On the scattering of entropy waves at sudden area expansions

In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. This is a canonical configuration representing internal flows with flow separation and stagnation pressure losses. The numerical approach is based on a triple decomposition of the flow variables into a steady mean, a small-amplitude coherent part, and a stochastic turbulent part. The coherent part contains acoustic, vortical, and entropy waves. The mean flow is obtained as the solution of the Reynolds-Averaged Navier–Stokes (RANS) equations. The equations governing the coherent perturbations are linearised and solved in the frequency domain. To account for the effect of turbulence on the coherent perturbations, a frozen eddy viscosity model is employed. When entropy fluctuations pass through the area expansion, the generated entropy noise behaves as a low-pass filter. The numerical predictions of the noise at low frequencies are compared to the predictions of compact, quasi-one-dimensional, and isentropic theory and large discrepancies are observed. An alternative model for the generated entropy noise tailored for area expansions is then proposed. Such model is based on the conservation of mass, momentum, and energy written in integral form. The model assumes zero frequency and the one-dimensionality of the flow variables far upstream and downstream of the expansion. The predictions of this model agree well with the numerical simulations across a range of finite subsonic Mach numbers including low, intermediate, and high Mach numbers. The contributions of this work are both numerical and theoretical. Numerically, a triple decomposition adapted to high-Mach-number, compressible flows is introduced for the first time in the context of acoustic simulations. From a theoretical point of view, the quasi-steady model proposed here correctly captures the low-frequency entropy noise generated at sudden area expansions, including at high subsonic Mach numbers

A Spalart-Allmaras turbulence model implementation in a discontinuous Galerkin solver for incompressible flows

In this paper the artificial compressibility flux Discontinuous Galerkin (DG) method for the solution of the incompressible Navier–Stokes equations has been extended to deal with the Reynolds-Averaged Navier–Stokes (RANS) equations coupled with the Spalart–Allmaras (SA) turbulence model. DG implementations of the RANS and SA equations for compressible flows have already been reported in the literature, including the description of limiting or stabilization techniques adopted in order to prevent the turbulent viscosity View the MathML sourceν˜ from becoming negative. In this paper we introduce an SA model implementation that deals with negative View the MathML sourceν˜ values by modifying the source and diffusion terms in the SA model equation only when the working variable or one of the model closure functions become negative. This results in an efficient high-order implementation where either stabilization terms or even additional equations are avoided. We remark that the proposed implementation is not DG specific and it is well suited for any numerical discretization of the RANS-SA governing equations. The reliability, robustness and accuracy of the proposed implementation have been assessed by computing several high Reynolds number turbulent test cases: the flow over a flat plate (Re=107Re=107), the flow past a backward-facing step (Re=37400Re=37400) and the flow around a NACA 0012 airfoil at different angles of attack (View the MathML sourceα=0°,10°,15°) and Reynolds numbers (Re=2.88×106,6×106Re=2.88×106,6×106)

Energy Harvesting from Natural Water Flow

The hydrokinetic energy contained in flowing water is plentiful and has the potential to be one of the environmentally friendly renewable sources of energy that can be harvested. A new energy harvesting system utilizing Vortex-induced Vibration (VIV) is presented and analysed in this thesis. The proposed energy harvester generates power by direct conversion of the hydrokinetic energy of water flow into mechanical vibrations. The harvester experiences alternating fluid forces due to the repeatable pattern of alternating vortices shed from the sides of the body which generates a wake with Von Kármán Vortex Street. The proposed harvester consists of two coupled components: a bluff body with specific geometry that produces mechanical oscillations from VIV resulting in periodic vibrations and a set of piezoelectric transducers that harvest the mechanical energy from the vibrations. This typical Fluid-structure Interaction (FSI) between fluid flow and the energy harvester was studied using numerical modeling and experimental tests. The vibrational power output of the energy harvester was directly measured from data acquisition system during experimental tests. The VIV response of the proposed harvester with two degrees-of-freedom (DOF) is also investigated numerically at different input velocities. Potential power output generated by the harvester was calculated based on the results from the two-way coupled numerical model and reported over a range of input velocity. A single energy harvester demonstrated a peak power output of 41 mW, from an input flow velocity of ~8 m/s