跨/超临界流体大涡模拟状态方程亚格子模型综述

周明烁, 丁思宇, 王兴建

清华大学学报（自然科学版） ›› 2023, Vol. 63 ›› Issue (4) : 473-486.

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清华大学学报（自然科学版） ›› 2023, Vol. 63 ›› Issue (4) : 473-486. DOI: 10.16511/j.cnki.qhdxxb.2023.25.013
综述

跨/超临界流体大涡模拟状态方程亚格子模型综述

  • 周明烁, 丁思宇, 王兴建
作者信息 +

Review of subgrid models of the equation of state in the large eddy simulation of transcritical and supercritical flows and combustion

  • ZHOU Mingshuo, DING Siyu, WANG Xingjian
Author information +
文章历史 +

摘要

随着高效率、大推力燃烧技术的发展,跨/超临界流体流动的情况在先进动力装置中日益增加。研究跨/超临界流体流动与燃烧具有重要的应用价值。由于真实工况下实验测量成本高、风险大,可得到的实验数据有限,使用大涡模拟(large eddy simulation,LES)可获取详细流场结构和燃烧动力学特性信息。跨/超临界流体流动过程中热物性参数经历非线性剧烈变化,须引入真实气体状态方程并修正现有亚格子尺度建模理论。该文讨论了工程计算中常用的真实气体状态方程及其适用条件,阐述了状态方程亚格子模型的发展思路与历程,总结了4种亚格子密度模型的原理和性能等,并指出了跨/超临界流体流动与LES未来可能的研究方向,为准确快速计算跨/超临界流体问题提供思路,进而支撑新一代先进动力系统的研制与开发。

Abstract

[Significance] With the requirement of high efficiency and heavy thrust, fluid mixing and combustion under transcritical and supercritical conditions have been increasingly used in advanced propulsion systems. Transcritical and supercritical fluids exhibit numerous mixing and combustion properties different from those of subcritical (low-pressure) fluids because of thermodynamic nonidealities and transport anomalies. Therefore, elucidating the fundamental characteristics of transcritical and supercritical fluid flows and combustion is vital. Extreme operating conditions pose severe challenges to experimental measurements and optical diagnostics, while large eddy simulation (LES) can be used to detail flow structures and combustion dynamics in a relatively affordable manner. To capture abnormal variations in thermophysical properties, introducing a real-fluid equation of state (EOS) is vital, as the EOS is required for the closure of governing equations. [Progress] In high-fidelity simulations of transcritical and supercritical flows, cubic EOSs, including the Soave-Redlich-Kwong EOS (SRK EOS), the Peng-Robinson EOS (PR EOS), and volume-translation methods, have been frequently used owing to their relatively simple forms and high computation efficiency. In LES-based system equations, EOS filtering introduces an unclosed subgrid term, which is generally neglected in ideal-gas problems. However, this subgrid term plays a substantial role in transcritical and supercritical flows owing to the highly nonlinear changes in thermophysical properties. For density-based solvers, subgrid pressure is required, while subgrid density is required for pressure-based solvers. For demonstration, the relative magnitude of the subgrid density with respect to the filtered density is evaluated using the results of direct numerical simulation (DNS) of the transcritical liquid oxygen/methane mixing layer. The contribution of the subgrid density increases with the filtering size, with up to 60% of the DNS-filtered density in the transcritical mixing regions. To account for the subgrid density effect, various types of subgrid density models are considered, including the Reynolds-filtered model (RFM), gradient model (GM), scale similarity model (SSM), and filtered density function (FDF) model. In RFM, the EOS is evaluated using Reynolds-filtered primitive variables rather than Favre-filtered variables, which leads to an underestimation of the filtered density and limited improvement in accuracy. GM is analogous to the Smagorinsky model with both static and dynamic forms, while SSM is formulated upon the assumption of scale similarity between the grid-filter and test-filter levels. Both GM and SSM improve the accuracy of the filtered density to some extent. FDF shows the overall best performance, with the lowest modeling errors. The model assumes a beta distribution form of the Favre FDF to model the subgrid-scale fluctuations. In summary, GM, SSM, and FDF show evident improvements in the filtered density, while RFM needs further improvement to consistently achieve the required accuracy. The development of the subgrid pressure is briefly introduced, and RFM best approximates the subgrid pressure. [Conclusions and Prospects] Future research on the subgrid modeling of the real-fluid EOSs for transcritical and supercritical flows is needed in the following aspects. First, a more accurate and computationally efficient EOS for high-fidelity simulations needs to be developed. Second, more universal and effective subgrid models of EOSs and other thermophysical properties should be explored. The prevailing multidisciplinary methods, such as deep neural networks and random forests, show great potential to improve both the accuracy and efficiency of LES. Enhanced models would strengthen the predictive capability of current modeling and simulation tools and support the development of next-generation propulsion systems.

关键词

跨/超临界流体 / 大涡模拟 / 真实气体状态方程 / 状态方程亚格子模型

Key words

transcritical and supercritical flows / large eddy simulation (LES) / real-fluid equation of state / subgrid models of equations of state

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周明烁, 丁思宇, 王兴建. 跨/超临界流体大涡模拟状态方程亚格子模型综述[J]. 清华大学学报（自然科学版）. 2023, 63(4): 473-486 https://doi.org/10.16511/j.cnki.qhdxxb.2023.25.013
ZHOU Mingshuo, DING Siyu, WANG Xingjian. Review of subgrid models of the equation of state in the large eddy simulation of transcritical and supercritical flows and combustion[J]. Journal of Tsinghua University(Science and Technology). 2023, 63(4): 473-486 https://doi.org/10.16511/j.cnki.qhdxxb.2023.25.013

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基金

王国家自然科学基金面上项目(52276123);航空发动机及燃气轮机基础科学中心项目(HT-P2022-B-II-020-001);国家科技重大专项(Y2019-I-0022-0021)

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