scholarly journals Oscillatory rarefied gas flow inside rectangular cavities

2014 ◽  
Vol 748 ◽  
pp. 350-367 ◽  
Author(s):  
Lei Wu ◽  
Jason M. Reese ◽  
Yonghao Zhang
Keyword(s):  
Aspect Ratio ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Scaling Law ◽  
Frequency Range ◽  
Damping Force ◽  
Driven Cavity ◽  
Linearized Boltzmann Equation ◽  
Wide Range ◽  
Oscillation Frequencies

AbstractTwo-dimensional oscillatory lid-driven cavity flow of a rarefied gas at arbitrary oscillation frequency is investigated using the linearized Boltzmann equation. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillating frequency on the damping force exerted on the moving lid is studied. Surprisingly, it is found that, over a certain frequency range, the damping is smaller than that in an oscillatory Couette flow. This reduction in damping is due to the anti-resonance of the rarefied gas. A scaling law between the anti-resonant frequency and the aspect ratio is established, which would enable the control of the damping through choosing an appropriate cavity geometry.

On the Rarefied Gas Flow in Pipes

2005 ◽  
Author(s):  
Vladan D. Djordjevic
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Natural Extension ◽  
Slip Boundary Condition ◽  
Molecular Flow ◽  
Rarefied Gas Flow ◽  
Number Range ◽  
Average Value ◽  
Linearized Boltzmann Equation

Rarefied gas flow in a pipe is treated in the paper by modeling the slip boundary condition by means of a fractional derivative. At that the order of the derivative is conveniently chosen to be a function of the average value of the Knudsen number so that the entire Knudsen number range, from continuum flow to free molecular flow, is covered. Very good agreement with the solutions of linearized Boltzmann equation is achieved. The paper represents a natural extension of the work of the same author on the rarefied micro channel flow, published earlier.

scholarly journals Simulation of Rarefied Gas Flow in a Rectangular Enclosure

2019 ◽  
Author(s):  
Sumit Chamling Rai ◽  
Jayesh Sanwal ◽  
K Ram Chandra Murthy
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Direct Simulation Monte Carlo ◽  
Stochastic Modelling ◽  
Dsmc Method ◽  
Driven Cavity ◽  
Simulation Monte Carlo ◽  
Computationally Intensive ◽  
Velocity Pressure ◽  
Good Agreement

The present work investigates the effects of rarefaction on gas flow patterns in a lid-driven cavity using the simulation package dsmcFoam, on the OpenFOAM platform. Direct Simulation Monte Carlo (DSMC) method is a simulation technique which caters to the regime in between the computationally intensive molecular dynamics solvers, as well as the often inaccurate NS based solvers (applied to the rarefied gas simulations). It was proposed by G.A. Bird which employs the stochastic modelling of particle motion.Simulations are performed and results are verified for the flow of a rarefied gas Argon) for different lid velocities within the domain. The results are presented as streamlines, contours of velocity, pressure and temperature, along with velocities in X and Y directions. They have been found to be in good agreement with the previous experimental and numerical observations. Our simulations show that these eddies are much harder to observe in the rarefied domain, and cannot be observed upto velocities as high as 200m/s in a cavity with aspect ratio 1.

Rarefied gas flow in double-sided lid driven cavity

2021 ◽  
Author(s):  
J. Baliti ◽  
M. Hssikou ◽  
Y. Elguennouni ◽  
A. Moussaoui ◽  
M. Alaoui
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Rarefied Gas Flow ◽  
Driven Cavity

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 Rarefied gas flow around a sharp edge induced by a temperature field

2012 ◽  
Vol 694 ◽  
pp. 191-224 ◽  
Author(s):  
Satoshi Taguchi ◽  
Kazuo Aoki
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Structural Similarity ◽  
Rarefied Gas Flow ◽  
Bgk Model ◽  
Thermally Induced ◽  
Wide Range ◽  
Flow Features ◽  
Limiting Behaviour

AbstractA rarefied gas flow thermally induced around a heated (or cooled) flat plate, contained in a vessel, is considered in two different situations: (i) both sides of the plate are simultaneously and uniformly heated (or cooled); and (ii) only one side of the plate is uniformly heated. The former is known as the thermal edge flow and the latter, typically observed in the Crookes radiometer, may be called the radiometric flow. The steady behaviour of the gas induced in the container is investigated on the basis of the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. The flow features are clarified for a wide range of the Knudsen number, with a particular emphasis placed on the structural similarity between the two flows. The limiting behaviour of the flow as the Knudsen number tends to zero (and thus the system approaches the continuum limit) is investigated for both flows. The detailed structure of the normal stress on the plate as well as the cause of the radiometric force (the force acting on the plate from the hotter to the colder side) is also clarified for the present infinitely thin plate.

Rarefied Gas Flow Analysis of a Suborbital Shuttle With the Academic CFD Code Galatea

2017 ◽  
Author(s):  
Angelos G. Klothakis ◽  
Georgios N. Lygidakis ◽  
Ioannis K. Nikolos
Keyword(s):  
Gas Flow ◽  
Microelectromechanical Systems ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Flow Analysis ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rarefied Gas Flows ◽  
Wide Range

During the past decade considerable efforts have been exerted for the simulation of rarefied gas flows in a wide range of applications, like the flow over suborbital vehicles, in microelectromechanical systems, etc. Such flows appear to be significantly different from those at the continuum regime, making the Navier-Stokes equations to fail without further amendment. In this study an in-house academic CFD solver, named Galatea, is modified appropriately to account for rarefied gases. The no-slip condition on solid walls is no longer valid, hence, velocity slip and temperature jump boundary conditions are applied instead. Additionally, a second-order accurate slip model has been incorporated, namely, this of Beskok and Karniadakis, increasing the accuracy in the same area but avoiding simultaneously the numerical difficulties, entailed by the computation of the second derivative of slip velocity when complex geometries and unstructured grids are coupled. The proposed solver is validated against rarefied laminar flow over a suborbital shuttle, designed by the Azim’UTBM team. The obtained results are compared with those extracted with the parallel open-source kernel SPARTA, which is based on the DSMC method. A satisfactory agreement is reported between the two methodologies, demonstrating the potential of the modified solver to simulate effectively such flows.

scholarly journals DSMC Simulation of Rarefied Gas Flow in a Single-sided and Double-sided Lid-Driven Cavity

2019 ◽  
Author(s):  
Jayesh Sanwal ◽  
Deepak Nabapure ◽  
Sreeram Rajesh ◽  
K Ram Chandra Murthy
Keyword(s):  
Melt Spinning ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Direct Simulation Monte Carlo ◽  
Industrial Applications ◽  
Dsmc Method ◽  
Driven Cavity ◽  
Flow Features ◽  
Dsmc Simulation ◽  
Vortex Patterns

The present study is to investigate the behavior of a monoatomic gas enclosed in a cavity with both the top and bottom walls imparting motion to the fluid. The problem is studied for single and double-sided lid-driven flow for various wall velocities as well as parallel and anti-parallel wall motions. These types of flow have many industrial applications such as drying and melt spinning. In contrast to the single-sided flows the vortex patterns obtained in the double-sided flows are different and hence it merits a thorough examination, which is studied in this paper using the Direct Simulation Monte Carlo (DSMC) method. The DSMC method proposed by G.A. Bird is based on the kinetic theory in which the molecular motion is modeled stochastically. The computational model has been implemented in OpenFOAM software using the solver named dsmcFoam. Various flow features have been examined such as eddies and vortices.

Numerical Analysis of the Time-Dependent Energy and Momentum Transfers in a Rarefied Gas Between Two Parallel Planes Based on the Linearized Boltzmann Equation

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Energy Transfer ◽  
Boltzmann Equation ◽  
Rarefied Gas ◽  
Numerical Data ◽  
Time Dependent ◽  
Sound Waves ◽  
Low Frequencies ◽  
Resonance Effects ◽  
Linearized Boltzmann Equation ◽  
Wide Range

Periodic time-dependent behavior of a rarefied gas between two parallel planes caused by an oscillatory heating of one plane is numerically studied based on the linearized Boltzmann equation. Detailed numerical data of the energy transfer from the heated plane to the unheated plane and the forces of the gas acting on the boundaries are provided for a wide range of the gas rarefaction degree and the oscillation frequency. The flow is characterized by a coupling of heat conduction and sound waves caused by repetitive expansion and contraction of the gas. For a small gas rarefaction degree, the energy transfer is mainly conducted by sound waves, except for very low frequencies, and is strongly affected by the resonance of the waves. For a large gas rarefaction degree, the resonance effects become insignificant and the energy transferred to the unheated plane decreases nearly monotonically as the frequency increases. The force of the gas acting on the heated boundary shows a remarkable minimum with respect to the frequency even in the free molecular limit.

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.

Sound Propagation Through a Gas in Microscale

2009 ◽  
Author(s):  
Felix Sharipov ◽  
Denize Kalempa
Keyword(s):  
Kinetic Equation ◽  
Free Path ◽  
Sound Wave ◽  
Gas Flow ◽  
Sound Propagation ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Sound Waves ◽  
Wave Source ◽  
Wide Range

A sound wave propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation by taking into account the influence of the receptor of sound waves on the solution of the problem. In order to do so, a plate oscillating in the normal direction to its own plane is considered as a sound wave source while a stationary one is considered as being the receptor of sound waves. The distance between the plates can be of the order of the molecular mean free path. It is assumed a fully established oscillation so that the solution of the kinetic equation depends on time harmonically. The main parameters of the problem are the oscillation speed parameter, defined as the ratio of intermolecular collision frequency to the sound frequency, and the Knudsen number, defined as the ratio of the molecular mean free path to a characteristic scale of the gas flow. The problem is solved over a wide range of both parameters and the amplitudes and phases of all the macrocharacteristics of the gas flow are calculated.

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