Study On POD-ROM Of Viscoelastic Drag-reducing Flow Based On The Spring-dumbbell Model

Turbulent drag reduction technology is of great practical value for saving energy,increasing throughput of crude oil pipeline and protecting environment.Its mature and wide-spread engineering applications depend on high-precision fast simulation.However,the present direct numerical simulation(DNS),Reynolds averaged simulation(RANS)and large eddy simulation(LES)can not meet the demand.DNS can abtain the most information and achieve the highest precision,but costs the longest time;RANS costs the shortest time.However,it needs to establish different closure models for different problems,so that it has poor universality and accuracy;the accuracy and speed of LES are both between DNS and RANS.LES can provide the information above the inertial subrange fluctuation scale,but the selection and establishment of sub-grid model is somehow artificial and empirical.Therefore,to further explore the efficient numerical simulation method of drag-reducing flow,proper orthogonal decomposition method(POD)is used in this thesis combined with the Galerkin projection method.POD-Galerkin reduced-order model(ROM)of viscoelastic drag-reducing flow based on the spring-dumbbell model is derived.Firstly,the influence of the modeling manners on the accuracy of POD-ROMs based on instantaneous velocity and fluctuate velocity is discussed.Principle for turbulent POD modeling is fixed.The computational accuracy of ROM is verified by using laminar,low-Reynolds-number turbulence and high-Reynolds-number turbulence cases,respectively.It is pointed out that the accuracy of the POD-ROM based on fluctuate velocity is higher than that based on instantaneous velocity for the turbulent flow.Then,the principle is applied to 2D lid-driven cavity flow and turbulent drag-reducing flow.Instantaneous velocity,average velocity,spectral coefficient,calculation time and other related physical quantities are employed to verify the calculation precision and speed of the POD-ROMs.The results indicate that the ROM can fast reproduce the original flow field with considerable accuracy.