Aerospace Science and Technology 91 (2019) 656–668 Contents lists available at ScienceDirect Aerospace Science and Technology www.elsevier.com/locate/aescte Comprehensive assessment of newly-developed slip-jump boundary conditions in high-speed rarefied gas flow simulations Nam T.P. Le a,b , Ehsan Roohi c,∗ , Thoai N. Tran d a Divison of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam c High Performance Computing (HPC) Laboratory, Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran d Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, Viet Nam a r t i c l e i n f o a b s t r a c t Article history: Received 18 January 2019 Received in revised form 23 May 2019 Accepted 3 July 2019 Available online 9 July 2019 Keywords: Rarefied gas flows Slip-jump boundary conditions Aoki et al. conditions Slip velocity Surface gas temperature In this paper we numerically evaluate the recently developed Aoki et al. slip and jump conditions in high-speed rarefied gas flows for the first time. These slip and jump conditions are developed to be employed with the Navier–Stokes–Fourier equations. They were derived based on the Boltzmann equation with the first order Chapman–Enskog solution, and the analysis of the Knudsen layer. Four aerodynamic configurations are selected for a comprehensive evaluation of these conditions such as sharp-leading-edge flat plate, vertical plate, wedge and circular cylinder in cross-flow with the Knudsen number varying from 0.004 to 0.07, and argon as the working gas. The simulation results using the Aoki et al. boundary conditions show suitable agreement with the DSMC data for slip velocity and surface gas temperature. The accuracy of these boundary conditions is superior to the conventional Maxwell, Smoluchowski and Le boundary conditions. © 2019 Elsevier Masson SAS. All rights reserved. 1. Introduction Rarefied gas flow generally has four distinct regimes. They are characterized according to their Knudsen number, Kn, that it is de- fined as the ratio of gas mean free path, i.e., the average distance a molecule moves between successive intermolecular collisions, to a characteristic length of the vehicle body. The continuum regime corresponds to very small Kn number, Kn ≤ 0.001. The slip regime with the temperature jump and slip velocity conditions at the sur- face is indicated by the range 0.001 ≤ Kn ≤ 0.1. When the gas flows become more and more rarefied then they are character- ized as the transition and free molecular regimes, respectively. The transition-continuum regime corresponds to 0.1 ≤ Kn ≤ 1, and the free molecular regime to Kn ≥ 1. Two typical methods have been used to solve the rarefied gas flows such as Direct Simulation Monte-Carlo (DSMC) and Computational Fluid Dynamics (CFD). The DSMC method has successfully simulated the rarefied gas flows for four regimes aforementioned, but its computational effort is quite expensive at small Knudsen number conditions. The CFD method that solves the Navier–Stokes–Fourier (N–S–F) equations accom- * Corresponding author. E-mail addresses: letuanphuongnam@tdtu.edu.vn (N.T.P. Le), e.roohi@ferdowsi.um.ac.ir (E. Roohi), tranngocthoai@iuh.edu.vn (T.N. Tran). panied with appropriate slip and jump boundary conditions may successfully simulate the rarefied gas flows in the slip regime and even beyond. The slip and jump conditions play an essential role in the accurate prediction of the surface quantities. During the last decades, several slip and jump boundary conditions were devel- oped based on the kinetic theory of gases, the Langmuir isotherm adsorption, and combination of the Langmuir isotherm adsorption and kinetic theory of gases in [1–9] to work with the N–S–F equa- tions to simulate the rarefied gas flows. However, they have not yet predicted well the surface quantities in rarefied gas simulations. The rarefied gas flow cannot be described by the ordinary macroscopic equations. In [10,11] the slip and jump boundary con- ditions have been recently derived from the Boltzmann equations on the basis of the first-order Chapman–Enskog solution of the Boltzmann equation, and the analysis of the Knudsen layer adja- cent to the boundary. These conditions were developed for large density and temperature variation to employ with the compress- ible N–S–F equations. They were derived for the rarefied gas flows applied to monatomic gas in [10], and polyatomic gas in [11]. They have been used and evaluated for the numerical analysis of the Taylor-vortex flow in [12]. In this paper, we only focus on the re- visit and assessment of the slip and jump boundary conditions for the monatomic gas in [10]. As for the Aoki et al. slip and jump conditions derived for poly- atomic gases in [11], we need to determine the term related to the https://doi.org/10.1016/j.ast.2019.07.005 1270-9638/© 2019 Elsevier Masson SAS. All rights reserved.