Research on Particle Collision Forward Search Algorithm and the CFD-DEM Variable Time Step Coupling Calculation Method

In CFD-DEM coupling calculations, an excessively large selection for particle calculation time step affects the calculation accuracy, and an extremely small selection affects the calculation efficiency. A search ball is constructed by taking each target particle as the center particle with the fastest displacement in the calculation domain. Subsequently, the particles that may collide are screened to establish a search list, and a forward search method is used to determine particle collisions. Finally, a particle calculation time step is proposed. The improved DEM method, which automatically adjusts the collision time, resolves the contradiction between particle calculation time step selection, accuracy, and efficiency. The relative error between the numerical simulation results of particle collision and the theoretical solution was less than 3%. The three calculation time steps selected in this study can guarantee excellent calculation accuracy and efficiency. For multi-particle and fluid coupling simulations, the traditional CFD-DEM method selects 10-7s or less in the calculation time step to obtain an accurate solution. The method proposed in this paper selects 10-5s to obtain an accurate solution, which increased the calculation efficiency by 19.8%.

Parametric Study of the Solidification Process Between Vertical Parallel Plates of a Storage System

A conduction model is developed to describe the phase change between the plates of a thermal storage system. The diffusion equation and the associated boundary, initial, and interface conditions are approximated numerically by finite differences and implicit approach with variable time-step. The developed computational code is validated against data and good agreement was found. It is found that the reduction of the surface temperature of the cold plate increases the interface advance rate and reduces the full solidification time. Opposite effects are found due to the increase of the spacing between plates. Further, fractions of Al2O3 nanoparticles are mixed with the phase change material (PCM) to enhance the thermal conductivity of the PCM. For 7% volumetric fraction of Al2O3, the full solidification time and latent heat values decreased by 25.5% and 4.5%, respectively.

Modeling Arbitrarily Shaped Liquid Pipelines Using a Segmented Transmission Line Model

This paper presents a new method of simulating the dynamic flow and pressure of laminar liquid flow through pipes of arbitrarily changing cross section. This method uses a segmented model based on the previously presented tapered transmission line model (TLM). This new method is computationally efficient and has comparable accuracy to previous methods such as the method of characteristics (MOC), but allow for more flexibility in solution time-step (such as accommodating variable time-step solvers), which is required if the rest of the system model has stiff equations. For the sample geometry presented, the new model calculates the dynamic response an order of magnitude faster than the previous method of characteristics solution, with minimal loss of accuracy.

One Phase Moving Boundary Problem

In this paper we introduced a variable time step method to obtain interface to moving boundary problem for Slab and Sphere. We present the basic difficulty, apart from the need to find the moving boundary, that there is no domain for the space variable. This difficulty is handled by the age old principles of basic mathematics. Naturally, giving symbolic names to the unknowns develop equations involving them and solve it using the conditions of the problem. High order accurate initial time step sizes for given space step size are obtained with the help of Green’s theorem. The Subsequent time steps are obtained by an iterative scheme. This variable time step method handles Dirichlet’s problem of freezing or melting of a Slab and spherical droplet.