Elliptic-blending k - ε model

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Formulation Equation-by-equation modifications Turbulent dissipation rate ε: Dρε Dt Modifications: 1 = Cε1 τ (fcPk +Pb)−ρC ∗ ε2ε + ∂ ∂xj ◮ Adding buoyancy source term Pb, µ µt ∂ε + 2 σε ∂xj ◮ Testing curvature correction fc, as suggested by Durbin for k −ω models: ◮ Option for C ∗ ε2 : fc = 1+α1|η3|+3α1|η3| C ∗ ε2 = ⎧ ⎨ Cε2 ⎩ Cε2 +α3 (0.4−Cε2 )tanh ∂ νt ∂k ∂xj σk ∂xj ε−1 3/2
Formulation Equation-by-equation modifications Reduced normal stress ϕ: Dρϕ Dt = ρ(1−α3 )fw+ρα 3 fh−ρCµτlimϕ 2 S 2 + ∂ with fw = − ϕε 2k ; fh = − 1 τ Modifications: C1 −1+C2 µ µt ∂ϕ + ∂xj 2 σϕ ∂xj Pk +Pb ϕ− ρε 2 3 ◮ Buoyancy source term added here Pb (is it correct?), ◮ Cross-diffusion term neglected: found to pose significant problems in many cases with coarse mesh. ◮ Dissipation term Pk ϕ k by ρCµτlimϕ 2 S 2 to avoid division by zero when k → 0.
Page 1 and 2: Elliptic-blending k −ε model Val
Page 3 and 4: Introduction Assessing performance
Page 5: Formulation Equation-by-equation mo
Page 9 and 10: Formulation All-y + wall-treatment
Page 11 and 12: Validation Convergence Best converg
Page 13 and 14: Results: validation of all-y + wall
Page 15 and 16: Validation — Wall-treatment Chann
Page 25 and 26: Validation — Performance Channel
Page 27 and 28: Validation — Performance Backward
Page 29 and 30: Validation — Performance Backward
Page 31 and 32: Validation — Performance Periodic
Page 37 and 38: Validation — Performance 2d diffu
Page 43 and 44: Part 1: Rotation and strong curvatu
Page 45 and 46: Failure — need for improvement NA
Page 47 and 48: Failure — need for improvement NA
Page 49 and 50: Part 2: Buoyancy-driven flows
Page 51 and 52: Failure — need for improvement Bu
Page 53: Failure — need for improvement Ve

Elliptic-blending k - ε model

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