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.

Study of Gas Flow in Micronozzles Using an Unstructured DSMC Method

2009 ◽  
Author(s):  
Ehsan Roohi ◽  
Masoud Darbandi ◽  
Vahid Mirjalili
Keyword(s):  
Boundary Layer ◽  
Knudsen Number ◽  
Gas Flow ◽  
Subsonic Flow ◽  
Flow Behavior ◽  
Boundary Layer Separation ◽  
Back Pressure ◽  
Viscous Force ◽  
Dsmc Method ◽  
Wide Range

The current research uses an unstructured direct simulation Monte Carlo (DSMC) method to numerically investigate supersonic and subsonic flow behavior in micro convergent–divergent nozzle over a wide range of rarefied regimes. The current unstructured DSMC solver has been suitably modified via using uniform distribution of particles, employing proper subcell geometry, and benefiting from an advanced molecular tracking algorithm. Using this solver, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number, on the flow field in micronozzles. We show that high viscous force manifesting in boundary layers prevents supersonic flow formation in the divergent section of nozzles as soon as the Knudsen number increases above a moderate magnitude. In order to accurately simulate subsonic flow at the nozzle outlet, it is necessary to add a buffer zone to the end of nozzle. If we apply the back pressure at the outlet, boundary layer separation is observed and a region of backward flow appears inside the boundary layer while the core region of inviscid flow experiences multiple shock-expansion waves. We also show that the wall boundary layer prevents forming shocks in the divergent part. Alternatively, Mach cores appear at the nozzle center followed by bow shocks and an expansion region.

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.

Modeling of Heat Transfer in Microchannel Gas Flow

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Tomasz Lewandowski ◽  
Tomasz Ochrymiuk ◽  
Justyna Czerwinska
Keyword(s):  
Heat Transfer ◽  
Gas Flow ◽  
Temperature Jump ◽  
Flow Behavior ◽  
Slip Flow ◽  
Velocity Slip ◽  
Gas Temperature ◽  
Viscous Effects ◽  
Strongly Connected ◽  
The One

Due to the existence of a velocity slip and temperature jump on the solid walls, the heat transfer in microchannels significantly differs from the one in the macroscale. In our research, we have focused on the pressure driven gas flows in a simple finite microchannel geometry, with an entrance and an outlet, for low Reynolds (Re<200) and low Knudsen (Kn<0.01) numbers. For such a regime, the slip induced phenomena are strongly connected with the viscous effects. As a result, heat transfer is also significantly altered. For the optimization of flow conditions, we have investigated various temperature gradient configurations, additionally changing Reynolds and Knudsen numbers. The entrance effects, slip flow, and temperature jump lead to complex relations between flow behavior and heat transfer. We have shown that slip effects are generally insignificant for flow behavior. However, two configuration setups (hot wall cold gas and cold wall hot gas) are affected by slip in distinguishably different ways. For the first one, which concerns turbomachinery, the mass flow rate can increase by about 1% in relation to the no-slip case, depending on the wall-gas temperature difference. Heat transfer is more significantly altered. The Nusselt number between slip and no-slip cases at the outlet of the microchannel is increased by about 10%.

scholarly journals Extended Macroscopic Study of Dilute Gas Flow within a Microcavity

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Hssikou ◽  
Jamal Baliti ◽  
Mohammed Alaoui
Keyword(s):  
Constant Velocity ◽  
Gas Flow ◽  
Continuum Theory ◽  
Point Of View ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Moment Equations ◽  
Macroscopic Theory ◽  
Dilute Gas ◽  
Opposite Motion

The behaviour of monatomic and dilute gas is studied in the slip and early transition regimes using the extended macroscopic theory. The gas is confined within a two-dimensional microcavity where the longitudinal sides are in the opposite motion with constant velocity ±Uw. The microcavity walls are kept at the uniform and reference temperature T0. Thus, the gas flow is transported only by the shear stress induced by the motion of upper and lower walls. From the macroscopic point of view, the regularized 13-moment equations of Grad, R13, are solved numerically. The macroscopic gas proprieties are studied for different values of the so-called Knudsen number (Kn), which gives the gas-rarefaction degree. The results are compared with those obtained using the classical continuum theory of Navier-Stokes and Fourier (NSF).

DSMC Analysis of Rarefied Gas Flow Over a Rectangular Cylinder at All Knudsen Numbers

2000 ◽  
Vol 122 (4) ◽  
pp. 720-729 ◽  
Author(s):  
Chin-Hsiang Cheng ◽  
Feng-Liang Liao
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Flow Behavior ◽  
Cross Flow ◽  
Direct Simulation Monte Carlo ◽  
Molecular Flow ◽  
Transfer Coefficients ◽  
Numerical Predictions ◽  
Special Cases

The present study is concerned with the flow behavior of the rarefied gas over a rectangular square cylinder. Attention has been focused on the transition regime between the continuous flow (at low Knudsen number) and the molecular flow (at high Knudsen number). The direct simulation Monte Carlo method (DSMC) is employed for predicting the distributions of density, velocity, and temperature for the external cross-flow. Meanwhile the pressure, skin friction, and net heat transfer coefficients on the surfaces of the cylinder are also evaluated. The length (l) and width (h) of the cross-section of the cylinder are both fixed at 0.06 m. The Mach number (Ma) ranges from 0.85 to 8, and the Knudsen number (Kn) is in the range 0.01⩽Kn⩽1.0. Results for various parameter combinations are presented. For some special cases, the numerical predictions are compared with existing information, and close agreement has been found. [S0098-2202(00)01404-8]

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 Kinetic Parameters of Nut Shells Pyrolysis

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 682
Author(s):  
Tomasz Noszczyk ◽  
Arkadiusz Dyjakon ◽  
Jacek A. Koziel
Keyword(s):  
Kinetic Parameters ◽  
Waste Treatment ◽  
Model Fitting ◽  
Thermal Conversion ◽  
Point Of View ◽  
The European Union ◽  
Heating Rates ◽  
Isothermal Model ◽  
Biomass Residues ◽  
Conversion Point

The European Union created a European Green Deal Program (EGDP). This program aims at a sustainable economy through the transformation of the challenges related to climate and the environment. The main goal of EGDP is climate neutrality by 2050. The increase of alternative biomass residues utilization from various food processing industries and cooperation in the energy and waste management sector is required to meet these expectations. Nut shells are one of the lesser-known, yet promising, materials that can be used as an alternative fuel or a pre-treated product to further applications. However, from a thermal conversion point of view, it is important to know the energy properties and kinetic parameters of the considered biowaste. In this study, the energy and kinetic parameters of walnut, hazelnut, peanut, and pistachio shells were investigated. The results showed that raw nut shells are characterized by useful properties such as higher heating value (HHV) at 17.8–19.7 MJ∙kg−1 and moisture content of 4.32–9.56%. After the thermal treatment of nut shells (torrefaction, pyrolysis), the HHV significantly increased up to ca. 30 MJ∙kg−1. The thermogravimetric analysis (TGA) applying three different heating rates (β; 5, 10, and 20 °C∙min−1) was performed. The kinetic parameters were determined using the isothermal model-fitting method developed by Coats–Redfern. The activation energy (Ea) estimated for β = 5 °C∙min−1, was, e.g., 60.3 kJ∙mol−1∙K−1 for walnut, 59.3 kJ∙mol−1∙K−1 for hazelnut, 53.4 kJ∙mol−1∙K−1 for peanut, and 103.8 kJ∙mol−1∙K−1 for pistachio, respectively. Moreover, the increase in the Ea of nut shells was observed with increasing the β. In addition, significant differences in the kinetic parameters of the biomass residues from the same waste group were observed. Thus, characterization of specific nut shell residues is recommended for improved modeling of thermal processes and designing of bioreactors for thermal waste treatment.

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.

Behavior of Radial Incompressible Flow in Pneumatic Dimensional Control Systems

2003 ◽  
Vol 125 (5) ◽  
pp. 843-850 ◽  
Author(s):  
G. Roy ◽  
D. Vo-Ngoc ◽  
D. N. Nguyen ◽  
P. Florent
Keyword(s):  
Gas Flow ◽  
Flow Behavior ◽  
Pressure Gauge ◽  
Axisymmetric Flow ◽  
Low Pressure ◽  
Industrial Applications ◽  
Nozzle Geometry ◽  
Machined Surface ◽  
Flow Area ◽  
Simpler Algorithm

The application of pneumatic metrology to control dimensional accuracy on machined parts is based on the measurement of gas flow resistance through a restricted section formed by a jet orifice placed at a small distance away from a machined surface. The backpressure, which is sensed and indicated by a pressure gauge, is calibrated to measure dimensional variations. It has been found that in some typical industrial applications, the nozzles are subject to fouling, e.g., dirt and oil deposits accumulate on their frontal areas, thus requiring more frequent calibration of the apparatus for reliable service. In this paper, a numerical and experimental analysis of the flow behavior in the region between an injection nozzle and a flat surface is presented. The analysis is based on the steady-state axisymmetric flow of an incompressible fluid. The governing equations, coupled with the appropriate boundary conditions, are solved using the SIMPLER algorithm. Results have shown that for the standard nozzle geometry used in industrial applications, an annular low-pressure separated flow area was found to exist near the frontal surface of the nozzle. The existence of this area is believed to be the cause of the nozzle fouling problem. A study of various alternate nozzle geometries has shown that this low-pressure recirculation area can be eliminated quite readily. Well-designed chamfered, rounded, and reduced frontal area nozzles have all reduced or eliminated the separated recirculation flow area. It has been noted, however, that rounded nozzles may adversely cause a reduction in apparatus sensitivity.

scholarly journals Matrix integrals & finite holography

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dionysios Anninos ◽  
Beatrix Mühlmann
Keyword(s):  
Critical Exponents ◽  
Continuum Theory ◽  
Point Of View ◽  
Leading Order ◽  
Minimal Models ◽  
Point Evaluation ◽  
Brst Cohomology ◽  
Matrix Integrals ◽  
The Matrix ◽  
The Continuum

Abstract We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

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