Computation of Unsteady Internal Flows

1 Introduction.- 1-1 The Importance of Modelling Unsteady Flows.- 1-2 The Nature and Causes of Unsteadiness.- 1-3 Flow Equations, their Mathematical Nature and Physical Implications.- 1-4 Summary of Book Content.- 2 Overview of Elementary Temporal Discretizations.- 2-1 Introduction.- 2-2 Profile Assumptions for Variables.- 2-3 The Generic Discretized Equation.- 2-4 Two-level Schemes.- 2-5 Three-level Schemes.- 2-6 Predictor-Corrector Methods.- 2-7 Splitting Methods.- 2-8 Time Marching and Stiffness.- 2-9 Characterizing Stability and Accuracy of Schemes.- 2-10 Boundary Conditions and Solution Initialization.- 2-11 Integration of Particle/Droplet Transport Equations.- 2-12 Two-level Scheme Exemplar.- 2-13 Conclusions.- 3 Temporal and Spatial Discretization Relationships.- 3-1 Introduction.- 3-2 The Substantial Derivative.- 3-3 Convective Term Treatments.- 3-4 Dissipation, Dispersion.- 3-5 Moving Boundaries.- 3-6 Time Adaptive Solutions.- 3-7 Conclusions.- 4 Solver Algorithms and General Solution Procedures.- 4-1 Introduction.- 4-2 Simultaneous Equation Solvers.- 4-3 Parallel Processing.- 4-4 Evaluation of the Pressure Field.- 4-5 Review of Commercial Programs and their Unsteady Flow Capabilities.- 4-6 Features of Codes used for Case Studies.- 4-7 Conclusions.- 5 Solution Adapted Time-Steps.- 5-1 Introduction.- 5-2 Numerical Methods.- 5-3 Discussion of Results.- 5-4 Conclusions.- 6 Turbulence Modelling.- 6-1 Introduction.- 6-2 VLES/URANS Modelling.- 6-3 LES Modelling.- 6-4 Zonal LES/DES.- 6-5 URANS Models used in Case Studies.- 6-6 Conclusions.- 7 Cyclic Annular Cavity Flows.- 7-1 Introduction.- 7-2 Numerical Details.- 7-3 Discussion of Results.- 7-4 Conclusions.- 8 Cyclic Aero Engine Motivated Cavity Flows.- 8-1 Introduction.- 8-2 Numerical Details.- 8-3 Lower Reynolds Number Results.- 8-4 Higher Reynolds Number Results.- 8-5 Adaptive Time Stepping.- 8-6 Conclusions.- 9 Cyclic Moving Boundary Flows.- 9-1 Introduction.- 9-2 Numerical Details.- 9-3 Discussion of Results for Journal Bearing.- 9-4 Discussion of Results for Magnetic Bearing.- 9-5 Conclusions.- 10 Cyclic Complex System Flow.- 10-1 Introduction.- 10-2 Numerical Details.- 10-3 Discussion of Results for Fluid Flow.- 10-4 Adaptive-Time Stepping.- 10-5 Discussion of Results for Scalar and Particle Transport.- 10-6 Conclusions.- 11 Transient Complex System Flow.- 11-1 Introduction.- 11-2 Numerical Details.- 11-3 Discussion of Results.- 11-4 Conclusions.- 12 Overall Conclusions with Future Perspectives.- Appendices.- A Discretization of The Governing Equations and Multilevel Convergence Operators.- A-l General Equation Discretization.- A-2 Treatment of Variables at the Axis of Rotation.- A-3 Discretization of Earth’s Acceleration Due to Gravity.- A-4 The Multilevel Restriction and Prolongation Operators.- B Derivation of Condif Scheme for Variable Density Fluid.- C Multilevel Convergence Performance Exemplars.- C-l Driven Box Flow.- C-2 Grid Embedding.- C-3 Cluttered Geometries.- C-4 Grid Aspect Ratio.- C-5 Heated Rotating Cavity Flow.- C-6 Conclusions.- D Further Chapter 10 Case Details.- E FLO_CAV Program User Information.- E-l FLO_CAV Program.- E-2 Description of Program Structure and Subroutines.- E-3 Program Input.- E-4 Boundary Conditions.- E-5 Post processing.- F FLO_BEARING Program User Information.- F-l FLO_BEARING Program.- F-2 Description of Program Structure and Subroutines.- F-3 Program Input.- F-4 Boundary Conditions.- F-5 Input Files.- G FLO_ELEC Program User Information.- G-l FLO_ELEC Program.- G-2 Description of Program Structure and Subroutines.- G-3 ProgramInput.- G-4 General Details.- References.