Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

EFFECTS OF RAREFACTION AND COMPRESSIBILITY OF GASEOUS FLOW IN MICROCHANNEL USING DSMC

The direct simulation Monte Carlo (DSMC) is performed for two-dimensional gaseous flow through a microchannel in both slip and transition regimes to understand the effects of compressibility and rarefaction. Results are presented in the form of axial pressure distribution, velocity profile, local friction coefficient, and local Mach number (Ma) and are compared with the available analytical and experimental results. The effect of compressibility is examined for the inlet to outlet pressure ratios ranging from 1.38 to 4.5. Low-pressure drop simulations with Knudsen numbers (Kn) ranging from 0.03 to 0.11 are performed to identify the effect of rarefaction. It was found that compressibility makes the axial pressure variation nonlinear and enhances the local friction coefficient. On the other hand, rarefaction does not affect pressure distribution but causes the flow to slip at the wall and reduces the local friction coefficient. In addition, it was found that the locally fully developed (LFD) assumption is valid for low Ma flows by comparison with DSMC results.     

Forced convective heat transfer in a microtube including rarefaction,viscous dissipation and axial conduction effects

Subsonic gas convective heat transfer in a microtube with a constant cross-sectional area and uniform wall temperature is investigated both analytically and numerically. First, the effect of rarefaction on heat transfer characteristics, at a distance from the inlet where Nu becomes constant, is analytically investigated for two cases: (i) including and (ii) neglecting the viscous dissipation effect. An exact solution for Nu in fully developed flow is presented for the case without viscous dissipation, while a closed-form solution for the asymptotic Nu is also provided for the case with viscous dissipation. Next, a numerical model is employed to investigate the simultaneous effects of rarefaction, viscous dissipation, and axial conduction for developing hydrodynamic and temperature conditions. The Nusselt number is substantially affected by viscous dissipation, rarefaction and axial conduction.     

Experimental Analysis of Pressure Drop and Laminar to Turbulent Transition for Gas Flows in Smooth Microtubes

The results of numerical and experimental works dealing with the behavior of gas flow through microchannels are by no means univocal, sometimes agreeing with the classical correlations and other times contradicting them. It is now agreed upon that the effects due to both rarefaction and compressibility must be accounted for. In addition, the experimental works have demonstrated that sometimes compressibility and rarefaction effects can be coupled in microchannels: because these two actions contrast each other, the scatter of the friction factor data for gaseous flows is remarkably large. This paper is aimed at determining the friction factor for commercial short and long Peek microtubes with nominal internal diameters between 300 and 100 μ m and values of the length-to-diameter ratio, L/D, ranging between 167 and 5000. Nitrogen flows inside the microtubes, with a maximum value of the supply pressure equal to 10 bar. Very low Knudsen numbers (Kn < 0.001) are considered in order to uncouple the rarefaction effects from the compressibility effects. The role of the minor losses related to the inlet and outlet of the test section and of the gas compressibility on the friction factor are analyzed and discussed in order to draw their limit of significance in microchannels. In addition, the effects of the gas compressibility and of the L/D ratio on the critical Reynolds number for which the laminar to turbulent transition takes place will be analyzed and discussed by comparing the experimental results with the other data published in the literature.     

微通道内气体-近壁颗粒流动传热数值模拟研究

数值模拟了微通道受限空间内气体-近璧颗粒流动与传热过程,所建模型考虑微尺度气体的可压缩与交物性特征,且在通道和颗粒壁面采用速度滑移和温度跳跃边界条件以考虑滑移区气体动量/能量非连续效应.在此基础上,计算分析了克努森数(Kn)和颗粒偏移比对颗粒表面拖曳力系数(CD)以及传热努塞尔数(Nu)的影响规律.研究结果表明:受气体...     

Unsteady Two-Dimensional Nitrogen Flow in Long Microchannels with Uniform Wall Heat Flux

The time-dependent characteristics of pressure-driven nitrogen flow in long microchannels under uniform wall heat flux input are numerically studied. The two-dimensional momentum and energy equations are solved, with variable properties, rarefaction, involving velocity slip, thermal creep and temperature jump, compressibility, and viscous dissipation effects taken into account. Two cases of unsteady convection are studied. The first one arises due to a sudden heat flux change at the channel wall and the second due to a sudden inlet pressure change. The resulting thermal field and fluid dynamics are determined, described, and discussed in detail. The approach to steady-state conditions and the overall transient response are investigated. It is found that the transient response for the case with a sudden increase in wall heat flux input is slower than that for the case with a sudden decrease in wall heat flux input. The transient response for the case with a sudden increase in inlet pressure is much faster than that for the case with a sudden decrease in inlet pressure. These trends are quantified and discussed on the basis of the underlying transport mechanisms. The difference in overall transient response is caused by the flow rate change and the energy taken up by the pressure work.     

Direct simulation of roughness effects on rarefied and compressible flow at slip flow regime

A two dimensional numerical simulation is performed for incompressible and compressible fluid flows through microchannels in slip flow regime with consideration of slip and temperature jump boundary conditions. The wall roughness is simulated in two cases with triangular microelements and random shaped micro peaks distributed on wall surfaces to study the effects of roughness shape and distribution on the flow field. Various Mach and Knudsen numbers have been used to investigate the effects of rarefaction as well as compressibility. It is found that rarefaction has a more significant effect on the flow field in microchannels with higher relative roughness. It is also found that the effect of compressibility will be more noticeable when relative roughness increases. In addition a high influence of roughness distribution and shape can be seen for both compressible and incompressible flows. The numerical results have also been checked with available theoretical and experimental relations and a good agreement has been achieved.     

The numerical computation of the evaporative cooling of falling water film in turbulent mixed convection inside a vertical tube

An analysis has been developed for studying the evaporative cooling of liquid film falling inside a vertical insulated tube in turbulent gas stream is presented. Heat and mass transfer characteristics in air–water system are mainly considered. A low Reynolds number turbulence model of Launder and Sharma is used to simulate the turbulent gas stream and a modified Van Driest model suggested by Yih and Liu is adopted to simulate the turbulent liquid film. The model predictions are first compared with available experimental data for the purpose of validating the model. Parametric computations were performed to investigate the effects of Reynolds number, inlet liquid temperature and inlet liquid mass flow rate on the liquid film cooling mechanism. Results show that significant liquid cooling results for the system with a higher gas flow Reynolds number Re, a lower liquid flow rate Γ₀ or a higher inlet liquid temperature T_L0.     

Heat Transfer Characteristics of Gaseous Flows in Micro-Channel with Negative Heat Flux

Two-dimensional compressible momentum and energy equations are solved to obtain the heat transfer characteristics of gaseous flows in micro-channels with constant heat flux for which the value is negative for no-slip flow. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian method. The computations are performed for channels with constant heat flux ranging from ?10⁴ to ?10² W/m². The channel height ranges from 10 to 100 μ m and the aspect ratio of the channel height and length is 200. The stagnation pressure is chosen such that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in micro-channels with negative heat flux are compared with those of positive heat flux cases obtained in our previous work and also those of the incompressible flow in a conventional sized channel. In the case of fast flow, temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the micro-channel is proposed. The rarefaction effect is investigated for the cases of channel height of 10 μ m with slip boundary conditions. The magnitudes of viscous dissipation term and compressibility term are also investigated. The effect of each term on heat transfer characteristics is discussed.     

Poiseuille flow of moderately rarefied gases in annular channels

In this study, rarefaction effects in pressure-driven gas flows in annular micro-channels are investigated. The influence of gas rarefaction, aspect ratio of the annulus, and surface accommodation coefficient on wall friction, mass flow rate, and thermal energy flow rate is studied. For this, the linearized Navier–Stokes–Fourier (NSF) and regularized 13-moment (R13) equations are solved analytically. The results are compared to available solutions of the Boltzmann equation to highlight the advantages of the R13 over the NSF equations in describing rarefaction effects in the process. Moreover, a second-order slip boundary condition is proposed to improve the accuracy of the classical NSF equations.     

Simulation of compressible flow in high pressure buried gas pipelines

The aim of this work is to analyze the gas flow in high pressure buried pipelines subjected to wall friction and heat transfer. The governing equations for one-dimensional compressible pipe flow are derived and solved numerically. The effects of friction, heat transfer from the wall and inlet temperature on various parameters such as pressure, temperature, Mach number and mass flow rate of the gas are investigated. The numerical scheme and numerical solution was confirmed by some previous numerical studies and available experimental data. The results show that the rate of heat transfer has not a considerable effect on inflow Mach number, but it can reduce the choking length in larger f_DL/D values. The temperature loss will also increase in this case, if smaller pressure drop is desired along the pipe. The results also indicate that for f_DL/D = 150, decreasing the rate of heat transfer from the pipe wall, indicated here by Biot number from 100 to 0.001, will cause an increase of about 7% in the rate of mass flow carried by the pipeline, while for f_DL/D = 50, the change in the rate of mass flow has not a considerable effect. Furthermore, the mass flow rate of choked flow could be increased if the gas flow is cooled before entrance to the pipe.     

Transport from a volatile meniscus inside an open microtube

A generalized model is developed which couples the evaporation at a liquid–air interface with the vapor diffusion processes in air to enable an investigation of the mass transport inside an open microtube. Tube inner diameters ranging from 100 to 1200 μm are considered. Evaporation is strongest at the meniscus junction with the tube wall due to the highest local vapor diffusion flux at this location. A temperature gradient is set up from the axis of the tube to the wall and results in Marangoni convection. The three-dimensional flow structure in the microtube is simulated with the effects of Marangoni convection, buoyancy, and the influx of fluid to the interface being included. For horizontal tubes of diameter 100 μm or larger immersed in a water bath, flow asymmetry due to buoyancy is observed. A large vortex is formed in the lower part of the tube cross-section, while a small vortex forms above. However, the primary cause of asymmetry is found to be the external thermal profile imposed on the microtube, especially when the meniscus is far from the outlet of the tube. The simulated flow patterns are found to be consistent with experimental measurements.     

NUMERICAL STUDY OF COMPRESSIBLE TURBULENT FLOW IN MICROTUBES

Micro- and conventional compressible, turbulent tube flows were solved numerically in this study. The numerical procedure solves the compressible, turbulent boundary-layer equations using an implicit finite-difference scheme. The parabolic character of the boundary-layer equations renders the numerical procedure a very efficient, accurate, and robust tool for studying compressible microtube flows. The Baldwin–Lomax two-layer turbulence model is adopted in the numerical procedure. The numerically calculated friction factors are compared with the Blasius correlation, the Fanno line flow prediction, and the experimental data. The comparison shows that the numerically calculated friction factors for conventional tube flows agree quite well with the Blasius correlation. The numerical friction factors for microtube flows are larger than the Blasius correlation due to the compressibility effects. They also are greater than the Fanno line flow prediction and the experimental data. This is because the Fanno line flow and the experimental data assume that the flow is adiabatic, but in reality, compressible, turbulent microtube flows are neither adiabatic nor isothermal, as demonstrated by the numerical results in this study.     

Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel

A flow and heat transfer numerical simulation was performed for a 2D compressible gas flow through a microchannel in the slip regime to investigate the effects of wall roughness. The wall roughness is simulated by rectangular microelements. This effect is examined for gas flows under inlet Mach number ranging from 0.0055 to 0.202. The numerical results demonstrate that the roughness elements have a significant impact on the flow characteristics. For rarefied gases, it is found that roughness effect leads to an increase in the Poiseuille number with increasing roughness height and decreasing element spacing. The surface roughness has a more significant effect on the flow with a lower inlet Kn. Compressible gas flow is also sensitive to the height of the wall roughness elements. In addition, an increase of the relative roughness height leads to a pronounced decrease in the local heat flux for both rarefied and compressible flow. The average Nusselt numbers have a much more significant reduction for a rarefied flow than a compressible flow. The influence of wall roughness on the average heat transfer rate is smaller than that on the Poiseuille number.     

Condensation from gas–vapour mixtures in small non-circular tubes

Careful measurements have been made during condensation of steam from steam–air mixtures flowing in a small, flattened, horizontal tube. The ranges of the relevant variables covered (inlet temperature, pressure, air mole fraction and mixture mass flow rate) were chosen to simulate those occurring in an exhaust heat-exchanger tube of a proposed fuel-cell engine. The experimental tube was cooled by water in laminar counter flow to simulate the external heat-transfer coefficient (air flowing over fins) in the application. The total heat-transfer rate was found from the mass flow rate and temperature rise of the coolant. The tube wall temperature was measured by thermocouples attached in grooves along its length. Special arrangements were made to ensure good mixing of the coolant (in laminar flow) prior to measuring the inlet and outlet temperatures. The condensate was separated using a cyclone at exit from the tube. A simple model was developed to predict local and total heat-transfer and condensation rates and local bulk vapour composition, temperature and pressure along the tube in terms of the inlet parameters and the wall temperature distribution. The measured heat-transfer and condensation rates for the tube were found to be in good agreement with the calculated values without having recourse to empirical adjustment.     

Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation

Graetz problem inside the microtube is revisited considering rarefaction effect, viscous dissipation term and axial conduction in the fluid for uniform wall temperature boundary condition in the slip flow regime. The flow is assumed to be hydrodynamically fully developed, thermally developing, and the velocity profile is solved analytically. The temperature field is determined by the numerical solution of the energy equation. The rarefaction effect is imposed to the problem via velocity-slip and temperature jump boundary conditions. The local and fully developed Nu numbers are obtained in terms of dimensionless parameters; Pe, Kn, Br, κ. Fully developed Nu numbers and the thermal entrance length are found to increase by the presence of the finite axial conduction.     

Simulation of gas species and temperature separation in the counter-flow Ranque–Hilsch vortex tube using the large eddy simulation technique

A computational fluid dynamic model is used to predict the species and temperature separation within a counter flow Ranque–Hilsch vortex tube. The large eddy simulation (LES) technique was employed for predicting the gas flow and temperature fields and the species mass fractions (nitrogen and helium) in the vortex tube. A vortex tube with a circumferential inlet stream of nitrogen–helium mixture and an axial (cold) outlet stream and a circumferential (hot) outlet stream was considered. The temporal evolutions of the axial, radial and azimuthal components of the velocity along with the temperature, pressure and mass density and species concentration fields within the vortex tube are simulated. Even though a large temperature separation was observed, only a very minimal gas separation occurred due to diffusion effects. Correlations between the fluctuating components of velocity, temperature and species mass fraction were calculated to understand the separation mechanism. The inner core flow was found to have large values of eddy heat flux and Reynold’s stresses. Simulations were carried out for varying amounts of cold outlet mass flow rates. Performance curves (temperature separation/gas separation versus cold outlet mass fraction) were obtained for a specific vortex tube with a given inlet mass flow rate.     

滑移区气体-颗粒流动与传热特性研究

针对气体-颗粒微尺度流动与传热过程开展数值模拟研究,所构建模型中气体处理为可压缩、变物性流体,并在颗粒表面采用速度滑移和温度跳跃边界条件以考虑气体稀薄效应。在数值模拟基础上,研究分析稀薄效应对颗粒与其周围气体流动与换热的影响程度,并进一步提出新的阻力系数与传热努谢尔特数关联式。研究结果表明,气体稀薄效应将减小颗粒阻力系数,同时抑制颗粒与其周围气体的传热过程。     

Mixed laminar convection in a horizontal tube with natural convection around its boundaries

The laminar flow and heat transfer within a horizontal tube surrounded by a liquid medium are studied both experimentally and numerically. Emphasis is given to flow regimes where a buoyant effect on the forced flow is exhibited inside the tube. The outer surface of the tube is also subjected to natural convection resulting from the temperature difference between the wall and the surrounding fluid. Detailed analyses are performed for a number of cases with various fluids, inlet temperatures and fluid flows. It is found that the variable wall temperature has a marked effect on the secondary flow patterns within the tube as well as on the heat transfer.     

Unsteady CFD simulation on ash particle deposition and removal characteristics in tube banks: Focusing on particle diameter,flow velocity,and temperature

This study establishes a numerical deposition and removal model coupled with unsteady gas–solid turbulent flow to predict transport, impaction, sticking, and removal (or rebounding) characteristics of ash particles with high alkali metals based on Ansys Fluent software extended by user–defined functions. Dynamic mesh analytical strategy is employed to adjust the grid on the interface of flue gas and deposition layer to illustrate ash deposit growth characteristics. In this study, the effects of particle size, flow velocity, and inlet gas temperature on formation and distribution of ash deposits are studied. The results indicate that ash deposit distribution has significant particle size dependence. Larger particles tend to deposit on the windward side of first–row tubes, and account for the greatest share of total deposited mass. Smaller particles may deposit on the leeward side of the tube surfaces. Variation in impaction rates with time are influenced by the thermophoretic force and enlarged deposition area. With the increase in flow velocity, total deposited mass increases gradually. The influence of flow temperature on impacting rates is mainly embodied in the effect of flow temperature on thermophoretic force. However, the increase in inlet gas temperature has little effect on the sticking efficiency and ash deposit distribution. Nevertheless, the total deposited mass shows an increasing trend with inlet flue gas temperature.