Turbulence Modelling for CFD by Hrvoje Jasak

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Turbulence Modelling for CFD Hrvoje Jasak hrvoje.jasak@fsb.hr Faculty of Mechanical Engineering and Naval Architecture University of Zagreb, Croatia NUMAP-FOAM Summer School, Zagreb 2-15 Sep 2009 Turbulence Modelling for CFD – p. Outline Objective ã Review turbulence modelling practices in modern CFD: assumptions, choice of model and performance Topics ã Handling turbulent flows ã Vortex dynamics and energy cascade ã Direct numerical simulation ã Reynolds-averaged Navier-Stokes equations ◦ E
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  NUMAP-FOAM Summer School, Zagreb 2-15 Sep 2009 Turbulence Modelling for CFD Hrvoje Jasak hrvoje.jasak@fsb.hr Faculty of Mechanical Engineering and Naval ArchitectureUniversity of Zagreb, Croatia Turbulence Modelling for CFD – p.  NUMAP-FOAM Summer School, Zagreb 2-15 Sep 2009 Outline Objective ã Review turbulence modelling practices in modern CFD: assumptions, choice ofmodel and performanceTopics ã Handling turbulent flows ã Vortex dynamics and energy cascade ã Direct numerical simulation ã Reynolds-averaged Navier-Stokes equations ◦ Eddy viscosity models ◦ Reynolds stress transport models ◦ Near-wall effects and low- Re models ◦ Special topics: transient RANS and transitional flows ã Large Eddy Simulation (LES) ã Choosing a turbulence model for you application ã Review of two popular turbulence models ◦ Spalart-Allmaras model; k − ω SST model by Menter ã Future of turbulence modelling Turbulence Modelling for CFD – p.  NUMAP-FOAM Summer School, Zagreb 2-15 Sep 2009 Why Model Turbulence? ã The physics of turbulence is completely understood and described in all itsdetail: turbulent fluid flow is strictly governed by the Navier-Stokes equations ã ...but we do not like the answer very much! ◦ Turbulence spans wide spatial and temporal scales ◦ When described in terms of vortices (= eddies), non-linear interaction iscomplex ◦ Because of non-linear interactions and correlated nature, it cannot beattacked statistically ◦ It is not easy to assemble the results of full turbulent interaction and describethem in a way relevant for engineering simulations : we are more interestedin mean properties of physical relevance ã In spite of its complexity, there is a number of analytical, order-of-magnitude andquantitative result for simple turbulence flows. Some of them are extremely usefulin model formulation ã Mathematically, after more than 100 years of trying, we are nowhere near todescribing turbulence the way we wish to Turbulence Modelling for CFD – p.  NUMAP-FOAM Summer School, Zagreb 2-15 Sep 2009 Handling Turbulent Flows ã Turbulence is irregular, disorderly, non-stationary, three-dimensional, highlynon-linear, irreversible stochastic phenomenon ã Characteristics of turbulent flows (Tennekes and Lumley: First Course inTurbulence) ◦ Randomness , meaning disorder and no-repeatability ◦ Vorticality : high concentration and intensity of vorticity ◦ Non-linearity and three-dimensionality ◦ Continuity of Eddy Structure , reflected in a continuous spectrum offluctuations over a range of frequencies ◦ Energy cascade, irreversibility and dissipativeness ◦ Intermittency : turbulence can only occupy only parts of the flow domain ◦ High diffusivity of momentum, energy, species etc. ◦ Self-preservation and self-similarity : in simple flows, turbulence structuredepends only on local environment ã Turbulence is characterised by higher diffusion rates: increased drag, mixing,energy diffusion. In engineering machinery, this is sometimes welcome andsometimes detrimental to the performance ã Laminar-turbulent transition is a process where laminar flow naturally and withoutexternal influence becomes turbulent. Example: instability of free shear flows Turbulence Modelling for CFD – p.
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