Finflo Ltd: CFD

What is CFD?

The physics of any fluid flow is governed by three fundamental principles. Newton's second law determines the acceleration of fluid, and mass and energy are conserved. Since Newton's second law is expressed in a vector form, the number of governing differential equations is five. These equations are known as Navier-Stokes equations and they were derived at the beginning of nineteenth century.

Although some fascinating solutions for these equations have been known for a long time, their application to real flow problems can be made only numerically. The numerical methods applied today were developed as late as during the 1970's and 1980's and the development is still going on especially in the physical parametrization of the flow models.

The acronym CFD stands for 'computational fluid dynamics' and it is used for this relatively young branch of science that includes all the steps involved in simulating a fluid flow. The establishment of the computational domain is also known as 'pre-processing'. At this stage the geometry of the case is specified and the domain is divided into a large number of cells, which form a network called a computational grid. The grid is used to approximate the derivatives of the Navier-Stokes equations. This results in a large number of algebraic nonlinear equations. There are five equations per cell and the grid may contain millions of cells.

The number of unknowns is thus five times the number of grid cells. In addition auxiliary equations are formed to describe the flow physics. A common phenomenon to be modeled in the case of all practical flows is turbulence. Depending on the case, there may be many other differential equations and constitutive models that describe the flow. The task of the flow simulation is to solve these equations with the user-specified boundary conditions.

The solution contains a huge number of data. In order to gain an insight to the calculated result, visualization methods are used. This stage is also called 'post-processing'. With new visualization methods it has been easier to understand the structures of fluid flow, which has facilitated theoretical fluid mechanics. The role of CFD has become so strong that it can be considered as a third area of fluid dynamics. The other two classical fields are experimental and theoretical fluid dynamics.

The origin of CFD is in the aerospace industry. Today it has become an essential tool in almost every field of engineering science. There are also other type of applications such as environmental flows and perhaps most important of all: weather prediction. The same Navier-Stokes equations govern all flows - from blood vessels to large oceanographic flows, from jet engines to room ventilation etc. However, the physics of the flow is very different in these cases.

As was mentioned above, turbulence is the most important and a common factor that requires sophisticated modeling in all cases. Also the solution algorithms differ from each others in different fields of application. Everyone has noticed that a numerical weather prediction sometimes may fail completely. The same concerns almost every other field of flow simulation and in order to produce reliable simulations a lot of expertise is required. In many cases CFD resembles an art: the parameters selected, required simplifications for the geometry and (sometimes) ad hoc boundary conditions, require experience and intuition in addition to pure science.

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