CFD codes are structured around the numerical algorithms which solve fluid flow problems [42, 293]. These codes consist of three basic user interface that defines a problem parameters for which results are examined and are: The pre-processor, solver and post- processor.
1. Pre-processor: This is where inputs of flow problems to a CFD program is mainly
carried out (also called flow domain) and is dominated by user activities that includes:
Defining the computational domain
Generating meshes from the domain
Selecting the physical and chemical processes to be modelled
Defining fluid properties
Specifying boundary conditions
2. Solver: The solver is the numerical algorithm that incorporate three basic steps that are
employed based on the control-volume techniques or finite volume method, which is the method identified for the formulation of most stablished CFD codes, example include: CFX/ANSYS FLUENT, PHOENICS, STAR CD. The following are the major steps:
Integrating the governing equations of the fluid flow over the finite control volume,
Discretizing the resulting integral equation into sets of algebraic equations,
Solving the algebraic equations iteratively.
The choice of a solver in FLUENT CFD code is limited to pressure - based or density - based and is characterised as either segregated or coupled types [264].
1. Post-processor: This displays the domain grid, vector plots, contours, particle tracking,
animation of the dynamic results, etc. The increased popularity of engineering workstations has led to the development of large amount of work which has recently taken place in the post - processing field.
3.5 Grid Generation
The grid defines the cells on which flow (velocity vectors, static pressure, shear stress, TKE, etc.) and heat transfer variables (HTC, Nu, heat flux, temperature etc.) are calculated throughout the computational domain. The accuracy of a CFD solution is governed by the number of cells in the grid [42, 293]. It is generally shown that the larger the number of cells the better the solution’s accuracy [42, 263]. Though the number of grid is a significant factor but the accuracy of the solution, costs of running the simulation in terms of computer hardware and the time of carrying out the calculations are all dependent on the fineness of
the grid, which also depends on the cell size [42, 264, 293]. Optimal grid are often non - uniform, they are finer in regions of large variations and coarser in regions with relatively insignificant change. Grid generators are incorporated in either the CFD solver (ANSYS workbench) or are operated independently (ICEM CFD meshing tool) and can be read and incorporated to the solver.
3.5.1 Types of Grid
The present work CHT CFD grid generation tool is the ANSYS ICEM CFD code which can be use in generating (or discretizing) either structured, unstructured or hybrid grids.
1. Structured grid: A structured grid [42] consists of planar cells with four edges for 2D
and are called tetra grid or volumetric cells with six faces for 3D and are referred to as hexahedral (or hex) grid. It is rectangular in shape by which the cells can be distorted to represent another shape, each cell is numbered according to indices (i, j, k) which do not necessary correspond to x, y and z coordinates. In structured grid, fewer cells can be generated and it enables much finer resolution when highly resolved grids are required closed to the wall boundary layer.
2. Unstructured grid: Unstructured grid [42] consists of cells of various shapes typically
triangles or quadrilaterals for 2D (or tetra) and tetrahedrons or hexahedrons for 3D (or tet) grids. The grid are not uniquely identify by indices i and j, but instead cells are numbered in another way internally in the CFD code. For complex geometries, an unstructured grid is usually much easier to create.
3. Hybrid grid: This combines regions or blocks of both structured and unstructured grids
[42]. It enables high resolution near wall without requiring high resolution away from it.
3.5.2 Grid Sensitivity
A highly qualitative grid is a requirement for accurate and reliable CFD solution [42]. Grid independence test has been shown to be an important requirement to ascertain the number of cells and quality of a chosen grid size [32, 33, 263, 265, 266] and is grouped into two: Firstly, Adaptive (self) meshing capability incorporated in the simulation software (Fluent CFD solver), it allows for automatic refinement of grid in areas of rapid variations. Secondly, initial refinement of coarse grid until certain key results do not change, which is a systematic search of grid independent results using the meshing software (ICEM CFD). Generally for volume meshing [42, 264, 292], the tetrahedral grid provides a more automatic solution with the ability to add grid controls (based on non-uniformity in edge intervals) to improve the accuracy in critical regions, as calculation are nodes based centre. While, for hexahedral grid it provides a better accurate solution but is more difficult to
generate, which is based on uniformity in opposite edge intervals and calculations are on cell centre based.
3.6 Boundary Conditions
Boundary condition (BC) is a mathematical statement or function of the flow field variables (velocity, temperature, density, pressure, etc.) from governing equations that is specified at the surface of the computational domain [42, 264, 265]. The accuracy of CFD solution is also dependent on the imposed BC which is also a determining factor for the type of flow that is being modelled. This is in addition to the dependency of the CFD solution on the equations of motion, the computational domain and the grid. Several types of boundary conditions terminologies are generally available for used in a CFD code which is based on the type of package selected [264]. The available BCs that ANSYS Fluent CFD code employed includes: Wall, inflow/outflow, miscellaneous and internal BCs. These BCs are specified at the face or plane surfaces for 3D flow and or edge or line for 2D flow.
The simplest BC [42] is the Wall at which the velocity is set to zero (no-slip condition), either the wall temperature or heat flux and wall roughness are specified here. The options at the boundaries through which fluid enters (inflow) or leaves (outflow) the computational domain are generally categorized as velocity-specified (e.g. velocity inlet or mass flow BC) or pressure specified (pressure inlet) conditions. The miscellaneous BCs are neither of the two boundaries stated above and are enforced as either periodicity BC - useful when geometry involves repetition or symmetry BC - where force flow field variables are mirror imaged across a plane. Finally, the internal (or interior) BC which are imposed on the faces or edges that do not define the BC of the computational domain, it exists inside the domain.
3.7 Convergence Criteria
Iteration in CFD, is a simulation procedure that is used to determine the smoothness and readiness of a numerical calculation, it also shows the accuracy of CFD predictions [42, 264, 293]. In order to understand that an iteration has yielded the required predicted results, convergence criteria should be satisfied. Judging for convergence requires that residual levels are carefully examined by monitoring the relevant integrated quantities and finally checking for mass and energy balances. The residual plots shows an indication that residual values have reached the specified tolerance. For example by using a pressure-based solver in ANSYS Fluent CFD, the default residuals have to decrease by at least 10-3: The scaled energy residual decreases to 10-6 while that of the scaled species residual decreases to 10-5.
Using the k - ɛ turbulence model for example, the residuals that have been shown for the convergence plots are [22, 25, 33]: The energy, continuity, TKE k, dissipation rate of TKE and species velocities. The energy residual define the solution equation for flow of heat for example temperature, continuity residual show the solution for the continuous flow of the fluid used, TKE and dissipation of TKE residuals interprets the solution for the transport equation of k and respectively. The velocities residual solve for the individual directional flow velocities of the fluid along the surfaces of the model geometry. These residuals indicates an imbalance left inside a cell and for each residual the specified criteria must be satisfied [42, 264].
Solution Stability: The requirement for a numerical stability is a needed characteristic of
numerical algorithms that is necessitated based on the use of elliptic solver in order to get a solution [264, 292]. A converged steady solution may not be stable and can be physically not realisable, as calculation performed on digital computers might damp out or magnify approximation errors that can yield different results [292]. In order to confirm the accuracy of the algorithm used that will stabilized the converged solution, a transient state solution incorporated in most commercial CFD codes is used and stability is monitored based on calculated flow time and when data (example HTC) no longer changes with flow.