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LES of Internal Combustion Engine Flows Using Cartesian Overset Grids

T. Falkenstein1, S. Kang2, M. Davidovic1, M. Bode1, H. Pitsch1 1 Institute for Combustion Technology RWTH Aachen University 2 Sogang University, South Korea

Institute for Combustion Technology | Prof. Dr.-Ing. H. Pitsch

Tobias Falkenstein

Cartesian Grids for Complex Geometries?

• High-Quality LES Solution • Insignificant Meshing Effort

• Uncertainty in LES Grid Quality

Reduced to Choosing Appropriate

Resolution

• Computational Performance

Academic Interest Industrial Application

Challenges

• Local Grid Refinement

• Wall Treatment


Tobias Falkenstein

Contents

• Motivation

• Numerical Framework

o Baseline Code

o Recent Enhancements

• Fundamental Verification

• Validation on Steady Engine Port Flow

• Sensitivities

• Conclusions


Tobias Falkenstein

Spatial Discretization

• Momentum Eq.: Central Difference

• Scalar Eq.: WENO This Study: 2nd Order Accuracy

Features of CIAO Flow Solver

Incompressible

Low-Mach Number

Compressible

Governing Equations

Physical Models

Representation of Turbulence

DNS

RANS

LES

Multiphase

Combustion

SFS Model

• Dyn. Smagorinsky

• Coherent Structure

• Sigma


Tobias Falkenstein

Spatial Discretization

• Momentum Eq.: Central Difference

• Scalar Eq.: WENO This Study: 2nd Order Accuracy

Features of CIAO Flow Solver

Governing Equations

Incompressible

Low-Mach Number

Compressible

Physical Models

Representation of Turbulence

DNS

RANS

LES

Multiphase

Combustion

SFS Model

• Dyn. Smagorinsky

• Coherent Structure

• Sigma

Numerical Schemes

• 2nd-order low-storage RK

• 6th-order spatial filtering to

remove spurious wiggles


Tobias Falkenstein

Enhanced Numerical Framework

Fluid

Kang, S., Iaccarino, G., Ham, F., Moin, P., Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method, Journal of Computational Physics 228

(2009) 6753–6772

Gaitonde, D. V., Visbal, M. R., Padé-Type Higher-Order Boundary Filters for the Navier–Stokes Equations, AIAA Journal Vol. 38, No. 11, November 2000

Roman, F.; Armenio, V.; Fröhlich, J., A simple wall-layer model for large eddy simulation with immersed boundary method, Physics of Fluids, Volume 21, Issue 10, pp. 101701-

101701-4 (2009)

Immersed Boundary Method Wall Model

Velo

city

Err

or

y-location

Prev. Revised

Velo

city

Err

or

y-location

Overset Grid Method Higher-Order Filtering Near Walls


Tobias Falkenstein

Overset Grid Method

• Patches with different grid spacing can be flexibly

combined during mesh generation (no AMR)

• Hole Cutting:

o Equations are solved on the finest available patch &

small overlap region

• Currently, all patches are integrated on the same

time step

• Same RK scheme as baseline solver, with additional

coupling procedures after each solution variable has

been updated

x x x x x x x x x x x x x x x x x x x x x x x x x

Overlap

grid1

grid2 Masked cells on grid1,

active (fine) cells on grid2


Tobias Falkenstein

Contents

• Motivation


o Baseline Code




• Sensitivities

• Conclusions


Tobias Falkenstein

Overset Grid Method Verification

• Method has 2nd-order accuracy

• Can be effectively used to reduce

computational cost

Inviscid Vortex Convection (1)

Base grid

Overset

2x finer peri

odic

U0

peri

odic


Tobias Falkenstein

Overset Grid Method Validation

• Inviscid Vortex Convection (2)


Base grid

Overset

2x finer peri

odic

U0

peri

odic

• Mass and kin. energy are well conserved


Tobias Falkenstein

Overset Grid Method Validation

• Inviscid Vortex Convection (2)


Base grid

Overset

2x finer peri

odic

U0

peri

odic

• Vortex well preserved after 1 cyle


Tobias Falkenstein

1) Wall Treatment: Approx. Immersed Boundary Method

• Exact solution prescribed at IB

• Nearly 2nd-order in both cases

Grid Convergence Study on Taylor-Green Vortex Problem

Case A

Case B

IB

IB


Tobias Falkenstein

2) Wall Treatment: Wall Function

• Here, a combination of two models for

the shear stress is used:

o Eddy-Viscosity-based model for IBs

(Roman et al.)

o Body-Fitted approach based on modified

shear stress (Lee at al.), if BC location is

close to actual IB wall location

• Both models assume LOG-Law

o Velocity BC and shear stress / eddy

viscosity are evaluated from time-

averaged velocity field

Wall Model

IB

BC

IP

IB : Actual Wall Location

BC: Velocity Boundary Condition

IP : Interpolation of Avg. LES Solution

𝑦𝐵𝐶

Roman, F., Armenio, V., Froehlich, J.: „A Simple Wall-Layer Model for Large-Eddy Simulations with Immersed Boundary Method“, Physics of

Fluids Vol. 21, 101701, 2009

Lee, J., Cho, M., Choi, H.: „Large-Eddy Simulations of Turbulent Channel Flows at High Reynolds Number with Mean Wall Shear Stress

Boundary Condition“, Physics of Fluids Vol. 25, 110808, 2013


Tobias Falkenstein

2) Wall Treatment: Wall Function

• Here, a combination of two models for

the shear stress is used:

o Eddy-Viscosity-based model for IBs

(Roman et al.)

o Body-Fitted approach based on modified

shear stress (Lee at al.), if BC location is

close to actual IB wall location

• Both models assume LOG-Law

o Velocity BC and shear stress / eddy

viscosity are evaluated from time-

averaged velocity field

Wall Model Channel Flow (Re = 2000)


Tobias Falkenstein

Contents

• Motivation


o Baseline Code




• Sensitivities

• Conclusions


Tobias Falkenstein

Validation Case: Compressible Flowbench

• Production SI Engine Geometry with High Tumble

• Valve Lift: 8 mm

• Air as Working Fluid

• Inlet & Outlet Pressures Prescribed

• Resulting Mass Flow is Similar to Max. at 3000rpm

• PIV Measurements in Planes Perpendicular

to Cylinder Axis


Tobias Falkenstein

Simulation Setup

• Non-Reflective Boundary Conditons at

Inlet and Outlet

• Dyn. Smagorinsky Model with

Lagrangian Averaging

Name # of Cells Lift / x

Port 1.7 Mio. 16

Cyl. 1 39.4 Mio. 32

Cyl. 2 5.4 Mio. 16

𝑃𝑡𝑜𝑡

𝑃𝑠𝑡𝑎𝑡

Wall Model


Tobias Falkenstein

Characteristic Flow Quantities

• Mach Numbers Up to 0.4

• Reynolds Numbers on the Order of 100,000

• Pressure Loss Occurs Mostly as Flow

Passes Valves


Tobias Falkenstein

Integral Flow Measures

• Overprediction of Mass Flow by ~3 %

• Good Agreemen in Tumble Intensity

Mass Flow Tumble Ratio

Numerical Wall Treatment is Suitable


Tobias Falkenstein

In-Cylinder Flow Field

Simulation PIV


Tobias Falkenstein

Comparison with PIV Data: Vertical Velocity

• Avg. Vertical Velociy Component in Good

Agreement with Experimental Data

• RMS Profile Seems Shifted, But Similar

Magnitudes

𝑥𝑚𝑖𝑛


Tobias Falkenstein

Comparison with PIV Data: Horizontal Velocity

• Avg. x-Velociy Component Overall in

Good Agreement, but Some Deviation

Near Cylinder Axis

• RMS Profile Agrees Well with PIV

𝑥𝑚𝑖𝑛


Tobias Falkenstein

Contents

• Motivation


o Baseline Code




• Sensitivities

• Conclusions


Tobias Falkenstein

• Similar Results, But Statistics Not Yet Converged

Sensitivity of Vertical Velocity to SGS Model

Dyn. Smag. PIV CSM

Menevau, C.; Lund, T.S.; Cabot, W.H.: “A Lagrangian dynamic subgrid-scale model of turbulence” Journal of Fluid Mechanics 319, pp. 353–385, 1996

Kobayashi, H.: „The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow “,

Phys. Fluids, Vol. 17, pp. 045104-045104-12 (2005)


Tobias Falkenstein

Effect of Applied Methods on Integral Flow Quantities

• Mass Flow (=Pressure Loss) is Very

Sensitive to Wall-Numerical Method

• Tumble is Very Sensitive to Wall Model

Mass Flow Tumble Ratio

Case 1 Single Grid (SG); Prev. Code

Case 2 SG; IB; Higher Order Filter

Case 3 Overset Grids; Refined Near Valves

Case 4 OG; Wallfunction in Port

Case 5 OG; Refined Down to z=-D


Tobias Falkenstein

Contents

• Motivation


o Baseline Code




• Sensitivities

• Conclusions


Tobias Falkenstein

Conclusions

• Methods to Reduce Drawbacks of Cartesian Approach in Complex Wall-

Bounded Flows have been Implemented

• 2nd-order accuracy has been demonstrated

• Pressure Loss in Port Flow is Governed by Singular/Local Losses in the Valve

Region

o Additional Friction from Wall Model has Minor Effect

o Accuracy of Upstream Velocity Field is Most Important

• Successful Validation of Extended Framework in Steady SI Engine Port Flow

• Next steps

o Finalize Developments for Moving Geometries

Acknowledgements

Honda R & D

Gauss Centre for Supercomputing e.V.

Leibniz Supercomputing Centre

Thank you for your attention

Tobias Falkenstein Institute for Combustion Technology RWTH Aachen University

http://www.itv.rwth-aachen.de

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