Effect of fluid elasticity on the numerical stability of high-resolution schemes for high shearing contraction flows using OpenFOAM

Viscoelastic fluids due to their non-linear nature play an important role in process and polymer industries. These non-linear characteristics of fluid, influence final outcome of the product. Such processes though look simple are numerically challenging to study, due to the loss of numerical stability. Over the years, various methodologies have been developed to overcome this numerical limitation. In spite of this, numerical solutions are considered distant from accuracy, as first-order upwind-differencing scheme （UDS） is often employed for improving the stability of algorithm. To elude this effect, some works been reported in the past, where high-resolution-schemes （HRS） were employed and Deborah number was varied. However, these works are limited to creeping flows and do not detail any information on the numerical stability of HRS. Hence, this article presents the numerical study of high shearing contraction flows, where stability of HRS are addressed in reference to fluid elasticity. Results suggest that all I-IRS show some order of undue oscillations in flow variable profiles, measured along vertical lines placed near contraction region in the upstream section of domain, at varied elasticity number E ~ 5. Furthermore, by E, a clear relationship between numerical stability of HRS and E was obtained, which states that the order of undue oscillations in flow variable profiles is directly proportional to E.

VARIATIONAL PRINCIPLES OF FLUID FULLFILLED ELASTIC SOLIDS

The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation

Direct numerical simulations（DNSs） of purely elastic turbulence in rectilinear shear flows in a three-dimensional（3D） parallel plate channel were carried out,by which numerical databases were established.Based on the numerical databases,the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns,the wall effect on the turbulent kinetic energy spectrum,and the local relationship between the flow motion and the microstructures＇ behavior.Moreover,to address the underlying physical mechanism of elastic turbulence,its generation was presented in terms of the global energy budget.The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length,and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched.In addition,the patterns of microstructures＇ elongation behave like a filament.From the results of the turbulent kinetic energy budget,it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.

Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow

In this paper,we present a direct numerical simulation（DNS） of elastic turbulence of viscoelastic fluid at vanishingly low Reynolds number（Re = 1） in a three-dimensional straight channel flow for the first time,using the Giesekus constitutive model for the fluid.In order to generate and maintain the turbulent fluid motion in the straight channel,a sinusoidal force term is added to the momentum equation,and then the elastic turbulence is numerically realized with an initialized chaotic velocity field and a stretched conformation field.Statistical and structural characteristics of the elastic turbulence therein are analyzed based on the detailed information obtained from the DNS.The fluid mixing enhancement effect of elastic turbulence is also demonstrated for the potential applications of this phenomenon.

Calculation and Analysis of Velocity and Viscous Drag in an Artery with a Periodic Pressure Gradient

Blood as a fluid that human and other living creatures are dependent on has been always considered by scientists and researchers.Any changes in blood pressure and its normal velocity can be a sign of a disease.Whatever significant in blood fluid＇s mechanics is Constitutive equations and finding some relations for analysis and description of drag,velocity and periodic blood pressure in vessels.In this paper,by considering available experimental quantities,for blood pressure and velocity in periodic time of a thigh artery of a living dog,at first it is written into Fourier series,then by solving Navier-Stokes equations,a relation for curve drawing of vessel blood pressure with rigid wall is obtained.Likewise in another part of this paper,vessel wall is taken in to consideration that vessel wall is elastic and its pressure and velocity are written into complex Fourier series.In this case,by solving Navier-Stokes equations,some relations for blood velocity,viscous drag on vessel wall and blood pressure are obtained.In this study by noting that vessel diameter is almost is large（3.7 mm）,and blood is considered as a Newtonian fluid.Finally,available experimental quantities of pressure with obtained curve of solving Navier-Stokes equations are compared.In blood analysis in rigid vessel,existence of 48% variance in pressure curve systole peak caused vessel blood flow analysis with elastic wall,results in new relations for blood flow description.The Resultant curve is obtained from new relations holding 10% variance in systole peak.