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

ISBN-13: 9781447112044 / Angielski / Miękka / 2014 / 218 str.

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

Opis

A follow on from the author's work "Finite Elements in Heat Transfer" which we published 11/94, and which is a powerful CFD programme that will run on a PC. The fluid flow market is larger than the previous, and this package is good value in comparison with other software packages in Computational Fluid Dynamics, which are generally very expensive. The work in general copes with non-Newtonian laminar flow using the finite element method, and some basic theory of the subject is included in the opening chapters of the book.

Spis treści

1 Introduction.- 1.1 Preamble.- 1.2 Objectives and Layout.- 2 Governing Differential Equations.- 2.1 Introduction.- 2.2 Governing Equations.- 2.3 Constitutive Equation.- 2.3.1 Viscous shear flow.- 2.3.2 Inelastic generalised Newtonian flow.- 2.3.3 Power law fluid.- 2.4 Elastic Liquids.- 2.4.1 Maxwell model.- 2.4.2 Oldroyd’s liquid B model.- 2.4.3 White-Metzner model.- 2.5 Equation in Steady State Flow.- 2.6 Initial and Boundary Conditions.- 2.7 Stream Function.- 3 Finite Element Method.- 3.1 Introduction.- 3.2 Variational Principle and Rayleigh-Ritz Method.- 3.3 Galerkin Weighted Residual Method.- 3.4 Virtual Work Principle.- 3.5 Finite Element Method in Two Dimensions.- 3.5.1 Introduction.- 3.5.2 K Matrix and load vector.- 3.5.3 Triangular elements.- 3.5.4 Natural coordinate system.- 3.5.5 Numerical integration.- 4 Steady Non-Newtonian Flow.- 4.1 Introduction.- 4.2 Creeping Motion.- 4.2.1 Extra stress and strain rate relations.- 4.3 Finite Element Formulation for Creeping Flow....57.- 4.3.1 Finite element spatial discretisation.- 4.3.2 Slippage and friction.- 4.3.3 Numerical examples.- 5 Temporal Discretisation.- 5.1 Introduction.- 5.1.1 Transient Newtonian flow equations in two dimensions.- 5.1.2 Boundary conditions.- 5.2 Finite Element Formulation.- 5.3 Temporal Discretisation.- 5.3.1 Generalized trapezoidal and mid-point family of methods.- 5.3.2 High order scheme - Taylor series in time.- 5.3.3 Predictor-corrector scheme.- 5.3.4 Automatic time step selection.- 5.4 Solution of Nonlinear System of Equations.- 6 Finite Element Analysis for Transient non-Newtonian Flow.- 6.1 Introduction.- 6.2 The Taylor-Galerkin Method.- 6.3 The Pressure Correction Method.- 6.3.1 Pressure correction method with midpoint rule.- 6.3.2 Pressure correction method with higher order scheme.- 6.3.3 Stability considerations.- 6.4 Transient Non-Newtonian Flow.- 6.4.1 Transient Generalised Newtonian Flow.- 6.4.2 Oldroyd’s liquid B model.- 6.5 Non-isothermal Flow.- 6.6 Adaptive Analysis.- 6.7 Error Estimation for Fluid Flow.- 6.8 Numerical Examples.- 6.8.1 Newtonian flow.- 6.8.2 Non-Newtonian flow.- 6.8.3 Adaptive method.- A Software Description for NSTEAD.- A.1 Introduction....129.- A.2 Glossary of Variable Names.- A.2.1 Main variables.- A.2.2 Main arrays.- A.2.3 Main subroutines.- A.3 Program Overview.- A.4 Input Instructions.- A.5 Element Stiffness Calculations.- A.6 Documented Examples.- A.6.1 Example 1: Flow in a plane channel…..147.- A.6.2 Example 2: Flow over a step.- B Software Description for NFLOWG.- B.1 Introduction.- B.2 Glossary of Variable Names.- B.2.1 Main logical variables for the code.- B.2.2 Main variables for the geometry and mesh data…..181.- B.2.3 Main arrays used in the Code.- B.2.4 Main subroutines.- B.3 Main Routine of NFLOWG.- B.4 Input Instructions.- B.4.1 Input instruction for file PARA.DAT.- B.4.2 Input instruction for file GEOM.DAT.- B.5 Documented Example.