真实流体准守恒方法：力学平衡机制与液面上风异常

中文摘要 AI 辅助

从连续介质热力学的角度出发，我们重新审视了真实流体有限体积法中的压力振荡问题，并阐明了真实流体准守恒（RFQC）方法的物理对应物。RFQC方法通过沿流线演化等熵内能-压力关系的仿射参数ξ和E0来恢复力学平衡压力，同时热力学重新投影将与等熵轨迹的偏差转化为内能误差，从而确保该方法的热力学一致性和数值稳定性。然后，我们研究了RFQC方法的适用极限，并在极端相变情况下识别出液面上风异常（LUA）。对于涉及液-气相变的黎曼问题，如果初始叠加的液面上风平移速度超过一定阈值，可能会出现数值异常。理论分析表明，这种异常是由相变期间仿射斜率ξ的数量级跳跃引发的，随后延迟了下游低压单元中的压力上升。同时，重新投影等效地消除了正压力增量。结果，在这个异常单元中反复产生大的重新投影内能误差，并且该单元被困在延迟的低压恢复循环中。分析表明，LUA是一种启动异常，可以通过在初始不连续处引入正则化策略来解决。通过所提出的正则化策略，RFQC方法对于极端热力学流动（如声相变射流）具有更高的精度和鲁棒性。

英文摘要

From the perspective of continuum thermodynamics, we revisit the pressure oscillation problem in finite-volume methods for multiphase real fluids and clarify the physical counterpart of the Real Fluid Quasi-Conservative (RFQC) method. The pressure oscillation in conservative finite-volume methods originates from their implicit thermodynamic equilibrium assumption, whereas recovering an oscillation-free pressure requires additional physical information. The RFQC method achieves this by evolving the affine parameters xi and E0 of the isentropic internal-energy-pressure relation along pathlines, while the thermodynamic re-projection converts the deviation from the isentropic trajectory into an internal-energy error, thereby ensuring the thermodynamic consistency and numerical stability of the method. We then investigate the applicability limit of the RFQC method and identify a Liquid-upwind Anomaly (LUA) in extreme phase-change cases. For a Riemann problem involving liquid-vapor phase change, a numerical anomaly may occur if a liquid-upwind translational velocity is initially superimposed. Theoretical analysis reveals that this anomaly is initiated by the jump in the affine slope xi during phase change, which delays pressure rise in the downstream vapor cell. Concurrently, the re-projection removes the positive pressure increment, repeatedly generating large internal-energy errors and trapping the vapor cell in a cycle of delayed pressure recovery. The analysis indicates that the LUA is a start-up anomaly, which can be resolved by introducing a regularization strategy at the initial discontinuity. With the proposed regularization strategy, the RFQC method is equipped with enhanced accuracy and robustness for extreme thermodynamic flows, such as sonic phase-change jets.

发表机构

• Advanced Propulsion Technology Laboratory, National University of Defense Technology（国防科技大学先进推进技术实验室）
• College of Aerospace Science and Engineering, National University of Defense Technology（国防科技大学航空航天学院）
• Institute of Power Plants and Automation, Shanghai Jiao Tong University（上海交通大学动力与能源研究所）

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37 Pages, 20 figures