Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session MR: General Fluid Mechanics: Computations |
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Chair: Jacques Richard, Texas A&M University Room: 203A |
Tuesday, November 25, 2008 8:00AM - 8:13AM |
MR.00001: Geometric Sensitivity Analysis of Low-Dimensional Galerkin Models Imran Akhtar, Jeff Borggaard Reduced-order models have a number of practical engineering applications where low-dimensional approximations are required. For example, analysis and control of unsteady flows over a parameter range. The standard method for building reduced-order models for these applications combines the proper orthogonal decomposition (POD) and Galerkin projection. However, the model may be inaccurate when used ``off-design'' (at parameter values not used to generate the POD). This talk investigates the use of POD sensitivity vectors to improve the accuracy and dynamical system properties of the reduced-order models to problems with \textit{geometric parameters}. In this study, we consider flows past an elliptic cylinder for various major axes. Flow sensitivities (derivatives of the flow variables with respect to this geometric parameter) are used to compute POD sensitivity vectors. Two strategies for utilizing these POD sensitivity vectors are included in this study: expand the POD basis by adding the corresponding POD sensitivity vectors or extrapolate the POD basis functions to those for nearby geometric parameter values. Numerical studies test the accuracy of the basis to represent the flow and the accuracy of the resulting reduced-order models over a large range of parameter values. [Preview Abstract] |
Tuesday, November 25, 2008 8:13AM - 8:26AM |
MR.00002: A Reduced Model for the Magnetorotational Instability Ben Jamroz, Keith Julien, Edgar Knobloch The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale. [Preview Abstract] |
Tuesday, November 25, 2008 8:26AM - 8:39AM |
MR.00003: Differential diffusion of high Prandtl number scalars in stratified turbulence Hideshi Hanazaki, Takehiro Miyao Differential diffusion in stratified turbulence is investigated by direct numerical simulations (DNS) when the stratifying/active scalar has a Prandtl number Pr=6 (or 1), and the coexisting passive scalar has a Prandtl number of Pr=1 (or 6). When the stratifing scalar has Prandtl number larger than unity ($Pr=6>1$), energy spectrum of high-Pr stratifying scalar fluctuations approaches to that of kinetic energy in five buoyancy oscillations ($Nt/2\pi<5$), where N is the Brunt-Vaisala frequency. This occurs through persistently negative buoyancy flux at small scales, which transfer potential energy to wave part of kinetic energy. The process continues until the balance between potential energy and wave kinetic energy is satisfied. Time development of the ratio of Ozmidov scale to Kolmogorov scale, or the Froude number defined at the Kolmogorov scale, becomes smaller than unity in one buoyancy period ($Nt/2\pi<1$), supporting the appearance of this dominantly linear process at small scales. Then, the time scale of this phenomenon seems to be determined largely by the buoyancy time scale, and not by the turbulent time scale. In contrast, when the stratifying scalar has Prantdl number equal to unity ($Pr=1$) the coexisting high-Pr ($Pr=6$) passive scalar maintains high level of fluctuations at small scales, in agreement with Batchelor scalings. [Preview Abstract] |
Tuesday, November 25, 2008 8:39AM - 8:52AM |
MR.00004: A Computational Study on the Internal Splash Effect Lauren Cooper , Chris Wojtan, Nipun Kwatra, Peter Mucha We present a comparison of computational results with published experimental results regarding a falling sphere in stratified fluid. It has been shown experimentally [1] that a sphere falling through a stratified fluid may experience a temporary reversal of direction near the miscible interface between different density fluids. This is attributed to the hydrodynamic coupling experienced by the sphere with the entrained lighter density fluid that is dragged into the heavier surrounding fluid. We consider simulations of this system both in 2D and in 3D, treating the hydrodynamic coupling to the rigid ball by a distributed Lagrange multiplier technique [2], with suitable modification of the ``Rigid Fluid'' code [3]. [1] Abaid N., Adalsteinsson D., Akua A., McLaughlin, R.M. 2004. In Physics of Fluids 16,5. [2] Patankar, N.A. 2001. Center for Turbulence Research Annual Research Briefs 2001, 185-196. [3] Carlson, M., Mucha P.J., Turk, G. 2004. In ACM SIGGRAPH 2004 conference proceedings. [Preview Abstract] |
Tuesday, November 25, 2008 8:52AM - 9:05AM |
MR.00005: The Karman Vortex Street behind a Moving Rectangular Cylinder Mario Sanchez Sanz, Belen Fernandez, Angel Vel\'azquez This work studies the flow around a square cylinder at a relatively large Reynold number $Re=\rho U_\infty h/\mu \sim 200$ , where $\rho, U_\infty, h$ and $\mu$ represent the inlet flow density and average velocity, cylinder height and flow viscosity respectively. For this value of Re, the flow develops the well known von Karman vortex street causing the cylinder to experience unsteady lift and drag forces that will induce an oscillatory movement in the cylinder. To model the interaction between the fluid and the solid, we assume a damped coupling with the damping parameter A chosen to give the biggest oscillation amplitude. The motion of the rigid body is therefore governed by the equation $m d^2 y_c/dt^2 + A d y_c/d t = C_l/2$ where $m$ is the solid-to-fluid density ratio, $C_l$ is the time-dependent lift coeficient and $y_c$ is the position of the solid. The movement of the cylinder changes dramatically the dynamics of the flow, driving to the modification of the vortex shedding frequency and to pressure drops much higher than those provoked by a steady cylinder. In the present work we study the shedding frequency and the pressure drop variation with the aspect ratio of the solid $\delta$ and with $m$ by integrating numerically the two dimensional Navier-Stokes equations of a constant density fluid in a square chanel with blockage ratio $H/h=2.5$, where $H$ and $h$ represents the channel and the cylinder heights respectively. [Preview Abstract] |
Tuesday, November 25, 2008 9:05AM - 9:18AM |
MR.00006: Analysis of traffic flow models in phase space R.M. Velasco, P. Saavedra Traffic flow can be studied by means of hydrodynamic concepts, through an analogy with Navier-Stokes compressible flow or with models coming from kinetic equations. In this work we will consider two models for which the density and the average velocity are the relevant variables. The Kerner-Konh\"{a}user [1] is a phenomenological model proposed in complete analogy with a viscous flow, whereas the so called kinetic model [2] comes from the Paveri-Fontana kinetic equation [3]. Both models are seen from a moving reference frame and a phase space is defined where all the analysis is done, some orbits exemplify and contrast the behavior in these models [4]. [1] B.S. Kerner, P. Konh\"{a}user; Phys. Rev. E \textbf{48}, R2335 (1993). [2] R.M. Velasco, W. Marques Jr.; Phys. Rev. E \textbf{72}, 046102 (2005). [3] S.L. Paveri-Fontana; Transp.. Res. \textbf{9}, 225 (1975). [4] H.K. Lee, H.W. Lee, D. Kim; Phys. Rev. E \textbf{69}, 016118 (2004). [Preview Abstract] |
Tuesday, November 25, 2008 9:18AM - 9:31AM |
MR.00007: Dynamic Mode Decomposition of numerical and experimental data Peter Schmid, Joern Sesterhenn The extraction of dynamically relevant structures from time-resolved flow data has commonly be restricted to numerically generated flow fields. Equivalent structures, however, could not be obtained from experimental measurements, since the commonly used mathematical techniques required the explicit or implicit availability of an underlying model equation. A numerical scheme based on a Krylov subspace method for the extraction of dynamic modes directly from flow fields --- without the need to resort to a model equation --- will be introduced. This technique can be applied equally to numerically generated or experimental data and thus provides a means to decompose time-resolved measurements into dynamically dominant structures. The treatment of subdomains, spatially evolving flows, PIV data and simple flow visualizations will be demonstrated; a connection to the proper orthogonal decomposition (POD) technique, which is a byproduct of the dynamic mode decomposition, will be pointed out. [Preview Abstract] |
Tuesday, November 25, 2008 9:31AM - 9:44AM |
MR.00008: Direct Numerical Simulation of turbulent flows generated by fractal grids Sylvain Laizet, John Christos Vassilicos, Eric Lamballais Recently at Imperial College London, experiments of turbulence generated by fractal grids placed at the entrance of a wind tunnel have shown that complex multiscale boundaries/initial conditions can generate a far downstream decaying homogeneous isotropic turbulence with broad power law (approximately -5/3) energy spectra but laminar-like dissipation (Hurst {\&} Vassilicos, Seoud {\&} Vassilicos 2007 in PoF). Although the wind tunnel measurements have provided invaluable time-resolved informations on the unique properties of multiscale generated turbulent flows, understanding the spatial structure of these flows is necessary to discover the origins of these properties. The goal of the present numerical study is to investigate the spatio-temporal flow structure and the properties of the turbulent flow generated by these fractal objects. To solve the incompressible Navier-Stokes equations, we use a numerical code (called ``Incompact3d'') based on sixth-order compact schemes for spatial discretization and second order Adams-Bashforth scheme for time advancement. These are very large simulations, in particular because of the multi-scale nature of the fractal turbulence generators, and require state-of-the art top-end parallel computing. [Preview Abstract] |
Tuesday, November 25, 2008 9:44AM - 9:57AM |
MR.00009: Discretization of the Vorticity Field of a Planar Jet Natalie Ross, Elizabeth Bradley, Jean Hertzberg When initializing a vortex method simulation of a flow, typically vortexes are placed on a rectangular grid. Here, in the context of a data assimilation scheme, we seek to model a flow using far fewer vortexes than grid points. The flow was a planar jet which was excited into a small number of vortexes arranged in a street configuration. Velocity data was acquired using particle image velocimetry, providing a well-resolved vorticity field. Two standard vortex extraction techniques were applied, vorticity thresholding and Okubo-Weiss. These techniques were modified using a `connected component' technique from computational topology to determine the boundaries of the vortexes. One or several point vortexes were then placed inside each boundary. The results were analyzed by comparing the velocity fields induced by the point vortexes to the original velocity field. Thresholding was found to give comparable results to Okubo-Weiss, with far lower computational cost. [Preview Abstract] |
Tuesday, November 25, 2008 9:57AM - 10:10AM |
MR.00010: Modification of three-dimensional transition in bluff-body wakes David Lo Jacono, Justin Leontini, Mark Thompson, John Sheridan A study of the flow past an oscillatory-rotating cylinder has been conducted, where the frequency of oscillation has been matched to the natural frequency of the vortex street generated in the wake of a stationary cylinder, for Reynolds number ($\mathrm{Re} = 300$). Using Floquet stability analysis, it was found that the fine-scale three-dimensional mode that typically dominates the wake as $\mathrm{Re}$ is increased beyond that at transition to three-dimensional flow (referred to as mode B) was suppressed for amplitudes of rotation beyond a critical amplitude, confirming past studies. However, the rotation did not suppress the three-dimensional transition completely, as other modes were discovered that would lead to three-dimensional flow. In particular, the longer-wavelength mode that leads the three-dimensional transition in the wake of a stationary cylinder (referred to as mode A) was left essentially unaffected at low amplitudes of rotation. At higher amplitudes of oscillation, mode A was also suppressed, however other modes were predicted to render the flow three-dimensional, one of these modes appearing to be a spatial harmonic of mode A. [Preview Abstract] |
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