Numerical study of flow and energy fields in thermoacoustic couples of non-zero thickness

A limitation in many previous numerical studies of thermoacoustic couples has been the use of stack plates which are of zero thickness. In this study, a system for modelling thermoacoustic couples of non-zero thickness is presented and implemented using a commercial CFD code. The effect of increased drive-ratio and plate thickness upon the time-average heat transfer through the stack material is investigated. Results indicate that the plate thickness strongly controls the generation of vortices outside the stack region, perturbing the flow structure and heat flux distribution at the extremities of the plate. An increase in plate thickness is also shown to improve the spatial integral of the total heat transfer rate but at the expense of increased entropy generation.     

Computation of the flow and thermal fields in a thermoacoustic refrigerator

The hydro- and thermodynamic processes near and within two-dimensional stack plates are simulated by numerical solution of the unsteady compressible Navier–Stokes, continuity, energy equations, and the equation of state (for air as the working fluid). The stack is assumed to consist of flat plates of equal thickness. The second order mean velocity field is computed in the neighborhood of the stack plates. In the stack plate extremities the vortical mean flow is observed which is due to the abrupt change of a slip condition to a no-slip velocity boundary condition. The temperature of the stack is governed by the energy equation; therefore the entire problem is treated as a conjugate heat transfer problem. The temperature fields in the neighborhood of the solid stack plate are also observed. From the location of the heat exchangers in Fig. 1(a), it is obvious that knowledge of the flow and thermal fields at the edges of the stack plates is the key for the development of a systematic design methodology for heat exchangers in thermoacoustic devices.     

Computation of the time-averaged temperature fields and energy fluxes in a thermally isolated thermoacoustic stack at low acoustic Mach numbers

A simplified calculus model to investigate on the transverse heat transport near the edges of a thermally isolated thermoacoustic stack in the low acoustic Mach number regime is presented. The proposed methodology relies on the well-known results of the classical linear thermoacoustic theory which are implemented into an energy balance calculus-scheme through a finite difference technique. Details of the time-averaged temperature and heat flux density distributions along a pore cross-section of the stack are given. It is shown that a net heat exchange between the fluid and the solid walls takes place only near the edges of the stack plates, at distances from the ends not exceeding the peak-to-peak particle displacement amplitude. The structure of the mean temperature field within a stack plate is also investigated; this last results not uniform near its terminations giving rise to a smaller temperature difference between the plate extremities than that predicted by the standard linear theory. This result, when compared with experimental measurements available in literature, suggests that thermal effects localized at the stack edges may play an important role as sources of the deviations found between linear theory predictions and experiments at low and moderate Mach numbers.     

Estimation of heat transfer coefficients in oscillating flows: The thermoacoustic case

The classical linear thermoacoustic theory is integrated through a numerical calculus with a simple energy conservation model to allow estimates of the optimal length of thermoacoustic heat exchangers and of the magnitude of the related heat transfer coefficients between gas and solid walls. This information results from the analysis of the temperature and heat flux density distributions inside a thermally isolated thermoacoustic stack. The effects of acoustic amplitude, plate spacing, plate thickness and Reynolds number on the heat transfer characteristics are examined. The results indicate that a net heat exchange between the acoustically oscillating gas and the solid boundary takes place only within a limited distance from the stack edges. This distance is found to be an increasing function of the plate spacing in the range (0 ⩽ y₀/δ_κ ⩽ 2), becoming constant for y₀/δ_κ ⩾ 2. The calculated dimensionless convective heat transfer coefficients, the Nusselt numbers, between gas and solid wall are comparable to those evaluated from classical correlations for steady laminar flow revised under the “Time-Average Steady-Flow Equivalent” (TASFE) and “root-mean-square Reynolds number” (RMSRe) models. Numerical results agree with measurements of the heat transfer coefficient found in literature to within 20%.     

Numerical computation for parallel plate thermoacoustic heat exchangers in standing wave oscillatory flow

A simplified computational method for studying the heat transfer characteristics of parallel plate thermoacoustic heat exchangers is presented. The model integrates the thermoacoustic equations of the standard linear theory into an energy balance-based numerical calculus scheme. Details of the time-averaged temperature and heat flux density distributions within a representative domain of the heat exchangers and adjoining stack are given. The effect of operation conditions and geometrical parameters on the heat exchanger performance is investigated and main conclusions relevant for HX design are drawn as far as fin length, fin spacing, blockage ratio, gas and secondary fluid-side heat transfer coefficients are concerned. Most relevant is that the fin length and spacing affect in conjunction the heat exchanger behavior and have to be simultaneously optimized to minimize thermal losses localized at the HX-stack junctions. Model predictions fit experimental data found in literature within 36% and 49% respectively at moderate and high acoustic Reynolds numbers.     

Three-dimensional multi-scale plate assembly for maximum heat transfer rate density

This paper extends the design concept for generating multi-scale structures in forced convection for a finite-size flow system to a three-dimensional heat-generating plate with the objectives of maximising heat transfer rate density, or the heat transfer rate per unit volume. The heat-generating plates, arranged in a stack form channels in which the fluids are forced through by an applied pressure difference. The first stage of this work consists of numerical simulation of the flow and heat transfer in a large number of flow configurations, to determine the optimum plate spacing, and the maximum heat transfer rate density. In the subsequent stages, shorter plates are inserted in the centers at adjacent (longer) plates in the entranced region were the boundary layer are thin and there is a core of unused fluid. The heat transfer density is further increased by progressively inserting another set of even shorter plates between the plates and then optimizing the whole structure. The resulting structure is an optimized multi-scale and multi channel structure with horizontal equidistant heated plates of decreasing lengths scales. Further more the effects of plate thickness and dimensionless pressure drop number on the multi-scale structure was investigated. The numerical results are found to be in good agreement with predicted analytical results.     

Transient temperature profile inside thermoacoustic refrigerators

The linear theory used to calculate the thermal quantities inside the stack in the classical thermoacoustic refrigerators always overestimates those measured. The causes of these discrepancies have to be found in the complex processes of thermal exchanges. The analytical study of the transient response should provide an interpretation of these complex processes. This present paper provides such analytical modelling. This modelling remains within the framework of the classical linear theory. It includes the effects of the thermoacoustic heat flux carried along the stack, the conductive heat flux returning in the solid walls of the stack and through the fluid inside the stack, the transverse heat conduction in the stack and the heat leakages through the duct walls, the heat generated by viscous losses in the stack, the heat generated by vorticity at the ends of the stack, and the heat transfer through both ends of the stack. A modal analytical solution for the temperature profile is proposed, assuming the usual approximations in such thermal problems to avoid intricate calculations and expressions. The theoretical transient response of a thermoacoustic refrigerator is compared with experimental data. A good qualitative agreement is obtained between analytical and experimental results after fitting empirical coefficients.     

Investigating the magnetohydrodynamic flow of a couple stress dusty fluid along a stretching sheet in the presence of viscous dissipation and suction

A computational study for investigating the flow and heat transfer phenomena in the unsteady magnetohydrodynamic couple stress dusty fluid flow over a linearly stretching porous surface in the presence of viscous dissipation effects is presented. The governing equations, in nondimensional form, are tackled by the exploitation of the standard spectral quasi-linearization methodology. The estimations of flow rate and temperature profiles are pictured diagrammatically. In contrast, the local skin friction and heat transfer rates are placed in tabular form for various values of thermofluidic parameters. The numerical results of a current investigation are compared with previously available results and located to be sensible agreement as shown in Tables 1 and 2. It is analyzed that by elevating the specific heat parameter and couple stress parameter, the temperature profile and the resulting thickness of the boundary layer are depressed. In comparison, an increase in thermal boundary layer thickness and a decrease in thickness of the momentum boundary layer were found with the rising magnetic parameter values.     

Performance of an air-cooled looped thermoacoustic engine capable of recovering low-grade thermal energy

An air-cooled looped thermoacoustic engine is designed and constructed, where an air-cooled cold heat exchanger (consisting of copper heat transfer block, aluminum flange, and aluminum fin plate) is adopted to extract heat and the resonant tube is spiraled and shaped to fit to the available space. Experiments have been conducted to observe how onset temperature difference and resonant frequency are affected by mean pressure, working fluid, and diameter of compliance tube. Besides, the influences of temperature difference, mean pressure, working fluid and diameter of compliance tube on pressure amplitude, output acoustic power, and thermal efficiency of the system have been investigated. The air-cooled looped thermoacoustic engine can start to oscillate at a lowest temperature difference of 46°C, with the working fluid of carbon dioxide at 2.34 MPa. A highest output acoustic power obtained is 6.65 W at a temperature difference of 199°C, with the working gas of helium at 2.58 MPa, and the thermal efficiency is 2.21%. This work verifies the feasibility of utilizing low-grade thermal energy to drive an air-cooled looped thermoacoustic engine and extends its application in the water deficient areas.     

Effects of non-Darcian on forced convection heat transfer over a flat plate in a porous medium-with temperature dependent viscosity

The non-Darcian effect on forced convection heat transfer over a flat plate in a porous medium is examined. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The effects of inertia forces and the distance from the leading edge of the plate on the velocity and temperature fields as well as on the skin friction and heat transfer coefficients in the boundary layer over a semi-infinite plate are studied. The nonlinear boundary layer equations, governing the problem under consideration, are solved numerically by applying an efficient numerical technique based on the Keller box method. The velocity profiles, temperature profiles and the skin friction components on the plate are computed and discussed in detail numerically for various values of the variable viscosity parameter, the modified Reynolds number, the stream wise coordinate and the Prandtl number.     

MHD mass transfer flow past an inclined plate with variable temperature and plate velocity embedded in a porous medium

An exact solution of unsteady MHD free convective mass transfer flow past an infinite inclined plate embedded in a saturated porous medium with variable plate velocity, temperature, and mass diffusion has been presented. An attempt has been made to analyze the Soret effect and the influence of the angle of inclination on the flow and transport properties, in the presence of thermal radiation, heat source, and chemical reaction. The equations governing the flow, heat, and mass transfer are solved by employing the Laplace transform technique, in closed form. The variations in fluid velocity, temperature, and concentration profiles are shown graphically whereas the numerical values of shear stress, the rate of heat transfer, and the rate of mass transfer from the plate to the fluid are presented in tabular form for various values of the flow parameters. The results show that the flow is accelerated due to the Soret effect while the angle of inclination sustains a retarding effect on fluid velocity. Further it is observed that the viscous drag at the plate and the mass diffusion from the plate to the fluid decrease under the influence of thermal diffusion.     

Effect of chemical reaction and thermal radiation on heat and mass transfer flow of MHD micropolar fluid in a rotating frame of reference

This paper studies the effect of first order chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer flow of a micropolar fluid via a porous medium bounded by a semi-infinite porous plate with constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using small perturbation approximation. The effect of the various dimensionless parameters entering into the problem on the velocity, temperature and concentration profiles across the boundary layer are investigated through graphs. Also the results of the skin friction coefficient, couple stress coefficient, the rate of heat and mass transfer at the wall are prepared with various values of the parameters.     

Turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

Turbulent natural convection in a vertical parallel plate channel has been investigated both experimentally and numerically. The experimental channel is formed of a uniform temperature heater wall and an opposing glass wall. A fibre flow laser doppler anemometer (LDA) is used to measure velocity profiles along the channel. Simultaneous velocity and temperature profile measurements are made at the channel outlet. A commercial computational fluid dynamics (CFD) code is used to simulate heat transfer and fluid flow in the channel numerically. The code is customised building in some low Reynolds number (LRN) k–ε turbulence models. The numerical method used in this study is found to predict heat transfer and flow rate fairly accurately. It is also capable of capturing velocity and temperature profiles with some accuracy. Experimental and numerical data are presented comparatively in the form of velocity, temperature, and turbulent kinetic energy profiles along the channel for a case. Correlating equations are obtained from the numerical results for heat transfer and induced flow rate and, are presented graphically comparing with other studies available in the literature.     

Oscillatory Flow in Thermoacoustic Sound Wave Generator

Oscillatory flow in a thermoacoustic sound wave generator is described. The thermoacoustic sound wave generator plays an important role in thermoacoustic equipment. The heat exchange between the working fluid and the stack, the acceleration and deceleration of the working fluid and viscous friction loss both in the stack and in the resonance tube influence the performance of the thermoacoustic sound wave generator. Particularly, oscillatory flow significantly influences the heat exchange mechanism between the working fluid and the stack. Temporal changes in pressure and velocity are sinusoidal inside the resonance tube. Flow forms an oscillatory jet just behind the tube outlet, and becomes intermittent far downstream outside the resonance tube. The open-end corrections of 0.63R, that is, the region where oscillatory flow characteristics are maintained downstream in spite of being outside the tube outlet, are confirmed by velocity measurements and flow visualization. Also, they are almost equal to acoustical theoretical results.     

Experimental study on the heat transfer at the heat exchanger of the thermoacoustic refrigerating system

Oscillatory flow heat transfer at the heat exchanger of the thermoacoustic refrigeration system was studied. The study identified significant factors that influence this heat transfer as well as the construction of the system. The results from the experimental study were correlated in terms of Nusselt number, Prandtl number and Reynolds number to obtain a useful new correlation for the heat transfer at the heat exchangers. Results show that using straight flow heat transfer correlations for analyses and design of this system could result in significant errors. Results also show the relationship between the oscillatory heat transfer coefficient at the heat exchangers, the mean pressure and frequency of oscillation. Higher mean pressures result in greater heat transfer coefficients if the thermoacoustic refrigerating system operates at the corresponding resonant frequency. However, a compromise has to be reached to accommodate construction of the stack.     

Steady free convection boundary layer over a vertical flat plate embedded in a porous medium filled with water at 4 °C

This paper reports a theoretical investigation of the boundary layer flow over a vertical flat plate embedded in a porous medium filled with water near the vicinity of its density maximum associated with the temperature of 3.98 °C at atmospheric pressure. The study aims at determining similarity solutions of the governing boundary layer equations for a class of problems where the variable wall temperature (VWT), variable heat flux (VHF), or variable heat transfer coefficient (VHTC), vary as power functions of the distance from the leading edge of the plate. The existence and uniqueness of the solutions are considered and studied. The analytical and numerical solutions of the similarity form of the boundary layer equations yield velocity and temperature profiles as well as values of the stream function at the edge of the boundary layer, the heat transfer coefficient and the temperature on the plate.     

Effect of wavy plate geometry configurations on the temperature and flow distributions

As fluid flowing through the wavy plate, breaking and destabilizing in the thermal boundary layer are induced. In the present study, the numerical investigation on the heat transfer and flow distributions in the channel with various geometry configuration wavy plates under constant heat flux conditions is considered. A finite volume method with the structured uniform grid system is used to solve the turbulent model. Effects of geometry configuration of wavy plates, wavy plate arrangements, and air flow rates on the temperature and flow developments are considered. The sharp edge of wavy plate has a significant effect on the flow structure and heat transfer enhancement. The results of this study are expected to lead to guidelines that will allow the selected wavy plate geometry configuration for designing heat exchanger which increase thermal performance.     

CFD simulation of thermoacoustic cooling

In the field of thermoacoustic energy conversion, the application of numerical analysis techniques, specifically computational fluid dynamics (CFD) simulations, have gained ground in recent years. Previous efforts have focused on single thermoacoustic couples that were subjected to the thermoacoustic effect through an oscillatory boundary condition. CFD simulations of an entire thermoacoustic device are computationally expensive and few examples exist. The present work presents an extension of a simulation of a whole thermoacoustic engine that also includes a refrigeration stack. Through interaction of thermally generated sound waves, cooling of the working gas in this stack is demonstrated.     

Two-Phase Heat Spreaders Utilizing Microfabricated Boiling Enhancement Structures

Results from various enhancement techniques to improve the performance of a recently developed two-phase heat spreader are reported. The spreader has a central evaporator section, with an integrated condenser along the edges. A micro-fabricated three-dimensional enhancement structure is employed to improve the heat transfer performance of the spreader. This study considers the performance of several liquid coolants to be used with the device and evaluates the effect of initial pressures on the thermal performance of the spreader plate. Liquids with lower boiling points were found to result in lower wall temperatures of the spreader plate due to earlier onset of boiling. Studies also showed an improvement in heat transfer performance with increase in stack height of the enhancement structures used in the evaporator section.     

Optimum packing factor of the stack in a standing‐wave thermoacoustic prime mover

A bench consisting of a pulse tube refrigerator driven by a standing‐wave thermoacoustic prime mover has been set up to study the relationship among stack, regenerator and working fluids. The stack of the thermoacoustic prime mover is packed with dense‐mesh wire screens because of their low cost and easy manufacture. The effect of the packing factor in the stack on onset temperature, refrigeration temperature and input power is explored. The optimum packing factor of 1.15 pieces per millimeter has been found experimentally, which supplies an empirical value to satisfy a compromise for enhancing thermoacoustic effect, decreasing heat conduction and fluid‐friction losses along the stack. The pulse tube cooler driven by the thermoacoustic prime mover is able to obtain refrigeration temperatures as low as 138 and 196K with helium and nitrogen, respectively. Copyright © 2002 John Wiley & Sons, Ltd.