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.     

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.     

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.     

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.     

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.     

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.     

非对称双级环路行波热声热机的实验研究*

对于双级环路行波热声热机,两个热声核的相对位置直接影响到其起振温度,而热声热机的起振温差决定了其可利用的热源品位。基于线性热声理论分析,通过改变两个热声核的相对位置,研究了两个热声核的相对位置改变对其起振温差、压力振幅和压比等的影响。结果表明,双级环路行波热声热机的起振温度随着两个热声核从中心对称位置逐步靠近时先下降再上升,当两个热声核之间的谐振管长度比例为1:3.5时,系统获得最小的起振温差为59.6℃（工质为N₂,充气压力为2.5 MPa）。在相同温差下,该系统在谐振管长度比例为1:3.5的位置相较于其他位置具有较大的压力振幅和压比。     

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.     

丝网热声板叠的最佳填充率

自行研制了热声驱动脉管制冷机实验台,着重研究了热声机械中热声转换的关键部件丝网板叠的填充率对热声驱动脉管制冷机起振温度,制冷温度和加热功率等的影响,并通过实验发现了丝网板叠的最佳填充率,以氮和氮作工质,分别获得了196K和138K的无负荷制冷制度,达到国际先进水平,为热声机械的实用化奠定了基础。     

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.     

Temperature distribution along stack in an acoustic-resonance tube: discussions on advanced linearized theory

Verification of the applicability of the linearized thermoacoustic theory proposed in 1988 by Swift, J. Acoust. Soc. Am., 84 , (4), 1145–1180, to an acoustic- resonance tube refrigerator and discussions on the advanced linearized theory were conducted through a comparison with the measured temperature distribution along the stack in a simulated acoustic-resonance tube. The measured temperature in all cases of various stack configurations such as stack plate spacing and length showed an almost linear distribution along the stack, while Swift's linearized theory gave a curved distribution with relatively large deviation from experimental data. Eddy diffusivity and/or steady streaming effects excited by sound waves were taken into account in the linearized model, and the effects of these terms on the prediction of temperature distribution were examined. The agreement between theory and experiment was markedly improved by the introduction of steady streaming. This provided a guideline for the construction of an advanced linearized theory. © 1999 Scripta Technica, Heat Trans Jpn Res, 27(8): 551–567, 1998     

NUMERICAL STUDY OF THERMOACOUSTIC HEAT EXCHANGERS IN THE THIN PLATE LIMIT

The velocity and temperature fields in an idealized thermoacoustic refrigerator are analyzed computationally. The numerical model simulates the unsteady mass, momentum, and energy equations in the thin-plate, low-Mach-number limits. Two-dimensional unsteady calculations of the flow field in the neighborhood of the stack and heat exchangers are performed using a vorticity-based scheme for stratified flow. The computations are applied to analyze the effects of heat-exchanger length and position on the performance of the device. The results indicate that the cooling load peaks at a well-defined heat-exchanger length, stack gap, and distance between the heat exchangers and the stack plates.     

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.     

Nonlinear temperature field near the stack ends of a standing-wave thermoacoustic refrigerator

The nonlinear temperature field in the vicinity of the stack of a standing-wave thermoacoustic refrigerator is investigated both theoretically and experimentally. First, the problem is addressed theoretically by a one-dimensional nonlinear model that predicts the generation of thermal harmonics near the ends of the stack. The model relies on a relaxation-time approximation to describe transverse heat transfer between the stack walls and the working fluid. It extends a previous model proposed by [Gusev et al., Thermal wave harmonics generation in the hydrodynamical heat transport in thermoacoustics, J. Acoust. Soc. Am. 109 (2001) pp. 84–90], by including the effect of axial conduction on temperature fluctuations. Second, the nonlinear temperature field is investigated experimentally. The amplitude of temperature fluctuations behind the stack at the fundamental frequency and second harmonic are measured using cold-wire anemometry. The measurements rely on a procedure recently developed by the authors that allows a full correction of the thermal inertia of the sensor. Experimental results are in good agreement with the predictions of the model. The generation of thermal harmonics behind the stack is thus validated. The influence of the Péclet number on the thermal field, which depends on the diffusivity of the working fluid and on the acoustic frequency and pressure level, is also demonstrated.     

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.     

Numerical analysis of the single electrode heat effect in molten carbonate fuel cells: temperature analysis of the electrolyte plate by applying irreversible thermodynamics

A temperature analysis model of a molten carbonate fuel cells (MCFC) stack is used to calculate the single electrode heat effects. The magnitude of heat which evolves from the cathode and absorbed at the anode is large, and in similar value to the electrical output of a MCFC. This suggests that the heat evolution of a single electrode causes a temperature difference between the electrodes. The temperature distribution in the electrolyte plate is evaluated to establish more accurate results concerning the temperature analysis model of the stack. The temperature distribution in the electrolyte plate is studied by applying irreversible thermodynamics. When the operating current density is less than 3000 A m^?2 and the thermal conductivity of the electrolyte is more than 2 W m^?1 K^?1, the temperature difference between cathode and anode is estimated to be less than approximately 1 K. This result proves that the temperature difference between the electrodes can be supposed constant in constructing the temperature analysis model of the MCFC stack. This results also allows us to construct a two‐dimensional heat production distribution in the cell plane and discrete heat production distribution in the stacking direction for the practical use of the temperature analysis model. Copyright © 2004 John Wiley & Sons, Ltd.     

Experimental study on the performance of the thermoacoustic refrigerating system

This study is on the performance of the thermoacoustic refrigerating system with respect to some critical operating parameters. Experiments were performed on the system under various operating conditions. The experimental setup consists of the thermoacoustic refrigerating system with appropriate valves for the desired controls, instrumentation and the electronic data acquisition system. The resonator was constructed from aluminum tubing but it had plastic tube lining on the inside to reduce heat loss by conduction. Significant factors that influence the performance of the system were identified. The cooling produced increases with the temperature difference between the two ends of the stack. High pressure in the system does not necessarily result in a higher cooling load. There exists an optimum pressure and an optimum frequency for which the system should be operated in order to obtain maximum cooling load. Consequently, for the thermoacoustic refrigeration system, there should be a related compromise between cooling load, pressure and frequency for best performance.     

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.     

On the phase difference of the temperature and pressure waves in the thermoacoustic effect

In this comment, the single-plate, linear theory for the thermoacoustic phenomenon in ideal conditions, Prandtl Number (σ) zero and a plate with infinite heat capacity, presented by Swift [1] has been used to find expressions for the phase difference α between the temperature and pressure waves. The effect of Prandtl Number different from zero and a plate with a finite heat capacity has also been analyzed. It has been found that the behavior is governed by the relation between a non-dimensional temperature gradient Γ and σ. Attenuation occurs for Γ < 1 + √σ and excitation for Γ > 1 + √σ which correspond to |α| < π/2 and |α| > π/2 respectively. Explicit expressions for a as a function of the transverse coordinate are given. A physical interpretation of the results is presented in the context of concepts offered by Lord Rayleigh.