Stack Ends Research Articles

Full-scale numerical simulations of standing-wave thermoacoustic engines with circular-pore and pin-array stacks

Thermoacoustic engines (TAEs) can convert thermal energy into acoustic energy with no moving parts. Previous numerical studies normally focused on the TAEs with a parallel-plate stack due to their simple structures and used two-dimensional (2-D) computational fluid dynamics (CFD) models to save computational costs. In this study, we conduct full-scale three-dimensional (3-D) CFD simulations on the standing-wave TAEs with more complicated circular-pore and pin-array stacks. Firstly, the dynamic behavior of the standing-wave TAEs in the start-up process is investigated. It is found that the optimal ratios of hydraulic radius rh to thermal penetration depth δk for the TAEs with circular-pore and pin-array stacks are 2 and 3.2, respectively. Secondly, the acoustic, hydrodynamic, and thermodynamic characteristics of the standing-wave TAEs in the steady-state process are explored. We find that when operating at optimal rh/δk, the TAE with a pin-array stack generates much larger acoustic power than that with a circular-pore stack. Examination of the vortex shedding at the stack ends indicates that the pin arrays exhibit less flow resistance than circular pores. At optimal rh/δk, the time-averaged transversal heat flux at the pin array ends is calculated to be around 1.2 × 105 W/m2, which is larger than 7.5 × 104 W/m2 of circular pores, corresponding to a better thermodynamic performance. The 3-D numerical investigations in this work give deeper insights into the performances of TAEs with circular-pore and pin-array stacks which were investigated in experiments, providing useful guidance for the future design and development of more sophisticated thermoacoustic devices for low-grade heat recovery.

Experimental investigation on the effect of resonator shapes on the temperature characteristic of thermoacoustic cooling device

Thermoacoustic refrigerator has emerged as one of new alternative ways of cooling. The use of this technology which converts sound energy to heat energy has not been popular despite its environmentally friendly and simple construction. A laboratory scale thermoacoustic cooling device has been constructed to conduct experiments on three different shapes of resonators that results in temperature difference occurring at its stack ends. Geometry of the device parts is one of the parameter that holds importance to its characteristic. The device applied a different shape of resonator for each experiment and record temperature data at stacks ends. The experiments were conducted with variations in resonator which are square tube, cylinder tube and tapered tube. The material of resonator is acrylic and its inner volume remains unchanged.

Experimental and theoretical study of density fluctuations near the stack ends of a thermoacoustic prime mover

This paper proposes the experimental and theoretical study of nonlinear heat transport processes generated by large amplitude acoustic oscillations at the ends of a stack of plates in the presence of a temperature gradient. These processes are notably involved in the operation of thermoacoustic engines. The measurement method, a time-resolved and full-field digital holography interferometry technique, enables to measure the density fluctuations from the optical phase difference between two laser beams. This technique is applied to the analysis of density fluctuations in the vicinity of a stack submitted to a temperature gradient, firstly for the case of (uncontrolled) self-sustained acoustic oscillations generated spontaneously in a standing wave thermoacoustic prime mover, and secondly for the case of an assigned acoustic field whose amplitude is controlled by an external sound source. A theoretical model describing the advective heat transport by sound at the ends of the heated stack is also presented, and numerical simulations are then carried out. The comparison between experimental data and numerical simulations is provided for several stack positions, several sound pressure levels, and several amounts of heat supplied to the stack, and the results show good agreement between the experiments and the model.

Performance analysis of the thermoacoustic refrigerator with the standing wave and air as a working fluid

Thermoacoustic refrigerator is a new and emerging technology capable of transporting heat from a low-temperature source to a high-temperature source by utilizing the acoustic power input. These devices, operating without hazardous refrigerants and owning no moving components, show advantages of high reliability and environmental friendliness. However, simple to fabricate, the designing of thermoacoustic refrigerators is very challenging. This paper illustrates the impact of significant factors on the performance of the thermoacoustic refrigerator which was measured in terms of the temperature difference generated across the stack ends. The experimental device driven by a commercial loudspeaker and air at atmospheric pressure as a working fluid was examined under various resonator length and operating frequencies. The results indicate that appropriate resonator’s length and operating frequency lead to an increase in the temperature difference created across the stack. The maximum values were achieved for operating frequency equalled to 200 and 300 Hz whereas resonator length corresponded to the half-length of the acoustic wave for these frequencies. The results of experiment also confirm that relationship between these parameters is strongly affected by the stack spacing, which in this research was equalled to 0.4 mm.

An Experimental Study on Heterogeneous Porous Stacks in a Thermoacoustic Heat Pump

Growing evidence suggests that research must be done to develop energy efficient systems and clean energy conversion technologies to combat the limited sources of fossil fuel, its high price, and its adverse effects on environment. Thermoacoustic is a clean energy conversion technology that uses the conversion of sound to thermal energy and vice versa for the design of heat engines and refrigerators. However, the efficient conversion of sound to thermal energy demands research on altering fluid, operational, and geometric parameters. The present study is a contribution to improve the efficiency of thermoacoustic devices by introducing a novel stack design. This novel stack consists of alternative conducting and insulating materials or heterogeneous materials. The author examined the performance of eight different types of heterogeneous stacks (combination 1–8) that are only a fraction of the displacement amplitude long and consisted of alternating aluminum (AL) and Corning Celcor or reticulated vitreous carbon (RVC) foam materials. From the thermal field measurements, the author found that combination eight performs better (12% more temperature difference at the stack ends) than all the other combinations. One interesting feature obtained from these experiments is that combination 7 produces the minimum temperature at the cold end (17% less than other combinations). The thermal performance of the heterogeneous stack is compared to that of the traditional homogeneous stack. Based on the study, the newly proposed stack design provides better cooling performance than a traditionally designed stack.

A 3D investigation of thermoacoustic fields in a square stack

The thermoviscous behavior of the oscillating gas within the porous medium of a thermoacoustic refrigerator enables the conversion of sound into heat in the process of typical standing-wave thermoacoustic refrigeration systems. Several nonlinear mechanisms, such as harmonics generation, self-induced streaming and possible turbulence, cause complicated flow behavior and influence the performance of such devices. Few analytical and numerical approximations (Cao et al., 1996; Worlikar and Knio, 1996; Worlikar et al., 1998) describe the flow field and the energy flux density in standing devices comprising stacks of parallel plates, but almost no 3-D simulation has been developed that models the large-amplitude excitations and enables the prediction of the oscillating-flow behavior within a porous medium made of square channels. Here, we build on existing effort (Abd El-Rahman and Abdel-Rahman, 2014) and report a computational fluid dynamics analysis of a Helium-filled half-wavelength thermoacoustic refrigerator. The finite volume method is used, and the solid and gas domains are represented by large numbers of hexahedral elements. The calculations assume a 3-D periodic cell structure to reduce the computational cost and apply the dynamic mesh technique to account for the adiabatically oscillating wall boundaries. The simulation uses an implicit time integration of the full unsteady compressible flow equations along with the conjugate heat transfer algorithm. For the sake of simulation, the geometry and operating conditions closely follow the experimental setup of Lotton et al. (2009) [5]. A typical run involves about 200,000 computational cells, whereas the working frequency and the applied drive ratio are 592.5Hz and 2.0%, respectively. The stationary system response is predicted and the numerical values are compared to theory. The results show good agreement with theoretical behavior in the linear regime of drive ratios up to 2.0% while a maximum cooling effect of 10 degrees is captured between the stack ends. This simulation provides an interesting tool for understanding the transient flow behavior, mean energy-flux density and flow streaming, and helps building 3-D computational fluid dynamics models for thermoacoustic devices.

Maximum cooling and maximum efficiency of thermoacoustic refrigerators

This work provides valid experimental evidence on the difference between design for maximum cooling and maximum efficiency for thermoacoustic refrigerators. In addition, the influence of the geometry of the honeycomb ceramic stack on the performance of thermoacoustic refrigerators is presented as it affects the cooling power. Sixteen cordierite honeycomb ceramic stacks with square cross sections having four different lengths of 26, 48, 70 and 100 mm are considered. Measurements are taken at six different locations of the stack hot ends from the pressure antinode, namely 100, 200, 300, 400, 500 and 600 mm respectively. Measurement of temperature difference across the stack ends at steady state for different stack geometries are used to compute the cooling load and the coefficient of performance. The results obtained with atmospheric air showed that there is a distinct optimum depending on the design goal.

Optimization of binary gas mixture as working fluid for the thermoacoustic prime mover

The thermoacoustic prime mover (TAPM) is an attractive alternative to the conventional drive used in the pulse tube cryocoolers (PTCs), owing to no moving components, less wear and tear, less vibrations, simplicity in construction and use of environmentally friendly working fluids. In our objective to develop such a system, we have designed and developed twin standing wave TAPM. This paper presents the results of an experimental investigation using binary gas mixtures as working fluid. The gas mixtures of different working fluids, namely nitrogen, argon, and helium are used in the experimentation. The measurement shows that the performance of the twin standing wave TAPM improves as the working gas Prandtl number decreases. The operating frequency, pressure amplitude, temperature difference between the stack ends have been studied at different operating pressures and by varying gas mixture composition. However this needs optimization of binary gas mixture composition. The experimental studies show that for the best performance of TAPM, correct binary mixture of working fluids should be used. Among the binary mixtures the pressure amplitude is high when argon is used as the working fluid. However temperature difference across the stack is higher for argon. In view of this an optimal mixture of Helium 60% and Argon 40% can be chosen to obtain best performance of TAPM.

Characteristic-based non-linear simulation of large-scale standing-wave thermoacoustic engine.

A few linear theories [Swift, J. Acoust. Soc. Am. 84(4), 1145-1180 (1988); Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and numerical models, based on low-Mach number analysis [Worlikar and Knio, J. Comput. Phys. 127(2), 424-451 (1996); Worlikar et al., J. Comput. Phys. 144(2), 199-324 (1996); Hireche et al., Canadian Acoust. 36(3), 164-165 (2008)], describe the flow dynamics of standing-wave thermoacoustic engines, but almost no simulation results are available that enable the prediction of the behavior of practical engines experiencing significant temperature gradient between the stack ends and thus producing large-amplitude oscillations. Here, a one-dimensional non-linear numerical simulation based on the method of characteristics to solve the unsteady compressible Euler equations is reported. Formulation of the governing equations, implementation of the numerical method, and application of the appropriate boundary conditions are presented. The calculation uses explicit time integration along with deduced relationships, expressing the friction coefficient and the Stanton number for oscillating flow inside circular ducts. Helium, a mixture of Helium and Argon, and Neon are used for system operation at mean pressures of 13.8, 9.9, and 7.0 bars, respectively. The self-induced pressure oscillations are accurately captured in the time domain, and then transferred into the frequency domain, distinguishing the pressure signals into fundamental and harmonic responses. The results obtained are compared with reported experimental works [Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and the linear theory, showing better agreement with the measured values, particularly in the non-linear regime of the dynamic pressure response.

Experimental investigation of the effects of driver housing and resonance tube on the temperature difference across a thermoacoustic stack

This paper studies the effects of the driver housing and the resonance tube length on the temperature difference generated across the stack ends. The experiment uses air as the working fluid. The results indicate that the size of the back volume and the length of the resonance tube have affected both the optimal frequency and the temperature difference across the stack. The relationship of these parameters is necessary to the design and measurement performance of the thermoacoustic system.

Acoustic field measurements in a standing wave thermoacoustic refrigerator using time-resolved particle image velocimetry

A standing-wave thermoacoustic refrigerator consists of a stack of plates placed in an acoustic resonator. Two heat exchangers are located at each stack extremity. The thermoacoustic effect takes place in the thermal and viscous boundary layers along each plate of the stack. It results in a heat transport along the plates and in a temperature difference between the two stack ends. In such devices, the full understanding of the heat transfer between the stack and the heat exchangers is a key issue to improve the global efficiency of these devices. The aim of this work is to investigate the vortex structures, which appear at the ends of the stack and modify the heat transfer. Here, the aerodynamic in the gap stack-exchanger is characterized using a time-resolved particle image velocimetry technique. Measurements are performed in a device operating at a frequency of 200 Hz. Instantaneous velocity fields are recorded at a frequency of 3125 Hz (ie 15 maps per acoustic period). Measurements show that vortex shedding occur at high pressure levels, when a nonlinear acoustic regime prevails, leading to an additional heating generated by viscous dissipation in the gap and a loss of efficiency.

Effect of Lamination Stack Ends and Radial Cooling Channels on No-Load Voltage and Inductances of Permanent-Magnet Synchronous Machines

The effect of lamination stack ends and radial cooling channels on the effective stator stack length, no-load voltage, and synchronous inductances of a permanent-magnet synchronous machine are studied using three-dimensional finite element analysis. The stack ends and the radial cooling channels decrease the equivalent electrical length of the machine, thus leading to the fact that a two-dimensional (2-D) approach overestimates the no-load voltage. The effect of stack ends and radial cooling channels on the electrical length of the machine can be compensated by making the rotor stack and permanent magnets longer than the corresponding stator stack. It is shown that in case of no radial cooling channels, synchronous inductances are typically overestimated with the 2-D approach. However, in the case of stator structure having several radial cooling channels, inductances are underestimated using the 2-D approach.

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.

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.

Second law analysis of porous thermoacoustic stack systems

Abstract The objective of this paper is to analyze the irreversibility of the porous thermoacoustic stacks in terms of entropy generation. Thermoacoustic stacks are modeled in this paper as porous channels having wall with finite thickness. The flow field in the porous channel is described by the Darcy momentum equation. The thermal field inside the porous stack is modeled by volume averaged energy equation with local thermal equilibrium assumption. While the thermal field inside the solid wall is modeled by the heat conduction equation. The entire problem is treated as a conjugate heat transfer problem. The governing momentum equation inside the porous stack and the energy equations inside both porous stack and solid wall are simplified and linearized using a first order perturbation expansion in the low Mach number limit. The linearized governing differential equations are solved using the complex exponential method. Velocity and temperature results thus obtained are applied for subsequent entropy generation analysis. Entropy generation rate is used as a measure of irreversibilities associated with viscous and heat transfer effects in the porous stack region. For the specific thermoacoustic situation considered in this paper, a time-averaged entropy generation rate followed by local and global entropy generation rates are calculated and graphically presented. The entropy generation distribution in the stack thus enables the designers to find and modify the parameters producing high energy losses characterized by large entropy production rates. A limited experimental work is performed to measure the temperature difference generated across the stack ends. A fair qualitative agreement between the experimental and analytical results is obtained.

Miniature thermoacoustic engine: Experiments and modeling.

A miniature standing-wave thermoacoustic engine was constructed and tested with four quarter-wavelength resonators having lengths in the range of 57–124 mm. 80-ppi reticulated vitreous carbon (RVC) foam was applied as a stack, and an atmospheric air served as a working fluid. The critical temperature difference between the stack ends, corresponding to the sound onset, was recorded in the range of 200–300 °C. A thermoacoustic model was developed to predict the critical temperature difference across the stack. The model allows for user-defined thermoacoustic functions for the stack. Results obtained with the capillary-based theory for tortuous media and thermoacoustic functions previously measured for RVC demonstrate a trend qualitatively consistent with our data, while the quantitative agreement is lacking. Modeling results obtained with thermoacoustic functions for a parallel-plate stack can approximate experimental data, if the appropriate plate spacing is selected. [Work supported by the NSF Grant No. 0853171.]

Geometry effects and scaling in thermoacoustics

Current work at TU Eindhoven on thermoacoustics will be discussed. The end effects of the geometry of a stack on the performance of thermoacoustic machines will be shown. End effects and the formation of vortices is an issue that contributes to enhanced convective losses at the stack ends. Influence of Reynolds and Strouhal numbers on the oscillatory flow field in the stack are studied. It is possible to plot Sr and Re number diagrams in which various zones can be identified that display characteristic flow patterns. Furthermore the influence of the type of regenerator material is studied in traveling wave engines. Performance of honeycomb material of high-density pores is compared with wire screen regenerators in a thermoacoustic motor. As a last point the effects of downscaling to miniature systems is discussed. Limits of how far the size of a thermoacoustic cooler can be downscaled before conduction effects limit the performance are relevant.

Acoustic streaming related to minor loss phenomenon in differentially heated elements of thermoacoustic devices.

It is demonstrated that the differentially heated stack, the heart of all thermoacoustic devices, provides a source of streaming additional to those associated with Reynolds stresses in quasi-unidirectional gas flow. This source of streaming is related to temperature-induced asymmetry in the generation of vortices and turbulence near the stack ends. The asymmetry of the hydrodynamic effects in an otherwise geometrically symmetric stack is due to the temperature difference between stack ends. The proposed mechanism of streaming excitation in annular thermoacoustic devices operates even in the absence of thermo-viscous interaction of sound waves with resonator walls.

211 多段式共鳴管冷凍機における蓄冷器の最適位置

A thermoacoustic refrigerator is a equipment that pumps up heat by acoustic sound. A resonance pipe refrigerator, which is one of thermoacoustic refrigerators, has many advantages, such as compact, simple structure, no moving parts, and so on. We made a resonance pipe refrigerator and verified its operation. A stack, which serves as a heat storage element, was inserted in the resonance pipe. Temperature difference of the stack ends, was measured by changing location of the stack in the pipe. It is indicated that the suitable position of the stack is in between pressure node and antinode of sound wave. Possibility of multi-stack operation is also discussed.

Flow and temperature fields in thermoacoustic stacks

The paper describes the flow patterns and the temperature distribution measured in a thermoacoustic engine. Experiments have been performed in a resonant standing wave thermoacoustic refrigerator model. The knowledge of temperature and flow fields in the microchannels and at the edges of the stack plates becomes an increasingly important issue in the design of heat exchangers for thermoacoustic engines. Different geometries of the stack plates have been investigated as well as at different pressure levels. Heat exchangers have also been placed on both sides of the stack, with adjustable gaps. 2-D particle image velocimetry was used to investigate the flow with enlarged observation fields near the ends of the stack plates. We present velocity profiles across the microchannels, 2-D velocity fields. Vorticity maps were deduced using a criterion based on a normalized angular momentum. Vortex motion close to the stack ends has been clearly observed, however, with a strong influence of the plate thickness. An array of miniaturized thermocouples permits us to follow in real time the building-up of the temperature gradient along the stack for different oscillating flow conditions and different gaps between the stack and the heat exchangers. Finally, comparisons are made with theoretical models and numerical simulations recently published in the literature. [Work supported by DGA.]