Computation of Hypersonic Shock Wave Flows of Diatomic Gases and Gas Mixtures Using the Generalized Boltzmann Equation
Computation of Hypersonic Shock Wave Flows of Diatomic Gases and Gas Mixtures Using the Generalized Boltzmann Equation
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使用广义玻尔兹曼方程计算双原子气体和气体混合物的高超声速冲击波流
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发表时间：
2010
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通讯作者：
Felix Tcherimmissine
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作者：
R. Agarwal;Felix Tcherimmissine
围绕航天器的高超音速流产生热力学非平衡流场，其局部努森数 L K n / （其中 是气体分子的平均自由程，L 是特征长度），该流场可能位于所有三种状态——连续态、过渡态和稀薄态。连续流域中的流动可以通过纳维-斯托克斯 (NS) 方程进行精确建模；然而，过渡态和稀薄态的流动需要动力学方法，例如直接模拟蒙特卡罗 (DSMC) 方法或玻尔兹曼方程的求解。本文描述了一种计算方法和代码的开发，用于在过渡和稀薄流态的努森数下使用广义玻尔兹曼方程（GBE）计算双原子气体的高超音速非平衡冲击波流。通过计算氮气中旋转-平移 (R-T) 弛豫的 1D 激波结构，并将数值结果与马赫数高达 15 的实验数据进行比较，对 GBE 求解器进行了验证。该求解器已成功用于计算氮气中的 2D 钝体流和真空中矩形氮气射流的 3D 流，以实现 R-T 弛豫。算法的稳定性问题以及在不影响解决方案准确性的情况下减少计算中旋转级别数量的可能性问题已得到严格解决。开发了一种新的两级动力学模型，用于计算双原子气体中的 RT 弛豫，并通过将结果与完整 GBE 的解决方案进行比较来验证。该模型在计算激波结构方面的效率比 GBE 大约高 20 倍。需要注意的是，该模型与BGK模型不同；它解释了弹性和非弹性碰撞。计算方法已扩展到计算双原子气体中的高超声速激波结构，包括 RT 和振动平移 (V-T) 弛豫。氮中的一维冲击结构已被计算，包括 R-T 和 V-T 弛豫，并通过将结果与实验数据进行比较进行了验证。还开发了一种计算方法来计算两种双原子气体的非反应混合物中的高超音速激波结构。已在氮气和氧气的惰性混合物中计算了 R-T 弛豫的一维冲击结构。为了实现这一目标，GBE 在“脉冲空间”而不是速度空间中进行公式化和求解。
Hypersonic flows about space vehicles produce flow fields in thermodynamic nonequilibrium with local Knudsen numbers L K n / (where is the mean free path of gas molecules and L is a characteristic length) which may lie in all the three regimes – continuum, transition and rarefied. Flows in continuum regime can be modeled accurately by the Navier-Stokes (NS) equations; however the flows in transition and rarefied regimes require a kinetic approach such as the Direct Simulation Monte Carlo (DSMC) method or the solution of the Boltzmann equation. This paper describes the development of a computational methodology and a code for computing hypersonic non-equilibrium shock wave flows of diatomic gases using the Generalized Boltzmann Equation (GBE) at Knudsen numbers in transitional and rarefied flow regimes. The GBE solver has been validated by computing the 1D shock structure in nitrogen for Rotational-Translational (R-T) relaxations and comparing the numerical results with the experimental data for Mach numbers up to 15. The solver has been exercised successfully for computing the 2D blunt body flows in nitrogen and 3D flow from a rectangular jet of nitrogen in vacuum for R-T relaxations. The issues of stability of the algorithm and the possibility of reducing the number of rotational levels in the computations without compromising the accuracy of the solutions have been rigorously addressed. A new two-level kinetic model has been developed for computing the RT relaxations in a diatomic gas and has been validated by comparing the results with the solutions of complete GBE. The model is about twenty times more efficient than the GBE in computing the shock structure. It should be noted that the model is different than the BGK model; it accounts for both elastic and inelastic collisions. The computational methodology has been extended to compute the hypersonic shock structure in diatomic gases including both the RT and Vibrational-Translational (V-T) relaxations. 1-D shock structure in nitrogen has been computed including both R-T and V-T relaxations and has been validated by comparing the results with the experimental data. A computational methodology has also been developed to compute the hypersonic shock structure in a non-reactive mixture of two diatomic gases. 1-D shock structure has been computed in an inert mixture of nitrogen and oxygen for R-T relaxations. To accomplish this, the GBE is formulated and solved in “impulse space” instead of velocity space.