Elliptic-blending k - ε model

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Formulation Original model, Billard & Laurence (2012) Dρk Dt = Pk +E −ρε+ ∂ µ µt ∂k + ∂xj 2 σk ∂xj Dρε 1 = Cε1 Dt τ Pk −ρC ∗ ε2ε + ∂ µ µt ∂ε + ∂xj 2 σε ∂xj Dρϕ Dt = ρ(1−α3 )fw +ρα 3 ϕ fh −Pk k +CDϕ + ∂ µ µt ∂ + ∂xj 2 σϕ ∂ L 2 ∂2 α ∂xj∂xj = α−1
Formulation Equation-by-equation modifications Turbulent kinetic energy k: Modifications: Dρk Dt = Pk +Pb +E −ρε+ ∂ ◮ Adding buoyancy source term Pb, ∂xj µ µt ∂k + 2 σk ∂xj ◮ What alternative formulation for E ? Expensive to compute, and only active very near the wall. ◮ Definition of time-scale τ and τlim: k2 τ = ε +C 2 t ν ε ; τlim CT = max τ, √ 3CµϕS with S = 2SijSij. Where is CT = 0.6 coming from?
Page 1 and 2: Elliptic-blending k −ε model Val
Page 3: Introduction Assessing performance
Page 7 and 8: 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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