A Study Of Macro-mesoscopic Simulation Of Non-newtonian Flows Using GPR-based Machine Learning

Non-Newtonian fluids are those which do not follow Newton’s law of viscosity,and they can be classified as generalized Newtonian fluids and viscoelastic fluids in engineering.Flow of non-Newtonian fluids is usually called non-Newtonian flow for short,and it exists widely in daily life and industrial production.The numerical simulation of the non-Newtonian flow has important theoretical and practical implication.The simulation framework of non-Newtonian flow problems is to solve the macroscopic governing equations coupled with a constitutive model.A distinguish feature of non-Newtonian fluids is that the microstructure has transient properties under different rheological conditions,which can be easily changed under the influence of micro-stress.Thus,the rheological properties of non-Newtonian fluid depend on the transient shear rate as well as the strain history.Therefore,the rheological parameters(such as fluid viscosity,relaxation time,etc.)in the macroscopic constitutive model of non-Newtonian fluid have high dependence on its microstructure.However,the rheological parameters in the traditional constitutive model cannot reflect this dependence,resulting the numerical results cannot accurately describe the rheological properties of non-Newtonian fluids.Therefore,coupling of the bulk rheology and the underlying microstructural dynamics for the nonNewtonian flow is an effective way to improve the reliability of non-Newtonian flow simulation.There are several problems in the existing macro-micro methods for the multiscale simulation of non-Newtonian flow.First,it is difficult to balance accuracy and stability for a macroscopic solver in the enhanced elastic systems for non-Newtonian viscoelastic fluids.Second,at the microscopic scale,the molecular dynamics(MD)method can usually cover the scales of nanometer and nanosecond.So it is difficult to apply MD method to practical problems.Next,in the traditional microscale simulation,the relation between cutoff radius and particle state is not considered.Thus the macroscopic rheological information can’t be predicted accurately.Lastly,it requires a large number of microscopic simulations to obtain an accurate rheological parameters for constitutive equation of the non-Newtonian fluid in terms of shear rate causing high computational cost.To solve the aforementioned problems,we develop a computational framework using active learning,based on Gaussian process regression(GPR),in multiscale simulations of non-Newtonian fluids to couple the macroscale and microscale.Moreover,we develop an accurate and stable method for modelling the viscoelastic flow.In addition,we propose a mesoscopic with variable cutoff radium.The main contribution of the current work is listed below.(1)To balance the accuracy and the stability of the numerical solver for macroscopic nonNewtonian flows,we employ the finite volume method(FVM)on an unstructured nonstaggered grid,to discretize the governing equation of the generalized Newtonian fluid,and develop an accurate and stable method coupled with spectral element method(SEM)and entropy viscosity method(EVM)for modelling the viscoelastic flow based on finitely extensible non-linear elastic-Peterlin(FENE-P)model.(2)To provide low-cost simulation paths to capture collective dynamics of complex fluids on larger temporal and spatial scales beyond the capability of MD simulations,the polymer fluid is modeled by bead-spring chains whose coarse-grained dynamics are computed by dissipative particle dynamics(DPD),which is used for modeling mesoscopic phenomena with much greater efficiency than MD.Moreover,we propose a DPD model with variable cutoff interaction range to correctly capture the shear-thinning viscosity.(3)To solve the prediction inaccuracy in the rheological properties of generalized Newtonian fluids using the phenomenological constitutive model,we simulate complex fluids by means of an on-the-fly coupling of the bulk rheology to the underlying microstructure dynamics.To couple the bulk rheology of polymeric fluids and the microscale dynamics of polymer chains,the continuum approach(based on the FVM)provides the transient flow field as inputs for the(mesoscopic)DPD,and in turn DPD returns an effective viscosity to close the continuum equations.In this multiscale modeling procedure,we employ an active learning strategy based on GPR to minimize the number of expensive DPD simulations,where adaptively-selected DPD simulations are performed only as necessary.(4)To solve the problem that the classic FENE-P model can’t accurately predict the rheological properties of viscoelastic fluids,induced by the viscosity and relaxation time ignoring the influence of microstructure,we develop a computational framework using active learning built on GPR to directly connect the bulk viscoelasticity of polymer solutions with the microscale dynamics of polymer chains.Specifically,in the microscale-macroscale coupling,the SEM coupled with EVM solver provides local transient flow field to initiate DPD simulations of polymer solution,while the DPD solver returns the shear viscosity and the first normal stress difference at selected shear strain rates,wherein an active learning scheme built on GPR is used to learn the dependence of viscosity and first normal stress difference on the shear strain rate,to close the macroscopic governing equations.The new model for viscoelastic flows can greatly improve the calculation efficiency while providing high accuracy.