基于直接模拟蒙特卡洛方法的真空羽流不确定量化研究

Uncertainty Quantification of Vacuum Plume Simulations Using Direct Simulation Monte Carlo Method

关键词:  不确定量化  直接模拟蒙特卡洛法  真空羽流  配置点方法  气动特性

Key words:  Uncertainty quantification  DSMC  Vacuum plume  Probabilistic collocation method  Aerodynamic properties

摘要:

真实流动环境下的真空羽流必然存在着各种不确定性，那么确定性输入条件的数值模拟必然会存在偏差，因此需进一步研究不确定性对羽流流动特征的影响规律。本文采用直接模拟蒙特卡洛（DSMC）方法，对不确定性输入的羽流流场进行模拟；采用稀疏的概率配置点方法对来流、壁面及模型参数等输入不确定量进行描述，对不确定性的传播和输出目标的平均值、方差及不确定度进行计算。研究表明，流场不确定性沿流线传播至流速最大处之后迅速增强，并在声速线前出现骤减的现象；传播至声速线之后，挡板壁面输入不确定性的影响凸显。其中最为显著的是，压力不确定度在挡板驻点位置达到全场最大值，约为输入不确定量（3.54%）的2.1倍。此外，温度跳跃不确定度受到壁面温度不确定性输入的限制而近似保持为一个恒定值，约为输入不确定度的0.8倍。进而，壁面热流不确定度（5.54%）比壁面正应力不确定度（6.25%）略小，切应力不确定度最小（5.07%）。Sobol’全局敏度分析表明，喉道速度和喉道压力的输入不确定性对气动力/热不确定度的贡献是最大的，且远远超过了壁面温度和模拟分子直径不确定性输入的贡献。

Abstract:

Vacuum plume in real environment is uncertain whereas the numerical simulation is always deterministic, thus the influence of uncertainty on the vacuum plume is required to be elaborately studied. In this paper, the direct simulation Monte Carlo (DSMC) method was used to simulate the plume flowfield with various input uncertainties. Meanwhile, the probabilistic collocation method with sparse grid technique was used to describe the input uncertainties stemming from the incoming flow, wall condition and model parameters. The mean, variance and uncertainty of the output parameters, and the propagation of uncertainty were also calculated by the probabilistic collocation method. The corresponding results indicate that the uncertainties in flowfield sharply increase along the streamline when the flow speed reaches its maximum, and then decrease when close to the sound speed line. The influence of input uncertainty in wall temperature dominates in the downstream area of the sound speed line. Note that, the increment of uncertainty in the pressure is the most significant, which approximately equals to 2.1 times the input uncertainty (3.54%). In addition, the temperature jump uncertainty is almost constant, which is about 0.8 times the input uncertainty. This may be caused by the input uncertainty in the wall temperature that bounds the temperature jump uncertainty. As a consequence, the uncertainty in the heat flux (5.54%) is slightly smaller than that in the normal stress (6.25%), meanwhile the uncertainty in the shear stress (5.07%) is the smallest one. Finally, the Sobol’ global sensitivity analysis shows that the input velocity uncertainty and pressure uncertainty in the throat contribute the most to the uncertainty in aerodynamic characteristics, and considerably exceed the influence of the input uncertainties in the wall temperature and in the reference diameter of simulated particles.