Abstract
An efficient and thorough strategy to introduce undergraduate students to a numerical approach of calculating flow is outlined. First, the basic steps, especially discretization, involved when solving Navier-Stokes equations using a finite-volume method for incompressible steady-state flow are developed with the main aim being for the students to follow through from the mathematical description of a given problem to the final solution of the governing equations in a transparent way. The well-known ‘driven-cavity’ problem is used as the problem for testing coding written by the students, and the Navier-Stokes equations are initially cast in the vorticity-streamfunction form. This is followed by moving on to a solution method using the primitive variables and discussion of details such as, closure of the Navier-Stokes equations using turbulence modelling, appropriate meshing within the computation domain, various boundary conditions, properties of fluids, and the important methods for determining that a convergence solution has been reached. Such a course is found to be an efficient and transparent approach for introducing students to computational fluid dynamics.
Highlights
Computational Fluid Dynamics (CFD) is the simulation of transport phenomena, reacting systems, heat transfer, etc., using modelling, i.e., mathematical physical problem formulation and numerical solution, which include discretization methods, solvers, numerical parameters and mesh generation.The efficient and thorough development, implementation and evaluation of a suitable curriculum, which incorporates both the theoretical and practical aspects of CFD, for undergraduate students as an extension of their knowledge in the thermo-fluids area is warranted and necessary in modern engineering programmes
Numerical methods have an advantage over analytical methods of solution in that analytical methods tend to be restrictive by commonly requiring simple geometries, unrealistic assumptions and until lately assumed linearity, whereas real engineering problems usually have quite complex geometries and highly non-linear phenomena
Despite the advantages of numerical methods, the latter may miss some finer aspects of fluid dynamics which, from the equations of analytical methods, may be more transparent, for example the question of uniqueness of weak solutions to Navier-Stokes equations in three dimensions
Summary
For Computational Fluid Dynamics laboratories, each student had a desktop computer on which was loaded software which provides the interface as a ‘three-dimensional’ fully interactive environment. The interface uses the concept of ‘virtual reality’ and allows a student to simulate a flow, including geometry, properties, boundary conditions, closure of equations, numerics, etc, from beginning to end without having to resort to specialized codes, or code writing. The virtual reality (VR) environment is designed as a general purpose CFD interface, which can handle such problems as fluid flow, heat transfer, reacting flows, or a combination of all, and consists of the VR-Editor (pre-processor), the VR-Viewer (post-processor) and the solver module which performs the actual calculations. The VR-Editor allows a student to set the overall computational domain size, define the position, size and properties of object introduced into the domain, specify the material properties which occupy the domain, specify inlet and outlet boundary conditions, specify initial conditions, select turbulence models (if necessary), specify the fineness and type of computational mesh, and set the numerics by choosing a suitable solution algorithm and which influence the speed of calculation to obtain a convergence solution. The post-processing graphical capabilities are vector plots, contour plots, iso-surfaces, streamlines and x-y plots
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