Phenomenological energy exchange of diatomic gases: Comparison of Pullin and Borgnakke-Larsen models in direct simulation Monte Carlo method

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.