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首页> 外文期刊>Journal of Computational Physics >A solution of the Boltzmann equation in the presence of inelastic collisions
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A solution of the Boltzmann equation in the presence of inelastic collisions

机译：存在非弹性碰撞时玻尔兹曼方程的解

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The effect of inelastic collisions between two molecules on the solution of the Boltzmann equation is taken into account by presenting the change of state of molecules after collisions as a random (with uniform probability distribution) movement along a surface of an N-dimensional sphere, the squared radius of which is equal to the total energy of the molecules before and after the collision in the reference system of the centre of mass. The projection of a point on the surface of this sphere in each of N directions gives the root square of the kinetic energy in one of three directions in the physical space, or the internal energy of one of degrees of freedom, of one of two molecules. The kinetic energies of two molecules are described by the first six dimensions of the system, and the remaining (N - 6) dimensions describe the internal energies. This approach is applied to three test problems: shock wave structure in nitrogen, one-dimensional heat transfer through a mixture of n-dodecane and nitrogen and one-dimensional evaporation of n-dodecane into nitrogen. In the first problem, the predictions of the model are shown to be close to experimental data and also to the predictions of the earlier developed model, based on a different approach to taking into account the effects of inelastic collisions. The predicted heat flux for the second problem and mass flux for the third problem are shown to be very weak functions of the number of internal degrees of freedom when this number exceeds about 15. These results open the way for considering systems with arbitrarily large numbers of internal degrees of freedom by reducing the analysis of these systems to the analysis of systems with relatively small numbers of internal degrees of freedom.
机译：通过将碰撞后分子的状态变化表示为沿N维球体表面的随机运动（具有均匀的概率分布），考虑了两个分子之间非弹性碰撞对Boltzmann方程解的影响。其平方半径等于质心参考系统中碰撞前后分子的总能量。在N个方向上每个点在此球体表面上的投影将给出物理空间中三个方向之一的动能的平方根，或者两个分子之一的内部自由度之一的内能。 。两个分子的动能由系统的前六个维度描述，其余（N-6）个维度描述内部能量。该方法适用于三个测试问题：氮气中的冲击波结构，通过正十二烷和氮的混合物进行的一维热传递以及正十二烷向氮中的一维蒸发。在第一个问题中，基于一种考虑非弹性碰撞影响的方法，模型的预测显示与实验数据接近，并且与较早开发的模型的预测接近。当第二个问题的预测热通量和第三个问题的质量通量显示为内部自由度数的非常弱的函数时，该数量超过约15。这些结果为考虑任意数量的系统自由度开辟了道路。内部自由度，方法是将这些系统的分析简化为内部自由度相对较小的系统的分析。

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