Mohammad Hadi Bordbar

Complex Flow Dynamics in Dense Granular Flows—Part I: Experimentation

By applying a methodology useful for analysis of complex fluids based on a synergistic combination of experiments, computer simulations, and theoretical investigation, a model was built to investigate the fluid dynamics of granular flows in an intermediate regime where both collisional and frictional interactions may affect the flow behavior In Part I, the viscoelastic behavior of nearly identical sized glass balls during a collision have been studied experimentally using a modified Newtons cradle device. Analyzing the results of the measurements, by employing a numerical model based on finite element methods, the viscous damping coefficient was determined for the glass balls. Power law dependence was found for the restitution coefficient on the impact velocity. In order to obtain detailed information about the interparticle interactions in dense granular flows, a simplified model for collisions between particles of a granular material was proposed to be of use in molecular dynamic simulations, discussed in Part II.

Multiscale Numerical Simulation of Radiation Heat Transfer in Participating Media

In this article, a numerical method for the simulation of radiative heat transfer is presented. The multiscale radiative exchange method (MREM) calculates the radiative source terms in a mesh structure that is coarser than the structures that are typically used in computational fluid flow calculations. To consider the effects of smaller scales on the overall predictions of the model, two dimensionless exchange factors are defined. An accurate simulation of self-extinction and rescattering in coarse volume cells is achieved if the exchange factors are used in the radiative energy balance. According to the location and size of each pair of coarse cells, integration elements of different sizes are used for the calculation of exchange factors. Therefore, the MREM takes into account the effects of a wide range of optical scales in its prediction. On the other hand, the MREM considers the radiative interaction between all of the geometric points in a quick and accurate manner. To improve the accuracy and the performance of the model, a mesh size analysis is performed and some sizes for various mesh structures are suggested for use in the MREM calculations. The model is verified by comparing it against some benchmarks. The predictions and computational cost of the method are compared to the results of other numerical methods, and the effects of different spatial scales on the accuracy of the method are addressed.

SIMULATION OF BUBBLE FORMATION AND HEAPING IN A VIBRATING GRANULAR BED

The Eulerian-Eulerian approach is used to simulate flow in a dense granular bed subjected to a slight, vertical, sinusoidal vibration. The bottom of the bed was subjected to a vertical vibration, ASin(ω v t)J 0(k m x), where J represents the profile of the bottom wall and is the first kind of Bessel function. The governing equations of the gas phase and particle phase are described and the results of the model with different vibration frequencies and amplitudes are presented. Bubble formation and upward and downward heaping were observed at different amplitudes and frequencies. The results of the model confirm that there is a change from upward to downward heaps according to the strength of the vibration. In addition, the location of the bubble and the shape of the heaping at the interface of the bed depend on the strength of the vibration and the profile of the bottom of the container.

A Realistic Model for Visco-Elastic Contact Between Spherical Particles

The contact force model is very important to describe the grain collision process accurately. In this research, the linear/nonlinear contact force models and normal coefficient of restitution in different impact velocities has been studied. A new contact force model for describing the normal collision between two visco-elastic spherical particles has been suggested and the ability of this new model in predicting the correct behavior of normal contact has been confirmed. The constitutive equations of this model have been solved numerically and the result shows a better conformity with experimental result reported by Bridge et al. [1] than the previous models, such as the model presented by Brilliantov et al. [2]. By using the suitable finite elements model, the stress and deformation of particles during the collision has been obtained and the result of the finite elements model shows a good conformity with our new suggested contact force model in the case of elastic and visco-elastic contact. The behavior of normal coefficient of restitution in multisize spherical particles in different impact velocities and effect of the size on it has been experimentally studied. In addition to our more suitable contact force model, we achieved some nice conclusions from our experimental data about the loss of energy during the multisize collision and effect of size difference on this loss.© 2006 ASME

Simulation of Radiation Heat Transfer of Three Dimensional Participating Media by Radiative Exchange Method

This paper describes the theoretical bases of the Radiative Exchange Method, a new numerical method for simulating radiation heat transfer. By considering radiative interaction between all points of the geometry and solving the radiation balance equation in a mesh structure coarser than the structure used in computational fluid flow calculation, this method is able to simulate radiative heat transfer in arbitrary 3D space with absorbing, emitting and scattering media surrounded by emitting, absorbing and reflecting surfaces. A new concept is introduced, that of the exchange factors between the different elements that are necessary for completing the radiative balance equation set. Using this method leads to a set of algebraic equations for the radiative outgoing power from each coarse cell being produced and the result of this set of equations was then used to calculate the volumetric radiative source term in the fine cell structure. The formulation of the exchange factor for a three-dimensional state and also a mesh size analysis that was conducted to optimize the accuracy and runtime are presented. The results of this model to simulate typical 3D furnace shape geometry, is verified by comparison with those of other numerical methods.Copyright

Dynamical States of Bubbling in Vertically Vibrated Granular Materials: Part I — Collective Processes; Part II — Theoretical Analysis and Simulations

PART I: Granular materials deform plastically like a solid under weak shear and they flow like a fluid under high shear. These materials exhibit other unusual kinds of behavior, including pattern formation in shaking of granular materials for which the onset characteristics of the various patterns are not well understood. Vertically shaken granular materials undergo a transition to a convective motion which can result in the formation of bubbles. In Part I, a detailed overview is presented of collective processes in gas-particle flows useful for developing a simplified model for molecular dynamic type simulations of dense gas-particle flows. The large eddy simulation method (LES) has been employed for simulating fluid flows through irregular array of particles. The results obtained may lead to scale-dependent closures for quantities such as the drag, stresses and effective dispersion. These are of use for developing a continuum approach for describing the deformation and flow of dense gas-particle mixtures described in Part II. PART II: Granular materials deform plastically like a solid under weak shear and they flow like a fluid under high shear. As discussed in Part I, these materials exhibit other unusual kinds of behavior, including pattern formation in shaking of granular materials for which the onset characteristics of the various patterns are not well understood. Vertically shaken granular materials undergo a transition to a convective motion which can result in the formation of bubbles. In this part, hydrodynamic continuum equations are presented for describing the deformation and flow of dense gas-particle mixtures. The constitutive equation used for the stress tensor provides an effective viscosity with a liquid-like character at low shear rates and a gaseous-like behavior at high shear rates. The numerical solutions are obtained for the aforementioned hydrodynamic equations for predicting the flow dynamics of dense mixture of gas and particles in a vertical cylindrical container, whose base wall is subjected to sinusoidal oscillation in the vertical direction given as z = A sin(kv x) sin(lv y) cos(ωv t), where (ωv = Clv2 + kv2), C is speed of wave in base wall of container, A is a constant, and kv = mv π and lv = nv π. For a heptagonal prism shaped container under vertical vibrations, the model results were found to predict bubbling behavior analogous to those observed experimentally. This bubbling behavior may be explained by the unusual gas pressure distribution found in the bed. In addition, oscillon type structures are found to be formed using a vertically vibrated, pentagonal prism shaped container. The latter, however, seems to strengthen the observation that the pressure distribution plays a key role in deformation and flow of dense mixtures of gas and particles under vertical vibrations.© 2005 ASME