On the Influence of Viscoelastic Modeling in Fluid Flow Simulations of Gum Acrylonitrile Butadiene Rubber

Computational fluid dynamics (CFD) simulation is an important tool as it enables engineers to study different design options without a time-consuming experimental workload. However, the prediction accuracy of any CFD simulation depends upon the set boundary conditions and upon the applied rheological constitutive equation. In the present study the viscoelastic nature of an unfilled gum acrylonitrile butadiene rubber (NBR) is considered by applying the integral and time-dependent Kaye–Bernstein–Kearsley–Zapas (K-BKZ) rheological model. First, exhaustive testing is carried out in the linear viscoelastic (LVE) and non-LVE deformation range including small amplitude oscillatory shear (SAOS) as well as high pressure capillary rheometer (HPCR) tests. Next, three abrupt capillary dies and one tapered orifice die are modeled in Ansys POLYFLOW. The pressure prediction accuracy of the K-BKZ/Wagner model was found to be excellent and insensitive to the applied normal force in SAOS testing as well as to the relation of first and second normal stress differences, provided that damping parameters are fitted to steady-state rheological data. Moreover, the crucial importance of viscoelastic modeling is proven for rubber materials, as two generalized Newtonian fluid (GNF) flow models severely underestimate measured pressure data, especially in contraction flow-dominated geometries.

New Approach to Melt Pressure Determination during Screw Channel Flow

Basic equations describing steady, two-directional, isothermal and fully developed drag-pressure flow of generalized Newtonian fluid between parallel plates assumed as the appropriate flow model in flat, shallow screw channel, are given. It is shown that the flow output for any generalized Newtonian fluid in the two-directional case can be described by a simple expression with a few parameters depending in a complicated way on pressure gradient, channel geometry and constants of the constitutive model. The expression is also valid for unidirectional flow as the limiting case of the two-directional flow. The parameters must be determined as a rule with numerical methods. To simplify the practical calculations, a few (semi)analytical methods of parameters determination for unidirectional power law flow are discussed first. These methods make possible to calculate analytically the pressure gradient for known output that is typical of screw flow characterization. The results obtained for the unidirectional flow 1-D were generalized to describe the two-directional flow 2-D, which takes into account both longitudinal and transverse velocity components. The generalization is based on translation and dilation of the 1-D flow characteristics by introducing a few additional parameters, which are only dependent on the helix angle and power law exponent. It was found a very good agreement between exact numerical and approximate ( semi)analytical characteristics for both flows.

Rapid Numerical Estimation of Pressure Drop in Hot Runner System

To determine dimensions in the hot runner systems, given a material, it is necessary to predict the pressure drop according to them. Although modern injection molding simulators are able to evaluate such pressure drops, they are expensive and demanding to be employed as a design utility. This work develops a computer tool that can calculate a pressure drop from the sprue to the gate assuming a steady flow of a generalized Newtonian fluid. For a four drop hot runner system, the accuracy has been verified by comparing the obtained results with those by a commercial simulator. This paper presents how to utilize the proposed method in the hot runner design process.

Non-isothermal Bingham fluid flow between two horizontal parallel plates with Ion-slip and Hall currents

This study presents the numerical solution of velocity and temperature fields based on mass conservation, momentum and energy balances for the time-dependent Couette-Poiseuille flow of Bingham materials through channels. The channel flow of Bingham fluid concerns the flow of cement paste in the building industry and the mudflow in the drilling industry. The specific aim is to introduce the magnetohydrodynamic (MHD) phenomena specified by both Ion-slip and Hall currents into the non-isothermal channel flow in a theoretical approach. The Bingham constitutive equation is formulated by the generalized Newtonian fluid technique and solved by employing the explicit Finite Difference Method (FDM) using the MATLAB R2015a and Compaq Visual FORTRAN 6.6a both. For the exactness of numerical performance estimations, the criteria for stabilization and the convergence factor are analyzed. The velocity and temperature profiles are discussed individually at the moving and stationary walls of the channel. It is observed that magnetohydrodynamic phenomena accelerate the flow, and the temperature distributions reach the steady-state situation earlier than velocity distributions. Furthermore, the dominance of MHD parameters on the velocity distributions, shear stress, temperature distributions, and Nusselt number are discussed.

On unsteady flows of pore pressure-activated granular materials

We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid matrix behaves as an ideal plastic material before the activation takes place and then it starts to flow as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between the given lithostatic pressure and the pressure of the fluid in a pore space. We study unsteady three-dimensional flows in an impermeable container, subject to stick-slip boundary conditions. Under realistic assumptions on the data, we establish long-time and large-data existence theory.