Two-Dimensional Numerical Simulation Of Flow Past A Superelliptic Cylinder And Multi-Superelliptic Particles

Understanding the momentum and heat transfer characteristic of bluff bodies immersed in flowing fluids is fundamental to many industrial applications.This work present a numerical study of fluid flow over a superelliptic cylinder body by applying a finite volume method with an adaptive mesh refinement technique.The influence of the Reynolds number(Re),incidence angle(),aspect ratio(E)and shape index(n)on the detailed kinetics of the flow(streamline and surface pressure profiles)and the macroscopic properties(drag coefficient C_d and surface mean Nusselt number Nu)have been examined over wide ranges of conditions as:0.3?Re?200,0°??45°,1/4?E?4 and 1/2?n?5.The critical Reynolds numbers,corresponding to the onset of flow separation and the onset of the laminar unsteady regime,have been identified for all the considered cylinders at=0°.The results show that the characteristics of flow and heat transfer of the fluids are affected in an intricate manner by the value of Re,,E and n.In particular,the drag force and heat transfer rate over hypoelliptic cylinders(n<2)are more sensitive to shape index than hyperelliptic ones(n>2),probably due to the existence of singularity corners.The hypoelliptic and hyperelliptic cylinders show opposite trends of C_d and averaged Nu versus the incidence angle,while circular ones(n=2,E=1)always achieve their extreme values.In addition,a special range of incident angle(~[30°,45°])has been observed in the flows of relatively high Re conditions,reflecting negligible effect of n on the heat transfer rate.Based on the simulated results,new equations have been proposed to estimate the drag coefficient and surface mean Nusselt number.On the other hand,multi-superelliptic particles with different porosity were built by Discrete Element Method,and the flow characteristics,drag coefficient and heat transfer was investigated as well.It is found that the C_d decreases sharply as the porosity(k)increases from0.303 to 0.836,which shows an opposite trend with Nu.Besides,the C_d and Nu get less affect from k when 0.60<k at low Re conditions and 0.72<k at high Re condition.It has been improved that,for multi-superelliptic particles,the relationship between superficial velocity and pressure gradient also obeys the Darcy'law at low Re conditions.Then,the permeability(e)of multi-superelliptic particles with different n,is positively correlated with k and always achieves its maximum value at n=2.