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TURBULENCE MODELING A Discussion on Different Techniques used in Turbulence Modeling -Reni Raju

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2 Topics Covered zConcept zDefinition zMethods of Solving Turbulent Equations zNavier Stokes Equation zModels

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3 Turbulence zExamples: zWake of a water near the columnn of a bridge. zDispersion of Smoke in the atmosphere.

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4 Definition zA Fluid motion in which velocity,pressure, and other flow quantities fluctuate irregularly in time and space. z“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 obsevered.” - Hinze z“Turbulence is due to the formation of point or line vortice on which some component of the velocity becomes infinite.:” -Jean Leray

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5 Methods for Solving Turbulent Equations zDIRECT NUMERICAL SIMULATION (DNS) zLARGE-EDDY SIMULATION (LES) zREYNOLDS AVERAGED NAVIER-STOKES (RANS)

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6 Navier Stokes Equation For a Steady, Incompressible Fluid the Continuity and x-momentum equations

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7 For turbulent flow, The time averages,

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8 Time averaged Navier Stokes Equation For all the Three Momentum Equation

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9 Turbulence Models zIntegral Method zEddy-Viscosity Models yZero-Equation Models yOne-Equation Models yTwo- Equation Models zReynolds Stress Models

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10 1.Integral Method Advantages -Computational Simplicity and Ease. -Useful for same kind of flow. -Easy to interpolate with experimental bench marks. Disadvantages -Lack of Flexibility.

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11 2.Eddy Viscosity models For 2-D incompressible boundary layer equation Momentum Equation, or

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12 (a) ZERO-EQUATION MODELS

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13 (a) ZERO-EQUATION MODELS Advantages -Simplest of Models satisfying the requirements. Disadvantages -Some ad hoc assumptions have to be made regarding boundary layer and velocity.

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14 (b) ONE-EQUATION MODELS Turbulence Kinetic Energy Dimensionless Turbulent Viscosity Mean Strain Rate

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15 (b) ONE-EQUATION MODELS Advantages -Additional assumptions can be avoided. -Break from the equilibrium concepts in a practical consderation. Disadvantages -The length scale is still a algebraic quantity. -Computationally more difficult.

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16 (c) TWO-EQUATION MODELS Turbulence K.E. Dissipation Rate

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17 (c) TWO-EQUATION MODELS Advantages -Overcomes the short comings of zero and one equation model. Disadvantages -Not appropriate to use in a viscous sublayer. -Still need to make assumptions.

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18 3.Reynolds Stress Models Advantages -More General than Eddy-Viscosity Models. -Better Prediction for flow with sudden changes. -Possible Ultimate turbulence models. Disadvantages -None of the equations can be solved exactly. -Computational difficulty because of more no. of PDE.

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19 zCauses of Turbulent Motion. zSteady State. zMass Weighted averaging.

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

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

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