THE SEDIMENTATION OF A SPHERE THROUGH AN ELASTIC FLUID .1. STEADY MOTION

被引:84
作者
ARIGO, MT
RAJAGOPALAN, D
SHAPLEY, N
MCKINLEY, GH
机构
[1] HARVARD UNIV, DIV APPL SCI, CAMBRIDGE, MA 02138 USA
[2] DUPONT CO INC, CENT RES & DEV, WILMINGTON, DE 19880 USA
基金
美国国家科学基金会;
关键词
AXIAL SEDIMENTATION; NUMERICAL SIMULATION; LDV; SPHERE; VISCOELASTIC FLUID;
D O I
10.1016/0377-0257(95)01379-6
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The first direct comparisons of finite element simulations and detailed point-wise experimental velocity measurements are presented for the international benchmark problem of a sphere sedimenting axially under gravity through a cylindrical tube of viscoelastic fluid. In addition to measurements and calculations of the viscoelastic correction to the drag force exerted by the fluid on the sphere, the non-invasive technique of laser Doppler velocimetry is used to probe the kinematics of the fluid over a wide range of Deborah numbers, 0.4 less than or equal to De less than or equal to 9, and dimensionless radius ratios, 0.12 less than or equal to a/R less than or equal to 0.64. These observations are augmented in Part 2 of this work (Rajagopalan et al., 1995) by digital video-imaging studies and fully-implicit time-dependent numerical simulations of the initial acceleration of the sphere from rest and the resulting overshoot in the velocity that arises from fluid viscoelasticity. Numerical simulations are reported for the upper-convected Maxwell (UCM) model, the Chilcott-Rallison model (each with a single relaxation time constant) and the multimode Phan-Thien-Tanner model. For the radius ratio of a/R = 0.5, flow simulations using the UCM model have been extended well above the commonly reported limit point of De = 1.6 through careful mesh refinement. The multimode simulations with a spectrum of time constants allow a quantitative description of the fluid rheology in both viscometric shear flows and transient extensional experiments. However, the range of computationally attainable De is limited by the inability to resolve intense stress boundary layers. Both experimental measurements and numerical calculations indicate the wall correction factor for the motion of a sphere through a viscoelastic fluid is a sensitive function of the radius ratio and the Deborah number. They also show that non-Newtonian effects in the strong extensional how near the rear stagnation point result in the formation of a pronounced viscoelastic wake effect extending up to 30 sphere radii behind the sphere and corresponding to a downstream shift in the fluid streamlines. However there is no experimental indication of the formation of a negative wake or a flow instability in the wake, and the flow remains stable for all radius ratios and Deborah numbers investigated experimentally.
引用
收藏
页码:225 / 257
页数:33
相关论文
共 46 条
[1]   MIGRATION OF MACROMOLECULES UNDER FLOW - THE PHYSICAL ORIGIN AND ENGINEERING IMPLICATIONS [J].
AGARWAL, US ;
DUTTA, A ;
MASHELKAR, RA .
CHEMICAL ENGINEERING SCIENCE, 1994, 49 (11) :1693-1717
[2]   ON THE ROLE OF STRESS-INDUCED MIGRATION ON TIME-DEPENDENT TERMINAL VELOCITIES OF FALLING SPHERES [J].
AMBESKAR, VD ;
MASHELKAR, RA .
RHEOLOGICA ACTA, 1990, 29 (03) :182-191
[3]  
ARIGO MT, 1994, 29 FOR CAV MULT FLOW, V194, P139
[4]   THE UNSTEADY MOTION OF A SPHERE IN A VISCOELASTIC FLUID [J].
BECKER, LE ;
MCKINLEY, GH ;
RASMUSSEN, HK ;
HASSAGER, O .
JOURNAL OF RHEOLOGY, 1994, 38 (02) :377-403
[5]  
Bird RB, 1987, DYNAMICS POLYM LIQUI, V91, P1397, DOI DOI 10.1016/0377-0257(78)80009-3
[7]   HIGHLY ELASTIC CONSTANT-VISCOSITY FLUID [J].
BOGER, DV .
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 1977, 3 (01) :87-91
[8]   STREAMLINE UPWIND PETROV-GALERKIN FORMULATIONS FOR CONVECTION DOMINATED FLOWS WITH PARTICULAR EMPHASIS ON THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS [J].
BROOKS, AN ;
HUGHES, TJR .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1982, 32 (1-3) :199-259
[9]   REPORT ON THE VIIITH INT WORKSHOP ON NUMERICAL-METHODS IN VISCOELASTIC FLOWS [J].
BROWN, RA ;
MCKINLEY, GH .
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 1994, 52 (03) :407-413
[10]   CALCULATIONS OF VISCOELASTIC FLOW THROUGH AN AXISYMMETRIC CORRUGATED TUBE USING THE EXPLICITLY ELLIPTIC MOMENTUM EQUATION FORMULATION (EEME) [J].
BURDETTE, SR ;
COATES, PJ ;
ARMSTRONG, RC ;
BROWN, RA .
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 1989, 33 (01) :1-23