Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session M8: General Fluid Dynamics II: Theory I |
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Chair: Mark Hoefer, North Carolina State University Room: 330 |
Tuesday, November 26, 2013 8:00AM - 8:13AM |
M8.00001: Size-Dependent Fluid Mechanics Ali Hadjesfandiari, Arezoo Hajesfandiari, Gary Dargush Classical fluid mechanics provides a reasonable basis for analyzing the behavior of fluid flow at the macro scale. However, experiments show that the behavior of fluid in small scales is different from their behavior at macro scales. An additional concern relates to the absence of a length scale in the governing Navier-Stokes equations, when the present description of turbulence seems to need the clear definition of a characteristic size. Consequently, there is need for a more complete fluid dynamics, which spans many scales and, of course, must reduce to classical fluid mechanics for flows with macro-scale size. Here we develop the consistent size-dependent fluid mechanics by discovering the skew-symmetric character of couple stress tensor. As a result, the skew-symmetric mean curvature rate vector as the consistent measure of deformation is introduced. It is demonstrated that this theory may provide a basis for fundamental studies of flows at the finest scales for which a continuum representation is valid and, perhaps, for gaining additional insight into the problem of turbulence. [Preview Abstract] |
Tuesday, November 26, 2013 8:13AM - 8:26AM |
M8.00002: An Implicit Immersed Boundary Method for Low Reynolds Number Incompressible Flows Hyun Wook Park, Changhoon Lee, Jung-il Choi We develop a new formulation of immersed boundary (IB) method based on direct forcing for incompressible viscous flows. The new algorithm for the present IB method is derived using a block LU decomposition and Taylor series expansion, and the direct forcing for imposing no-slip condition on the IB surface is calculated in an iterative procedure. We perform simulations of two-dimensional flows around a circular cylinder and three-dimensional flows over a sphere for low and moderate Reynolds numbers. The result shows that present method yield a better imposition of no-slip condition on IB surface for low Reynolds number with a fairly larger time step than other IB methods based on direct forcing. [Preview Abstract] |
Tuesday, November 26, 2013 8:26AM - 8:39AM |
M8.00003: Anisotropy in RT flows Ye Zhou, W. Cabot This work investigates several key statistical measurements of turbulence induced by Rayleigh-Taylor instability using data from well resolved numerical simulations at moderate Reynolds number with the goal of determining the degree of departure of this inhomogeneous flow from that of homogeneous, isotropic turbulence. The simulations use two miscible fluids with unity Schmidt number and moderate density contrast (3/2 to 9). The results of this study should find application in subgrid-scale modeling for large-eddy simulations and Reynolds-averaged Navier-Stokes modeling used in many engineering and scientific problems. [Preview Abstract] |
Tuesday, November 26, 2013 8:39AM - 8:52AM |
M8.00004: Interfacial dynamics of dissolving objects in fluid flow Chris Rycroft, Martin Bazant An advection--diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow will be presented. By taking advantage of conformal invariance of the model, a numerical method will be introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of several dissolving objects will be shown, all of which show collapse to a single point in finite time. The simulations reveal a surprising connection between the position of the collapse point and the initial Laurent coefficients, which was subsequently derived analytically using residue calculus. [Preview Abstract] |
Tuesday, November 26, 2013 8:52AM - 9:05AM |
M8.00005: Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier-Stokes equation Maciej Balajewicz, Earl Dowell, Bernd Noack We generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier-Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier-Stokes equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term--contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with three test cases: two-dimensional flow past a stationary cylinder, two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier-Stokes constraints, e.g. Reynolds equations, can be achieved in straightforward variation of the presented results. [Preview Abstract] |
Tuesday, November 26, 2013 9:05AM - 9:18AM |
M8.00006: Stratified Euler flows in a channel and conservation laws Giovanni Ortenzi, Roberto Camassa, Shengqian Chen, Gregorio Falqui, Marco Pedroni We analyze the consequences of density stratification for the motion of an incompressible two dimensional Euler fluid confined to move under gravity between rigid lids and otherwise free to move along horizontal directions. The conserved quantity related to the horizontal translation invariance (impulse) does not coincide with the horizontal momentum, which is not conserved for generic initial conditions. The classical form of the impulse is given by Benjamin (1986) and it is affected by the boundary limiting values of physical fields such as density or density weighted vorticity. Therefore, the intersection between isopycnals and boundaries could affect the conservation laws of the system even if symmetries are not broken. While the failure to conserve quantities is naturally implied by geometrical changes of the fluid-domain boundary, regardless of fluid stratification, in this case the fluid domain maintains invariance under symmetry and the relevant cause of the failure is the connection properties of pycnoclines. Some results on this topological (non)conservation are exposed in the examples of impulse and total circulation. [Preview Abstract] |
Tuesday, November 26, 2013 9:18AM - 9:31AM |
M8.00007: Shock Waves in Dispersive Eulerian Fluids Mark Hoefer Shock waves in dispersive media with negligible dissipation are studied in the context of the compressible Euler equations with weak dispersion. Example fluids of this type include superfluids, shallow water flows, and ion-acoustic plasma. A characterization of one-dimensional dispersive shock waves (DSWs) will be presented. DSWs are sharply distinct from classical, dissipatively regularized shock waves both in terms of physical significance and mathematical description. Drawing on terminology from classical gas dynamics, jump conditions (shock loci and speeds) and admissibility criteria for the long time evolution of step-like initial data will be presented utilizing a nonlinear wave averaging technique. While entropy conditions determine admissible, dissipatively regularized shock waves, conservative, dispersive systems are time reversible and can exhibit positive or negative dispersion. The universal structure of weak shocks will be shown to depend solely upon the dispersion sign and pressure law. Large amplitude DSWs can exhibit novel effects such as cavitation and ``implosion'' yielding internal, multi-phase dynamics. [Preview Abstract] |
Tuesday, November 26, 2013 9:31AM - 9:44AM |
M8.00008: Wavelet-based Simulations of Unsteady Compressible Flows Eric Brown-Dymkoski, Oleg V. Vasilyev In this talk we present an extension of adaptive wavelet-based methodologies for unsteady compressible fluid simulations. This approach takes advantage of spatio-temporal intermittency of unsteady flows through a dynamically adaptive grid. It is built upon the adaptive wavelet collocation method, which allows for efficient mesh refinement at each time step with the error well-bounded by a prescribed threshold. Several benchmark simulations have been performed for compressible subsonic flows, including turbulent channel flow and flow around a bluff body. Atypically for channel flow simulations, a dyadic adaptive grid was used instead of the usual stretched mesh. While the external flow simulations are at a subcritical Reynolds number, spanwise instabilities create vortex loops that lead to a complex, three-dimensional wake. This work provides the basis for continuing development of adaptive, compressible turbulence models, including wavelet-based adaptive LES where the filter threshold is dynamically prescribed by global or local criteria. [Preview Abstract] |
Tuesday, November 26, 2013 9:44AM - 9:57AM |
M8.00009: Non-uniqueness of solutions in asymptotically self-similar shock reflections Sebastien SM. Lau-Chapdelaine, Matei I. Radulescu The present study numerically addresses the self-similarity of an unsteady shock reflection on an inclined wedge. The wedge-tip conditions are modified, allowing for a finite radius of curvature, and the following shock reflection configuration is observed at large distances from the tip. It is found that the type of shock reflection observed far from the corner, namely regular or Mach reflection, depends intimately on the wedge tip geometry, as the flow ``remembers" how it was started. Substantial differences from a sharp-tipped wedge (without curvature) were found. For example, a shock with incident Mach number $M=6.6$ and an isentropic exponent $\gamma =1.2$ reflecting over wedge with a sharp tip will result in a Mach reflection when a wedge angle of $44^\circ$ is used, while a $45^\circ$ wedge will result in a regular reflection. This transition angle increases to between $57^\circ$ and $58^\circ$ when a wedge with a concave, curved tip is introduced. A vanishing length scale is introduced with the curved tip in a way which is similar to those of viscous and relaxation effects. While the length scale only dominates the solution at early times, this study shows that its effects play a dominant role in determining the asymptotic pseudo-steady shock reflection configuration. [Preview Abstract] |
Tuesday, November 26, 2013 9:57AM - 10:10AM |
M8.00010: Single series skewness representation for passive scalar advection in laminar pipe and channel flow Richard M. McLaughlin, Francesca Bernardi, Roberto Camassa, Keith Mertens In this talk, we present an exact single series representation for scalar skewness time evolution. Prior studies have naturally derived multiple nested Fourier series solutions which suffer from slow convergence and cloud physical interpretation. Judicious change of variables and complex residue theory lead to single series representation formulae for the moments along streamwise slices from which quantities such as variance and skewness can be reconstructed. Instantaneous symmetry breaking gives rise to non-zero skewness on transient time scales arising as a non-trivial competition between advection and diffusion which is captured by the simplified formulae. Small and long time asymptotics will be discussed for the first three moments in both channel and pipe geometries in steady Poiseuille flow, and nontrivial Peclet dependence in the skewness along slices will be examined. [Preview Abstract] |
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