Introductory FLUENT Notes Fluent User Services cente ANSYS LUENT v6. 3 December 2006 wwfluentusers. com FLUENT The k-e Turbulence models Standard k-8(SKE)model The most widely-used engineering turbulence model for industrial applications Robust and reasonably accurate Contains submodels for compressibility, buoyancy, combustion, etc Limitations u The a equation contains a term which cannot be calculated at the wall. Therefore wall functions must be used Generally performs poorly for flows with strong separation, large streamline curvature,and large pressure gradient Renormalization group (rngak-8 model Constants in the k-e equations are derived using renormalization group theory Contains the following submodels Differential viscosity model to account for low Re effects Analytically derived algebraic formula for turbulent Prandtl /Schmidt number Swirl modification Performs better than SKe for more complex shear flows, and flows with high strain rates swirl. and separation C 2006 ANSYS. nc All ANSYS, Inc. Proprietar
© 2006 ANSYS, Inc. All rights reserved. 6-11 ANSYS, Inc. Proprietary Fluent User Services Center www.fluentusers.com Introductory FLUENT Notes FLUENT v6.3 December 2006 The k–ε Turbulence Models ◆ Standard k–ε (SKE) model ⚫ The most widely-used engineering turbulence model for industrial applications ⚫ Robust and reasonably accurate ⚫ Contains submodels for compressibility, buoyancy, combustion, etc. ⚫ Limitations ◼ The ε equation contains a term which cannot be calculated at the wall. Therefore, wall functions must be used. ◼ Generally performs poorly for flows with strong separation, large streamline curvature, and large pressure gradient. ◆ Renormalization group (RNG) k–ε model ⚫ Constants in the k–ε equations are derived using renormalization group theory. ⚫ Contains the following submodels ◼ Differential viscosity model to account for low Re effects ◼ Analytically derived algebraic formula for turbulent Prandtl / Schmidt number ◼ Swirl modification ⚫ Performs better than SKE for more complex shear flows, and flows with high strain rates, swirl, and separation
Introductory FLUENT Notes Fluent User Services cente ANSYS LUENT v6. 3 December 2006 wwfluentusers. com FLUENT The k-e Turbulence models Realizable k-8(RKE)model o The term realizable means that the model satisfies certain mathematical constraints on the reynolds stresses, consistent with the physics of turbulent fle a Positivity of normal stresses: uu >0 SchwarZ' inequality for Reynolds shear stresses:(uu; ) suu Neither the standard k-e model nor the rng k-e model are realizable Benefits More accurately predicts the spreading rate of both planar and round jets Also likely to provide superior performance for flows involving rotation boundary layers under strong adverse pressure gradients, separation, and recirculation C 2006 ANSYS. nc All ANSYS, Inc. Proprietar
© 2006 ANSYS, Inc. All rights reserved. 6-12 ANSYS, Inc. Proprietary Fluent User Services Center www.fluentusers.com Introductory FLUENT Notes FLUENT v6.3 December 2006 The k–ε Turbulence Models ◆ Realizable k–ε (RKE) model ⚫ The term realizable means that the model satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of turbulent flows. ◼ Positivity of normal stresses: ◼ Schwarz’ inequality for Reynolds shear stresses: ⚫ Neither the standard k–ε model nor the RNG k–ε model are realizable. ⚫ Benefits: ◼ More accurately predicts the spreading rate of both planar and round jets. ◼ Also likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation. ( ) 2 2 2 ui uj ui uj ui u j 0
Introductory FLUENT Notes Fluent User Services cente ANSYS LUENT v6. 3 December 2006 wwfluentusers. com FLUENT The k-o Turbulence models The k-o family of turbulence models have gained popularity mainly because The model equations do not contain terms which are undefined at the wall, i.e. they can be integrated to the wall without using wall functions They are accurate and robust for a wide range of boundary layer flows with pressure gradient FLUENT offers two varieties of k-o models Standard k-o(SK W) model Most widely adopted in the aerospace and turbo-machinery communities Several sub-models/options of k-o: compressibility effects, transitional flows and shear-flow corrections Shear Stress Transport k-o(SSTK W) model(Menter, 1994) The Sstk-o model uses a blending function to gradually transition from the standard k-o model near the wall to a high Reynolds number version of the k-8 model in the outer portion of the boundary layer Contains a modified turbulent viscosity formulation to account for the transport effects of the principal tur bulent shear stress C 2006 ANSYS. nc All ANSYS, Inc. Proprietar
© 2006 ANSYS, Inc. All rights reserved. 6-13 ANSYS, Inc. Proprietary Fluent User Services Center www.fluentusers.com Introductory FLUENT Notes FLUENT v6.3 December 2006 The k–ω Turbulence Models ◆ The k–ω family of turbulence models have gained popularity mainly because: ⚫ The model equations do not contain terms which are undefined at the wall, i.e. they can be integrated to the wall without using wall functions. ⚫ They are accurate and robust for a wide range of boundary layer flows with pressure gradient. ◆ FLUENT offers two varieties of k–ω models. ⚫ Standard k–ω (SKW) model ◼ Most widely adopted in the aerospace and turbo-machinery communities. ◼ Several sub-models/options of k–ω: compressibility effects, transitional flows and shear-flow corrections. ⚫ Shear Stress Transport k–ω (SSTKW) model (Menter, 1994) ◼ The SST k–ω model uses a blending function to gradually transition from the standard k–ω model near the wall to a high Reynolds number version of the k–ε model in the outer portion of the boundary layer. ◼ Contains a modified turbulent viscosity formulation to account for the transport effects of the principal turbulent shear stress
Introductory FLUENT Notes Fluent User Services cente ANSYS LUENT v6. 3 December 2006 wwfluentusers. com FLUENT Large eddy simulation Large Eddy Simulation (LEs LES has been most successful for high-end applications where the rans models fail to meet the needs. For example Combustion Mixing External Aerodynamics(flows around bluff bodies) Implementations in FLUENt Subgrid scale(SGs) turbulent models Smagorinsky-Lilly model Wall-Adapting Local Eddy-Viscosity WALE Dynamic Smagorinsky-Lilly model Dynamic Kinetic Energy Transport Detached eddy simulation(DES)model LES is applicable to all combustion models in FlUent Basic statistical tools are available: Time averaged and rms values of solution variables, built-in fast Fourier transform (FFT) Before running LES, consult guidelines in theBest Practices For LES (containing advice for meshing, subgrid model, numerics, BCs, and more) C 2006 ANSYS. nc All ANSYS, Inc. Proprietar
© 2006 ANSYS, Inc. All rights reserved. 6-14 ANSYS, Inc. Proprietary Fluent User Services Center www.fluentusers.com Introductory FLUENT Notes FLUENT v6.3 December 2006 Large Eddy Simulationn ◆ Large Eddy Simulation (LES) ⚫ LES has been most successful for high-end applications where the RANS models fail to meet the needs. For example: ◼ Combustion ◼ Mixing ◼ External Aerodynamics (flows around bluff bodies) ◆ Implementations in FLUENT: ⚫ Subgrid scale (SGS) turbulent models: ◼ Smagorinsky-Lilly model ◼ Wall-Adapting Local Eddy-Viscosity (WALE) ◼ Dynamic Smagorinsky-Lilly model ◼ Dynamic Kinetic Energy Transport ⚫ Detached eddy simulation (DES) model ◆ LES is applicable to all combustion models in FLUENT ◆ Basic statistical tools are available: Time averaged and RMS values of solution variables, built-in fast Fourier transform (FFT). ◆ Before running LES, consult guidelines in the “Best Practices For LES” (containing advice for meshing, subgrid model, numerics, BCs, and more)
Introductory FLUENT Notes Fluent User Services cente ANSYS LUENT v6. 3 December 2006 wwfluentusers. com FLUENT Law of the Wall and Near -Wall treatments Dimensionless velocity data from a wide variety of turbulent duct and boundary-layer flows are shown here Wall shea Ur=251m(Ury/v)+545 p y where y is the normal distance from the wall For equilibrium turbulent all- adjacent cells in the log-la fully turbulent region Upper lim buffer layer region have known velocity log-law region Reynolds no nd wall shear stress data viscous sublayer C 2006 ANSYS. nc All ANSYS, Inc. Proprietar
© 2006 ANSYS, Inc. All rights reserved. 6-15 ANSYS, Inc. Proprietary Fluent User Services Center www.fluentusers.com Introductory FLUENT Notes FLUENT v6.3 December 2006 Law of the Wall and Near-Wall Treatments ◆ Dimensionless velocity data from a wide variety of turbulent duct and boundary-layer flows are shown here: where y is the normal distance from the wall ◆ For equilibrium turbulent boundary layers, walladjacent cells in the log-law region have known velocity and wall shear stress data Wall shear stress = w U = + U y y + = U u u