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SPECIAL SECTION ON THE FLUID MECHANICS AND RHEOLOGY OF NONLINEAR MATERIALS AT THE MACRO, MICRO AND NANO SCALE

Calculation of the Die Entry Flow of a Concentrated Polymer Solution Using Micro-Macro Simulations

[+] Author and Article Information
Kathleen Feigl

Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295

Deepthika C. Senaratne1

Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295feigl@mtu.edu

1

Current address: Department of Mathematics and Computer Science, Fayetteville State University, 1200 Murchison Road, Fayetteville, NC 28301.

J. Fluids Eng 128(1), 55-61 (May 26, 2005) (7 pages) doi:10.1115/1.2136922 History: Received April 28, 2004; Revised May 26, 2005

A micro-macro simulation algorithm for the calculation of polymeric flow is developed and implemented. The algorithm couples standard finite element techniques to compute velocity and pressure fields with stochastic simulation techniques to compute polymer stress from simulated polymer dynamics. The polymer stress is computed using a microscopic-based rheological model that combines aspects of network and reptation theory with aspects of continuum mechanics. The model dynamics include two Gaussian stochastic processes, each of which is destroyed and regenerated according to a survival time randomly generated from the material’s relaxation spectrum. The Eulerian form of the evolution equations for the polymer configurations is spatially discretized using the discontinuous Galerkin method. The algorithm is tested on benchmark contraction domains for a polyisobutylene solution. In particular, the flow in the abrupt die entry domain is simulated and the simulation results are compared to experimental data. The results exhibit the correct qualitative behavior of the polymer and agree well with the experimental data.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 3

Axial velocity profiles in the tapered contraction domain along the centerline and along an axial cross section of the downstream channel for Q=30cm2∕s

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Figure 4

Simulation results in the tapered contraction domain for Q=30cm2∕s: (a)NF=2000 and (b)NF=4000. Horizontal lines are the exact steady-state values.

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Figure 5

Simulation results in the tapered contraction domain for Q=30cm2∕s: (a)NF=2000 and (b)NF=8000. Horizontal lines are the exact steady-state values.

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Figure 6

Streamline patterns in the abrupt contraction domain

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Figure 7

Centerline velocity profiles and elongation rates: experimental data (closed symbols), simulation (open symbols)

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Figure 2

Streamline patterns in the tapered contraction domain for Q=30cm2∕s

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Figure 1

Model predictions of PIB solution in simple shear flow and comparison to experimental data

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