Introduction to Computational Fluid Dynamics
Fluid dynamics, actually is the study of fluid under motion, governed with a certain set of conservation equations, wherein things are conserved, with reference to mass, momentum & energy.
If these three quantities i.e. mass, momentum & energy are solved entirely we can define any fluid flow. The conservation laws are formulated in the form of equations which we try to solve and that’s what simulation is all about.
The aim of any fluid flow analysis is primarily two fold:
to know the effect of flow on the boundaries
- Drag on a car
- Heat transfer rate in heat exchangers
- Heat sink performance
- Pressure rise across pump
- Temperature distribution in a room
Flow visualization allows us to find the nature of flow , ie. if there is a flow separation into primary & secondary flows, find out recirculation zones and is any widely used in heating ventilation & air-conditioning (HVAC) studies. Flow visualization is a very important aspect wherein CFD scores over many other studies.
We had people across the centuries who had greatly contributed to fluid mechanics. Archimedes discovered the phenomena called as buoyancy effect, on the basis of which we can now do natural convection studies, that is still a challenging task in CFD. Newton has a great contribution in the field of mathematics & fluid mechanics and to what we study in CFD today. Also we had people who contributed to mathematical modeling like Leibniz, Bernolloi, Euler, Navier & Stokes about whom we shall frequently come across. In the last 2 centuries the study of fluid mechanics had been primarily mathematical that has helped many mathematician to contribute. We had Reynolds who with his number, the Reynolds number helped us determine whether the inertial forces will dominate the viscous forces and cause the flow to be turbulent. Prandtl in early twentieth century with his boundary layer theory is helped in predicting more accurate the drag on aerofoils, also contributed in heat transfer with the Prandtl number, i.e. a relative measure of velocity boundary layer & thermal boundary layer. Taylor has contributed with his series expansion dealing with numerical methods especially in finite difference method. So we had may researchers contributing to fluid mechanics & its solutions, mathematical models & formulating the models across the centuries. We are now living in a time wherein the software firms/ packages have exploited all this work with the advancement of computational speed.
Where is a fluid flow …?
Fluid flows encountered in everyday life include:
- meteorological phenomena (rain, wind, hurricanes, floods, fires)
- environmental hazards (air pollution, transport of contaminants)
- heating, ventilation and air conditioning of buildings, cars etc.
- combustion in automobile engines and other propulsion systems
- interaction of various objects with the surrounding air/water
- complex flows in furnaces, heat exchangers, chemical reactors etc.
- processes in human body (blood flow, breathing, drinking . . . ) and so on and so forth.
Fluid flow process occur almost everywhere in the universe, in fact its difficult to find a process that does not involve a flow of fluid. Even if you do not find exactly a fluid flowing you would surely find heat flow existing over in the universe. More specifically on our earth we have weather & climate changes which are very much function of fluid flow, driven by heat transfer & pressures, of-course also assisted by the earth’s rotation revolution around the sun.
We have fluid flow and heat transfer application for as high as an aircraft, as low as in sea, in surface ships, under the sea in submarines and locomotives.
We have the fluid flow in recreational activities as well to reduce the drag so as to increase the fuel efficiency and the performance of cars/ bike riders & for water sports.
Overall we deal with a very beautiful phenomena of fluid dynamics !
Methods of Solving Fluid Flow:
- Analytical Fluid Dynamics (AFD)
Before the high speed computers of today arrived, the usual process followed by researchers were using manual/ hand calculations with some approximations. With the made assumptions, approximations they generally made a free body diagram of it simplifying the complex 3-D geometry into simple 1-D or 2-D analysis and ended up doing an integration of these equations. Setting up the constraints in the form of initial and boundary conditions to find constants of integration and ultimately getting values at discrete points, where they could end-up having results getting plots, force variation across a plate (e.g. fig below).
where D, is the drag on the flat plate.
Now for the simple case as above of a flow over flat plate the AFD, might be easy to apply but not in cases of complex problem as of a heat sink for example. However, its always not just the complex geometries but also more often we are limited in defining the exact physics in terms of concerned mathematical equations.
We have the general transport equation given as below:
The quantity “phi” with different values represent different equations. To solve the general transport equation on a real geometry is a challenge and if we do not want face this one can have another approach, with experimental studies i.e. of experimental fluid dynamics (EFD).
- Experimental Fluid Dynamics (EFD):
Here we have a scale down model often based on engineering dimensional analysis, wherein we create a prototype model, perform appropriate experiments under conditions that would reflect exactly what would happen in reality. Further we introduce a lot of probe points for data collection thereby introducing disturbances in the flow itself. Also its not so always easy to make an exact prototype of the real problem and there are problems with cost and feasibility too.
So we can see that both methods; the AFD & EFD have some limitations, AFD with respect to complex geometries and physics capturing and EFD with issues like time, cost & feasiblility.
That’s why we have CFD wherein we have the mathematical model i.e. the physics clearly defined, and these physics equations that are usually the partial differential equations, are solved through numerical methods. With the assumptions that we can neglect some higher order terms we can use computer to solve them we end-up having a CFD result, a result that is numerical solution of our physics. The advantages of this are many like we have a low cost simulation, we are able to do a lot of analysis within a short period of time as we don’t have to actually make a physical model of our study. With short variation in some parameters we can study the problem using the high speed computer can take about hours or days time to obtain the results. So in brief, with CFD approach we can have a low cost solution, in short time and a comprehensive information as compared to any other approach.
Having pointed out the advantages of CFD over the AFD and the EFD, its important to know the limitations of CFD too. CFD results can never be 100% correct as those depend on the following things:
- the input data may involve too much guessing or imprecision
- the mathematical model of the problem at hand may be inadequate
- the accuracy of the results is limited by the available computing power
Also although CFD does not replace the measurements completely but the amount of experimentation and the overall cost can be significantly reduced.
Coming up next: CFD Simulation Process
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