Showing papers by "Stefan Stefanov published in 2012"

Thermal and second-law analysis of a micro- or nanocavity using direct-simulation Monte Carlo

Abstract: In this study the direct-simulation Monte Carlo (DSMC) method is utilized to investigate thermal characteristics of micro- or nanocavity flow. The rarefied cavity flow shows unconventional behaviors which cannot be predicted by the Fourier law, the constitutive relation for the continuum heat transfer. Our analysis in this study confirms some recent observations and shows that the gaseous flow near the top-left corner of the cavity is in a strong nonequilibrium state even within the early slip regime, Kn=0.005. As we obtained slip velocity and temperature jump on the driven lid of the cavity, we reported meaningful discrepancies between the direct and macroscopic sampling of rarefied flow properties in the DSMC method due to existence of nonequilibrium effects in the corners of cavity. The existence of unconventional nonequilibrium heat transfer mechanisms in the middle of slip regime, Kn=0.05, results in the appearance of cold-to-hot heat transfer in the microcavity. In the current study we demonstrate that existence of such unconventional heat transfer is strongly dependent on the Reynolds number and it vanishes in the large values of the lid velocity. As we compared DSMC solution with the results of regularized 13 moments (R13) equations, we showed that the thermal characteristic of the microcavity obtained by the R13 method coincides with the DSMC prediction. Our investigation also includes the analysis of molecular entropy in the microcavity to explain the heat transfer mechanism with the aid of the second law of thermodynamics. To this aim, we obtained the two-dimensional velocity distribution functions to report the molecular-based entropy distribution, and show that the cold-to-hot heat transfer in the cavity is well in accordance with the second law of thermodynamics and takes place in the direction of increasing entropy. At the end we introduce the entropy density for the rarefied flow and show that it can accurately illustrate departure from the equilibrium state.

Nonisothermal oscillatory cylindrical Couette gas flow in the slip regime: A computational study

Abstract: The oscillatory Couette flow between a stationary inner cylinder and an oscillating outer cylinder or a stationary outer cylinder and an oscillating inner cylinder is numerically investigated by using a continuum model with temperature-dependent transport coefficients based on the Navier–Stokes equations for compressible fluid, completed with the equations of continuity and energy transport. The first order velocity-slip boundary conditions, imposed at the outer cylinder wall, are linked to two types of motion of the outer cylinder—harmonic oscillations and stepwise oscillations. The first order slip conditions are also imposed at the inner cylinder combined with two types of energy transfer at the gas–wall interface. The first one is related to a constant wall temperature and the second one to an adiabatically isolated cylinder. Thus, the capabilities of model and numerical solution are extended to some cases, which might be important from a practical viewpoint. Calculated results for density, velocity, pressure and temperature variation are presented. The spectral characteristics of the gas flow oscillations in some interesting cases are analyzed. The numerical calculations for the case of harmonically oscillating inner cylinder are compared with the available analytical solution for incompressible viscous fluid and Direct Simulation Monte Carlo (DSMC) data. It is shown that for low speed oscillations the model of compressible viscous gas gives almost equivalent to incompressible fluid model solution for the macroscopic velocity profiles. At the same time noticeable temperature variations in the gas flow are observed that should be taken into consideration when the heat transfer in such a microfluidic system is analyzed. The presented results are interesting when non-planar microfluidic problems are considered.

Low speed/low rarefaction flow simulation in micro/nano cavity using DSMC method with small number of particles per cell

Abstract: The aim of this study is to extend the validity of the simplified Bernoulli-trials (SBT)/dual grid algorithm, newly proposed by Stefanov [1], as a suitable alternative of the standard collision scheme in the direct simulation Monte Carlo (DSMC) method, for solving low speed/low Knudsen number rarefied micro/nano flows. The main advantage of the SBT algorithm is to provide accurate calculations using much smaller number of particles per cell, i.e., ≈ 1. Compared to the original development of SBT [1], we extend the application of the SBT scheme to the near continuum rarefied flows, i.e., Kn = 0.005, where NTC scheme requires a relatively large sample size. Comparing the results of the SBT/dual grid scheme with NTC, it is shown that the SBT/dual grid scheme could successfully predict the thermal pattern and hydrodynamics field as well as surface parameters such as velocity slip and temperature jump. Nonlinear flux-corrected transport algorithm (FCT) is also employed as a filter to extract the smooth solution from the noisy DSMC calculation for low-speed/low-Knudsen number DSMC calculations. The results indicate that combination of SBT/dual grid and FTC filtering can decrease the total sample size needed to reach smooth solution without losing significant accuracy.

Role of surface shape on boundary slip and velocity defect.

Abstract: Although many gas-phase microfluidic devices contain curved surfaces, relatively little research has been conducted on the degree of slip over nonplanar surfaces. The present study demonstrates the influence of the surface shape (i.e., convex/concave) on the velocity slip and formation of the Knudsen layer. In addition, the study reveals that there is a simple relationship between the shear stress exerted on the surface and the velocity defect in the Knudsen layer.

DSMC collision algorithms based on Kac stochastic model

Abstract: The paper presents a set of Monte Carlo algorithms, based on the Kac's stohastic gas model for simulation of the binary collision process in a homogenous rarefied gas. These collision algorithms avoid the repeat collisions and can be used for simualtion of the collsions in grid cells with small average number of particles, when the DSMC method is applied and the simulation requires computational resources of very large proportions.

Monte Carlo analysis of thermal transpiration effects in capacitance diaphragm gauges with helicoidal baffle system

Abstract: The Capacitance Diaphragm Gauge (CDG) is one of the most widely used vacuum gauges in low and middle vacuum ranges. This device consists basically of a very thin ceramic or metal diaphragm which forms one of the electrodes of a cap acitor. The pressure is determined by measuring the variation in the capacitance due to the deflection of the diaphragm caused by the pressure difference established across the membrane. In order to minimize zero drift, some CDGs are operated keeping the sensor at a higher temperature. This difference in the temperature between the sensor and the vacuum chamber makes the behaviour of the gauge non-linear due to thermal transpiration effects. This effect becomes more significant when we move from the transitional flow to the free molecular regime. Besides, CDGs may incorporate different baffle systems to avoid the condensation on the membrane or its contamination. In this work, the thermal transpiration effect on the behaviour of a rarefied gas and on the measurements in a CDG with a helicoidal baffle system is investigated by using the Direct Simulation Monte Carlo method (DSMC). The study covers the behaviour of the system under the whole range of rarefaction, from the continuum up to the free molecular limit and the results are compared with empirical results. Moreover, the influence of the boundary conditions on the thermal transpiration effects is investigated by using Maxwell boundary conditions.

DSMC simulation of the gas flow through a bend and a short microchannel

Abstract: The present work is related to the study of the gas flows through micro-channels with 90° bend, and short straight channels. The direct simulation Monte Carlo (DSMC) method has been used to study the flow. The DSMC simulations of the gas flow through micro-channels of real dimensions, which are used in the laboratory or in industry, are computationally very expensive, requiring large amounts of the computer resources and time. This fact places a limit on the applicability of the DSMC method while considering the real channel dimensions. It is a good practice to approximate the three dimensional micro-channel into two dimensions, and to study the flow characteristics, when the channel width is essentially large in comparison with their heights. However, the simulation of gas flows in more complicated channels with rectangular cross-section having comparable height and width unavoidably requires a 3D consideration. In the present paper, the 3D flow through a bend and short straight channels are presented, and the flow characteristics studied using the DSMC method. The complete 3D simulations were carried out for the case the height H at 19.83e-6m considering to the same as the one used in the laboratory (without taking similarity of the flow into consideration for the reduction of the actual dimensions of the channel). However, the other dimensions (length and width) were chosen different from the real channel due to the computational requirements. Two types of pressure boundary treatment have been implemented in three dimensions using the DSMC method

Velocity inversion and predicting velocity slip on curved surfaces

Abstract: Couette flow between two concentric rotating cylinders is a classical fluid dynamics problem that is discussed in many textbooks. However, under certain conditions, the flow between the cylinders can exhibit a highly non-intuitive behavior. For example, when the inner cylinder is rotating and the outer cylinder is stationary, it is possible to obtain an inverted velocity profile where the velocity increases unexpectedly from the rotating inner cylinder to the stationary outer cylinder. This unusual phenomenon has often been attributed to the effects of curvature since it does not occur in the equivalent planar case of Couette flow between two parallel plates. In the present study, we investigate the mechanism of velocity inversion using the direct simulation Monte Carlo method and novel velocity slip formulae. The results demonstrate that the velocity inversion cannot be explained solely by the effects of curvature. The present study shows that velocity inversion occurs due to an anomalous acceleration of gas molecules at the outer cylinder. Moreover, the study reveals that the presence of the S-layer plays an important role in the occurrence of velocity inversion. The S-layer only exists over convex surfaces (i.e. the inner cylinder), and the effects of this layer may explain why velocity inversion does not occur when the outer cylinder is rotating and the inner cylinder is stationary.