Research About Transient Inverse Heat Conduction Problem With Multi-variables Based On Conjugate Gradient Methods And Applications In Nuclear Power

With the development of social economy, the energy demand in China is growing. Nuclear power as a kind of efficient and clean energy is booming.And the topic of nuclear safety has become the subject of much attention. In the pipeline of nuclear power, the temperature fluctuations resulting from the mixture of cold and hot fluid or temperature stratification often occur. The temperature fluctuations in pipeline may induce thermal fatigue failure, and then lead to leakage in nuclear power station. Take the surge line with temperature stratification for example, the nuclear power countries, including China, are required to complete thermal stratification analysis and risk assessment of surge line, regardless the nuclear power station is in service or proposed. It's enough to see the importance of pipe fatigue failure caused by thermal stratification.Due to the demand of structural completeness, it is not allowed to install thermocouples in the pipeline system of the nuclear power directly or through the open pore to measure the fluid temperature or inner wall temperature.Therefore a kind of indirect and nondestructive temperature measurement or evaluation method is needed to explore to obtain the temperature of the inner wall. Transient Inverse Heat Conduction Problem with Multi-variable is proposed in this article to analyze the temperature fluctuations of the classical pipeline in nuclear power. That is using the easily measured temperature of outer wall to estimate fluid temperature, inner wall temperature and the convective heat transfer coefficient between them based on conjugate gradient methods (CGM). And the results also include the transient temperature field of entire pipe.The following aspects are mainly studied in this article:(1) Two- and three- dimensional direct heat conduction problem (DHCP)and transient inverse heat conduction problem (IHCP) with multi-variables in circular pipe were studied. The solving models of two- and three- dimensional DHCP were constructed based on finite element method (FEM). The verifications of grid independence and sensitive analysis of time step were done, and the results provided theoretical basis for the arrangement scheme of measuring point and the determination of temperature acquisition frequency.The models of transient IHCP with multi-variables were constructed based on CGM, and the concrete procedures of implementation of the estimation of the third kind boundary condition on the inner wall through using the measured temperature on the outer wall were given.(2) The experimental calibration and results analysis about transient IHCP with multi-variables have been done. The test bench about inverse heat conduction problem (IHCP) based on the principle of thermal stratification was built. The model and inversion results of IHCP have been verified and improved based on the experimental results. The influence of the number of the measuring points on the calculated results was investigated. And the results show that the more measuring points, the higher computing accuracy.However when the measuring points reduce to 2 in the two-dimensional IHCP and 6 in the three-dimensional IHCP, the average relative error reaches 4.3%and 6.8%, respectively. It is can be concluded from the experimental and calculated results that the changing laws of thermal boundary layer thickness on different measuring points with the change of cold water flow presents different. The thermal boundary layer thickness of most measuring points becomes thick with the increase of cold water flow. The temperature distribution of pipe wall also changes obviously with the change of cold water flow.(3) The third kind boundary conditions on the inner wall of the pressurizer surge lines were estimated based on the two-dimensional transient.Four cross sections of the surge line were estimated using the calibrated model of two-dimensional transient IHCP with multi-variables. It is can be seen from the calculated results that the differences in locations of the cross sections lead to the differences in temperature distribution and temperature fluctuations. The maximum temperature points of 24D and 27D cross sections locate the top of the pipe, and the minimum temperature points locate the bottom of the pipe.However, the maximum temperature points of 20D and 22D cross sections moves to the right of the top. This is due to the change of fluid flow direction caused by the geometrical characteristics of the pipeline. In addition, it is also can be seen that the calculated convective heat transfer coefficients of the four cross sections are not the same, but the difference of the value is not big. This also illustrates that it is reasonable to use the average convective heat transfer coefficient to solve three-dimensional transient IHCP with multi-variables.(4) Numerical experiment of DHCP and results analysis of IHCP about three-dimensional elbow pipe with thermal stratification. Transient DHCP and IHCP with multi-variables have been done on the three-dimentional elbow pipe with thermal stratification. It is can be concluded from the noise resistence and measuring points discussion that, when there is a certain measurement error, the calculated results with a certain accuracy can still be obtained. The number of measuring points in the corner area has a greater influence on the inversion accuracy, the more measuring points in the area the higher accuracy the calculation. The measuring points in other area have little effect on the inversion accuracy.(5) The temperature distribution of T-junction with thermal stratification was estimated using three-dimensional transient IHCP with multi-variables.Based on the calibrated three-dimensional transient IHCP with multi-variables,the bend section of the T-junction with thermal stratification was estimated.The results reveal the different temperature distribution of the pipe wall under the effect of inertia force and buoyancy lift.A nondestructive and indirect temperature inverse method with multi-variables was proposed in this article can be used to simultaneously solve the variables of third kind boundary condition on the inner wall based on the temperature data of outer wall. The method was certified high accuracy by experiments. The method can provide reliable theory basis for the flow field analysis and thermal fatigue analysis of the piping system with higher requirement in structural completeness, such as nuclear power pipelines.