Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session GK: Free Surface Flows IV |
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Chair: A. Techet, Massachusetts Institute of Technology Room: Salt Palace Convention Center 250 E |
Monday, November 19, 2007 10:30AM - 10:43AM |
GK.00001: Imaging across the interface of small-scale breaking waves Alexandra H. Techet, Jesse L. Belden Flow characteristics on both the air and water side of small scale spilling and plunging waves are investigated using fully time-resolved particle image velocimetry (PIV). PIV at 1000 frames per second ($fps$) is used to capture the flow field in both the air and water for waves generated by shoaling. Reynolds number of the waves is on the order of $Re = 9x10^4$ to $2x10^6$, where $Re = \frac{\rho \sqrt{g \lambda^3}}{\mu}$, $\rho$ is fluid density, $\mu$ is fluid dynamic viscosity, $g$ is gravity, and $\lambda$ is the characteristic wavelength of the breaking wave before breaking. Isopropyl alcohol is mixed with the distilled water in the tank to reduce surface tension and thus achieve plunging breakers on this scale. Flow in the water is seeded using conventional silver-coated hollow glass spheres, whereas the quiescent air side (i.e. no wind) is seeded using micro-air balloons with high stokes drag and thus long settling times. Imaging of both the air and water are performed simultaneously and advanced image processing is performed to determine the water surface location and to avoid surface tracking during PIV processing. Repeatable, coherent vortical structures are revealed on the air-side of the waves and are considered mechanisms for energy transfer across the interface. [Preview Abstract] |
Monday, November 19, 2007 10:43AM - 10:56AM |
GK.00002: Numerical simulations of viscous Faraday waves Nicholas O'Connor, Edgar Knobloch, Paul Fischer, Mark Paul We conduct a numerical exploration of the nonlinear dynamics of surface gravity-capillary waves in a fluid layer oscillating vertically in a gravitational field (i.e. the Faraday system). A number of intriguing experimental observations still cannot be explained by available theory, although progress has been made by incorporating the complex interplay between streaming flows generated by oscillating boundary layers and the oscillations that are responsible for them. We perform numerical simulations of the time-dependent incompressible Navier-Stokes equations describing the free surface flow that includes surface tension and the complex moving fluid interface. The numerical approach uses an arbitrary-Lagrangian-Eulerian formulation of a parallel spectral element \newline solver. We explore a two-dimensional fluid layer with periodic and finite lateral boundary conditions, and use the results to quantify the resulting streaming flows which we relate to the overall wave dynamics and available theoretical predictions. [Preview Abstract] |
Monday, November 19, 2007 10:56AM - 11:09AM |
GK.00003: Progress on using a Lattice Boltzmann solver for water wave predictions Jannette Frandsen This research is focused on numerical model development to predict free-surface water wave behavior. The present numerical model is based on a Lattice Boltzmann (LB) formulation. The LB method simulates fluid flow by tracking particle distributions in a Lagrangian manner. We consider a model in which the collision processes are simplified to a single-time relaxation form. It is referred to as the Lattice Bhatnagar-Gross-Krook (LBGK) scheme. Further, the present model discretizes the nonlinear shallow water equations in rotational flows on uniform lattices. It is assumed that the waves do not overturn. It is notable that the LBGK model does not include the traditional boundary conditions at the free surface. Instead, the non-linear free-surface dynamics are accounted for through the non-equilibrium particle distribution function. In this contribution, we report on our recent experiences in which we have compared a standard LBGK solver and a high-order Finite Difference (FD) LB scheme. We shall demonstrate that various nonlinear free-surface flows are captured satisfactory. We recommend a second-order FD LB scheme to form a basis for free- surface water wave developments. [Preview Abstract] |
Monday, November 19, 2007 11:09AM - 11:22AM |
GK.00004: A study of the Nusselt-Rayleigh and Sherwood-Rayleigh scaling laws for water undergoing free-surface natural convection S.M. Bower, J.R. Saylor An experimental study is presented of free-surface natural convection, with a focus on the $Nu-Ra$ relationship. This relationship is typically studied using the traditional Rayleigh-Benard convection setup, where a fluid layer is bounded above and below by solid plates of different temperatures. Power laws of the form $Nu = A Ra^{n}$ are typically used in these studies to correlate the data, giving exponents that are usually close to $n = 1/3$. The experimental data obtained in this study yields values of $n$ that do not deviate significantly from 1/3 for $10^{7} < Ra < 10^{11}$. This result is surprising in that the effect of the free-surface boundary condition on $n$ is quite small when compared to the solid plate case. However, the prefactor $A$ in the $Nu-Ra$ relationship is significantly smaller than for the solid plate case. The Sherwood number, $Sh$ was also related to $Ra$ via a power law of the form $Sh = B Ra^{m}$, where Sh is the dimensionless mass transfer coefficient for evaporation. The exponent $m$ differed from that obtained by prior researchers. However, the prior research on evaporation that utilizes this scaling law is considerably smaller than for the heat transfer case. The effect of the tank aspect ratio on both scaling laws is also discussed. [Preview Abstract] |
Monday, November 19, 2007 11:22AM - 11:35AM |
GK.00005: A Numerical Study of Surface Renewal Statistics at a Free Surface Alireza Kermani, Lian Shen In order to investigate gas-liquid interfacial transport, direct numerical simulation of Navier-Stokes equations for the fluid motions of a turbulent open-channel flow and of the convective-diffusion equation for the transport of passive scalars has been performed. Surface renewal, the replacement of fluid close to the surface with bulk flow, is the most dominant interfacial transfer process. Correlations of scalar flux with various stages of surface renewal have been identified. Surface age of interfacial fluid elements, which is the interval of surface renewal encountered by surface elements, has been quantified with highly accurate Lagrangian and Eulerian methods. Based on extensive simulation data, we obtain valuable statistics of the surface renewal process. With the probability distribution function of surface ages obtained, various theoretical results, including exponential, Gamma, normal, and lognormal distributions have been examined. It has been concluded that surface renewal statistics can be best described by the lognormal distribution, which may be used as a basis for model development for interfacial scalar transfer. [Preview Abstract] |
Monday, November 19, 2007 11:35AM - 11:48AM |
GK.00006: Explosion in a kitchen sink - a theory of circular hydraulic jump and its gasdynamic analogue Aslan Kasimov We propose a theory of a stationary circular hydraulic jump that is based on the shallow water equations and a careful treatment of the far-field boundary conditions. We show that a unique solution for the radius of the hydraulic jump is obtained by matching the jump conditions and the critical flow downstream of the jump. A gasdynamic analogue of the hydraulic jump is pointed out and discussed. [Preview Abstract] |
Monday, November 19, 2007 11:48AM - 12:01PM |
GK.00007: Flow transition in surface switching of rotating fluid Yuji Tasaka, Kentaro Ito, Makoto Iima This study aims to investigate the flow transition appearing in a process of ``surface switching.'' In a flow driven by a rotating disk in a cylindrical open vessel, the free surface changes irregularly its shape from axisymmetric to nonaxisymmetric and v.v. while repeating its up-and-down motion of the center part of the free surface (so-called ``surface switching'' [Suzuki {\it et al.}, {\it Phys. Fluids}, {\bf 18} (2006), 101701(1-4)]). The instantaneous velocity profile of the flow along the radial direction was measured by ultrasonic velocity profiling, UVP, to investigate the flow transition quantitatively. It is revealed that the turbulent intensity shows a transition at the same Reynolds number as that for the surface switching. Also, the detailed analysis of the turbulent intensity and the power spectrum of velocity profile shows that the fluid-air interface becomes unstable at a smaller Reynolds number than the critical Reynolds number for the surface switching. By decreasing Reynolds number after the onset of the switching, a hysteresis phenomenon in the switching is observed; two different states stably exist at the same Reynolds number. [Preview Abstract] |
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