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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: [email protected],
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
Jordan International Energy Conference 2011 – Ammanـ
[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
Jordan International Energy Conference 2011 – Ammanـ
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.
Jordan International Energy Conference 2011 – Ammanـ
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
Jordan International Energy Conference 2011 – Ammanـ
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
Jordan International Energy Conference 2011 – Ammanـ
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
Jordan International Energy Conference 2011 – Ammanـ
Fig. 7: Transient Temperature Distribution
Fig. 8: Temperatures History
Jordan International Energy Conference 2011 – Ammanـ
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.
Jordan International Energy Conference 2011 – Ammanـ
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
Jordan International Energy Conference 2011 – Ammanـ
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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Jordan International Energy Conference 2011 – Ammanـ
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Jordan International Energy Conference 2011 – Ammanـ
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