer. 

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5. In situ adaptive tabulation of vapor-liquid equilibrium solutions for multi-component high-pressure transcritical flows with phase change

   https://doi.org/10.1016/j.jcp.2024.112752  

   Zhang, Hongyuan; Srinivasan, Navneeth; Yang, Suo (January 2024, Journal of Computational Physics)

   Vapor-liquid equilibrium (VLE) is a family of first-principled thermodynamic models for transcritical multiphase flows, which can accurately capture the phase transitions at high-pressure conditions that are difficult to deal with using other models. However, VLE-based computational fluid dynamics (CFD) simulation is computationally very expensive for multi-component systems, which severely limits its applications to real-world systems. In this work, we developed a new ISAT-VLE method based on the in situ adaptive tabulation (ISAT) method to improve the computational efficiency of VLE-based CFD simulation with reduced memory usage. We developed several ISAT-VLE solvers for both fully conservative (FC) and double flux (DF) schemes. New methods are proposed to delete redundant records in the ISAT-VLE table and the ISAT-VLE method performance is further improved. To improve the convergence of the VLE solvers, a modified initial guess for equilibrium constant is also introduced. Simulations of high-pressure transcritical two-phase temporal mixing layers and shock-droplet interaction were conducted using the ISAT-VLE CFD solvers. The simulation results show that the new method obtains a speed-up factor approximately from 10 to 60 and the ISAT errors can be controlled within 1%. The shock-droplet interaction results show that the DF scheme can achieve a higher speed-up factor than the FC scheme. The two sets of simulations exhibit the phase separation at high-pressure conditions. It was found that even at supercritical pressures with respect to each component, the droplet surface could still be in a subcritical two-phase state, because the mixture critical pressure is often significantly higher than each component and hence triggers phase separation. In addition, a shock wave could partially or completely convert the droplet surface from a subcritical two-phase state to a single-phase state by raising temperature and pressure. 

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