Thermal Cooling Enhancements in a Heated Channel Using Flow-Induced Motion

The paper presents the comparative study of the vortex-induced cooling of a heated channel for the four different cross-sections of the rigid cylinder, i.e., circular, square, semi-circular, and triangular, with or without the rigid/flexible splitter plate at the Reynolds number (based on the hydraulic diameter) of 200. The study presents a comprehensive analysis of the flow and thermal performance for all the cases. For flexible plate cases, a partitioned approach is invoked to solve the coupled fluid-structure-convection problem. The simulations show the reduction in the thermal boundary layer thickness at the locations of the vortices resulting in the improved Nusselt number. Further, the thin plate's flow-induced motion significantly increases the vorticity field inside the channel, resulting in improved mixing and cooling. It is observed that the plate-motion amplitude is maximum when the plate is attached to the cylinder with the triangular cross-section. The power requirement analysis shows that the flexible plate reduces the power required to pump the channel's cold fluid. Thus, based on the observations of the present study, the authors recommend using the flexible plate attached to the cylinder for improved convective cooling.

Local Two-Dimensional Splitting Schemes for 3D Suspended Matter Transport Problem Parallel Solution

A 3D model of suspended matter transport in coastal marine systems is considered, which takes into account many factors, including the hydraulic size or the rate of particle deposition, the propagation of suspended matter, sedimentation, the intensity of distribution of suspended matter sources, etc. The difference operators of diffusion transport in the horizontal and vertical directions for this problem have significantly different characteristic spatiotemporal scales of processes, as well as spectra. With typical sampling, applied to shallow-water systems in the South of Russia (the Sea of Azov, the Tsimlyansk reservoir), the steps in horizontal directions are 200-1000 meters, the coefficients of turbulent exchange (turbulent diffusion) are (103-104) m2/sec; in the vertical direction - - - steps of 0.1 m-1 m, and the coefficients of microturbulent exchange in the vertical — (0.1-1) m2/sec. If we focus on the use of explicit locally twodimensional - - - locally one-dimensional splitting schemes, then the permissible values of the time step for a two-dimensional problem will be about 10-100 seconds, and for a one-dimensional problem in the vertical direction - - - 0.1 – 1 sec. This motivates us to construct an additive locally-two-dimensional-locallyonedimensional splitting scheme in geometric directions. The paper describes a parallel algorithm that uses both explicit and implicit schemes to approximate the two-dimensional diffusion-convection problem in horizontal directions and the one-dimensional diffusion-convection problem in the vertical direction. The two-dimensional implicit diffusion-convection problem in horizontal directions is numerically solved by the adaptive alternating-triangular method. The numerical implementation of the one-dimensional diffusion-convection problem in the vertical direction is carried out by a sequential run-through method for a series of independent one-dimensional three-point problems in the vertical direction on a given layer. To increase the efficiency of parallel calculations, the decomposition of the calculated spatial grid and all grid data in one or two spatial directions - in horizontal directions-is also performed. The obtained algorithms are compared taking into account the permissible values of time steps and the actual time spent on performing calculations and exchanging information on each time layer.

Discontinuous Galerkin Isogeometric Analysis of Convection Problem on Surface

The objective of this work is to study finite element methods for approximating the solution of convection equations on surfaces embedded in R3. We propose the discontinuous Galerkin (DG) isogeometric analysis(IgA) formulation to solve convection problems on implicitly defined surfaces. Three numerical experiments shows that the numerical scheme converges with the optimal convergence order.