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.     

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.     

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.     

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.     

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。     

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.     

Thermodynamic analysis of onset characteristics in a miniature thermoacoustic Stirling engine

This paper analyzes the onset characteristics of a miniature thermoacoustic Stirling heat engine using the ther-modynamic analysis method. The governing equations of components are reduced from the basic thermodynamic relations and the linear thermoacoustic theory. By solving the governing equation group numerically, the oscillation frequencies and onset temperatures are obtained. The dependences of the kinds of working gas, the length of resonator tube, the diameter of resonator tube, on the oscillation frequency are calculated. Meanwhile, the influences of hydraulic radius and mean pressure on the onset temperature for different working gas are also presented. The calculation results indicate that there exists an optimal dimensionless hydraulic radius to obtain the lowest onset temperature, whose value lies in the range of 0.30 0.35 for different working gases. Furthermore, the amplitude and phase relationship of pressures and volume flows are analyzed in the time-domain. Some experiments have been performed to validate the calculations. The calculation results agree well with the experimental values. Finally, an error analysis is made, giving the reasons that cause the errors of theoretical calculations.     

A miniature thermoacoustic stirling engine

A miniature thermoacoustic stirling engine was simulated and designed, having overall size of length 0.65 m and height of 0.22 m. The acoustic field generated in this miniature system has been described and analyzed. Some efforts had been paid to coupling and matching, and a miniature thermoacoustic engine and some extra experimental components have been constructed. Analysis and experimental results showed that to obtain better performance of the engine, the diameter of the resonance tube must be chosen appropriately according to the looped tube dimension and the input heating power. It provided an effective way to miniaturize the thermoacoustic stirling heat engine. The experimental results showed that the engine had low onset temperature and high pressure amplitude and ratio. With the filling helium gas of 2 MPa and heating power of 637 W, the maximal peak to peak pressure amplitude and pressure ratio reached 2.2 bar and 1.116, respectively, which was able to drive a refrigerator, a heat pump or a linear electrical generator. The operating frequency of the engine was steady at 282 Hz.     

Study on energy flows in thermoacoustic engines utilizing two-temperature heat sources

The proposal of a novel thermoacoustic regenerator using multi-temperature heat sources (MTHS) makes it possible to utilize lower-grade energy and keep relatively high efficiency in a thermoacoustic engine (TE) simultaneously. Based on thermodynamic laws combined with linear thermoacoustic theory, the time-averaged total power, enthalpy flux, acoustic power, entropy flux, and exergy flux in each component are derived and calculated to further understand the mechanism of a TE with the regenerator using two-temperature heat sources (TTHS). The comparison of the energy flows between the traditional TEs and those utilizing TTHS shows that the improvement of the temperature gradient in the regenerator by adding a mid-heater with appropriate heating power can increase the acoustic power and efficiency of a TE.     

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     

Intrinsic thermoacoustic instabilities

It is accepted that the thermoacoustic behavior of a given combustion system can be analyzed by investigating how its natural acoustic modes are perturbed by the flame dynamics. As a result, the resonance frequency and structure of the resulting thermoacoustic mode – understood as a perturbed acoustic mode – are slightly modified with respect to the natural acoustic mode counterpart. However, experimental evidence shows that the frequency of unstable thermoacoustic modes sometimes lies far away from the natural acoustic frequencies of the system under study. In many cases, this frequency cannot be associated with hydrodynamic or entropy-related instabilities. In recent years, the intrinsic thermoacoustic (ITA) feedback loop has been formally recognized as the responsible mechanism in some of those situations. Theory and devoted experiments have been developed that have enormously contributed to the understanding of the particular behavior of intrinsic thermoacoustic instabilities.The present review encapsulates in a single theoretical framework the theory presented in the collection of today existing ITA papers, which spread through different cases of study regarding acoustic boundaries – anechoic, partially or fully reflecting – and geometries – duct flames, combustors composed by three coaxial ducts and annular configurations. Several examples are shown that summarize the most relevant results on ITA theory to this day. This review paper also gives special attention to the categorization of ITA modes, given the fact that there is no current agreement on the definition of an ITA mode: one example in this review paper explicitly shows that the proposed categorization methods can indeed be contradictory. Of high interest is also the review of papers illustrating the coexistence of thermoacoustic modes of acoustic and ITA nature, which in turn relate to the recently discovered exceptional points in the thermoacoustic spectrum. Additionally, this paper discusses the ‘counter-intuitive’ evidence that shows that ITA modes can be destabilized when acoustic dissipative elements are added into the system. Finally, it is shown how a single-mode Galerkin expansion may be able to model some ITA eigenfrequencies. This result is suggested in some recent works and is not obvious. The practical relevance of ITA modes in industrial combustion chambers of gas turbines is also discussed together with suggestions for future studies.     

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.     

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.     

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.     

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。     

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.     

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.     

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.