Jordan International Energy Conference 2011 – Ammanـ

Reliability Prediction of a Return Thermal Expansion Joint

O.M. Al-Habahbeh1,*

, D.K. Aidun2, P. Marzocca

2

1Mechatronic Engineering Dept., The University of Jordan, Amman, 11942 Jordan

2 Mechanical & Aeronautical Eng. Dept., Clarkson University, PO Box 5725, Potsdam, NY 13699 USA

* Corresponding author. Tel: +962 787156824, Fax: +962 65300813, Email: o.habahbeh@ju.edu.jo,

Abstract: An efficient reliability assessment approach is used to estimate the reliability of a return expansion

joint. This component is part of a large power generation system. In order to perform the reliability assessment

task, Computational Fluid Dynamics (CFD), Finite Element Method (FEM), Fatigue analysis, and Monte Carlo

Simulation (MCS) tools are integrated. The process starts with CFD simulation to determine the convective

terms necessary for the transient FEM thermal analysis. The thermal analysis provides maximum thermal stress

whereby the fatigue life of the component is estimated. As a result of input parameters uncertainty, the calculated

life is in the form of a Probability Density Function (PDF), which enables the calculation of the reliability of the

component. The application of this reliability prediction procedure to the return expansion joint can be used to

enhance the design and operation of the component by uncovering under-design or over-design. Under-design

warrants further studies using the same method to determine how to enhance the reliability. On the other hand,

over-design can be eliminated to reduce the manufacturing cost of the component. Furthermore, various

alternative designs and operational scenarios can be studies using this model.

Keywords: Integrated Reliability Prediction, CFD Simulation, FEM Simulation, Stress-Life Method, Return

Expansion Joint.

1. Introduction

Reliability is defined as the ability of a system to operate under normal and abnormal

conditions subject to a defined failure rate and for a specific life time [1]. While reliability can

be determined by accelerated life testing, it is more cost-effective to predict the reliability of

the system early during the design phase. Many researchers have dealt with reliability of

engineering systems. However, most of this work is related to structural systems not

involving fluid interaction. Basaran and Chandaroy [2] determined the reliability of a solder

joint subjected to thermal cycling loading by FEM instead of laboratory tests. Vandevelde et

al. [3] compared two solder joints reliabilities using non-linear FEM. Asghari [4] obtained

heat transfer coefficient (h) for surfaces in contact with air flow by running a steady-state

CFD model. Bedford et al. [5] used a CFD-based time-averaged heat transfer coefficient (h)

for thermal stress analysis. Stress in thermal structures can be determined by FEM simulation

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[6]. However, thermal stress affects service life more than mechanical stress; this effect

lowers life by a factor up to 2.5 [7]. Therefore, this factor is integrated into the simulations.

The alternating stress method is used to relate the thermal stress to the number of cycles. The

S-N curve of the material is used for this process. A thermo-mechanical study considering

only the steady-state operation and not the pulsed heating effects is not enough. Additional

study is necessary to consider the pulsed heating effects in the form of additional stress [8].

Thermal shock shares many characteristics with thermally-induced stress, except that its

behavior is time dependent as well as spatially dependent. During the operation of a thermal

system, the rapid start-up and shut-down leads to a large temperature difference between the

surface of a material and the mean body temperature [9].

Ichiro et al. [10] introduced the development of thermal transient stress charts for

screening evaluation of thermal loads in structural design works of fast reactor components.

Satyamurthy et al. [11] used FEM to calculate the transient thermal stresses in a long cylinder

with a square cross section resulting from convective heat transfer. Constantinescu et al. [12].

presented a computational approach for the lifetime assessment of structures under

thermomechanical loading. The proposed method is composed of a fluid flow, a thermal and a

mechanical finite element computation, as well as fatigue analysis. However, transient

analysis was not considered in their work. Liu et al. [13] investigated the Thermal-Mechanical

Fatigue (TMF) behavior of cast nickel-based super-alloy under In-Phase (IP) and Out-of-

Phase (OP) loading in the temperature range from 400 to 850°C. At corresponding strain

amplitude, the thermal-mechanical fatigue life was lower than that of isothermal fatigue.

Gue’de’ et al. [14] set up a probabilistic approach of the thermal fatigue design of nuclear

components. It aimed at incorporating all kinds of uncertainties that affect the thermal fatigue

behavior. The approach was based on the theory of structural reliability. Beside the

probability of failure calculation, the sensitivity of the reliability index to each random

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variable is estimated. The proposed method is applied to a pipe subjected to thermal loading

due to water flow. The results show that it is possible to perform a complete reliability

analysis to compute the failure probability. It was observed that the scatter of fatigue data and

the heat transfer coefficient are the most important variables in thermal fatigue reliability

analysis. Lee and Kim [15] discussed failure mechanisms of electronic packaging subjected to

thermal cyclic loads. It was found that mechanical load has longer fatigue life than thermal

load.

Fatigue Strength Reduction Factor (FSRF) must be assigned during the fatigue analysis. It

serves to adjust the stress-life or strain-life curve(s) used in the fatigue analysis. This setting is

used to account for a "real world" environment that may be harsher than a rigidly-controlled

laboratory environment in which fatigue data was collected [6]. The FSRF can be defined as a

reduction of the capacity to bear a certain stress level. Life predictions for fatigue failure

generally consist of a good determination of this factor [16]. Article NB-3200 in Section III of

the ASME Code provides the following definition for FSRF: “Fatigue strength reduction

factor is a stress intensification factor which accounts for the effect of a local structural

discontinuity (stress concentration) on the fatigue strength” [17]. This factor is applied to the

alternating stress only and does not affect the mean stress [18]. A FSRF of 2.0 for integral

parts and 4.0 for non-integral attachments has been assumed for calculating the amplitude of

peak stresses [19].

In this work, an efficient reliability assessment approach is employed to estimate the

reliability of a return expansion joint. This component is a critical part of a cooling system for

a large gas turbine. The reliability prediction method employed in this work was introduced

by the authors in a previous journal paper [20]. A model of the return expansion joint is built,

then a CFD analysis of the air flow is conducted, followed by a transient FEM analysis of the

Jordan International Energy Conference 2011 – Ammanـ

structure based on the results of CFD analysis. Finally, fatigue analysis is conducted in

conjunction with MCS in order to estimate the reliability of the component.

2. Reliability Prediction Method

The Reliability Prediction flow chart is shown in Fig. 1. It consists of two loops connected by

the Probability Density Functions (PDF) of heat convection coefficients. The left hand side

loop represents the stochastic CFD simulation stage, and the right hand side loop represents

the stochastic FEM stage.

Fig. 1: Reliability Prediction Method

3. Reliability Prediction of the Return Expansion Joint

The Reliability Prediction method is applied to a return expansion joint which is part of an

energy subsystem shown in Fig. 2. The system comprises four components; Heat exchanger,

moisture separator, and pressure-balanced expansion joints (supply and return). The heat

exchanger circuit is installed between the Low Pressure Compressor (LPC) and the High

Pressure Compressor (HPC) of the gas turbine. The heat exchanger increases the turbine

efficiency by cooling air before it enters the HPC [21]. Therefore, the reliability of these

components is critical to the reliability of the gas turbine.

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Fig. 2: Power Generation System [21]

The application of the Reliability Prediction method to the heat exchanger circuit is a

complex task. Here, the focus will be on the return expansion joint. The employed reliability

method depends on the Physics-based Modeling which consists of two phases; CFD for the

fluid side and FEM/Fatigue for the solid side. Physics-based modeling is used in conjunction

with reliability methods. The main interest in this work is to analyze the transient start-up of

the component, and to achieve this goal, the system is modeled using transient analysis. As a

result of heat flux, temperature gradients develop and cause thermal stresses in the structure.

The calculated heat transfer coefficients are for convections of air, while the mode of

heat transfer within the solid is conduction. The accuracy of the solution is verified by

refining the meshes in both the CFD and the FEM solutions. The Reliability Prediction

method is performed by integrating several software packages. iSIGHT® and

ANSYS/DesignXplorer®

software are used to simulate the reliability of the component, while

ANSYS/CFX®/Simulation

® is used for the physical modeling phase. The physical modeling

consists of Computational Fluid Dynamics (CFD) and Finite Element Method (FEM). The

stochastic CFD simulation is run by ANSYS/DesignXplorer®. On the other hand, iSIGHT

® is

interfaced with ANSYS/Simulation® using an ANSYS/Workbench

® Component in order to

perform Monte Carlo simulation (MCS), and consequently evaluate the reliability of the

component, which is based on thermal stress fatigue as failure criterion.

Supply Expansion Joint Heat

Exchanger

Moisture

Separator

Return Expansion Joint

Gas

Turbine

Jordan International Energy Conference 2011 – Ammanـ

Stochastic CFD Simulation

A CAD model of the return expansion joint is prepared for analysis. The model is meshed as

shown in Fig. 3. The mesh contains 1,341,000 elements. All input and output parameters of

this model are listed in Table 1. Selected CFD random input parameters are shown in Table 1

(marked with asterisks). These parameters were selected based on a sensitivity analysis. The

statistical distributions of these parameters are defined so as to perform stochastic CFD

analysis. After conducting the CFD analysis, velocity, temperature, and heat transfer

coefficient results are obtained. For example, air velocity and temperature distributions are

shown in Fig. 4 and Fig. 5 respectively. Some output parameters listed in Table 1 are selected

as random variables, and marked with double asterisks. Their statistical distributions are

defined in order to perform stochastic FEM simulations.

Fig. 3: A Section of the Return Joint CFD Mesh

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Table 1: CFD Parameters of Return Expansion Joint (REJ)

Parameter Explanation Unit

REJ Air Flow* Return Expansion Joint Air Flow Rate kg/s

REJ Air Pressure Return Expansion Joint Air Pressure kPa

REJ Density Return Expansion Joint Density kg/m3

REJ ID Return Expansion Joint Inner Diameter m

REJ OD Return Expansion Joint Outer Diameter m

REJ Return Temperature*

Return Expansion Joint Convective Ambient

Temperature °C

REJ Specific Heat Return Expansion Joint Specific Heat J/kg °C

REJ Thermal

Conductivity Return Expansion Joint Thermal Conductivity W/m °C

REJ Thermal Expansion Return Expansion Joint Thermal Expansion 1/°C

REJ Outlet

Temperature** Return Expansion Joint Temperature at Air Out (Output) °C

REJ RHTC**

Return Expansion Joint Convective Film Coefficient

(Output) W/m2 °C

Fig. 4: Air Velocity Distribution

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Fig. 5: Air Temperature Distribution

3.2. Stochastic FEM Simulation

The stochastic CFD results are used as input to the FEM analysis. All input and output

parameters used in the FEM analysis are listed in Table 2. The mesh used for the FEM

analysis is shown in Fig. 6. A transient thermal analysis is conducted and thermal stress is

computed at regular intervals to determine the maximum stress. The transient temperature

distribution is shown in Fig. 7, and the corresponding thermal stress distribution is shown in

Fig. 9.

The variation of transient temperature with time is plotted in Fig 8, while the variation

of transient stress with time is plotted in Fig. 10. The latter serves to determine when the

maximum stress occurs. By performing stochastic iterations at this point of time, the stress

results are obtained and used to determine fatigue life for each sample point using Fig. 11.

The resulting life distribution is used to obtain the reliability of the model as shown in Fig. 12

and Fig. 13.

Jordan International Energy Conference 2011 – Ammanـ

Fig. 6: FEM Mesh of Return Joint

Table 2: FEM Parameters of Return Expansion Joint (REJ)

Parameter Explanation Unit

REJ Compressive Yield Strength Return Expansion Joint Compressive Yield Strength MPa

REJ Convective Ambient

Temperature

Return Expansion Joint Convective Ambient

Temperature °C

REJ Convective Film Coefficient Return Expansion Joint Convective Film Coefficient W/m2 °C

REJ Density Return Expansion Joint Density kg/m3

REJ ID Return Expansion Joint Inner Diameter m

REJ OD Return Expansion Joint Outer Diameter m

REJ Poisson's Ratio Return Expansion Joint Poisson's Ratio ---

REJ Pressure Magnitude Return Expansion Joint Air Pressure kPa

REJ Specific Heat Return Expansion Joint Specific Heat J/kg °C

REJ TensileUltimateStrength Return Expansion Joint Tensile Ultimate Strength MPa

REJ TensileYieldStrength Return Expansion Joint Tensile Yield Strength MPa

REJ Thermal Conductivity Return Expansion Joint Thermal Conductivity W/m °C

REJ Thermal Expansion Return Expansion Joint Thermal Expansion 1/°C

REJ Young's Modulus Return Expansion Joint Young's Modulus Pa

REJ Maximum Shear Stress Return Expansion Joint Maximum Shear Stress (Output) MPa

REJ Life Minimum Return Expansion Joint Fatigue Life (Output) Cycles

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Fig. 7: Transient Temperature Distribution

Fig. 8: Temperatures History

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Fig. 9: Transient Stress Distribution

Fig. 10: Max Transient Thermal Stress

3.3. Stress Life Estimation

The maximum transient stress result is used to determine the corresponding stress life of the

component. The S-N curve shown in Fig. 11 is used for this purpose. Latin Hypercube

technique is used to generate 25 maximum stress points. These points represent the variation

in operational and environmental conditions as shown in the CFD and FEM analyses sections.

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Approximation surface regression is used to generate 10,000 points based on the original 25

points. Those points are used to plot the Life Probability Density Function (PDF) shown in

Fig. 12. This PDF is used to calculate the reliability of the component.

Fig. 11: Semi-Log S-N Curve of the Model Material [22]

Fig. 12: Life PDF

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Fig. 13: Reliability Calculation using Life PDF

4. Conclusions

The implemented reliability prediction method can easily be used to predict the reliability of

return expansion joints by means of numerical physics-based modeling. By implementing

stochastic CFD and FEM analyses, uncertainties of operational and environmental conditions

such as flow velocity and temperature can be reflected into the reliability prediction process.

Transient thermal analysis produces variable thermal stress. Therefore, critical stress is

determined by investigating the whole transient phase. This integrated reliability prediction

method is a powerful method for designing return expansion joints with optimum

performance and reliability.

Acknowledgment

The Authors would like to thank GE Energy, Texas, for their support of this research.

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