Mechanical & Aerospace Engineering

Biography

Biography: Narima Ashrafi

Abstract

The influence of fluid elasticity is examined for the plane Couette flow (PCF) of a Johnson Segalman (J.S) fluid.The Johnson Segalman model is a nonlinear viscoelastic model that accounts for the combined rheological nonlinearity and time dependency phenomena by inclusion of the upper-convected time derivative of stress tensor in the constitutive equation. In the special cases of the proposed model, typical upper convected Maxwell model can be recovered. The model takes into account the interrelations of velocity gradients and stress components through introduction of appropriate coefficients in the elastic terms of constitutive equation. The proposed form of constitutive equation almost completely models the physical behavior of a wide range of nonlinear materials, yet it is computationally appropriate as well. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. It consists of expanding the velocity and stress in terms of orthogonal functions and projecting onto each mode of expansion to generate a set of ordinary differential equations that govern the time dependent expansion coefficients. The type of orthogonal functions depends on the geometry and boundary conditions. Effect of several values of governing parameters such as introduced coefficients, Reynolds number and Weissenberg number on velocity and normal and shear stresses profiles are explored in detail. The results show that the oscillating behavior of velocity profile tends to grow as the coefficients increase. For higher Wiessenberg, the oscillations are more intensive, whereas the amplitude of oscillation tends to reduce. This reveals that, the deviation decreases by increasing the coefficients. The amplitude of normal stress differences tend to grow as the coefficients of the convected terms grow, revealing more elastic behavior in the fluid. On the other hand the effect of the convected terms on the steady behavior of normal stress difference is strongly dependent on the value of Weissenberg number. The shear stress behavior is also dependent on the coefficients of the convected terms and the flow properties, that is, for higher Reynolds the shear stress reaches a maximum and then decreases to minimum. For lower Reynolds, the opposite occurs . From a numerical point of view, the model also allows for the velocity and stress components to be represented by truncated series.