Second‐law analysis and optimization of microchannel flows subjected to different thermal boundary conditions

Entropy generation and transfer in microchannel flows were calculated and analyzed for different thermal boundary conditions. Due to the small flow cross‐sectional area, fluid temperature variation in the lateral direction was neglected and a laterally lumped model was developed and used in the first‐ and second‐law analyses. Since the Peclet numbers of microchannel flows are typically low, heat conduction in the flow direction was taken into consideration. Computed fluid temperature and entropy generation rate were cast into dimensionless forms, thus can be applied to different fluids and channels of different sizes and configurations. Local entropy generation rate was found to be only dependent upon the temperature gradient in the flow direction. The optimization results of microchannel flows exchanging heat with their surroundings indicate the optimal fluid temperature distribution is a linear one. Copyright © 2004 John Wiley & Sons, Ltd.     

Bias effects on heat transfer measurements in microchannel flows

This work is devoted to both experimental and numerical investigations of the hydrodynamics and associated heat transfer in two-dimensional microchannels from 700 μm to 200 μm in height. The design of the test section enabled to vary the channel height and to set a quasi-constant heat flux at the microchannel surface. Laminar developing, transitional and turbulent regimes of water flows were explored (200 < Re < 8000). A significant decrease in the Nusselt number was observed in the laminar regime when the channel spacing was decreased while the Poiseuille number remained unchanged in regard to conventional channel flow. It is shown that a bias effect in the solid/fluid interface temperature measurements is most likely responsible for this scale effect. The temperature error was estimated and accounted for in the determination of the Nusselt number. The corrected values have been found to be consistent with the conventional laws both in the laminar and in the beginning of the turbulent regime.     

Soret effects on the mixed convection flow using Robin boundary conditions

An investigation has been undertaken as Soret and Schmidt outcomes on the mixed convection flow using Robin boundary conditions. The results use a vertical channel being kept at constant cold temperature and concentration at the left wall and hot temperature and concentration at the right wall. The exchange of heat is done by help of plates with a fluid. We consider the external fluid with equal and different temperatures. This physical problem is solved by using nondimensional parameters with the corresponding boundary conditions. To find analytical solution, the regular perturbation series method is used, and for finding the numerical solution, the well‐known Runge–Kutta method with shooting technique is employed. Comparison of the current study is favorable with the previous published results. The obtained results depend on the governing parameters such as thermal Grashof number, solutal Grashof number, Biot numbers, symmetric and asymmetric wall temperatures, Schmidt number, Soret number, and Brinkman number. An influence of these parameters on the fields of velocity, temperature, and concentration is reported. Further, the numerical results for the Nusselt number, mean value of the velocity, dimensionless bulk temperature, skin friction, and molecular diffusion coefficient are tabulated for different parametric conditions and explained. For small value of Brinkman number, the obtained values agree with other published results for all considered cases.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Simulation of Unsteady Flows with Fluctuating Inflow or Outflow Boundary Conditions

This paper describes the numerical simulation of unsteady flows due to incoming wakes and/or varying back pressure. The solution method is based upon the one-step finite-volume TVD Lax-Wendroff scheme. Dual time-step approach and multigrid algorithm are adopted to improve the computational efficiency of the baseline scheme. Numerical results for the transonic unsteady flow in a channel bump and the unsteady flow in a flat plate cascade and the VKI cascade are presented.     

The Effect of Non-Equilibrium Condensation on Supersonic Air Flows over Rectangular Cavities

Numerical simulations have been carried out for a supersonic two-dimensional flow over open,rectangular cavi-ties(length-to-depth ratios are L/D=1.0 and 3.0)in order to investigate the effect of non-equilibrium condensa-tion of moist air on supersonic internal flows around the cavity for the flow Mach number 1.83 at the cavity en-trance.In the present computational investigation,a condensing flow was produced by an expansion of moist airin a Laval nozzle.The computational results showed that the upstream traveling compression waves becomeweaker than those without the condensation.Consequently,the weaker compression waves cannot excite theshear layer strongly and amplitudes of oscillation in the cavity became smaller than those without the condensa-tion.The occurrence of the non-equilibrium condensation in case of L/D=1.0 affected strongly the amplitude andfrequency of oscillation in the cavity compared with L/D=3.0.     

Microtube gas flows with second-order slip flow and temperature jump boundary conditions

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, second-order boundary conditions assuming an effective mean free path model predict a lower slip velocity than a first-order model assuming a hard sphere mean free path model. Heat transfer effects associated with rarefied flow are reduced for the second-order model. The effect of the second-order terms is most significant at the upper limit of the slip regime. For airflow at standard conditions, the maximum second-order change to the Nusselt number is on the order of 15%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.     

Simulation of microchannel flows using a 3D height function formulation for surface tension modelling

Simulations of multiphase flow and phase change heat transfer in microchannels require accurate calculation of the surface tension force to provide accurate interface locations and to avoid spurious velocities that distort the flow at the interface. Building on previous work, where we implemented a 2D height function technique, the 3D height function method has been modified and implemented in ANSYS Fluent to enable such calculations to be performed on structured meshes. Firstly, simulations are presented for test cases that demonstrate the correct and accurate calculation of the surface tension force. Then the model is used to investigate both Taylor bubble formation in a square section channel and the development of an elongated vapour bubble from a small spherical nucleated bubble in a heated channel.     

Influence of number of simulated particles on DSMC modeling of micro-scale Rayleigh-Bénard flows

Two-dimensional micro-scale Rayleigh-Bénard flows are investigated numerically using direct simulation Monte Carlo method. An enclosure of length-to-height aspect ratio of AS = 4 is taken to explore the influence of initial setting of simulated molecules. The simulation domain is divided into 81 × 21 sampling cells and the range of Rayleigh number from 3000 to 10 000 corresponds to the convection state. Cases of 8, 10, 12, 14, 16 and 24 simulated particles in each collision cell are examined. It is shown that flow patterns with three-, four- or five-roll modes may appear depending on the number of simulated particles.     

The effect of secondary flows on the starting pressure for a second-throat supersonic ejector

The effect of the secondary flow on the starting pressure of a second-throat supersonic ejector has been investigated by adapting the height of the secondary flow inlet. The obtained results show that an optimum value of the secondary inlet height exists, and the starting pressure of the ejector becomes a minimum at that condition. Based on the results of the pressure measurements, a qualitative analysis has been made to clarify the flow behavior and the physical meaning of the performance diagram. It appears that the choking phenomenon of the secondary flow plays an important role in the starting process of the ejector. When the secondary inlet height is relatively small, the choked secondary flow and the supersonic primary flow could be employed to protect the static pressure in the suction chamber from being disturbed by the back pressure effect at a certain primary stagnation pressure, which is lower than the starting pressure for the case of the zero-secondary flow. However, as the secondary inlet height increases and exceeds a critical value, the static pressure in the suction chamber rapidly increases, and the starting pressure of the ejector increases accordingly.     

Numerical study of the inlet/outlet arrangement effect on microchannel heat sink performance

In this study, fluid flow and heat transfer in microchannel heat sinks are numerically investigated. The three-dimensional governing equations for both fluid flow and heat transfer are solved using the finite-volume scheme. The computational domain is taken as the entire heat sink including the inlet/outlet ports, inlet/outlet plenums, and microchannels. The particular focus of this study is the inlet/outlet arrangement effects on the fluid flow and heat transfer inside the heat sinks.The microchannel heat sinks with various inlet/outlet arrangements are investigated in this study. All of the geometric dimensions of these heat sinks are the same except the inlet/outlet locations. Because of the difference in inlet/outlet arrangements, the resultant flow fields and temperature distributions inside these heat sinks are also different under a given pressure drop across the heat sink. Using the averaged velocities and fluid temperatures in each channel to quantify the fluid flow and temperature maldistributions, it is found that better uniformities in velocity and temperature can be found in the heat sinks having coolant supply and collection vertically via inlet/outlet ports opened on the heat sink cover plate. Using the thermal resistance, overall heat transfer coefficient and pressure drop coefficient to quantify the heat sink performance, it is also found these heat sinks have better performance among the heat sinks studied. Based on the results from this study, it is suggested that better heat sink performance can be achieved when the coolant is supplied and collected vertically.     

Slip/jump boundary conditions for rarefied reacting/non-reacting multi-component gaseous flows

General concentration-jump, velocity-slip, and temperature-jump conditions on solid surfaces in a rarefied multi-component gas flow are developed using the kinetic theory of gases. The surface is allowed to be catalytic and hence some or all of the species may take part in surface reactions. The presented model provides general boundary conditions which can be simplified according to the problem under consideration. In some limiting cases, the results of the current work are compared to the previously available and widely used boundary conditions. The details of the mathematical procedure are also provided to give a better insight about the physical importance of each term in the slip/jump boundary conditions. Also the disagreements between previously reported results are investigated to arrive at the most proper expressions for the slip/jump boundary conditions. The temperature-jump boundary condition is also modified to handle polyatomic gas flows unlike previously reported studies which were mostly concerned with monatomic gases.     

Large eddy simulation of hydrogen combustion in supersonic flows using an Eulerian stochastic fields method

An Eulerian Monte-Carlo approach, the so-called Eulerian stochastic fields (ESF) method is implemented and evaluated for simulation of non-premixed hydrogen/air combustion in supersonic flows. The ESF method is integrated into a compressible flow large eddy simulation (LES) solver, and validated on a supersonic combustor with a strut as flame-holder. Comparison with experimental data and with results from a well-stirred reactor (WSR) model demonstrates the advantage of the LES-ESF method for simulation of local-extinction and re-ignition phenomena. The hydrogen/air flame structure and the stabilization of the combustion process in the supersonic combustor are analysed based on the present LES-ESF method. Oscillation of the recirculation zones is found to be the dominant mechanism for the local-extinction/re-ignition and the flame stabilization under the present condition.     

Optimization of fractal-like branching microchannel heat sinks for single-phase flows

Fractal-like branching flow networks in disk-shaped heat sinks are numerically optimized to minimize pressure drop and flow power. Optimization was performed using a direct numerical search, gradient-based optimization, and genetic algorithm. A previously validated one-dimensional pressure drop and heat transfer model, with water as the working fluid, is employed as the objective function. Geometric constraints based on fabrication limitations are considered, and the optimization methodology is compared with results from a direct numerical search and a genetic algorithm.The geometric parameters that define an optimal flow network include the length scale ratio, width scale ratio, and terminal channel width. Along with disk radius, these parameters influence the number of branch levels and number of channels attached to the inlet plenum. The geometric characteristics of the optimized flow networks are studied as a function of disk radius, applied heat flux, and maximum allowable wall temperature. A maximum inlet plenum radius, minimum interior channel spacing, and ranges of terminal channel widths and periphery channel spacing are specified geometric constraints. In general, all geometric constraints and the heat flux have a significant influence on the design of an optimal flow network. Results from a purely geometrically derived network design are shown to perform within 15% of the direct search and gradient-based optimized configurations.     

Aerodynamic study on supersonic flows in high-velocity oxy-fuel thermal spray process

To clarify the characteristics of gas flow in high velocity oxy-fuel (HVOF) thermal spray gun, aerodynamic research is performed using a special gun. The gun has rectangular cross-sectional area and sidewalls of optical glass to visualize the internal flow. The gun consists of a supersonic nozzle with the design Mach number of 2.0 followed by a straight passage called barrel. Compressed dry air up to 0.78 MPa is used as a process gas instead of combustion gas which is used in a commercial HVOF gun. The high-speed gas flows with shock waves in the gun and jets are visualized by schlieren technique. Complicated internal and external flow-fields containing various types of shock wave as well as expansion wave are visualized.     

Effective boundary conditions for buoyancy-driven flows and heat transfer in fully open-ended two-dimensional enclosures

The present work achieves an accurate representation of the effective boundary conditions at the aperture plane of a two-dimensional open-ended structure for wide range of pertinent parameters. The presented effective boundary conditions are correlated in terms of Rayleigh number, Prandtl number, and the aspect ratio of the open-ended geometry. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. Comprehensive comparisons between the present investigation using the effective boundary conditions for the anticipated closed-ended model and the results for the fully extended computational domain confirm successful implementation of the proposed model. Implementation of this representation reduces the main difficulties associated with specifying the open-ended boundary conditions and results in very substantial savings in CPU and memory usage. The present work plays an important role on modeling a basic and generic set of effective boundary conditions at the aperture plane for several applications of practical interest.     

Effect of inclined and low magnetic field in gaseous slip flow in two‐dimensional rectangular microchannel using first‐order boundary conditions

In the present work, the effect of an oriented low magnetic field on near‐continuum gaseous slip flow inside a two‐dimensional rectangular microchannel has been studied using first‐order boundary conditions. The flow was assumed to be compressible, laminar, and steady. The governing equations were solved analytically to obtain the solutions of velocity, temperature, and the pressure of the flow. The influence of different parameters such as Knudsen number, aspect ratio, Hartmann number, and pressure ratio were studied and analyzed. It was found that the electric and magnetic field with an inclined angle had significant effects on the flow properties. The results showed that the velocity increases and the temperature decreases as the inclination angle of the magnetic field decreases. The velocity increases as the Knudsen number, pressure ratio, and aspect ratio increase, while it decreases with increasing of the Hartmann number. The temperature decreases with increasing of the Knudsen number, pressure ratio, and aspect ratio, while the temperature increases as the Hartmann number increases. The results of the present study were validated with published results in the literature.     

Boundary Layer Ignition of Hydrogen-Air Mixtures in Supersonic Flows

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Comparison of heat pump performance using fin-and-tube and microchannel heat exchangers under frost conditions

Vapor compression heat pumps are drawing more attention in energy saving applications. Microchannel heat exchangers can provide higher performance via less core volume and reduce system refrigerant charge, but little is known about their performance in heat pump systems under frosting conditions. In this study, the system performance of a commercial heat pump using microchannel heat exchangers as evaporator is compared with that using conventional finned-tube heat exchangers numerically and experimentally. The microchannel and finned-tube heat pump system models used for comparison of the microchannel and finned-tube evaporator performance under frosting conditions were developed, considering the effect of maldistribution on both refrigerant and air sides. The quasi-steady-state modeling results are in reasonable agreement with the test data under frost conditions. The refrigerant-side maldistribution is found remarkable impact on the microchannel heat pump system performance under the frost conditions. Parametric study on the fan speed and the fin density under frost conditions are conducted as well to figure out the best trade-off in the design of frost tolerant evaporators.