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Title: 1-D closure models for slender 3-D viscoelastic free jets: von Karman flow geometry and elliptical cross section

Abstract

In this paper we derive one space dimensional, reduced systems of equations (1-D closure models) for viscoelastic free jets. We begin with the three-dimensional system of conservation laws and a Maxwell-Jeffreys constitutive law for an incompressible viscoelastic fluid. First, we exhibit exact truncations to a finite, closed system of 1-D equations based on classical velocity assumptions of von Karman. Next, we demonstrate that the 3-D free surface boundary conditions overconstrain these truncated systems, so that only a very limited class of solutions exist. We then proceed to derive approximate 1-D closure theories through a slender jet asymptotic scaling, combined with appropriate definitions of velocity, pressure and stress unknowns. Our nonaxisymmetric 1-D slender jet models incorporate the physical effects of inertia, viscoelasticity (viscosity, relaxation and retardation), gravity, surface tension, and properties of the ambient fluid, and include shear stresses and time dependence. Previous special 1-D slender jet models correspond to the lowest order equations in the present asymptotic theory by an a posteriori suppression to leading order of some of these effects, and a reduction to axisymmetry. Solutions of the lowest order system of equations in this asymptotic analysis are presented: For the special cases of elliptical inviscid and Newtonian freemore » jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and drawdown of the cross section, in agreement with observed behavior. 15 refs.« less

Authors:
; ; ;
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
OSTI Identifier:
7124842
Report Number(s):
LA-UR-88-1742; CONF-880786-1
ON: DE88014478
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: IUTAM meeting, Cincinnati, OH, USA, 1 Jul 1988; Other Information: Paper copy only, copy does not permit microfiche production
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; INCOMPRESSIBLE FLOW; FLOW MODELS; BOUNDARY CONDITIONS; EQUATIONS OF MOTION; JETS; THREE-DIMENSIONAL CALCULATIONS; DIFFERENTIAL EQUATIONS; EQUATIONS; FLUID FLOW; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; 640410* - Fluid Physics- General Fluid Dynamics

Citation Formats

Bechtel, S E, Forest, M G, Holm, D D, and Lin, K J. 1-D closure models for slender 3-D viscoelastic free jets: von Karman flow geometry and elliptical cross section. United States: N. p., 1988. Web.
Bechtel, S E, Forest, M G, Holm, D D, & Lin, K J. 1-D closure models for slender 3-D viscoelastic free jets: von Karman flow geometry and elliptical cross section. United States.
Bechtel, S E, Forest, M G, Holm, D D, and Lin, K J. 1988. "1-D closure models for slender 3-D viscoelastic free jets: von Karman flow geometry and elliptical cross section". United States. https://www.osti.gov/servlets/purl/7124842.
@article{osti_7124842,
title = {1-D closure models for slender 3-D viscoelastic free jets: von Karman flow geometry and elliptical cross section},
author = {Bechtel, S E and Forest, M G and Holm, D D and Lin, K J},
abstractNote = {In this paper we derive one space dimensional, reduced systems of equations (1-D closure models) for viscoelastic free jets. We begin with the three-dimensional system of conservation laws and a Maxwell-Jeffreys constitutive law for an incompressible viscoelastic fluid. First, we exhibit exact truncations to a finite, closed system of 1-D equations based on classical velocity assumptions of von Karman. Next, we demonstrate that the 3-D free surface boundary conditions overconstrain these truncated systems, so that only a very limited class of solutions exist. We then proceed to derive approximate 1-D closure theories through a slender jet asymptotic scaling, combined with appropriate definitions of velocity, pressure and stress unknowns. Our nonaxisymmetric 1-D slender jet models incorporate the physical effects of inertia, viscoelasticity (viscosity, relaxation and retardation), gravity, surface tension, and properties of the ambient fluid, and include shear stresses and time dependence. Previous special 1-D slender jet models correspond to the lowest order equations in the present asymptotic theory by an a posteriori suppression to leading order of some of these effects, and a reduction to axisymmetry. Solutions of the lowest order system of equations in this asymptotic analysis are presented: For the special cases of elliptical inviscid and Newtonian free jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and drawdown of the cross section, in agreement with observed behavior. 15 refs.},
doi = {},
url = {https://www.osti.gov/biblio/7124842}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 1988},
month = {Fri Jan 01 00:00:00 EST 1988}
}

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