Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session E18: Flow Instability: Global Modes |
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Chair: Clarence Rowley, Princeton University Room: D135 |
Sunday, November 20, 2016 5:37PM - 5:50PM |
E18.00001: Efficient randomized methods for stability analysis of fluids systems Scott Dawson, Clarence Rowley We show that probabilistic algorithms that have recently been developed for the approximation of large matrices can be utilized to numerically evaluate the properties of linear operators in fluids systems. In particular, we present an algorithm that is well suited for optimal transient growth (i.e., nonmodal stability) analysis. For non-normal systems, such analysis can be important for analyzing local regions of convective instability, and in identifying high-amplitude transients that can trigger nonlinear instabilities. Our proposed algorithms are easy to wrap around pre-existing timesteppers for linearized forward and adjoint equations, are highly parallelizable, and come with known error bounds. Furthermore, they allow for efficient computation of optimal growth modes for numerous time horizons simultaneously. We compare the proposed algorithm to both direct matrix-forming and Krylov subspace approaches on a number of test problems. We will additionally discuss the potential for randomized methods to assist more broadly in the speed-up of algorithms for analyzing both fluids data and operators. [Preview Abstract] |
Sunday, November 20, 2016 5:50PM - 6:03PM |
E18.00002: Global-mode based linear feedback control of a supersonic jet for noise reduction Mahesh Natarajan, Jonathan Freund, Daniel Bodony The loudest source of high-speed jet noise appears to be describable by unsteady wavepackets that resemble instabilities. We seek to reduce their acoustic impact with a control strategy that uses global modes to model their dynamics and structural sensitivity of the linearized compressible Navier-Stokes operator to identify an effective linear feedback control. For a case with co-located actuators and sensors adjacent the nozzle, we demonstrate the method on an axisymmetric Mach 1.5 jet. Direct numerical simulations using this control show significant noise reduction. Eigenanalysis of the controlled mean flows reveal fundamental changes in the spectrum at frequencies lower than that used by the control, with the quieter flows having unstable eigenvalues that correspond to eigenfunctions without significant support in the acoustic field. A specific trend is observed in the mean flow quantities as the flow becomes quieter, with changes in the mean flow becoming significant only further downstream of the nozzle exit. The quieter flows also have a stable shock-cell structure that extends further downstream. A phase plot of the POD coefficients for the flows show that the quieter flows are more regular in time. [Preview Abstract] |
Sunday, November 20, 2016 6:03PM - 6:16PM |
E18.00003: Linear stability analysis of axisymmetric flow over a sudden expansion in an annular pipe Behnaz Beladi, Hendrik Christoph Kuhlmann A global temporal linear stability analysis is performed of the fully-developed axisymmetric incompressible Newtonian flow in an annular pipe with a sudden radially-inward expansion. The geometry is characterized by the radial expansion ratio (radial step height to the outlet gap width) and the outlet radius ratio (inner-to-outer radius). Stability boundaries have been calculated with finite volumes for an outlet radius ratio of $0.1$ and expansion ratios from $0.25$ to $0.75$. For expansion ratios less than $0.55$ the most dangerous mode has an azimuthal wave number $m=3$, whereas $m=2$ for larger expansion ratios. An a posteriori analysis of the kinetic energy transferred between the basic state and the critical mode allows to check the energy conservation and to identify the physical instability mechanism. For all expansion ratios considered the basic flow arises as an annular jet between two separation zones which are located immediately after the step. The jet gradually widens downstream before reattaching to the cylinders. The deceleration of the flow associated with the widening of the jet is found to be the primary source of energy for the critical modes. [Preview Abstract] |
Sunday, November 20, 2016 6:16PM - 6:29PM |
E18.00004: Stabilization of flow past a rounded cylinder Ravi Samtaney, Wei Zhang We perform global linear stability analysis on low-\textit{Re} flow past a rounded cylinder. The cylinder corners are rounded with a radius $R$, normalized as $R^+=R/D$ where $D$ is the cylinder diameter, and its effect on the flow stability characteristics is investigated. We compute the critical Reynolds number ($Re_{cr}$) for the onset of first instability, and quantify the perturbation growth rate for the super-critical flows. It is found that \textit{the flow can be stabilized by partially rounding the cylinder}. Compared with the square and circular cylinders, the partially rounded cylinder has a higher $Re_{cr}$, attaining a maximum at around $R^+=0.30$, and the perturbation growth rate of the super-critical flows is reduced for $Re\le100$. We perform sensitivity analysis to explore the source of the stabilization. The growth rate sensitivity to base flow modification has two different spatial structures: the growth rate is sensitive to the wake backflow in a large region for square-like cylinders ($R^+\to0.00$), while only the near-wake backflow is crucial for circular-like cylinders ($R^+\to0.50$). The stability analysis results are also verified with those of the direct simulations and very good agreement is achieved. [Preview Abstract] |
Sunday, November 20, 2016 6:29PM - 6:42PM |
E18.00005: Stability of optimal streaks in the buffer layer of a turbulent channel flow with variable viscosity Ashish Patel, Enrico Rinaldi, Rene Pecnik, Philipp Schlatter, Shervin Bagheri Direct Numerical Simulations (DNS) of turbulent channel flows with variable viscosity (Patel et al., 2015, PoF) show that low speed streaks in the buffer layer strengthen and are stabilized for increasing viscosity away from the wall, as they do not lift and tilt as intensely as in a constant property flow. The opposite holds for cases where viscosity decreases away from the wall. In this work, we investigate the above observation by studying the linear stability of the mean turbulent velocity profile obtained from DNS of variable viscosity flows. Examples of such studies for constant property turbulent flows include work of del Alamo \& Jiménez, 2006, JFM and Pujals et al., 2009, PoF. The calculated optimal buffer layer streaks show larger transient energy growth for a case where the viscosity increases away from the wall. We further study the stability of the saturated optimal streaks by imposing a secondary sinuous perturbation and by following the nonlinear evolution of the structures in time. The present investigation will improve the understanding of the near-wall turbulence cycle for wall-bounded turbulent flows with viscosity gradients. [Preview Abstract] |
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