Linear and nonlinear modelling of a theoretical travelling-wave thermoacoustic heat engine

Abstract

We have carried out three-dimensional Navier-Stokes simulations, from quiescent conditions to the limit cycle, of a theoretical traveling-wave thermoacoustic heat engine (TAE) composed of a long variable-area resonator shrouding a smaller annular tube, which encloses the hot (HHX) and ambient (AHX) heat-exchangers, and the regenerator (REG). Simulations are wall-resolved, with no-slip and adiabatic conditions enforced at all boundaries, while the heat transfer and drag due to the REG and HXs are modeled. HHX temperatures have been investigated in the range 440K -500K with AHX temperature fixed at 300K. The initial exponential growth of acoustic energy is due to a network of traveling waves thermoacoustically amplified by looping around the REG/HX unit in the direction of the imposed temperature gradient. A simple analytical model demonstrates that such instability is a localized Lagrangian thermodynamic process resembling a Stirling cycle. An inviscid system-wide linear stability model based on Rott's theory is able to accurately predict the operating frequency and the growth rate, exhibiting properties consistent with a supercritical Hopf bifurcation. The limit cycle is governed by acoustic streaming -a rectified steady flow resulting from high-amplitude nonlinear acoustics. Its key features are explained with an axially symmetric incompressible model driven by the wave-induced stresses extracted from the compressible calculations. These features include Gedeon streaming, Rayleigh streaming in the resonator, and mean recirculations due to flow separation. The first drives the mean advection of hot fluid from the HHX to a secondary heat exchanger (AHX2), in the thermal buffer tube (TBT), necessary to achieve saturation of the acoustic energy growth. The direct evaluation of the nonlinear energy fluxes reveals that the efficiency of the device deteriorates with the drive ratio and that the acoustic power in the TBT is balanced primarily by the mean advection and thermoacoustic heat transport.

Measurement of density fluctuations using digital holographic interferometry in a standing wave thermoacoustic oscillator

“…Such an extension of the impact of entrance effects beyond the distance 2u has already been reported by Berson et al [21] both numerically and experimentally (from the measurement of T 0 using cold wire anemometry), and can be explained (at least partially) by accounting for the axial conduction within the fluid in Eq. (12). However, the large discrepancy in terms of amplitudes as well as the differences in terms of spatial distribution (notably for the fundamental and the quasi-static components) is not explained.…”

“…In Eq. (12), the dimensionless temperature is defined as h ¼ T 0 =T c where T c is a characteristic amplitude of adiabatic temperature fluctuations in a standing wave, while the parameter R is a dimensionless relaxation time used to account for the thermal coupling between the gas and the stack walls. In the following, we will consider that inside the stack (n 6 0) one has R ¼ 1 while outside the stack (n P 0) it tends towards infinity: this assumption amounts to considering that the distance between two stack plates is such that the thermoacoustic process is optimum (R ¼ 1) while the process is purely adiabatic outside the stack (R !…”

“…However, despite their simplicity in terms of geometry, thermoacoustic engines are not very well understood due to the complexity and the variety of the phenomena saturating the acoustic wave amplitude. Among these nonlinear phenomena are the ones impacting unsteady heat and mass transfer through the thermoacoustic core, such as acoustic streaming [10], or hydrodynamic/thermal entrance effects occurring notably at the stack termination (vortex shedding [11], transitional turbulence [12], nonlinear temperature fluctuations [13]). …”

Spectral energy cascade and decay in nonlinear acoustic waves

“…Nonlinear wave processes are observed in a variety of engineering and physics applications such as acoustics [1,2], combustion noise [3,4], jet noise [5][6][7], thermoacoustics [8,9], surface waves [10], and plasmaphysics [11], requiring nonlinear evolution equations to describe the dynamics of perturbations. In the case of high amplitude planar acoustic wave propagation, two main nonlinear effects are present: acoustic streaming [2,12] and wave steepening [1,13].…”

Numerical modeling of thermoacoustic systems

“…However, the applicability of CFD is restricted due to the required computational cost. In 2014, modeling of a thermoacoustic engine from start-up to steady-state still required a super computer or computing cluster to keep the computation (wall clock) times manageable [36]. Therefore, CFD can be used for the design, however, this requires one to take into account smaller computational domains, such that only the interesting part of the domain is modeled.…”