Thermoacoustic Wave Propagation Research Articles

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.

Multiple Back Projection With Impact Factor Algorithm Based on Circular Scanning for Microwave-Induced Thermoacoustic Tomography

Back-projection (BP) algorithm is a common image reconstruction method for microwave-induced thermoacoustic tomography (MITAT). According to the thermoacoustic (TA) signals obtained, which are superimposed with the corresponding time inversion of each pixel in the region of interest (ROI), the BP algorithm can function in a quick response and is suitable for fast real-time MITAT applications. However, high artifacts and background noises caused by incomplete sampling of TA signals seriously affect the image quality. In this paper, a multiple back-projection with impact factor (MBP-IF) algorithm based on circular scanning geometry is proposed to address this problem. Compared with the BP algorithm, the MBP-IF approach calculates not only the initial acoustic pressure of the TA signal of each pixel (i.e., the image obtained by BP), but also the complete acoustic pressure distributions at different time points during the thermoacoustic wave propagation. Then impact factors can be obtained and used to effectively suppress artifacts and eliminate noises. Numerical simulation and phantom experiments prove that the MBP-IF algorithm is advantageous in suppressing image artifacts and noises. Some figures of merit are also obtained to quantify the results. In addition, due to the independence of acoustic pressure distributions at different time points, the MBP-IF can be computed in parallel by GPU, which can be widely used in real-time clinical MITAT system construction.

One-step simulation of thermoacoustic waves in two-dimensional enclosures

Abstract This paper reports on a one-step simulation study of the generation and propagation of thermoacoustic waves in a two-dimensional enclosure using a finite-difference lattice-Boltzmann-type method (FDLBM) with a single relaxation time and one equilibrium particle distribution function (EPDF), and a direct aeroacoustic simulation (DAS) technique that solves the primitive Navier–Stokes (N–S) equations. Conventional expansion of the EPDF is not adopted; instead, it is expanded in terms of the particle velocity alone, and the expansion coefficients are determined by requiring the FDLBM to fully recover the N–S equations. The expansion coefficients are found to depend on the flow and thermal properties and their nonlinear interactions. Thus formulated, physical boundary conditions can be specified for the FDLBM. This EPDF has been validated against simple aeroacoustic problems and good agreement with DAS results is obtained. In this paper, the EPDF is further validated against three thermoacoustic cases: 1) a sudden increase of temperature on the left vertical wall of the enclosure; 2) a sudden increase of temperature on the left vertical wall coupled by a sudden decrease of temperature on the right vertical wall in the enclosure; 3) a gradually heated up left vertical wall of the enclosure. Comparisons with DAS simulations show that FDLBM and DAS give essentially identical results; hence, the validity and extent of the EPDF is ascertained for the calculation of these thermoacoustic waves. The FDLBM results are also compared with known theoretical and numerical results. These known solutions are found to be less accurate compared to the FDLBM results. The discrepancy could be attributed to the partially linearized equations solved in the theoretical analysis, and the inadequacy of the numerical scheme to replicate the nonlinear effects accurately in the generation and propagation of thermoacoustic waves.

A multi-physics and multi-time scale approach for modeling fluid–solid interaction and heat transfer

A novel non-conservative formulation for equations governing thermo-mechanical phenomena is developed to address multi-material and multi-physics issues. The first key point is that this formulation achieves a unifying equation for compressible viscous fluid flow and elastic solid deformation. The second is that the thermo-mechanical equations are both written with velocity and thermal flux variables to solve them simultaneously. With that formulation, interaction conditions at the fluid–structure interface become implicit and state equation is no longer necessary. Multi-time scale problems are solved, from the time scale of acoustic and thermoacoustic wave propagation, to longer time scale of fluid flow and thermal diffusion.

Thermoacoustic transport in supercritical fluids at near-critical and near-pseudo-critical states

► Numerical simulations of the generation and propagation of thermoacoustic waves in near-pseudo-critical carbon dioxide. ► Accurate representation of the thermo-physical properties of supercritical carbon dioxide near the critical and pseudo-critical states. ► Increase of the relative strength of the generated acoustic field as the initial state of the fluid approaches critical or pseudo-critical states. ► Characterization of the strengths of the generated acoustic field as a function of the rate of boundary heating. ► Investigation of a novel thermoacoustic wave driven thermal transport device using near-critical and near-pseudo-critical carbon dioxide. Thermoacoustic wave induced transport in carbon dioxide near its critical and pseudo-critical states is investigated numerically. A real-fluid computational fluid dynamic model has been developed considering all of the relevant fluid property variations (including bulk viscosity) near the critical and pseudo-critical states. The predicted results provide interesting details regarding the thermal transport mechanisms at near-critical and pseudo-critical state fluids. As a layer of supercritical fluid (near the critical or the pseudo-critical states) is heated rapidly, the combination of very high thermal compressibilities and vanishingly small thermal diffusivities affect the thermal energy propagation, leading to the formation of acoustic waves as carriers of thermal energy (the so called piston effect ). The results show that under the same temperature perturbation at the boundary, the induced acoustic field becomes stronger as the critical point or the corresponding pseudo-critical state is approached. The heating rate, at which the boundary temperature is raised, is a key factor in the generation of these acoustic waves. We also study the effect of critically diverging bulk viscosity and different rates of boundary heating on the temperature equilibration mechanism near the critical point. An application of the piston effect in near-critical and near-pseudo-critical fluids for effective thermal transport over a long distance is demonstrated for a supercritical heat pipe.

Effects of heat conduction in a wall on thermoacoustic-wave propagation

AbstractThis paper examines the effects of heat conduction in a wall on thermoacoustic-wave propagation in a gas, as a continuation of the previous paper (Sugimoto, J. Fluid Mech., 2010, vol. 658, pp. 89–116), enclosed in two-dimensional channels by a stack of plates or in a periodic array of circular tubes, both being subject to a temperature gradient axially and extending infinitely. Within the narrow-tube approximation employed previously, the linearized system of fluid-dynamical equations for the ideal gas coupled with the equation for heat conduction in the solid wall are reduced to single thermoacoustic-wave equations in the respective cases. In this process, temperatures of the gas and the solid wall are sought to the first order of asymptotic expansions in a small parameter determined by the square root of the product of the ratio of heat capacity of gas per volume to that of the solid, and the ratio of thermal conductivity of the gas to that of the solid. The effects of heat conduction introduce into the equation two hereditary terms due to triple coupling among viscous diffusion, thermal diffusion of the gas and that of the solid, and due to double coupling between thermal diffusions of the gas and solid. While the thermoacoutic-wave equations are valid always for any form of disturbances generally, approximate equations are derived from them for a short-time behaviour and a long-time behaviour. For the short-time behaviour, the effects of heat conduction are negligible, while for the long-time behaviour, they will affect the propagation as a wall becomes thinner. It is unveiled that when the geometry of the channels or the tubes, and the combination of the gas and the solid satisfy special conditions, the asymptotic expansions exhibit non-uniformity, i.e. a resonance occurs, and then the thermoacoustic-wave equations break down. Discussion is given on modifications in the resonant case by taking full account of the effects of heat conduction, and also on the effects on the acoustic fields.

Effects of heat conduction in wall on thermoacoustic wave propagation in a gas-filled, channel subject to temperature gradient

This paper examines effects of heat conduction on acoustic wave propagation in a gas-filled, channel subject to temperature gradient axially and extending infinitely. Within the narrow-tube approximation in the sense that a typical axial length is much longer than a channel width, the system of linearized equations for the gas supplemented by the equation for heat conduction in the solid wall is reduced to a thermoacoustic-wave equation for excess pressure uniform over the cross-section. This is the one-dimensional equation taking account of the wall friction and the heat flux at the wall surfaces given in the form of hereditary integrals. This equation is derived rigorously under the narrow-tube approximation, and is valid for any form of disturbances. The effects of heat conduction appear in the form proportional to the square root of the product of the ratio of the heat capacity per volume of the gas to that of the solid, and the ratio of the thermal conductivity of the gas to that of the solid. Although the product is very small usually, which endorses validity in neglect of the heat conduction, it is revealed that there are situations in which its effects are enhanced, depending on geometry and materials.

Thermoacoustic wave propagation and reflection near the liquid-gas critical point

We study the thermoacoustic wave propagation and reflection near the liquid-gas critical point. Specifically, we perform a numerical investigation of the acoustic responses in a near-critical fluid to thermal perturbations based on the same setup of a recent ultrasensitive interferometry measurement in CO2 [Y. Miura, Phys. Rev. E 74, 010101(R) (2006)]. The numerical results agree well with the experimental data. Different features regarding the reflection pattern of thermoacoustic waves near the critical point under pulse perturbations are revealed by the proper inclusion of the critically diverging bulk viscosity.

Effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography

The effects of acoustic heterogeneities on transcranial brain imaging with microwave-induced thermoacoustic tomography were studied. A numerical model for calculating the propagation of thermoacoustic waves through the skull was developed and experimentally examined. The model takes into account wave reflection and refraction at the skull surfaces and therefore provides improved accuracy for the reconstruction. To evaluate when the skull-induced effects could be ignored in reconstruction, the reconstructed images obtained by the proposed method were further compared with those obtained with the method based on homogeneous acoustic properties. From simulation and experimental results, it was found that when the target region is close to the center of the brain, the effects caused by the skull layer are minimal and both reconstruction methods work well. As the target region becomes closer to the interface between the skull and brain tissue, however, the skull-induced distortion becomes increasingly severe, and the reconstructed image would be strongly distorted without correcting those effects. In this case, the proposed numerical method can improve image quality by taking into consideration the wave refraction and mode conversion at the skull surfaces. This work is important for obtaining good brain images when the thickness of the skull cannot be ignored.

Measurement of thermo-acoustic waves induced by rapid heating of nickel sheet in open and confined spaces

Experimental investigation on the generation and propagation of thermo-acoustic waves induced by rapid heating of the metal sheet was carried out. This study focuses on the temperature profiles, measurement of pressure wave induced by rapid heating of nickel sheet in open and confined spaces. The R– C (resistance–capacitance) heating devices and high-speed measurement systems are designed, and methodologies on measurement are established. Results show that the waves have sharp and weak pin profile in an open space, but these waves have sharp front shape and decay with tail in the case of confined space. Results also show that the propagation velocity of thermo-acoustic wave, that is estimated as Mach number ( M), generated by rapid heating of nickel sheet, is located in the range of M = 0.99–1.04.

A numerical study of the generation and propagation of thermoacoustic waves in water

The generation and propagation of thermoacoustic waves in water are investigated by solving the fully compressible form of the Navier–Stokes equations. A square enclosure filled with water is considered as the computational domain. Thermally induced pressure waves are generated by rapidly heating the left wall. The thermodynamic properties of water are calculated via an accurate equation of state. The effect of the rapidity of the heating process on the production of thermoacoustic waves is studied, using both impulse (sudden) and gradual changes in the left wall temperature. The thermoacoustic waves are significantly stronger for impulse heating and are found to eventually damp out with time due to viscous losses. Gradual change of the left wall temperature reduced the strength of the pressure wave peaks.

Enhancement of laser-based ultrasonic wave detection through signal processing techniques

Laser generation and detection of ultrasonic signals is a technology that expands the applications for ultrasonic nondestructive evaluation. It is a remote, noncontacting method of generating and detecting acoustic energy in materials. Laser-based ultrasonics has been shown to have less sensitivity than traditional ultrasonic testing because the amount of optical energy that can be introduced to a material to generate ultrasonic waves nondestructively is limited by the ablation threshold of the material. In addition, detection sensitivity is limited by the surface conditions of the material as well as the feasible power of the laser used in the interferometer. To increase the signal-to-noise ratio of laser-based acoustic detection, beamforming techniques were applied to modeled and measured data. A thermoacoustic wave propagation model of laser generation and detection was used to simulate data from a bistatic array. The corresponding measured bistatic data set was beamformed in the same manner as the simulated data. Filters derived by matching measured and modeled beamformed data were applied to other measured data sets with good results. These filters can be used to enhance images generated from bistatic laser- based ultrasonic data. [Work performed under auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.]

Analysis of thermoacoustic wave propagation in elastic media

Wave propagation in a material continuum is a thermodynamic process that is governed, not only by the mechanical character of the propagation medium, but by the thermal character as well. The dispersion relation derived on the basis of linear thermoelastic theory shows that two distinct types of dilatational waves can propagate in an isotropic elastic medium. In each such wave, mechanical and thermal effects are coupled. The behavior of these thermoacoustic waves, in particular, their speeds and absorption coefficients as functions of frequency, is described. Three models of thermoacoustic wave propagation are considered. The classic model, which incorporates the Fourier description of heat conduction, is analyzed first. The shortcomings of this model are pointed out. Two models incorporating the Vernotte hypothesis of heat conduction are examined next—a ‘‘lattice’’ model, which is based upon an idea implicit in the Debye theory of specific heats, and a ‘‘phonon-gas’’ model. Both models incorporating the Vernotte hypothesis are shown to describe linear thermoacoustic wave propagation in a more physically realistic fashion than does the classic model. Thermoacoustic wave propagation is considered from a general phenomenological (i.e., from a macroscopic) standpoint, and only the most general assumptions about the constitution of the propagation medium are made. In the analysis, only the dissipation of energy by heat conduction is considered; the medium is assumed to be elastic in that no purely mechanical mechanisms for energy dissipation (e.g., classic viscosity) are considered to be present.