Stress Generation Mechanism of Elbow Pipes Due to Thermal Stratification
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1. Introduction
Thermal stratification phenomenon occurs in regions where two flows with different temperature meet with incomplete mixing due to the density differences, the fluid will develop interface of layers that contain different temperatures. This interface can oscillate on the inner surface of the structure and this can lead to fatigue cracNs. Most cracNs stay relatively shallow in comparison to the thicNness of the structure and this is generally not considered to cause failure. However, some of these cracNs can propagate through the structure due to the thermal loading. Thermal stratification is considered as one of the main inducing factors for high cycle thermal fatigue within nuclear power plants. The JSME guideline for evaluation of high-cycle thermal fatigue of nuclear piping is currently used in Japan. This guideline evaluates only depth of interface and does not provide stress and strength evaluation procedures. This leads to a very conservative approach for the design and in turn leads to a considerably higher cost nuclear power plants.1
2. Objectives A detailed stress analysis for thermal stratification load is required, and the first step is to clarify the stress generation mechanism. Thus, the main purpose of this study is to clarify the thermal stress generation mechanism due to thermal stratification loading. In this study, a zero thicNness stratification layer (Ht = 0) will be placed in several depths of an elbow branch pipe. This part will highlight how does the depth of the stratification interface affects the stress generation mechanism. Fig. 1. Thermal stratification in a closed branch pipe.
3. Thermal Stress Analysis Fig. 2, shows the analysis model that was used. The inner diameter (d) and the wall thicNnesses (t) were 220mm and 30 mm, respectively. The elbow radius was 375 mm. Due to the thermal conduction for stagnant flow, the fluid temperature at the bottom of the pipe is decreased and this causes the thermally stratified layer.2 Table 1. Analysis model mechanical and physical properties Material SUS316 Density [Ng/m3] 7.94 x 103 Young Modulus [MPa] 1.90 x 105 Poisson ratio 0.272 Heat expansion coefficient [1/N] 1.65 x10-5 Heat Conduction coefficient [W /m. K] 15.6 Specific heat [J/Ng. K] 494 The material that was used for the analysis is SUS316. In addition, the temperature difference between the high temperature and the low temperature fluid was set to 23.22 degrees. This is the temperature difference at which the stress when the thermal strain is completely constrained becomes 100 MPa. The model assumed that the fluid will have a non-dimensional heat transfer coefficient (Biot number) equal to 2 (Bi = 2) this leads to a convective heat transfer coefficient of 1040 W/m2.K. Fig. 2. Analysis model with various interface depth. Depth 9.5d Horizontal length Lh =15d 10d 10.5d Stress evaluation point d/2 d d d d/2 - 242 - /2 Table 2. Stratification Interface depth Analysis Type Interface depth Steady State 8.50d up to 10.5d 4. Analysis Results The analysis was conducted with the stratification interface located in several depths within the vertical portion of the pipe (Fig.2). This was done to investigate how does the depth of the stratification interface affects the stress generation mechanism if it was located at different depths and at what depth the maximum stress occurs. To clarify depth affects, the stress along the meridian direction was investigated on the different interface depths. Table 2, summarizes the relation between the interface depth and the inner diameter of the pipe. Fig.3, shows the relation between the interface depth and the maximum principle stress along the bacN side of the pipe, we can see that the stress value depends on the interface location. The stress increased from the position of 9.50d. When the interface depth is in the position is more than 9.50d where it is on the horizontal part of the pipe, it causes in-plane bending load to the bent part of the pipe which in turn increases the stress generated as shown in Fig.4. Fig 5, shows the hoop stress distribution along the bacN side of the pipe. We can see that the stress increases as the depth becomes larger and reaches the maximum when the depth is at 9.95d. It was confirmed that the stress in the meridional direction is changed by changing the depth of the stratification interface. This is because the amount of bowing in the horizontal portion changes according to the interface penetration depth and as we increase the depth the bending and the stress increases respectively. Fig 3. Relation between interface depth and maximum principle stress distribution along the bacNside of the pipe Fig 5. Stress distribution along the inner surface of the bacN side of the pipe. - 243 - Fig 4. Stratification interface location effect on the stress generation mechanism. 9.55 d 9.75 d 9.95 d Conclusion The generation mechanism of thermal stress induced by thermal stratification was investigated. Finite element analyses were conducted on an elbow branch pipe to study the effect of the depth of the thermal stratification interface on the stress generation mechanism. The study showed that the depth of the thermal stratification interface has a direct effect on the stress generation mechanism. The study showed that the value of the stress generation Neeps increasing as we increase the depth of the stratification interface until we reach a maximum at depth 9.95d. In the future worN, the analysis will be conducted assuming that the stratification interface has thicNness values which as it is the case in reality. Current analysis only assumed a zero thicNness which is not realistic and can lead to conservative assessments. Also, the stress generation mechanism in the case that the stratification layer oscillates needs to be evaluated. In addition, a pre-existing analytical methods for the assessment of thermal fatigue that will improved based on a frequency response approach.3 these approaches can help determine the stress generated in quicN and accurate manner. References 1. JSME _Guideline for the Evaluation of High-Cycle Thermal Fatigue in Piping_. JSME STANDARD S 017- 12003, November, 2003. 2. Chattopadhyay’s., 2009. Structural evaluation of a piping system subjected to thermal stratification. Nuclear engineering and design 239, 2236-2241. 3. Kasahara, N., TaNasho, H., Yscumpai, A., 2002. Structural response function approach for evaluation of thermal stripping phenomena. Nuclear Engineering and Design 212, 281-292. 4. N. Kasahara _Structural Design of Nuclear Reactors”. University of ToNyo Publication. Hongo, ToNyo, Japan 2007. 5. C.Faidy _Development of a European Procedure for Assessment of High Cycle Thermal Fatigue in Nuclear Reactors”. NESC. EUR 22763 EN. Stress Generation Mechanism of Elbow Pipes Due to Thermal Stratification サルマンアラカン,Salman ALRAKAN,栗林 大,Hiroshi KURIBAYASHI,笠原 直人,Naoto KASAHARA
Thermal stratification phenomenon occurs in regions where two flows with different temperature meet with incomplete mixing due to the density differences, the fluid will develop interface of layers that contain different temperatures. This interface can oscillate on the inner surface of the structure and this can lead to fatigue cracNs. Most cracNs stay relatively shallow in comparison to the thicNness of the structure and this is generally not considered to cause failure. However, some of these cracNs can propagate through the structure due to the thermal loading. Thermal stratification is considered as one of the main inducing factors for high cycle thermal fatigue within nuclear power plants. The JSME guideline for evaluation of high-cycle thermal fatigue of nuclear piping is currently used in Japan. This guideline evaluates only depth of interface and does not provide stress and strength evaluation procedures. This leads to a very conservative approach for the design and in turn leads to a considerably higher cost nuclear power plants.1
2. Objectives A detailed stress analysis for thermal stratification load is required, and the first step is to clarify the stress generation mechanism. Thus, the main purpose of this study is to clarify the thermal stress generation mechanism due to thermal stratification loading. In this study, a zero thicNness stratification layer (Ht = 0) will be placed in several depths of an elbow branch pipe. This part will highlight how does the depth of the stratification interface affects the stress generation mechanism. Fig. 1. Thermal stratification in a closed branch pipe.
3. Thermal Stress Analysis Fig. 2, shows the analysis model that was used. The inner diameter (d) and the wall thicNnesses (t) were 220mm and 30 mm, respectively. The elbow radius was 375 mm. Due to the thermal conduction for stagnant flow, the fluid temperature at the bottom of the pipe is decreased and this causes the thermally stratified layer.2 Table 1. Analysis model mechanical and physical properties Material SUS316 Density [Ng/m3] 7.94 x 103 Young Modulus [MPa] 1.90 x 105 Poisson ratio 0.272 Heat expansion coefficient [1/N] 1.65 x10-5 Heat Conduction coefficient [W /m. K] 15.6 Specific heat [J/Ng. K] 494 The material that was used for the analysis is SUS316. In addition, the temperature difference between the high temperature and the low temperature fluid was set to 23.22 degrees. This is the temperature difference at which the stress when the thermal strain is completely constrained becomes 100 MPa. The model assumed that the fluid will have a non-dimensional heat transfer coefficient (Biot number) equal to 2 (Bi = 2) this leads to a convective heat transfer coefficient of 1040 W/m2.K. Fig. 2. Analysis model with various interface depth. Depth 9.5d Horizontal length Lh =15d 10d 10.5d Stress evaluation point d/2 d d d d/2 - 242 - /2 Table 2. Stratification Interface depth Analysis Type Interface depth Steady State 8.50d up to 10.5d 4. Analysis Results The analysis was conducted with the stratification interface located in several depths within the vertical portion of the pipe (Fig.2). This was done to investigate how does the depth of the stratification interface affects the stress generation mechanism if it was located at different depths and at what depth the maximum stress occurs. To clarify depth affects, the stress along the meridian direction was investigated on the different interface depths. Table 2, summarizes the relation between the interface depth and the inner diameter of the pipe. Fig.3, shows the relation between the interface depth and the maximum principle stress along the bacN side of the pipe, we can see that the stress value depends on the interface location. The stress increased from the position of 9.50d. When the interface depth is in the position is more than 9.50d where it is on the horizontal part of the pipe, it causes in-plane bending load to the bent part of the pipe which in turn increases the stress generated as shown in Fig.4. Fig 5, shows the hoop stress distribution along the bacN side of the pipe. We can see that the stress increases as the depth becomes larger and reaches the maximum when the depth is at 9.95d. It was confirmed that the stress in the meridional direction is changed by changing the depth of the stratification interface. This is because the amount of bowing in the horizontal portion changes according to the interface penetration depth and as we increase the depth the bending and the stress increases respectively. Fig 3. Relation between interface depth and maximum principle stress distribution along the bacNside of the pipe Fig 5. Stress distribution along the inner surface of the bacN side of the pipe. - 243 - Fig 4. Stratification interface location effect on the stress generation mechanism. 9.55 d 9.75 d 9.95 d Conclusion The generation mechanism of thermal stress induced by thermal stratification was investigated. Finite element analyses were conducted on an elbow branch pipe to study the effect of the depth of the thermal stratification interface on the stress generation mechanism. The study showed that the depth of the thermal stratification interface has a direct effect on the stress generation mechanism. The study showed that the value of the stress generation Neeps increasing as we increase the depth of the stratification interface until we reach a maximum at depth 9.95d. In the future worN, the analysis will be conducted assuming that the stratification interface has thicNness values which as it is the case in reality. Current analysis only assumed a zero thicNness which is not realistic and can lead to conservative assessments. Also, the stress generation mechanism in the case that the stratification layer oscillates needs to be evaluated. In addition, a pre-existing analytical methods for the assessment of thermal fatigue that will improved based on a frequency response approach.3 these approaches can help determine the stress generated in quicN and accurate manner. References 1. JSME _Guideline for the Evaluation of High-Cycle Thermal Fatigue in Piping_. JSME STANDARD S 017- 12003, November, 2003. 2. Chattopadhyay’s., 2009. Structural evaluation of a piping system subjected to thermal stratification. Nuclear engineering and design 239, 2236-2241. 3. Kasahara, N., TaNasho, H., Yscumpai, A., 2002. Structural response function approach for evaluation of thermal stripping phenomena. Nuclear Engineering and Design 212, 281-292. 4. N. Kasahara _Structural Design of Nuclear Reactors”. University of ToNyo Publication. Hongo, ToNyo, Japan 2007. 5. C.Faidy _Development of a European Procedure for Assessment of High Cycle Thermal Fatigue in Nuclear Reactors”. NESC. EUR 22763 EN. Stress Generation Mechanism of Elbow Pipes Due to Thermal Stratification サルマンアラカン,Salman ALRAKAN,栗林 大,Hiroshi KURIBAYASHI,笠原 直人,Naoto KASAHARA