Reynolds Method to Diagnosize Symptoms of Infected Flows.... P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Reynolds Averaged.

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Presentation transcript:

Reynolds Method to Diagnosize Symptoms of Infected Flows.... P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Reynolds Averaged NS Equations

Averaging of x-momentum Equation

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

The Reynolds View of Cross Correlation

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

Reynolds Averaged Navier Stokes equations

Reynolds Stress Tensor This is usually called the Reynolds stress tensor Reynolds stresses : total are unknown Total 4 equations and = 10 unknowns

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

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.

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

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

Modeling of Turbulent Viscosity Fluid property – often called laminar viscosity Flow property – turbulent viscosity MVM: Mean velocity models TKEM: Turbulent kinetic energy equation models