CFD Platform for Turbo-machinery Simulation

Transcription

1 CFD Platform for Trbo-machinery Simlation Lakhdar Remaki BCAM- Basqe Centre for Applied Mathematics

2 Otline p BCAM-BALTOGAR project p CFD platform design strategy p Some new developments p Some reslts p Conclsions

3 BCAM-BALTOGAR Project p Selected BALTOGAR prodcts BALTOGAR centrifgal trbofan BALTOGAR Axial trbofan

4 CFD - Comptational Flid Dynamic

5 CFD - ndstry Aerospace, atomotive, ventilation, power generation, chemical manfactring, polymer processing, petrolem exploration, medical research, meteorology,.

6 BCAM-BALTOGAR CFD Platform POD- Model Redction Aero-Elastics Models Aero-Acostics Models Optimization Tools Mesh Generator Steady-RANS Solver Rotating Effects Post-Processing tools URANS LES-SST

7 BCAM-BALTOGAR CFD Platform NetGen (Johannes Kepler University Linz SU2 (Stanford University Mesh Generator Steady-RANS Solver Rotating Effects Post-Processing tools Paraview

8 (2 ( ( ( D v f p v v v t µ λ [ ] (2 ( ( ( ( ( v D v f p v p E E v v t µ λ θ κ Continity eqation Momentm eqation Energy eqation p Navier-Stokes Eqations 0 ( v t ij k k i j j i ij x v x v x v D δ Navier-Stokes Eqations

9 Navier-Stokes Eqations: Weak formlation 1,2,3 ( ( S S V S S V d n G d n F d dt d E δ δ δ p E p p p F ( β τ τ τ τ q G β β β β µ δ µ τ x x x k k 3 2 Stress tensor β x T k q Average heat flx

10 Eqations Discretization p Finite Volme Method n n n Cell vertex finite volme soltion (Dal mesh Time discretization: explicit mlti-stage Rnge Ktta Convergence acceleration to steady state by local time stepping and an agglomerated mltigrid process.

11 nviscid flx Approximation Λ J F d n F ~ ( S S q p E pn q pn q pn q q F ( ~ n q

12 nviscid flx Approximation p Riemann Problem ~ F t s (0, s ( p Most poplar Riemann approximation solvers n Roe solver n Osher-Solomon n HLLC solver J if if s s < > 0 0 0

13 HLLC solver Acostic wave Contact wave Acostic wave L S M S R S L R J e Schematic illstration of the HLLC Riemann solver.

14 HLLC solver Flx approximation commonly sed ~ L F F( Correct flx approximation ~ F F( S L ( L

15 p Case of Discontinos Waves Riemann Solver for a Scalar Hyperbolic Eqations with Discontinos Coefficients ϕ β ( x ϕ 0, on Ω t x ϕ < 0 0 L if x ϕ(0, x ϕ ϕ R if x > 0 β L β ( x β R if if x < 0 x > 0 [ 0, T ]

16 p Case of Discontinos Waves Proposed soltion β L <, β R > 0 β L, β > 0 > R Acostic wave β L Acostic wave β R Acostic wave β R ϕl λ λ ϕr ϕ L ϕ R ϕ R 0 β, β < 0 β L, β < 0 L < R 0 > R Acostic wave β L ϕl ϕr ϕr ϕl ϕr 0 0

17 p Case of Discontinos Waves Nmerical proof (finite volme soltion β, β > 0 β L >, β R > 0 L < R β, β < 0 β L, β < 0 L < R > R

18 p Case of Discontinos Waves Nmerical proof (finite volme soltion β, β > 0 β L >, β R > 0 L < R β, β < 0 β L, β < 0 L < R > R

19 p Case of Discontinos Waves Nmerical proof (finite volme soltion Analytical formla of λ λ 1 β L ϕ L 1 β L 1 ϕr βr 1 β R

20 HLLC Second order p Modification of the left and right vales in Riemann problem J J Δ Δ J p Stabilization n Limiter: Limit the gradient in the vicinity of discontinities (for instance to ensre local extremm diminishing (LED

21 p Barth and Jespersen limiter Limiter < > Φ Else h if h Min Min h if h Max Min K K J J K K J J K , 0 1., K N K MinΦ Φ Φ is replaced by

22 p mprovement Limiter Limiter < > Φ Else h if h Min sg h if h Max sg K K J J n K K J J n K n n n t t t sg 1 (1 ( 2 1 ( t t t sg Generalized sigmoid fnction

23 p mprovement Limiter Limiter sg n ( t C sg n ( t t sg n ( t 1 for t 0 and Lim( sg ( t Min(1, t, for t 0 n n

24 p mprovement Limiter Limiter h K is replaced by Φ K h K Conservation violated

25 Limiter p Recover the conservation propriety L V V R L R J J Δ Δ J h Δ Δ J J h J J h minmod( a, b 0 Else a b if if if ab < 0 a b b < a

26 Rotating Simlation p Single Reference Frame (SRF NS NS Coriolis

27 Rotating Simlation p Mltiple Reference Frame Method (MRF VolteRotor Rotor BALTOGAR centrifgal trbofan

28 Rotating Simlation

29 p Rotating Simlation BC Drag force approach BC on Blades: Flid Velocity Rotating velocity F d 1 2 C d V 2 A Rotating direction BALTOGAR centrifgal trbofan: Rotating part

30 p Axial Trbofan Reslts Streamlines showing he rotating effect with the BC method

31 Reslts p BALTOGAR Centrifgal Trbofan

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