Numerical simulation of heat transfer in a micro-cavity

2017 ◽  
Vol 95 (1) ◽  
pp. 85-94 ◽  
Author(s):  
J. Baliti ◽  
M. Hssikou ◽  
M. Alaoui
Keyword(s):  
Aspect Ratio ◽  
Knudsen Number ◽  
Specular Reflection ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Temperature Ratio ◽  
Cold Flow ◽  
Extended Approach ◽  
Cold Walls ◽  
Micro Cavity

The behaviour of rarefied monatomic gas of Maxwell particles within a rectangular enclosure is investigated, with the Navier–Stokes and Fourier field of equations with first- (NSF) and second-order boundary conditions (NSF2) of the velocity slip and temperature jump, and the regularized 13 moments approach (R13). The enclosure considered has a heated bottom with lateral walls that have specular reflection. The effect of the three dimensionless parameters characterizing the simulated problem, the cavity aspect ratio, the Knudsen number, and the temperature ratio of the hot over the cold walls, on the flow and bulk quantities is examined. For the small Knudsen numbers the flow presents one type of streamlines from the cold to hot plate in both NSF and R13 theories, while by increasing the Knudsen number the flow becomes more complex and presents hot to cold flow streamlines in the extended approach of R13. These rarefaction effects cannot be predicted by the classical continuum approach of NSF. The increase of the temperature ratio in R13 affects the hot to cold flow, which begins to vanish, while this type of streamline does not appear by decreasing the aspect ratio.

scholarly journals Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow

2016 ◽  
Vol 20 (6) ◽  
pp. 1825-1833
Author(s):  
Snezana Milicev ◽  
Nevena Stevanovic
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Velocity Slip ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Microscopic Approach ◽  
First Order ◽  
Continuum Flow ◽  
Macroscopic Approach ◽  
Steady Plane

The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls) is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn?0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy.

Simulation of Flow in Continuum-Transition Regime in Stepped-Microchannels Using Burnett Equations

2008 ◽  
Author(s):  
Reza Kamali ◽  
Saleh Rezaei Ravesh ◽  
Saeid Movahed
Keyword(s):  
Knudsen Number ◽  
Temperature Jump ◽  
Stokes Equations ◽  
Velocity Slip ◽  
Heat Fluxes ◽  
Navier Stokes ◽  
Burnett Equations ◽  
Navier Stokes Equations ◽  
Microfluidic Flows ◽  
Explicit Finite Difference

In present study, the Navier-Stokes equations and the Burnett equations with Maxwell-Smoluchowski slip conditions for some values of Knudsen number are used to resolve the viscous compressible fluid flow of air in the stepped microchannel. An explicit finite difference scheme is employed to develop a two-dimensionl numerical Burnett solver for microfluidic flows and the second order stresses and heat fluxes in the Burnett equations are implemented into the code. Velocity slip/temperature jump conditions on the wall of the channel and on the step within duct are also used. Results are compared with those obtained by using the Navier-Stokes equations with and without the slip-wall conditions using flow in a microchannel. The effects of Knudsen number on the flow and the heat transfer characteristics of the microchannel are also investigated.

scholarly journals Continuum Analysis of Rarefaction Effects on a Thermally Induced Gas Flow

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Mohamed Hssikou ◽  
Jamal Baliti ◽  
Mohammed Alaoui
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Flow Behavior ◽  
Continuum Theory ◽  
Velocity Slip ◽  
Nonlinear Effects ◽  
Point Of View ◽  
Heating Rates ◽  
Micro Cavity ◽  
Maxwell Gas

A Maxwell gas confined within a micro cavity with nonisothermal walls is investigated in the slip and early transition regimes using the classical and extended continuum theories. The vertical sides of the cavity are kept at the uniform and environmental temperature T0, while the upper and bottom ones are linearly heated in opposite directions from the cold value T0 to the hot one TH. The gas flow is, therefore, induced only by the temperature gradient created along the longitudinal walls. The problem is treated from a macroscopic point of view by solving numerically the so-called regularized 13-moment equations (R13) recently developed as an extension of Grad 13-moment theory to the third order of the Knudsen number powers in the Chapman-Enskog expansion. The gas macroscopic properties obtained by this method are compared with the classical continuum theory results (NSF) using the first and second order of velocity slip and temperature jump boundary conditions. The gas flow behavior is studied as a function of the Knudsen number (Kn), nonlinear effects, for different heating rates T0/TH. The micro cavity aspect ratio effect is also evaluated on the flow fields in this study.

Simulation of Low Knudsen Number Isothermal Flow Past a Confined Spherical Particle in a Micro-Pipe

2004 ◽  
Author(s):  
Robert W. Barber ◽  
X. J. Gu ◽  
David R. Emerson
Keyword(s):  
Spherical Particle ◽  
Knudsen Number ◽  
Slip Flow ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Hydrodynamic Drag ◽  
Flow Past ◽  
Proper Formulation ◽  
Isothermal Slip ◽  
The Continuum

Low Knudsen number isothermal slip flow past a confined spherical particle has been investigated using a specially adapted Navier-Stokes solver. Knudsen numbers covering the continuum and slip-flow regimes (Kn ≤ 10−1) are considered while the Reynolds number is varied between 10−3 ≤ Re ≤ 0.5. In addition, blockage effects are studied by varying the ratio between the diameter of the pipe (H) and the diameter of the particle (D). A particularly important aspect of the present study is the proper formulation of the slip-velocity boundary condition over the curved surface of the particle. This is achieved by recasting Maxwell’s conventional velocity-slip equation as a function of the wall shear stress in order to account correctly for the curvature. The results show that blockage effects are extremely important in the continuum regime and cause amplification in the hydrodynamic drag on the particle. However, blockage phenomena are shown to be less important as the Knudsen number is increased. At the upper limit of the slip-flow regime, Kn ≈ 10−1, blockage amplification effects are reduced by almost 50% for a pipesphere geometry of H/D = 2.

Laminar Forced Convection in Annular Microchannels With Slip Flow Regime

2009 ◽  
Author(s):  
Arman Sadeghi ◽  
Abolhassan Asgarshamsi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Graphical Form ◽  
Uniform Temperature

Fluid flow and heat transfer at microscale have attracted an important research interest in recent years due to the rapid development of microelectromechanical systems (MEMS). Fluid flow in microdevices has some characteristics which one of them is rarefaction effect related with gas flow. In this research, hydrodynamically and thermally fully developed laminar rarefied gas flow in annular microducts is studied using slip flow boundary conditions. Two different cases of the thermal boundary conditions are considered, namely: uniform temperature at the outer wall and adiabatic inner wall (Case A) and uniform temperature at the inner wall and adiabatic outer wall (Case B). Using the previously obtained velocity distribution, energy conservation equation subjected to relevant boundary conditions is numerically solved using fourth order Runge-Kutta method. The Nusselt number values are presented in graphical form as well as tabular form. It is realized that for the case A increasing aspect ratio results in increasing the Nusselt number, while the opposite is true for the case B. The effect of aspect ratio on Nusselt number is more notable at smaller values of Knudsen number, while its effect becomes slighter at large Knudsen numbers. Also increasing Knudsen number leads to smaller values of Nusselt number for the both cases.

Relationship between accuracy and number of velocity particles of the finite-difference lattice Boltzmann method in velocity slip simulations

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Minoru Watari
Keyword(s):  
Relaxation Process ◽  
Stokes Equations ◽  
Velocity Slip ◽  
Simulation Models ◽  
Knudsen Layer ◽  
Navier Stokes ◽  
Flow Area ◽  
Navier Stokes Equations ◽  
Conservation Of Momentum ◽  
Boltzmann Method

Relationship between accuracy and number of velocity particles in velocity slip phenomena was investigated by numerical simulations and theoretical considerations. Two types of 2D models were used: the octagon family and the D2Q9 model. Models have to possess the following four prerequisites to accurately simulate the velocity slip phenomena: (a) equivalency to the Navier–Stokes equations in the N-S flow area, (b) conservation of momentum flow Pxy in the whole area, (c) appropriate relaxation process in the Knudsen layer, and (d) capability to properly express the mass and momentum flows on the wall. Both the octagon family and the D2Q9 model satisfy conditions (a) and (b). However, models with fewer velocity particles do not sufficiently satisfy conditions (c) and (d). The D2Q9 model fails to represent a relaxation process in the Knudsen layer and shows a considerable fluctuation in the velocity slip due to the model’s angle to the wall. To perform an accurate velocity slip simulation, models with sufficient velocity particles, such as the triple octagon model with moving particles of 24 directions, are desirable.

Numerical Study on Supersonic Combustor with an Allotype Cavity

2014 ◽  
Vol 694 ◽  
pp. 187-192
Author(s):  
Jin Xiang Wu ◽  
Jian Sun ◽  
Xiang Gou ◽  
Lian Sheng Liu
Keyword(s):  
Alternative Model ◽  
Numerical Study ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Experimental Result ◽  
Navier Stokes ◽  
Cold Flow ◽  
Hypersonic Inlet ◽  
Good Agreement

The three-dimensional coupled explicit Reynolds Averaged Navier–Stokes (RANS) equations and the two equation shear-stress transport k-w (SST k-w) model has been employed to numerically simulate the cold flow field in a special-shaped cavity-based supersonic combustor. In a cross-section shaped rectangular, hypersonic inlet with airflow at Mach 2.0 chamber, shock structures and flow characteristics of a herringbone-shaped boss and a herringbone-shaped cavity models were discussed, respectively. The results indicate: Firstly, according to the similarities of bevel-cutting shock characteristics between the boss case and the cavity case, the boss structure can serve as an ideal alternative model for shear-layer. Secondly, the eddies within cavity are composed of herringbone-spanwise vortexes, columnar vortices in the front and main-spanwise vortexes in the rear, featuring tilting, twisting and stretching. Thirdly, the simulated bottom-flow of cavity is in good agreement with experimental result, while the reverse flow-entrainment resulting from herringbone geometry and pressure gradient. However, the herringbone-shaped cavity has a better performance in fuel-mixing.

Cold Flow Measurements of Supersonic Low Aspect Ratio Jet-Surface Interactions

2019 ◽  
Vol 105 (1) ◽  
pp. 1-30
Author(s):  
Florian Baier ◽  
Aatresh Karnam ◽  
Ephraim Gutmark
Keyword(s):  
Aspect Ratio ◽  
Surface Interactions ◽  
Flow Measurements ◽  
Cold Flow ◽  
Low Aspect Ratio
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