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改进CLL模型中关键能量参数的近似确定方法

AN APPROXIMATE THEORETICAL METHOD FOR DETERMINING KEY ENERGY PARAMETERS IN THE MODIFIED CLL MODEL

  • 摘要: 超低轨飞行器所在环境的自由分子流特性, 使其气动阻力预测高度依赖于气固表面相互作用的建模精度. 传统 Cercignani-Lampis-Lord(CLL)模型因采用动量−能量耦合的简单适应系数表达, 在刻画超低轨高能来流的气固表面非平衡散射时仍存在一定局限性, 难以满足精细气动分析需求. 针对这一问题, 本文从CLL模型切向与法向反射温度的近似解出发, 结合自由分子流入射的理论反射温度, 基于温度等效原理推导了CLL模型中能量系数关于宏观入射条件的一般化表达式, 构建了只依赖切向与法向动量适应系数这两个待定参数的改进CLL模型. 为了验证改进模型的可靠性, 采用分子动力学方法模拟了氮气与光滑金属铂表面的气固相互作用, 入射温度涵盖300 ~ 2300 K, 入射速度涵盖0 ~ 10 000 m/s. 研究结果表明, 任意方向的宏观动能输入均会引起其他方向的散射行为发生变化, 这种不同方向相互关联的散射行为直接导致了具有独立切向与法向散射核的CLL模型局部失效. 改进CLL 模型由于在新的能量系数定义中引入了全局信息影响, 因此能在一定范围内的宏观动能输入、气固大温差等工况下取得与分子动力学方法较为一致的散射速度分布预测结果. 尽管当单一方向的入射速度大于5000 m/s时, 改进CLL模型的精度开始下降, 但其预测的散射速度分布结果仍显著优于传统 CLL 模型.

     

    Abstract: In the very low Earth orbit (VLEO) environment, free molecular flow characteristics make aerodynamic drag prediction highly dependent on accurate gas-surface interaction modeling. Due to the simple expression of coupled momentum and energy accommodation coefficients, the traditional Cercignani–Lampis–Lord (CLL) model exhibits inherent limitations in characterizing the non-equilibrium scattering of gas molecules from solid surfaces under high-energy incoming flows in VLEO. These deficiencies significantly restrict the model’s applicability for high-fidelity aerodynamic analysis requirements. To address this issue, this paper derives a generalized expression for the energy coefficient in the CLL model based on the temperature equivalence principle, which combines approximate solutions for tangential and normal reflection temperatures of the CLL model with the theoretical reflection temperature of free molecular flow. This leads to an improved CLL model that relies only on two undetermined parameters: the tangential and normal momentum accommodation coefficients. To verify the improved model, molecular dynamics (MD) simulations are employed to model the gas-surface interactions between nitrogen and a smooth platinum surface, covering an incident temperature range of 300-2300 K and incident velocity ranges of 0-10000 m/s. The results indicate that macroscopic kinetic energy input in any direction can alter scattering behavior in other directions. This cross-directional coupling causes local failure of the standard CLL model, which features independent tangential and normal scattering kernels. By introducing the influence of global information into the definition of the new energy coefficient, the improved CLL model yields predictions of scattering velocity distributions that are consistent with MD simulations under conditions such as macroscopic kinetic energy inputs within a certain range and large gas-solid temperature differences. Although the accuracy of the improved CLL model begins to decline when the velocity in single direction exceeds 5000 m/s, its predicted scattering velocity distribution remains significantly superior to that of the traditional CLL model.

     

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