Science and Technology of Nuclear Installations

Volume 2017, Article ID 1812835, 7 pages

https://doi.org/10.1155/2017/1812835

## Development and Application of the Power Plant Real-Time Temperature and Stress Monitoring System

Cracow University of Technology, Institute of Thermal Power Engineering, Al. Jana Pawła II 37, 31-864 Kraków, Poland

Correspondence should be addressed to Piotr Duda; lp.ude.kp.hcem@adudp

Received 25 July 2017; Accepted 24 October 2017; Published 20 November 2017

Academic Editor: Keith E. Holbert

Copyright © 2017 Piotr Duda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The paper presents a method of temperature and stress estimation in pressure components of conventional or nuclear power plants. The proposed algorithm can be applied without the information concerning the thermal boundary condition on the component inner surfaces and it is fast enough to be applied in an online mode. The solution is possible thanks to “measured” temperature histories determined in easily accessible points located on the component outer surface. The presented model has been recently verified analytically, numerically, and experimentally. The proposed algorithm was used to calculate the transient temperature and stress distribution in the outlet header of a steam reheater and the results indicate that the component lower part is loaded the most, but allowable stresses are not exceeded. If the presented heating process was shortened, the calculated stresses would exceed the allowable values. Monitoring the boiler thermal and strength operating conditions makes it possible to identify dangerous loads of the power boiler pressure elements during transient-state operations. The presented method for controlling thermal and pressure-related stresses is suitable for nuclear power plants because it does not require drilling holes for sensors in the pressure element walls.

#### 1. Introduction

The behaviour of components of conventional or nuclear power plants has been investigated in numerous research projects [1]. During their operation, high stresses occur in thick-walled pressure elements. The operation cyclic character resulting from the cooling and heating of pressure elements causes the low-cycle fatigue phenomenon, which may lead to cracks. As power plants become older engineers need screening criteria to eliminate the risk of thermal fatigue. A number of programs have been launched to develop fatigue monitoring systems for the nuclear power plant components [2, 3]. The use of monitoring systems has a significant impact on the remnant life prediction, highlighting hot zones in the boiler and the influence of modified operations on safe extension of the plant life [4]. The control system quality depends on the accuracy of stress calculations in selected elements of the power unit. The offline method of thermal stress evaluation by using the fluid-structure interaction in the piping system -connections is presented in [5]. The whole area where the fluid is contained has to be discretized. Then the mass, momentum, and energy balance equations have to be written. Depending on the flow nature, it may also be necessary to introduce a suitable turbulence model. The calculations are more difficult in the case of two-phase flows that involve boiling or condensation processes. Green’s function method with consideration of temperature-dependent material properties is shown in [6]. The main disadvantage of this method is the need to find the heat transfer coefficient. Another way to determine the distribution of temperatures and stresses is to solve the inverse heat conduction problem in the device under analysis. Inverse methods enable determination of the entire time- and space-dependent temperature distribution in an element based on measured temperature histories in selected spatial points [7, 8]. The temperature distribution reconstructed in this manner makes it possible to calculate stresses in the analysed elements as accurately as possible [9].

The aim of this work is to present an online temperature and stress monitoring method. The commercial computational software, which is available on the market today, does not make it possible to solve the problem under consideration in an online mode because thermal boundary conditions are not defined on the monitored component inner surfaces. The proposed method has already been tested on a laboratory stand [9]. This paper presents the application of the proposed algorithm for the calculation of the transient-state temperature and stress distribution in the outlet header of a power plant steam reheater. The presented method for controlling thermal and pressure-related stresses is suitable for nuclear power plants because it does not require drilling holes for sensors in the pressure element walls.

#### 2. Formulation of the Method

The equation governing the transient-state heat conduction problem has the following form:where is the heat flux vector. Fourier’s law for an isotropic material takes the following form:

All material properties (: specific heat, : density, and : thermal conductivity) are assumed as known functions of temperature. The control volume finite element method is used [10]. Equation (1) is integrated over general control volume with bounding surface :

By applying the mean value theorem for integrals on the left and the divergence theorem on the right, the following equation is obtained:where the bar indicates an average value in volume and** n** is a normal unit surface vector directed to the outside of the control volume.

If temperature does not vary in a cylindrical component along the generatrix but changes along the circumference and on the wall thickness, the unsteady-state temperature distribution is two-dimensional .

For such a problem, the analysis can be carried out only for a cross-section as presented in Figure 1. The cross-section is divided into control volumes. Assuming that the component outer surface is perfectly insulated and an unknown boundary condition occurs on the inner surface, the inverse problem may be solved starting with a heat balance equation for the control volume associated with node .