Most of the engineering flow problems are turbulent in nature. So knowledge in turbulence is imperative for an engineer. In this video lesson we will see how to predict and quantify effect of turbulence.

## Why Turbulence ?

There is no universally accepted answer for reason behind turbulence. Many scientific searches to find out reason behind turbulence of flow have ended up in vain. Take a look at a famous witticism made by Heisenberg regarding this.

But engineers and scientists have developed a good understanding on nature of turbulence and way to quantify effect of it. So here we will learn**‘How Turbulence’**instead of

**‘Why Turbulence’**.

## How to distinguish a Turbulent flow ?

All turbulent flows have got following 3 characteristics

- 3 dimensional
- Fluctuating
- Chaotic - With eddies and vortices

## A Daily Life Experience to Predict Turbulence

To understand nature of turbulence we will consider a daily life experience, a tap water problem. Consider following 3 cases, where in each case flow rate of water increases. It is clear that as flow rate increases turbulence of flow also increases. So finding number one turbulence increases with increase in flow velocity.

Fig.1 Increase in turbulence of flow as flow rate of water is increased |

Fig.2 Decrease in turbulence of flow as flow as viscosity of fluid is increased |

From above findings it can be summarized that turbulence increases with increase in flow velocity and decrease in fluid viscosity. Flow velocity increases with increase *inertial force* on the fluid and if fluid viscosity is high viscous force in fluid will also be high. So it can be summarized that turbulence increases with increase in inertial force and decrease in viscous force.

## Concept of Reynolds number

Ratio of *inertial force* to *viscous force* is know as Reynolds number .

*Reynolds number*can be represented as Where D is diameter of pipe. So you can define a

*Critical Reynolds number*for a particular problem above which flow is turbulent and below which flow is laminar

## More analysis - Concept of Averaging

Consider a turbulent tap water case with constant flow rate input. If you measure velocity at tap outlet for this case you will find that velocity is highly unsteady as shown in figure below.

Fig.3 Fluctuating velocity field at outlet of a turbulent flow problem |

Fig.4 Result of averaging operation in constant flow input flow problem |

## Averaging operation

Averaging is defined as follows

Where*time interval*used for integration should be carefully chosen. It should be small enough to take care of any unsteadiness in flow, at the same time it should be big enough to take care of any fluctuation in the flow.

An engineer always speak about averaged quantities when he comes across a turbulent flow. Because averaged quantities are pretty enough for his purpose. Knowledge of actual fluctuating value of a turbulent flow might be useful in scientific world, but for an engineer it is of no use most of the time. Figure below shows averaging operation in a turbulent-unsteady flow.

Fig.5 Averaging operation on a turbulent-unsteady problem |

## Shear stress in a Turbulent Flow & Turbulence Modeling

Let us consider a turbulent pipe flow case, if you want to determine shear stress near pipe wall, first thing you have to obtain is averaged velocity profile near wall as shown in figure below.

Fig.6 Average velocity profile and inter layer mixing in a turbulent flow |

*laminar shear stress*. Second component arises due to mixing of different fluid layers in a turbulent flow as shown in figure above. This is known as

*turbulent shear stress*or

*Reynolds stress*. So shear stress in a turbulent flow can be represented as One can note

*Reynolds stress*is in terms of fluctuating parts of velocity components, which are unknown to the user. Determination of

*Reynolds stress*in terms of known quantities (averaged quantities)is considered to be one of the toughest problem in fluid mechanics. And this is known as

*Turbulence Modeling*.

## Applications Utilizing Effect of Turbulence

Most of the time turbulence has positive effect on engineering devices. It increases convective heat transfer, it increases mixing and reduces drag around a body.

### Heat Transfer Enhancement

Convective heat transfer coefficient increases drastically when the flow becomes turbulent, due to effective mixing of different fluid layers in the flow. This behaviour is shown in following figure.So it is a common practice among designers to covert laminar flows into turbulent by introducing suitable vortex generators in the flow.
### Drag reduction

Coefficient of drag around a body reduces by a huge amount when flow changes from laminar to turbulent.This phenomenon is shown in following figure.This is the reason why golf ball has got lot of dimples on it.This irregularities on surface of the ball will help in transforming laminar flow into turbulent and reduces drag, with low drag ball can travel more distance.

Fig.7 Increase in heat transfer coefficient due to turbulence |

Fig.8 Change in drag coefficient over a sphere when flow changes from laminar to turbulent |