Three-dimensional flow in cavity with elevated helicity driven by parallel walls

The proposed flow in a 3-D cubic cavity is driven by its parallel walls moving in perpendicular directions to create a genuinely three-dimensional highly separated vortical flow yet having simple single-block cubical geometry of computational domain. The elevated level of helicity is caused by motion of a wall in the direction of axis of primary vortex created by a parallel wall. The velocity vector field is obtained numerically by using second-order upwind scheme and 200^3 grid. Helicity, magnitude of normalized helicity and kinematic vorticity number are evaluated for Reynolds numbers ranging from 100 to 1000. Formation of two primary vortices with their axis oriented perpendicularly and patterns of secondary vortices are discussed. Computational results are compared to the well-known 3-D recirculating cavity flow case where the lid moves in the direction parallel to the cavity side walls. Also results are compared to the diagonally top-driven cavity and to cavity flow driven by moving top and side walls. The streamlines for the proposed flow show that the particles emerging from top and bottom of cavity do mix well. Quantitative evaluation of mixing of two fluids in the proposed cavity flow confirms that the mixing occurs faster than in the benchmark case.Comment: 38 pages, 13 figures The revised includes quantification of mixing rate; numerical modeling of the transient version.The revised version has four substantially improved figures and three new figures; number of literature references increased from 26 to 4

Mixing in 3-D Cavity by Moving Cavity Walls

The mixing in three-dimensional enclosures is investigated numerically using flow in cubical cavity as a geometrically simple model of various natural and engineering flows. The mixing rate is evaluated for up to the value of Reynolds number Re=2000 for several representative scenarios of moving cavity walls: perpendicular motion of the parallel cavity walls (Case A), motion of a wall in its plane along its diagonal (Case B1), motion of two perpendicular walls outward the common edge (Case B2), and the parallel cavity walls in motion either in parallel directions (Case B3) or in opposite directions (Case B4). The mixing rates are compared to the well-known benchmark case in which one cavity wall moves along its edge (Case C). The intensity of mixing for the considered cases was evaluated for (i) mixing in developing cavity flow initially at rest, which is started by the impulsive motion of cavity wall(s), and (ii) mixing in the developed cavity flow. For both cases, the initial interface of the two mixing fluids is a horizontal plane located at the middle of the cavity. The mixing rates are ranked from fastest to slowest for twenty time units of flow mixing. The pure convection mixing is modeled as a limit case to reveal convective mechanism of mixing. Mixing of fluids with different densities is modeled to show the advantage in terms of mixing rate of genuinely 3-D cases A and B1. Grid convergence study and comparison with published numerical solutions for 3-D and 2-D cavity flows are presented. The effects of three-dimensionality of cavity flow on the mixing rate are discussed.Comment: 52 pages, 17 figures, 4 Tables, 36 Ref

Parallelization of the Pipelined Thomas Algorithm

In this study the following questions are addressed. Is it possible to improve the parallelization efficiency of the Thomas algorithm? How should the Thomas algorithm be formulated in order to get solved lines that are used as data for other computational tasks while processors are idle? To answer these questions, two-step pipelined algorithms (PAs) are introduced formally. It is shown that the idle processor time is invariant with respect to the order of backward and forward steps in PAs starting from one outermost processor. The advantage of PAs starting from two outermost processors is small. Versions of the pipelined Thomas algorithms considered here fall into the category of PAs. These results show that the parallelization efficiency of the Thomas algorithm cannot be improved directly. However, the processor idle time can be used if some data has been computed by the time processors become idle. To achieve this goal the Immediate Backward pipelined Thomas Algorithm (IB-PTA) is developed in this article. The backward step is computed immediately after the forward step has been completed for the first portion of lines. This enables the completion of the Thomas algorithm for some of these lines before processors become idle. An algorithm for generating a static processor schedule recursively is developed. This schedule is used to switch between forward and backward computations and to control communications between processors. The advantage of the IB-PTA over the basic PTA is the presence of solved lines, which are available for other computations, by the time processors become idle

Vorticity Confinement and TVD Applied to Wing Tip Vortices for Accurate Drag Prediction

The vorticity confinement (VC) method was used with total variation diminishing (TVD) schemes to reduce possible over-confinement and applied to tip vortices shed by edges of wings in order to predict induced drag using far-field integration. The optimal VC parameter was determined first by application to 2-D vortices and then to tip vortices shed by a 3-D wing. The 3-D inviscid simulations were post-processed using the wake-integral technique to determine lift-induced drag force. Dependence of the VC parameter on the flight Mach number and the angle of attack was evaluated. Grid convergence studies were conducted for 2-D vortices and for induced drag generated by 3-D wing. VC was used with TVD minmod and differentiable flux limiters to evaluate their effect on the VC method. Finally, the VC approach was combined with the Reynolds stress equation turbulence model, and the results were compared to experimental data of tip vortex evolution.Comment: 40 pages, 12 Figure

Coupled Continuum and Molecular Model of Flow through Fibrous Filter

A coupled approach combining the continuum boundary singularity method (BSM) and the molecular direct simulation Monte Carlo (DSMC) is developed and validated using Taylor-Couette flow and the flow about a single fiber confined between two parallel walls. In the proposed approach, the DSMC is applied to an annular region enclosing the fiber and the BSM is employed in the entire flow domain. The parameters used in the DSMC and the coupling procedure, such as the number of simulated particles, the cell size, and the size of the coupling zone are determined by inspecting the accuracy of pressure drop obtained for the range of Knudsen numbers between zero and unity. The developed approach is used to study flowfield of fibrous filtration flows. It is observed that in the partial-slip flow regime, Kn ⩽ 0.25, the results obtained by the proposed coupled BSM-DSMC method match the solution by BSM combined with the heuristic partial-slip boundary conditions. For transition molecular-to-continuum Knudsen numbers, 0.25 \u3c Kn ⩽ 1, the difference in pressure drop and velocity between these two approaches is significant. This difference increases with the Knudsen number that confirms the usefulness of coupled continuum and molecular methods in numerical modeling of transition low Reynolds number flows in fibrous filters

Modeling of Sedimentation of Particles near Corrugated Surface by Boundary Singularity Method

The velocity and trajectory of particle moving along the corrugated surface under action of gravity is obtained by meshless Boundary Singularity Method (BSM). This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with no-slip boundary conditions are solved using the Green function for Stokeslets. In the present study, the velocity of a moving particle is not known and becomes a part of the BSM solution. This requires an adjustment of the matrix of BSM linear system to include the unknown particle velocity and incorporate in the BSM the balance of hydrodynamic and gravity forces acting on the particle. Comparison has been made to prior published analytical and experimental results to verify the effectiveness of this methodology to predict the trajectory of particle including its deviation from vertical trajectory and select the optimal set of computational parameters. The developed BSM methodology is applied to sedimentation of two spherical particles in proximity for which the analytical solution is not feasible.Comment: 14 pages, 6 figure

Modeling of Chemical Vapor Infiltration Using Boundary Singularity Method

Boundary Singularity Method (BSM) was used to model Chemical Vapor Infiltration (CVI) in a fibrous preform. Straight, long fibers of varying cross-sectional geometry, representing fibers of a preform, were placed within a domain of a pre-determined size. The preparation of dense fiber-reinforced Silicon-Carbon (SiC) composites was considered as a representative of CVI methodology, where methyl-trichlorosilane (MTS) was used as both the silicon and carbon donor for the silicon carbide matrix. Concentrations of MTS were then set at the domain boundaries, and the domain was gradually infiltrated with MTS as time progressed. The concentration of MTS at the surface of the preform fibers was calculated using the adopted BSM. For quasi-equilibrium considered, the reaction rate at solid surface is equal to the diffusion rate towards the surface. The Robin or third type boundary condition, which is a linear combination of the values of a function and the values of its derivative on the boundary of the domain, are developed and implemented to BSM. From the fibers surface concentrations obtained by BSM, deposition rates were calculated, and the geometry was updated to reflect the fiber growth during the time step, therefore, the fiber size growth and pore filling was modeled over time. The BSM analysis was verified by comparisons to a known analytical solution of concentric cylinders with a concentration set at the outer cylinder and a reaction at the inner. BSM solutions were also compared to experimental data as well as computational results obtained by a Level-Set Method (LSM). Obtained dynamics of pore size and location will help to evaluate quality of material manufactured by CVI. Porosity transients were obtained to show the relation between initial and current porosities as time progresses.Comment: 23 pages, 13 Figure

Predictors of In-School Weapon-Carrying

Delinquent and violent behaviors have become a major concern of parents, teachers, and school administrations across the country as media images of school violence permeate perceptions of school safety. Although national surveys show a slight decline in school delinquency, schools continue to search for ways to improve safety. This investigation seeks to understand the predictors of weapon-use in schools. Literature related to school shootings, disorder, and weapon-carrying as well as various theories, including control, social disorganization, and subculture, guide hypotheses that explore the school characteristics related to in-school weapon-carrying as well as the interaction effects between school and student characteristics. Using a large, national sample, this unprecedented investigation explores whether school characteristics predict weapon-carrying net of individuals' propensity to carry weapons. The study also investigates whether school characteristics condition the relationships between student characteristics and weapon-carrying. Findings indicate that school characteristics, specifically those related to school location and violent environments, are important in explaining recent in-school weapon-carrying even when controlling for past weapon-carrying. Further, results suggest that school-level predictors are more important in explaining student weapon-carrying in urban schools than in non-urban schools. Implications and directions for future research will be discussed

Teen Court: Does it Reduce Recidivism?

Teen Court is a diversion program designed to intercept the process of sending first-time misdemeanor juvenile offenders though the traditional juvenile justice system. Despite its widespread popularity throughout the United States, very little research has been conducted on Teen Court's effectiveness at reducing recidivism. Those studies that do exist lack rigorous methodologies. The present evaluation uses data from a Teen Court in Maryland and a comparable group of juvenile offenders who went through the Department of Juvenile Services. A logistic regression indicates that Teen Court is positively related to recidivism. Conclusions and recommendations are discussed

Link-wise Artificial Compressibility Method

The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences (at least in the present paper), at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Importantly, with an efficient implementation, this algorithm may be one of the few which is compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.Comment: 62 pages, 20 figure