Gas-kinetic unified algorithm for computable modeling of Boltzmann equation and application to aerothermodynamics for falling disintegration of uncontrolled Tiangong-No.1 spacecraft

Zhi-Hui Li,Xue-Zhou Sun,Qiang Ma,Xiao-Wei Tang,Lei-Ning Dang,Ao-Ping Peng

doi:10.1186/s42774-019-0009-4

Abstract

How to solve the hypersonic aerothermodynamics around large-scale uncontrolled spacecraft during falling disintegrated process from outer space to earth, is the key to resolve the problems of the uncontrolled Tiangong-No.1 spacecraft reentry crash. To study aerodynamics of spacecraft reentry covering various flow regimes, a Gas-Kinetic Unified Algorithm (GKUA) has been presented by computable modeling of the collision integral of the Boltzmann equation over tens of years. On this basis, the rotational and vibrational energy modes are considered as the independent variables of the gas molecular velocity distribution function, a kind of Boltzmann model equation involving in internal energy excitation is presented by decomposing the collision term of the Boltzmann equation into elastic and inelastic collision terms. Then, the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions by developing the discrete velocity ordinate method and numerical quadrature technique. The unified algorithm of the Boltzmann model equation involving thermodynamics non-equilibrium effect is presented for the whole range of flow regimes. The gas-kinetic massive parallel computing strategy is developed to solve the hypersonic aerothermodynamics with the processor cores 500~45,000 at least 80% parallel efficiency. To validate the accuracy of the GKUA, the hypersonic flows are simulated including the reentry Tiangong-1 spacecraft shape with the wide range of Knudsen numbers of 220~0.00005 by the comparison of the related results from the DSMC and N-S coupled methods, and the low-density tunnel experiment etc. For un-controlling spacecraft falling problem, the finite-element algorithm for dynamic thermal-force coupling response is presented, and the unified simulation of the thermal structural response and the hypersonic flow field is tested on the Tiangong-1 shape under reentry aerodynamic environment. Then, the forecasting analysis platform of end-of-life large-scale spacecraft flying track is established on the basis of ballistic computation combined with reentry aerothermodynamics and deformation failure/disintegration.

Highlights

Large-scale spacecraft in low orbit of 300 km~ 500 km faces the problems of de-orbiting fall around the end of life, and disintegrates during reentering back to the earth because they suffer tremendous aerothermodynamics environment and overloads [1]
To establish the forecasting platform of flying track for the uncontrolled spacecraft falling from outer space to earth as the first attempt, the Direct Simulation Monte-Carlo (DSMC) for hypersonic reentry thermochemical non-equilibrium flow, N-S/DSMC, slip N-S as verifying tools, and the computational methods of thermal environment and structural heat transfer/composite material pyrolysis, and disassembly and separation have been developed [7, 9, 43, 44] by taking the coupling simulation with trajectory and aerothermodynamic calculation as the main line combined with statistical analysis and 3D scene visualization, the forecasting analysis platform of flying track for the end-of-life large-scale spacecraft is established for the unified computation of reentry aerothermodynamics, deformation failure/ablation/disintegration with engineering treatment
4 Results and discussion To verify the accuracy and reliability of the present computable modeling of Boltzmann equation and Gas-Kinetic Unified Algorithm (GKUA) in solving thermodynamic non-equilibrium flows with vibrational energy excitation, the cylinder flows of Nitrogen gas with Kn∞ = 0.01, Ma∞ = 5, n∞ = 1.4966E20/m3, T∞ = Tw = 500k are solved by the present GKUA and the DSMC, (2019) 1:4

Summary

Introduction

Large-scale spacecraft in low orbit of 300 km~ 500 km faces the problems of de-orbiting fall around the end of life, and disintegrates during reentering back to the earth because they suffer tremendous aerothermodynamics environment and overloads [1].

Results

Conclusion