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Analysis of Turbulent ( Infected by Disturbance ) Flows

Analysis of Turbulent ( Infected by Disturbance ) Flows. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi. Quantification of the Infection & its Effect on Mean Fow. An intermittently laminar-turbulent flow. Intermittency Factor. On Set of Turbulence.

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Analysis of Turbulent ( Infected by Disturbance ) Flows

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  1. Analysis of Turbulent (Infected by Disturbance) Flows P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Quantification of the Infection & its Effect on Mean Fow....

  2. An intermittently laminar-turbulent flow

  3. Intermittency Factor

  4. On Set of Turbulence Laminar Flow fighting against the Disturbances Laminar Flow Accepting the Disturbances Laminar Flow Hosting the growth of the Disturbances Fully Developed Turbulent Flow

  5. 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

  6. First Method of Analyzing Steady 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

  7. Averaging of Continuity Equations

  8. Time Averaging Operations

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

  10. Averaging of x-momentum Equation Write x-momentum equations in a short format:

  11. Reynolds Averaged Steady Turbulent Momentum Equations Reynolds averaged x-momentum equation for steady incompressible turbulent flow

  12. The Reynolds View of Cross Correlation

  13. Reynolds averaged y-momentum equation for steady incompressible turbulent flow Reynolds averaged z-momentum equation for steady incompressible turbulent flow

  14. Reynolds Averaged Navier Stokes equations

  15. Reynolds Stress Tensor This is usually called the Reynolds stress tensor Reynolds stresses : total 9 - 6 are unknown Total 4 equations and 4 + 6 = 10 unknowns

  16. Time averaged Infected Navier Stokes Equation For all the Three Momentum Equations, turbulent stress tensor:

  17. Reynolds stresses • Performing the Reynolds Averaging Process, new terms has arisen, namely the Reynolds-stress tensor: • This brings us at the turbulent closure problem, the fact that we have more unknowns than equations. • Three velocities + pressure + six Reynolds-stresses • Three momentum equations + the continuity equation • To close the problem, we need additional equations to solve infected flow.

  18. Derivation of Conservation Equations for Reynolds Stresses • Derivations of Reynolds-stress conservation Equations • Introduces new unknowns (22 new unknowns)

  19. Simplified Reynolds Averaged Navier Stokes equations 4 equations 5 unknowns → We need one more ???

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