In the present work, it is proposed to use a helical coordinate system for mathematical modeling of non-isothermal Giesekus fluid flow in the extruder in the metric zone. The convenience of using a helical coordinate system is to reduce the three-dimensional problem to two-dimensional without the use of additional assumptions. The helical coordinate system is applicable only for steady flow conditions. Particular results of the numerical implementation of the use of a helical coordinate system are presented on the example of a Giesekus fluid flow in an extruder with a single flight, the results are compared with the flow of Newtonian fluid.
A two-dimensional mathematical model for a steady viscoelastic laminar flow in a confusor was developed under the condition of swirled flow imposed at the inlet. Low density polyethylene was considered as a working fluid. Its behavior was described by a two-mode Giesekus model. The proposed mathematical model was tested by comparing it with some special cases presented in the literature. Additionally, we propose a system of equations to find the nonlinear parameters of the multimode Giesekus model (mobility factor) based on experimental measurement. The obtained numerical results showed that in a confusor with the contraction rate of 4:1, an increase in the swirl intensity at Wi < 5.1 affects only the circumferential velocity, while the axial and radial velocities remain constant. The distribution pattern of the first normal stress difference in the confusor is qualitatively similar to the one in a channel with abrupt contraction, i.e., as the viscoelastic fluid flows in the confusor, the value of N1 increases and reaches a maximum at the end of the confusor. Dimensionless damping coefficients of swirl are used to estimate the swirl intensity. The results show that the swirl intensity decreases exponentially.
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