In the present work, a deterministic approach is applied for the first time ever to simulate the rarefied gas flow in the particle exhaust system of a nuclear fusion device. As an example of such a system, the pumping area of the DEMO (DEMOnstration Fusion Power Plant) fusion reactor is considered, which is characterized by high geometrical complexity and strong gradients of macroscopic quantities. The Knudsen number in this system may vary from free molecular up to the slip regime and the flow behavior must be described by the Boltzmann equation. In the present work, the Boltzmann equation is approximated by the well-known Bhatnagar–Gross–Krook and Shakhov kinetic models supplemented with the deterministic discrete velocity method. In addition, in order to assess the capabilities of the deterministic modeling, the problem has also been studied by solving the Boltzmann equation with the stochastic direct simulation Monte Carlo (DSMC) method. Extended comparisons between the deterministic and stochastic methods in terms of all macroscopic quantities of practical interest, namely, pressure, number density, temperature, and pumping fluxes, are performed and remarks about the effectiveness of the implemented deterministic approach have been drawn. Results are obtained by assuming He and D2 gas flows, various values of the capture coefficient at the pumping opening, and two different scenarios of the inlet gas temperature. In all examined cases, the deterministic results are in very good agreement with the DSMC ones, with the maximum relative deviation being less than 4%. The nonlinear deterministic code is significantly faster than the stochastic DSMC code for acceptable noise levels. The pumping fluxes and the pressure values in the vicinity of the pumping opening, both quantities useful for pumping system evaluation, have been calculated in terms of the capture coefficient. The present work may support decision making on the suitability of the pumping technology of DEMO and the design of the pumping system.

中文翻译：

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聚变粒子排气系统中稀薄气体流动的确定性和随机建模

在目前的工作中，首次应用确定性方法来模拟核聚变装置粒子排放系统中的稀薄气体流动。作为这种系统的一个例子，我们考虑了 DEMO（DEMOnstration Fusion Power Plant）聚变反应堆的泵浦区，其特点是几何复杂度高，宏观量梯度强。该系统中的克努森数可能从自由分子到滑移状态变化，流动行为必须由玻尔兹曼方程描述。在目前的工作中，玻尔兹曼方程由众所周知的 Bhatnagar-Gross-Krook 和 Shakhov 动力学模型近似，并辅以确定性离散速度方法。此外，为了评估确定性建模的能力，还通过使用随机直接模拟蒙特卡罗 (DSMC) 方法求解 Boltzmann 方程来研究该问题。在所有实际感兴趣的宏观量（即压力、数密度、温度和泵送通量）方面，确定性方法和随机方法之间进行了扩展比较，并对所实施的确定性方法的有效性进行了评论。结果是通过假设 He 和 D2 气体流量、泵开口处捕获系数的各种值以及入口气体温度的两种不同情况获得的。在所有检查的情况下，确定性结果与 DSMC 的结果非常吻合，最大相对偏差小于 4%。对于可接受的噪声水平，非线性确定性代码明显快于随机 DSMC 代码。泵送流量和泵送口附近的压力值，这两个对泵送系统评估有用的量，已根据捕获系数计算得出。目前的工作可以支持关于 DEMO 泵送技术的适用性和泵送系统设计的决策。