Adaptive Mesh Refinement with an automatic hybrid

Introduction AMR with HRL HRL turbulence model

Adaptive Mesh Refinement with an automatic hybrid RANS/LES strategy and overset grids

Octree method Adaptation Criteria Known issues

Industrial test cases

Alexandre Limare1

Pierre Brenner2

Houman Borouchaki3

Simplified after body flow A5 buffeting

Conclusion

18th September 2018

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Post Doctoral fellow, GAMMA3-UTT, [email protected] CFD Expert, Aerodynamics Department, [email protected] Professor, joint project-team GAMMA3, [email protected] 1 / 27

Introduction AMR with HRL

Context

HRL turbulence model Octree method Adaptation Criteria Known issues

Industrial test cases Simplified after body flow A5 buffeting

Conclusion

Aim: Understand and simulate complex physical phenomena more accurately

Ariane 5 design phase (1982-1996) • Stage separation − Take-off Ignition OverPressure wave > Reduced models (0D)

⇒ Aerothermal databases: wind tunnel tests

Ariane 6 conception (2012-2020) > more than 50% of the aero-budget in experimental studies > 70% of the studies using large numerical simulation tools

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Introduction AMR with HRL HRL turbulence model Octree method Adaptation Criteria Known issues

Context Fluid Mechanics for space launchers • Complex violent unsteady phenomena (aerodynamic efforts, turbulence,

chemistry, dispersed phases influence) • Flows about bodies in relative motion


Conclusion

Figure : Boosters separation (FLUSEPA-ArianeGroup) Figure : Missile stage separation, re-entry of the Huygens probe 3 / 27


Context FLUSEPATM4

Octree method

• 30-year-old in-house CFD tool

Adaptation Criteria

• Euler, Navier-Stokes, turbulence modeling (RANS, URANS, HRL)

Known issues


Conclusion

(a) A5 Ignition OverPressure wave at take-off

(b) Propeller simulation

Numerical formulation • Unstructured cell-centered 3D k-exact Finite Volume (Pont et al. [PBCR17]) • Adaptive explicit time integration scheme • Overset grids by conservative geometric intersections > Input cells: hexa, prism, penta and tets 4

Registered trademark in France with number 134009261 4 / 27


Industrial test cases Simplified after body flow

Overset grids Conservative mesh overlapping strategy > Simple part of bodies meshed independently > ALE, Large displacements, meshes adapted to attached boundary layers and bow shocks > Motion calculated by integration of the aerodynamic & propulsive loads for each body with (6-DoF model)

A5 buffeting

Conclusion

(c) Detail of the multi component mesh

(d) Assembled

Figure : Multi-level intersecting meshes

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Introduction AMR with HRL HRL turbulence model Octree method

Temporal integration numerical scheme • RANS, Implicit, steady

⇒ 90 % of the calculations, time < 2h

Adaptation Criteria Known issues


Conclusion

Figure : Ariane5 AEDB • Explicit, local time-stepping, unsteady simulations, hybrid RANS/LES turbulence

modeling ⇒ 1∼3 weeks, 200 CPUs (stage separation, buffeting)

Figure : Ariane5 model buffeting simulation • Explicit, unsteady, URANS ⇒ Debris trajectory 6 / 27


Industrial goals - why AMR ?



Conclusion

Reliability:

Figure : Example of an AMR mesh for an after body flow

• Put cells where they are needed • Limit error-prone user interventions

Efficiency: • Reduce mesh generation effort • Less cells for the same result OR same number of cells for an improved result ⇒ Resolve as much turbulence as possible with a given computational cost

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Outline



Conclusion

1 Introduction

2 AMR with HRL


3 Industrial test cases

Simplified after body flow Ariane5 model with booster buffeting

4 Conclusion

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Outline



Conclusion

1 Introduction

2 AMR with HRL




4 Conclusion

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Introduction AMR with HRL HRL turbulence model Octree method Adaptation Criteria

Turbulence model DDES [SDS+ 06] k − why? k 3/2 • turbulent characteristic size from the model l RANS =

Known issues


l HRL = min(l RANS, , CDES ∆) , CDES = 0.62 where ∆ is the size defined in ZDES mode II by Deck [Dec12]:

Conclusion

∆=

if fd > fd0 , if fd > fd0 ,

∆ω ∆max

with fd0 = 0.8

∆ω from Pont [Pon15] adapted from Chauvet et al. [CDJ07]:

s ∆ω =

PNf i=1

|ω·Si |

2|ω|

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Octree method

HRL turbulence model Octree method Adaptation Criteria

⇒Octree-AMR : Large error correction and simple implementation

Known issues


Full hexa meshes Adaptation method chosen: Octree per cell:

Advantages

Conclusion

• simple algorithmic method • FLUSEPA’s solver allows general

polyhedra • low memory overhead due to AMR

structures (15 %) • modular definition of adaptation criteria

Figure : Octree method

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Octree



Technical challenges • High-order, conservative, redistribution method of the conservative variables (

Limare et al. [LBB16]) • Modification of the intersection algorithms

A5 buffeting

Conclusion

• Load balancing in a HPC framework

Figure : Non-conform zone

3rd-order accurate redistribution

Figure : Moving vortex test case 11 / 27


Geometric - Cell size progression constraint



Adaptation sensor • minimum cell size in the 1st

neighborhood

U

> local grid resolution adapted in the intersection area

MOVIE

Conclusion

Figure : Turbulent structure moving from the black mesh to the purple one

(a) 3D view

(b) 2D view

Figure : Grids colored by priority levels 12 / 27


Geometric - Cell size progression constraint



Conclusion

Adaptation sensor • minimum cell size in the 1st

neighborhood

U

> local grid resolution adapted in the intersection area

MOVIE too expansive for moving grids ! → compatibility must only be enforced when needed

Figure : Turbulent structure moving from the black mesh to the purple one

Figure : Grids colored by priority levels 12 / 27



Physical criteria For each criteria i, two associated thresholds ti,1 and ti,2 . Then, for each cell Tα : - if ∀i ∈ J1, ncrit K, fi (Tα ) < ti,1 then Tα is refined

- if ∀i ∈ J1, ncrit K, fi (Tα ) > ti,2 then Tα is coarsened In our study, we always used the three criteria :

Simplified after body flow

• an boundary layer protection criteria: tanh([8rd ]3 ) = 1 − fd

A5 buffeting

• a strain detection criterion

Conclusion

• a geometrical criterion, maximum cell size ratio is 1.5.

Then, we compared the three following criteria: νl 1 an eddy viscosity criterion: fνT = , νT 2

a Taylor size criterion: ftaylor =

1 ∆ref

r 10ν

k representing a scale of the

turbulence,

p 3

a Von Kármán size criterion from SAS model [ME10]: fV.K. =

2Sij Sij

|H|∆ref

, with

|H| Hessian matrix of the velocity 13 / 27


HRL with AMR



Hypothesis Commonly: ∂∆ '0 ∂xi

Simplified after body flow A5 buffeting

Conclusion

Figure : Simple mesh

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HRL with AMR





Not the case with AMR or overset grids !

A5 buffeting

Non-commutative derivation and filtering operation:

Conclusion

∂f ∂f ∂∆ = − ∂xi ∂xi ∂xi

Z

∂G(x − η, ∆) f (η)dη ∂∆

(1)

Figure : Simple AMR mesh

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HRL with AMR






A5 buffeting


Conclusion

∂f ∂f ∂∆ = − ∂xi ∂xi ∂xi

Z

∂G(x − η, ∆) f (η)dη ∂∆

⇒ Proper treatment: add corrective terms to the LES model, Hamba [Ham03] Neglected for now

(1)


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HRL with AMR

HRL turbulence model Octree method Adaptation Criteria

Hypothesis Commonly:

Known issues

∂∆ '0 ∂xi



A5 buffeting


Conclusion

∂f ∂f ∂∆ = − ∂xi ∂xi ∂xi

Z

∂G(x − η, ∆) f (η)dη ∂∆

⇒ Proper treatment: add corrective terms to the LES model, Hamba [Ham03] Neglected for now

(1)


Aim Local and extremely frequent mesh adaptation Future work will focus on this issue

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Outline



Conclusion

1 Introduction

2 AMR with HRL




4 Conclusion

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Introduction AMR with HRL HRL turbulence model Octree method Adaptation Criteria

Simplified after body flow • • • •

Experimentally studied by Deprés et al. [DRD04] and Meliga et al. [MR07] Numerically studied by Weiss [Wei10] Re = 1.2 × 106 AMR calculations : 3 criteria tested, number of cells ' 8 × 106

Known issues


Conclusion

(a) A space launcher after body

(b) Sketch of the axisymmetric backward facing step

(c) Initial AMR mesh, 6 levels of priority

Figure : Case description 15 / 27





Conclusion

Figure : Meshes used for the calculations 16 / 27





Conclusion

Figure : Eddy viscosity 17 / 27





Conclusion

Figure : Eddy viscosity 18 / 27


Simplified after body flow Initial mesh too coarse in the Kelvin Helmholtz departure region



Conclusion

Figure : Meshes used for the calculations

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Simplified after body flow νt /ν ' 20 → 1 ∼ 4



Conclusion

Figure : Eddy viscosity

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Axisymmetric backward facing step AMR Results not-converged ! (next week)



Conclusion

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Ariane5 model with booster buffeting


P 66500

T 270

Uinf 263

Re 1.2 × 106

Table : Inflow conditions


Conclusion

Figure : Ariane5 1/60th model and AMR mesh colored by grid priority

Comparison made with the study of Pont [Pon15] (18M cells) AMR : 3 basic criteria + Eddy viscosity criterion ⇒ initial number of cells 3M, mean number of cells 18M (target 20) 22 / 27





Conclusion

Figure : Mesh comparison A5 buffeting

Recirculation bubble 23 / 27





Conclusion


Vortices impact on the boosters 24 / 27





Conclusion


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Outline



Conclusion

1 Introduction

2 AMR with HRL




4 Conclusion

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Conclusion



Conclusion

Mesh adaptation so far... • AMR toolbox module integrated in the FLUSEPA code tested for industrial cases • Globally coherent strategy (HRL + numerical scheme + AMR) • Quantification, control and reduction of uncertainties • Coarser (3-20 ratio) and simpler initial meshes for industrial applications (steady

& unsteady)

Perspectives • PROPER VALIDATION ! • Non-commutative terms of the LES model to implement, explicit filtering ? • Boolean operators for criteria (only intersection of all the criteria) • Use of dynamically weighted (locally and temporally) criteria > machine learning algorithms for setting the adaptation thresholds and weights

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Thank you for your attention

Conclusion

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Introduction

N. Chauvet, S. Deck, and L. Jacquin.

AMR with HRL

Zonal detached eddy simulation of a controlled propulsive jet. AIAA journal, 45(10):2458–2473, 2007.



Conclusion

S. Deck. Simulation numérique des charges latérales instationnaires sur des configurations de lanceur. PhD thesis, 2002. S. Deck. Recent improvements in the zonal detached eddy simulation (zdes) formulation. Theoretical and Computational Fluid Dynamics, pages 1–28, 2012. D Deprés, P Reijasse, and JP Dussauge. Analysis of unsteadiness in afterbody transonic flows. AIAA journal, 42(12):2541–2550, 2004. F. Hamba. A hybrid rans/les simulation of turbulent channel flow. Theoretical and computational fluid dynamics, 16(5):387–403, 2003. R. E. Harris and B. Williams. Ventus: An overset adaptive cartesian simulation framework for moving boundary problems. In 21st AIAA Computational Fluid Dynamics Conference, page 2866, 2013. J. C. Jouhaud. Méthode d’Adaptation de Maillages Structurés par Enrichissement. PhD thesis, University of Bordeaux I, 1997. C. Kavouklis and Y. Kallinderis. Parallel adaptation of general three-dimensional hybrid meshes. Journal of Computational Physics, 229(9):3454–3473, 2010. A. Limare, P. Brenner, and H. Borouchaki. An adaptive remeshing strategy for unsteady aerodynamics applications. In 46th AIAA Fluid Dynamics Conference, page 3180, 2016. T. Leicht and R. Hartmann. Anisotropic mesh refinement for discontinuous galerkin methods in two-dimensional aerodynamic flow simulations. 27 / 27

Introduction

International Journal for Numerical Methods in Fluids, 56(11):2111–2138, 2008.

AMR with HRL

T. Leicht and R. Hartmann.



Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations. Journal of Computational Physics, 229(19):7344–7360, 2010. F. R. Menter and Y. Egorov. The scale-adaptive simulation method for unsteady turbulent flow predictions. part 1 : Theory and model description. Flow Turbulence Combust., 138:85–113, 2010. P. Moreau, J. Labbe, F. Dupoirieux, and R. Borghi. Experimental and numerical study of a turbulent recirculation zone with combustion. In Turbulent Shear Flows 5, pages 337–346. Springer, 1987. Philippe Meliga and Philippe Reijasse. Unsteady transonic flow behind an axisymmetric afterbody equipped with two boosters. In 25th AIAA Applied Aerodynamics Conference, page 4564, 2007.

A5 buffeting

Conclusion

G. Pont, P. Brenner, P. Cinnella, and J-C. Robinet. Multiple-correction hybrid k-exact schemes for high-order compressible rans-les simulations on general unstructured grids. Journal of Computational Physics, 2017. Article under review. G. Pont. Self-adaptive turbulence models for unsteady compressible flows. PhD thesis, DynFluid, Arts et Metiers ParisTech, 2015. P. R. Spalart, S. Deck, M. L. Shur, K. D. Squires, M. K. Strelets, and A. Travin. A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theoretical and computational Fluid Dynamics, 20:181–195, 2006. P-E. Weiss. Simulation numérique et analyse physique d’un écoulement d’arrière-corps axisymétrique et application au contrôle des charges latérales. PhD thesis, Paris 6, 2010.

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