In this paper, a recently developed direct numerical simulation technique, the Finite Element Fictitious Boundary Method (FEM-FBM) [K. Walayat et al., “An efficient multi-grid finite element fictitious boundary method for particulate flows with thermal convection,” Int. J. Heat Mass Transfer 126, 452–465 (2018)], is used to simulate sedimentation of an elliptic particle with thermal convection. The momentum and temperature flow fields are coupled with the aid of Boussinesq approximation. The thermal and momentum interactions between solid and fluid phases are handled by using the fictitious boundary method (FBM). The continuity, momentum, and energy equations are solved on a fixed Eulerian mesh which is independent of flow features by using a multi-grid finite element scheme. Two validation tests are conducted to show the accuracy of the present method, and then the effects of thermal properties of fluid on the sedimentation of an elliptic particle are studied. It is demonstrated that the dynamics of hot elliptic particle sedimentation depend on the thermal diffusivity and thermal expansion of the fluid. A comparative study of the forces and torque acting on the hot, cold, and isothermal particle is reported. Moreover, different sedimentation modes of hot and cold elliptic particles are identified in an infinitely long channel. The mechanism of transitions of particle settling modes from tumbling to inclined and then to the horizontal mode is discovered. Also, we discovered a new sedimentation mode of the hot elliptic particle in cold fluid, i.e., the vertical mode. Furthermore, buoyancy effects for the catalyst particle are studied at different initial orientations.
This paper presents the stationary Bingham fluid flow simulations past a circular cylinder placed in a channel. The governing equations of motion are discretized using the mixed finite element method. The biquadratic element Q 2 is used to approximate the velocity space and P 1 disc for the pressure space. This LBB-stable finite element pair Q 2 =P disc 1 leads to an accuracy of third and second order in L 2-norm for velocity and pressure approximations, respectively. The discrete version of the nonlinear system is linearized by the Newton's method, and the linear subproblems as an inner loop are coped with UMFPACK solver. Code validation and grid independence study is also presented to confirm the reliability of the results. Simulations are carried out for various values of dimensionless Bingham number Bn, and its impact is investigated with great detail by demonstrating the velocity, viscosity and pressure contours. The benchmark quantities like drag coefficient (C D) and lift coefficient (C L) are also discussed graphically and quantitatively. Moreover, two different locations of the circular cylinder are considered for the analysis of hydrodynamic forces.
The present work is concerned with a comprehensive analysis of hydrodynamic forces, under MHD and forced convection thermal flow over a heated cylinder in presence of insulated plates installed at walls. The magnetic field is imposed in the transverse direction of flow. The Galerkin finite element (GFE) scheme has been used to discretize the two-dimensional system of nonlinear partial different equations. The study is executed for the varying range of flow behavior index n from 0.4 to 1.6, Hartmann number Ha from 0 to 100, Reynolds number Re from 10 to 50, Grashof number Gr from 1 to 10, thickness ratio e from 0.5 to 1.0, and Prandtl number Pr from 1 to 10, respectively. A coarse hybrid computational grid is developed, and further refinement is carried out for obtaining the highly accurate solution. The optimum case selection is based on flow patterns, drag and lift coefficients, and pressure drop reduction against cylinder thickness ratios and average Nusselt numbers. Drag coefficient increases with an increase in thickness ratio e . The drag force reduction for e = 0.5 and e = 0.75 is also observed for a range of the power law index as compared with e = 1.0 cylinder. Maximum pressure drop over the back and front points of cylinder is reported at Ha = 100 .
In this paper, a direct numerical simulation technique, the Finite Element Fictitious Boundary Method (FBM), is used to simulate fluid–solid two-phase flows of different general shaped particles. The momentum interactions between solid and fluid phases are handled by using the FBM. The continuity and momentum equations are solved on a fixed Eulerian grid that is independent of flow features by using a discrete projection scheme inside a multi-grid finite element approach. A detailed description is presented for the geometric representation and modeling of two-dimensional particles of different general shapes, i.e., circular, elliptical, square, rectangular, triangular, and pentagonal shapes inside the fluid. We discussed the effects of particle shapes and the influences on the settling behavior of the particles. A comparison of the settling trajectories of the particles of the same mass but with different shapes is presented. Moreover, depending upon the particle’s shape, some interesting facts are discovered, which have a great influence on the particles’ trajectory and settling velocity. Some very important correlations between the drag force coefficient and particle’s Reynolds numbers with different density ratios of particles are obtained. Furthermore, we also studied the settling behavior of elliptical and rectangular particles with different axis ratios and a boomerang particle with different concave angles. The authors of the article agree to the retraction of the article effective AUGUST 20, 2021.
We have examined the behavior of solid particles in particulate flows. The interaction of particles with each other and with the fluid is analyzed. Solid particles can move freely through a fixed computational mesh using an Eulerian approach. Fictitious boundary method (FBM) is used for treating the interaction between particles and the fluid. Hydrodynamic forces acting on the particle’s surface are calculated using an explicit volume integral approach. A collision model proposed by Glowinski, Singh, Joseph and coauthors is used to handle particle-wall and particle-particle interactions. The particulate flow is computed using multigrid finite element solver FEATFLOW. Numerical experiments are performed considering two particles falling and colliding and sedimentation of many particles while interacting with each other. Results for these experiments are presented and compared with the reference values. Effects of the particle-particle interaction on the motion of the particles and on the physical behavior of the fluid-particle system has been analyzed.
It has been analyzed that the particle motion inside a vertical channel while passing across diamond shaped obstacles produces severe effects on the fluid. Particle interaction with outer boundary, internal obstacles and with the fluid is inspected. An Eulerian based approach using a computational mesh is used in which solid particles are allowed to move freely in fluid domain. Fluid and particle interaction inside the whole domain is carried using Fictitious boundary method (FBM). A multigrid finite element method combined with the fictitious boundary method (FEM-FBM) is used for the simulation of in-compressible fluid flow along with rigid particle falling and colliding inside a fluid domain. A collision model to treat the Particle-obstacle and particle-wall interactions is used to avoid particle overlapping. The particulate flow is evaluated using an open source multigrid finite element solver FEATFLOW. Numerical investigations are executed in view of different particle positions and different alignment of diamond shaped obstacles. Effects on the movement of the particle and on the interaction of the fluid-particle system due to particle-wall, particle-Obstacle, particle-fluid interactivity has been analyzed.
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