Low computational cost CFD analysis of thermoacoustic oscillations

The numerical analysis of thermoacoustic oscillation phenomena by means of time-dependent CFD simulations usually requires a great computational effort, which may not be reasonable in industrial design. On the other hand, CFD tools provide the only approach that includes all the physical and chemical aspects involved in the thermoacoustic coupling between flame heat release and the acoustic modes of the burner/combustion chamber system. This paper presents some guidelines to reduce the computational effort required to perform a CFD analysis of the thermoacoustic oscillations with commercial codes. These guidelines are organized in a procedure that can be followed to analyze thermoacoustic coupling conditions that actually lead to unstable oscillations or are identified as potentially critical in the design phase. This procedure is also illustrated by an example of application, the partially-premixed flame type burner of a real 10 MW industrial boiler which shows noisy pressure fluctuations at a low frequency.     

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.     

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.     

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.     

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.     

Flow distribution in U-type layers or stacks of planar fuel cells

The flow distribution features in U-type layers or stacks with certain practical configurations have been investigated analytically. The formulations suggest general designing strategies to improve the flow uniformity, and narrowing some positions of the channels proves effective. The flow uniformity among the layers in a U-type stack is relatively easy to achieve in comparison with that among the channels in a U-type layer, due to the large stack headers and low-pressure loss in them. CFD simulations confirm the formulations, and the discrepancies between the analytical and CFD results have been attributed to the ignored factors during the analytical formulations.     

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.     

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。     

Optimization of the Stack Unit in a Thermoacoustic Refrigerator

ABSTRACT

A thermoacoustic refrigerator is a device that uses acoustic power to pump heat in the absence of harmful refrigerants with no or few moving parts. However, the performance of the thermoacoustic refrigerator, particularly the standing wave types, is currently not competitive compared to its counterpart, the conventional vapor-compression refrigerator. Presently, thermoacoustic refrigeration prototypes only achieved 0.1–0.2 relative coefficient of performance, compared with that of 0.33–0.5 for the conventional vapor-compression refrigerators. Past optimization efforts had been completed based on parametric studies where individual parameters are discretely varied and the final optimized outcome was based on the limited series of numerical/experimental tests. This paper discusses the initial investigation of the optimization of the thermoacoustic refrigerator stack parameters using a multi-objective genetic algorithm. The desired outputs, the maximization of the cooling load and the minimization of the acoustic power at the stack, are obtained with the parameters to be optimized set within some range of values. The stack length and center position are then optimized simultaneously. The optimized results showed that the coefficient of performance of the thermoacoustic refrigerator improves from the published value of 1.3 to 1.37.     

Multi-scale design simulation of a novel intermediate-temperature micro solid oxide fuel cell stack system

This paper presents a multi-scale simulation technique for designing a novel intermediate-temperature planar-type micro solid oxide fuel cell (mSOFC) stack system. This multi-scale technique integrates the fundamentals of molecular dynamics (MD) and computational fluid dynamics (CFD). MD simulations are carried out to determine the optimal composition of a potential electrolyte that is capable of operation in the intermediate-temperature region without sacrifice in performance. A commercial CFD package plus a self-written computational electrochemistry code are employed to design the fuel and air flow systems in a planar five-cell stack, including the preheating manifold. Different samarium-doped ceria (SDC) electrolyte compositions and operating temperatures from 673 K to 1023 K are investigated to identify the maximum ionic conductivity. The electrochemical performance simulation using an available 5-cell yittria-stablized-zirconia (YSZ) mSOFC stack shows good agreement with our experimental results. The same stack design is used to predict a novel SDC-mSOFC performance. Feasibiulity studies of this intermediate-temperature stack are presented using this multi-scale technique.     

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.     

CFD simulation of a thermoacoustic engine with coiled resonator

Thermoacoustic energy conversion is based on the Stirling cycle. In their most basic forms, thermoacoustic devices are comprised of two heat exchangers, a porous medium, both placed inside a resonator. Work is created through the interaction of strong sound waves with the porous medium that is subject to external heating. This work explores the effect of resonator curvature on the thermoacoustic effect. A CFD analysis of a whole thermoacoustic engine was developed and the influence of a curved resonator on the thermoacoustic effect is discussed. The variation of pressure amplitude and operating frequency serves as metrics in this investigation. It was found that the introduction of curvature affects the pressure amplitude achieved. Severely curved resonators also exhibited a variation in operating frequency.     

Influence of acoustic pressure amplifier dimensions on the performance of a standing-wave thermoacoustic system

A standing-wave thermoacoustic engine, employing an acoustic pressure amplifier (APA), is simulated with linear thermoacoustics to study the influence of APA’s dimensions on performance of the thermoacoustic system. Variations of operating parameters, including pressure ratio, acoustic power, hot end temperature of stack etc., versus length and diameter of APA are presented and discussed based on an analysis of pressure and velocity distribution in APA. Simulation results indicate that a largest amplification effect of both pressure ratio and acoustic power output is achieved at a critical length for the occurrence of pressure node and velocity antinode in APA, close to but less than one fourth of the wavelength. The distribution characteristics of pressure and velocity in APA are similar to a standing-wave acoustic field, which is the reason for the amplification effect. From the viewpoint of energy, the amplification effect results from the changed distribution of acoustic energy and acoustic power loss in the thermoacoustic system by APA. Experiments have been carried out to validate the simulation, and experimental data are presented.     

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.     

Geometric optimization of a thermoacoustic regenerator

This work illustrates the optimization of thermoacoustic systems, while taking into account thermal losses to the surroundings that are typically disregarded. A simple thermoacoustic engine is used as an example for the methodology. Its driving component, the thermoacoustic regenerator (also referred to as the stack), is modeled with a finite element method and its dimensions are varied to find an optimal design with regard to thermal losses. Thermoacoustic phenomena are included by considering acoustic power, and viscous and capacitive losses that are characteristic for the regenerator. The optimization considers four weighted objectives and is conducted with the Nelder–Mead Simplex method. When trying to minimize thermal losses, the presented results show that the regenerator should be designed to be as short as possible. It was found that there is an optimal regenerator diameter for a given length. The results are presented for a variety of materials and weights for each objective.     

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.     

Thermoacoustic energy analysis of transverse-pin and tortuous stacks at large acoustic displacements

A simplified method based on Rayleigh's criterion is developed for evaluating thermoacoustic power conversion in transverse-pin and tortuous stacks. Heat transfer and viscous losses are approximated by steady-flow correlations valid at large acoustic displacements with respect to a longitudinal pitch of a pin stack or a characteristic pore size of a random stack. A Lagrangian approach is employed to calculate temperature fluctuations of oscillating gas parcels inside the stack. A computational example is presented for a stack with an inline pin arrangement placed in a standing acoustic wave. Power conversion and efficiencies are evaluated for conditions relevant to a small-scale system. An indirect comparison is also made between theoretical results and experimental data for a prime mover with a wire mesh stack.     

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.     

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.