Book contents
- Frontmatter
- Contents
- Nomenclature
- Preface
- 1 Introduction
- 2 1D Heat Conduction
- 3 1D Conduction–Convection
- 4 2D Boundary Layers
- 5 2D Convection – Cartesian Grids
- 6 2D Convection – Complex Domains
- 7 Phase Change
- 8 Numerical Grid Generation
- 9 Convergence Enhancement
- Appendix A Derivation of Transport Equations
- Appendix B 1D Conduction Code
- Appendix C 2D Cartesian Code
- Bibliography
- Index
6 - 2D Convection – Complex Domains
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Nomenclature
- Preface
- 1 Introduction
- 2 1D Heat Conduction
- 3 1D Conduction–Convection
- 4 2D Boundary Layers
- 5 2D Convection – Cartesian Grids
- 6 2D Convection – Complex Domains
- 7 Phase Change
- 8 Numerical Grid Generation
- 9 Convergence Enhancement
- Appendix A Derivation of Transport Equations
- Appendix B 1D Conduction Code
- Appendix C 2D Cartesian Code
- Bibliography
- Index
Summary
Introduction
In practical applications of CFD, one often encounters complex domains. A domain is called complex when it cannot be elegantly described (or mapped) by a Cartesian grid. By way of illustration, we consider a few examples.
Figure 6.1 shows the smallest symmetry sector of a nuclear rod bundle placed inside a circular channel of radius R. There are nineteen rods: one rod at the channel center, six rods (equally spaced) in the inner rod ring of radius b1, and twelve rods in the outer ring of radius b2. The rods are circumferentially equispaced. The radius of each rod is r0. The fluid (coolant) flow is in the x3 direction. The flow convects away the heat generated by the rods and the channel wall is insulated. It is obvious that a Cartesian grid will not fit the domain of interest because the lines of constant x1 or x2 will intersect the domain boundaries in an arbitrary manner. In such circumstances, it proves advantageous to adopt alternative means for mapping a complex domain.
These alternatives are to use
curvilinear grids or
finite-element-like unstructured grids.
Curvilinear Grids
It is possible to map a complex domain by means of curvilinear grids (ξ1, ξ2) in which directions of ξ1 and ξ2 may change from point to point. Also, curvilinear lines of constant ξ1 and constant ξ2 need not intersect orthogonally either within the domain or at the boundaries. Figure 6.2 shows the nineteen-rod domain of Figure 6.1 mapped by curvilinear grids.
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- Introduction to Computational Fluid Dynamics , pp. 161 - 213Publisher: Cambridge University PressPrint publication year: 2005