Gas Flow In Microchannels Research Articles

Investigation of local Nusselt number in a rarefied microchannel gas flow using Direct Simulation Monte Carlo method

Heat transfer in microscale and rarefied gaseous flows has been investigated for high Knudsen number (Kn) flows using the Direct Simulation Monte Carlo (DSMC) method. A wide range of Kn [0.05 – 5], pressure ratio [1.2 – 4] and wall temperature [323 K – 723 K] is studied. The heat flux and local Nusselt number (Nu) are found to exhibit three distinct sections along the length of the microchannel – heat transfer-dominated section, constant heat transfer section and exit section. The defining roles of different effects such as non-equilibrium conditions at the wall, viscous dissipation, axial conduction, pressure work, and shear work have been considered implicitly in the DSMC method. These parameters are seen to influence the heat transfer differently at lower and higher Kn. These results help to quantify the fraction of total heat exchange and reveals the complex interplay of various terms of the energy equation in gas flow in microchannels.

Microchannel Gas Flow in the Multi-Flow Regime Based on the Lattice Boltzmann Method.

In this work, a lattice Boltzmann method (LBM) for studying microchannel gas flow is developed in the multi-flow regime. In the LBM, by comparing previous studies' results on effective viscosity in multi-flow regimes, the values of the rarefaction factor applicable to multi-flow regions were determined, and the relationship between relaxation time and Kn number with the rarefaction factor is given. The Kn number is introduced into the second-order slip boundary condition together with the combined bounce-back/specular-reflection (CBBSR) scheme to capture the gas flow in the multi-flow regime. Sensitivity analysis of the dimensionless flow rate to adjustable parameters using the Taguchi method was carried out, and the values of adjustable parameters were determined based on the results of the sensitivity analysis. The results show that the dimensionless flow rate is more sensitive to j than h. Numerical simulations of Poiseuille flow and pulsating flow in a microchannel with second-order slip boundary conditions are carried out to validate the method. The results show that the velocity profile and dimensionless flow rate simulated by the present numerical simulation method in this work are found in the multi-flow regime, and the phenomenon of annular velocity profile in the microchannel is reflected in the phases.

Numerical study of microdevice with surface acoustic waves for separation of gas mixtures

Recently, it was shown that traveling surface acoustic waves (SAWs) can affect gas flow in microchannels. The effect of SAWs was studied in free-molecular flow regime, and it was shown that SAWs can induce separation of gas mixtures. In the present work, this effect is studied for denser flow regimes, which are more interesting from a practical point of view. The problem is studied numerically using own modification of the direct simulation Monte Carlo method on the example of a neon–argon mixture. The main finding is that SAWs still enhance separation of gas mixtures outflowing into vacuum through a microchannel under all studied rates of gas rarefaction up to Kn≈0.1. Another important practical result is that effect is present for wave speeds typical for existing SAWs (≈1000 m/s) and in a wide range of SAW amplitude to channel height ratios. Influence of other practical aspects, such as channel length, masses of species, and available magnitudes of material surface speed, are also briefly discussed.

A review of frictional pressure drop characteristics of single phase microchannels having different shapes of cross sections

Abstract This paper theoretically studied pressure drop variation in microchannels having different cross sections (circular, rectangular, square, trapezoidal, triangular, elliptical, parallel plate, co-centric circles, hexagonal, wavy, smoothed or rounded corners cross sections, and rhombus) for single phase Newtonian fluid (gas and liquid) flow. Based on 41 years (approximately) prior literature (1981–till now), 249 articles were studied and number of correlations of pressure drop calculation in microchannels with or without friction factor equation for four cross sections i.e., rectangular, square, circular, trapezoidal, wavy and triangular is collected and also mentioned their limitations at one place. Other than these four cross sections, there is very few experimental/numerical works was present in the literature. A comparable study was performed for laminar as well as turbulent friction factor to calculate the pressure drop with the help of classical theory for gas and liquid flow in microchannels with circular and rectangular cross sections. Results show wonderful outcomes i.e., correlations of laminar pressure drop study can be extendable for transition and turbulent regime in both types (circular and rectangular) of cross sections of microchannels. In different types of flow regime, it is suggested that for each type of cross section (circular and rectangular) we can go for single correlation for gas/liquid system. It is also investigated that the macro channels pressure drop equations can be used for microchannels up to the certain values of Reynolds number. Basically, this paper provides all possible equations of friction factor related to the microchannels that helps to calculate the pressure drop, is collected at one platform also compared their deviation with conventional channels.

Free-molecular gas flow in microchannels with surface acoustic waves: Effect of mixture separation

Present paper studies the possibility to separate gas mixtures in microchannels using surface acoustic waves (SAW). Considered flow regime is free-molecular and the problem is studied numerically using probe particle method. Two types of surfaces waves are considered, namely standing SAW (SSAW) and travelling SAW (TSAW). It was shown that TSAW and SSAW have qualitatively different influence on gas flow but demonstrate compatible separation efficiency. For both types of waves separation factor is shown to decrease with increasing ratio of wave length to wave amplitude and is shown to be negligible for values of this ratio around 10000 and higher. Separation factor also decreases with decreasing ratio of wave amplitude to channel height from 0.1 to 0.01 but almost does not change with further decrease. Using only one surface with SAW instead of two is demonstrated to approximately halve the magnitude of effect. Phase shift between upper and lower surfaces motion is shown to have negligible effect in general.

Estimation of surface roughness from friction loss of gaseous flow though stainless steel microtubes

Effects of surface roughness on microchannel gas flow are significant since the surface roughness of a microchnnel is relatively large compared to conventional size tubes. Therefore, in this study, the effects of surface roughness on friction factors of nitrogen gas flow through stainless steel microtubes experimentally investigated under atmospheric back pressure and variable inlet pressure. The experiments were carried out with six different diameters stainless steel microtubes whose diameters range from 256 to 867 μm. The average values of Mach number and Fanning & Darcy friction factors between the inlet and outlet considering decrease in gas temperature were obtained from measured stagnation temperatures & pressures and mass flow rates. The effects of surface roughness on the compressibility effect were described with Fanning and Darcy friction factor correlations as a function of Mach number. The arithmetic mean height of the surface (Ra) of the microtube was also measured with a 3D laser scanning confocal microscope for profilometry. Comparing the measured Ra and the equivalent sand grain surface roughness (Ks) determined from Colebrook-White correlation, a correlation between Ra and Ks was obtained.

Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

In the present paper, we provide an analytical expression for the first- and second-order thermal slip coefficients, σ1,T and σ2,T, by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules. The Cercignani-Lampis scattering kernel of the gas-surface interaction has been considered in order to take into account the influence of the accommodation coefficients (αt, αn) on the slip parameters. Comparing our theoretical results with recent experimental data on the mass flow rate and the slip coefficient for five noble gases (helium, neon, argon, krypton, and xenon), we found out that there is a continuous set of values for the pair (αt, αn) which leads to the same thermal slip parameters. To uniquely determine the accommodation coefficients, we took into account a further series of measurements carried out with the same experimental apparatus, where the thermal molecular pressure exponent γ has been also evaluated. Therefore, the new method proposed in the present work for extracting the accommodation coefficients relies on two steps. First of all, since γ mainly depends on αt, we fix the tangential momentum accommodation coefficient in such a way as to obtain a fair agreement between theoretical and experimental results. Then, among the multiple pairs of variational solutions for (αt, αn), giving the same thermal slip coefficients (chosen to closely approximate the measurements), we select the unique pair with the previously determined value of αt. The analysis carried out in the present work confirms that both accommodation coefficients increase by increasing the molecular weight of the considered gases, as already highlighted in the literature.

Integrating multiple physical properties of microchannel gas flow to extend the Navier–Stokes equations over a wide Knudsen number range

Gas flow in microchannels can be predicted by the Navier–Stokes equations with slip boundary conditions, but only limited to a slightly rarefied flow regime. To improve that, the considerations of the effective mean free path and the volume diffusion phenomena were introduced to the non-kinetic model by previous studies separately. In this study, these two effects, along with the newly proposed wall-to-wall-collision effect, are integrated to extend the Navier–Stokes equations for the planar Poiseuille flows over a wide Knudsen number (Kn) range. The dimensionless mass flow rates calculated by the proposed model can be consistent among different working fluids or flow conditions and mostly agree with the experimental data with Kn≅0.03−57. This analysis facilitates an understanding of the mutual effects on the physical properties of microchannel gas flows and shows a promising prospect for developing a non-kinetic model for highly rarefied flows.

Experimental and Numerical Studies of Gas Permeability through Orthogonal Networks for Isotropic Porous Material.

With regard to the problem of gas flow through isotropic porous deposits, the issues were considered in the category of description of gas movement mechanisms for structural models of the skeleton. As part of experimental tests of gas permeability through porous material in the form of polyamide, the numerical simulation method was used, using the k–ε turbulence model. The analysis of hydrodynamic phenomena occurring in the porous material made it possible to confront experimental research with numerical calculations. The analysis shows that, for a porous polyamide bed, there is a certain limit range of gas velocity (10−4–1) ms−1 at which flow resistance is the lowest. On the other hand, the highest value of the flow resistance is gradually achieved in the range of gas velocity (1–10) ms−1. This is due to the different structure of the isotropic polyamide material. The validation of the numerical model with experimental data indicates the validity of the adopted research methodology. It was found that the permeability characteristics of the tested porous material practically did not depend on the direction of gas flow. For porous polyamide, the permeability characteristic is non-linear, which, from the point of view of the measurements carried out, indicates the advantage of turbulent gas flow over its laminar movement. The novelty of the article is a proprietary method of measuring gas permeability for a cube-shaped sample made of a material constituting a sinter of spherical particles of equal dimensions. The method enables the determination of gas flow (in each flow direction) in microchannels forming an orthogonal network, characteristic of isotropic materials.

Analysis of Thermal Creep Effects on Fluid Flow and Heat Transfer in a Microchannel Gas Heating

Abstract Thermal creep effects on fluid flow and heat transfer in a microchannel gas flow at low velocities are studied numerically. The continuity and Navier–Stokes equations in vorticity–stream function form, coupled with the energy equation, are solved, considering the thermal creep effect due to the longitudinal temperature gradient along the channel wall in addition to the combined effects of viscous dissipation, pressure work, axial conduction, shear work, and nonequilibrium conditions at the gas–wall interface. The governing equations are also solved without thermal creep, and comparisons between the two solutions are presented to evaluate the thermal creep effect on the flow field in the slip flow regime at relatively low Reynolds numbers. The results presented show that the thermal creep effect on both velocity and temperature fields become more significant as the Reynolds number decreases. Thermal creep effect on the velocity field also extends a longer distance downstream the channel as the Reynolds number decreases, hence increasing the hydrodynamics entrance length. Thermal creep can cause high positive velocity gradients at the upper channel wall for gas heating and hence reverse the flow rotation in the fluid layers adjacent to the wall. Thermal creep also results in a higher gas temperature in the developing region and higher heat exchange between the fluid and the channel wall in the entrance region. Thermal creep effect on heat exchange between the gas and the channel wall becomes more significant as the Knudsen number decreases.

Verification of the method for determining heat fluxes and heat loses in experiments with a shear-driving liquid film

The cooling of microelectronic equipment is currently one of the most difficult problems of thermal physics. To achieve high heat fluxes and reduce the volume of liquid used, the technological solution looks especially promising, where heat is transferred from the fuel element to a thin, intensely evaporating film of liquid moving under the action of friction of a forced gas flow in a mini-or micro-channel. In recent works, the study of heat losses and determination of the true heat flux in experiments with an intensely evaporating liquid film moving under the action of a gas flow in a mini-channel was carried out. In this paper, the task is to verify the method for determining heat losses. Heat transfer in the convective flow regime is investigated. The experimental and calculated Nusselt numbers in convection experiments with complete channel flooding are in good agreement. In addition, the experimental and calculated Nusselt numbers for film flows are in good agreement. This indicates the correctness of the method for determining heat flux and heat losses in previous studies.

Effect of aspect ratio and inlet manifold shape on the laminar-to-turbulent transition of gas flow in rectangular microchannels

A combined experimental and numerical study on the laminar-to-turbulent transition in microchannels using gas flow is presented. The effects of two geometric parameters, namely aspect ratio (height to width) of microchannels and inlet manifold shape, are considered on the value assumed by the critical Reynolds number linked to the laminar-to-turbulent transition. To study the effect of aspect ratio, seven rectangular microchannels having an aspect ratio between 0.25 and 1.04 are micro-milled in PMMA plastic with a constant length of 100 mm. Four rectangular microchannels with different inlet shapes, namely sudden contraction, rounded entrance, V shape and bellmouth, are fabricated to analyze the effects of inlet shape. Pressure loss analyses are then performed for all 11 microchannels by evaluating both average and semi-local friction factors. The Reynolds number in correspondence of which the transition takes place is determined by observing the trend of the friction factor. In parallel, numerical simulations using an intermittency-based transitional turbulence model are also performed and results are compared with the experiments. Experimental and numerical results have demonstrated that both of the investigated geometrical characteristics (aspect ratio and inlet manifold shape) play an important role on the range of the Reynolds number between the onset of transition and the onset of fully turbulent regime for gas microflows. Experimental critical Reynolds numbers show a good agreement with the predictions of the conventional theory and are in the range of 1863–3470 for all the tested microchannels. The role of gas compressibility on the laminar-to-turbulent transition is also discussed.Graphic abstract

Pumping Power Performance and Frictional Resistance of Textured Microchannels in Gaseous Slip Flows

The investigation of pressure drop characteristics along the microchannels with surface texturing is crucial to arrive at a desired structural size and performance of a microchannel. This study presents the comparison of flow friction and pumping power for two different Reynolds numbers (Re = 1.01 and 50.31) for rarefied gas flows in textured microchannels. The three-dimensional microchannel is computationally modeled with ratios of the height of texture to the height of the microchannel taken as 20, 40, and 60 and texture shapes as rectangular, circular, and triangular. All simulations are conducted in the slip flow regime for the Knudsen number ranging from 1.10 A� 10-3 to 2.07 A� 10-2 and tangential momentum accommodation coefficient (TMAC) ranging from 0.1 to 0.9. The time- and cost-effective Taguchi statistical analysis of the L18 orthogonal array is carried out to find the efficiency of the textured microchannels in terms of Poiseuille number and pumping power per unit mass flow rate. It is found that the height of texture is the most important control factor for efficiency, while the shape is the least important factor for both Reynolds numbers. The second most significant factor for Re = 50.31 is the Knudsen number and that for Re = 1.01 is the TMAC. The present numerical work can be applied for designing micropiping systems and diffusers with lower pumping power, lower frictional resistance, and higher efficiency. ©

Effect of Ballistic Bouncing of Gas Particles across a Microchannel on Rarefied Gas Flows

This paper proposes a novel computationally efficient method of modeling rarefied gas flow in microchannels based on the newly discovered and mathematically proven Ballistic Principle of the Property Balance in Space (BPPBS). The mechanism of influence of the effect of rarefication on the gas flow is specifically investigated. Also, a differential form of the momentum balance equation governing gas flow in the channel between two parallel plates due to the pressure gradient along the channel and its exact implicit solution in the form of an integral equation have been derived. The theory does not use the generalized concept of viscosity based on the variable mean free path (MFP) in the Knudsen layer (KL). Comparing the normalized flow rate as a function of the inverse Knudsen number according to the current theory and the experimental data shows good agreement in the range of the inverse Knudsen number from 0.01 to about 40. The correlation factor is found to be about 0.995. The results show that our approach based on the BPPBS offers substantial and practical advantages in modeling and simulation of rarefied gases. The validity of the widely disseminated claim of the geometry-dependent MFP in the KL was analyzed.

Mach number correlation for microchannel gas flow considering temperature decrease

Mach number correlation for microchannel gas flow considering temperature decrease

Local friction factors of microchannel gas flow by means of adiabatic wall temperatures

Local friction factors of microchannel gas flow by means of adiabatic wall temperatures

Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values

AbstractThe analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,” J. Microscale Thermophys. Eng., 3, pp. 43–77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.

The UGKS Simulation of Microchannel Gas Flow and Heat Transfer Confined Between Isothermal and Nonisothermal Parallel Plates

Abstract The unified gas kinetic scheme (UGKS) is introduced to simulate the near transition regime gas flow and heat transfer in microchannel confined between isothermal and nonisothermal parallel plates. The argon gas is used and its inlet Knudsen number (Knin) ranges from 0.0154 to 0.0715. It is found that: (1) both microchannel gas flows under isothermal and nonisothermal parallel plates display a trend of speed acceleration and temperature decrease along flow direction, for which the microscopic mechanism explanation is first proposed; (2) inlet gas streamlines under nonisothermal plates condition deviate from the parallel distributions under isothermal plates condition due to the dual driving effects of pressure drop along flow direction and temperature difference along cross section; (3) gas temperature, pressure, density and viscosity distributions along cross section under nonisothermal plates condition deviate from the parabolic distributions under isothermal plates condition, while the gas velocity keeps the parabolic distribution due to the effect of Knudsen layer; (4) as channel height increases or channel length and gas molecular mean free path decrease, the gas temperature distribution along cross section under nonisothermal plates condition tends to transition from linear to curve one due to the decreasing effect of heat transfer along cross section and increasing effect of gas acceleration along flow direction, this transition from linear to curve one becomes more obvious along flow direction. (5) the gas velocity under nonisothermal plates condition decreases with the increase of inlet gas temperature (Tin), lower plate temperature (Tl) and Knin, while the gas temperature increases with the increase of Tin, Tl and Knin.

Jump in the conduction heat flux at the gas/solid interface in micro-channels

In micro-channel gas flows, velocity slip and temperature jump must be applied at the fluid/solid interface to take the thermodynamic non-equilibrium into account in the vicinity of the wall. In this work, simulations at molecular scale have been carried out and shown a jump in the conduction heat flux, in agreement with the boundary condition proposed by Maslen (1958) [1] in continuum mechanics.

A simplified quasi-2D model for gas flow in microchannels and microtubes

The analytic equations of mass flow rate for gas flow in microchannels or microtubes developed in the 1990s have been widely validated by experimental results for slow-speed flow, but the applicability for high-speed flow might be constrained. A new model for analyzing the modified Navier–Stokes equations of the gas flow in 2D microchannels and microtubes is proposed in this study, named the simplified quasi-2D (SQ2D) model. The applicability of the SQ2D model can be in the range from slow-speed flow to high-speed flow with no-slip boundary conditions or high-order slip boundary conditions. The flows in 2D microchannels and microtubes, with hydraulic diameters sized from 5 µm to 100 µm and various hydraulic-diameter-to-length ratios, were analyzed by the SQ2D model under different pressure conditions. The mass flow rates calculated by the SQ2D model meet the data computed by the computational fluid dynamics-based method better than the analytic equations in the high Mach number region. The results were also compared with the numerical or experimental data from other studies, good agreements could be reached. Some particular characteristics of micro gas flow were also identified and briefly discussed with the data computed by the SQ2D model.