10.9 Computational fluid dynamics

Computational fluid dynamics (CFD) provides insight into transient and turbulent flow. The mechanical principles governing fluids and solids are the same. CFD uses numerical methods such as the finite element method, the finite difference method, the boundary element method, and the finite volume method. It allows analysis and optimization of structural component geometry for efficient fluid flow. It also allows one to view pressure, velocity, and temperature in the flow. Dynamics is the study of motion of objects. A fluid actually means anything that isn't a solid. Both air and water are fluids from this point of view. Fluids are considered as any "shapeless" substance which cannot remain at rest under a sliding stress. The following are examples of the problem that can be solved by CFD: A. Hanging wet clothes out to dry. B. Burning gasoline in an automobile engine. C. Sailing. D. A jet of water issuing from a slit. E. Dissolution. F. Melting, boiling . G. Mechanical movement of a fan. H. Gas flow in jet engine. n the CFD-based analysis the Navier-Stokes equations take the form of a large system of nonlinear equations. There are three fundamental principles of computational fluid dynamics: Energy is conserved. Mass is conserved. Momentum is conserved. Temperature, the pressure, the three velocity components, and density are typical variables for fluid flow. The flow variables can be stored at the center of the computational cell (Cell Centered methods) or at the vertices of the cell (Cell Vertex or Vertex Centered methods). The acoustic-fluid model is the simplest: the fluid only transmits pressure waves, fluid-particle motions are small. Only one degree of freedom (the potential) needs to be calculated at each finite-element node in potential-based analysis. CFD simulates steady and unsteady flow in air and in boundary layers. The mesh is created to represent the air configuration surrounding a solid. The mesh is more dense for the boundary layers. Zones with turbulence flow demand a fine local grid resolution. Zone A for water falling from a step is an example of such a region There are two different quantitive results for a jet of water issued at a constant low velocity (<5 cm/s) from a long slit into air chamber: 1. The distortion in the inlet hole can be observed in the exact model and the experiment. 2. The enlargement of the flow in the center may be caused by numerical errors in the boundary layer between water and air. This is a rough estimation of the turbulence depending on Reynolds Number Re. Re is meant to measure the relative importance of fluid inertia to viscous forces. Outside the boundary layer, the flow is independent of the Reynolds Number. Viscous forces are negligible if the Reynolds number is large. n is the kinematic viscosity of the fluid; L and U are characteristic length and velocity scales for a flow. The result of CFD modeling is color contours of pressure, velocity, and temperature. Contrary to solid bodies where stress concentration usually takes place at notches or holes, the concentration of CFD parameters can be observed on a smooth surface. Supersonic flow in a jet engine with a spike: the primary shock wave originates at nose of the spike and impinges on the inner surface of the intake nozzle. This is a the region of pressure concentration. The relative difficulty or ease of the CFD-based analysis depend on dimensionality in time (varying or not varying with time), dimensionality in space (one- , two-, or three-dimensional space), complexity of the geometry of the solids, and complexity of the flow-influencing boundary conditions. If available computer resources are not sufficient for the necessary numerical accuracy, and assumptions were made for the input data the result of CFD-based modeling may not be reliable . The reliability is greater for laminar rather than turbulent flows, and for chemically-inert rather than chemically-reactive gases.