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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. CompressedLUT: An Open Source Tool for Lossless Compression of Lookup Tables for Function Evaluation and Beyond

   https://doi.org/10.1145/3626202.3637575  

   Khataei, Alireza ; Bazargan, Kia ( April 2024 , ACM)

   Lookup tables are widely used in hardware to store arrays of constant values. For instance, complex mathematical functions in hardware are typically implemented through table-based methods such as plain tabulation, piecewise linear approximation, and bipartite or multipartite table methods, which primarily rely on lookup tables to evaluate the functions. Storing extensive tables of constant values, however, can lead to excessive hardware costs in resource-constrained edge devices such as FPGAs. In this paper, we propose a method, called CompressedLUT, as a lossless compression scheme to compress arrays of arbitrary data, implemented as lookup tables. Our method exploits decomposition, self-similarities, higher-bit compression, and multilevel compression techniques to maximize table size savings with no accuracy loss. CompressedLUT uses addition and arithmetic right shift beside several small lookup tables to retrieve original data during the decoding phase. Using such cost-effective elements helps our method use low area and deliver high throughput. For evaluation purposes, we compressed a number of different lookup tables, either obtained by direct tabulation of 12-bit elementary functions or generated by other table-based methods for approximating functions at higher resolutions, such as multipartite table method at 24-bit, piecewise polynomial approximation method at 36-bit, and hls4ml library at 18-bit resolutions. We implemented the compressed tables on FPGAs using HLS to show the efficiency of our method in terms of hardware costs compared to previous works. Our method demonstrated 60% table size compression and achieved 2.33 times higher throughput per slice than conventional implementations on average. In comparison, previous TwoTable and LDTC works compressed the lookup tables on average by 33% and 37%, which resulted in 1.63 and 1.29 times higher throughput than the conventional implementations, respectively. CompressedLUT is available as an open source tool. 

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