Standing-wave Thermoacoustic Engine Research Articles

Energy conversion performance in looped and stirling traveling-wave and standing-wave thermoacoustic engines

This present study conducts a comprehensive comparison of looped traveling-wave thermoacoustic engines (TWTAEs) and Stirling TWTAEs using two- and three-dimensional (2D and 3D) time-domain models. These models, validated through comparisons with existing experimental results, confirm the accuracy of our developed full-scale numerical TWTAE models. By evaluating the acoustic characteristics and comparing them with conventional standing-wave thermoacoustic engines, this work highlights the superior performance of the Stirling TWTAE. It achieves the highest heat-driven acoustic power and thermoacoustic energy conversion efficiency. This superior performance is attributed to its operation at a lower oscillation frequency (115 Hz) and an optimized phase between acoustic velocity and pressure oscillations (40 degrees). Additionally, our study explores rich nonlinear phenomena within the flow fields of the Stirling TWTAE. Notably, varying the temperature gradients between 410 K and 485 K introduces a bistable zone with distinct pressure amplitudes. Moreover, mass streaming under varying temperature gradients, and mode transitions due to external flow perturbations are observed inside the engine. These findings not only quantitatively confirm the high efficiency potential of the Stirling TWTAE but also demonstrate the effectiveness of CFD in the development of full-scale numerical models for predicting and optimizing the heat-driven acoustic characteristics and nonlinear phenomena of traveling-wave thermoacoustic systems.

Analysis of a standing wave thermoacoustic engine with multiple unit stages

The thermoacoustic engine is an eco-friendly technology capable of harnessing solar and waste energy for electricity generation, in conjunction with a linear alternator, and can function as a heat pump. This engine type holds significant appeal due to its simplistic design, devoid of any mechanical moving components, comprising only a stack sandwiched between heat exchangers within a resonator. When the temperature gradient across the stack reaches the critical threshold (onset temperature), the working gas undergoes spontaneous oscillation. Typically, a high onset temperature is necessary to induce gas oscillation in a thermoacoustic engine due to viscous losses within the system. A method to lower the onset temperature by increasing the number of unit stages consisting of stacks and heat exchangers so that the engine can utilize low-grade thermal sources has been developed to overcome this challenge. However, this method has only been applied to traveling-wave thermoacoustic engines. Its application in standing-wave engines, which offer a more compact and straightforward structure, remains unexplored. This research aims to examine how the number of unit stages in a standing-wave thermoacoustic engine influences the onset temperature and acoustic field. The onset temperature is estimated using a fundamental hydrodynamics equation and the investigation of the acoustic field throughout the engine using DeltaEC software. Results showed that the strategic positioning of multiple unit stages is essential to achieve a low onset temperature. The minimum onset temperature, approximately 92°C, is obtained when three- or four-unit stages are installed. Additionally, increasing the number of unit stages does not affect the acoustic impedance and phase difference between pressure and velocity in the stack, while simultaneously enhancing both acoustic power output and thermal efficiency.

Investigating the synergy of blockage ratio and external cold heat exchanger in standing-wave thermoacoustic engines: An experimental study

Thermoacoustic engines (TAE) offer a promising avenue for converting low-grade heat into useable energy. Despite its simplicity in fabrication, designing thermoacoustic engines face efficiency challenges hindering their widespread adoption. One key obstacle faced by current thermoacoustic devices is their lack of efficiency. The core components of TAE are the stack, Cold Heat Exchanger (CHX), Hot Heat Exchanger (CHX) and the resonator. These components are crucial in advancing the performance of thermoacoustic engines. The CHX keeps the working gas cool, which is essential for the engine to function efficiently and create the desired acoustic wave. However, many existing efforts in this field have not taken into consideration the effect of the CHX design which may have effect on the operating temperature and the engines performance. This study examines the influence of different CHX blockage ratios (28 %, 36 %, 42 %, 47 %, and 59 %), along with the addition of an external CHX, on performance metrics. Measurements were conducted using air at room temperature and atmospheric pressure to assess temperature difference, startup time, volumetric velocity, and sound pressure levels. Key findings indicate that Efficiency directly correlates with volumetric velocity and inversely with onset temperature. Even though decreasing the blockage ratio increases operating temperature, it lengthens startup and reduces volumetric velocity, suggesting increased axial conduction. In addition, External CHX lowers operating temperature, reducing volumetric velocity and sound pressure. Interestingly, resonance frequency remains unaffected by CHX blockage ratio changes. An optimal configuration with a 42–47 % blockage ratio achieves 5.92 m/s velocity, 136 s startup time, and 77 °C onset temperature. These findings offer valuable insights for optimizing thermoacoustic engine efficiency and advancing their potential as sustainable energy solutions.

First experimental realization of a thermoacoustic-based flue-gas analyzer

Flue-gas analyzers are critical for various applications, including the optimization of combustion efficiency and air quality monitoring. While capable of accurately measuring gas concentrations, current sensors require frequent calibration, suffer short lifespans, and can be susceptible to inference from trace gases. In this report, we provide a first physical implementation of a thermoacoustic-based gas analyzer by investigating the sensitivity of a standing-wave thermoacoustic engine to variations in three different flue-gas components, CO2, O2, and N2. Experimentally measured shifts in both the onset temperature difference and the fundamental resonance frequency with varying gas compositions confirm the feasibility of a thermoacoustic system for flue-gas analysis. The presented data paves the way for further exploration of this innovative approach, offering an efficient and cost-effective acoustic-based alternative to existing flue-gas analysis methodologies.

Influence of resonator length and temperature configuration on the performance of a supercritical CO2 thermoacoustic engine

The peculiar properties of CO2 at supercritical pressures and transcritical temperature conditions are favorable for thermoacoustic devices. The printed circuit heat exchanger has been employed to fabricate a standing-wave thermoacoustic engine that works under these conditions. Experiments performed in this paper are devoted to exploring the influences of resonator length and temperature configuration on its performance. Results demonstrate that the oscillation frequency drops when the resonator is elongated, while the pressure amplitude is strengthened. To generalize the experimental data, the power-law relation for pressure amplitude and the bilinear law of frequency are extended to include resonator length as an independent variable, serving as the basis for tuning performance through resonator length. The best temperature configuration is to put the pseudo-critical temperature at the midpoint of heating and cooling temperatures to induce the pressure oscillation at maximum amplitude. Guided by the above results, experiments are performed to explore the extremum of low onset temperature difference. The current record is finally identified as 8.6 °C, close to the literature record of 7.0 °C. This paper elucidates the effects of resonator length and temperature configuration. Conclusions drawn in this paper can guide the design and operation of thermoacoustic devices working with supercritical CO2.

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.

Enhancing energy conversion performances in standing-wave thermoacoustic engine with externally forcing periodic oscillations

The present work focuses on enhancing thermo-acoustics energy conversion performance and nonlinear dynamics of heat-driven acoustics oscillations in standing-wave thermoacoustic engines (SWTAE) in the presence of externally forcing perturbations. Such perturbations could be applied in either pressure or velocity fluctuations. 2D numerical SWTAE models are developed and validated, and then applied to examine the effects of 1) the forcing perturbation frequencies, 2) its amplitudes, and 3) the inlet diameter of applying such perturbations on heat-driven acoustics behavior. Our results show that pressure perturbations attenuate heat-driven acoustic limit cycles, while forcing velocity perturbations at a specific frequency range can enhance the thermo-acoustics conversion in the SWTAEs. Our results also show that frequency lock-in is observed, when the ratio of the forcing velocity perturbations' energy to the self-excited acoustical energy is ranged from 0.11 to 0.66. Furthermore, Hopf supercritical bifurcations are observed, resulting in transitions from steady state to quasi-periodic and limit cycle oscillations. As the forcing perturbation frequency is approaching to that of the self-excited heat-driven acoustic oscillations (i.e. the ratio of the forcing frequency to that of self-excited oscillations is ranged from 0.89 to 1.11), apparent improvements are observed on the output heat-driven acoustic power and thermo-acoustic energy conversion efficiency, especially when the two frequencies are coincided (i.e. ∼180 Hz). Increasing the forcing perturbation's energy or enlarging the inlet diameter of applying such perturbations further enhances these improvements. Overall, the developed numerical model may serve as a valuable tool for predicting the heat-driven acoustic power output from a SWTAE in the presence of externally forcing perturbations.

Prediction of Onset Temperature in Standing Wave Thermoacoustic Engine with Mesh Screen Stack

A thermoacoustic engine is a engine that converts thermal energy into acoustic energy, which can be used to generate electricity or cooling. This engine is attractive because it consists only of a stack, heat exchangers, and a resonator. The stack serves as the primary component for the energy conversion process and consists of porous materials like an array of stainless steel mesh screens. To generate the acoustic energy, a minimum temperature difference is necessary between the two sides of the stack, called the onset temperature difference. However, the calculation for prediction of onset temperature on the stack made of mesh screen has not been addressed. Therefore, the objective of this paper is to propose a method that can be used to estimate the onset temperature difference in standing wave thermoacoustic engine with stacks made of mesh screen arrays. The onset temperature difference is predicted numerically using linear stability theory and matrix transfer methods. Experimental verification is carried out by using standing wave thermoacoustic engine from pervious study. The results showed that the lowest onset temperature difference (TH - TC = 140ºC) is obtained when rh = 0.497 mm. Furthermore, the numerical and experimental onset temperature difference comparisons show a qualitative agreement, allowing the onset temperature prediction method to be used in designing standing wave thermoacoustic engines with stacks made of mesh screens.

Performance comparison of a standing-wave thermoacoustic engine with different resonator shapes with air working gas

The resonator is one of the key components of thermoacoustic machines and the choice of its geometry is of course of crucial importance, as it determines the way the machine operates. The resonator must be designed so that the quality factor of the resonance is as high as possible and must satisfy the technological production constraints related to the high pressurization of the working fluid and the presence of temperature non-uniformities. The shape of the resonator can be modified to reduce certain loss phenomena, particularly on the walls, and to limit the formation of harmonics in the high-level acoustic field. In this work, an acoustic power losses analysis and a numerical study of a standing-wave TAE with air working gas, considering changes in resonator shape, are performed to investigate the effect of resonator geometry on the thermoacoustic energy conversion. The acoustic power dissipation in the resonator is analyzed based on the simplified thermoacoustic theory and the numerical study is conducted based on a 2D numerical model based on a CFD analysis. Results show that the shape of the resonator significantly affects the frequency, the temperature along the stack, and the acoustic pressure produced on the TAE. In addition, it is shown that the resonator composed of two different diameters showed its ability to produce a high acoustic pressure amplitude (20.5% than the iso-diameter resonator) and minimize the viscous and thermal losses.

Delta EC Simulation on Influence of Resonator Length in Close-Open Standing Wave Thermoacoustic Engine

<p class="Abstract"><em><span lang="EN-US">Many applications of thermoacoustic engines in engineering. With its pressure of it, the energy can be harvested and can be converted to many other needs of energies like electrical energy. Energy in thermal form is converted to become acoustic energy and subsequently used to activate a bidirectional turbine. The resonator is very influential toward the power of the thermoacoustic engines. Simulation study with Delta EC fit to make predictions acoustic power as representative performance in thermoacoustic engine with close-open type and standing wave of oscillation. In this study, the material of the resonator is made from a stainless-steel duct with a diameter size of 50.8 mm with three variations of the length. The Standing-Wave Thermoacoustic Engine (SWTE) generates acoustic energy from a temperature gradient of 315 – 993 K. </span></em><em><span lang="IN">In this simulation, Acoustic Power decreased when the resonator length was extended. The shortest resonator had an acoustic power of 50.4 W, and the longest resonator had an acoustic power of 35.7 W.</span></em></p>

Enhancing heat-driven acoustic characteristics of standing wave thermoacoustic engines by using corrugated stack

The present work considers the heat-driven acoustic characteristics and dynamic thermal-fluid flow fields of a standing-wave thermoacoustic engine (SWTAE) by using sinusoidally shaped corrugated stack surfaces. 3-D numerical SWTAE models are developed and validated, aiming to examine the heat-driven acoustic effects caused by different corrugation amplitudes and wave-lengths of the sinusoidal stack surface. The results demonstrate that corrugated-shaped stack channels increase the contact area of the working gas in the stack area, and the thermos-acoustic conversion is more amplified. Compared to the SWTAE with uniform-shaped stack, the corrugated-shaped stack exhibit enhanced acoustic power output while maintaining a constant acoustic oscillation frequency. With the corrugation peak and wave-length of the sinusoidal stack are 2 and 0.2 mm, respectively, the amplitude and acoustic power of the acoustic pressure oscillations increase by 10.12% and 17.31%, respectively, in comparison with that of the conventional SWTAE. However, when the corrugation peak exceeds 0.4 mm, stronger nonlinear acoustics and flow effects are observed in the stack channels, leading to a reduction in the heat-driven acoustic power output, and thermo-acoustics energy conversion efficiency. The developed model highlights the effects of the corrugated-shaped stack on enhancing acoustic power output and thermo-acoustic conversion efficiency.

Numerical investigations on energy conversion performances in twin standing-wave thermoacoustic engines with various geometric and operational conditions

The present work considers the heat-driven acoustic characteristics and dynamic thermal-fluid flow fields in a twin standing-wave thermoacoustic engine (TSWTAE). Emphasis is placed on enhancing its acoustic power output performances for efficiently driving thermoacoustic refrigerators by varying operating conditions and geometric shapes. For this, a time-domain 2D twin TAE model is developed to analyze the TSWTAE in the presence of different working gases and various operating pressures first. It is then applied to examine the geometry effect on the thermo-acoustics energy conversion performances of the twin SWTAE. The model is validated by comparing with those results obtained from DeltaEC (Design Environment for Low-amplitude ThermoAcoustic Energy Conversion) software and experimental data available in the literature. The results indicate that the acoustic oscillation pressure and sound pressure level are increased with the charge pressure and the molecular weight of the working gases, while the acoustic power and thermo-acoustics energy conversion efficiency of the different working gases remain roughly constant. Considering the comprehensive acoustic characteristics, the optimal engine performance is achieved with a 0.6 MPa charge pressure, as helium is applied. Furthermore, the implementation of the tapered conical resonator demonstrates a substantial enhancement in oscillation pressure and thermal efficiency, yielding improvements of 82.03% and 32.60% respectively compared to the utilization of a cylindrical narrow resonator in the experimental setup. The present study provides a design tool for predicting and optimizing twin SWTAE performances.

Effect of channel size on the performance of a PCHE-based supercritical [formula omitted] thermoacoustic engine

Thermoacoustic engine is a promising energy conversion device. Recently, supercritical CO2 has been successfully employed as the working fluid in a standing-wave thermoacoustic engine operating under transcritical temperature conditions. The core components of the device are integrated as a printed circuit heat exchanger (PCHE), where the CO2 channel size plays a vital role in the performance of the device. In the present work, guided by approaching two to four times thermal penetration depth, a PCHE module with improved channel size is designed, fabricated, and tested. Results suggest improvements are achieved in pressure amplitude Δp (the highest record increases from 0.419 to 0.455 MPa) and onset temperature difference (the lowest record drops from 14.8 to 11.2 °C), which are attributed to the enhanced thermally-driven expansion and contraction during one oscillation period. This paper shows that the average thermal penetration depth is a notable variable generally positively correlated to the applied temperature difference. By studying the transition and saturation in operation mode observed in the experiments, it is revealed that three to four times the average thermal penetration depth is the best interval for the CO2 channel size. Beyond this interval, the power law relation between dimensionless pressure amplitude and the temperature difference holds. Below this interval, the saturation becomes so strong that the growth of pressure amplitude with temperature difference decelerates significantly.

A numerical investigation on stack sides thermo-gas dynamic in a large amplitude standing wave thermoacoustic engine

The non-linear unsteady thermal field of a standing wave thermoacoustic engine (SWTE) was investigated using a finite volume computational code in a two-dimensional domain. The transient interaction between temperature and pressure fields and the level of non-linearity especially close to and out of stack plates are studied in 3 cases with different hot heat exchanger (HHX) temperatures of 700,500,450 K and ambient heat exchanger with constant temperature of 300 K. The results show regions with extremum temperatures far different from our understanding of the linear theory of thermoacoustic and the second law of thermodynamics. The gasdynamic field (pressure oscillations) close but out of the stack plates, approached its saturated single harmonic quasi-steady state in a short time (less than 0.3 s), but afterward the thermal field starts and keeps a non-sinusoidal temperature variation. Particle tracking through a Lagrangian analysis revealed that the difference of the thermodynamic cycles for particles that cross a particular region adjacent to the heat exchangers leads to these non-harmonic patterns. Furthermore, in case 1 with HHX temperature and drive ratio of 700 K and 18.2%, respectively, time-averaged temperature extremums with –23 K and +49 K differences (in comparison to AHX and HHX, respectively) were found in the final quasi-steady-state solution. The temperature differences become less considerable when the Drive ratio decreases. For the low temperature close to the AHX, Hybrid Eulerian-Lagrangian analysis, and temperature-entropy diagrams were used to explain this strange physics of generation of extremum temperatures. Thermo-acoustic cycles for ten gas parcels are analyzed to show that parcels in the resonator section visiting shortly the AHX (or HHX) region are responsible for this phenomenon. The thermodynamic cycle for different particles, including interactions of the gas-dynamic field with the thermal field, are analyzed with different tools to justify its strange physics. It is concluded that linear theories do not observe important phenomena in thermoacoustic engines with high-pressure amplitudes. A similar logic holds for the formation of a hot temperature region out of the HHX side of the stack.

Numerical investigation of nonlinear effects in a standing wave thermoacoustic engine using the discontinuous Galerkin method

Understanding the nonlinear effects in thermoacoustic heat engines operating under high-pressure amplitude conditions plays a crucial role in improving their operational performance and efficiency. The discontinuous Galerkin (DG) method has several advantages, including high accuracy, adaptability, efficiency, and the ability to handle the coupling of multiple physical fields, making it suitable for accurately simulating the flow and heat transfer characteristics in thermoacoustic engines. The simulation code was developed based on MFEM, an open-source C++ library for modular finite element methods. The fully compressible Navier-Stokes equations and Fourier heat conduction equation were solved to investigate the nonlinear effects, which cannot be captured by the linear theory. To verify the accuracy of the simulation code, the numerical investigation of the thermoacoustic wave propagations induced by thermal effects in a square enclosure was first conducted. The simulation results presented the details of the generation and propagation of thermoacoustic waves, which were largely consistent with the results obtained using the flux-corrected transport (FCT) algorithm. Second, a quarter-wavelength standing wave thermoacoustic engine was simulated. The simulation results captured the process of pressure wave generation in the thermoacoustic engine, which was consistent with the pressure wave generation process in the enclosure. The results revealed the flow and heat transfer characteristics and nonlinear effects in the thermoacoustic engine under high-pressure amplitudes, which were consistent with the results obtained using finite volume method. The simulation results showed that the DG method is an effective numerical method for simulating thermoacoustic engines.

Theoretical and experimental investigation of acoustic field adjustment of a gas-liquid standing-wave thermoacoustic engine

Theoretical and experimental investigation of acoustic field adjustment of a gas-liquid standing-wave thermoacoustic engine

Experimental investigation of a novel standing-wave thermoacoustic engine based on PCHE and supercritical CO2

The pursuit of high amplitude and low onset temperature difference is one important topic in thermoacoustic engines. In this paper, a novel standing-wave thermoacoustic engine is constructed working with supercritical CO2, whose core components are integrated as a printed circuit heat exchanger (PCHE). Our experimental results confirm that at any location on the resonator, the pressure obeys a cosine law with time, and the whole pressure field exhibits a seesaw-like spatiotemporal behavior. Under a fixed charging mass, the amplitude of pressure oscillation increases with temperature difference, obeying a power law relation. The maximum amplitude achieved in this work is 0.419 MPa at a temperature difference of 151.0 °C and a mean pressure of 9.621 MPa. Besides, the frequency with an average of 7.6 Hz shows weak variations. The onset temperature difference decreases as the critical pressure is approached, and the minimum value achieved is 14.8 °C. Moreover, the cooling effect of oscillating CO2 to the high-temperature portion of the stack is revealed, causing the strongly nonlinear temperature profile along the stack. This paper manifests that supercritical CO2 and PCHE are highly prospective to be employed in thermoacoustic devices.

Optimal cross-sectional area ratio between porous material and resonance tube for the onset of self-excited oscillations in standing-wave thermoacoustic engines

Optimal cross-sectional area ratio between porous material and resonance tube for the onset of self-excited oscillations in standing-wave thermoacoustic engines

Application of the porous media approach to a Standing Wave Thermoacoustic Engine for CFD simulations

In this article, an application of the macroscopic porous media approach, suitable for CFD simulations in oscillating flows, is proposed for a simplified Standing Wave Thermo-Acoustic Engine (SWTAE), composed of a hot buffer tube, a stack - where the energy conversion takes place - and the rest of the resonator. While for a Travelling Wave Thermo-Acoustic Engine (TWTAE) a macroscopic model for porous media has been successfully applied to both regenerators (similar to the stack in a SWTA) and heat exchangers, for SWTAE this is not true. The results illustrate that a Local-Thermal Non-Equilibrium model is required to start up the SWTAE, otherwise (with the Local Thermal Equilibrium model) the thermoacoustic instability cannot arise. Furthermore, the comparison between the simulation conducted at the microscopic scale and that one at the macroscopic level, depicts that a purely Darcy-linear model employed for the macroscopic model, characterized for oscillating flows, overpredicts the pressure amplitude at periodic steady-state. For this reason, a Forchheimer-like coefficient needs to be implemented to fit the macroscopic solution with the microscopic one.

Numerical prediction nonlinear heat-driven acoustics behaviours in standing-wave thermoacoustic engines using stress-blended Eddy simulation method

The present work investigated a standing-wave heat-driven thermoacoustic engine (SWTAE) system by capturing its nonlinear thermoacoustic features with three-dimensional (3D) unsteady Reynolds-Averaged Navier-Stokes (URANS) and hybrid URANS/LES (large Eddy simulation) models such as detached-Eddy simulations (DES) and stress-blended Eddy simulation (SBES) models. The comparison studies show that the prediction of the acoustic power of SWTAE using URANS is about 21.0% lower than that using LES, while the results from SBES and DES are relatively in good agreement with LES. Comparative studies of nonlinear hydrodynamics in the flow fields show that the results from SBES are closer to LES than DES, which can be attributed to the SBES model providing a faster transition to an explicit LES model outside the wall boundary layer. Furthermore, the heat transfer characteristics are compared by analyzing heat leaks and transversal heat flux, and it is found that the URANS model over-estimates the heat transfer characteristics, while the results of the other three models are relatively smaller than those obtained by URANS. In conclusion, the SBES model has great potential to be applied in simulating thermoacoustic nonlinear, heat transfer and flow behaviors of heat-driven SWTAEs.