Non-isothermal And Laminar Pulsating Flow Problems Based On EFG Simulation

As a new numerical method,the element-free Galerkin(EFG)method has been quickly recognized by many researchers for its enormous advantages such as simple pretreatment,high precision,and easy convergence.The current EFG method has been widely used in the field of solid mechanics,but its application is less in computational fluid dynamics,and most of the attention is paid to the solution of N-S equations.However,fluid flow conclude not only has momentum but also energy transfer.Therefore,the coupling of N-S equations and energy equations can better reflect the true flow of the fluid.So,this paper mainly studies the coupling solution of incompressible laminar flow and heat transfer problem by EFG method,the main contents and results are as follows:(1)Using EFG method to develop numerical simulation of non-isothermal flow problem.In this paper,the EFG method is applied to the coupling solution of N-S equations and energy equations,the steady NS equation and energy equation of EFG method was deduced and discrete,at the same time,numerical simulation was conducted for a closed square cavity natural convection and non-newtonian fluid forced convection question.The natural convection problem in the enclosed cavity is discussed with emphasis on the velocity field,temperature field and vorticity.With the increase of Ra,the physical quantities change more and more obviously:The wall area of the velocity field changes more and more violently,the temperature field gradually expresses the thermal convection characteristics from the heat conduction,and the vorticity vortex gradually splits from one concentric circle into two vortices.For the non-Newtonian fluid forced convection problem,the power law exponent n and the Beckley number Pe are emphatically analyzed for the flow field and the temperature field.With the increase of n,Fully develop the length of the area and Central area speed smoothness are reduced;With changes in the Pe,the temperature inlet section has also been lengthened.(2)Taking into account the time terms and the changes in velocity,the pulsating laminar flow and heat transfer problems are analyzed on the basis of periodic changes in inlet velocity.The EFG format discrete equations for the N-S equations and energy equations of two-dimensional unsteady velocity laminar pulsations are established.The convection term is solved by the Velocity term proposed law and the linearized alternate iteration method is used to solve the nonlinear equations.By changing the amplitude and frequency of the entrance pulsation velocity to analyze the effect of pressure and temperature,the pressure fluctuation is proportional to the amplitude and frequency of the velocity,the temperature is proportional to the amplitude of the pulsation velocity,and inversely proportional to the pulsation frequency.(3)Consider practical engineering problems,it is extended to three-dimensional problems based on two-dimensional flow and heat transfer.The EFG method was used to study the flow and heat transfer of the three-dimensional backsteps.The discrete forms of the three-dimensional EFG flow and heat transfer equations were deduced,according to deduce the three-dimensional and written MATLAB program.The influence of the Reynolds number on the flow and heat transfer at the rear stage is analyzed in detail.The results show that the length of the recirculation zone at the step increases with increasing Reynolds number.And the existence of wall effect is found through streamline diagrams of different cross-sections,and fully embodies the characteristics of 3D model flow.