A Numerical Study Of Flow And Heat Transfer Past And Through A Porous Cylinder Under Thermal Forcing

Flow and heat transfer around and through porous bluff bodies widely exists in nature,and can be commonly found in biological engineering,energy and chemical industry,aerospace,nuclear,and ocean engineering.Since such transport processes involve complicated flow mechanisms and thermal characteristics,the research on this topic has important academic significance and practical application value.Although the investigation carried out on this issue gradually increases,there is still a lack of understanding on the physical mechanism underlying flow and heat transfer around and through a porous circular cylinder.Based on the finite volume method,the present study numerically and systematically investigated steady mixed convective heat transfer from a porous circular cylinder with internal heat generation under thermal buoyancy.The main results and conclusions are briefly provided as follows:Considering the effect of aiding buoyancy(the free stream orientation is the same as the thermal buoyancy direction),mixed convective heat transfer from a porous circular cylinder is studied.The physical mechanism of the onset and disappearance of the recirculating wake behind this cylinder with the effect of aiding buoyancy is explored.The bifurcation diagram of wake existence is obtained.Results of wake structure and thermal performance are compared with those of a solid counterpart.The calculation method of the drag coefficient on the porous surface is analyzed.It is found that the recirculating wake either penetrates the porous cylinder or develops downstream apart from the cylinder.Both the Darcy number(Da)and aiding buoyancy suppress the development of the recirculating wake and precipitate its disappearance.Compared to impermeable cases,the recirculating wake behind this porous cylinder forms at a higher Reynolds number(Re)and vanishes at lower strength of aiding buoyancy.Indeed,the onset and disappearance of the recirculating wake are significantly dependent on the flow inside and outside the cylinder and the generation and decay of vorticity.Compared to impermeable cases,the heat transfer performance of the porous cylinder is significantly advanced,especially at higher Da and thermal forcing.Surface drag coefficient obtained by the control volume method instead of the surface integrate method is relatively accurate due to the permeation of the cylinder and the momentum loss caused by the obstruction of the solid part inside the porous cylinder.Effect of the Prandtl number(Pr)on the flow and heat transfer from a porous circular cylinder under aiding buoyancy is investigated.The bifurcation diagram of wake existence at different Pr is obtained.Besides,the distribution of the thermal boundary layer around the porous cylinder and heat transfer mechanism are analyzed.Our results indicate that an increase in Pr weakens the flow inside and around the porous cylinder and precipitates the development of the recirculating wake.The critical Reynolds number for the onset of the recirculating wake reduces when Pr increases.On the other hand,to some extent,an increase in Pr also cripples the effect of aiding buoyancy on the flow.Pr plays a crucial role in temperature distribution since its increase triggers the twisting and undulating of isotherms,forming the concave or saddle-shaped structures behind the cylinder.The overall size(including the length)of this structure is almost the same as that of the recirculating wake.Isotherms densely assemble behind the porous cylinder due to its twisting and undulating structures,which promotes the heat transfer performance.It is also found that the thickness of the thermal boundary layer around the cylinder significantly becomes thinner with an increase in Pr.In addition,temperature decays fast along the downstream direction,and the heat diffuses rapidly downstream.As a result,the heat transfer performance is enhanced.Combining with the interaction of the free-stream orientation and thermal buoyancy,the wake property and heat transfer performance of the porous cylinder are investigated.The physical mechanism behind the asymmetric characteristics of the flow field and the recirculating wake is discussed.Our results show that the recirculating wake exhibits various structures and behaviors under the coupled effects of the free-stream orientation and thermal buoyancy.The overall structure of the recirculating wake may no longer be symmetric about the horizontal axis of the cylinder.Instead,it is composed of the upper recirculating wake and lower recirculating wake with different structures.The behaviors of the two components are also different with the variation of governing parameters.The effect of the free-stream orientation on the wake asymmetry is dependent on Da and thermal buoyancy.When Da increases,the asymmetric magnitude initially decreases and then increases.An increase in the strength of thermal buoyancy promotes the asymmetric feature of the overall recirculating wake.Over the range of parameter investigated,the entire flow field may experience two or three patterns of the recirculating wakes,including the two-vortex pattern,a sing-vortex pattern,and no vortex pattern.Such behaviors of wake structure are related to the velocity around the cylinder,the exit velocity from the cylinder,and vorticity.The asymmetric feature of the recirculating wakes is attributed to the component of thermal buoyancy perpendicular to the direction of the free stream.The porous cylinder experiences a force perpendicular to the direction of the free stream due to this buoyancy component.The effect of thermal buoyancy on heat transfer is dependent on the free-stream orientation and thermal buoyancy may not blindly enhance thermal performance.When the free stream is perpendicular to the direction of thermal buoyancy,thermal buoyancy weakens heat transfer.Our results also show that the better heat transfer performance can be achieved under aiding buoyancy.