Finite Element Analysis of Non-Newtonian Flow: Theory and Software

by Huang, Hou-Cheng; Li, Zheng-Hua; Usmani, Asif S.

• ISBN13: 9781852330248
• ISBN10: 1852330244
• Edition: CD
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Springer Verlag

Summary

Presents the finite element simulation for non- newtonian flow, with the basic theory of the subject being included in the opening chapters. CD-ROM included. DLC: Non-Newtonian fluids.

Table of Contents

1 Introduction	1	(6)
1.1 Preamble	1	(2)
1.2 Objectives and Layout	3	(4)
2 Governing Differential Equations	7	(16)
2.1 Introduction	7	(1)
2.2 Governing Equations	8	(1)
2.3 Constitutive Equations	9	(4)
2.3.1 Viscous shear flow	9	(2)
2.3.2 Inelastic generalised Newtonian flow	11	(1)
2.3.3 Power law fluid	11	(2)
2.4 Elastic Liquids	13	(1)
2.4.1 Maxwell model	13	(1)
2.4.2 Oldroyd's liquid B model	14	(1)
2.4.3 White-Metzner model	14	(1)
2.5 Equation in Steady State Flow	14	(1)
2.6 Initial and Boundary Conditions	15	(1)
2.7 Stream Functions	16	(7)
3 Finite Element Method	23	(30)
3.1 Introduction	23	(3)
3.2 Variational Principle and Rayleigh-Ritz Method	26	(5)
3.3 Galerkin Weighted Residual Method	31	(2)
3.4 Virtual Work Principle	33	(2)
3.5 Finite Element Method in Two Dimensions	35	(18)
3.5.1 Introduction	35	(1)
3.5.2 K Matrix and load vector	36	(1)
3.5.3 Triangular elements	37	(9)
3.5.4 Natural coordinate system	46	(3)
3.5.5 Numerical integration	49	(4)
4 Steady Non-Newtonian Flow	53	(22)
4.1 Introduction	53	(3)
4.2 Creeping Motion	56	(1)
4.2.1 Extra stress and strain rate relations	57	(1)
4.3 Finite Element Formulation for Creeping Flow	57	(18)
4.3.1 Finite element spatial discretisation	58	(3)
4.3.2 Slippage and friction	61	(2)
4.3.3 Numerical examples	63	(12)
5 Temporal Discretisation	75	(20)
5.1 Introduction	75	(2)
5.1.1 Transient Newtonian flow equations in two dimensions	76	(1)
5.1.2 Boundary conditions	76	(1)
5.2 Finite Element Formulation	77	(6)
5.3 Temporal Discretisation	83	(8)
5.3.1 Generalized trapezoidal and mid-point family of methods	83	(2)
5.3.2 High order scheme-Taylor series in time	85	(1)
5.3.3 Predictor-corrector scheme	86	(2)
5.3.4 Automatic time step selection	88	(3)
5.4 Solution of Nonlinear System of Equations	91	(4)
6 Finite Element Analysis for Transient non-Newtonian Flow	95	(34)
6.1 Introduction	95	(5)
6.2 The Taylor-Galerkin Method	100	(1)
6.3 The Pressure Correction Method	101	(4)
6.3.1 Pressure correction method with midpoint rule	102	(1)
6.3.2 Pressure correction method with higher order scheme	103	(1)
6.3.3 Stability considerations	104	(1)
6.4 Transient Non-Newtonian Flow	105	(1)
6.4.1 Transient Generalised Newtonian Flow	105	(1)
6.4.2 Oldroyd's liquid B model	106	(1)
6.5 Non-isothermal Flow	106	(3)
6.6 Adaptive Analysis	109	(4)
6.7 Error Estimation for Fluid Flow	113	(2)
6.8 Numerical Examples	115	(14)
6.8.1 Newtonian flow	115	(1)
6.8.2 Non-Newtonian flow	116	(1)
6.8.3 Adaptive method	117	(12)
A Software Description for NSTEAD	129	(50)
A.1 Introduction	129	(1)
A.2 Glossary of Variable Names	129	(3)
A.2.1 Main variables	129	(2)
A.2.2 Main arrays	131	(1)
A.2.3 Main subroutines	131	(1)
A.3 Program Overview	132	(4)
A.4 Input Instructions	136	(7)
A.5 Element Stiffness Calculations	143	(4)
A.6 Documented Examples	147	(32)
A.6.1 Example 1: Flow in a plane channel	147	(18)
A.6.2 Example 2: Flow over a step	165	(14)
B Software Description for NFLOWG	179	(36)
B.1 Introduction	179	(1)
B.2 Glossary of Variable Names	179	(5)
B.2.1 Main logical variables for the code	179	(2)
B.2.2 Main variables for the geometry and mesh data	181	(2)
B.2.3 Main arrays used in the Code	183	(1)
B.2.4 Main subroutines	183	(1)
B.3 Main Routine of NFLOWG	184	(2)
B.4 Input Instructions	186	(14)
B.4.1 Input instruction for file PARA.DAT	187	(2)
B.4.2 Input instruction for file GEOM.DAT	189	(11)
B.5 Documented Example	200	(15)
Subject Index	215