ASSESSMENT OF HYBRID URANS/LES TURBULENCE MODELING …projet.ifpen.fr/Projet/upload/docs/application/pdf/... · ASSESSMENT OF HYBRID URANS/LES TURBULENCE MODELING FOR ICE FLOW SIMULATION:

ASSESSMENT OF HYBRID URANS/LES TURBULENCE MODELING FOR ICE FLOW SIMULATION: A ZDES STUDY

V. K. Krastev1, F. Piscaglia2, G. Bella3

1DEIM, University of Tuscia2Energy Dept., Politecnico di Milano3”Mario Lucertini” Engineering Dept., University of Rome “Tor Vergata”

LES4ICE 2016

Outline

V. K. Krastev et al. 2

Conclusions

Implementation/calibration

Modeling

Motivations

Engine-like flow benchmarks

LES4ICE 2016

Motivations


LES popularity constantly increasingthrough years, whereas…

Why hybrid URANS/LES turbulence modeling?

Per-year number of published papers with relevant LES and hybrid ICE flow applications (source: www.scopus.com)

LES4ICE 2016

Motivations


LES popularity constantly increasingthrough years, whereas…

…hybrid URANS/LES methods are stillrelatively unexplored for ICE flow modeling



LES4ICE 2016

Motivations



Assuming that the scale-resolving capabilityis mostly preserved, hybrids can bringsignificant improvements:

increased computational efficiencyand robustness;

easier management of inlet and wallBCs.


LES4ICE 2016

Motivations






Several approaches has already shown a good potential (LNS, SAS, DES)


LES4ICE 2016

Motivations






Several approaches has already shown a good potential (LNS, SAS, DES)

Goals of our work: Development of a zonal DES-based turbulence simulation method for ICE flow

predictions Validation of the proposed methodology on well established flow benchmarks


LES4ICE 2016

Modeling


Steady, attached zones of the flow efficientlysimulated by URANS

LES triggering in massive separation, by lengthscales switching in the eddy viscosity destructionmechanism (from modeled to grid-dependent)

All seamlessly managed by a single modelingframework (RANS-based)

Very good accuracy in massively separatedexternal flows

The Detached Eddy Simulation (DES) principle

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Modeling


Starting point: improved RANS k-g model

Equations:Main features:

Originally derived from the k- by Kalitzin et al. (1996); the -equation is reformulated in terms of the root-squared turbulent time scale g ( ).

Straightforward wall bc (g→0) and linearnear-wall scaling (g~yn).

Modified by the authors includingrealizability constraints for the turbulenttime scale

*1 //g k

3

*2 2

3

i tk

gi i i

t

g i i

u g g g gPx x x k

g g gx x

i tk

i i ik

u k k kPx x x

*t k

22*

; 1min ,6

ag aS

(1)

(2)

(3)

(4)

LES4ICE 2016

Modeling


DES reformulation

Basis:

Strelets (2001) showed that a two-equationmodel can be reduced to a DES model by implementing a “grid sensitive” length scale in the destruction term of the k-equation

Destruction term modification

i tk

i i ik

u k k P Dx xk

xt

LES4ICE 2016

i tk

i i ik

u k k P Dx xk

xt

Modeling


DES reformulation

Basis:


The same approach has been followed in the present work

Destruction term modification

LES4ICE 2016

i tk

i i ik

u k k P Dx xk

xt

Modeling


DES reformulation

Basis:



Destruction term modification (1)

1/23/2

; ·RANS RANSRANS

kD l kl

3/2; , ·DES DES RANS DES

DES

kD l min l Cl

(gridf )

DESC O(1)

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i tk

i i ik

u k k P Dx xk

xt

Modeling


DES reformulation

Basis:



Destruction term modification (2)

DES RANSDES DD F

max ( · ), 1/DES RANS DESF l C

Finalform

3/2; , ·DES DES RANS DES

DES

kD l min l Cl

1/23/2

; ·RANS RANSRANS

kD l kl

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Modeling


Application of the DDES concept

The concept:

Avoid Modeled Stress Depletion (MSD) in grids with ambiguous near-wall spacing(CDES∙ < BL thickness)

Spalart et. al (2006) proposed the use of a “delaying function” to force the extention of the pure RANS region towards BL’s outer edge

Adaptation of the delaying function to the present formulation

DDES form of the destruction term:

/ , 1max RANS DESdDDES l CF

DDES RANSDDES DD F

0 ; 1DDESd F

31 tanhd d dk r

kd = constant

rd = function of flow quantities and wall distance

Final form(DDES)

Forced RANS mode

LES4ICE 2016

Modeling


Why Zonal-DES?

Seamless (D)DES:

URANS-to-LES managed entirely by the model (userdecisional load kept to a minimum), but…

…the triggering mechanism is not always efficientin complex internal flows (too early/too late transition*)

Zonal (D)DES:

URANS and LES (or DES) regions explicitly markedby the user

Better control of the solution behavior (at the expense of nontrivial a-priori decisions)

Potentially good candidate for complete ICE simulation(e. g., ducts in RANS mode, in-cylinder in LES mode)

*V. K. Krastev et al., SAE 2015-24-2414

Zonal form of the destruction term:

* *DDES DDES RANSDD F

*1 11DDES z DDES z ZDESF C F C F

2 21ZDESRANS

z zDES

lF C C C

(1)

(2)

(3)

LES4ICE 2016

Cz1 Cz2

1 0

1 DDES RANS

0 DDES LES

Modeling


Why Zonal-DES?

Seamless (D)DES:

URANS-to-LES managed entirely by the model (userdecisional load kept to a minimum), but…

…the triggering mechanism is not always efficientin complex internal flows (too early/too late transition*)

Zonal (D)DES:

URANS and LES (or DES) regions explicitly markedby the user

Better control of the solution behavior (at the expense of nontrivial a-priori decisions)

Potentially good candidate for complete ICE simulation(e. g., ducts in RANS mode, in-cylinder in LES mode)

*V. K. Krastev et al., SAE 2015-24-2414

Zonal form of the destruction term:

* *DDES DDES RANSDD F

*1 11DDES z DDES z ZDESF C F C F

2 21ZDESRANS

z zDES

lF C C C

(1)

(2)

(3)

LES4ICE 2016

Implementation


Overview

Why OpenFOAM® ?

Open source unstructured finite volume computational framework

Quite extensively validated for LES

Hexa-dominant automatic mesher (SHM) with local volumetric refinement

LES4ICE 2016

Implementation


Overview

Why OpenFOAM® ?




Potentially attractivefor zonal methods

LES4ICE 2016

Implementation


Overview

Why OpenFOAM® ?




Methodology calibration:

1. Numerical schemes choice• Focus on convective transport in LES

mode

2. CDES constant calibration• Checking model’s consistency in LES mode

(lDES ≡ CDES ·)• Focus on the CDES constant calibration

Potentially attractivefor zonal methods

LES4ICE 2016

Implementation


Turbulence box: momentum convection schemes

Standart test for DNS and SGS models

Cubic domain with cyclic BCs in eachdirection; spatial discretization obtained with N3

perfectly cubic cells (N=64)

Flow field initialized with an incompressibledivergence-free turbulent spectrum

To evaluate convection schemes, Eulerequations are solved (zero-viscosity, no SGS modeling)

Three alternatives considered:1. Central Differencing (CD)2. Linear Upwind Stabilized Transport

(LUST)3. Filtered Central Differencing (FCD)

LES4ICE 2016

Implementation


Turbulence box: momentum convection schemes

Volume-averaged kinetic energy of the flow monitored through time

LUST is highly dissipative compared to CD

FCD is in between, the amount of dissipation depending on the filteringparameter 0<

FCD with = 0.25 chosen as a compromise between energy conservation and stability

LES4ICE 2016

Implementation


Turbulence box: CDES calibration

Standart test for DNS and SGS models

Cubic domain with cyclic BCs in eachdirection; spatial discretization obtained with N3

perfectly cubic cells (N=64)

Flow field initialized with an incompressibledivergence-free turbulent spectrum

Turbulence is left to spontaneously decaydriven by the k-g pure LES model (lDES ≡ CDES ·)

CDES is decreased, starting from CDES = 0.78 (k- SST DES standard value)

Energy spectra evaluated at differentsimulation times

LES4ICE 2016

Implementation


Turbulence box: CDES calibration

3D spectra compared to Comte-Bellot and Corrsin’s experimental data

FCD 0.25 set for momentum convection, bounded NVD scheme for k and g

The initial energy decay is well describedby the k-g LES model, regarldess of CDES

For longer decaying times CDES = 0.5 is the best-matching option

CDES = 0.5 chosen as baseline value

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Benchmarks


Axisymmetric sudden expansion

Preliminary remarks (1):

Sudden circular flow expansion with/without imposed swirling motion at the inlet (Dellenbacket al., 1988)

Swirling case taken as reference (Si = 0.6), inlet bulk Reynolds number Reb ≈ 3 · 104

LES4ICE 2016

Benchmarks




Sudden circular flow expansion with/without imposed swirling motion at the inlet (Dellenbacket al., 1988)

Swirling case taken as reference (Si = 0.6), inlet bulk Reynolds number Reb ≈ 3 · 104

Unstructured hexa-dominant grids, with extrusion layers at the walls: Coarse grid, R0 = Du, R5 = Du/25, 4 · 105 cells; Fine grid, R0 = Du, R6 = Du/26, 2.36 · 106 cells.

LES4ICE 2016

Benchmarks




Two different settings tested:

I. Pure RANS, Cz1 = 0, Cz2 = 1, Linear Upwind (LU) scheme

LES4ICE 2016

Benchmarks






II. ZDES + numerical schemes splitting, Cz1 = 0, Cz2 = 1 + LU, Cz2 = 0 + FCD 0.25

LES4ICE 2016

Benchmarks




ZDES computational procedure:1. RANS solution to initialize the flow (experimental data mapped on inlet);2. ZDES run for 2 domain flow throughs with statistics turned off;3. ZDES run for 10 flow throughs with statistics on (mean values and fluctuations)4. Post-separation turbulence statistics extracted from the resolved flow field time history

Boundary conditions: standard incompressible inflow/outflow, wall functions for k and momentum (y+ < 20)

LES4ICE 2016

Benchmarks



Results, Si = 0.6:

ZDES slightly improves post-separation mean axial velocity profiles, but the enhancements are not as expected (even for the fine grid case)

Much more significant “boost” in the predicted axial turbulence levels, but only in the outer region (r > 0.5Rd)

Axial velocities Axial velocity fluctuations

LES4ICE 2016

Benchmarks



Results, Si = 0.6:

ZDES slightly improves post-separation mean axial velocity profiles, but the enhancements are not as expected (even for the fine grid case)

Much more significant “boost” in the predicted axial turbulence levels, but only in the outer region (r > 0.5Rd)


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Benchmarks



Results, Si = 0.6:

Still small improvements (outer region at x/Du = 0.5, more distributed elsewhere)

Similar trends for tangential turbulence

Tangential velocities Tangential velocity fluctuations

LES4ICE 2016

Benchmarks



LES4ICE 2016

Benchmarks



Comments, Si = 0.6:

Role of the URANS mode is to provide accurate mean-flow conditions at the URANS/LES interface

Tangential velocitiesAxial velocities

LES4ICE 2016

Benchmarks



Comments, Si = 0.6:

Role of the URANS mode is to provide accurate mean-flow conditions at the URANS/LES interface

The improved k-g RANS has shown close to the k- SST results in several tests, but still it is an isotropic eddy viscosity model (well known limitations in swirling flows)

Tangential velocitiesAxial velocities

LES4ICE 2016

Benchmarks


Fixed valve intake port


Intake port geometry with an axis-centered fixed poppet valve, Reb ≈ 3 · 104

LDA measurements of mean flow and RMS fluctuations available at x = 20 mm and x = 70 mm; DLRM results from Piscaglia et al. (2015) also taken as reference (coarse: 7 · 105 cells; fine: 5 · 106 cells)

Two levels of maximum grid refinement (R0 = Di/4): coarse (R3, 9.8 ·105 cells) and fine (R4, 5.97 · 106 cells)

LES4ICE 2016

Benchmarks






LES4ICE 2016

Benchmarks






II. ZDES + numerical schemes splitting, Cz1 = 0, Cz2 = 1 + LU, Cz2 = 0 + FCD 0.25

LES4ICE 2016

Benchmarks




ZDES computational procedure:1. RANS solution to initialize the flow (experimental data mapped on inlet);2. ZDES run for 2 domain flow through with statistics turned off;3. ZDES run for ~5 flow throughs with statistics on (mean values and fluctuations)4. All turbulence statistics extracted from the resolved flow field time history

Boundary conditions: standard incompressible inflow/outflow, wall functions for k and momentum (y+ < 30)

LES4ICE 2016

Benchmarks



Profiles, x = 20 mm (coarse grid):

RANS is competitive for the mean velocity profiles prediction, DLRM slightly outperforms ZDES in the peak region

The two scale-resolving methods are much superior for turbulence prediction (well captured peaks, differences in the outer region)


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Benchmarks



Profiles, x = 20 mm (fine grid):

ZDES seems to be more sensitive to grid refinement (significant improvements)

Similar trend for resolved turbulence


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Benchmarks



Contours, coarse grid:

2D contours confirm differences between the ZDES-C and the DLRM-C cases

ZDES seems to have a slightly more diffusive jet structure


ZDES-C ZDES-CDLRM-C DLRM-C

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Benchmarks



Contours, fine grid:

Fine grid cases become much more similar

DLRM has a less grid-dependent behavior


ZDES-F ZDES-FDLRM-F DLRM-F

LES4ICE 2016

Benchmarks


Fixed valve intake port: evaluating quality of the solution

TKE ratio

Defined as the ratio between resolved and total(modeled + resolved) mean tke:

A-posteriori resolution parameter (requiresconverged turbulence statistics).

Current LES ICE applications are usually able to guarantee tke > 0.8 in most of the flow domain

In general, tke is not sufficient to characterize the flow resolution level (e. g., L. Davidson, 2009)

DLRM filtering of the RANS field (1)

DLRM belongs to the Limited Numerical Scales(LNS) modeling approaches

Based on the dynamic evaluation of a filter functionG:res

tke resmod

tketke tke

1/23/2

·RANSl kk

max | | ,f dt U

min ,DLRM RANS fl l

4/32 DLRM

RANS

lG l

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Benchmarks




In the original dynamic approach, G is used for the run-time filtering of the turbulent quantities of a givenRANS turbulence model

The filter form is general and can be applied to anytwo-equation turbulence model

When f ≥ lRANS , the standard RANS behavior isautomatically recovered (G2 = 1):

restke resmod

tketke tke

lRANS f

G2

TKE ratio





LES4ICE 2016

Benchmarks




Here, we calculate G2 from a converged URANS solution (same CFL and grids as for the ZDES runs)

Purpose: using G2 as an a-priori resolutionestimator

restke resmod

tketke tke

TKE ratio





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Benchmarks



TKE ratio (ZDES) G2 (URANS, = 3, = 5)

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Benchmarks



TKE ratio (ZDES) G2 (URANS, = 3, = 5)

LES4ICE 2016

Conclusions


Final comments

The next development steps will be focused on:

1. eventual swirl correction for the modified k-g RANS;

2. extension to compressible flows and flows with moving boundaries/topological changes;

3. interaction with physical sub-models (combustion);

The results here shown represent a promising basis for future ICE applications and can be summarizedas follows:

1. the proposed k-g ZDES model has demonstrated significant turbulence resolving features, even when the overallcomputational requirements are kept comparable to what typically needed by RANS;

2. the importance of providing accurate mean-flow conditions at the URANS/LES interface has been evidenced;

3. a filtering function G, originally developed for dynamic scale-adaptive turbulence modeling, has been evaluated forthe a-priori estimate of the grid+time step actual resolution capability; the G distribution, calculated from aconverged URANS field, has shown a good correspondence with a typical a-posteriori resolution parameter such asthe tke ratio.

LES4ICE 2016

Conclusions


Acknowledgments

Cluster CPU time

OpenFOAM® trademark ownership

Prof. Elio Jannelli, University of Naples‘’Parthenope’’

OpenCFD Ltd.

LES4ICE 2016

Conclusions


References Krastev, V. and Bella, G., "A Zonal Turbulence Modeling Approach for ICE Flow Simulation," SAE Int. J. Engines 9(3):2016,

doi:10.4271/2016-01-0584.

Krastev, V., Bella, G., and Campitelli, G., "Some Developments in DES Modeling for Engine Flow Simulation," SAETechnical Paper 2015-24-2414, 2015, doi:10.4271/2015-24-2414.

Piscaglia, F., Montorfano, A., and Onorati, A., "A Scale Adaptive Filtering Technique for Turbulence Modeling of UnsteadyFlows in IC Engines," SAE Int. J. Engines 8(2):426-436, 2015, doi:10.4271/2015-01-0395.

Batten, P., Goldberg, U., and Chakravarthy, S., ‘’ LNS − an approach towards embedded LES,” AIAA Paper 2002-0427,2002.

Spalart, P. R., “Detached-Eddy Simulation,” Annu. Rev. Fluid Mech., 41:181-202, 2009,doi:10.1146/annurev.fluid.010908.165130.

Deck, S., "Zonal-Detached-Eddy Simulation of the Flow Around a High-Lift Configuration", AIAA Journal, Vol. 43, No. 11(2005), pp. 2372-2384, doi:10.2514/1.16810.

Lysenko, D. A., Ertesvåg, I. S. and Rian, K. E., “Large-Eddy Simulation of the Flow Over a Circular Cylinder at ReynoldsNumber 2 × 104,” Flow Turbulence Combustion, 92:673-698, 2014, doi:10.1007/s10494-013-9509-1.

Davidson, L., “Large Eddy Simulations: How to evaluate resolution,” International Journal of Heat and Fluid Flow, Volume30, Issue 5, October 2009, Pages 1016–1025, doi:10.1016/j.ijheatfluidflow.2009.06.006.

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Conclusions


Documents

ASSESSMENT OF HYBRID URANS/LES TURBULENCE MODELING …projet.ifpen.fr/Projet/upload/docs/application/pdf/... · ASSESSMENT OF HYBRID URANS/LES TURBULENCE MODELING FOR ICE FLOW SIMULATION: