Inverse Estimation Of Inner Surface Temperature Fluctuations Of Thermal Mixing Pipes Based On Inverse Heat Conduction Problem

When hot and cold fluids mix in a T-junction pipe,not only heat transfer but also mass transfer(such as evaporation and condensation phase transition)and momentum transfer can occur.Influenced by heat and mass transfer mechanism,unsteady thermal mixing procedure of T-junction pipe can easily induce fluid temperature fluctuations.When fluid temperature near the inner surface of T-junction pipe fluctuates,wall temperature of T-junction pipe will also fluctuate under convective heat transfer and heat conduction.The wall temperature fluctuations easily induced structural fatigue cumulative damage,especially in areas where the safety and structural integrity are extremely demanding,such as nuclear power pipelines.It is usually not allowed to destroy the wall of the pipeline to measure the temperature on the inner surface or the temperature of the fluid near the inner surface.Therefore,it becomes one of the key issues that need to be resolved urgently in the nuclear thermal fatigue analysis to develop a non-destructive indirect temperature evaluation method of assessing the temperature on the inner surface through the temperature on the outer surface without damaging the pipe structure.In this paper,in terms of monitoring inner surface temperature fluctuation of thermal mixing T-junction pipe,based on the inverse heat conduction problem,outer surface temperature of pipe is used to develop and improve an indirect and lossless method for inverse estimating of the inner surface temperature fluctuation of thermal mixing T-junction pipe.It is expected that this method will lay a certain theoretical foundation for the online monitoring of temperature for thermal fatigue assessment of nuclear power pipelines.Aiming to achieve the inverse estimating of the inner surface temperature fluctuations of the transient thermal mixing,this paper works on the mathematical model of the inverse heat conduction problem,numerical validation,numerical methods,optimization algorithms,experimental validation,and the application in monitoring the inner surface temperature fluctuations of the test sample of T-junction pipe in nuclear power engineering,etc.The main research work and conclusions are as follows:(1)Mathmatical model construction of inverse heat conduction problem and numerical experiments validation.Based on mathmatical model of inverse heat conduction problem and numerical solution,numerical experiments are constructed under regular and random fluctuations of fluid near the inner surface.Then the mathmatical model of inverse heat conduction problem and solution method are validated by comparing the estimated and numerical experimental temperatures of inner and outer surfaces of pipe.The validation shows that the IHCP model is of high accuracy.When the maximum fluctuation of temperature of fluid near the inner surface is 160 ?,the estimated and numerical experimental temperatures of pipe inner surface are nearly the same.(2)Optimization of numerical solution method of inverse heat conduction problem and development of inverse estimating program for wall temperature fluctuations of thermal mixing pipes.Based on the need of grid independence and time-step independence for a numerical solution,the way to realize auto grid-independence verification and auto time-step-independence verification is discussed in detail.The reasons why search directions of conjugate gradient method and Davidon Fletcher Powell method may not be a descent direction and even occur computational divergence after several iteration steps are analysed theoretically when an inexact one-dimensional search is conducted.Grid-independence verification and time-step-independence verification guarantee the accuracy and stability of numerical solution,while cycle iteration step independence verification of different optimization algorithms make numerical solution efficient.(3)Experimental validation of inverse estimated inner surface temperature fluctuations of thermal mixing pipes.At normal temperatures and pressures,large temperature fluctuatons are obtained by steam direct contact condensation in T-junction pipe.The experimental data of temperature fluctuation of thedirect contact condensation pipe wall in the experimental section are abtained,and then,experimental validation of inverse estimated results for wall temperature fluctuations of thermal mixing pipes are conducted.The inversion results of the pipe wall temperature fluctuation under the experimental conditions,not onlyindependence verification of the grid,time step and iterationstep are considered,but also the noise reduction method is utilized to improve the stability and convergence of inverse heat conduction problem.The results of temperature fluctuations obtained from the uniform thermal conductivity are consistent with that of measured temperature fluctuations in both time and frequency domain,the average relative errors of the inversion temperature fluctuation amplitude are not more than 14.32%.(4)Application of inverse heat conduction problem in monitoring temperature fluctuation of inner wall surface of Nuclear Power T section pipes.Considering measured temperature noise reduction,grid independence verification,time stepindependence verification,often with uniform thermal conductivity,temperature-dependent thermal conductivity inverse heat conduction models,optimization algorithm and the computing time of an inverse heat conduction problem,the inner temperature fluctuation monitoring of a nuclear power T section pipe is applied in wuhan nuclear power operation institute.The partial pipe outer surface measured temperatures,measuring point locations and physical model parameters are used as input data of monitoring program,and other measuring points of pipe outer surface are used as verified data.The data is analyzed by comparing the calculated value of the monitoring program with the experimental measurement value.The inverse estimated results take into grid-independent solution,time-step-independent solution,highcalculation efficiency accout.Under experimental conditions,the trends of temperature fluctuations obtained from the uniform thermal conductivity and temperature-dependent thermal conductivity models are consistent with that of measured temperature fluctuations in both time and frequency domain,and the relative errors of the calculated temperature fluctuations are less than 15.6%.Inverse heat conduction problem model of uniform thermal conductivity and inversion numerical calculation after optimization iteration step have high computational efficiency and stability.The above research results are expected to be applied to the on-line temperature inversion and monitoring of the nuclear power thermal mixing T section pipe wall.temperature fluctuation.Through the above research,a method for inverse estimating of inner surface temperature fluctuations of thermal mixing pipe based on inverse heat conduction problem has been studied.This method is expected to be applied to occasions where safety and structural integrity of nuclear power pipes are strict,and laid a certain theoretical foundation for developing a lossless and indirect temperature measurement technology.