双原子气体现象学能量交换：在直接模拟蒙特卡罗方法中比较Pullin和Borgnakke-Larsen模型
Phenomenological energy exchange of diatomic gases: Comparison of Pullin and Borgnakke-Larsen models in direct simulation Monte Carlo method
AI总结：
本文比较了Pullin与Borgnakke-Larsen模型在DSMC方法中的表现，验证了Pullin模型在稀薄流中的可靠性与准确性。
摘要：
在高超声稀薄流中，分子间碰撞不足导致平动温度与转动温度之间出现显著偏差，从而产生强烈的热非平衡。对于氮气和氧气等双原子气体，直接模拟蒙特卡罗（DSMC）方法通常采用Borgnakke-Larsen（BL）模型来模拟平动-转动能量交换（弛豫）过程。尽管被广泛使用，但BL模型缺乏严格的理论基础，并假设只有部分碰撞导致转动弛豫。为解决这些不足，Pullin在气体动力学理论中引入了动能一致的弛豫模型。通过使用Beta函数进行能量分配，构建了一个满足详细平衡条件的具体碰撞截面。在本研究中，基于DSMC框架对BL和Pullin模型进行了比较研究，其中考虑了原始和简化方程，并通过Beta函数中的物理适应系数进行参数化。一系列测试案例——包括氮气的零维转动弛豫、一维平面Couette流和正常激波、二维高速流过圆柱体、以及三维高速流围绕X38型车辆——被进行以评估这些模型的准确性和效率。结果证实了Pullin和BL模型之间的一致性。由于其严格的理论基础和准确的物理表示，Pullin模型预计将为后续的理论研究和数值模拟提供实质性支持。此外，在高度稀薄的流场 regime（Knudsen数大于1，或海拔高于100公里）中，简化版的Pullin模型表现出与BL模型相当的性能。
英文摘要：
In hypersonic rarefied flows, insufficient intermolecular collisions cause significant deviations between translational and rotational temperatures, leading to strong thermal nonequilibrium. For diatomic gases such as nitrogen and oxygen, the direct simulation Monte Carlo (DSMC) method commonly employs the Borgnakke-Larsen (BL) model to simulate translational-rotational energy exchange (relaxation) processes. Although widely used, the BL model lacks a rigorous theoretical foundation and assumes that only a fraction of collisions lead to rotational relaxation. To address these shortcomings, Pullin introduced a kinetically consistent relaxation model into the gas kinetic theory. By employing the Beta function for energy partitioning, a concrete collision cross section that satisfies the detailed balance condition is constructed. In this study, a comparative investigation of the BL and Pullin models is performed within the DSMC framework, where both original and simplified equations are considered and parameterized by physical accommodated coefficient in the Beta function. A series of test cases--including zero-dimensional rotational relaxation of nitrogen, one-dimensional planar Couette flow and normal shock wave, two-dimensional hypersonic flow past a cylinder, and three-dimensional hypersonic flow around an X38-like vehicle--are performed to assess the accuracy and efficiency of these models. The results confirm the consistency between the Pullin and BL models. Owing to its rigorous theoretical foundation and accurate physical representation, the Pullin model is expected to provide substantial support for the extension of subsequent theoretical studies and numerical simulations. Moreover, in the highly rarefied flow regime (Knudsen number greater than 1, or altitudes above 100 km), the simplified Pullin model exhibits performance comparable to that of the BL model.
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