Carlo Scalo

High-fidelity simulations of a standing-wave thermoacoustic-piezoelectric engine

We have carried out wall-resolved unstructured fully-compressible Navier--Stokes simulations of a complete standing-wave thermoacoustic piezoelectric (TAP) engine model inspired by the experimental work of Smoker et al. (2012). The model is axisymmetric and comprises a 51 cm long resonator divided into two sections: a small diameter section enclosing a thermoacoustic stack, and a larger diameter section capped by a piezoelectric diaphragm tuned to the thermoacoustically amplified mode (388 Hz). The diaphragm is modelled with multi-oscillator broadband time-domain impedance boundary conditions (TDIBCs), providing higher fidelity over single-oscillator approximations. Simulations are first carried out to the limit cycle without energy extraction. The observed growth rates are shown to be grid-convergent and are verified against a numerical dynamical model based on Rotts theory. The latter is based on a staggered grid approach and allows jump conditions in the derivatives of pressure and velocity in sections of abrupt area change and the inclusion of linearized minor losses. The stack geometry maximizing the growth rate is also found. At the limit cycle, thermoacoustic heat leakage and frequency shifts are observed, consistent with experiments. Upon activation of the piezoelectric diaphragm, steady acoustic energy extraction and a reduced pressure amplitude limit cycle are obtained. A heuristic closure of the limit cycle acoustic energy budget is presented, supported by the linear dynamical model and the nonlinear simulations. The developed high-fidelity simulation framework provides accurate predictions of thermal-to-acoustic and acoustic-to-mechanical energy conversion (via TDIBCs), enabling a new paradigm for the design and optimization of advanced thermoacoustic engines.

A Coherent vorticity preserving eddy viscosity correction for Large-Eddy Simulation

Abstract This paper introduces a new approach to Large-Eddy Simulation (LES) where subgrid-scale (SGS) dissipation is applied proportionally to the degree of local spectral broadening, hence mitigated or deactivated in regions dominated by large-scale and/or laminar vortical motion. The proposed coherent-vorticity preserving (CvP) LES methodology is based on the evaluation of the ratio of the test-filtered to resolved (or grid-filtered) enstrophy, σ. Values of σ close to 1 indicate low sub-test-filter turbulent activity, justifying local deactivation of the SGS dissipation. The intensity of the SGS dissipation is progressively increased for σ 1 which corresponds to a small-scale spectral broadening. The SGS dissipation is then fully activated in developed turbulence characterized by σ ≤ σ e q , where the value σ e q is derived assuming a Kolmogorov spectrum. The proposed approach can be applied to any eddy-viscosity model, is algorithmically simple and computationally inexpensive. LES of Taylor–Green vortex breakdown demonstrates that the CvP methodology improves the performance of traditional, non-dynamic dissipative SGS models, capturing the peak of total turbulent kinetic energy dissipation during transition. Similar accuracy is obtained by adopting Germanos dynamic procedure albeit at more than twice the computational overhead. A CvP-LES of a pair of unstable periodic helical vortices is shown to predict accurately the experimentally observed growth rate using coarse resolutions. The ability of the CvP methodology to dynamically sort the coherent, large-scale motion from the smaller, broadband scales during transition is demonstrated via flow visualizations. LES of compressible channel are carried out and show a good match with a reference DNS.

Delayed-time domain impedance boundary conditions (D-TDIBC)

Defining acoustically well-posed boundary conditions is one of the major numerical and theoretical challenges in compressible Navier–Stokes simulations. We present the novel Delayed-Time Domain Impedance Boundary Condition (D-TDIBC) technique developed to impose a time delay to acoustic wave reflection. Unlike previous similar TDIBC derivations (Fung and Ju, 2001–2004 [1], [2], Scalo et al., 2015 [3] and Lin et al., 2016 [4]), D-TDIBC relies on the modeling of the reflection coefficient. An iterative fit is used to determine the model constants along with a low-pass filtering strategy to limit the model to the frequency range of interest. D-TDIBC can be used to truncate portions of the domain by introducing a time delay in the acoustic response of the boundary accounting for the travel time of inviscid planar acoustic waves in the truncated sections: it gives the opportunity to save computational resources and to study several geometries without the need to regenerate computational grids. The D-TDIBC method is applied here to time-delayed fully reflective conditions. D-TDIBC simulations of inviscid planar acoustic-wave propagating in truncated ducts demonstrate that the time delay is correctly reproduced, preserving wave amplitude and phase. A 2D thermoacoustically unstable combustion setup is used as a final test case: Direct Numerical Simulation (DNS) of an unstable laminar flame is performed using a reduced domain along with D-TDIBC to model the truncated portion. Results are in excellent agreement with the same calculation performed over the full domain. The unstable modes frequencies, amplitudes and shapes are accurately predicted. The results demonstrate that D-TDIBC offers a flexible and cost-effective approach for numerical investigations of problems in aeroacoustics and thermoacoustics.

Linear Stability Analysis of Compressible Channel Flow over Porous Walls

We have investigated the effects of permeable walls, modeled by linear acoustic impedance with zero reactance, on compressible channel flow via linear stability analysis. Base flow profiles are taken from impermeable isothermal-wall laminar and turbulent channel flow simulations at bulk Reynolds number, Re b = 6900 and Mach numbers, M b = 0. 2, 0.5, 0.85. For a sufficiently high value of wall-permeability, two dominant modes are made unstable: a bulk pressure mode, associated with symmetric expulsion and suction of mass from the porous walls (Mode 0); a standing-wave-like mode, with a pressure node at the centerline (Mode I). In the case of turbulent mean flow profiles, both modes generate additional Reynolds shear stresses augmenting the (base) turbulent ones, but concentrated in the viscous sublayer region; the trajectories of the two modes in the complex phase velocity space follow each other closely for values of wall permeability spanning two orders of magnitude, suggesting their coexistence. The transition from subcritical to supercritical permeability does not alter the structure of the two modes for the range of streamwise wavenumbers investigated, suggesting that wall permeability simply accentuates pre-existing otherwise stable modes. Results from the present investigation will inform future studies of compressible turbulent boundary layers over assigned wall-impedance.

Quasi-Spectral Sparse Bi-Global Stability Analysis of Compressible Channel Flow over Complex Impedance

We have developed a fully sparse, compact-scheme based biglobal stability analysis numerical solver applied, for the scope of the current paper, to the investigation of the effects of impedance boundary conditions (IBCs) on the structure of a fully developed compressible turbulent channel flow. A sixth-order compact finite difference scheme is used to discretize the linearized Navier-Stokes equations leading to a Generalized Eigenvalue Problem (GEVP). Sparsity is retained by explicitly introducing derivatives of the perturbation as additional unknowns, increasing the overall problem size (number of columns

Coherent-vorticity Preserving Large-Eddy Simulation of trefoil knotted vortices

\times

Spectral energy cascade in nonlinear acoustic and thermoacoustic waves

number of rows) while significantly reducing the number of non-zeros and the computational cost with respect to traditional implementations yielding otherwise dense matrix blocks. The resulting GEVP is coded in Python and solved employing an Message Passing Interface (MPI) parallelized PETSc-based sparse eigenvalue solver adopting a modified Arnoldi algorithm. Base flow is taken from impermeable isothermal-wall turbulent channel flow simulations at bulk Reynolds number,

Standing-wave and traveling-wave thermoacoustics in solid media

Re_b= 6900

Thermoacoustic instability in solid media

and Mach number,

Thermoacoustics of solids: A pathway to solid state engines and refrigerators

M_b = 0.85