Predicting the Thermal Conductivity of AlSi/Polyester Abradable Coatings: Effects of the Numerical...

European Workshop on New Aero Engine ConceptsMunich, 30 June – 1 July 2010

Predicting the thermal conductivity of AlSi/polyester abradable coatings:

effects of the numerical method

NEWAC is an Integrated Project Co-funded by the European Commission within the Sixth Framework Programme(2002-2006) under Thematic Priority 4 Aeronautics and Space. 1

Presenter : Rodolphe BOLOT, UTBM – LERMPS

Authors : Rodolphe BOLOT, Jean-Louis SEICHEPINE,Jiang-Hao QIAO, Christian CODDET, UTBM – LERMPS


Introduction

First results(2008)

New developments

Role of UTBM – LERMPS in NEWAC:WP 5.4: Blade/casing rub management for tight tip c learancesTask: Numerical modelling of abradable coatings

Abradable coatings are used as seals between the st atic and rotating parts of aero engines

Scope of the present study: to model the effective properties


New results

ConclusionsPerspectives

Scope of the present study: to model the effective propertiesof AlSi/polyester abradable coatings

In order to predict these propertiesfrom micrographs, numerical studieswere performed Blade tip

Abradable coatingon casing


2 different codes were applied to estimate the effe ctive thermal conductivity of AlSi/polyester abradable se als

OOF2: Object Oriented Finite Element Analysis of Microstructures – software developed by NIST under L INUXMain drawback: requires much RAM (4 Gbytes: 0.4 mil lion of cells)(not possible to consider big images without geometric approximations, e.g. mesh with one cell/pixel not possible above 0.4 million of pixels)

Introduction

First results(2008)

New developments


with one cell/pixel not possible above 0.4 million of pixels)

TS2C1 in-house (finite differences)� Real architecture of the coating structure� Image analysis (… choice of adequate thresholds)� Mesh = image (pixels = cells)� System of equations (size = number of pixels of the image)� Solving procedure (SOR or LSOR methods)� Main advantage :

no problem of RAM (about 32Mbytes for an image of 0.4 million of pixels)

1See Bolot et al. (Num. Heat Trans., 47(9), 2005)

New results



OOF2Geometric

approximations



TS2CEach pixel of the original

image is a cell



Typical structure of an

Des

peck

le fi

lterin

g

ImageResolution

κ (W.m-1.K-1)

TS2C OOF2

100%* 0.467 0.485

75% 0.468 0.500

50% 0.458 0.511

Introduction

First results(2008)

New developments

Synthesis of the computed results


Typical structure of anAlSi/polyester coating(SM Durabrade 1605 powder)

Simplified structure of the same AlSi/polyester coating

Des

peck

le fi

lterin

g

25% 0.402 0.549

* corresponding to an image of 756x541 (0.4 M of pixels)

0

0.1

0.2

0.3

0.4

0.5

0.6

20% 40% 60% 80% 100%

Image resolution

The

rmal

con

duct

ivity

(W.m

-1.K

-1)

TS2C

OOF2

New results



Introduction

First results(2008)

New developments

Conclusions(ITSC Conference, Maastricht, 2008)

� Quite significant differences were noticed especially for low resolution images (difference of 30% at the lowest resolution of 25%)

� A converging tendency was obtained for the highest resolution (difference of 3-4% at the highest resolution level)


New results


The reasons are now explained:� OOF2 uses a nodal approach whereas our original version

of TS2C uses a cell-centered approach� A nodal version of TS2C was developed during 2009 as well

as a "split pixel" formulation (4 cells or more per pixel)� Complementary results could be obtained for simplified or

non simplified coating structures (i.e. with and without applying the Despeckle filtering)


•

2D heat conduction equation:

0=

∂∂

∂∂−

∂∂

∂∂−

yT

yxT

xκκ

T(i,j) T(i+1,j)T(i-1,j)

T(i,j+1)

T(i,j-1)

Pix(i,j)

Pix(i,j+1)

Pix(i+1,j)

Pix(i+1,j+1)

T(i,j)T(i-1,j) T(i+1,j)

T(i,j+1)

T(i,j-1)Y

Introduction

First results(2008)

New developments

Centered and nodal formulations


Linearized equation:

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )1j,iAyj,iAyj,1iAxj,iAxj,iAp

with

1i,jκ

1i,jκ

12

Ay(i,j) and

,j1iκ1

i,jκ

12

Ax(i,j)

:nformulatio Centered

+++++=

−+

=

−+

=

)1,()1,()1,(),(),1(),1(),1(),(),(),( +++−++++−= jiTjiAyjiTjiAyjiTjiAxjiTjiAxjiTjiAp

1 linear equation per pixel

X

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )1j,iAyj,iAyj,1iAxj,iAxj,iAp

with2

,j1iκi,jκAy(i,j) and

21i,jκi,jκ

Ax(i,j)

:nformulatioNodal

+++++=

++=++=

New results



Introduction

First results(2008)

New developments

0.50.60.7

Pre

dict

ed th

erm

al

cond

uctiv

ity

Complementary results produced with the nodal version of TS2C

Additional results for the 200% resolution(i.e. 4 cells/pixel )


New results


00.10.20.30.4

0% 50% 100% 150% 200%

Image resolution

Pre

dict

ed th

erm

al

cond

uctiv

ity

TS2C

TS2C_NF

OOF2

Assumed properties:κAlSi=130 W.m-1.K-1

κPolyester=0.17 W.m-1.K-1


Powder Image type

TS2Cversion

Picture resolution

50% 100% 200%

Durabrade 1605

Binary CC 0.561 0.614 0.634

NF 0.852 0.725 0.701

Ternary CC 0.507 0.551 0.574

� Synthesis of the computed thermal conductivities

DurabradeGrey level

Introduction

First results(2008)

New developments

No application of the Despeckle filtering


Ternary CC 0.507 0.551 0.574

NF 0.791 0.669 0.641

Metco601 NS

Binary CC 0.421 0.486 0.500

NF 0.619 0.562 0.545

Ternary CC 0.395 0.455 0.471

NF 0.593 0.537 0.518

CC stands for Cell-Centered versionNF stands for Nodal FormulationThe measured value was about 0.53 W.m-1.K-1

With Despeckle filter: 0.47 / 0.48 W.m-1.K-1 for the coatings produced with Durabrade 1605

DurabradeTernary

DurabradeBinary

New results



0.400

0.600

0.800

1.000

Pre

dict

ed th

erm

al c

ondu

ctiv

ity(W

.m-1

.K-1

)

1: Measure=0.53

2: Dura_Des_OOF2

3: Dura_Des_CC

4: Dura_Des_NF

5: Dura_bin_CC

6: Dura_bin_NF

7: Dura_ter_CC

Introduction

First results(2008)

New developments

Graphical representation of the results


0.000

0.200

0.400

0% 50% 100% 150% 200%

Picture resolution

Pre

dict

ed th

erm

al c

ondu

ctiv

ity(W

.m-1

.K-1

)

7: Dura_ter_CC

8: Dura_ter_NF

9: Metco_bin_CC

10: Metco_bin_NF

11: Metco_ter_CC

12: Metco_ter_NF

New results


Conclusion: Results obtained with the nodal and centered formulations tend to converge when using high resolution images or when splitting the pixels (4 cells per pixel)


Introduction

First results(2008)

New developments

Example 1 of effective elasticity moduli calculated from the tensile test simulation with OOF2 for different mag nification levels and in both directions


Assumed properties:EAlSi=17.5 GPa, ν=0.23Epolyester=0.75 GPa, v=0.3

New results


(1Ref ECM UTBM/WP5.4/2007/2R1)


Introduction

First results(2008)

New developments

OOF2 and TS2C tend to provide similar predictions o f the effective thermal conductivity of AlSi/polyester ab radable coatings if the nodal version of TS2C is used .

The differences become noticeable if the Cell-Cente red version of TS2C is used especially for low resoluti on images .

In all cases the computed results present a converg ing


New results


In all cases the computed results present a converg ing tendency with the increase in the picture resolutio n.

The development of a "split pixel" formulation contr ibuted to provide converging results (i.e. that do not vary a nymore with the picture resolution)

There is no more need to use simplified structures produced for example by applying successive Despeckle filter ing


Introduction

First results(2008)

New developments

Up to now, all mechanical calculations were perform ed with OOF2 (or with ANSYS for the simulation of tests)

An in-house mechanical code based on a finite volum e approach is under development to preserve memory fo r considering large images without simplification

Comparisons will be performed with results provided with OOF2: each pixel will be considered as a cell


New results

ConclusionsPerspectives Example of deformation of

a 10 cm by 10 cm steel piece for a compressive

test (amplification factor of the displacements x20)

Data: E=210 GPa, v=0.3

OOF2: each pixel will be considered as a cell

Predicting the Thermal Conductivity of AlSi/Polyester Abradable Coatings: Effects of the Numerical...

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