Modelling and fault analysis of APROS-based moisture separation reheater

A modular modelling approach was adopted to build a dynamic simulation model of the moisture separation reheater on a high-precision APROS real-time platform to investigate the dynamic operating characteristics of the moisture separation reheater. The model was subjected to steady-state and step dynamic tests at different loads. The results show that the established model can correctly reflect the steam flow and heat transfer properties and can meet the requirements of the simulation. Using the one-dimensional distribution of the model, the effect of a small breakage failure in the heat exchanger bundle was further investigated. The results showed that the heat transfer tube bundle had leaks, reducing the heat transfer capacity and affecting the quality of the steam used to work in the low-pressure turbine. Simultaneously, the effect on steam outlet parameters increased with the degree of leakage in the heat exchanger.


Introduction
Unlike thermal power units, a moisture separation reheater (MSR) is a special component in nuclear power plants, between the high-pressure turbine and low-pressure turbine, removing water and heating it to increase the efficiency and diminish the risk of erosion or corrosion damage to the components connected downstream of the MSR [1].Since the actual operating data of nuclear power units are difficult to obtain and experiments are not easily carried out, it is of great significance to analyse the operating characteristics of MSR with the help of simulation for the economical and reliable operation of nuclear power units.
The specificity and importance of the MSR have led to many studies carried out by domestic and foreign scholars.To obtain the external parameters, modular modelling was used to build models based on different simulation platforms [2][3] to study the variation of its outlet parameters.The flow and heat transfer characteristics of the fluid inside the device were analysed with the help of CFD techniques [4][5][6].Due to the condensing heat transfer in the reheater, there is a two-phase flow and temperature difference inside the tube [7], which leads to thermal fatigue of the tube bundle [8] and can lead to pipe rupture during long-term operation.Microscopic analysis of the heat exchanger tube leakage yields erosion effects as the main cause [9].The above literature analyses the modelling simulation of MSR and the cause of rupture failure but lacks the specific performance and impact of small rupture failure to provide early warning for field operation.
In this work, the MSR of the Changjiang nuclear power unit is used as the research object, and a dynamic simulation model is established on the APROS platform using a modular modelling approach to investigate the operational characteristics of the MSR in depth.The analysis focuses on the effect of small breakage failures of heat exchanger tubes to provide data reference for unit operation evaluation and fault diagnosis.

Moisture separator reheater model
The moisture separation reheater (MSR) is an important auxiliary equipment of the second circuit system in nuclear power plants and is located inside the turbine unit.MSRs in actual operating pressurized water reactor (PWR) nuclear power plants are mainly horizontal and consist of a vapor separation unit, primary reheater, secondary reheater, and shell [10].The separation unit is generally of wave plate type, arranged in an inverted V-shape at the bottom of the MSR, and the primary and secondary reheaters are placed horizontally in an upward order.The structural sketch is shown in Figure 1.The steam discharged from the high-pressure turbine unit contains about 15% water, which enters the cylindrical shell from the bottom of the MSR and flows upward through the waveform plate separator.Due to inertia, the separated hydrophobic water flows from the bottom to the deaerator.In contrast, the separated steam goes upward through the primary and secondary reheat bundle to absorb heat in turn.Finally, it flows from the discharge port above the MSR to the low-pressure turbine to continue work.The steam in the primary reheater tube is the pumped steam for the high-pressure turbine, the steam in the secondary reheater tube comes from the main steam, and the condensed hydrophobic water from both reheaters is sent to the feedwater heater.

Mathematical model
The mathematical model was modelled modularly and divided into a separator and a reheater.The corrugated plate separator has a single role and a complex internal structure with incomplete clarity of local parameters, so it is simplified to a one-in-two-out vessel.The heat transfer tube bundle of the reheater is arranged in a U-shaped tube with many parallel tube roots.To facilitate the analysis, the Ushaped heat transfer tube is equated to a single straight section with a circulation area that is the sum of all actual tube areas and a length of a single tube [11].The following assumptions are made to simplify the model: (1) The fluid in the MSR is incompressible.
(2) The gas-liquid phase in the MSR is in phase equilibrium.
(3) The temperature of the reheater is constant along the tube length.
(4) We ignore the change in specific heat capacity and density of the medium.
(5) We ignore the shell to the external environment of heat dissipation.(6) The efficiency of the separator is 100%.The mathematical model is composed mainly of mass balance, energy balance, and heat transfer equations, and the moisture separator also considers volumetric inertia.
where subscripts w, in, and out represent a metal wall, entry, and exit.V represents separator volume.ρ is density.G is mass flow.cp is constant pressure-specific heat capacity.M is mass.Q is heating transfer.
T is temperature.
The reheater differs from the general shell-and-tube heat exchanger in that the fluid inside the heat exchanger tube is hot steam, condensation exothermic so that the cold steam on the shell side warms up.Its heat transfer coefficient should be calculated by the requirements of condensation in the horizontal tube, according to the Nusselt-type correlation type [12].
( ) ( ) where subscripts l and v represent the liquid and vapor phases.k2 is the reheat steam heat transfer coefficient.μ is the dynamic viscosity.d is the tube inner diameter.r is the latent heat of vaporization.
g is the acceleration of gravity.

Simulation model
On the theoretical basis of the mathematical model, the model is built using the MATLAB/Simulink platform.To achieve accurate and real-time simulation, the simulation model of MSR is built based on the APROS platform, as shown in Figure 2. Figure 2 shows the moisture separator, primary, and secondary reheater in the order from bottom to top.The first-stage reheat steam comes from a certain stage of the high-pressure turbine extraction and flows into the heat exchanger tube from the right side of the MSR, while the second-stage reheat steam originates from the main steam and flows into the heat exchanger tube from the left side.The moisture separator in Figure 2 is represented by a water tank in the APROS module library, and the first and second stage reheaters are simulated using a crossover heat exchanger, where the heat exchanger tube bundle is set up in two rows to simulate an actual U-tube arrangement.

Model accuracy validation 2.3.1. Steady-state validation
To correctly reflect the parameters of the equipment under steady-state operating conditions and to verify the established model and simulation method, the actual operating process of MSR from rated operating conditions to lower load operating conditions is continuously simulated without changing the design parameters of the model.The steady-state operating data of the equipment under different operating conditions are recorded.The simulated values of the parameters are compared with the design values, and the data comparison is shown in Table 1.As can be seen from Table 1, the relative errors of the Simulink-based solution data are almost all within 1% for different operating conditions.The deviation increases with the decrease in load.And the relative error of the data of the APROS model under different operating conditions is within 1% of the design value, which indicates that the model is more accurate in steady-state operating conditions and has the guarantee of low operating accuracy compared with the mathematical model.

Dynamic validation
Since installing measurement points in actual nuclear power plants and operational data are difficult to obtain, this paper compares different simulation models for verification.It compares the dynamic data with other literature for different sizes of MSRs in different nuclear power plants.Due to the different boundary conditions and structure dimensions, the dynamic data in the [2,13] are normalized with the dynamic results in this paper for the convenience of data processing and comparison and then compared to obtain the dynamic characteristics verification results shown in Figure 3.
In comparison to the literature, Figure 3 displays the changes in steam pressure within the separator and the temperature of the circulating steam outlet in the first and second stage reheaters.These changes occurred during a 100-second steady operation of the model at rated operating conditions, following a 10% decrease in circulating steam inlet flow rate.As can be seen from Figure 3, the dynamic simulation results and the literature during the dynamic simulation trend match.Figure 3 indicates that when the circulating steam flow rate decreases, the density of the internal steam decreases, leading to a decrease in pressure.The change curve is consistent with the theoretical analysis trend, and the simulation results agree.It also exhibits the increasing trend of the circulating steam outlet temperature when the circulating steam flow rate decreases.The APROS results fit well with the Simulink results.They are consistent with the trends of [2] and [13], which indicates that the dynamic response of the established simulation model is more accurate.

Heat exchanger tube breakage failure
The simulation model is distributed in one dimension along the tube length, and each stage of the reheater consists of six aggregate models.The simulation model is simulated by adopting a control valve connecting the circulating steam and reheat steam paths for the test of reheater heat exchanger tube rupture failure.In this paper, four different degrees of breakage were set at the large temperature difference between reheat steam and circulating steam in the primary reheater, and the valve opening at the breakage was controlled to simulate the amount of leakage.Figure 4 shows the simulation results for different degrees of breakage in the heat exchanger tube.When the heat exchanger bundle starts to break, the flow of reheat steam inside the tube changes continuously and flows into the shell side, causing the flow of circulating steam to increase with time.The leakage of reheat steam causes the outlet temperature to decrease, and the outlet temperature of circulating steam also decreases due to the excessive flow of circulating steam and the heat balance principle.As the leakage continues to increase, the impact of the breach on the MSR outlet parameters increases, and the quality of the steam sent to the low-pressure turbine to do work continues to decrease, which affects the efficiency and safety of the unit in the long term.

Conclusion
Thermal deviations exist around the heat exchanger tubes inside the nuclear moisture separation reheaters, and long-term operation is prone to heat exchanger tube breakage failures that threaten the efficiency and safety of the unit.In this paper, we build a model of MSR based on the APROS simulation platform and simulate the small breakage failure of heat exchanger tubes after accuracy verification.A

Figure 3 .
Figure 3.Comparison of step test results for circulating steam inlet flow.

Table 1 .
Data comparison of simulation model under different operating conditions a Subscripts 1, dr, 2, 3, and 4 are separator outlet steam, drainage, primary reheater outlet, and secondary reheater outlet.