Showing papers by "Paul Fischer published in 2009"

Forces on a finite-sized particle located close to a wall in a linear shear flow

Abstract: To understand and better model the hydrodynamic force acting on a finite-sized particle moving in a wall-bounded linear shear flow, here we consider the two limiting cases of (a) a rigid stationary spherical particle in a linear wall-bounded shear flow and (b) a rigid spherical particle in rectilinear motion parallel to a wall in a quiescent ambient flow. In the present computations, the particle Reynolds number ranges from 2 to 250 at separation distances to the wall from nearly sitting on the wall to far away from the wall. First we characterize the structure of the wake for a stationary particle in a linear shear flow and compare with those for a particle moving parallel to a wall in a quiescent ambient [see L. Zeng, S. Balachandar, and P. Fischer, J. Fluid Mech. 536, 1 (2005)]. For both these cases we present drag and lift results and obtain composite drag and lift correlations that are valid for a wide range of Re and distance from the wall. These correlations have been developed to be consistent with all available low Reynolds number theories and approach the appropriate uniform flow results at large distance from the wall. Particular attention is paid to the case of particle in contact with the wall and the computational results are compared with those from experiments.

Stochastic Finite-Element Approach in Nuclear Reactor Uncertainty Quantification

Abstract: Polynomial approximations are arguably the most common representation of uncertainty [2]. Such approximations are computed by either local Taylor expansions, e.g., first-order derivatives, or by fitting the approximation at well-chosen sample points, e.g., collocation or surface response methods [4,6]. In this work we present a hybrid approach, where the polynomial approximation is computed based on function and derivative information at sample points in the uncertainty region. This approach is shown to efficiently approximate both the distribution and the major global sensitivity effects of the target functional.

Proposed Experiment for Validation of CFD Methods for Advanced SFR Design: Upper Plenum Thermal Striping and Stratification

Abstract: In response to the goals outlined by the U.S. Department of Energy’s Advanced Fuel Cycle Initiative, an effort is underway to develop an integrated multi-physics, multi-resolution thermal-hydraulic simulation tool package for the evaluation of nuclear power plant design and safety. As part of this effort, initial guidance has been proposed for the development of experiments to supply validation data sets for the CFD-based thermo-fluid simulation capability. To demonstrate that the proposed data requirements can be achieved using current generation measurement methods and to refine correlation and data comparison methods suitable for very large data sets, an initial experiment focused on turbulent mixing in the upper plenum of an advanced sodium fast reactor has been proposed. Prior validation efforts to support the use of one-dimensional lumped parameter models in the analysis of reactor safety performance relied primarily on data from carefully scaled integral system experiments to validate and tune correlations used to represent the physics associated with a particular transient in a particular reactor design. Unlike the correlation-based lumped parameter codes, computational fluid dynamics simulations reduce the reliance on experimentally derived correlations to the prediction of local turbulence effects rather the prediction of integral quantities like pressure drop and heat transfer coefficients. As a consequence, simpler separate effects experiments, which capture the turbulence effects but not necessarily the integral effects within a specific component of a system, can be utilized as the primary validation basis for the CFD codes. However, while the need for large carefully scaled integral experiments is reduced, the high spatial and temporal resolution of these codes requires that experimental data be collected at fine spatial and temporal resolutions. An initial series of simulations has been completed to support the development of the proposed experimental facility using air as a surrogate for the sodium coolant. Design options considered in RANS simulations using the commercial CFD code Star-CCM+ include mixing facility dimensions, the number of inlet jets to be included and outlet position. The use of RANS simulations is supported by an initial benchmarking comparison with predictions from the spectral element large eddy simulation code Nek5000 for the nominal experimental geometry.© 2009 ASME

Instabilities in free-surface Hartmann flow at low magnetic Prandtl numbers

Abstract: We study the linear stability of the flow of a viscous electrically conducting capillary fluid on a planar fixed plate in the presence of gravity and a uniform magnetic field, assuming that the plate is either a perfect electrical insulator or a perfect conductor. We first confirm that the Squire transformation for magnetohydrodynamics is compatible with the stress and insulating boundary conditions at the free surface but argue that unless the flow is driven at fixed Galilei and capillary numbers, respectively parameterizing gravity and surface tension, the critical mode is not necessarily two-dimensional. We then investigate numerically how a flow-normal magnetic field and the associated Hartmann steady state affect the soft and hard instability modes of free-surface flow, working in the low-magnetic-Prandtl-number regime of conducting laboratory fluids (Pm ≤ 10−4). Because it is a critical-layer instability (moderately modified by the presence of the free surface), the hard mode exhibits similar behaviour as the even unstable mode in channel Hartmann flow, in terms of both the weak influence of Pm on its neutral-stability curve and the dependence of its critical Reynolds number Rec on the Hartmann number Ha. In contrast, the structure of the soft mode's growth-rate contours in the (Re, α) plane, where α is the wavenumber, differs markedly between problems with small, but non-zero, Pm and their counterparts in the inductionless limit, Pm ↘ 0. As derived from large-wavelength approximations and confirmed numerically, the soft mode's critical Reynolds number grows exponentially with Ha in inductionless problems. However, when Pm is non-zero the Lorentz force originating from the steady-state current leads to a modification of Rec(Ha) to either a sub-linearly increasing or a decreasing function of Ha, respectively for problems with insulating or perfectly conducting walls. In insulating-wall problems we also observe pairs of counter-propagating Alfven waves, the upstream-propagating wave undergoing an instability driven by energy transferred from the steady-state shear to both of the velocity and magnetic degrees of freedom. Movies are available with the online version of the paper.

DNS of three-dimensional separation in turbulent diffuser flows

Abstract: The spectral-element method (SEM), is a high-order numerical method with the ability to accurately simulate fluid flows in complex geometries. SEM has opened the possibility to study – in great detail – fluid phenomena known to be very sensitive to discretization errors, e.g. flows undergoing pressureinduced separation [4]. Recently, Cherry et al. [1] performed experiments using Magnetic Resonance Velocimetry (MRV) of turbulent diffuser flow exhibiting unsteady three-dimensional separation at Re = 10 000 based on bulk velocity and height of the inflow duct. Two geometries with different opening angles were investigated and it was found that the flow was extremely sensitive to slight changes in the geometrical setup. To understand this sensitivity and to analyze its causes, we present a direct numerical simulation (DNS) of one of these cases (denoted by “Diffuser 1“ in [1]) by means of the SEM. Here, we focus on careful analysis of mean flow results in order to assess the quality of the simulation data.

Large-scale electromagnetic modelings based on high-order methods: Nanoscience applications

Abstract: This paper presents large-scale computations and theoretical or computational aspects of the spectral element methods for solving Maxwell's equations that have potential applications in nanoscience for surface-enhanced Raman scattering (SERS) and solar cell devices. We study the surface-enhanced electromagnetic fields near the surface of metallic nanoparticles using spectral element discontinuous Galerkin method. We solve Maxwell's equations in time-domain and provide accuracy and efficiency of our method compared to the conventional finite difference method. We demonstrate light transmission properties for nanoslab and nanoslits, and time-averaged electric fields over the cross sections of nanoholes in a hexagonal array.