INTRODUCTION
As process fluid flows past the thermowells in pipelines, low-pressure vortices are formed with a vortex shedding frequency that would cause damaging vibrations during resonance and lead to rupture.
Hence, a fatigue life prediction model needs to be developed using finite-element analysis so that the thermowells can be replaced before being in critical condition. The research investigates the effects of fluid velocity, density, and cyclic loading on the thermowell using AutoCAD 2022 and ANSYS Workbench 21.1.
By comparing the results for the proposed method to previous research in supercritical conditions, the percent error obtained was 0.11%, which indicates that the proposed method is a reliable tool to perform fatigue analysis. For the parametric study, six load cases were investigated for two thermowells designed based on the minimum and maximum dimensional limits of the thermowell performance test code PTC 10.3 TW-2016. The minimum thermowell performed better for all load cases, which obtained a maximum number of 8898 cycles to failure. Furthermore, the higher the fluid velocity and density, the higher the Received: 6 September 2021, Accepted: 14 December 2021, Published: 31 March 2022, Publisher: UTP Press, Creative Commons: CC BY 4.0
THERMOWELL FATIGUE LIFE PREDICTION USING FINITE ELEMENT ANALYSIS
Danish Luqman bin Norazmi1, Tamiru Alemu Lemma1, 2*
1Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Malaysia
2Gas Separation Research Centre, Institute of Contaminant Management, Universiti Teknologi PETRONAS, Malaysia
*Email: [email protected]
ABSTRACT
The objectives of the research involve developing the procedure for fatigue life prediction using the S-N curve for the thermowell material and investigating the effects of fluid velocity, fluid density and cyclic loading on the thermowell structure using the engineering drawing tool, AutoCAD 2022, and simulation software, ANSYS Workbench 21.1.
By comparing the results for the proposed fatigue life estimation to Diwakar’s study on fatigue life estimation of thermowells in supercritical operation, the percent error obtained was 0.11%, which indicates that the proposed method is an accurate and reliable tool to perform fatigue analysis. Afterward, the parametric study of the thermowell model was conducted to investigate the effects of fluid velocity, fluid density and geometric dimensions on the fatigue life of a thermowell. There were six load cases investigated for two thermowells, which were designed based on the minimum and maximum dimensional limit of the thermowell performance test code PTC 10.3 TW-2016. The parametric study results showed that the minimum thermowell performed better for all the load cases, which obtained a maximum number of cycles to failure of 8898 cycles for a maximum stress value of 869 MPa. Furthermore, the higher the fluid velocity and density, the higher the likelihood and occurrences of resonance, the lower the number of cycles to failure. Similarly, the higher the natural frequency of the thermowell, the lower the likelihood and occurrences of resonance; hence, the higher the number of cycles to failure. It was observed that the point where the stress value is highest, or the stress concentration zone, is the area between the flange and thermowell neck, which was consistent with the thermowell performance standard codes of practice, PTC 19.3 TW-2016.
Keywords: Fatigue analysis, parametric study, resonance, stress concentration zone, supercritical, vortex shedding frequency
likelihood of resonance and the lower the number of cycles to failure. It was observed that the stress concentration zone is the area between the fl ange and thermowell neck, which was consistent with the standard codes of practice.
In petrochemical plants, oil and gas need to be processed before usage. The oil and gas are stored and transported in pipelines which require constant observation and monitoring. The properties of these fl uids also need to be measured periodically by temperature sensors such as thermometers, thermistors, thermocouples and RTDs. However, these instruments are exposed to excessive pressure, material velocity and high induced vibrations in the pipelines, which will damage these sensors [1]. To protect the sensors, the thermowells are mounted on the pipeline to act as a barrier between the fl uids and the sensing element of a temperature measuring device. A thermowell is a closed-ended hollow cantilever welded to a heavy fl ange bolted through a gasket to a mating fl ange on the exterior of the pipe as shown in Figure 1.
As fl uids inside the pipeline fl ow past the thermowell, l ow-pressure vortices are formed on both sides of
the component, which creates a vortex wake. The drag forces from the fl uid fl ow and lift forces from the alternating vortex shedding generate alternating lateral forces, which form a turbulent wake or a ‘Von Karmann Trail’ in a phenomenon known as the Von Karmann eff ect [3] ,which can be seen in Figure 2.
The high fl ow velocity of the fl uids inside the pipeline formed by the vortex shedding against the thermowell could increase the wake frequency. The shedding lift forces and the vortex-shedding can suddenly shift to the thermowell natural frequency in a phenomenon known as ‘Lock-on’ or synchronization. Similar magnitudes of the wake frequency and natural frequency of the thermowell cause a resonance of the two frequencies, which results in massive, amplifi ed energy absorption by the thermowell. At resonance, the resultant coherent forces cause damaging vibrations to the mechanical structure of the thermowell [1]. The resultant vibration that is produced by the combination of high stresses from the fl uid velocity could cause structural damage and the formation of cracks or material fatigue, which could lead to mechanical failure of the thermowell in the pipeline. In industrial practices, if the wake frequency is within 20% of the natural frequency of the thermowell, the resultant vibration could cause mechanical failure of the well [5]. Thermowells are in optimal condition when the wake frequency is eight times lower than the natural frequency, as this prolongs the occurrence of fatigue failure [5].
The thermowell performance test code PTC 19.3 TW- 2016 is an accurate and reliable guide commonly used in the oil and gas industry to design thermowells for various applications as well as diff erent confi gurations inside pipelines [6]. The test code includes standards for the dimensional limits of the thermowells, all governing stress equations, which include the natural
Figure 2 Von Karmann eff ect on fl uid fl ow through thermowell [4]
Figure 1 Straight type fl anged thermowell [2]
Vortex Shodding Induced Force
Fluid Flow
frequency, vortex-shedding or wake frequency, steady- state stress, dynamic stress and examples and sample calculations to reduce fatigue failure of the equipment during operation. In addition to that, there are also thermowell wake frequency solvers available online to help compute the required dimensions and suitability of a thermowell for a specifi c pipeline [7].
Thermowells have an important role in protecting temperature-sensing sensors against fl uid velocity in petrochemical plants. The biggest factor that causes fatigue to the thermowells is vortex-induced vibrations which form turbulent vortex shedding and wakes [8].
These forces produce shedding frequencies that can rise to reach the same magnitude of the thermowell natural frequencies and encourages resonance. As the fl uid fl ows past the thermowell inside the pipeline, low-pressure vortices are shed on both sides of the component. The in-line (drag) forces from the fl uid fl ow and transverse (lift) forces from the vortex shedding as shown in Figure 3, generates alternating lateral forces, which form a turbulent wake or a ‘Von Karmann Trail’ [5].
fatigue fracture occurs. These fluid-induced forces’
frequency has various effects on the thermowell structure. Vibrations of relatively small magnitude can be suppressed by applying support systems, but for systems that are not designed for fatigue failures, fl ow- induced vibrations may result in mechanical damage to the piping system, and fatigue failure may occur [1].
Fatigue life prediction for the thermowells need to be developed to monitor the fatigue damage and replace the thermowells before fatigue failure occurs.
Hen ce, an accurate Finite-Element Model (FEM) that calculates the number of cycles to failure will improve the maintenance of the thermowells and allow the components to be replaced before the integrity of the equipment suff ers signifi cant damage from fatigue.
Proper management of the thermowell fatigue life will reduce technical complications from measuring fl uid temperatures and unscheduled downtimes.
The research aims to calculate the number of cycles before failure for the thermowell using engineering simulation, ANSYS Workbench 21.1, and to investigate the eff ects of fl uid velocity, density, and cyclic loading on thermowells based on PTC 19.3 TW-2016. For the parametric study, the straight-type flanged thermowell was selected due to the straight neck for the simplification of calculations based on the fi llet radius at the support plane, root diameter and tip diameter. Furthermore, the model has a uniform surface continuity to facilitate the ideal conditions for the fi nite element analysis. The material that was used for the thermowell was the AISI 304 Stainless Steel (SS-304) [9].
Mathematical formulation of fatigue in pipes The Reynold’s number for the fl uid fl ow of the process fl uid can be calculated as:
Re = ρVB
–––μ (1)
where ρ = fluid density, V = fluid velocity, B = tip diameter, μ = dynamic viscosity.
Natural frequency of thermowell
The approximate natural frequency of a straight uniform thermowell is given by,
fn = 1.8752 –––––
2π
(
––EIm)
–12 ––L12 (2)Figure 3 Fluid-induced forces and assignment of axes on thermowell [6]
Fluid vortices downstream
Transverse forces
In-line forces X
V
Y Z
The shedding frequency of the shedding vortices resonates with the natural frequency of the thermowell and amplifies the damaging vibrations absorption on the thermowell. Turbulent wakes contribute to cyclic stresses, which exacerbates the fatigue damage at the base. The thermowell neck became a stress concentration zone that propagates the fatigue cracks deeper along the neck due to fl uctuating stresses until
where E is the modulus of elasticity, I is the second moment of inertia, L is the unsupported length, and m is the mass per unit length, including external added mass and internal mass. For values of Reynold’s number higher than 5.0E+5, the dimensionless Strouhal number, NS is 0.22 represented by:
NS =
0.2
(
1 – 22Re––)
, for 22 ≤ Re < 1300 0.213 – 0.0248[log(
––––1300Re)]
2+0.0095
[
log(
––––1300Re)]
3, for 1300 ≤ Re < 5e105 0.22, for 5e105 ≤ Re < 5e107(3)
Conventionally, NS = 0.22 is used in relation to calculating the vortex-shedding frequency [10]. At resonance, the shedding frequency, fs equals the natural frequency, fn.
Vortex shedding frequency
The frequency of vortex shedding is given in terms of a dimensionless Strouhal number S,
fs = –––SV
D , (Hz) (4)
where V is the mean flow velocity normal to the thermowell, D is the thermowell outside diameter, and S is the dimensionless Strouhal number, which is approximately S = 0.22 in most petrochemical piping conditions and applications.
Forces acting on thermowell
The forces acting on the thermowell during pipeline operations are conventional steady-drag forces FD , oscillating-drag (in-line) forces Fd and oscillating-lift (transverse) forces FL. The forces are expressed in terms of the researched contact area, a steady-drag co-efficient CD, oscillating-drag coefficient Cd and oscillating-lift coefficient along with the dynamic head of the stream –12ρV 2, which are as follows:
FD = Ap–12ρCDV 2 Fd = Ap–12ρCDV 2 FL = Ap–12ρCLV 2 (5)
where CD = 1.4, Cd = 0,1 and CL = 1.
The magnitude and direction of these forces are used to simulate the loading on the thermowells to conduct the stress analysis and fatigue analysis of the structure.
METHODOLOGY
The research methodology describes the process of executing the research towards obtaining the desired results and achieving the research objectives. The criterion for evaluating the prediction model proposed in this research is to be within 10% percentage error of the number of cycles to failure based on the results from the research studies on the fatigue life prediction model of thermowells at specified operating conditions.
This validation of results is essential to ensure that the prediction model is a viable fatigue prediction technique before investigating the other parameters for the thermowells, such as fluid velocity, fluid density and cyclic loadings induced from the turbulent wakes due to the Von Karman effect.
Problem identification and justification
The first step in research methodology is the problem identification which involves the background study for the research parameters, such as fatigue failure due to vortex shedding. In addition to that, the problem identification includes selecting the material from the ASME Performance Test Codes PTC 19.3 TW-2016 and the thermowell design. Furthermore, the properties for the chosen material, such as the endurance limit, yield stress, ultimate tensile stress, and density need to be identified, which in this case, is AISI 304 Stainless Steel.
Develop the finite element model (FEM)
The next step is to develop a thermowell CAD model.
The thermowell used in the study was designed in accordance with the dimensional limits and other parameters provided in the performance test code PTC 19.3 TW-2016. The engineering design tool that was used to develop the CAD model for the Finite Element Analysis (FEA) of the thermowell was AutoCAD 2021 Version 24, which is compatible with ANSYS Workbench as its drawings can be imported into the engineering simulation software to perform finite element simulation [11]. The geometric dimensions for the thermowell CAD model that was used for the validation step of the proposed fatigue life method can be viewed in Table 1.
After designing the thermowell model, the ANSYS Workbench software was used to generate the static structural system and the material properties for
the thermowell. The ANSYS Workbench software can be used for modal analysis, structural analysis, fatigue analysis along with other Computational Fluid Dynamics (CFD) applications [12]. The mesh was generated for the model as shown in Figure 4 before applying the boundary conditions, such as the fi xed support surfaces on the model. The mesh properties for the Minimum and Maximum thermowell can be seen in Table 2.
The steady drag force, oscillating in-line (drag) force and oscillating transverse (lift) forces were calculated.
The forces were then inserted into the model in the appropriate magnitude and directions for the analysis of the thermowell to be conducted.
Establishing procedure for fatigue life prediction The following step is to develop the procedure for fatigue life prediction. This involves using the S-N curve for the selected thermowell material, AISI 1040 Carbon Steel for the validation process and AISI 304 Stainless Steel for the parametric study to determine the number of cycles to failure in ANSYS 21.1. The tapered, flange-welded thermowell to be used for the simulation was designed in AutoCAD based on the geometrical dimensions from the research on the fatigue life of thermowell in supercritical condition by Diwakar et al. [5]. As part of the simulation of the cyclic loads and stresses on the thermowell, the material properties were adjusted in the engineering database of the ANSYS software for AISI 1040 Carbon Steel to match the thermowell material that was used in the past research for a reliable comparative analysis. The stress variations were used in correlation with the S-N curve for the equipment, stainless steel, and carbon steel to determine the number of cycles to failure for the operations of the thermowell.
The results from the proposed method using ANSYS for the natural frequencies, maximum stresses and Table 1 Thermowell dimensions based on Diwakar’s
research paper (all dimensions are in inches)
Parameters Symbol Values
Root diameter A 1.60
Tip diameter B 1.00
Fillet radius at the base b 0.00
Bore diameter d 0.26
Unsupported length L 16.89
Minimum wall thickness t 0.20
Figure 4 Hex dominant mesh generated for a) minimum and b) maximum thermowell
(a) (b)
Table 2 Mesh properties for minimum and maximum thermowell
Mesh
properties Minimum
Thermowell Maximum Thermowell Method Hex dominant
(hexahedral) Hex dominant (hexahedral)
Elements 6126 7466
Nodes 22945 24516
fatigue life were analysed, evaluated, and compared to the results from previous research papers to validate the accuracy of the data. For this purpose, Diwakar’s paper on the fatigue life of thermowell in supercritical condition was used to validate the results [5]. The results from the study can be summarised in Table 3.
If the values obtained were within ±10% percentage error of the previous study on thermowell fatigue life and the PTC 19.3 TW-2016, then the results from the proposed method have passed the criterion, given by:
Percentage
error (%) = |theoretical – experimental|
––––––––––––––––––––––
theoretical × 100% (6) where theoretical = results from Diwakar et al., experimental = results from ANSYS simulation.
However, if the results do not fulfil this criterion, the calculations in the method will have to be rectified until the number of cycles to failure have reached within 10%
of the estimated value from past studies. Subsequently, the parametric study of the varying fluid properties and the geometric dimension of the thermowell can be conducted.
Study of frequency
For validation purposes, the fatigue life calculations from past research need to be analysed and evaluated against the proposed fatigue life method in this research.
Prior to the fatigue life calculations, a frequency analysis needs to be performed to evaluate the percentage error of the first two-mode frequencies from past research and the proposed method to establish the dynamic characteristics of a vibrations system in terms of natural frequencies and mode shapes [13]. These parameters could then be used to formulate a mathematical model for the system’s dynamic behaviour.
Study of stress
The stress analysis is a numerical method used to calculate the maximum stress and strain in the thermowell that was subjected to cyclic loading conditions during pipeline operations [14]. It is an important finite element analysis method as the stress values are used to evaluate the damage accumulation and remaining life through the values of the S-N curve of the material structure. The maximum stress value was computed through the ANSYS simulation, and the location of the stress concentration zone was obtained, which was then compared to previous research to validate the results. The obtained stress results need to be below the maximum allowable stress for the static loading and below the fatigue allowable stress for the cyclic loading to ensure that the structural integrity of the thermowell is maintained and avoids fatigue stress.
Study of fatigue
The fatigue analysis is the focus of the research, which involves the use of stress-life cumulative damage models to predict the fatigue life of the structure.
The governing equations take into consideration the cumulative fatigue damage in which failure occurs after a number of loading cycles at a particular stress range [15]. From the S-N curve for AISI 1040 carbon steel, the endurance limit is 175 MPa. If the value of the maximum alternating stress is lower than the endurance limit, the thermowell would have an infinite number of cycles of life. It is conventionally accepted in the industry that an infinite life for a structure has a value of 1.0E+6 cycles or higher [6].
Conducting a parametric study and simulation The research work proceeded to conduct a parametric study and simulation of the thermowell performance against the fluid flow for various conditions. For the purposes of the parametric study, two thermowells of different dimensions were used to conduct the simulation using the ANSYS simulation software.
For reference, the thermowell with the minimum dimensional limits was labelled as Minimum Thermowell, while the thermowell with the maximum dimensional limits was labelled as Maximum Thermowell. The specific dimensions of the thermowells can be viewed in Table 4.
The parameter values for the fluid velocity and the fluid density of superheated steam were varied in the Table 3 Fatigue life results from Diwakar’s paper on
thermowell in supercritical conditions [5]
Parameters 109 Hz 490 Hz
Average velocity
(m/s) 6.3 12.6 28.3 56.6
Alternating stress
(ksi) 3.6 14.1 7.1 284.1
Cycles to failure 1.0E+6 1.0E+6 1.0E+6 5.0E+3
simulation. Firstly, for cases 1, 2 and 3, the fluid velocity was varied for the Minimum thermowell by 25 m/s, 35 m/s and 102 m/s, respectively, while the fluid density was maintained at 1.60 kg/m3. For cases 4, 5 and 6, the fluid density was varied at 0.5974 kg/m3, 1.6 kg/m3 and 8 kg/m3, while the fluid velocity was maintained at 40 m/s. The maximum stress fatigue life results from the ANSYS simulation were collected and analysed for the structure of the thermowell during various pipeline conditions. The simulation and data collection process were repeated for the Maximum thermowell, with the same cases and boundary conditions to analyse the effect of fluid properties and geometric properties on the fatigue life of the thermowell.
RESULTS AND DISCUSSION
Validation by frequency comparison
The fatigue life estimate in this study focuses on using the ANSYS simulation software to determine the natural frequencies, maximum stresses, and the number of cycles to failure for the thermowell during pipeline operations. Diwakar’s study on fatigue life of the thermowells during supercritical operations showed that the thermowell’s first two modes were 109 Hz and 490 Hz [5].
Through the ANSYS software, the modal analysis that was conducted on the designed thermowell based on dimensions, boundary conditions and cyclic loadings of Diwakar’s research, the computed value of the first two-mode frequencies for the mounted thermowell were 107.37 Hz and 498.13 Hz, respectively. The
number of modes to find for the modal analysis of the thermowell were adjusted in the ANSYS platform to be ten modes. However, only the first two modes of the analysis were relevant to the study. The percentage error of the two-mode frequencies from Diwakar’s research and the ANSYS software was calculated in Table 5.
The percentage error from the natural frequency calculations results in an average value of 1.58%, which is lower than the 10% passing criterion for the validation purpose of this method. This indicates that the ANSYS workbench software is a reliable tool that can be used to perform modal analysis. The stress analysis can be used to study the maximum stresses exerted on the thermowell by the pipeline operating conditions based on the performance test codes.
Validation by stress comparison
The stress analysis was performed using the ANSYS platform to obtain the maximum stress value based on the fluid properties and cyclic loading on the thermowell as shown in Table 2. The fatigue life results from Diwakar’s research paper on the thermowells in supercritical conditions. The forces acting on the thermowell from Diwakar’s research, the results from the stress analysis and the percent error from the ANSYS simulation can be seen in Table 6.
The results from the stress analysis of the thermowell based on the ANSYS simulation and the research paper by Diwakar et al. were evaluated. The location of the stress concentration zone was consistent with the research paper written by El-Batahgy and Fathy on the fatigue failure of the thermowells in feed gas supply downstream, where the crack initiation site of the fatigue failure was at the outer surface of the thermowell neck [16]. The average percent error calculated for the maximum stresses between Table 4 Minimum and maximum thermowell dimensions
for parametric study (all dimensions are in centimetres) Parameters Symbol Minimum
Thermowell Maximum Thermowell
Root diameter A 0.92 4.65
Tip diameter B 0.92 4.65
Fillet radius at
base b 0.00 0.00
Bore diameter d 0.32 2.10
Unsupported
length L 6.35 60.96
Minimum wall
thickness t 0.3 1.28
Table 5 Percentage error of natural frequency calculation Parameters 1st Mode 2nd Mode Frequency from Diwakar,
(theoretical) 109 Hz 490 Hz
Frequency from ANSYS,
(experimental) 107.37 Hz 498.13 Hz
Percent error (%) 1.50 1.66
Average percentage error (%) 1.58
the theoretical value from Diwakar’s study and the experimental value from the ANSYS simulation is 1.48%.
This indicates that the stress analysis performed has high accuracy and that the proposed fatigue life estimation using the ANSYS 21.1 software has high potential. . Before proceeding to the parametric study, the fatigue analysis for the thermowell based on Diwakar’s study still needed to be performed to validate the proposed method using ANSYS Workbench for fatigue life estimation.
Validation by fatigue comparison
The fatigue analysis was performed using the ANSYS platform to obtain the number of cycles to failure based on the fatigue life results from Diwakar’s research paper on the thermowells in supercritical conditions. To calculate the fatigue life of the thermowell under the
Table 6 Stress analysis and percent error of Diwakar’s study against ANSYS results
Parameters 109 Hz 490 Hz
Average velocity (m/s) 6.3 12.6 28.3 56.6
Steady state drag force (N) 630 2519 12709 50837
Oscillating in-line (drag) force (N) 45 180 908 3631
Oscillating transverse (lift) force (N) 450 1800 9078 36312
Diwakar’s alternating stress (ksi) 3.6 14.1 71.0 284.1
Diwakar’s alternating stress (MPa) 25.8 97.2 489.5 1958.8
ANSYS alternating stress (MPa) 24.9 99.4 501.5 2005.9
Percent error (%) 0.12 2.25 2.44 2.40
Average percent error (%) 1.81
fl uid properties and cyclic loading as shown in Table 7, the S-N curve for AISI 1040 carbon steel was used. The fatigue life and corresponding maximum stress for 56.6 m/s fl uid velocities is shown in Figure 5.
The fatigue analysis results using the proposed fatigue life estimation using ANSYS for the thermowell under the same fluid properties, geometric dimensions, and boundary conditions from Diwakar’s study of the thermowells in supercritical operations are summarised in Table 7.
For AISI 1040 carbon steel, 1.0E+6 cycles are conventionally accepted as an infi nite life cycle. The number of cycles for fl uid velocities of 6.3 m/s and 12.6 m/s are greater than 1.0E+6, which indicates that thermowell life at those conditions are infi nite. The
Figure 5 (a) Maximum stress of 2005.9 MPa and (b) fatigue life of 5013 cycles for 56.6 m/s
(a) (b)
results from the fatigue analysis of the thermowell based on the ANSYS simulation and the research paper by Diwakar et al. were evaluated. The average percent error calculated for the fatigue life between the theoretical value from Diwakar’s study and the experimental value from the ANSYS simulation is 0.11%.
This indicates that the fatigue analysis performed has high accuracy and that the proposed fatigue life estimation using the ANSYS Workbench 21.1 software has been validated as a reliable method to estimate the number of cycles to failure. The parametric study can be conducted to investigate the effects of fluid properties such as fluid velocity and fluid density on the fatigue life of the thermowell.
Parametric study
The next step of the methodology is to conduct a parametric study, which involves varying the properties of the pipeline fluid and thermowell dimensions for fatigue analysis. This study is used to investigate the effect of the fluid and thermowell properties on the fatigue life of the thermowells under investigation. The fluid used in the study is superheated steam with flow velocities based on average velocity ranges for steamed systems [17].
For this purpose, two thermowells were designed based on the dimensional limits from the thermowell performance test codes. The fatigue analysis was performed for both the Minimum thermowell and Maximum thermowell for Cases 1, 2, 3, 4, 5 and 6. The fatigue analysis was first conducted on the Minimum thermowell.
Minimum thermowell dimensional limit design Prior to the fatigue life estimation, the frequency analysis was performed to obtain the natural frequency of the designed thermowell under study.
For safe operation, the vortex shedding frequency
needed to be lower than the natural frequency of the thermowell by a factor of 0.4 to avoid resonance and Fluid-Induced Vibrations (FIV) [5]. The first mode obtained from the ANSYS simulation was 1560 Hz while the second mode was 9135 Hz.
In addition to that, if the vortex shedding frequency was larger than the natural frequency by a factor of 1.2, the thermowell would be operating in supercritical conditions. The vortex shedding frequency can be calculated from the thermowell geometric dimensions and fluid properties. From the modal analysis, the calculated vortex shedding frequency that was below the frequency criterion was only applicable for Case 1. Furthermore, it was highly likely that the thermowell would be in supercritical operation for Case 3 and susceptible to resonance and FIV. The maximum stress and the fatigue life for Case 1 can be seen in Figure 6. The stress and fatigue analysis results for the Minimum thermowell subjected to the fluid properties by Case 1 to Case 6 are summarised in Table 8.
The highest number of cycles to failure for the Minimum thermowell under the cyclic loading was 8898 cycles, which was for Case 1. The properties of the processing fluid for the following conditions in Case 1 exerted a maximum stress value of 869 MPa. The maximum stress value was greater than the endurance limit of the material; hence fatigue stress was subjected to the thermowell structure.
The lowest number of cycles to failure for the Minimum thermowell was 0 cycles, which was for Case 3, Case 5, and Case 6. The obtained maximum stresses significantly exceeded the endurance limit, maximum allowable stresses, and allowable fatigue stress, which resulted in the structural failure of the thermowell under the applied loading and pipeline operations, resulting in 0 cycles to failure.
Table 7 Fatigue analysis and percent error of Diwakar’s study against ANSYS results
Parameters 109 Hz 490 Hz
Average velocity (m/s) 6.3 12.6 28.3 56.6
Diwakar’s cycles to failure 1.0E+32 1.00E+12 13000 5000
ANSYS cycles to failure 1.0E+32 9.98E+11 12996 5013
Percent error (%) 0 0.15 0.03 0.26
Average percent error (%) 0.11
Maximum thermowell dimensional limit design The process was repeated for the thermowell maximum dimensional limit CAD model. The modal analysis was performed for the parametric study to obtain the natural frequency of the Maximum thermowell. For safe operations, the vortex shedding frequency needed to be lower than the natural frequency of the thermowell by a factor of 0.4 to avoid resonance and FIV [5]. The fi rst mode obtained from the ANSYS simulation was 53.45 Hz while the second mode was 326.56 Hz.
From the modal analysis, the calculated vortex shedding frequency below the frequency criterion was only applicable for Case 1. Furthermore, it was likely that the thermowell would be in supercritical operation for Case 3 and susceptible to resonance and FIV. The maximum stress and the fatigue life for Case 1 can be seen in Figure 7. The stress and fatigue analysis results
for the Maximum thermowell subjected to the fl uid properties by Case 1 to Case 6 can be summarized in Table 9.
The number of cycles to failure for the Maximum thermowell under the cyclic loading for Case 1 to Case 6 was 0 cycles. The properties of the processing fl uid for the following conditions in the fatigue analysis exerted a maximum stress value of 58516 MPa, which was signifi cantly greater than the endurance limit of the material. As a result, the maximum stresses signifi cantly exceeded the maximum allowable stresses and allowable fatigue stress, which resulted in the structural failure of the thermowell under the applied loading and pipeline operations, resulting in 0 cycles to failure.
From the parametric study, the higher the fluid velocity and density, the higher the likelihood and occurrences of resonance, the lower the number of cycles to failure. Similarly, the higher the natural Figure 6 (a) Maximum stress of 869.32 MPa and (b) fatigue life of 8898 cycles for Case 1
(a) (b)
Table 8 Fatigue analysis of minimum thermowell for Case 1 to Case 6
Parameters Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
Fluid velocity (m/s) 25 35 102 35 35 35
Fluid density (kg/m3) 1.6 1.6 1.6 0.5974 2.0 8.0
Steady state drag force (N) 1.33E+03 2.61E+03 2.22E+04 9.74E+02 3.26E+03 1.30E+04 Oscillating drag force (N) 9.51E+01 1.86E+02 1.58E+03 6.96E+01 2.33E+02 9.32E+02 Oscillating lift force (N) 9.51E+02 1.86E+03 1.58E+04 6.96E+02 2.33E+03 9.32E+03
Maximum stress (Pa) 8.69E+08 1.71E+09 1.45E+10 6.37E+08 2.13E+09 8.50E+09
Number of cycles 8.90E+03 5.60E+03 Fail at 1 1.10E+04 Fail at 1 Fail at 1
frequency of the thermowell, the lower the likelihood and occurrences of resonance; hence, the higher the number of cycles to failure. This is because the natural frequency of the thermowell was larger than the vortex shedding frequency induced by the cyclic loading of the processing fluid, which reduced the likelihood and occurrence of resonance and fluid-induced vibrations.
It is recommended for the thermowell to be redesigned to obtain a high natural frequency within the limits of the PTC 19.3 TW-2016 to avoid the occurrence of resonance with the vortex shedding frequency during pipeline operations. The value of the vortex shedding frequency for the applied loading should be lower than the natural frequency by a factor of 0.4 to ensure safe operations [5]. The supercritical operation of the thermowell should also be avoided as it becomes susceptible to fatigue stress and fluid-induced
vibrations, which could potentially result in fracture or fatigue failure.
CONCLUSION AND RECOMMENDATION
In conclusion, with the aid of the S-N curve for the thermowell material and the research paper regarding thermowell fatigue life estimate during supercritical operations by Philip Diwakar in 2018, the percent error calculated by comparing the results from the proposed method and Diwakar’s study was 0.11%. After the validation of the proposed fatigue life prediction model using ANSYS, the parametric study of the thermowell model was conducted. The results of the parametric study showed that the Minimum thermowell performed better for all the load cases, which obtained a maximum number of cycles to failure of 8898 cycles for a maximum stress value of 869 MPa. The higher the fluid velocity and Figure 7 (a) Maximum stress of 3510.5 MPa and (b) fatigue life of 0 cycles for Case 1
(a) (b)
Table 9 Fatigue analysis of maximum thermowell for Case 1 to Case 6
Parameters Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
Fluid velocity (m/s) 25 35 102 35 35 35
Fluid density (kg/m3) 1.6 1.6 1.6 0.5974 2.0 8.0
Steady state drag force (N) 6.35E+04 1.25E+05 1.06E+06 4.65E+04 1.56E+05 6.23E+05 Oscillating drag force (N) 4.54E+03 8.89E+03 7.55E+04 3.32E+03 1.11E+04 4.45E+04 Oscillating lift force (N) 4.54E+04 8.89E+04 7.55E+05 3.32E+04 1.11E+05 4.45E+05
Maximum stress (Pa) 3.51E+09 6.90E+09 5.85E+10 2.57E+09 8.61E+09 3.44E+10
Number of cycles Fail at 1 Fail at 1 Fail at 1 Fail at 1 Fail at 1 Fail at 1
density, the higher the likelihood and occurrences of resonance, the lower the number of cycles to failure.
For the recommendations, the results for the fatigue analysis could be further improved by incorporating historical data for the dynamic loading exerted on the thermowell based on field data of the cyclic stress over a period of operation. The future work would result in a non-constant amplitude load and non-zero mean stress, which increases the accuracy of the proposed fatigue life prediction model. Furthermore, this could reduce time on service, repair, and maintenance as the thermowells would be able to be replaced before it reaches the end of its useful life to avoid fatigue failure and unscheduled downtimes that ultimately improve facilities’ efficiency operations.
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