1. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi
Turbulent Flows
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Flows Infected by Disturbance…

2. This change, however, does not occur suddenly.
The Infection
Instability may drastically change the flow pattern from laminar to turbulent
This change, however, does not occur suddenly.
The instability triggers a transition process, which is characterized by its intermittently laminar-turbulent nature.

3. An intermittently laminar-turbulent flow

4. Intermittency Factor

5. On Set of Turbulence

6. Definition
A Fluid motion in which velocity, pressure, and other flow quantities fluctuate irregularly in time and space.
“Turbulent Fluid motion is an irregular condition of flow in which the various quantities show a random variation with time and space coordinates, so that statistically distinct average values can be observed.” - Hinze
“Turbulence is due to the formation of point or line vortice on which some component of the velocity becomes infinite.:” Jean Leray

7. What is turbulence?
Unsteady, aperiodic motion in which all three velocity components fluctuate, mixing matter, momentum, and energy.
Time

8. First Methods on Analyzing Turbulent Flow
Reynolds (1895) decomposed the velocity field into a time average
motion and a turbulent fluctuation
- Likewise
f stands for any scalar: u, v, w, T, p, where:
Time averaged Scalar

9. Averaging Navier Stokes equations
Substitute into Steady incompressible Navier Stokes equations
Instantaneous velocity
fluctuation
around
average
velocity
Average
velocity
time
Continuity equation:

10. Averaging of Continuity Equations

11. Time Averaging Operations

12. Average x-momentum Equation
Write x-momentum equations in a short format:
=0 continuity
Short format of momentum equation in x direction:

13. Averaging of x-momentum Equation