P M V Subbarao Professor Mechanical Engineering Department I I T Delhi

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Presentation transcript:

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…

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.

An intermittently laminar-turbulent flow

Intermittency Factor

On Set of Turbulence

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

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

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

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

Averaging of Continuity Equations

Time Averaging Operations

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

Averaging of x-momentum Equation