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
So if a fluid flow under consideration has got all 3 above characteristics it is turbulent in nature, otherwise flow is laminar.
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 |
If you replace water in tap by a fluid which is more viscous in
nature(oil), you will find that flow is not turbulent even at high flow
rate. So finding number two turbulence decreases with increase in fluid
viscosity.
|
| 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 .
It is clear that when Reynolds number increases turbulence increases. So
Reynolds number is the criterion which decides whether a flow is
laminar or turbulent. For this pipe problem
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 |
This is one big characteristic of turbulent flow, strictly speaking all
flow variables in a turbulent flow are unsteady in nature.
But if you do a mathematical operation called averaging in this case on
flow velocity, the result becomes steady in nature. So you could say a
turbulent flow is in steady state if averaged flow variable is in steady
state.
 |
| 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 |
It is clear from above figure that actual velocity can have 2
components, one average component and another fluctuating component.
Similarly one can define averaging for any other flow variable say
pressure,temperature,other components of velocity etc.
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 |
Assuming this is 2 dimensional flow case one can express shear stress parallel to flow direction as
Thus shear stress has got 2 components. First component which is similar to shear stress in a laminar case is known as
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
 |
| Fig.7 Increase in heat transfer coefficient due to turbulence |
Drag reduction
 |
| Fig.8 Change in drag coefficient over a sphere when flow changes from laminar to turbulent |
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