# Introduction to Computational Fluid Dynamics

# 1.0 Introduction

We live in a world of motion. In this world, every movement that you make interacts with fluids. Walking down a corridor, air flows around you. Your body heats the air over your head, which rises to the ceiling. A ship turning in a channel gets driven by water flow around the hull and rudder. Every aspect of change in our world gets shaped by fluid mechanics. Given its pervasive presence, we need the ability to predict and control fluid mechanics. One of the best tools in the arsenal is computational fluid dynamics (CFD).

# 2.0 Methods of Analysis

CFD works best as one of many tools available for analysis of fluid mechanics. These divide into three major categories:

- Analytical
- Computational
- Experimental

For analytical methods, imagine someone at a chalkboard, white dust on their trousers, deriving lengthy, complicated hand equations. But hand equations still remain too simplistic to be accurate for anything but the most basic of scenarios.

On the other end lies the experimental, requiring expensive testing facilities custom built for detailed experiments. (Figure 2‑1) Plus, these facilities are often targeted towards specific types of problems and experiments. So we can only test for known theories and designs. They restrict our ability to explore new possibilities.

Computational methods offer a happy medium. They work like experimental methods, but we construct virtual test facilities on the computer. No construction costs, and infinite flexibility to customize the experiment for each purpose.

# 3.0 The Solution of CFD

## 3.1 Fluids Are Complicated

The problem behind CFD was that fluids remain complicated. The mathematics to describe the physics of fluid mechanics get very messy. There was an anecdote that Albert Einstein one day sat down to try and derive the fundamental equations for fluid mechanics. After many weeks of intense frustration, he gave up and pronounced it as too difficult. He moved on to other easier tasks . . . like special relativity. Sure, this was just a tall tale, but it explains the problem of fluid mechanics. We needed a way to simplify overly complicated mathematics, but keep them applicable to the real world.

## 3.2 The Answer of the Box

The solution was a box. By applying the fluid dynamic equations to the very simple geometry of a cube, the equations became manageable. Imagine a simple cube of fluid where you knew the fluid flow properties on every side (Figure 3‑2) Combine this with the simple geometry of the box, and the equations for fluid mechanics become manageable. Still intensely complicated, but now simple enough for a human to program and a computer to solve. We can now predict everything about the fluid flow for any point within that box. This was the basic unit of CFD: a single cell.

The real magic happens when we start stacking thousands and millions of these cells together, in any generalized pattern necessary. CFD became a generalized tool: create a generalized physics solver capable of adapting to literally any shape of geometry.

# 4.0 CFD Accuracy

Everyone questions whether CFD can be trusted. Wrong question. The software and methodology are only as good as the CFD engineer that operates the software. Yes, the software possesses great potential, capable of extreme accuracy, even matching the capabilities of experimental methods. But the CFD engineer must demonstrate and prove that accuracy for every single CFD project. The accuracy lies in the CFD engineer, not the software.

# 5.0 Conclusion

CFD is not a magic bullet; it adds to our toolbox in fluid mechanics analysis. We don’t throw away all the other tools as a result. That being said, **this is one impressive tool**, when used correctly. If used improperly, it can become an incredible waste of time and money. The key rests with finding the right CFD engineer. The best CFD engineer’s are fluid experts first, and build on that knowledge to efficiently drive their CFD software. With the right operator, CFD can be cost effective, incredibly informative, and offer unparalleled flexibility. Those are the qualities that anyone wants from their tools, and **CFD can deliver.**

# 6.0 References

[1] |
Wikipedia Authors, “MD11 12ft Wind Tunnel Test,” Wikmedia Commons, 7 January 2007. [Online]. Available: https://ar.wikipedia.org/wiki/%D9%85%D9%84%D9%81:MD-11_12ft_Wind_Tunnel_Test.jpg. [Accessed 2019 18 Febuary]. |

[2] |
Wikipedia Authors, “Albert Einstein Head.jpg,” Wikimedia Commons, 25 11 2014. [Online]. Available: https://commons.wikimedia.org/wiki/File:Albert_Einstein_Head.jpg. [Accessed 31 12 2018]. |