POD Reduced–Order Model For Turbulent Flow Of Viscoelastic Fluid

Turbulent drag reduction with additives plays an important role in long-distance transportation and liquid circulation system,while the study on viscoelastic fluid is also very necessary.In this paper,the proper orthogonal decomposition method(POD)for turbulent flows of Newtonian fluid and viscoelastic fluid has been studied,since direct numerical simulation(DNS)is not a realistic possibility because the cost of such simulation remains far beyond our means.The specific decaying isotropic turbulent flow is studied in this thesis firstly.Establish the reduced-order models for two-dimensional turbulent flows of Newtonian fluid and viscoelastic fluid respectively.Then apply the reduced-order models to decaying isotropic turbulent flows.Extract basis functions from sampling matrices and analyze the coherent structures of the flows.At last,calculate the desired flow fields efficiently.For studies in which one wishes stationarity for statistical sampling,forced turbulence is preferable over decaying turbulence.Therefore,we focus on forced isotropic turbulent flow next.Establish the reduced-order models for there-dimensional turbulent flows of Newtonian fluid and viscoelastic fluid respectively.Then apply the established reduced-order models to forced isotropic turbulent flows successfully.Sequentially,the velocity basis functions and deformation basis functions can be extracted from corresponding sampling matrices and then the coherent structures can be analyzed.Finally,the flow fields(velocity field and deformation field)of the isotropic forced turbulence could be obtained via solving the reduced-order models efficiently.In addition,a more complex and practical problem—the heterogeneous turbulent channel flow is able to be processed.Also,the reduced-order models for Newtonain fluid and viscoelastic fluid are established respectively.Employ the POD method to calculate the flow fields of the complex three-dimensional turbulent channel flow.Analyze the influence of viscoelasticity based on the velocity basis functions and the results.In the end,the performance of the studied POD method is evaluated.The above studies can provide theoretical guidance for the application of turbulent drag reduction technology on long-distance pipeline transportation of oil.