atw - International Journal for Nuclear Power | 05.2020

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atw Vol. 65 (2020) | Issue 5 ı May RESEARCH AND INNOVATION 274 | Fig. 6. Temperature Contours of structure and fluid. Results Considering the results of the sensitivity analysis of the mesh it can be seen that the results of Mesh id 1 and Mesh id 2 have converged, therefore mesh id 2 was used to perform further analysis in order to reduce the computational cost. T structure (l line , T fluid ) = p 00 + p 10 l line + p 01 T fluid + p 20 l line 2 + p 11 l line T fluid + p 02 T fluid 2 Line 1 p 00 = -276.7 (-652.7, 99.2) p 10 = -0.8854 (-1.385, -0.3856) p 01 = 7.531 (3.653, 11.41) p 20 = -9.293e-05 (-0.0001075, -7.835e-05) p 11 = 0.00458 (0.002426, 0.006734) p 02 = -0.02453 (-0.03519, -0.01387) Line 2 p 00 = -1222 (-2119, -324.9) p 10 = -0.5261 (-0.7273, -0.325) p 01 = 14.59 (6.563, 22.61) p 20 = -3.921e-05 (-4.695e-05, -3.147e-05) p 11 = 0.002607 (0.001698, 0.003516) p 02 = -0.0366 (-0.05454, -0.01866) Line 3 p 00 = 228.1 (191, 265.2) p 10 = 0.04682 (-0.03542, 0.1291) p 01 = -0.1856 (-0.3752, 0.004024) p 20 = -0.0001034 (-0.0001209, -8.582e-05) p 11 = 0.0005824 (0.0002221, 0.0009427) p 02 = -0.0005446 (-0.001159, 6.955e-05) Line 4 p 00 = 204.4 (174.8, 234) p 10 = -0.1004 (-0.1327, -0.06796) p 01 = 0.657 (0.3585, 0.9555) p 20 = -6.994e-05 (-7.681e-05, -6.307e-05) p 11 = 0.001042 (0.0008915, 0.001193) p 02 = -0.003653 (-0.004466, -0.002839) | Tab. 3. Temperature relations. Goodness of fit: SSE: 2048 R-square: 0.9404 Adjusted R-square: 0.9352 RMSE: 5.942 Goodness of fit: SSE: 156.3 R-square: 0.9708 Adjusted R-square: 0.9683 RMSE: 1.642 Goodness of fit: SSE: 3139 R-square: 0.9134 Adjusted R-square: 0.9059 RMSE: 7.357 Goodness of fit: SSE: 342.5 R-square: 0.9832 Adjusted R-square: 0.9818 RMSE: 2.43 As we are interested in the effects on structure under surge line operational conditions we first carried out the conjugate heat transfer analysis on the pipe, during this analysis the effects of both convection of liquid and the consequent heat conduction with the structure are considered and we are provided with a comprehensive temperature profile of the structure ,which considering the thickness of pipe is necessary for an accurate analysis as the surface temperature of the fluid doesn’t provides the complete picture. These temperature are then exported to ANSYS mechanical where further analysis on the stress resulting from these conditions were calcu lated, further the deformations as a result of the stress were also com puted. Temperature of Structure The temperature of the surgeline surface is given in Figure 5. It can be observed from the graph that at the starting point of plot a severe case of thermal stratification is present, as the O° line experiences lower temperature while 180° line is sub jected to higher temperature. This is as expected and has been widely reported in the literature. As the section near the hot leg is the location where the mixing of fluids takes place. As we move upwards along the pipe away from the main pipe the thermal stratification reduces and at 0.5 m distance all the temperature achieves the uniform temperature, which is the temperature of the fluid entering from the pressurizer. Temperature Relations The structure temperature is the temperature we are interested in however in the working conditions the temperature sensors are present in the fluid instead of the structure so it is useful to have a relation that gives an approximate temperature for the structure at a particular point if temperature of the fluid is available from the sensors. Using the simulated data a second order equation was developed that provides the temperature of the structure corresponding to the line length and the temperature of fluid at that point and are given as follows, the co-efficient provided are with 95 % confidence interval, Table 3. Equivalent stress To compute the stress in the structure the thermal temperature were loaded onto the structure, as we are only interested in the thermal stress the Research and Innovation Fluid Structure Interaction Analysis of a Surge-line Using Coupled CFD-FEM ı Muhammad Abdus Samad, Xiang bin li and Hong lei Ai
atw Vol. 65 (2020) | Issue 5 ı May mechanical stresses due to fluid flow were ignored. The sections of surge line where it is connected with the pressurizer and main pipe are con sidered as fixed supports for this analysis. The results of stress can be divided into three regions broadly, the first section is the section that is near the main pipe, this section experiences very high stress as expected, we can also see that in Figure 7, where180° line experiences lower stress as compared to the other lines however after reaching a minimum value it starts to rise and then we see that all the lines having a same general trend with 180° line and 0° line experiencing more stress than 90° line and 270° line. In section 2 graph this can be observed even more clearly as we can see a clear division between the stresses experienced by one section of the pipe as compared to the other section. In section 3 we observe that the previous trend reaching the end at 14 m where the pipe experiences a sharp turn and a new trend of extremely high stress is observed due to the incoming stream of hot water from the pressurizer. Deformation In the total Figure 8 we can observe the deformation experienced by the structure under the above mention stresses, the deflection is mostly observed in the middle region of the pipe which is the unsupported region of the pipe, in our model this region was considered as unsupported but in an actual plants these regions movements are usually limited by supporting structures. Conclusions The thermal stresses in the surge lines due to thermal stratification is a widely observed phenomenon, in this paper a steady state analysis of the flow in surge line was conducted to analyze a long term outlook of surge line under continued stress, the results are concluded in the flowing points. 1. The stresses in the surge line are present in the steady state especially in the section of the surge line near the main pipe, these stress exists due to the thermal stratification where the mixing of hot and cold water takes place. 2. The equivalent stress show that as we move further away from the hot leg of the main pipe the stresses first decrease and then start to reach a very high value near the pressurizer opening, this is due to the extremely high temperature at the inlet of the surgeline. | Fig. 7. Equivalent stress in surge line. | Fig. 8. Deformation in surge line. 3. The deformation resulting from these stresses effect mostly the middle of the surge line pipe as there is no support between the endpoints in a considerably large structure, for practical purposes support of some kind are recommended in between the pressurizer and the main pipe. 4. An approximation of the outer surface structure temperature based on the temperature of fluid at the boundary was also calculated from the simulated results, this can be useful in practical implementation where fluid data from sensors is generally available. References [1] NEA, 2005. Thermal Cycling in LWR Components in OECD-NEA Member Countries, NEA/CSNI/R(2005)8, NEA CSNI, CSNI Integrity and Ageing Working Group. Organization for Economic Co-operation and Development. [2] Grebner, H. and Höfler, A. (1995). Investigation of stratification effects on the surge line of a pressurized water reactor. Computers & Structures, 56(2-3), pp.425-437. [3] Ensel, C., Colas, A. and Barthez, M. (1995). Stress analysis of a 900 MW pressurizer surge line including stratification effects. Nuclear Engineering and Design, 153(2-3), pp.197-203. [4] Kumar, R., Jadhav, P., Gupta, S. and Gaikwad, A. (2014). Evalu a- tion of Thermal Stratification Induced Stress in Pipe and its Impact on Fatigue Design. Procedia Engineering, 86, pp.342-349. [5] Kang, D., Jhung, M. and Chang, S. (2011). Fluid-structure interac tion analysis for pressurizer surge line subjected to thermal stratification. Nuclear Engineering and Design, 241(1), pp.257-269. [6] Zhang, Y. and Lu, T. (2017). Unsteady-state thermal stress and thermal deformation analysis for a pressurizer surge line subjected to thermal stratification based on a coupled CFD-FEM method. Annals of Nuclear Energy, 108, pp.253-267. [7] Similar shaped models [7] Cai, B., Gu, H., Weng, Y., Qin, X., Wang, Y., Qiao, S. and Wang, H. (2017). Numerical investigation on the thermal stratification in a pressurizer surge line. Annals of Nuclear Energy, 101, pp.293-300. [8] Baik, S. (n.d.). [online] Inis.iaea.org. Available at: https://inis.iaea.org/collection/NCLCollectionStore/_ Public/32/068/32068795.pdf [Accessed 19 Dec. 2018]. [9] Schuler, X., & Herter, K.H. (2004). Thermal fatigue due to stratification and thermal shock loading of piping. 30 MPA-Seminar 'Safety and reliability in energy technology' in conjunction with the 9th German-Japanese seminar Vol 1 (Papers 1-26), (p. 464). [10] NEA, 2005. Thermal Cycling in LWR Components in OECD-NEA Member Countries,NEA/CSNI/R(2005)8, NEA CSNI, CSNI Integrity and Ageing Working Group. Organization for Economic Co-operation and Development. [11] Grebner, H. and Höfler, A. (1995). Investigation of stratification effects on the surge line of a pressurized water reactor. Computers & Structures, 56(2-3), pp.425-437. [12] Ensel, C., Colas, A. and Barthez, M. (1995). Stress analysis of a 900 MW pressurizer surge line including stratification effects. Nuclear Engineering and Design, 153(2-3), pp.197-203. [13] Sang-Nyung Kim, Seon-Hong Hwang,Ki-Hoon Yoon. Experiments on the Thermal Stratification in the Branch of NPP Journal of Mechanical Science and Technology ( KSME Int. J.), 2005, 19(5):1206-1215 [14] Sang-Nyung Kim, Cheol-Hong Kim, Bum-Su Youn, Hag-Ki Yum, Experiments on Thermal Stratification in Inlet Nozzle of Steam Generator, Journal of Mechanical Science and Technology, 2007(21):654-663 [15] T.H.Liu, E.L.Cranford. An Investigation of Thermal Stress Ranges Under stratification Loadings [J]. Transactions of the ASME 326/ Vol. 113, 1991 Authors Muhammad Abdus Samad Xiang bin li School of Nuclear Science and Engineering North China Electric Power University Beijing, China Hong lei Ai Nuclear Power Institute of China Sichuan, China RESEARCH AND INNOVATION 275 Research and Innovation Fluid Structure Interaction Analysis of a Surge-line Using Coupled CFD-FEM ı Muhammad Abdus Samad, Xiang bin li and Hong lei Ai
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