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 $\mathrm{\mu}$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.Comment: 55th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201

Investigation of Transitional Shock-Wave/Boundary Layer Interactions Using Direct Numerical Simulations

Interaction of a transitional boundary layer with a normal-shock is investigated using unstructured tetrahedral meshes under the numerical framework of the space-time conservation element, solution element (CESE) method. The computations mimic recent experimental efforts at the University of Tennessee Space Institute, where a Mach 2.0 flow interacts with a tall cylinder attached to a flat plate. The location of the cylinder with respect to the flat plate leading edge determines if the incoming boundary layer is laminar, transitional or fully turbulent. Four representative flow conditions exemplifying laminar and transitional boundary layers are analyzed by direct numerical simulations. Similar to what was observed in the experiments for the case of transitional interaction, the computations reveal an intermittent upstream influence (UI) shock that repeatedly travels upstream from the lambda-foot toward the leading edge before vanishing. Through detailed unsteady flow analysis obtained using Fourier analysis and dynamic mode decomposition techniques, the presence of disturbances with similar frequencies as those measured in experiments were identified in the flow along with locations that appear to influence the dynamics of the flow

The prospect of using LES and DES in engineering design, and the research required to get there

In this paper we try to look into the future to divine how large eddy and detached eddy simulations (LES and DES, respectively) will be used in the engineering design process about 20-30 years from now. Some key challenges specific to the engineering design process are identified, and some of the critical outstanding problems and promising research directions are discussed.Comment: accepted for publication in the Royal Society Philosophical Transactions

Numerical and experimental investigations of buffet on a diamond airfoil designed for space launchers applications

The capability to reuse space launchers for new missions requires to better understand flow phenomena in the transonic regime, such as buffet, and its interaction with the structure. Indeed, the mechanical integrity of the launcher can be compromised by shock/boundary layer interactions, that induce lateral forces responsible for plunging and pitching moments. This work reports some numerical and experimental investigations about the aerodynamic and aeroelastic behavior of a diamond airfoil, designed for microsatellite-dedicated launchers, with a particular interest for the fluid/structure interaction during buffeting. Experiments have been conducted, based on Schlieren visualizations, and compared with numerical predictions obtained with unsteady RANS and Large-Eddy Simulation. Finally, the effect of buffeting on the composite aileron is studied by solving the equation of the dynamics, showing that the aerodynamic response of the airfoil tends to damp the structural displacement, and thus limit the effect of buffeting

Numerical and experimental investigations of buffet on a diamond airfoil designed for space launcher applications

Purpose – The development of reusable space launchers requires a comprehensive knowledge of transonic flow effects on the launcher structure, such as buffet. Indeed, the mechanical integrity of the launcher can be compromised by shock wave/boundary layer interactions, that induce lateral forces responsible for plunging and pitching moments. Design/methodology/approach – This paper aims to report numerical and experimental investigations on the aerodynamic and aeroelastic behavior of a diamond airfoil, designed for microsatellite-dedicated launchers, with a particular interest for the fluid/structure interaction during buffeting. Experimental investigations based on Schlieren visualizations are conducted in a transonic wind tunnel and are then compared with numerical predictions based on unsteady Reynolds averaged Navier–Stokes and large eddy simulation (LES) approaches. The effect of buffeting on the structure is finally studied by solving the equation of the dynamics. Findings – Buffeting is both experimentally and numerically revealed. Experiments highlight 3D oscillations of the shock wave in the manner of a wind-flapping flag. LES computations identify a lambda- shaped shock wave foot width oscillations, which noticeably impact aerodynamic loads. At last, the experiments highlight the chaotic behavior of the shock wave as it shifts from an oscillatory periodic to an erratic 3D flapping state. Fluid structure computations show that the aerodynamic response of the airfoil tends to damp the structural vibrations and to mitigate the effect of buffeting. Originality/value – While buffeting has been extensively studied for classical supercritical profiles, this study focuses on diamond airfoils. Moreover, a fluid structure computation has been conducted to point out the effect of buffeting

Tetrahedral-Mesh Simulations of Shock-Turbulence Interaction

Despite decades of development of unstructured mesh methods, direct numerical simulations (DNS) of turbulent flows are still predominantly performed on structured or unstructured hexahedral meshes with high-order finite-difference methods, weighted essentially nonoscillatory (WENO) schemes, or hybrid schemes formed by their combinations. Tetrahedral meshes offer easy mesh generation and adaptation around complex geometries and the potential of an orientation-free grid that would benefit the isotropic nature of small-scale dissipation, as well as the solution accuracy of intermediate scales. To advance the state of the art of unstructured-mesh simulation capabilities for shock/turbulence interaction, DNS using pure tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method in this research. By its design, the CESE method is constructed based on a non-dissipative scheme and is a genuinely multidimensional numerical framework that is free from the use of an approximate Riemann-solver. The numerical framework also provides the ability to add numerical dissipation (the nondissipative scheme acts as the reference state like that of the reversible state in thermodynamics) when needed (with justification from mathematics/physics). The above-mentioned features along with the CESE method's consistent shock-capturing approach and strong enforcement of flux conservation in spacetime offers a novel method to accurately simulate turbulent flows and their interaction with shocks using tetrahedral meshes. Two canonical problems, namely, isotropic turbulence interaction with a normal shock and a Mach 2.9 turbulent boundary layer flow over a 24deg compression corner are investigated in this study. Computational results show reasonably good agreement with experimental data and results from structured-mesh, high-order simulations available in the literature. Successful validation of these canonical problems demonstrated here paves the way for future high-fidelity supersonic flow simulations involving complex-geometries