Computational FluidDynamics, the term most used by academics, is also known by the acronym CFD(Computational Fluid Dynamics). It allows problems to be approached through numerical simulation applied to fluid flow, heat transfer and other related phenomena. It is an area of engineering that is constantly developing, as its applicability and potential increase with the evolution of available computing resources.
In order to understand CFD simulation, one must be familiar with two main areas: numerical methods and thermofluid dynamics.
Numerical Methods
These are methods in which algorithms are applied to solve mathematical problems, such as: algebraic equations, systems of linear equations, interpolation and extrapolation, adjusting points on a curve, differential equations, etc.
Fluid mechanics and thermodynamics
Thermal sciences include fluid mechanics, thermodynamics and heat transfer. Dealing specifically with fluid mechanics, it can be said that this area of knowledge studies the behavior of fluids divided into two categories:
- fluids at rest, or fluid statics;
- fluids in motion, or fluid dynamics.
Based on these categories, engineering has several highly complex industrial applications for fluid mechanics, but which, at the same time, are very simple in most people's everyday lives. All movement occurs in some kind of fluid, whether it's air, water or other more specific fluids. Here are some examples:
- Airflow for cooling notebooks;
- The air that air conditioning throws at people in an auditorium;
- Opening and closing hydraulic valves in apartments;
- The transportation of people by air with airplanes or by sea with ships;
- Discharge into toilets.
Até mesmo nas aplicações citadas, percebe-se que o estudo da mecânica dos fluidos está intimamente ligado às disciplinas de termodinâmica e transferência de calor. Tomando como exemplo um sistema de refrigeração, o fluido de trabalho, também chamado de refrigerante, é usado para a transferência de calor de uma região mais fria para uma mais quente. Portanto, a análise CFD abrange a aplicação de todas as ciências térmicas para o estudo dos fluidos. Para conhecer mais sobre a Termodinâmica, veja este artigo.
Mathematics behind CFD
As you might expect, fluids obey the fundamental laws of physics regarding the conservation of mass, quantity of movement and energy. These fundamental laws lead us to the continuity, energy and Navier-Stokes equations. These are commonly referred to as the Navier-Stokes equations, a set of equations composed of partial derivatives that describe the behavior of fluids. In simple flows, the Navier-Stokes equations can be reduced to others that allow analytical solutions, for example, Bernoulli's fluid equations.
However, most real engineering cases do not involve simple flows. Therefore, Computational Fluid Dynamics (CFD) replaces complex geometries with thousands (even millions) of known elements and systems of partial differential equations with a set of approximate algebraic equations.
The vast majority of software used in these simulations uses the finite volume method. Thus, each cell can be seen as a small control volume in which the discretized versions of the equations are solved. In other situations, a two-dimensional analysis can be more practical and efficient, using small areas as cells.
CFD simulations
Based on the aforementioned physical and mathematical knowledge, various software programs available on the market can be used to obtain the desired results. It is possible to obtain velocity, pressure and temperature distributions of a fluid in a pipe; analyze aero and hydrodynamic forces acting on a building; quantify the heat lost by equipment in an industrial plant; among many other applications.
Figure 1: Simulation of pressure and velocity in a region of turbulence - SOURCE: Kot Collection.
More than just simulating the behavior of a fluid, it is essential to interpret its results correctly. CFD simulation can be used in a variety of cases where experimentation may be unfeasible or where the costs of full-scale models are prohibitive. It is a simulation technique that requires know-how so that the analysis generates good results with low computational costs.
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References:
[1] ÇENGEL, Yunus A.; CIMBALA, John M. Fluid mechanics: fundamentals and applications. AMGH Editora, 2012.
