Non-darcy Flow And Heat Transfer Characteristics In A Porous-free Channel

In the process of developing geothermal resources or natural gas,the fluid flow rate is higher near the wellbore or in the formation with fractures,there will also be large fluid velocity in the solid base heat exchanger and the surrounding rock area of the pumped storage high-pressure bifurcation pipe.At this time,due to the high velocity of fluid flow,the inertia effect becomes more and more obvious.The Darcy law,which is the most basic when describing fluid flow behavior,is no longer applicable.Fluid flows in a non-Darcy form,so it is necessary to study the non-Darcy flow and heat transfer of fluid in porous media.In this paper,the non-Darcy flow heat transfer characteristics in the porous media-free flow channel are studied by using the channel model filled with porous medium layer on both sides of the upper and lower inner wall.The Brinkman-Forchheimer extended Darcy model considering inertia effect and the LTNE model considering flue-solid two-phase temperature difference of porous media are adopted for the porous media region,due to the existence of Forchheimer inertia term,the velocity analytical solution cannot be obtained,so finite difference and Newton iteration method are used for numerical programming,numerical solutions of velocity,temperature and Nussel number in each region of the porous media-free flow channel under coupled conditions are obtained.The effects of interfacial jump coefficientβ,hollow ratio S,Darcy number Da,thermal conductivity ratio K,especially the inertia parameter F_f,on the flow and heat transfer were further analyzed,and the temperature and Nussel number under different thermal boundary conditions were compared.The results show that:the maximum velocity at the center of the channel increases with the increase of inertia parameter F_fand interface jump coefficientβ,and the decrease of hollow rate S.The pressure drop distribution curves with different inertia parameter F_fshow a monotonically decreasing trend with the increase of S,and the influence of inertia parameter F_fon the fluid resistance and temperature distribution in the channel should be considered only when Da>10^-3.Decreasing H_scan increase the fluid-solid two-phase temperature difference in the porous media region,and the maximum temperature difference gradually appears at the interface with the decrease of H_s.Under different thermal boundary conditions,when H_s=0.1,the decrease of Da will increase the temperature difference in porous media region under model 2,but it is opposite to model 1.When H_s=10,the decrease of Da will reduce the temperature difference under model2,and model 1 is consistent with it.For different K and Bi,Nu and S relationship curves have different curve types.Different from the use of thermal boundary model 1,the type of Nu curve of thermal boundary model 2 is also related to H_s,and with the increase of H_s,the Nu calculated by model 2 will gradually approach but not exceed the Nu value of model 1.In the LTNE model,the influence of the internal heat source is considered,and the distribution law of the temperature and Nusselt number in the composite channel with the internal heat source is obtained.The results show that when the internal heat source is considered,the temperature difference between the fluid-solid phase decreases with the increase of F_f.When the absolute value of W_sis the same but the heat-absorption and heat-release properties are different,the fluid-solid phase temperature distribution in the porous medium is not completely symmetric and temperature bifurcation occurs.In addition,under different inertial parameters F_f,considering W_smay cause the singularity of Nu,and the heat transfer phenomenon will be more complicated.Similar to the case without considering the internal heat source,there is a large gap between the Nu results of the two thermal boundary models when considering the internal heat source H_s=0.1.With the increase of H_s,the Nu value calculated by model 2 will gradually approach the Nu value of model 1.