Gas-Kinetic Unified Algorithm for Re-Entering Complex Flows Covering Various Flow Regimes by Solving Boltzmann Model Equation

Complex flow problems involving atmosphere re-entry have been one of the principal subjects of gas dynamics with the development of spaceflight. To study the aerodynamics of spacecraft re-entering Earth's atmosphere, Tsien (1946) early presented an interesting way in terms of the degree of gas rarefaction, that the gas flows can be approximately divided into four flow regimes based on the order of the Knudsen number ( Kn ), that is, continuum flow, slip flow, transition flow, and free molecular flow. In fact, the aerothermodynamics around space vehicles is totally different in various flow regimes and takes on the complex characteristics of many scales. In the continuum flow regime with a very small Knudsen number, the molecular mean free path is so small and the mean collision frequency per molecule is so sizeable that the gas flow can be considered as an absolute continuous model. Contrarily in the rarefied gas free-molecule flow regime with a large Knudsen number, the gas molecules are so rare with the lack of intermolecular collisions that the gas flow can but be controlled by the theory of the collisionless or near free molecular flow. Especially, the gas flow in the rarefied transition regime between the continuum regime and free molecular regime is difficult to treat either experimentally or theoretically and it has been a challenge how to effectively solve the complex problems covering various flow regimes. To simulate the gas flows from various regimes, the traditional way is to deal with them with different methods. On the one hand, the methods related to high rarefied flow have been developed, such as the microscopic molecular-based Direct Simulation Monte Carlo (DSMC) method. On the other hand, also the methods adapted to continuum flow have been well developed, such as the solvers of macroscopic fluid dynamics in which the Euler, Navier-Stokes or Burnett-like equations are numerically solved. However, both the methods are totally different in nature, and the computational results are difficult to link up smoothly with various flow regimes. Engineering development of current and intending spaceflight projects is closely concerned with complex gas dynamic problems of low-density flows (Koppenwallner & Legge 1985, Celenligil, Moss & Blanchard 1991, Ivanov & Gimelshein 1998, and Sharipov 2003), especially in the rarefied transition and near-continuum flow regimes.