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.     

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.     

Numerical comparison of thermoacoustic couples with modified stack plate edges

It has been demonstrated that the bulk of time-averaged heat transfer between the oscillating fluid and a thermoacoustic couple is concentrated towards the edges of the stack plate. Previous numerical studies which have considered thermoacoustic couples of finite thickness have used a rectangular form for the plate edge. In practice however, current manufacturing practices allow for a variety of stack edges which may improve the efficiency of heat transfer and/or reduce entropic losses. In this numerical study, the performance of a thermoacoustic couple is investigated at selected drive ratios and using a variety of stack plate edge profiles. Results indicate that stack profiles with enlarged and blunter shapes improve the rate of heat transfer at low drive ratios but retard the rate of heat transfer at higher drive ratios due to increased residence time of the fluid in contact with the stack plate. The improvement in COP through minimisation of acoustic streaming on the inside face of the stack, and increased effective cooling power by greater retention of stack thickness at the plate extremities, leads to recommendation of the Rounded edge shape profile for thermoacoustic stack plates in practical devices.     

Numerical simulation of the onset characteristics in a standing wave thermoacoustic engine based on thermodynamic analysis

In this paper, a simplified physical model of standing wave thermoacoustic engines (SWTE) is developed based on thermodynamic analysis. Transient pressure drop and heat transfer data are first calculated based on linear thermoacoustic theory. The effects of stack spacing, charge pressure, and resonator length on onset temperature were investigated and compared with experimental results. The calculations agree well with the experimental results, which validates the model for calculating the onset conditions.     

Nonlinear thermoacoustics of ducted premixed flames: The influence of perturbation convection speed

When a premixed flame is placed within a duct, acoustic waves induce velocity perturbations at the flame’s base. These travel down the flame, distorting its surface and modulating its heat release. This can induce self-sustained thermoacoustic oscillations. Although the phase speed of these perturbations is often assumed to equal the mean flow speed, experiments conducted in other studies and Direct Numerical Simulation (DNS) conducted in this study show that it varies with the acoustic frequency. In this paper, we examine how these variations affect the nonlinear thermoacoustic behaviour. We model the heat release with a nonlinear kinematic G-equation, in which the velocity perturbation is modelled on DNS results. The acoustics are governed by linearised momentum and energy equations. We calculate the flame describing function (FDF) using harmonic forcing at several frequencies and amplitudes. Then we calculate thermoacoustic limit cycles and explain their existence and stability by examining the amplitude-dependence of the gain and phase of the FDF. We find that, when the phase speed equals the mean flow speed, the system has only one stable state. When the phase speed does not equal the mean flow speed, however, the system supports multiple limit cycles because the phase of the FDF changes significantly with oscillation amplitude. This shows that the phase speed of velocity perturbations has a strong influence on the nonlinear thermoacoustic behaviour of ducted premixed flames.     

Heat transfer in a rectangular chamber with differentially heated horizontal walls: Effects of a vibrating sidewall

Heat transfer in a gas-filled closed enclosure with differentially heated horizontal walls is investigated numerically. One of the sidewalls vibrates with specified frequency and amplitude to induce forced convective flows in the enclosure. The vibrating and the stationary sidewalls are considered to be thermally insulated while the two horizontal walls are differentially heated. To simulate the flow field, the full compressible form of the Navier–Stokes equations is considered and solved by a highly accurate flux-corrected transport algorithm. In the numerical model, temperature dependant heat conductivity and viscosity are taken into account. The presence of acoustic streaming is found to have significant effect on the heat transfer. Also the presence of temperature gradients in the enclosure is found to affect the formation of acoustically induced streaming flows.     

Investigation of convective heat transfer augmentation using acoustic streaming generated by ultrasonic vibrations

An investigation of acoustic streaming induced by ultrasonic flexural vibrations is experimentally and numerically presented. The investigation includes acoustic streaming pattern, velocity, and associated heat transfer characteristics. Acoustic streaming patterns visualized using Acetone agree well with the prediction by Nyborg’s theory. Tests of streaming velocity utilizing Styrofoam showed that the acoustic streaming velocity measured prove to be two orders greater than that by Nyborg’s theory. CFD simulations also showed the same order of the velocity as the one measured. By virtue of acoustic streaming, a notable temperature drop of 40 °C was obtained in 4 min and maintained. Tests identifying major heat flow paths indicated that gaps and the vibrating beam serve as major heat flow paths.CFD simulations were conducted to observe acoustic streaming patterns and velocities in the gap. Simulation results were validated by performing heat transfer analysis based on a lump-energy method. Simulation predicted that two symmetric vortices within half wavelength, rise of air at anti-nodes, and descent at nodes as Nyborg’s theory predicts. The presence of the upper plate has no effect on the acoustic streaming patterns. However, when an upper plate shorter than the vibrating plate is used, a drastic increase in streaming velocity occurs at the edges of the upper plate due to entrainment of air, which also alters streaming pattern in the vicinity of the open end. Estimated streaming velocities from CFD simulations are found to be two orders greater than those based on Nyborg’s theory.The results of CFD simulation indicated the vortical flows induced by a ultrasonic flexural standing wave (UFSW) can be reproduced. The CFD results are experimentally validated, qualitatively through flow pattern comparisons and quantitatively by the transient temperature drop comparison. The CFD results showed that the velocity near the plates is of the order of 10–100 cm/s, which is over 100 times higher than the results from theoretical studies based on sonically induced acoustic streaming assuming inviscid flow.     

Numerical and experimental study of a looped travelling‐wave thermoacoustic electric generator for low‐grade heat recovery

Thermoacoustic technology has drawn increasing attention due to its advantages such as reliability and environmental benignity. Aiming at low‐grade heat recovery, we developed a travelling‐wave thermoacoustic electric generator consisting of a looped travelling‐wave thermoacoustic engine and a linear alternator. In order to explore the operating characteristics of the electric generator, we numerically analyzed the acoustic field characteristics with a modified model. The analysis shows that high acoustic impedance appears in all three stages, and the travelling‐wave component dominates the acoustic field of the loop, which is significant for both thermoacoustic conversion and acoustic power propagation. Furthermore, we also investigated the effects of external electric compliance, resistance, and hot end temperature on the output electric power, thermal‐electric efficiency, and other related parameters. In the experiments, a thermal‐electric efficiency of 3.7% with an output electric power of 24 W has been achieved, when the hot end temperature is 120°C. The relative Carnot efficiency can exceed 14% when the hot end temperature is between 120°C and 190°C. The promising results demonstrate the significant potential of thermoacoustic electric generation in low‐grade heat recovery.     

Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue

In this article, the parabolic (Pennes bioheat equation) and hyperbolic (thermal wave) bioheat transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The bioheat transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat transfer equations. The non-Fourier bioheat transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic bioheat transfer equations.     

ON THE MODELING OF THE HYPERBOLIC HEAT TRANSFER PROBLEMS IN PERIODIC LATTICE-TYPE CONDUCTORS

The aim of this contribution is to propose, compare, and apply two kinds of simplified mathematical models for the analysis of hyperbolic problems describing heat transfer in dense periodic lattice-type conductors of an arbitrary form. The considerations are based on the Cattaneo-type constitutive heat transfer law. We begin with the formulation of a discrete model represented by a system of ordinary differential equations that have a finite difference form with respect to the spatial coordinates. By using some smoothness operations we derive continuum models from the aforementioned finite difference formulation. The general results are illustrated and compared in the example of a temperature wave propagating in a certain special lattice-type periodic conductor.     

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%.     

Design and optimization of a heat driven thermoacoustic refrigerator

The present paper deals with the design and optimization of a heat driven thermoacoustic refrigerator. A simplified model is developed which enables to pinpoint and examine the most important physical characteristics of a compact traveling wave thermoacoustic refrigerator driven by a traveling wave thermoacoustic engine. The model can explain the so-called traveling standing wave effect in thermoacoustics very well. The position, length and hydraulic radius of the refrigerator are optimized for the maximum total COP. The prime mover efficiency, refrigerator COP and dimensionless dissipation and their impacts on total COP are investigated and discussed. The results indicate that a COP of 28.7% at T_RF,cold = 273 K is achievable.     

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.     

Influence of differentially heated horizontal walls on the streaming shape and velocity in a standing wave resonator

Influence of differentially heated horizontal walls on shape and amplitude of acoustic streaming velocity field inside a gas-filled rectangular enclosure subject to acoustic standing wave are experimentally investigated. The synchronized particle image velocimetry (PIV) technique has been used to measure the streaming velocity fields. The results show that the temperature difference between the top and the bottom walls deforms the symmetric streaming vortices to the asymmetric ones. As the temperature difference increases, the amplitude of streaming velocity increases.     

The thermagoustic irreversibility for a single-plate thermoacoustic system

The problem of thermagoustic (thermo-magneto-acoustic) irreversibility near a single-plate, representative of the stack in a thermoacoustic engine, is modeled and analyzed in this paper. Assumptions (long wave, short stack, small amplitude oscillation, boundary layer type flow, etc.) are made to enable simplification of the governing continuity, momentum, and energy equations to achieve analytical solutions for velocity, temperature, and pressure. A general equation for entropy generation is derived from first principles that accounts for the transverse magnetic force present in a magnetohydrodynamic system. This entropy generation equation is then simplified in order to model the specific thermoacoustic situation considered in this paper. Finally, a time-averaged entropy generation rate followed by a global entropy generation rate are calculated and graphically presented for further analysis.     

Heat transfer from a vibrating circular cylinderTransfert thermique par un cylindre vertical vibrantWärmeübertragung von einem vibrierenden kreiszylinderПepeнoc тeплa oт вибpиpyющeгo кoльцeвoгo цилиндpa

Theoretical results are obtained for heat transfer from a circular cylinder oscillating in an unbounded viscous fluid which is otherwise at rest. The amplitude of the oscillation is assumed small compared to the radius of the cylinder, which for most of the examples considered is assumed to be at a constant temperature. The analysis is based upon use of the acoustic streaming flow field and consideration is given to the cases of small and large streaming Reynolds numbers. For large streaming Reynolds numbers, a solution for the previously undetermined steady streaming flow field is computed. The results obtained cover a wide range of Prandtl number. The method of matched asymptotic expansions is exploited in the analysis and the computed results are also supplemented by an approximate method based on an integrated form of the governing equations. The relationship between the present work and other relevant contributions in the literature is discussed. In a final section, attention is devoted to a technique for determining the temperature distribution which results when a line source of heat is embedded at the centre of the oscillating cylinder.     

Convective heat transport along a thermoacoustic couple in the transient regime

This work proposes a simple calculus procedure based on the linear thermoacoustic theory. The methodology applies on rate of change (time derivative) rather than on steady state temperature distributions so it constitutes a complementary to conventional analysis to perform test on the reliability and applicability of the linear theory. The procedure has been applied to experimental data collected by means of a simple prototype of thermoacoustic device. The apparatus, whose technical characteristics are described in detail along with the data acquisition procedure, has been able to highlight the general features of the thermoacoustic effect. Measurements concern the acoustically generated temperature gradients across a ThermoAcoustic Couple, a structure firstly introduced by Wheatley and coworkers in 1983. The obtained results indicate that heat transfer phenomena are more critical than non linear acoustic behavior in determining the overestimation that theoretical predictions make on experimental values.     

On an acoustics–thermal–fluid coupling model for the prediction of temperature elevation in liver tumor

The present study is aimed at predicting liver tumor temperature during a high-intensity focused ultrasound (HIFU) thermal ablation using the proposed acoustics–thermal–fluid coupling model. The linear Westervelt equation is adopted for modeling the incident finite-amplitude wave propagation. The nonlinear hemodynamic equations are also taken into account in the simulation domain that contains a hepatic tissue domain, where homogenization dominates perfusion, and a vascular domain, where blood convective cooling may be essential in determining the success of HIFU. Energy equation for thermal conduction involves two heat sinks to account for tissue perfusion and forced convection-induced cooling. The effect of acoustic streaming is also included in the development of the current HIFU simulation study. Convective cooling in large blood vessel and acoustic streaming were shown to change the temperature near blood vessel. It was shown that acoustic streaming effect can affect the blood flow distribution in hepatic arterial branches and leads to the mass flux redistribution.     

Performance comparison of looped thermoacoustic electric generators with various thermoacoustic stages

Thermoacoustic engine is a kind of novel heat engine based on thermoacoustic effect, with the merits of environmental benignity, simplicity, and reliability. In this work, looped travelling-wave thermoacoustic electric generators (LTTEGs) with one to four thermoacoustic stages have been developed and experimentally studied. It is observed that adding thermoacoustic stages can improve the thermal-electric efficiency of LTTEGs, while whether the extra stages lead to efficiency gain depends on the number of existing stages and other operating parameters (hot temperature, for instance). One main reason is that the Gedeon streaming, which might cause severe heat loss, can be enhanced by adding thermoacoustic stages and increasing hot temperature. The results suggest that the suppression of streaming in the looped thermoacoustic engine with multiple stages is even more urgent than in the traditional travelling-wave engine with only one stage.     

Brinkman–Forchheimer modeling for porous media thermoacoustic system

In this paper, analytical studies have been conducted on the flow and thermal fields of unsteady compressible viscous oscillating flow through channels filled with porous media representing stacks in thermoacoustic systems. The flow in the porous material is described by the Brinkman–Forchheimer–extended Darcy model. Analytical expressions for oscillating velocity, temperature, and energy flux density are obtained after linearizing and solving the governing differential equations with long wave, short stack, and small amplitude oscillation approximations. Experimental work is also conducted to verify the temperature difference obtained across the porous stack ends. To produce the experimental results, a thermoacoustic heat pump is designed and constructed where reticulated vitreous carbon (RVC) is used as the stack material. A very good agreement is obtained between the modeling and the experimental results. The expression of temperature difference across the stack ends obtained in the present study is also compared with the existing thermoacoustic literature. The proposed expression surpasses the existing expression available in the literature. The system of equations developed in the present study is a helpful tool for thermal engineers and physicist to design porous stacks for thermoacoustic devices.