2008-01-0973

400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-0790 Web: www.sae.org

SAE TECHNICALPAPER SERIES 2008-01-0973

Conjugate Heat Transfer in CI EngineCFD Simulations

Mika Nuutinen, Ossi Kaario and Martti LarmiHelsinki University of Technology

Reprinted From: Multi-Dimensional Engine Modeling, 2008(SP-2171)

2008 World CongressDetroit, MichiganApril 14-17, 2008

Downloaded from SAE International by Kwang Yang Industry Co Ltd, Wednesday, July 16, 2014

By mandate of the Engineering Meetings Board, this paper has been approved for SAE publication uponcompletion of a peer review process by a minimum of three (3) industry experts under the supervision ofthe session organizer.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, ortransmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise,without the prior written permission of SAE.

For permission and licensing requests contact:

SAE Permissions400 Commonwealth DriveWarrendale, PA 15096-0001-USAEmail: [email protected]: 724-772-4028Fax: 724-776-3036

For multiple print copies contact:

SAE Customer ServiceTel: 877-606-7323 (inside USA and Canada)Tel: 724-776-4970 (outside USA)Fax: 724-776-0790Email: [email protected]

ISSN 0148-7191Copyright 2008 SAE InternationalPositions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE.The author is solely responsible for the content of the paper. A process is available by which discussionswill be printed with the paper if it is published in SAE Transactions.

Persons wishing to submit papers to be considered for presentation or publication by SAE should send themanuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE.

Printed in USA


ABSTRACT

The development of new high power diesel engines is continually going for increased mean effective pressures and consequently increased thermal loads on combustion chamber walls close to the limits of endurance. Therefore accurate CFD simulation of conjugate heat transfer on the walls becomes a very important part of the development. In this study the heat transfer and temperature on piston surface was studied using conjugate heat transfer model along with a variety of near wall treatments for turbulence. New wall functions that account for variable density were implemented and tested against standard wall functions and against the hybrid near wall treatment readily available in a CFD software Star-CD.

INTRODUCTION

Accurate prediction of the piston surface temperature and heat flux is difficult mainly because of the very large temperature and velocity gradients of highly turbulent flow near the wall and also because of the transient interaction between the gas phase and solid wall temperatures. Instead of resolving the temperature and velocity profiles down to the wall, wall functions based on some simplifying assumptions of the near wall turbulence are used. Standard wall functions and hybrid near wall treatment in the form they are usually implemented in commercial CFD codes assume incompressible flow. Therefore straightforward adoption of them into engine simulations might not be appropriate, since the gas in the cylinder is highly compressible indeed and large density variations are likely to appear near the walls. To tackle this problem momentum and energy equations near the wall are integrated in their compressible form to new modified wall functions that are sensitive to density variation. Also variable turbulent Prandtl number near the walls is included in the modified wall functions.

Heat transfer in combustion engines has bee widely studied, e.g. by Schubert, Wimmer and Chamela [1], who developed quasi-dimensional heat transfer models for combustion ignition engines, by Han and Reitz [2], who studied the effect of density variations on convective heat transfer, by Urip, Liew, Yang and Arici [3], who studied the effect of unsteady thermal boundary

conditions, by Urip, Yang and Arici [4], who studied conjugate heat transfer in actual internal combustion engine CFD simulations, by Tiainen, Kallio, Leino and Turunen [5], who studied heat transfer in diesel engines with density dependent wall functions in CFD and combining the obtained average heat transfer coefficients to FEM calculations of the heat transfer in solid piston material and also by Huuhilo [6], who studied and developed a FEM code for transient heat transfer in the piston surface. A good motivation for this work is figure 1 from Huuhilos Masters Thesis that shows the effect of the piston surface material on the transient maximum piston surface temperature.

Fig. 1. The simulated maximum temperature of the piston surface layer fabricated from steel, aluminium or zirconium oxide [6].

2008-01-0973

Conjugate Heat Transfer in CI Engine CFD Simulations Mika Nuutinen, Ossi Kaario and Martti Larmi

Helsinki University of Technology

Copyright 2008 SAE International


VARIABLE DENSITY WALL FUNCTIONS

In deriving the wall functions following assumptions are made:

1) wall normal derivatives are much larger than tangential ones, so the tangential derivatives are neglected.

2) near wall fluid flow is tangential to wall. 3) near wall pressure gradient can be neglected. 4) near wall heat flux consists only of laminar and turbulent conduction.

5) gas obeys ideal gas law 6) near wall specific heat capacity is constant 7) near wall mass fractions of mixture components are constant.

8) near wall shear stress and heat flux are constant. Now the simplified near wall momentum and heat equations (1) and (2) can be written as

( ) wt dydu

=+ , (1)

w

t

tp qdy

dTc =

+

PrPr

. (2)

Equations (1) and (2) are conveniently solved in non-dimensional form. In constant density formulation, which is the basis of the standard wall functions, the non-dimensional velocity, temperature and wall distance are written as

fw uyyy ==+ / , (3)

f

w

w

w

u

uuuuu

=

=+

/ (4)

( ) ( )w

wfp

w

wwp

qTTuc

qTTc

T

=

=+

/. (5)

For turbulent viscosity Mellor [7] suggested that

( )( ) 5.3823

4

+==

+

++

y

yt

(6)

Usually the turbulent Prandtl number is treated as a constant, but Kays [8] formulated a near wall correlation as

85.0Pr

7.0Pr +=+t

(7)

In [2] Han and Reitz made a change of variables from y to y+, u to u+ and T to T+ by using equations (3-5) directly, but with the assumption

fu

dydy +

= , (8)

which is not strictly correct, since in compressible flow the gas density and consequently friction velocity uf are functions of temperature and temperature in turn is a function of the wall distance y. Only after the change of variables was density treated as a variable but friction velocity was still treated as a constant.

To overcome these shortcomings, new dimensionless parameters are obtained by replacing variable density in equations (3-5) with a reference density from point yp that lies in the center of the near wall cell. With this choice, the new dimensionless parameters are

21

41

,

,

/

/

ppwpf

pfppwp

kCu

uyyy

=

==

, (9)

pf

w

pw

w

u

uuuuu

,/

=

=

(10)

( )w

wpfppp

qTTuc

T

= ,,

. (11)

The dimensionless parameters are now functions of only their dimensional counterparts and the change of variables can be made correctly. The temperature enters equations (1) and (2) through turbulent viscosity and turbulent Prandtl number, equations (6) and (7), since they depend on y+ which is a function of temperature. Inserting the new dimensionless distance y* and using the ideal gas law equations (6) and (7) become


( )( )

TT

y

y

yTT

yTT

p

p

p

=

+=

+

=

5.382

5.3823

4

3

4

(12)

85.0Pr

7.0Pr +=t

. (13)

Rearranging equations (1) and (2) they become

+=

1dydu , (14)

{ }

++

=

Pr85.07.0Pr

Pr1 2

dydT . (15)

Equations (14) and (15) are coupled by *, so their integration is not straightforward, but has to be made both numerically and iteratively.

INTEGRATION OF WALL FUNCTIONS

To integrate the equations (14) and (15) an initial discretized profile for * has to be guessed e.g. assuming linear temperature profile

( ) += piwpwp

i yyTTTT

/ . (16)

The discretized form of eq. (15) can be integrated with trapezoid method

( )0

20

11*

=

++=

T

yAATT iiiii

, (17)

where Ai is the integrand of eq. (15). Because the wall heat flux is constant, * can be re-evaluated

( )wpipw

ppi TTTTT

TT+

=

. (18)

Now the iterative process is to repeat equations (12, 13, 17 and 18) in a sequence until pT changes less than a specified tolerance. Wall heat flux or heat transfer coefficient can be computed from the obtained pT as

( )

=

p

wppfpppw T

TTucq ,,

(19)

=

p

pfppp

Tuc

h ,,

. (20)

Dimensionless velocity can be integrated in a single trapezoid round, since i is now known

( )0

211

=

++=

o

iiiii

u

yBBuu

, (21)

where Bi is the integrand of eq. (14). Wall shear stress can be computed from the obtained pu

pp

wpw

u

uu

2

=

. (22)

With the assumption that Han & Reitz [2] made, temperature variation cancels from the momentum equation, so the dimensionless velocity can be computed by using just the Mellor profile for turbulent viscosity. Dimensionless temperature becomes according to Han & Reitz [2]

( ) ( ) 5.2ln1.2/ln, +== ++ pw

wpwpppp yq

TTTcT

(23)

COMPARISON OF WALL FUNCTION FORMULATIONS

In figure 2 is a comparison between the velocity laws of wall in laminar, logarithmic (turbulent), incompressible Mellor and the new variable density formulations in a typical engine simulation situation with

7.0Pr1500700200

=

=

=

=

KTKT

y

p

w

p

It can be seen that the laminar and logarithmic curves intersect at y* = 10.9577, which is a switching point from turbulent to laminar law of wall in standard high Reynolds


number wall treatment. The profile computed with Mellor turbulent viscosity transits smoothly from the laminar to logarithmic curve and there is no need to define a switching point. The new variable density formulation follows smoothly the laminar curve at small values of y* and lags the constant density logarithmic profile and the Mellor profile when y* gets larger in a case where the gas is hotter than the wall. If the temperature ratio was inversed the new formulation curve would be above logarithmic and Mellor profiles. Interpreting eq. (22) this means that the new formulation tends to produce larger near wall drag than the standard wall functions when the gas is hotter than the walls and vice versa.

In figures 3 and 4 is a comparison between the temperature laws of the wall in constant density Mellor & Kays, variable density Han & Reitz and the new variable density formulations. The new formulation and Han & Reitz formulation both predict smaller T* values than the constant density formulation, but the difference between the two variable density formulations seems quite small and this raises a question if there is any reason to use the new, computationally more expensive formulation. The answer is yes. Inspecting equations (11) and (23) it is noted that the dimensionless temperatures are defined differently in the two formulations. Comparing the predicted heat fluxes the difference of the two variable density formulation becomes more pronounced. In figure 5 is a comparison between the predicted heat fluxes relative to the constant density formulation heat flux as a function of near wall cell center dimensionless distance. There is a huge relative difference in the predicted heat fluxes, so there is indeed motivation to use the new, more rigorously formulated temperature law of the wall. The conclusion is that the constant density law of the wall will underestimate the heat flux whereas the variable density Han & Reitz wall function tends to overestimate it.

100 101 1020

2

4

6

8

10

12

14

16

18

y*

u*

LaminarTurbulent (log)Mellor incompressibleCurrent formulation

Fig 2. Velocity wall functions.

100 101 1020

2

4

6

8

10

12

14

16

18

y*

T*

Mellor & Kays incompressibleCurrent formulationHan & Reitz

Fig. 3. Temperature wall functions.

101 1026

7

8

9

10

11

12

13

14

y*

T*

Mellor & Kays incompressibleCurrent formulationHan & Reitz

Fig. 4. Temperature wall functions.

100 101 1020.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

y*p

q w/q

w0

Current formulationHan & Reitz

Fig. 5. Effect of wall functions on heat flux.


SIMULATION PROCEDURE

Simulations were carried out with Star-CD on a simplified flat piston - cylinder model of Wrtsil 20 engine with conjugate heat transfer CFD model. Detailed CFD-models of Wrtsil 20 engine can be found e.g. in [9] by Antila et. all. Since the aim of this study was to test the conjugate heat transfer model along with different near wall treatments, only the piston was modeled as a solid block with three dimensions, as it receives the largest thermal load, whereas cylinder and cylinder head were modeled just as conducting walls with constant temperature boundary condition. The lower boundary of the thin piston layer was modeled as a constant temperature wall and the peripheral boundary as an adiabatic wall. The simulations were also confined to compression and expansion strokes, so intake and exhaust through valves were not considered. The situation was also considered periodic so only a 45 (periodic angle of the 8-hole nozzle) slice of the cylinder was modeled. Piston wall temperatures and heat fluxes as well as cylinder pressures and heat release rate were monitored in each simulation. Between simulations only the turbulence models and near wall treatments were changed, except for the low Reynolds number k- model with hybrid wall treatment, where the mesh near the piston wall was refined to meet the requirements of the hybrid wall model. The specifications of the modeled engine are presented in table 1.

Table 1. Specifications for the simulated engine. Bore [mm] 200

Stroke [mm} 280

Connecting rod [mm] 510

Displacement [dm3] 8.8

Engine speed [revs/min] 1000

Rated power [kW] 200

Compression ratio [-] 15

Injector nozzles [-] 8

Nozzle hole diameter [mm] 0.37

Fuel mass/cycle [g] 1.0

Fuel (name, formula) Dodecane, C12H26 Lambda(relative air/fuel ratio) [-] 2.46

Initial swirl number 0.5

COMPUTATIONAL GRID

The computational grid was a 45 section of the cylinder. The solid piston mesh was 2mm thick (about 3 times the estimated temperature penetration depth), with 30 cells in axial direction and the height of the first cell next to the solid-gas interface was approximately 5m and graded with the expansion ratio of 1.2. In radial direction there were 25 cells and in azimuth direction 20 cells, both evenly spaced. The fluid domain had 10 evenly spaced 0.6mm thick cells next to the gas-solid interface and the rest of the domain had 75 deforming cells in axial direction. Part of the deforming cells were removed from the simulation during the compression and then added again during expansion to maintain a desired mesh density. The mesh in the hybrid wall treatment case was otherwise identical but the 10 0.6mm fluid cells were replaced by 30 graded (expansion ratio 1.2) cell layers with approximately 5m gas-solid interface cell thickness. The coarser computational mesh at TDC is presented in figure 7.

TURBULENCE AND COMBUSTION MODELS

Simulations were made with 4 combinations of turbulence models and near wall treatments:

1) High Reynolds number k- model with standard wall functions.

2) High Reynolds number k- model with the new variable density wall functions, computed in user subroutines.

3) High Reynolds number RNG k- model with standard wall functions.

4) Low Reynolds number k- model with hybrid wall treatment. In hybrid wall treatment the flow field is resolved all the way down to the wall without any wall functions whenever the near wall mesh density is sufficient and when it is not the wall function solution is blended to the solution.

In all simulations Eddy Break Up LaTCT one reaction model without any ignition model was used to compute the reaction rates. Thus the ignition depends solely on the reaction rates determined by the EBU LaTCT model. Details of the used turbulence and combustion models can be found in [10] and their application to diesel engine simulation in Kaarios doctoral thesis [11].

LAGRANGIAN MULTI-PHASE MODELS

Injected droplets were simulated with Lagrangian multi-phase model with turbulent dispersion and standard models for momentum, heat and mass transfer. Reitz and Diwakar droplet break-up model [12] was used together with Bais [13] spay impingement model including droplet-wall heat transfer and boiling.


Temperature dependent droplet properties were computed in a user subroutine. The injection profile of a single nozzle is presented in figure 6.

350 355 360 365 370 375 380 3850

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

CA

ma

ss fl

ow ra

te [k

g/s]

Fig. 6. Nozzle mass flow rate.

CONJUGATE HEAT TRANSFER

Conjugate heat transfer is very simple as the energy equation in the solid part is just a degenerate form (velocity is set to zero) of its counterpart in the fluid domain. The code only needs to know that there is a step jump in the material properties (heat conductivity, density and specific heat capacity). When solving the energy equation the code has to adjust the interface temperature such that the heat flux across the surface is continuous. However, due care needs to be taken in the discretization of the solid domain, since the heat conductivities of metals and thus the resulting temperature gradients differ by orders of magnitude, e.g. comparing the heat conductivities of nitrogen and steel: knitrogen = 0.02583W/m/K, ksteel = 43W/m/K. This means that the solid domain mesh near the interface has to be very dense in the normal direction. Another important assessment is the penetration depth of the oscillating temperature. Huuhilo [6] used an approximation based on an analytical solution of a 1-dimensional heat equation with sinusoidally varying temperature boundary condition

( )

/0

2

cos,

=

=

p

z

c

k

tz

eTtzT

(24)

where is the angular frequency of the temperature variation and is the penetration depth where the temperature fluctuation is e-1 times the amplitude. The thickness of the modeled solid layer has to be at least few times the penetration depth in order to avoid disturbances from the bottom constant temperature boundary condition.

SIMULATION RESULTS

Maximum piston surface temperature, total piston surface heat transfer and cylinder pressure were extracted from all 4 simulations. To avoid misinterpretation, standard wall functions refer to those constant density wall functions that are by default in Star-CD. The maximum piston surface temperatures are presented in figure 7. It is noted that the new modified variable density wall functions (MWF) predict clearly higher peak temperatures than the other standard (SWF) and hybrid (HWF) wall functions. This information would be invaluable when designing pistons for extreme thermal loads. Total piston heat transfer is presented in figure 8. The new wall functions also predict higher heat transfer from the charge to the piston surface as expected. Cylinder pressures are presented in figure 9. The new modified wall treatment produces marginally (approximately 0.2bar) higher peak pressure than the corresponding simulation with standard wall functions, which is surprising because more heat is flowing through the piston with the new wall treatment. However the relative difference is very small and can be explained by inspecting the energy balance of the charge gas. In figure 10 is the cumulative energy difference (heat release - heat loss through boundaries) between simulations with the new modified wall treatment and the standard wall functions. It is noted that while the heat loss is greater with the new wall treatment, also the heat release from the burning charge is more rapid. The total of these is positive between approximately CA 369 and 375, where the pressure also peaks and consequently the maximum cylinder pressure is higher with the new modified wall treatment. In figure 11 is a snapshot from the piston surface temperature distribution and spray at 12 after the TDC, when the piston surface temperature has its maximum value, approximately 656K. An order of magnitude comparison can be made with figure 1, where a same engine was modeled, although the shape of the piston and running speed were different.

The CPU times of the simulations are listed in table 2. Simulation with the hybrid wall treatment was the most time consuming, but it also had a denser mesh than the other three. There is no big difference between the standard and RNG k-, but with the new modified wall treatment the CPU time is increased some 20%. Of course the increase in the CPU time depends on the number of points used in numerical integration and the tightness of the stopping criterion (now 200 and 0.5%).

Table 2. CPU times. Turbulence model/wall treatment/cells CPU time [s]

k- / SWF / 57500 cells 11744

RNG k- / SWF / 57500 cells 10844

k- / HWF / 67500 20109

k- / MWF / 57500 cells 14186


Fig. 6. Computational mesh.

360 380 400 420 440 460 480 500570

580

590

600

610

620

630

640

650

660

CA

Pist

on s

urfa

ce te

mpe

ratu

re, T

max

[K

]

k SWFRNG k SWFk HWFk MWF

Fig. 7. Maximum piston surface temperature.

355 360 365 370 375 380 385 390 395 400 405 4100

50

100

150

200

250

CA

Tota

l pist

on h

eat t

rans

fer [k

W]


Fig. 8. Total piston heat transfer.

360 362 364 366 368 370 372 374 376 378 3801.6

1.65

1.7

1.75x 107

CA

Cylin

der p

ress

ure

[Pa]


Fig. 9. Cylinder pressures.

350 360 370 380 390 400 410 420 430 440 450250

200

150

100

50

0

50

CA

Cum

ulat

ive d

iffer

ence

in (h

eat p

roduc

tion

heat

loss)

[J]

Fig. 10. Cumulative difference in energy balance in simulations performed with the new modified and standard wall functions (k- model).

Fig. 11. Piston surface temperature and spray.


CONCLUSION

To conclude, the new variable density formulation for wall functions works well and gives reasonable and expected results compared to constant density wall functions. That the new variable density wall functions predict higher heat loss and higher cylinder pressure simultaneously seems inconsistent, but the difference is so small that it can be explained by the changes caused by the new wall functions in turbulent kinetic energy and dissipation rate that control the reaction rate in the used EBU LaTCT combustion model. One could do even better by including the effect of temperature dependent specific heat capacity to the formulation, but this is left for future work. However the quality of the modified wall functions can not be verified without careful comparison with experimental data, but that is beyond the scope of this research.

ACKNOWLEDGMENTS

The authors wish to thank the Helsinki University of Technology Internal Combustion Engine Laboratory for the opportunity and facilities to carry out this work.

REFERENCES

1. C. Schubert, A. Wimmer and F. Chmela, Advanced Heat Transfer Model for CI Engines, SAE Technical Paper Series 2005-01-0695, (2005).

2. Z: Han et. R. D. Reitz, A temperature wall function formulation for variable-density turbulent flows with application to convective heat transfer modeling, Int. J. Heat Mass Transfer. Vol 40, No. 3, 613-625, (1997)

3. E. Urip, K. H. Liew, S. L. Yang and O. Arici, Numerical Investigation of Heat Conduction with Unsteady Thermal Boundary Conditions for Internal Combustion Engine Application, Proceedings of IMECE04 2004 ASME International Mechanical Engineering Congress and Exposition, IMECE2004-59860, (2004).

4. E. Urip, S. L. Yang and O. Arici, Conjugate Heat Transfer for Internal Combustion Engine Application using KIVA code, Mechanical Engineering-Engineering Mechanics Department, Michigan Technological University Houghton, Michigan 49931.

5. J. Tiainen, I. Kallio, A. Leino and R. Turunen, Heat Transfer Study of a High Power Density Diesel Engine, SAE Technical Paper Series 2004-01-2962, (2004).

6. P. Huuhilo, Finite Element Analysis of Transient Heat Transfer in the Piston Surface of Combustion Engine, Masters Thesis, Helsinki University of Technology, Department of Engineering Physics and Mathematics, (2006).

7. G. L. Mellor, Proc. Symp. Fluidics Internal Flow, Pennsylvania State University (1968).

8. W. M. Kays, Turbulent Prandtl number where are we?, ASME J. Heat Transfer 116, 284 (1994).

9. E. Antila, O. Kaario, P. Kilpinen, T. Lahtinen, M. Larmi, H. Pokela, A. Saarinen, K. Stalsberg-Zarling, P. Taskinen, J. Tiainen, O. Toivanen, Mastering The Diesel Process, Publications of the Internal Combustion Engine Laboratory, Helsinki University of Technology 79, ISBN 951-22-6998-8, (2004).

10. CD-Adapco, METHODOLOGY, Star-CD version 3.26.

11. O. Kaario, The Influence of Certain Submodels on Diesel Engine Modeling Results, Doctoral Thesis, Publications of the Internal Combustion Engine Laboratory, Helsinki University of Technology, (2007).

12. R. D. Reitz et. R. Diwakar, Effect of drop breakup on fuel sprays, SAE Technical Paper Series 860469, (1986).

13. C. Bai and A. D. Gossman, Development of methodology for spray impingement simulation, SAE Technical Paper Series 950283, (1995).

CONTACT

Mika Nuutinen, Research Scientist

Helsinki University of Technology, Internal Combustion Engine Laboratory, PO BOX 4300, FIN-02015 HUT, Finland

[email protected]


NOMENCLATURE

cp specific heat

c turbulence model constant = 0.09

h heat transfer coefficient

k heat conductivity, turbulent kinetic energy

kt turbulent heat conductivity

Pr Prandtl number = cp/k

Prt turbulent Prandtl number = tcp/kt

qw wall heat flux

T temperature

Tw wall temperature

T+ dimensionless temperature

T* dimensionless temperature with reference density

u magnitude of gas velocity

uf friction velocity

uw magnitude of tangential wall velocity

u+ dimensionless velocity

u* dimensionless velocity with reference density

y distance to the wall

y+ dimensionless distance to the wall

y* dimensionless distance to the wall with reference density

Greek symbols

dimensionless temperature parameter (Tp/T)

von Karman constant = 0.419

molecular viscosity

t turbulent viscosity

+ dimensionless viscosity t/

density

w wall shear stress


/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects true /CheckCompliance [ /PDFX1a:2001 ] /PDFX1aCheck true /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError false /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (U.S. Web Coated \050SWOP\051 v2) /PDFXOutputConditionIdentifier (CGATS TR 001) /PDFXOutputCondition () /PDFXRegistryName (http://www.color.org) /PDFXTrapped /False

/CreateJDFFile false /Description

Documents

2008-01-0973