arXiv subjects

Carlo Scalo

Publications and source records attributed to Carlo Scalo.

25 records · Page 2Linked to original sources

arXiv2017

High-fidelity simulation of an ultrasonic standing-wave thermoacoustic engine with bulk viscosity effects

We have carried out boundary-layer-resolved, unstructured fully-compressible Navier--Stokes simulations of an ultrasonic standing-wave thermoacoustic engine (TAE) model. The model is constructed as a quarter-wavelength engine, approximately 4 mm by 4 mm in size and operating at 25 kHz, and comprises a thermoacoustic stack and a coin-shaped cavity, a design inspired by Flitcroft and Symko (2013). Thermal and viscous boundary layers (order of 10 $\mathrmμ$m) are resolved. Vibrational and rotational molecular relaxation are modeled with an effective bulk viscosity coefficient modifying the viscous stress tensor. The effective bulk viscosity coefficient is estimated from the difference between theoretical and semi-empirical attenuation curves. Contributions to the effective bulk viscosity coefficient can be identified as from vibrational and rotational molecular relaxation. The inclusion of the coefficient captures acoustic absorption from infrasonic ($\sim$10 Hz) to ultrasonic ($\sim$100 kHz) frequencies. The value of bulk viscosity depends on pressure, temperature, and frequency, as well as the relative humidity of the working fluid. Simulations of the TAE are carried out to the limit cycle, with growth rates and limit-cycle amplitudes varying non-monotonically with the magnitude of bulk viscosity, reaching a maximum for a relative humidity level of 5%. A corresponding linear model with minor losses was developed; the linear model overpredicts transient growth rate but gives an accurate estimate of limit cycle behavior. An improved understanding of thermoacoustic energy conversion in the ultrasonic regime based on a high-fidelity computational framework will help to further improve the power density advantages of small-scale thermoacoustic engines.

physics.flu-dyn↗

arXiv2017

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 $\times$ 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, $Re_b= 6900$ and Mach number, $M_b = 0.85$. The eigenvalue spectrum calculated in the biglobal stability analysis shows distinct groups of modes associated with a discrete set of streamwise wave numbers accommodated by computational domain. An iterative strategy for the imposition of the complex IBCs, which are a nonlinear function of the real-valued (Fourier) frequency in the GEVP, has been devised. The adopted IBC specifically represents an array of sub-surface-mounted Helmholtz cavities with resonant frequency, $f_{res}$, covered by a porous sheet with permeability inversely proportional to the impedance resistance $R$. The tunable resonant frequency has been shown to be an attractor for the instability, yielding a single unstable mode at that frequency.

physics.flu-dyn↗

arXiv2017

Towards Impedance Characterization of Carbon-Carbon Ultrasonically Absorptive Cavities via the Inverse Helmholtz Problem

We present a numerical method to determine the complex acoustic impedance at the open surface of an arbitrarily shaped cavity, associated to an impinging planar acoustic wave with a given wavenumber vector and frequency. We have achieved this by developing the first inverse Helmholtz Solver (iHS), which implicitly reconstructs the complex acoustic waveform--at a given frequency--up to the unknown impedance boundary, hereby providing the spatial distribution of impedance as a result of the calculation for that given frequency. We show that the algebraic closure conditions required by the inverse Helmholtz problem are physically related to the assignment of the spatial distribution of the pressure phase over the unknown impedance boundary. The iHS is embarrassingly parallelizable over the frequency domain allowing for the straightforward determination of the full broadband impedance at every point of the target boundary. In this paper, we restrict our analysis to two-dimensions only. We first validate our results against Rott's quasi one-dimensional thermoacoustic theory for viscid and inviscid constant-area rectangular ducts, test our iHS in a fully unstructured fashion with a geometrically complex cavity, and finally, present a simplified, two-dimensional analysis of a sample of carbon-carbon ultrasonically absorptive coatings (C/C UACs) manufactured in DLR-Stuttgart, and used in the hypersonic transition delay experiments by Wagner et al. in AIAA 2012-5865. The final goal is to model C/C UACs with multi-oscillator Time Domain Impedance Boundary Conditions (TDIBC) developed by Lin et al. in JFM (2016) to be applied in direct numerical simulations (DNS) focused on the overlying boundary layer, eliminating the need to simultaneously resolve the microscopic porous structure of the C/C UACs.

physics.flu-dyn↗

arXiv2017

Separation delay via hydro-acoustic control of a NACA4412 airfoil in pre-stalled conditions

We have performed large-eddy simulations of turbulent separation control via impedance boundary conditions (IBCs) on a \nacafft airfoil in near-stalled conditions. The uncontrolled baseline flow is obtained for freestream Mach numbers of $M_\infty=0.3$, chord-Reynolds numbers $Re_c = 1.5\times10^6$ and angle of attack, $α=14^{\circ{}}$. Flow control is applied via imposition of complex IBCs using the time-domain implementation developed by Scalo, Bodart, and Lele, $\textit{Phys. Fluids} $(2015). Separation is delayed due to the enhanced mixing associated with convectively amplified spanwise-oriented Kelvin-Helmholtz (KH) rollers, generated via hydro-acoustic instabilities. The latter are the result of the interaction of the wall-normal transpiration through the impedance panel and the overlying mean background shear. The result is an alteration of the coupled instability between the separating shear layer and the vortex shedding in the wake (already present in the uncontrolled baseline flow) yielding unique wake topologies associated with different intensities for the passively generated KH vortical structures. Specifically, enhancements up to +13\% in the lift coefficients have been obtained. Results show that tuning of the resonant cavities below the natural shedding frequency is required to generate KH rollers structures with a sufficiently large entrainment diameter to encompass the full extent of the separated region, thereby enhancing mixing and promoting reattachment. Overall, the results presented in this work show that the adoption of hydro-acoustically tuned resonant panels is a promising passive control technique for boundary layer separation control.

physics.flu-dyn↗

arXiv2016

High-fidelity simulation 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 Rott's 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.

physics.flu-dyn↗

arXiv2015

Linear Stability Analysis of Compressible Channel Flow with 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 (LSA). 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 permeability, Two dominant modes are made unstable: a bulk pressure mode, causing 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 wavenumbers investigated, suggesting that wall permeability simply accentuates pre-existing otherwise stable modes. Results from the present investigation will inform the design of new compressible turbulent boundary layer control strategies via assigned wall-impedance.

physics.flu-dyn↗

arXiv2014

Linear and Nonlinear Modeling of a Traveling-Wave Thermoacoustic Heat Engine

We have carried out three-dimensional Navier-Stokes simulations, from quiescent conditions to the limit cycle, of a 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 amplified by looping around the REG/HX unit in the direction of the imposed temperature gradient. A simple analytical model demonstrates that such thermoacoustic instability is a Lagrangian thermodynamic process resembling a Stirling cycle. A system-wide linear stability model based on Rott's theory is able to accurately predict the frequency and the growth rate, exhibiting properties consistent with a supercritical Hopf bifurcation. The limit cycle is governed by acoustic streaming -- a rectified flow resulting from high-amplitude 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 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 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.

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