Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix

In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method （EMM） is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 x 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.

Validation of EMMS-based drag model using lattice Boltzmann simulations on GPUs

lnterphase momentum transport in heterogeneous gas-solid systems with multi-scale structure is of great importance in process engineering. In this article, lattice Boltzmann simulations are performed on graphics processing units （GPUs）, the computational power of which exceeds that of CPUs by more than one order of magnitude, to investigate incompressible Newtonian flow in idealized multi-scale particle-fluid systems. The structure consists of a periodic array of clusters, each constructed by a bundle of cylinders. Fixed pressure boundary condition is implemented by applying a constant body force to the flow through the medium. The bounce-back scheme is adopted on the fluid-solid interfaces, which ensures the no-slip boundary condition. The structure is studied under a wide range of particle diameters and packing fractions, and the drag coefficient of the structure is found to be a function of voidages and fractions of the clusters, besides the traditional Reynolds number and the solid volume fractions. Parameters reflecting multi-scale characters are, therefore, demonstrated to be necessary in quantifying the drag force of heterogeneous gas-solid system. The numerical results in the range 0.1 〈 Re 〈 10 and 0 〈 Ф 〈 0.25 are compared with Wen and Yu＇s correlation, Gibilaro equation, EMMS-based drag model, the Beetstra correlation and the Benyahia correlation, and good agreement is found between the simulations and the EMMS-based drag model for heterogeneous systems.

3D full-loop simulation and experimental verification of gas-solid flow hydrodynamics in a dense circulating fluidized bed

Because of their advantages of high efficiency and low cost, numerical research methods for large-scale circulating fluidized bed （CFB） apparatus are gaining ever more importance. This article presents a numer- ical study of gas-solid flow dynamics using the Eulerian granular multiphase model with a drag coefficient correction based on the energy-minimization multi-scale （EMMS） model. A three-dimensional, full-loop, time-dependent simulation of the hydrodynamics of a dense CFB apparatus is performed. The process parameters （e.g., operating and initial conditions） are provided in accordance with the real experiment to enhance the accuracy of the simulation. The axial profiles of the averaged solid volume fractions and the solids flux at the outlet of the cyclone are in reasonable agreement with experimental data, thereby verifying the applicability of the mathematical and physical models. As a result, the streamline in the riser and standpipe as well as the solids distribution contours at the cross sections is analyzed. Computational fluid dynamics （CFD） serves as a basis for CFB modeling to help resolve certain issues long in dispute but difficult to address experimentally. The results of this study provide the basis of a general approach to describing dynamic simulations of gas-solid flows.