A 3D investigation of thermoacoustic fields in a square stack

El-Rahman, Ahmed I. Abd; Abdelfattah, Waleed; Fouad, Mahmoud

doi:10.1016/j.ijheatmasstransfer.2016.12.015

Cited by 31 publications

(15 citation statements)

References 17 publications

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“…, (14) where and simply denote the discrete locations between the wall and channel centreline (here, the maximum is = 14 ) and the phase number in the cycle (here, the maximum is = 20), respectively. It attempts to describe the deviation of the CFD-based profile from the experimental profile, or in other words, the "goodness" of predictions.…”

Section: Turbulent Flow Modelsmentioning

confidence: 99%

Numerical Predictions of Early Stage Turbulence in Oscillatory Flow across Parallel-Plate Heat Exchangers of a Thermoacoustic System

Saat

Jaworski

2017

Applied Sciences

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This work focuses on the predictions of turbulent transition in oscillatory flow subjected to temperature gradients, which often occurs within heat exchangers of thermoacoustic devices. A two-dimensional computational fluid dynamics (CFD) model was developed in ANSYS FLUENT and validated using the earlier experimental data. Four drive ratios (defined as maximum pressure amplitude to mean pressure) were investigated: 0.30%, 0.45%, 0.65% and 0.83%. It has been found that the introduction of the turbulence model at a drive ratio as low as 0.45% improves the predictions of flow structure compared to experiments, which indicates that turbulent transition may occur at much smaller flow amplitudes than previously thought. In the current investigation, the critical Reynolds number based on the thickness of Stokes' layer falls in the range between 70 and 100. The models tested included four variants of the RANS (Reynolds-Averaged Navier-Stokes) equations: k-ε, k-ω, shear-stress-transport (SST)-k-ω and transition-SST, the laminar model being used as a reference. Discussions are based on velocity profiles, vorticity plots, viscous dissipation and the resulting heat transfer and their comparison with experimental results. The SST-k-ω turbulence model and, in some cases, transition-SST provide the best fit of the velocity profile between numerical and experimental data (the value of the introduced metric measuring the deviation of the CFD velocity profiles from experiment is up to 43% lower than for the laminar model) and also give the best match in terms of calculated heat flux. The viscous dissipation also increases with an increase of the drive ratio. The results suggest that turbulence should be considered when designing thermoacoustic devices even in low-amplitude regimes in order to improve the performance predictions of thermoacoustic systems.

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Section: Turbulent Flow Modelsmentioning

confidence: 99%

Numerical Predictions of Early Stage Turbulence in Oscillatory Flow across Parallel-Plate Heat Exchangers of a Thermoacoustic System

Saat

Jaworski

2017

Applied Sciences

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“…A high-order spectral difference numerical framework (Kopriva & Kolias 1996;Kopriva 1996;Sun et al 2007;Jameson 2010) combined with an artificial Laplacian viscosity (Persson & Peraire 2006) shock-capturing scheme has been adopted for the present study. Moreover, the computational setup has been reduced to a minimal-unit (or singlepore) configuration, as done by El-Rahman et al (2017), to reduce the computational cost and ensure the maximum possible numerical resolution in the direction of shock propagation for a given number of discretization points, or degrees of (numerical) freedom. In spite of this choice, full resolution of the propagating shocks was still not attainable with the available resources.…”

Section: Introductionmentioning

confidence: 99%

Spectral energy cascade in thermoacoustic shock waves

2017

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We have investigated thermoacoustically amplified quasi-planar nonlinear waves driven to the limit of shock-wave formation in a variable-area looped resonator geometrically optimized to maximize the growth rate of the quasi-travelling-wave second harmonic. Optimal conditions result in velocity leading pressure by approximately 40• in the thermoacoustic core and not in pure travelling-wave phasing. High-order unstructured fully compressible Navier-Stokes simulations reveal three regimes: (i) Modal growth, governed by linear thermoacoustics; (ii) Hierarchical spectral broadening, resulting in a nonlinear inertial energy cascade; (iii) Shock-wave dominated limit cycle, where energy production is balanced by dissipation occurring at the captured shock-thickness scale. The acoustic energy budgets in regime (i) have been analytically derived, yielding an expression of the Rayleigh index in closed form and elucidating the effect of geometry and hot-to-cold temperature ratio on growth rates. A time-domain nonlinear dynamical model is formulated for regime (ii), highlighting the role of second-order interactions between pressure and heat-release fluctuations, causing asymmetry in the thermoacoustic energy production cycle and growth rate saturation. Moreover, energy cascade is inviscid due to steepening in regime (ii), with the k th harmonic growing at k/2-times the modal growth rate of the thermoacoustically sustained second harmonic. The frequency energy spectrum in regime (iii) is shown to scale with a −5/2 power law in the inertial range, rolling off at the captured shock-thickness scale in the dissipation range. We have thus shown the existence of equilibrium thermoacoustic energy cascade analogous to hydrodynamic turbulence.

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“…Initially, the fluid is motionless and the temperature inside the resonator is fixed at the ambient temperature T m : At the loudspeaker side, the velocity is expressed as follows 35 u…”

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

Numerical investigation of porous stack for a solar-powered thermoacoustic refrigerator

Miled

Dhahri

Mhimid

2014

Advances in Mechanical Engineering

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This article proposes a numerical analysis for performance improvement of the stack, which represents a crucial element on the solar-powered thermoacoustic refrigerator. The stack is considered as a saturated parallelepiped homogeneous porous media. Numerical simulation of the flow and the heat transfer in the thermoacoustic refrigerator is carried out. The physical flow is governed by the modified Darcy–Brinkmann–Forchheimer model. The governing equations are solved numerically using the lattice Boltzmann method. Furthermore, the local thermal equilibrium assumption is applied to examine heat transfer. Particular attention is paid a new form of the lattice Boltzmann equation system describing the flow and the heat transfer in porous media and fluid regions. The effects of several parameters characterizing the thermal behaviour in the porous medium are studied. The parametric results lead to the optimization of the porous media form. The presence of the viscous dissipation term in the heat transfer formulation within the thermoacoustic system is particularly highlighted, due to its significant effects introduced by the Eckert number.

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A 3D investigation of thermoacoustic fields in a square stack

Cited by 31 publications

References 17 publications

Numerical Predictions of Early Stage Turbulence in Oscillatory Flow across Parallel-Plate Heat Exchangers of a Thermoacoustic System

Numerical Predictions of Early Stage Turbulence in Oscillatory Flow across Parallel-Plate Heat Exchangers of a Thermoacoustic System

Spectral energy cascade in thermoacoustic shock waves

Numerical investigation of porous stack for a solar-powered thermoacoustic refrigerator

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