scholarly journals Method for investigating rarefied gas flow around a cylindrical surface at arbitrary Knudsen numbers

2021 ◽  
Vol 2094 (2) ◽  
pp. 022078
Author(s):  
Vladimir N Belov ◽  
Evgeny G Mayasov ◽  
Elena A Pervushkina ◽  
Aleksey A Statuev ◽  
Viacheslav B Trukhmanov
Keyword(s):  
Cylindrical Surface ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Unit Length ◽  
Collision Integral ◽  
Resistance Force ◽  
Hard Sphere Model ◽  
Knudsen Numbers ◽  
The Moment ◽  
Moment Of Resistance

Abstract A moment method for solving the linearized kinetic Boltzmann equation for arbitrary Knudsen numbers is presented. The isothermal flow of a rarefied gas around a cylindrical surface (the limiting cylindrical Couette problem) is investigated. The moments of the collision integral are calculated for the hard sphere model. The moment of resistance force acting per unit length of the surface, the profile of the gas flow velocity in the transient regime, and the gas velocity on the surface are calculated.

A Hybrid Fokker-Planck-DSMC Solution Algorithm for the Whole Range of Knudsen Numbers

2013 ◽  
Author(s):  
M. Hossein Gorji ◽  
Stephan Küchlin ◽  
Patrick Jenny
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Time Integration ◽  
Computational Cost ◽  
Direct Simulation Monte Carlo ◽  
Large Cell ◽  
Solution Algorithm ◽  
Rarefied Gas Flows ◽  
Knudsen Numbers ◽  
Fokker Planck

In this work, we present a hybrid algorithm based on the Fokker-Planck (FP) kinetic model and direct simulation Monte Carlo (DSMC) for studies of rarefied gas flows. A particle based FP solution algorithm for rarefied gas flow simulations has recently been devised by the authors. The motivation behind the FP approximation is purely computational, i.e. due to the fact that the resulting random processes are continuous in time the computational cost of the corresponding time integration becomes independent of the Knudsen number. However, the method faces limitations for flows with very high Knudsen numbers (larger than approximately 5). In the method presented here, the FP approach is coupled with DSMC in order to gain from the efficiency of the FP model and from the accuracy of DSMC at small and large cell based Knudsen numbers, respectively.

scholarly journals A rarefied gas flow around a rotating sphere: diverging profiles of gradients of macroscopic quantities

2019 ◽  
Vol 862 ◽  
pp. 5-33 ◽  
Author(s):  
Satoshi Taguchi ◽  
Kazuyuki Saito ◽  
Shigeru Takata
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Velocity Distribution Function ◽  
Normal Derivative ◽  
Accommodation Coefficient ◽  
Jump Discontinuity ◽  
Rotating Sphere ◽  
Wide Range ◽  
Normal Distance ◽  
The Moment

The steady behaviour of a rarefied gas around a rotating sphere is studied numerically on the basis of the linearised ellipsoidal statistical model of the Boltzmann equation, also known as the ES model, and the Maxwell diffuse–specular boundary condition. It is demonstrated numerically that the normal derivative of the circumferential component of the flow velocity and that of the heat flux diverge on the boundary with a rate $s^{-1/2}$, where $s$ is the normal distance from the boundary. Further, it is demonstrated that the diverging term is proportional to the magnitude of the jump discontinuity of the velocity distribution function on the boundary, which originates from the mismatch of the incoming and outgoing data on the boundary. The moment of force exerted on the sphere is also obtained for a wide range of the Knudsen number and for various values of the accommodation coefficient.

scholarly journals New temperature jump boundary condition in high-speed rarefied gas flow simulations

2017 ◽  
Vol 39 (2) ◽  
pp. 165-176
Author(s):  
Nam Tuan Phuong Le ◽  
Ngoc Anh Vu ◽  
Le Tan Loc ◽  
Tran Ngoc Thoai
Keyword(s):  
High Speed ◽  
Gas Flow ◽  
Sliding Friction ◽  
Temperature Jump ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Jump Condition ◽  
Rarefied Gas Flow ◽  
Flow Simulations ◽  
Knudsen Numbers

The effect of the sliding friction has been important in calculating the heat flux of gas flow from the surface since there is some slip over the surface. There has not been any the temperature jump condition including the sliding friction part so far. In this paper, we will propose a new temperature jump condition that includes the sliding friction. Our new temperature jump condition will be evaluated for NACA0012 micro-airfoil in high-speed rarefied gas flow simulations using the CFD method, which solves the Navier-Stokes equations within the OpenFOAM framework with working gas as air. The airfoil case is simulated with various Knudsen numbers from 0.026 to 0.26, and the angles-of-attack (AOAs) from 0-deg to 20-deg. The surface gas temperatures predicting by our new temperature jump condition give good agreements with the DSMC data, especially the NACA0012 micro-airfoil cases with the high Knudsen numbers, Kn = 0.1, and Kn = 0.26 with AOA = 20-deg. for the lower surface.

Efficient Deterministic Modelling of Three-Dimensional Rarefied Gas Flows

2012 ◽  
Vol 12 (1) ◽  
pp. 162-192 ◽  
Author(s):  
V. A. Titarev
Keyword(s):  
Gas Flow ◽  
Parallel Machines ◽  
High Efficiency ◽  
Rarefied Gas ◽  
Three Dimensional ◽  
Collision Integral ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Deterministic Modelling ◽  
Model Collision

AbstractThe paper is devoted to the development of an efficient deterministic framework for modelling of three-dimensional rarefied gas flows on the basis of the numerical solution of the Boltzmann kinetic equation with the model collision integrals. The framework consists of a high-order accurate implicit advection scheme on arbitrary unstructured meshes, the conservative procedure for the calculation of the model collision integral and efficient implementation on parallel machines. The main application area of the suggested methods is micro-scale flows. Performance of the proposed approach is demonstrated on a rarefied gas flow through the finite-length circular pipe. The results show good accuracy of the proposed algorithm across all flow regimes and its high efficiency and excellent parallel scalability for up to 512 cores.

Measurement of negative thermophoretic force

2016 ◽  
Vol 805 ◽  
pp. 207-221 ◽  
Author(s):  
Ryan W. Bosworth ◽  
A. L. Ventura ◽  
A. D. Ketsdever ◽  
S. F. Gimelshein
Keyword(s):  
Spherical Particle ◽  
Atmospheric Pressure ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Force Production ◽  
Heated Wall ◽  
Rarefied Gas Flow ◽  
Thermophoretic Force ◽  
Knudsen Numbers ◽  
Close Proximity

The rarefied gas flow phenomenon of thermophoresis is studied experimentally on a macroscopic spherical particle with a diameter of 5.1 cm for pressures ranging from 0.01 to 10 Pa (Knudsen numbers $Kn$ from 10 to 0.01, respectively). Size scaling with matching Knudsen numbers makes the results applicable to microscale particles such as aerosol droplets at atmospheric pressure. Two sets of measurements are presented. The first set, complemented by numerical modelling based on the solution of the ellipsoidal statistical Bhatnagar–Gross–Krook kinetic equation, is focused on a spherical particle of high thermal conductivity in close proximity to a heated wall. The second set is conducted for the same particle placed in a linear thermal gradient established between two parallel walls. Results show the first reproducible measurements of negative thermophoretic force acting on a spherical particle in the direction from cold to hot, with values of the order of 5 % of the maximum hot to cold force production.

scholarly journals One-way flow over uniformly heated U-shaped bodies driven by thermal edge effects

2021 ◽  
Author(s):  
Satoshi Taguchi ◽  
Tetsuro Tsuji
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Flow ◽  
Microelectromechanical Systems ◽  
Rarefied Gas ◽  
Shaped Body ◽  
Knudsen Numbers ◽  
Wide Range ◽  
Edge Flow

Abstract The thermal edge flow is a gas flow typically induced near a sharp edge (or a tip) of a uniformly heated flat plate. This flow has potential applicability as a nonmechanical flow controller in microelectromechanical systems (MEMS). However, it has a shortcoming: the thermal edge flows from each edge cancel out, resulting in no net flow. In this study, to circumvent this difficulty, the use of a U-shaped body is proposed and is examined numerically. More specifically, a rarefied gas flow over an array of U-shaped bodies, periodically arranged in a straight channel, is investigated using the direct simulation Monte-Carlo (DSMC) method. The U-shaped bodies are kept at a uniform temperature different from that of the channel. Two types of U-shaped bodies are considered, namely, a square-U shape and a round-U shape. It is demonstrated that a steady one-way flow is induced in the channel for both types. The mass flow rate is obtained for a wide range of the Knudsen numbers, i.e., the ratio of the molecular mean free path to the characteristic size of the U-shape body. For the square-U type, the direction of the overall mass flow is in the same direction for the entire range of the Knudsen numbers investigated. For the round-U type, the direction of the total mass flux is reversed when the Knudsen number is moderate or larger. This reversal of the mass flow rate is attributed to a kind of thermal edge flow induced over the curved part of the round-U-shaped body, which overwhelms the thermal edge flow induced near the tip. The force acting on each of the bodies is also investigated.

Flow generated by oscillatory uniform heating of a rarefied gas in a channel

2016 ◽  
Vol 800 ◽  
pp. 433-483 ◽  
Author(s):  
Jason Nassios ◽  
Ying Wan Yap ◽  
John E. Sader
Keyword(s):  
Gas Flow ◽  
Numerical Solutions ◽  
Rarefied Gas ◽  
Mass Conservation ◽  
Stat Phys ◽  
Dilute Gas ◽  
Knudsen Numbers ◽  
Flow Phenomena ◽  
Underlying Mechanisms ◽  
Asymptotic Analyses

Kinetic theory provides a rigorous foundation to explore the unsteady (oscillatory) flow of a dilute gas, which is often generated by nanomechanical devices. Recently, formal asymptotic analyses of unsteady (oscillatory) flows at small Knudsen numbers have been derived from the linearised Boltzmann–Bhatnagar–Gross–Krook (Boltzmann–BGK) equation, in both the low- and high-frequency limits (Nassios & Sader, J. Fluid Mech., vol. 708, 2012, pp. 197–249 and vol. 729, 2013, pp. 1–46; Takata & Hattori, J. Stat. Phys., vol. 147, 2012, pp. 1182–1215). These asymptotic theories predict that unsteadiness can couple strongly with heat transport to dramatically modify the overall gas flow. Here, we study the gas flow generated between two parallel plane walls whose temperatures vary sinusoidally in time. Predictions of the asymptotic theories are compared to direct numerical solutions, which are valid for all Knudsen numbers and normalised frequencies. Excellent agreement is observed, providing the first numerical validation of the asymptotic theories. The asymptotic analyses also provide critical insight into the physical mechanisms underlying these flow phenomena, establishing that mass conservation (not momentum or energy) drives the flows – this explains the identical results obtained using different previous theoretical treatments of these linear thermal flows. This study highlights the unique gas flows that can be generated under oscillatory non-isothermal conditions and the importance of both numerical and asymptotic analyses in explaining the underlying mechanisms.

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