book of abstract 2002

7/30/2019 Book of Abstract 2002

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1

2L

2W

nonwetting

material

weting

material

2002 ME Graduate Student Conf erenceAp ri l 13, 2002

HEAT TRANSFER AND FLUID FLOW IN AN IDEALIZED MICRO HEAT PIPE

J in ZhangM.S. Candidate

Thesis advisor: Prof. Harris Wong

ABSTRACTMicro heat pipes have been used as a heat-dissipating

device in many systems, such as micro electroniccomponents and the leading edge of hypersonic aircraft.

[1, 2]

Micro heat pipes transfer heat by evaporation, convection,and condensation, same as the conventional heat pipes.

However, the effective thermal conductivity of micro heatpipes is only 1/40 that of conventional heat pipes. Due tothe complexity of the coupled heat and mass transport, andto the complicated three-dimensional bubble geometryinside micro heat pipes, there is a lack of rigorous analysis.As a result, the relative low effective thermal conductivityremains unexplained. This work conceptualized an idealizedmicro heat pipe that eliminates the complicated geometry,but retains the essential physics. The simplified bubblegeometry allows a direct comparison between theoreticalpredictions and experimental data.

The idealized micro heat pipe is a rectangular heat pipe,the top portion of which is made of a non-wetting material,and the bottom portion a wetting material. The lower

portion is filled to the rim by a wetting liquid, and theupper portion is filled by its vapor. This configurationensures that the contact line of the liquid-vapor interface ispinned at the interception between the wetting and non-wetting materials. Pinning of the interface allows a capillarypressure gradient to drive the liquid flow. When this microheat pipe is driven at small temperature differences, theinterface should be roughly flat, allowing the analysis to begreatly simplified.

The evaporation and condensation in the idealizedmicro heat pipe is analyzed. It is found that the interface canbe separated into two regions: an inner region near the wallwhere evaporation occurs and an outer region away from thewall. The evaporation rate is solved by the method of

matched asymptotic expansions, and the leading orderevaporation rate is obtained as ln, where measures theratio of conductive heat flux in the liquid to evaporativeheat flux at the interface. The small parameter is

where kfis the liquid thermal conductivity, T is the walltemperature, c=(2RT)

-1/2with R being the universal gas

constant per unit mass of the vapor as determined by the

kinetic theory, is vapor density, hfg is liquid latent heatand W is the half width of the pipe. The Stokes flowinduced by the surface tension gradient (Marangoni stress)along the interface and by the evaporation at the interface issolved using a finite-difference method.

Fluid flowand heat transfer along the micro heat pipe

are also studied. Liquid temperature distribution along themicro heat pipe is given in Figure 2. It is found that thetemperature profile is relatively flat except the region nearthe evaporator, which is the evaporation region. The lengthscale of the region is calculated as

where Aw and A fare cross-sectional area of the wall andliquid, respectively, and kw is wall thermal conductivity.For a micro heat pipe with larger L/W the length of theevaporation region is shorter. Vapor pressure distributionalong the micro heat pipe is also given in Figure 3. It isclear that the pressure goes approximately linearly and notaffected strongly by L/W. Effective thermal conductivity keffis evaluated. A longer or wider micro heat pipe will have alarger keff. And it is found that increasing the evaporationarea at the evaporator will increase keff. It is also affected bythe latent heat of the working fluid. A fluid with largerlatent heat will produce larger keff.

FIGURES AND TABLES

Figure 1 an Idealized Micro Heat Pipe

= Awkw + A fkf2 kf - ln

,

= kfT

chfg2 W,


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2

ACKNOWLEDGMENTSThis work was supported by NASA and LaSPACE.

REFERENCES

1. G. P. Peterson, Appl. Mech. Rev. 45 (1992) 175-89.2. P. Dunn & D. A . Reay, in "Heat Pipes" (Pergamon

Press, 1982) 16-18.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

L/W = 20L/W = 50L/W = 100L/W = 200

p*

z*

p

z

0

50

100

150

200

250

0.0002 0.0004 0.0006 0.0008 0.001

L/W = 20

L/W = 50L/W = 100L/W = 200

keff

W

W

keff

Figure 4 Effective Thermal Conductivity along anIdealized Micro Heat Pipe

Figure 3 Pressure Distribution along anIdealized Micro Heat Pipe

Figure 2 Temperature Distribution along anIdealized Micro Heat Pipe

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

L/W = 20

L/W = 50

L/W = 100

L/W =200

T*

z*

T

z


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3

2002 ME Graduate Student Conference

April 13, 2002

PHYSICAL PARAMETER ESTIMATION OF VIBRATING STRUCTURE FROM ITS

SPECTRAL DATA: A NEW MATHEMATICAL MODEL

Kumar Vikram Singh

Ph.D. Candidate

Faculty Advisor: Y. M. Ram

ABSTRACT

The problem of reconstructing a model with prescribed

spectral data is known as inverse eigenvalue problem.

Reconstruction of the distribution of physical parameters of

a continuous vibratory system by using its eigenvalues isaddressed here. Considering a unit length piecewise

continuous rod as shown in figure 1. The eigenvalue

problem associated with this rod is given by the following

set of differential equations

======+==+

)()()()(

0)(0)0(where,,0

where,,02

2

avauavau

Lvusvvr

quup

. (1)

Applying the boundary and matching conditions of

displacement and force leads to problem of finding the non-

trivial solution of

o=

4

3

2

sincos0

sincoscos

cossinsin

z

z

z

LL

aaa

aaa

. (2)

We named this problem the Transcendental Eigenvalue

Problem (TEP).The general form of this problem is

( ) ozA = . (3)

Frequently the classical finite element and finite difference

formulation are used in approximating such a continuous

system. The characteristic equation of the obtained

eigenvalue problem is a polynomial. In contrast, the

continuous systems are characterized by TEP [1]. By using

finite element or finite difference method, the TEP is

transformed into an algebraic eigenvalue problem. It has

been concluded by [2,3] that the solution to the discrete

problem is not a good approximation to the continuous one.

Past research associated with inverse problems of the

continuous vibratory system can be found in [4,5,6,7,8].Since the behavior of a finite dimensional polynomial is

fundamentally different from the transcendental function,

such an approach may involve inaccurate approximation of

the physical parameters, as illustrated in figure 2.

For the given continuous system in figure 1, the inverse

problem can be defined as follows:

Given the resonant frequencies21

, , anti-resonant

frequency1 and the total mass of the rod.

Determine the physical parameters21

,pp and21

,qq .

The problem now is of determining the roots of the system

of transcendental frequency equations,

( )( )( )( )( )( )

==

==

==

=

=

=

0,,det),,(

0,,det),,(

0,,det),,(

1

2

1

3

2

1

A

A

A

F

F

F

, (4)

for the given values of21

, and1 . The research aims at

developing low dimensional analytical models allowing

estimation of the physical parameters of the structures from

measured vibration test data. The main idea presented hereis to replace the continuous system with variable physical

parameters by a continuous system with piecewise uniform

properties as shown in figure 3. The boundary and matching

conditions between the various parts of the continuous

model can be expressed in the TEP form. A rapidly

converged algorithm is used for evaluation of the physical

parameters of the system. The algorithm implements the

Newtons iterative method for determining the physical


4/38

4

parameters of the system. Formulation of such mathematical

models for non-uniform axially vibrating rods and

reconstruction of their area distribution by using this

algorithm, as illustrated in figure 4, is presented. This

proposed solution of TEP can also be used to solve classical

direct problems in structural dynamics such as buckling [9]

and vibration control [10].

FIGURES AND TABLES

Fig.1. Piecewise continuous axially vibrating rod

Fig.2.Physical parameter Identification of piecewise rod

from its associated discrete model

Fig.3. New mathematical model used for the approximation

of a non-uniform rod

Fig.4. Reconstruction of the shape of the exponential rod

with model ordern=4 and n=8

ACKNOWLEDGMENTS

The research work presented here is supported by a

National Science Foundation research grant CMS-9978786.

REFERENCES

1. Singh K. V. and Ram Y. M., A mathematical model to

overcome the discrepancies between continuous

systems and their discrete approximation, ASME ETCE

2002.

2. Boley D. and Golub G.H., A Survey of matrix eigenvalue

problems, Inverse Problems, Vol. 3, pp. 595-622, 1987.

3. Paine J., A numerical method for the inverse Sturm-

Liouville problem, SIAM Journal on Scientific and

Statistical Computing, Vol. 5(1), pp. 149-156, 1984.

4. Ram Y.M. and Caldwell J., Physical parameters

reconstruction of a free-free mass-spring system from

its spectra, SIAM Journal of Applied Mathematics, Vol.

52(1), pp. 140-152, 1992.

5. Frieland S., Nocedal J. and Overton M.L., The

formulation and analysis of numerical methods for

inverse eigenvalue problems, SIAM Journal of

Numerical Analysis, Vol. 244, pp. 634-667, 1987.

6. Ram Y.M. and Elhay S., Constructing the shape of a

rod from eigenvalues, Communications in Numerical

methods in Engineering, Vol. 14, pp. 597-608, 1998.

7. Gladwell G.M.L., Inverse problems in vibration,

Applied Mechanics Review, Vol. 39, pp. 1013-1018, 1986.

8. Gladwell G.M.L., Inverse Problem in vibration, Martin

Nijhoff publishers, First Edition, 1986.9. Singh K.V. and Ram Y.M., The Transcendental

Eigenvalue Problem and Its Applications, Accepted for

publication in AIAA Journal, 2002.

10. Singh K.V. and Ram Y.M., Dynamic Absorption by

Passive and Active Control, ASME Journal of vibration

and acoustics, Vol. 122(4), pp. 429-433, 2000.

1

1

n

n

q

p

1

1

q

p

2

2

q

p

3

3

q

p

L

L

n

n

q

p

L

L

L

L

1x2

x3

x

1nx

nxnu

1nu

2nu

3u

1u2u

h h

L

1

1

n

n

q

p

1

1

q

p

2

2

q

p

3

3

q

p

L

L

n

n

q

p

L

L

L

L

1x2

x3

x

1nx

nxnu

1nu

2nu

3u

1u2u

h h

L

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

n=4 n=8

Original shape Estimated

0 0.2 0.4 0.6 0.8 10 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 10 0.2 0.4 0.6 0.8 1

n=4 n=8

Original shape Estimated

L

222,, AE

111,, AE

a


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5


April 13, 2002

EFFECT OF WALL THICKNESS OF CENOSPHERES ON THE COMPRESSIVE

PROPERTIES OF SYNTACTIC FOAMS

Nikhil Gupta

Ph.D. Candidate

Faculty Advisor: Dr. Eyassu Woldesenbet

ABSTRACT

Cenospheres are incorporated in polymeric materials to

obtain composites of low density and high compressive

strength, known as syntactic foams. Some studies on themodeling and experimental behavior of such composites are

available in the literature [1-14]. However, no comprehensive

studies could be found which characterize the behavior of

syntactic foams with respect to various parameters like

cenosphere wall thickness (density) and size distribution.

This experimental work investigates the effect of wall

thickness of cenospheres on the compressive properties of

syntactic foams. As the matrix material D.E.R. 331, a di-epoxy

resin, manufactured by DOW Chemical Company was

selected. This resin is called diglycidyl ether of bisphenol A

(DGEBA). To lower the viscosity of the resin a diluent is

added to it. It is difficult to mix large volume of cenospheres

in the epoxy resin if the viscosity is very high. Adding 5% ofdiluent, C12-C14 aliphatic glycidyl ether, brings down the

viscosity of the resin from about 9000 cps at 20C to about

2000 cps at the same temperature. Average equivalent

epoxide weight (EEW) of the diluent is 285. For a 95 wt%

resin and 5 wt% diluent mixture the EEW is 177.5.

Triethylene tetramine (TETA), C6H18N4, is used as curing

agent. This chemical is commercially known as D.E.H. 24 and

manufactured by DOW Chemical Company. Molecular

weight of this hardener is 146.4 and weight per active

hydrogen is 24.4. Phr (parts per hundred parts of resin) of

amine hardener for 95-5 resin-diluent mix was calculated to

be 13.74. Stainless steel molds having inner dimensions of

990.5 in3 are used to cast the syntactic foams. Fourdifferent types of cenospheres were used for the fabrication

of syntactic foam specimens. These microballoons were

manufactured and supplied by 3M. Specimen size used for

the test was 12.712.725.4 mm3. Compression test wasconducted at constant crosshead movement rate of 0.5

mm/min. Minimums of five specimens of each type of

syntactic foam were tested. Stress-strain cures for each type

of specimens are presented here [Figs. 2-5]. Trends of peak

stress [Fig. 6] and modulus [Fig. 7] of the specimens with

respect to cenosphere density are also presented.

FIGURES AND TABLESTable 1. Particle size distribution of microballoons.

Ceno-

sphere

type

Average

Particle Size

(m)

Top Size

(m)Cenosphere

density

(g/cc)

Syntactic

foam density

(kg/m3)

S22 35 75 205 493

S32 40 80 320 545

K37 40 85 380 575

K46 40 80 460 650

Fig.1. Compressive fracture behavior of syntactic foam.

S22, ASTM D695

0

5

10

15

20

25

30

35

0 0.05 0.1 0.15Strain (mm/mm)

Stress(N

)

Fig. 2. Compression test results of S22 syntactic foam.


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6

S 3 2 , A S T M D 6 9 5

0

10

20

30

40

50

0 0.05 0.1 0.15

Strain (mm/mm)

S

tress(N)

Fig. 3. Compression test results of S32 syntactic foam.

K 37, ASTM D695

0

10

20

30

40

50

60

0 0.02 0.04 0.06 0.08 0.1Strain (mm/mm)

Stress(MPa)

Fig. 4. Compression test results of K37 syntactic foam.

K 46 , ASTM D695

0

20

40

60

80

0 0.02 0.04 0.06 0.08Strain (mm/mm)

Stre

ss(N)

Fig. 5. Compression test results of K46 syntactic foam.

Change in Peak Compressive Strength

6000

7000

8000

9000

10000

11000

12000

200 300 400 500

Cenosphere Density (kg/m 3)

Peak

Stress

(M

Pa)

Fig. 6. Dependence of Peak strength of syntactic foam on

cenosphere density.

Cenosphere Density Dependence of

Modulus

1000

1200

1400

1600

1800

2000

2200

200 250 300 350 400 450 500Density of Cenospheres (Kg/mm3)

Modulus(MPa)

Fig. 7. Dependence of Modulus of syntactic foam on

cenosphere density.

REFERENCES

1. Gupta, N., Kishore, Woldesenbet, E., Sankaran, S.; J.

Mater. Sci., 36, 18 (2001) 4485-4491.

2. Gupta, N., Brar, B. S., Woldesenbet, E.; Bull. Mater Sci.,24, 2 (2001) 219-223.

3. Gupta, N., Kishore, Sankaran, S.; J. Reinf. Plast. Compo.

18, 14 (1999) 1347-1357.

4. Gupta, N., Karthikeyan, C. S., Sankaran, S., Kishore;

Mater. Charact., 43, 4 (1999) 271-277.

5. Gupta, N., Woldesenbet, E., Kishore, Sankaran, S.; J.

Sand. Str. and Mater., accepted, in press.

6. Gupta, N., Woldesenbet, E., Kishore; J. Mater. Sci.,

accepted, in press.

7. Gupta, N., Woldesenbet, E.; in proceedings of ETCE-

2002, Feb 2002, Houston, TX.

8. Gupta, N., Woldesenbet, E.; (accepted) in proceedings of

10th US-Japan Conference on Composite Materials,

September 16-18, 2002, Stanford University, CA.

9. Gupta, N., Woldesenbet, E.; in proceedings of ASC 16th

Annual Conference, Blacksburg, VA, Sept. 9-12, 2001.

10. Gupta, N., Woldesenbet, E.; in proceedings of ETCE-

2001, Feb 2001, Houston, TX.

11. Rizzi, E., E. Papa and A. Corigliano, Intl. J. Solids and

Struct. 37 (2000) 5773.

12. Corigliano, A., E. Rizzi and E. Papa, Compo. Sci. Tech. 60

(2000) 2169.

13. Ishai, O., C. Hiel and M. Luft, Composites 26, 1 (1995) 47.

14. Malloy, R. A., J. A. Hudson, in Intl. Encylop. of Compos.,

Ed. S. M. Lee (VCH, 1990).


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7


April 13, 2002

EFFECT OF TIP GEOMETRY ON BLADE TIP FLOW AND HEAT TRANSFER

David Kontrovitz

M.S. Candidate

Faculty Advisor: Dr. Srinath Ekkad

ABSTRACT

In an attempt to increase thrust to weight ratio and

efficiency of modern gas turbines, engine designers are

always interested in increasing turbine operating

temperatures. The benefits are attributed to the fact that

higher temperature gases yield a higher energy potential.

However, the detrimental effects on the components along

the hot gas path can offset the benefits of increasing the

operating temperature. The HPT first stage blade is one

component that is extremely vulnerable to the hot gas.

The cause for tip failures are fairly well understood and

can be explained as follows. A clearance gap between the

rotating blade tip and stationary shroud is necessary to

allow for the blades mechanical and thermal growth during

operation. Unfortunately, the gap allows for leakage flow

from the pressure side to the suction side. The gas is

accelerated as it passes through the small gap. This leads to

enhanced heat load to the blade tip region. Leakage flow, orclearance flow, also leads to undesirable aerodynamic losses

not unlike the losses associated with airplane wing tips. In

fact, one third of the losses through the turbine section can

be attributed to leakage flow. Other relevant studies by Azad

et al. [1-2], Bunker et al. [3], Bunker and Bailey [4-5]

presented detailed heat transfer results on high-pressure

turbine blade tips with different pressure ratios. The effect of

tip geometry was also considered in some of these studies.

The present study explores the effects of gap height

and squealer depth on heat transfer and flow distribution.

This investigation differs from those in the other studies

because the tip profile is for an in-service High Pressure

Turbine of an aircraft engine. Other experiments have usedthe E

3test blade or a power generation blade that have

different characteristics. The pressure ratio used was 1.2,

which is lower than the actual pressure ratio this blade sees

in service (PR = 1.7). A transient liquid crystal technique

was used to obtain the tip heat transfer distributions.

Pressure measurements were made on the blade surface and

on the shroud for different tip geometries and tip gaps.

FIGURES AND TABLES

Figure 1. Leakage Flow

Figure 1 shows the typical leakage flow behavior for a

turbine blade [1]. The plain tip is a flat tip and flow leaksthrough a constant area across the blade. The squealer tip

has a groove cut on top of the blade which increases the

area and stalls the flow thus creating back pressure and

restricts leakage flow and reduces heat transfer. In this

study, we focus on the plain tip and two different squealer

depths (shallow and deep).


8/38

8

Figure 2: Blade Pressure Distribution

Figure 2 shows the pressure distribution on the bladesurface at different span of the blade. The 100% span is on

the tip of the blade with clearance gap. The pressure

distribution changes as the blade span moves towards the

gap as expected. Figure 3 shows the pressure distributions

on the shroud for a blade with squealer tip. The reduced

static pressures are the cause of reduced leakage flows.

Figure 3: Shroud Measurements

Figure 4 presents a typical heat transfer distribution on

the blade tip with a shallow squealer. The heat transfer

distributions show the local hot spots near the leading edge

on the floor of the cavity and the reduced heat transfer

towards the trailing edge of the blade. The leakage flow is

stronger at the leading edge and weaker along the trailing

edge of the blade.

Figure 4: Heat Transfer Distribution

ACKNOWLEDGMENTS

This study was sponsored by the NSF through a

GOALI grant. The author would like to acknowledge Drs.Srinath Ekkad and Sumanta Acharya for their instruction and

advice. Also, thanks to Dr. Ron Bunker, at G.E. Corporate

Research and Development, for his input to this project.

Acknowledgments are also due to my colleagues in the

Turbine Blade Research Lab.

REFERENCES

1. G.S. Azad, J.C. Han, R.S. Bunker, C.P. Lee, Effect of

Squealer Geometry Arrangement on Gas Turbine Tip

Heat Transfer, in Proceedings of the ASME International

Mechanical Engineering Congress and Exposition, New

York, November 2001, HTD-243142. G.S. Azad, J.C. Han, R.J. Boyle,Heat Transfer and Flow on

the Squealer Tip of a Gas Turbine Blade, in Proceedings

of the 2000 ASME Turboexpo, Munich, Germany, May

2000, 2000-GT-1955

3. R.S. Bunker, J.C. Bailey, A.A. Ameri, Heat Transfer and

Flow on the First Stage Blade Tip of a Power

Generation Gas Turbine Part1: Experimental Results, in

Proceedings of the 1999 ASME International Gas Turbine

Conference, Indianapolis, 1999, ASME 99-GT-169.

4. R.S. Bunker, J.C. Bailey, Effect of Squealer Cavity Depth

and Oxidation on Turbine Blade Tip Heat Transfer, in

Proceedings of the 2001 ASME International Gas Turbine

Conference, New Orleans, June 2001.

5. R.S. Bunker, J.C. Bailey, An Experimental Study of

Heat Transfer and Flow on a Gas Turbine Blade Tip

With Various Tip Leakage Sealing Methods, in

Proceedings of the 4th ISHMT / ASME Heat and Mass

Transfer Conference, Pune, India, 2000, HNT-2000-055 p.

411-416.


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9


April 13, 2002

LARGE EDDY SIMULATIONS OF ROTATING SQUARE DUCT WITH NORMAL RIB

TURBULATORS

Mayank Tyagi

Ph.D. Candidate

Faculty Advisor: Dr. Sumanta Acharya

ABSTRACT

The goal of the present work is to develop a generalized

Large Eddy Simulations (LES) methodology for complex

geometries, and to apply this methodology to gas turbineblade cooling applications. Results from one such

application, that of internal cooling in a turbine blade, are

reported in this abstract.

The internal cooling configuration selected in this study

corresponds to the experimental study of Wagner et al.

(1992). The computations were performed at a Reynolds

number (Re) of 12,500, rotation number (Ro) of 0.12 and the

inlet coolant-to-wall density ratio (/) of 0.13. The ribheight-to-hydraulic diameter ratio (e/D) is 0.1 and the rib

pitch-to-height ratio (P/e) is 10. The ribs are square in cross-

section and are placed transverse to the flow in the duct. Of

specific interest in this study are the dynamics of the

coherent structures, and how they influence the heattransfer.

RibA

RibB

Trailin

g Wall

Leadi

ngWa

ll

BackWall

Front Wall

Inflow

Rotation

Lz

Ly

Lx

RibHeight: eRibX-section : SquareL

x= L

y= L

z= L

e/L= 0.1,Rmean

= 49.5P/L= 1.0Re

m=12500

Ro= 0.12

P/2

P /4

/= 0.13

Figure 1: Schematic of the computational domain

A novel direct method for computing the source term in

the energy equation (which arises due to unsteadiness and

uniform wall temperature in periodic geometries) is

presented. This is in contrast to the iterative approach of

Wang and Vanka, 1995, which has been used to date.

The details of flow field and the temperature fieldobtained from the LES are presented and analyzed in this

study. The LES procedure is based on a dynamic mixed

model for subgrid stresses and scalar flux.

RESULTSRib A

Rib B

Rib A

Rib B

Time-averaged VelocityVectors at Y/D= 0.5

Figure 2: Details of time-averaged vectors near the ribs

Figure 2 shows the time-averaged flow field at the spanwise

center-plane, and reveals the recirculating eddies generated

in the vicinity of the ribs. The coherent structures (Figure 3)are educed from the instantaneous flow field using the

positive levels of Laplacian of pressure field. Near the

trailing wall, the Coriolis -induced secondary flow lead to a

breakup of the flow structures along the spanwise center

plane. The roller vortices formed on the rib are connected

with the streamwise or braid vortices originating either at the

side walls or around the centerplane, thus forming a hairpin

coherent structure. The unsteady dynamics show several


10/38

10

packets of such hairpin vortices between the ribs at trailing

wall. The vortices near the leading wall are weaker than the

vortices near trailing wall. Moreover, the roller vortices

generated at the ribs are stretched and tilted into the core of

duct by the secondary flow. Hairpin packets on these ribbed

walls evolve in different fashions.

X

ZY

Leading wall

Trailing wall

X

Y

Z

Leading wall

Trailing wall

Figure 3: Coherent structures in a rotating ribbed duct

The proper orthogonal decomposition (POD) of the flow-

field using the method of snapshots is performed (Sirovich,

1987). About 99% of the turbulent energy is captured in the

first 75 POD modes (Figure 4). Clearly, the chaotic dynamics

of these coherent structures can be modeled by a low-

dimensional system.

POD mode number

EnergycontainedinthePODmod

e

50 100 150 200

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Figure 4: Distribution of energy in POD modes based on

200 snapshots.

Heat transfer calculations show the unsteady hot streaks on

the duct walls. The distribution of the time-averaged Nusselt

number is in agreement with the experimental observations.

It is illustrated that scalar mixing is related to the scalar

dissipation of the temperature.

ACKNOWLEDGMENTS

Discussion with Dr. A.K. Saha on the preliminary resultsis gratefully acknowledged.

REFERENCES1. Sirovich, L. (1987) Turbulence and the dynamics of

coherent s tructures, Part I-III, Quarterly of Appl. Math.,

XLV(3), pp. 561-82.

2. Tyagi, M., Saha, A.K. and Acharya, S. (2001) Large eddy

simulations of rotating square duct with normal rib

turbulators, DNS/LES: Progress and Challenges, 3rd

AFOSR Intl. Conference, Eds. C. Liu, L. Sakell and T.

Beutner, pp. 807-814.

3. Wagner, J.H., Johnson, B.V., Graziani, R.A. and Yeh, F.C.

(1992) Heat transfer in rotating serpentine passages

with trips normal to the flow, J. Turbomachinery, Vol.

114, pp. 847-857.

4. Wang, G. and Vanka, S.P. (1995) Convective heat transfer

in periodic wavy passages, Int. J. Heat Mass Transfer,

Vol. 38, pp. 3219-3230.


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1


April 13, 2002

NODAL CONTROL OF A VIBRATING BEAM

Akshay N Singh

Ph.D. Candidate

Faculty Advisors: Dr. Y. M. Ram and Dr. Su-Seng Pang

ABSTRACT

Vibration control is an important engineering problem

and many methods for both active and passive vibration

absorption have been developed. This paper deals with

developing a method to achieve nodal control at the point of

excitation in a Bernoulli-Euler beam. Singh and Ram in [3]

have shown that under certain conditions that have been

characterized in [3] the steady state motion of a certain

degree of freedom in a harmonically excited conservative

system may be absorbed by both passive and active means.

Ram in [1] has developed a method to eliminate the steady

state motion of a prescribed location in a continuous system

like rod under the influence of a harmonic excitation. He has

presented a closed form solution for the control gain in

terms of infinite product of eigenvalues. This thesis extends

the approach in [1] to achieve nodal control for suppressing

vibration at prescribed location in beams and provides a

simpler formula for the control gain in terms ofeigenfunctions. It is established that, for a uniform

Bernoulli-Euler beam, the steady state motion at the point of

excitation can be absorbed by means of a control force

determined from displacement information at the point of

application. A closed form solution for the control gain is

presented and a criterion for implementing the control by

active and passive means is developed. The result for the

control gain is generalized for the case of a non-uniform

beam. It is also shown through some examples that the

theory can be also applied to eliminate the steady state

motion at any desired location other than the point of

excitation. Analysis is also performed to determine the

optimal control force and investigate the stability of theoverall system. Several controllability graphs are shown and

meaningful conclusions are drawn from these graphs. An

experiment is designed to validate the proposed theory and

display its practicality.

The developed theory will provide a strong foundation

for realizing realistic and convenient methodologies in

control applications in cases like surgical procedures,

drilling and turning operations etc. However, one of the

many direct applications of this method is structural

vibration control in an aircraft wing. Several measurements

such as vibrational response, air temperature, wind velocity

etc are required in order to monitor flight conditions in an

aircraft. These data also assist the pilot in flying the aircraft.

Sensors and data collection circuitry form an entire network

of the electrical wiring all in and around the airplane body.

Data acquisition devices are also located on the wing of the

airplane. Shielding of these devices from undesirable

vibration of the wing is critical in order to avoid noise in the

gathered data and prevent physical damage. Exclusion of

steady state vibration at the locations of these devices

provides the motivation for this investigation.

Consider a uniform Bernoulli-Euler beam of length L .

Suppose that the beam is excited by a harmonic force

( ) ttf cos= , as shown in Figure 1(a). The steady statemotion of a prescribed point of the beam may be vanished

by applying a concentrated control force ),( tau at ax= asshown in Figure 1(b).

( ) ( )tawtau ,, = , (1)

where is the control gain. The partial differential equation

for the controlled Bernoulli-Euler beam shown in Figure 1(b),

for Lx


12/38

2

( )0

,2

2

=

x

tLw, no moment, (5)

( )t

x

tLwEI

xcos

,2

2

=

shear force. (6)

The work here focuses on determining a closed form

solution for the control gain that absorbs the motion of

the beam at Lx = .

A closed form expression for the control gain

obtained from mathematical manipulation is expressed as

( )( ) ( )

( )

=

av

avavEIa

1

12, , (7)

where 1v and 2v are the deflections of the beams with spanax


13/38

13


April 13, 2002

ON THERMALLY INDUCED SEIZURES (TIS) IN JOURNAL BEARINGS

Rajesh Krithivasan

M.S. Candidate

Faculty Advisor : Dr. Michael M Khonsari

ABSTRACT

Thermally induced seizure (TIS) in journal bearings is a

mode of failure that can occur quite suddenly and end up

with a catastrophic damage to the system. A failure, as such,

can occur quite suddenly and often the damage to the

system is catastrophic. Although it can take place in

lubricated bearings, thermally induced seizure is

predominant when a hydrodynamic bearing happens to

operate in the boundary or mixed lubrication regimes. These

conditions occur during start-up or in an event of lubricant

supply blockage. The objective of this work is to perform acomprehensive study of seizure in bearings during start-up

and arrive at a seizure time evaluation formula that is a

function of the various operating parameters. Dufrane and

Kannel1

analyzed the catastrophic seizure of bearings due to

dry friction by a simple 1D equation relating the seizure time

to the bearing operating parameters and material properties.

Hazlett and Khonsari2

performed a detailed finite element

analysis to gain insight into the nature of the contact forcesand encroachment of the mating pair leading to TIS of a dry

bearing during start up.

The finite element modeling is done using ANSYS 5.73.

First, the TIS analysis of Hazlett and Khonsari2

was

recreated. The finite element model of the present work

employs a finer mesh than the mesh used by Hazlett and

Khonsari to evaluate the contact forces with more accuracy.

The analysis of a bearing undergoing TIS during start up

was done by the following steps: 1. A 2-D static contact

analysis was performed to determine the contact forces and

the contact angle. 2. A transient heat transfer analysis was

done to model thermal effects of dry frictional heating on the

journal and the bearing. 3. A transient thermoelastic analysis

was performed to study the interactions of the journal-

bearing pair during bearing start -up. The variation of radial

clearance, contact forces and ovalization of the bearing were

studied in this analysis.

The loading applied in the thermal analysis consists of

the heat generated by the frictional contact at the shaft-

bushing interface, which is a function of the load, speed and

coefficient of friction. The heat generated is applied to the

journal and the bushing according to the areas of contact on

the shaft and the bushing2

and cooled convectively at the

areas not in contact. The external surface is also cooled by

free convection as shown in Fig 2. The loading for the non-

linear thermoelastic analysis consists of the thermal loads

applied as nodal temperatures and the radial force acting on

the journal. The time dependent thermal load is obtained

from the results of the transient thermal analysis. The static

load, W is applied to act in the negative y-direction on the

shaft. As the model utilizes half-symmetry, a load of W/2 is

applied. Symmetry boundary conditions are used to model

the one-half symmetry as shown in Figure 3. The constraint

of the bearing on its outer surface is modeled by fixing the

bearing at the node under the shaft on the outer edge of the

bearing on the symmetry plane. This constraint

approximates the boundary condition on the bottom surface

of a pillow block type of bearing as shown in Figures 1 and

3.

Due to the rise in temperature, the encroachment of theshaft on to the bushing with concomitant reduction in the

clearance continues until TIS occurs due to the increase in

frictional torque. This process is a complex, non-linear

phenomenon. Analysis shows that TIS is initiated by the

ovalization of the bearing combined with the uniform

outward expansion of the shaft yielding contact between the

top of the shaft and the inner bushing surface. This leads to

an increase in the contact forces and the formation of

multiple contact areas. Increase of contact forces raises the

frictional heat flux and sets up a positive feedback that

accelerates the loss of clearance. Analyses show that the

increase in the frictional torque is abrupt once the

ovalization of the bearing causes the shaft to encroach thebushing, as there is further loss in the operating clearance.

Seizure Criterion - Frictional torque is the torque

resisting the driving torque exerted by the motor. When the

frictional torque increases beyond the extent of the driving

torque capability, it can be concluded TIS is imminent. The

contact forces acting on the gap elements at any instant of

time determine the frictional torque at any time. The frictional

torque increased to exceedingly large values within typically


14/38

14

3 seconds after the first instance of establishment of new

areas of contact immediately after ovalization. See Figure 4.

The seizure time can be written as a function of the

speed, load, shaft radius, clearance, friction coefficient and

the bearing length. i.e.

ts = g (N, W, Rs, C, f, L).

The variation of the seizure time during the system start-upis studied when the operating parameters (variablesN, W, Rs,

C, f, L) are varied. Then a generalized equation is derived

depending on the individual relationships of the operating

parameters with the seizure time. Using the range of data

from 72 sets of simulations and applying a statistical

analysis4, we obtain the following expression for the seizure

time.

( ) ( )74.8172.126.15.14.628607 107.51105.1 +=s

LC

sRWfNeet

The empirical relationship is verified for its validity using

some of the results published by Hazlett and Khonsari2

and

Wang et.al.5. See comparitive results shown in Table 1.

FIGURES AND TABLES

REFERENCES

1. Dufrane K. and Kannel J. Thermally induced seizures of

journal bearings.ASME Journal of Tribology, 1989, 111,

288-92

2. Hazlett T.L. and Khonsari M.M. Finite element model of

journal bearing undergoing rapid thermally induced

seizure. Tribology International, 1992a, 25, No.3, 177-82

3. ANSYS 5.7 Online Users Manual, 2001,ANSYS Inc .

4. Hamrock B.J. Elastohydrodynamic lubrication of point

contacts. Ph.D Thesis, Institute of Tribology,

Department of Mechanical Engineering, The

University of Leeds, 1976, 44-66, pp. 93-102

5. Wang H., Conry C. and T.F., Cusano, Effects of

Cone/Axle Rubbing Due to Roller Bearing Seizure on

the Thermomechanical Behavior of a Railroad Axle.

ASME Journal of Tribology , 1996, Vol.118, pp.311-319


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15


April 13, 2002

AN EIGENVALUE CONFORMING MODEL FOR A VIBRATIING ROD

Jaeho ShimPh.D. Candidate

Faculty Advisor: Dr. Y. M. Ram

ABSTRACT

The natural frequencies determined by using finite

element or finite difference models of order n are fairly

accurate only about 3n of lower eigenvalues of the

underlying continuous system. The natural frequencies of a

uniform rod with 60=n and exact solution are demonstratedin Figure 1. The new model to improve this existing problemhas been developed. The model named as a spectral

conforming discrete model can estimate the n lowest

eigenvalues of the continuous system with uniform

accuracy. The essential ingredient in building of such a

model is the inverse eigenvalue problem of reconstructing a

chain of mass-spring system with prescribed spectral data

[1].

Consider a non-uniform axially vibrating rod of length

L , axial rigidity ( )xp , and mass per unit length ( )x ,

which is fixed at 0=x and free to oscillate at Lx = , asshown in Figure 2. The axial motion

( )txu ,of the rod at the

time t is governed by the differential equation (1) and two

boundary conditions (2).

( ) ( )2

2

t

ux

x

uxp

x =

(1)

( ) 0,0 =tu , ( ) 0, =

x

tLu , (2)

This non-uniform rod shown in Figure 3 may be

approximated as a piecewise continuous rod with runiform

parameters ip and i within the i th element. In order todetermine a higher order spectral conforming element model,

a uniform rod element of length L, axial rigidityp, and mass

per unit length in Figure 4 is considered. A matrix A

which is reconstructed from spectral data is defined as

2

1

2

1

= KMA . (3)

The matrix A is symmetric tridiagonal with positive diagonal

elementl

and negative off diagonalj

.

=

rr

rrr

1

112

211

11

OOOA (4)

From the matrixA , the stiffness matrix K and the mass

matrix M can be determined using the Lanczos method [2].

The essential novelty in the spectral conforming model

introduced here is that the dynamic response of the

continuous system is fitted to the spectrum of the discrete

estimating model.

As an example, an exponential rod of length L ,

constant Youngs modulus of elasticityE

, constant density

, and variable cross sectional areaxeA = , is presented.

The rod is fixed at 0=x and free to oscillate at Lx = , asshown in the figure 5. The eigenvalues of this system have

been approximated by using finite differences and spectral

conforming model. The finite difference model implemented

60=n elements of equal length. The spectral conformingmodel used 4=n elements of equal length, each of order

15=r . Hence, the global matrices in the three approximatingmethods used are of the same dimension 6060 . Thevarious results obtained are shown in Figure 6. As expected

the spectral conforming model yields superior overall

estimation with uniform accuracy for all eigenvalues

predicted.

Future research in this topic involves extending the

method to include tapered elements that can better capture

the geometry of a non-uniform rod. Broadening the method

over two and three-dimensional elements appears to be a

challenging problem.


16/38

16

FIGURES AND TABLES

Figure 1. Predicted natural frequencies using Finite

Difference Model, Finite Element Model and Exact Solution

for 60-digree-of-freedom model.

Figure 2. Non-uniform axially vibrating rod.

Figure 3. An r-degree-of-freedom element

Figure 4. An rth order spectral conforming element model

Figure 5. Exponential rod

Figure 6. Predicted natural frequencies using Finite

Difference Model, Spectral Conforming Model and Exact

Solution.

ACKNOWLEDGMENTS

The research work presented here is supported by a

National Science Foundation research grant CMS-9978786.

REFERENCES

1. D. Boley and G.H. Golub, A survey of matrix inverse

eigenvalue problem, Inverse Problems, Vol. 3, pp. 595-

622, 1987.

2. C. de Boor and G.H. Golub, The numerically stable

reconstruction of a Jacobi matrix from spectral data,

Linear Algebra and Its Application, Vol. 21, pp. 245-

260, 1978.

3. F.P. Gantmakher and M.G. Krein, Oscillation Matrices

and Kernels and Small Vibration of Mechanical Systems,

State Publishing House for Technical-TheoreticalLiterature, Moscow-Leningrad, 1961 (Translation: US

Atomic Energy Commission, Washington DC).

4. J. Paine, A numerical method for the inverse Sturm-

Liouville problem, SIAM J. Sci., Stat. Comput., Vol. 5, pp.

149-156, 1984.

5. J.W. Paine, F. de Hoog and R.S. Anderssen, On the

correction of finite difference eigenvalue approximations

for Sturm-Liouville problems, Computing, Vol. 26, pp.

123-139, 1981

0 10 20 30 40 50 600

50

100

150

200

250

k

k

Finite Difference Model

Finite Elements Model

Exact Solution

0 10 20 30 40 50 600

50

100

150

200

250

k

k



Exact Solution



Exact Solution

)(),( xpx

dx

),( txu

L

x

)(),( xpx

dx

),( txu

L

x 0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200

Exact Solution


Spectral Conforming Model

i

0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200

Exact Solution



Exact Solution



i

)(),(),( xxAxE

L

)(),(),( xxAxE

L

1k

2k

1m

2m3k

rk

rm

( )

( )

( )e

e

e

A

E

( )e

LD

( )eL

1k

2k

1m

2m3k

rk

rm

( )

( )

( )e

e

e

A

E

( )e

LDD

( )eL

1k

2k

1m

2m3k

rkrm

p, L

1k

2k

1m

2m3k

rkrm

p, L


17/38

1


April 13, 2002

BUCKLING ANALYSIS OF GRID STIFFENED COMPOSITE CYLINDERS

Samuel Kidane

M.S. Candidate

Faculty Advisor: Dr. Eyassu Woldesenbet

ABSTRACT

Due to their high stiffness to mass ratio, stiffened cylindrical

composite shells are major components of Aerospace and

Aircraft industries. These structures are employed in

fuselage and fuel tank applications, and are usually

subjected to combinations of compressive, shear or

transverse loads. Usually the failure mode associated with

these structures is buckling. This failure mode is further

subdivided into local skin and/or stiffener buckling, and

universal buckling.

In this paper buckling investigation of a grid stiffened

composite cylinder is presented using analytical model,

Finite elements model and experimentation. The cylinder

under discussion has orthotropic stiffeners integrally made

with an orthotropic shell. All the buckling analysis is based

on a uniaxial compressive load condition.

An analytical model is first developed that reduces the

grid/shell cylinder panel to an equivalent orthotropic

laminate (Fig. 1). This model makes use of the force and themoment interactions and derives the A, B and D matrix of the

equivalent laminate model. Consequently buckling loads are

calculated making use of the energy method. Using the

analytical model developed, parametric analysis is preformed

to determine optimum configuration of stiffeners and shell.

A Finite elements model is also built using ANSYS for

the same cylinder. Buckling analyses are performed on

different models built with different configurations of

stiffener and shell parameters. The effect of shell thickness

variation on buckling load and buckling mode is studied in

detail (Fig 2). Based on this the optimum skin thickness is

determined for a given stiffener configuration. In this section

correlation is made between failure mode and optimum skinthickness. In addition to skin thickness the effect of

stiffeners angle variation is also analyzed using ANSYS. The

result is plotted and conclusions are drawn on optimum

stiffener orientation.

Buckling experiment was also performed on a stiffened

composite cylinder specimen (Fig 3). The test setup and the

results obtained are discussed briefly.

Finally this paper tries to compare the different results

obtained using the three analysis methods. An attempt is

made to account for certain differences observed between

the three analysis methods. Conclusions are drawn on the

reliability of the analytical model developed and remarks

made on limitation of model.

FIGURES AND TABLES

l

x

t

Fig. 1 Unit cell.

Fig. 2 FEM analysis (local skin buckling)


18/38

18

-35

-30

-25

-20

-15

-10

-5

0T ime (s )

Load

Strain Gauge1

Strain Gauge2

h/2

1

2

Fig. 3 Experimental results.

ACKNOWLEDGMENTS

Support for this research was provided by a grant from

the NASA/Louisiana Space Consortium and the Louisiana

Board of Regents under LaSPACE (BOR12662) and LEQSF(2001-04)-RD-B-03.

REFERENCES

1. Helms JE, Li G, Smith BH. Analysis of Grid Stiffened

Cylinders. ASME/ETCE 2001.

2. Brush DO, Almroth BO. Buckling of Bars, Plates, and

Shells. McGraw-Hill Book Company, New York, NY

1975.

3. Bruhn EF. Analysis and Design of Flight Vehicle

Structures. Jacobs Publishing, Inc., Carmel, IN June

1973

4. Navin J, Norman FK, Damodar R. Formulation of AnImproved Smeared Stiffener Theory of Buckling

Analysis of Grid-Stiffened Composite Panels. NASA

technical Memorandum 110162, June 1995.

5. Ramm E. Buckling of Shells. Springer-Verlag, Berlin

1982.

6. Gerdon G, Gurdal Z. Optimal Desing of Geodesically

Stiffened Composite Cylindrical Shells. AIAA Journal,

November 1985; 23(11):1753-1761.

7. Troisky MS. Stiffened Plates, Bending, Stability and

Vibrations. Elsevier, 1976.

8. Phillips JL, Gurdal Z. Structural Analysis and Optimum

Design of Geodesically Stiffened Composite Panels.

Report NASA CCMS-90-50, (VPI-E-90-08), Grant NAG-1-643, July 1990.

9. Whitney JM. Structural Analysis of Laminated

Anisotropic Plates. Technomic, 1987.

10. Agarwal BD, Broutman LJ. Analysis and Performance of

Fiber Composites. John Wiley and Sons, 1990.

11. Dow NF, Libove C, Hubka RE. Formulas for Elastic

Constants of Plates with Integral Waffle-like Stiffening.

NACA RM L53L1 3a, August 1953.


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19


April 13, 2002

SYNTHESIS, PROPERTIES AND CHARACTERIZATION OF CR-DLC

NANOCOMPOSITE FILMS

Varshni Singh

Ph.D. Candidate

Faculty Advior: Dr E.I. Meletis

ABSTRACT

Diamondlike carbon (DLC) films have been extensively

studied over the past decade, due to their unique

combination of properties. One of the drawbacks with DLC

films is that they are thermally unstable beyond 350o

C [1].Above 400

oC the changes are more profound and

graphitization of the film occurs by conversion of C bonds

from sp3

to sp2, a phenomenon that is also observed during

wear at hot spots [2]. Thus for more than a decade

researchers have focused on metal-containing DLC (Me-

DLC) films in an effort to improve wear resistance, adhesion,

thermal stability and toughness. A number of studies on

synthesis and characterization of Me-DLC films have been

conducted on Si-, Ti-, Ta-, W- and Nb-DLC [3-10]. Even

though Cr is a carbide former and possesses an attractive

combination of other properties (corrosion resistance, wear

resistance, etc.) little work has been reported in this area

[6,11]. The purpose of the present work was to initiate asystematic study of the processing-structure-property

relationship in Cr-DLC films as a function of Cr content. The

objective is to develop a better understanding of this system

and identify possible compositional ranges where

tribological performance and thermal stability are

significantly improved.

Cr-DLC nanocomposite films were deposited on Si

(100) substrate, by reactive magnetron sputtering utilizing an

intensified plasma-assisted processing system. The

processing parameters (chamber pressure, bias voltage,

magnetron current, etc.) were varied to synthesize Cr-DLC

films, with Cr content ranging from ~0.1 at. % to 28 at. %.

Carbon and chromium content was determined by

wavelength dispersive spectroscopy (WDS) utilizing a JEOL

JXA 733 super electron probe microscope. X-ray diffraction

(XRD) experiments were performed, using a Rigaku Miniflex

2 diffractometer with a Cu - K source and transmissionelectron microscopy (TEM) was conducted in a JEOL JEM

2010 electron microscope. Pin-on-disc experiments were

conducted by utilizing an ISC-200 tribometer and the wear

rate was calculated by a Veeco 3D optical profilometer.

Mechanical properties, of the films were studied by

nanoindentation measurements, using a Hysitron

Triboscope instrumented nanoindentation/ nanoscratchdevice incorporated on a Digital Instrument Dimension 3100

atomic force microscope. The short-range order structure ofthe films is being studied by the x-ray absorption fine

structure (XAFS) spectra collected by using bending

magnet radiation at the double crystal monochromator 1

beamline. The thermal stability experiments were conducted

by utilizing a DSC-7 differential scanning calorimeter.

XRD patterns of DLC and Cr-DLC films, show that all

the films exhibited nearly the same XRD pattern, indicating

an amorphous structure. Electron diffraction and high-

resolution TEM studies show that the films, with ~ 9 at. %

Cr, deposited using low (-200 V) and high (-1000 V) specimen

bias during processing are composed of nanocrystalline

metallic Cr and nanocrystalline cubic chromium carbide,

respectively surrounded by an amorphous matrix. Fig. 1show the dark contrast clusters, diameter 1 5 nm,

surrounded by an amorphous matrix corresponding to

nanocrystalline Cr carbide. The XANES spectra of the Cr-

DLC films show that the Cr content (5 to 28 at. %) in the Cr-

DLC films, deposited at 1000 V bias, has little effect on its

structure and Cr atoms are incorporated in the carbon

network. This initial result is in agreement with that of the

TEM results. Furthermore, such preference for metal atoms

to be incorporated into the local carbon structure has also

been shown by our recent XAFS experiments on Si-DLC

films with ~10 at. % Si [12].

Fig. 2 presents the variation of the coefficient of

friction () and wear rate of Cr-DLC films (deposited at 1000V) with Cr content. The results in Figs. 2 show that in

general all Cr-DLC films exhibit a low (less than 0.2) forboth alumina and 440 stainless steel pins. It is interesting to

note that remains at low levels (less than 0.15) for up to aCr/C ratio of 0.24. At a higher Cr level, the results indicate

that the coefficient of friction increases. Very similar

behavior has been observed previously for W-DLC films [5].

The wear rate was also found to be relatively independent of


20/38

20

pin material. The wear rate was low and remained at almost

the same levels in films with a Cr/C ratio less than 0.24. At

higher Cr content (Cr/C equal to 0.35), the wear rate

increased significantly (by at least an order of magnitude),

which is consistent with the relatively higher observed forthat film. The present results are in general agreement with

the previous reports however, doesnt show high wear ratesat very low Cr content.

The DSC result qualitatively suggests that the thermal

stability of the Cr-DLC films increases with increasing Cr

content, due to stabilizing effect of Cr on the DLC matrix

network, up to the point where the DLC network is

completely stabilized. Nanoindentation results suggest that

the hardness of the films reduces with increasing Cr content

to ~3 atomic % and then it stabilizes around 13 GPa. With the

exception of an initial deep, reduced modulus (E/(1- ?2))

increases with increasing Cr content and stabilizes around

118 GPa at ~11 atomic % Cr. The H/E/(1- ?2) exhibits a peak

value of ~0.17 at 0.05 atomic % Cr and then gradually

decreases and stabilizes to values around 0.11. Compared toother Me-DLC films, the present profile of H/E/(1- ?

2) for Cr-

DLC exhibits this interesting region yet to be explored

between 0.05 at. % Cr and ~2.75 at. % Cr. Presently, the

reason for this peculiar behavior is unknown.

At present, the in-depth analysis of the spectra

obtained from Cr-DLC films is underway. Study of Cr-DLC

films deposited at lower substrate bias is planned for the

next period. In addition, a couple more compositions in the

aforementioned range between 0.05 at. % Cr and 2.75 at. %

Cr are planned to explore the lower range of the Cr content.

So as to completely understand the effect of Cr content and

the substrate bias on the short-range order around Cr in the

Cr-DLC films further analysis and experiments are underway.

ACKNOWLEDGMENTS

This work was supported by the Army Research Office

grant DAAG55-98-1-0279 and Louisiana Board of Regents.

TEM was performed at MCC facility of LSU with the help of

Dr J. Jiang. Nanoindentations were performed with the help

of Ms Tracy Morris and XAFS spectroscopy was done with

the help of Dr V. Palshin and Dr R. Tittsworth in CAMD,

LSU. WDS was performed using electron microscopy

facility of the Geology Department at LSU with the help of

Dr. Xie. Assistance of Mr. Pankaj Gupta in the deposition

experiments is also acknowledged.

REFERENCES

1. Z.L. Akkerman, H. Efstathiadis, and F.W. Smith,J. Appl.Phys., 80(5), 3068-3075 (1996).

2. Y.Liu and E.I. Meletis,J. Mater. Sci., 32, 3491(1997).

3. A. Varma, V. Palshin, K. Fountzoulas and E.I. Meletis,

Surface Engineering15(4), 301-306 (1999).

4. K. Oguri and T. Arai, J. Mater. Res., 7(6), 1313 (1992).

5. C.P. Klages and R. Memming,Materials Science Forum,

52-53, 609-644 (1989).

6. Y.L. Su and W.H. Kao, J. Mater. Eng. Perf., 9(1) (2000)

38-50.

7. M. Fryda, K. Taube and C-P Klages, Vacuum, 41(4-6)

(1990) 1291-1293.

8. H. Dimigen and C-P Klages, Surf. Coat. Technol., 49

(1991) 543-547.9. W.J. Meng and B.A. Gillispe,J. Appl. Phys. , 84(8) (1998)

4314-4321.

10. K. Bewilogua, C.V. Cooper, Surf. Coat. Technol., 132

(2000) 275-283.

11. X. Fan, E.C. Dickey, S.J. Pennycook and M.K. Sunkara,

Appl. Phys. Let., 75(18) (1999) 2740-2742.

12. V.A. Palshin, R.C. Tittsworth, K. Fountzoulas and E.I.

Meletis,Journal of Materials Science 37 , (2002).

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

1E-9

1E-8

1E-7

1E-6

wear rate

WearRa

te(mm

3/N-m)

Pin Material

440 Steel

Alumina

Cr/C (atomic ratio)

0.1

0.2

0.3

0.4

0.5Load 2.5 N

Pin dia 9.5 mmSliding speed 0.1m/s

Coeffice

intoffriction

Figure 1 HRTEM image of Cr-DLC films with Cr 9

at. % deposited at a bias of 1000V.

Figure 2 Coefficient of friction and wear rate of Cr-DLC

films of Cr/C ratio.


21/38

21


April 13, 2002

NUMERICAL SIMULATION OF FLOW AND HEAT TRANSFER IN MICRO HEAT

EXCHANGERS

Readul Islam

M.S. Candidate


ABSTRACT

Pin fin arrays have been used for turbine blade cooling

applications in the trailing edge where they can fulfill a

structural as well as a heat transfer function. A recently

proposed concept involves covering the outer surface of

turbine blades with an array of very short pin fins andadding a coating on top that is exposed to external gases [1].

The coating completely enshrouds the turbine blade, leaving

a micrometer-sized gap bridged by the pin fin array, and

preventing contamination of the coolant by the high

temperature gases outside. Cooling air bled from the

compressor stage flows through the gap, protecting the

blade surface.

A preliminary computational study using a commercial

CFD program (Fluent) was undertaken to provide support

and future guidance to the experimental evaluation of the

concept under way at LSU. The problem was modeled as

periodic flow with conjugate heat transfer through an array

of cylindrical pin fins bounded by parallel flat plates. Theenergy input from the external gases was modeled by a

uniform heat flux perpendicular to the fin axis applied to the

top endwall, while the bottom endwall was assumed to be

adiabatic.

To validate the computational model, simulations were

run to compare previous experimental work with various

types of pin fin arrays performed by Chyu [2] and Metzger

[3]. Good agreement with published friction factor and

Nusselt number results therein inspires a level of confidence

in the current computational model.

The computational study investigated the effects of

varying Reynolds number and Prandtl number on the friction

factor and heat transfer characteristics of the basic flow

configuration. Table 1 displays that, for the range of

Reynolds numbers in the present study, the heat transfer

enhancement increases with increasing Reynolds number.

However, this increased enhancement comes with rises in

the friction factor as flow becomes more turbulent. Friction

factors and Nusselt numbers can be incorporated into a

single quantity that contains information about the pressure

penalty paid for increased heat transfer, known as the

thermal performance factor (TPF):

TPF = Nu ?

Table 1 indicates a maximum TPF that falls within the range

of Reynolds numbers used.

Simulations were also performed to evaluate the effectsof modification of the fin array geometric parameters

changing the fin height (H/D), and the streamwise (L/D) and

spanwise fin (W/D) array density. Results presented in Table

Table 1: Results of increasing Reynolds number on friction

factor and Nusselt number (normalized by corresponding flat

channel values), and associated TPF

Re /flat Nu/Nuflat TPF

675 0.3974 1.79 2.43

1350 0.2950 13.49 20.26

2025 4.0011 17.66 11.12

3038 7.5495 22.72 11.58

Table 2: Results of changing geometry parameters (base

case: L/D = W/D = 5; H/D = 2.5) on friction factor and

Nusselt number (normalized by corresponding flat channel

/flat Nu/Nuflat TPF

1.25 15.7 7.9 3.16

2.5 4.6 10.3 6.20H/D

5 3.0 16.6 11.472 5.3 12.3 7.06

5 4.6 10.3 6.20L/D

8 4.8 8.8 5.19

2 29.8 23.0 7.42

5 4.6 10.3 6.20W/D

8 1.9 6.2 4.95


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22

2 indicate that from a heat transfer viewpoint, larger H/D

values are desiredthis seems to reflect the rising

effectiveness of the fluid to remove energy as the fin height,

and thus, the channel height is increased. Heat transfer canalso be increased by decreasing L/D and W/D, which means

increasing the fin array density. However, as Table 2

demonstrates, increasing fin density comes with severe

pressure penalties. Nusselt numbers are more responsive to

W/D changes than L/D, possibly because the wake of the

flow (L/D) isn't as important as the shear layers that form

around the fin region. Taken overall, the best performance

will be obtained from closely spaced arrays with large height

to diameter ratiosessentially, the current results are

predicating a move toward transverse flow across closely

spaced tube bundles. This observed trend matches well with

[4], where it was noted that the heat transfer enhancement

using pin fin arrays of intermediate H/D is lower than that for

classic tube bundles operating at the same Reynolds number

(until very high Reynolds numbers are reached).

While the pin fin arrays mentioned so far consist of

cylindrical pin fins, it is by no means certain that a circular

cross section produces the most effective heat transfer

enhancement. The computational study was extended to

investigate the effects of a variety of fin shapes at a

Reynolds number of 3000. The table associated with Figure 1

illustrates performance factors for square, diamond and

elliptical fins oriented parallel and perpendicular to the flow.

In terms of TPF, the last case offers a viable alternative to

cylindrical pin fin arrays.

The results presented allow optimal choices ofpromising geometric parameters and fin shapes to be made

for further experimental study.

ACKNOWLEDGMENTS

This study is supported by DARPA. The author wishes

to thank Dr. Acharya and Dr. Kelly for valuable insight and

guidance, and Christophe Marques for fruitful discussions.

Criticism from Dr. A. K. Saha, constructive much more often

than not, is gratefully acknowledged.

REFERENCES

1. J. C. COYNEL, MS thesis, Louisiana State University,

Baton Rouge, Louisiana, 1999.

2. M. K. CHYU, Y. C. HSING and V. NATARAJAN, J.

Turbomachinery. 120 (1998) 362-367.

3. D. E. METZGER, C. S. FAN and S. W. HALEY, J. Eng.

For Gas Turbines and Power. 106 (1984) 252-257.

4. D. E. METZGER, R. A. BERRY and J. P. BRONSON, J.

Heat Transfer. 104 (1982) 700-706.

A B

C D

Figure 1. Nusselt number contours on top surface of channel for different pin shapes for L/D = W/D = 5, H/D = 2.5

arra s and Re nolds number = 3x104

and associated erformance factors


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23


April 13, 2002

ADVANCED TURBULENCE MODELING FOR INDUSTRIAL APPLICATIONS

Raymond M. Jones

Ph.D. Candidate


ABSTRACT

Computational fluid dynamics ( CFD ) in industry is

typically performed using the Reynolds-averaged Navier-

Stokes equations ( RANS ). With RANS complex turbulent

flows at high Reynolds numbers can be solved with

reasonable accuracy and within an acceptable amount of

time. Other methods such as large eddy simulation ( LES )

and direct numerical simulations ( DNS ) can be used to

obtain more accurate results but require extensive

computational resources, even for complex turbulent flows

at moderately low Reynolds numbers.

With RANS, a turbulence model is needed to close the

momentum equations. Two-equation turbulence models

such as the k- model have been primarily used in industrybecause of their robustness. There are several different

types of two-equations turbulence models but they are

similar in that they all use damping functions to accurately

represent near wall turbulence. These damping functions

are usually derived for simple flows, such as flow in achannel, and are ill suited for most complex flows.

In the k- model, the eddy viscosity is computed as

2kCt = where C is typically 0.09. Figure 1 shows

computed values of t for 09.0=C and 075.0=C for a

turbulent channel flow. It can be seen that t is

overpredicted for both values of C . This shows that t

computed by the k- model can not accurately predict thenear wall eddy viscosity as long as C is a constant. The

damping functions mentioned above are used to replace C

with a function.Based on this observation Durbin (1991) introduced an

alternative eddy viscosity formulation defined as

kvCt2= where 2.0=C and

2v is the velocity

fluctuation normal to the wall. This formulation can also be

seen in Fig. 1. Durbin (1991) developed the kfv 2 model, which solves a scalar transport equation for k, , and

2v which are used to computed the eddy viscosity as

kvCt2= . The kfv 2 model has shown to

produce better results compared to conventional two-

equation models (Durbin (1992), Parneix et al. (1998)) .

Despite the improved accuracy, the kfv 2 model has

shown to be numerically stiff even for simple flows. In thepresent work a new model has been developed which uses

the general framework of the original kfv 2 model but

has shown to be more robust. In the new model, the

equation in the kfv 2 model has been replaced by the

equation of Wilcox and is called the kfv 2 model. A newrelationship between and is introduced based ondimensional arguments, and several of the closure constants

calibrated with respect to DNS data.

The kfv 2 model has been tested for predicting the

channel flow of Moser (1999) for Re .=395. The kfv 2

model was compared with the k- model and the kfv 2 model and the results for the streamwise velocity predictions

can be seen in Fig. 2. All of the models accurately predict

the correct velocity profile. Figure 3 shows kinetic energy

predictions. It can be seen that the kfv 2 model showsimproved predictions compared to both the k- model and

the kfv 2 model. The kfv 2 model was tested forpredicting the backward facing step of Kasagi (1993). Figure

5 shows that the kfv 2

model and the kfv 2

modelproduce better near wall velocity predictions compared to

the k- model.


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24

FIGURES AND TABLES

+

y+

0 0.02 0.04 0.06 0.08 0.10

50

100

150

200DNS

0.09k2/

0.075k2/

0.2kv2/

Fig. 1 Exact eddy viscosity compared with the k- model

(blue and orange) and the kfv 2 model (red line)

y+

u+

100

101

1020

4

8

12

16

20

24 Re = 39 5

v2f-k

k-

v2f-k

Fig. 2 Mean Velocity

k+

y+

0 1 2 3 4 5 60

80

160

240

320

400 Re = 395

v2f-k

v2f-k

k-

Fig. 3 Kinetic Energy

y+

diss

prod

0 25 50 75 100-0.3

-0.2

-0.1

0

0.1

0.2

0.3Re = 395

v2f-k

k-v

2f-k

Fig. 4 Production and Dissipation

x/H

y/H

0 1 2 3 4 5 6 7 8 9 10 110

0.5

1

1.5

2

2.5

3

Fig. 5 Streamwise velocity for the k- model (solid line),

kfv 2 model (dashed), kfv 2 model (dotted)

x/H

y/H

0 1 2 3 4 5 6 7 8 9 10 110

0.5

1

1.5

2

2.5

3

Fig. 6 Kinetic Energy for the k- model (solid line),

kfv 2 model (dashed), kfv 2 model (dotted)

ACKNOWLEDGMENTS

I would like to acknowledge The Dow Chemical for their

support on this project.

REFERENCES

1. P. A. DURBIN,AIAA Journal. 33 (1991) 659-664.

2. P.A. DURBIN,Annual Research Briefs, (1992) 3-16.

3. N.KASAGI, A. MATSUNAGA, and S. KAMARA, J.

Wind Eng. Ind. Aero. 46 (1993) 821-829.

4. R.D.MOSER, J.KIM, N.MANSOUR, Phys. Fluids. 11

(1999) 943-945.

5. S.PARNEIX, M.BEHNIA, P.DURBIN, Annual Research

Briefs, (1998) 149-164.


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25


April 13, 2002

TRIBOLOGICAL BEHAVIOR OF NANOSTRUCTURED NICKEL

Dean J. Guidry

M.S. Candidate

Faculty Advisor: Dr. Efstathios I. Meletis

ABSTRACT

The present study reports the effects of electroplating

parameters on the microstructure, and thus the mechanical

and tribological properties, of nanostructured nickel.

Electroplating was conducted in a Watts type bath at

current densities of 30 mA/cm2 and 15 mA/cm2 in

electroplating bath temperatures of 30C and 50C. The PHof the bath was maintained at 3.0 using sulfuric acid. The

electroplating was carried out using a direct current in

galvanostatic mode with a nickel anode contained in a

titanium wire basket. Average grain sizes and uniformity of

grains were determined from TEM and SEM micrographs.

Tribological tests were carried out on a pin-on-disc type

tribometer. The same tests were conducted on Ni-200 for the

purpose of comparison. Wear rates were calculated for the

nickel surfaces using optical profilometry and for the

alumina pins using optical microscopy. Nano-indention

techniques provided the nanohardness, stiffness, and

reduced modulus values for all samples. Microhardnessreadings were also recorded to further study the surface

properties. Result s show how grain size, mechanical

properties, and wear properties change with the variations in

plating parameters. Grain size reduction shows surface

hardness increases and improved tribological properties.

Plating bath temperature increases showed a decrease in

grain uniformity.

ACKNOWLEDGMENTS

The Author acknowledges Dr. Efstathios I. Meletis, Dr.

Kun Lian, Dr. Jie Chao Jiang and Varshni Singh for their help

and advice throughout this research project.

REFERENCES

1. G. Robinson, Electronic Engineering Times, 958 (1997)

33.

2. T. E. Buchheit, T. R. Christenson, D. T. Schmale, D. A.

Lavan,Mater. Res. Soc. Sym., 546 (1998) 126.

3. A. M. El-Sherik, U. Erb,J. Mater. Sci., 30 (1995) 5743.

4. V. Provenzano, R. Valiev, D. G. Rickerby, G. Valdre,

NanoStructured Mater., 12 (1999) 1103.

5. F. H. Froes and C. Suryanarayana, J. Mater. Sci., June

(1989) 12.

6. H. Gleiter,Acta Materialia, 48 (2000) 1.

7. H. Gleiter,NanoStructured Materials, 6 (1995) 3.

8. C. Meneau et. al., Surface and Coatings Technology,

100 (1998) 12.

9. F. Ebrahimi, G. R. Bourne, M. S. Kelly, T. E. Matthews,

NanoStructured Mater., 11 (1999) 343.

10. Z. N. Farhat, Y. Ding, D. O. Northwood, A. T. Alpas,

Mater. Sci. Eng. A, 206 (1996) 302.

11. S. W. Banovic, K. Barmak, A. R. Marder, J. Mater. Sci.,

33 (1998) 639.

12. E. O. Hall,Proc. Phys. Soc., B64 (1951) 747.

13. N. J. Petch,J. Iron Steel Inst., 174 (1953) 25.

14. L. S. Stephens, K. W. Kelly, E. I. Meletis, S. Simhadri,

Mat. Res. Symp. Proc., 518 (1998) 1.

15. A. H. Chokshi, A. Rosen, J. Karch and H. Gleiter, Scripta

Metall. Mater., 23 (1989) 1679.

16. K. Lu, W. D. Wei and J. T. Wang, Scripta Metall.Mater., 24 (1990) 2319.

17. G. E. Fougere, J. R. Weertman and R. W. Siegel, Scripta

Metall. Mater., 26 (1992) 1879.

18. G. Palumbo, U. Erb and K. T. Aust, Scripta Metall.

Mater., 24 (1990) 2347.

19. N. Wang, Z. Wang, K. T. Aust, U. Erb, Acta Metall.

Mater., 43 (1995) 519.

20. R. Z. Valiev, N. A. Krasilnikov, N. K. Tsenev, Mater. Sce.

Eng. A, 137 (1991) 35.

21. S. M. Myers, J. A. Knapp, D. M. Follstaedt, M. T.

Dugger,J. Appl. Phys., 83 (1998) 1256.

22. Y. Ichida, K. Kishi, Trans. of the ASME, 119 (1997) 110.

23. D. A. Rigney,Mat. Res. Innovat., 1 (1998) 231.24. V. Singh, X. Nie, P. Gupta, E.I. Meletis, 6

thNat. Cong.

Mech. Proc., 2 (2001) 1.

25. K. Laul, M. Dorfman, Adv. Mater. and Proc., 158 (2000)

46.

26. M. Legros et. al.,Phil. Mag. A, 80 (1999) 1017.

27. A. B. Witney, P. G. Sanders, J. R. Weertman, Scripta

Metall. Mater., 33 (1995) 2025.


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26

28. X. J. Wu et. al., NanoStructured Materials, 12 (1999)

221.

29. T. R. Christenson, T. E. Buchheit, D. T. Schmale, R. J.

Bourchier,Mat. Res. Soc. Symp. Proc., 518 (1998) 185.

30. E. Bonetti et. al.,NanoStructured Mater., 11 (1999) 709.

31. S. Greek, F Ericson,Mat. Res. Symp. Proc., 518 (1998) 51.

32. A. Cziraki et. al., Thin Solid Films, 318 (1998) 239.33. G. Auner, et. al., Thin Solid Films, 107 (1983) 191.

34. R. V. Nandedkar et. al.,Phys. Status Solidi, 72 (1982) 89.

35. J. C. Pivin et. al.,J. Mater. Sci., 22 (1987) 1087.

36. P. S. Barlow, R. A. Collins, G. Dearnaley,J. Phys. D: Appl

Phys., 22 (1989) 1510.

37. D. M. Mattox,J. Electrochem. Soc, 115 (1968) 1255.

38. K. Bouslykhane, J. P. Villain, P. Moine, Tribology

International, 29 (1996) 169.

39. L. Jun, W. Yiyong, W. Dianlong, H. Xinguo, J. Mater.

Sci., 35 (2000) 1751.

40. F. Ebrahimi, A. J. Liscano, Mater. Sci. Eng. A, 301 (2001)

23.

41. R. I. Pratt, G. C. Johnson, Mat. Res. Soc. Symp. Proc.,518 (1998) 15.

42. T. Bieger, U. Wallrabe,Microsystem Tech., 2 (1996) 63.

43. I. M. Hutchings,Mater. Sci. Eng. A, 184 (1994) 185.

44. J. Ferrante,Phys. World, July (1991) 46.

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48. LECO Corporation, Metallography Principles and

Procedures, (1994) 38.


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April 13, 2002

INTRINSIC STRESS DEVELOPMENT IN TI-C:H CERAMIC NANOCOMPOSITE

COATINGS

B. Shi

Ph. D. Candidate

Faculty Advisor: Dr. W. J. Meng

ABSTRACT

The development of intrinsic stresses within titanium-

containing hydrocarbon (Ti-C:H) coatings was monitored by

in-situ substrate curvature measurements using a multi-beam

optical sensing (MBOS) technique. Stress as a function of

the Ti-C:H layer thickness was monitored in a wide range ofspecimens, from nearly pure amorphous hydrocarbon (a-

C:H) to nearly pure titanium carbide (TiC). The intrinsic

stress within Ti-C:H was found to vary significantly in

magnitude and depend systematically on the Ti

composition.

Ti-containing hydrocarbon (Ti-C:H) coatings,

consisting of a nm-scale mixture of crystalline titanium

carbide (TiC) and amorphous hydrocarbon (a-C:H)1, form a

prototype of pseudo-binary ceramic nanocomposites. Ti-C:H

coatings possess mechanical properties and tribological

characteristics which depend systematically on coating

composition2, demonstrating the potential of engineering

ceramic nanocomposite coatings for specific applications.The dependence of tribological characteristics of Ti-C:H

coatings on the Ti composition has been related to a

percolation type transition3. In addition to the influence of

plasma characteristics, the coating composition may

therefore exert a significant influence on intrinsic stress

development within ceramic nanocomposite coatings.

This paper addresses the dependence of intrinsic

stresses within Ti-C:H coatings on the Ti composition. Ti-

C:H deposition was accomplished using a high-density

plasma assisted hybrid chemical vapor deposition

(CVD)/physical vapor deposition (PVD) process. Under

nominally identical plasma conditions, a series of Ti-C:H

coatings, ranging from nearly pure a-C:H to nearly pure TiC,

was deposited onto Si(100) substrates. The development of

intrinsic stresses was monitored by in-situ measurements of

substrate curvature change. Our results show that the

intrinsic stress within Ti-C:H coatings depends

systematically on the Ti composition. A significant increase

in stress was observed as the Ti composition increases

beyond 30 at. % and suggested to be related to the

percolation type transition in the coating mi crostructure.

Details of experimental setup and procedures will be

described in the presentation.

Figure 1 shows a typical substrate temperature time

history during a complete Ti-C:H deposition run. The Ti

cathode current was 1.0A during Ti-C:H deposition. During

the etch and cool stages, the substrate temperature rosefrom ~ 25 oC to ~ 225 oC and fell to ~ 150 oC. It stayed ~ 150oC during Ti interlayer deposition, and rose to ~ 225

oC

during Ti-C:H deposition. During the entire deposition run,

the temp erature difference between front and back beam

surfaces was 5 K. Such a temperature difference across a300 m thick Si wafer would induce a substrate curvature

change K of ~ 1/21 m-1. Figure 1 shows that, during Tiinterlayer and Ti-C:H deposition, change in relative reflected

laser spot spacing D/D0, which is measured experimentallyand linearly related to the curvature change, induced by

temperature gradient across the Si substrate is substantially

smaller than 10 %.

A multitude of Ti-C:H/Ti/Si(100) specimens weredeposited. During each deposition, the curvature change of

the Si(100) beam substrate was monitored by MBOS. Figure

2 shows the average composition of the Ti-C:H layers as a

function of the Ti cathode current obtained by combining

RBS and ERD measurements. The Ti and hydrogen

compositions respectively increase and decrease in a

monotonic fashion with increasing Ti cathode current. The

observed trend is consistent with our previous results and

supports the fact that Ti-C:H coatings are pseudo-binary

TiC/a-C:H nanocomposites, in which hydrogen inclusion

occurs only through incorporation into the a-C:H phase4.

Figure 3 shows measured D/D0 during Ti-C:H deposition asa function of time. The time origin coincides with the

beginning of Ti-C:H deposition. Only the curvature change

due to Ti-C:H deposition is taken into account, as D/D0was set to zero at time zero. In the early stage of growth, 0

400 sec, D/D0 increases approximately linearly to ~ 30%,independent of the Ti composition. In the late stage, 400

2500 sec, D/D0 continues to increase linearly with time, butin most cases with a distinctly different slope as compared

to the early stage.


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28

Temperature measurements, such as the one shown in

Figure 1, showed that during the early stage of Ti-C:H

growth, the substrate temperature rose ~ 70 K. In the late

stage, the substrate temperature change was 25 K at all Ticathode currents. This temperature change T would inducea substrate curvature change KT due to the difference in

thermal expansion between Si and the Ti-C:H coating s-c,

where Ys, ts, Yc, and tc are respectively the biaxial modulus

and thickness of the substrate and the coating. s-c wastaken to be ~ 410-6 K-1, according to measurements on W-C:H coatings

5. For the present measurements, a

conservative estimate yielded D/D0 +5% forT = +100 K6. It is thus concluded that thermal contribution to the

present measurements can be neglected, and that in all cases

the measured D/D0 reflects intrinsic stress development.The linear dependence of D/D0 on time during late stagegrowth indicates a constant level of incremental intrinsic

stress as the Ti-C:H layer thickens.

In summary, a detailed experimental study of the

dependence of intrinsic stress within Ti-C:H coatings on the

Ti composition was performed by measuring in-situ

substrate curvature change. The intrinsic stress within Ti-

C:H layers was found to vary significantly in magnitude and

depend systematically on the Ti composition. The observed

stress dependence on coating composition is suggested to

correlate with a percolation type transition in the coating

microstructure, and may be one generic characteristic of

ceramic nanocomposite coating systems.

ACKNOWLEDGMENTSWe gratefully acknowledge partial project support from

NIST through ATP program 70NANBH0H3048, NSF through

grant DMI-0124441, and Louisiana Board of Regents

through contracts LEQSF(2000-03)-RD-B-03 and

LEQSF(2001-04)-RD-A-07. The ion beam analysis work at the

Argonne National Laboratory was performed by L. E. Rehn

and P. M. Baldo and supported by the DOE Office of

Science, Basic Energy Sciences, under contract #W-31-109-

ENG-38.

FIGURES AND TABLES

REFERENCES

1. W. J. Meng, R. C. Tittsworth, J. C. Jiang, B. Feng, D. M.Cao, K. Winkler, V. Palshin, J. Appl. Phys., 88, 2415

(2000).

2. W. J. Meng, R. C. Tittsworth, L. E. Rehn, Thin Solid

Films 377/378, 222 (2000).

3. B. FENG, D. M. CAO, W. J. MENG, L. E. REHN, P. M. BA

4. LDO, G. L. DOLL, THIN SOLID FILMS 398/399, 210

(2001).

5. D. M. Cao, B. Feng, W. J. Meng, L. E. Rehn, P. M.

Baldo, M. M. Khonsari, Appl. Phys. Lett. 79, 329 (2001).

6. J. S. Wang, Y. Sugimura, A. G. Evans, W. K. Tredway,

Thin Solid Films 325, 163 (1998).

7. For the present Si(100) beam substrates, Ys = 180 GPa

and ts = 300 m. tc is taken to be 800 nm, the entire

thickness of the Ti-C:H layer. The maximum biaxial

modulus for Ti-C:H coatings is ~ 180 GPa (ref. 8), thus

Yc is taken to be 180 GPa.

Time (sec)

0 500 1000 1500 2000 2500

Temperature(C)

0

50

100

150

200

250

Ti cathode 1.0A, front surface

Ti cathode 1.0A, b

book of abstract 2002

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