Investigation on flow and heat transfer characteristics of the once-through cooling system in a nuclear power plant under cold source disturbance

1 Introduction

With the sustained and healthy development of China’s national economy, the demand for electricity continues to rise. Nuclear energy, owing to its advantages of being clean, low-carbon, and economical, has become a vital direction for meeting energy demands and optimizing the power structure. The “Carbon Peak” and “Carbon Neutrality” goals proposed by China in 2020 have further accelerated the large-scale development of the nuclear power industry (Huang et al., 2025a). However, nuclear power plants feature complex systems with stringent safety requirements, and their overall performance and economic efficiency largely depend on the optimized operation of key auxiliary systems.

The secondary circuit cold-end system, often referred to as the tertiary cooling system, is the core link for energy conversion and dissipation in a power plant. Its operational efficiency directly impacts the unit’s overall performance and thermal economy, making it a key focus for energy-saving optimization research (Wu et al., 2019). Figure 1 presents the schematic layout of the CES.

The primary function of this system is to supply a cooling medium (such as seawater) via the circulating water system to the condenser, where the exhaust steam from the turbine is condensed back into water. This process maintains the system vacuum and ensures efficient turbine operation. The condenser, as the core heat exchange equipment in this system, is critically important. Condenser back pressure is a key parameter affecting turbine output, and its optimal control is crucial for increasing the unit’s net power output. Theoretically, under constant load and cooling water temperature, there exists an optimal circulating water flow rate that maximizes the net power output. The corresponding back pressure at this point is the optimal back pressure, and the corresponding flow rate is the optimal circulating water flow rate. In actual operation, however, the cold-end system is subject to various cold source disturbances, which cause operational parameters to deviate from the optimal condition, significantly impacting the unit’s economy and stability:

• Seawater Temperature and Tide Level Disturbances: The circulating water inlet temperature fluctuates significantly with changes in seawater temperature and tide level, altering the heat transfer coefficient and subsequently causing variations in key parameters such as condenser pressure. For instance, at the Qinshan Nuclear Power Plant Unit 1, a rise in tide level during summer led to an increase in water intake temperature of over 3 °C, triggering significant fluctuations in reactor nuclear power. Tide level changes also directly affect the flow rate and head of the circulating water pumps. Furthermore, tidal action can cause the recirculation of plant thermal discharge, further elevate the circulating water temperature and create a vicious cycle (Chen, 2024).
• Condenser Cleanliness Coefficient Disturbance: Seawater is rich in microorganisms, salts, and impurities, which readily form scale deposits on the inner walls of the condenser heat exchange tubes. This creates a fouling thermal resistance, significantly reducing heat transfer efficiency. The cleanliness coefficient (the ratio of the heat transfer coefficient of a used tube to that of a new tube) is a key indicator of the fouling degree. A decrease in the cleanliness coefficient leads to a deterioration of condenser vacuum and a reduction in system heat exchange performance (Haifeng and Yanbin, 2012; Wenfeng et al., 2017; Zhiming et al., 2005).

The coupled effects of these disturbance factors often lead to significant deviations when applying traditional condenser off-design performance models in practical scenarios, making it difficult to provide precise guidance for operational optimization. Therefore, there is an urgent need to develop more accurate models and methods to systematically study the flow and heat transfer characteristics of the CES under coupled multi-disturbance conditions.

To this end, numerous studies have been conducted by researchers worldwide. In terms of modeling and optimization, Acir A (Acir, 2013). established a neural network model incorporating multiple parameters to predict unit power output, while Fu et al. (FU et al., 2022) employed a genetic algorithm for the multi-parameter collaborative optimization design of the CES. Regarding performance analysis and control, Qureshi et al. (Qureshi et al., 2016) proposed equations for evaluating the impact of fouling thermal resistance; Wang et al. (Wang et al., 2016) investigated the transient characteristics of condenser and cooling water systems in nuclear power plants; and Huang (Huang et al., 2025b) explored the influence of environmental parameter disturbances on AP1000 units, proposing an adaptive control strategy based on variable-frequency circulating water pumps to seek the optimal vacuum.

Currently, Optimizing the operating parameters of cooling water pumps in the thermal power plant CES can achieve approximately $210,000 in annual operational cost savings (Li et al., 2018). Meanwhile, the actual thermal efficiency of nuclear power plants often remains slightly lower than that of advanced coal-fired power plants. As one of the main power-consuming auxiliary systems in a nuclear plant, circulating water pumps account for approximately 1%–1.5% of the plant’s total power generation, representing significant potential for energy savings (Chen, 2024). Consequently, conducting in-depth research on the subsystems of the CES and their characteristics under cold source disturbances is a crucial pathway for nuclear power plants to achieve energy conservation, consumption reduction, and enhanced thermal economy.

Based on this, this paper focuses on the operational characteristics of the CES in nuclear power plants, aiming to integrate mechanistic analysis and data-driven methods to refine and calibrate an integrated simulation and key parameter prediction model for the CES under cold source disturbances. The disturbance factors studied are seawater temperature, tide level, and condenser cleanliness coefficient. The operational parameters of concern are condenser back pressure, circulating water flow rate, net power output, and pump power consumption. This study aims to provide a solid theoretical foundation for the operational optimization of the CES.

2 Energy transport model and mechanism analysis of CES

The research object of this paper is a 1.2 GW-class AP1000 pressurized-water reactor nuclear power unit adopting seawater once-through cooling system. Under TMCR condition with nominal seawater temperature of 14.95 °C, the nominal design circulating-water flow rate of this unit is 49.20 m³/s. Unit thermal-performance parameters such as turbine exhaust pressure and exhaust mass flow rate are derived from the power-plant thermal-balance technical report. Condenser geometrical and thermal design parameters are summarized in Table 1. Note that the given overall heat transfer coefficient is only the design reference value under TMCR condition. The flow-head and flow-efficiency characteristic curves of circulating-water pumps are obtained from the equipment manufacturer’s official documents. Pipeline resistance characteristics are determined based on system design data and further calibrated with field operation data. Environmental and equipment-state boundary conditions, including seawater temperature, tide level, and condenser cleanliness coefficient, are defined as disturbance-setting conditions in this study.

TABLE 1. Condenser design parameters.

2.1 Transient numerical calculation model for pipelines

Based on the momentum equation of fluid flow within a pipeline, since the pressure wave speed is much greater than the fluid flow velocity in the pipeline, the propagation process of pressure waves can be neglected. Additionally, ignoring the compressibility of the fluid and the elasticity of the pipe wall, the fluid velocity (or flow rate) in the pipeline does not vary with spatial position, leading to a lumped-parameter model describing the dynamic hydraulic process in the pipeline. Figure 2 is a schematic diagram illustrating the derivation of the momentum equation for transient fluid flow in a pipeline.

The cross-sectional area of the pipeline is A, the thickness of the control volume is δx, the positive direction of the coordinate axis x is along the pipeline centerline, and the elevation of the control volume is z. According to Newton’s second law, the following Equation 1 is obtained:

p A − p A + p A x δ x + p + p x δ x 2 A x δ x − τ 0 π D δ x − γ A δ x ⁡ sin ⁡ ϕ = A δ x ρ v ˙ (1)

Where p is the pressure distribution of the fluid along the coordinate axis x (Pa); A is the cross-sectional area (m²); γ is the specific weight, i.e., γ = ρg* (kg/(m²·s²)); τ _*0* is the shear stress exerted by the wall on the fluid (Pa); and φ is the angle between the pipeline centerline and the horizontal plane (°).

Neglecting the higher-order terms in the equation and considering steady-state conditions, for a horizontal pipeline of length L and diameter D, the resistance caused by wall shear stress should be equal to the resistance calculated using the Darcy formula, satisfying the following Equation 2:

Δ p π D 2 4 = τ 0 π D L (2)

Neglecting the propagation and attenuation processes of pressure waves in the pipeline, and considering that the pressure propagation speed in the pipeline is much faster than the dynamic variation of flow rate, the hot water in the pipeline can be approximated as incompressible fluid. Given the rapid propagation speed of pressure waves along the pipeline fluid, it can be approximated as zero. For horizontal pipelines, integrating the results from x = 0 to x = L along the pipeline length and substituting flow rate for velocity yields the following form of the transient hydraulic model equation for pipelines (Equation 3):

Δ H = 8 f L D 5 π 2 g Q 2 + 4 L D 2 π g d Q d t (3)

For a pump, the pump head curve is given by the following Equation 4:

H = a Q 2 + b Q + c (4)

According to the first law of thermodynamics, the frictional head loss along the pipeline should equal the pump head. Therefore, the following Equation 5 can be established to characterize the dynamic relationship between pressure change and flow rate:

a Q 2 + b Q + c = 8 f L D 5 π 2 g Q 2 + 4 L D 2 π g d Q d t (5)

However, during the operation of a variable-frequency pump, the pump head curve continuously changes. This requires using similarity points to solve for the rotational speed and subsequently determine the pump head curve under varying speeds, which complicates the problem. Hence, the pipeline characteristic curve is employed to express the pump head Equation 6:

H c = H s + r Q 2 (6)

By rearranging the above equations, the dynamic relationship between pressure change and flow rate is given by Equation 7:

r Q 2 + H s = 8 f L D 5 π 2 g Q 2 + 4 L D 2 π g d Q d t (7)

2.2 Variable-frequency calculation model for pumps

The operating point of a pump is determined by the intersection of its performance curve and the pipeline characteristic curve, as shown in Figure 3. Variable-frequency pumps adjust the flow rate by varying the motor speed, thereby altering the performance curve. Based on affinity laws, a functional relationship among flow rate, head, and rotational speed of the variable-frequency pump is established, providing theoretical support for the dynamic regulation of the system.

The pump characteristic curve is given by the following equation:

H = 16.35 + 0.4776 Q − 0.02875 Q 2 (8)

In the equation, H represents the pump head, and Q represents the pump flow rate.

The efficiency curve of the circulating water pump is shown in Figure 4. When pumps operate in parallel, the performance curve of the pump system changes, as illustrated in Figure 5. The operating point shifts from point A for a single pump to point B. If the two pumps are of the same model, the operating point becomes point C, with both pumps delivering the same flow rate. For variable-frequency pumps, the motor speed is adjusted by modifying the pump system, thereby altering the pump characteristic curve to regulate the flow rate. The operating point of a variable-frequency pump shifts from point A to point B, as shown in Figure 6.

The ratio of the actual rotational speed of a variable-frequency pump to its rated speed is defined as the speed ratio, expressed as Equation 9:

ω = n i / n 0 (9)

In the equation, n _*i* represents the actual rotational speed of the pump, and n _*0* represents the rated rotational speed of the pump.

Based on the affinity laws, the flow rate and head of a variable-frequency pump are calculated as follows:

Q i / Q 0 = n i / n 0 = ω H i / H 0 = n i / n 0 2 = ω 2 (10)

Where Q _*i* is the actual flow rate, Q _*0* is the flow rate at the rated speed, H _*i* is the actual head, and H _*0* is the head at the rated speed. Substituting Equation 10 into Equation 8 can be expressed as follows (Equation 11):

H i = a 1 ω 2 + a 2 ω Q i + a 3 Q i 2 (11)

2.3 Cold-end two-phase flow coupled calculation model

The gas on the shell side of the condenser consists of exhaust steam from the turbine and a small amount of non-condensable gases. The partial pressure expression for the condenser is:

P c = P s + P a P a = α · P s P s V s = M s R s T s (12)

Where P _*c* is the partial pressure in the condenser, P _*s* is the partial pressure of steam, P _*a* is the partial pressure of non-condensable gases, V _*s* is the volume of the gas space inside the condenser (m³), M _*s* is the mass of steam (kg), R _*s* is the gas constant for steam (461.5 J/kg·K), and T _*s* is the temperature of the steam (K).

The total differential of Equation 12 is given by Equation 13:

P s d V s d τ + V s d P s d τ = R s T s d M s d τ + M s R s d T s d τ (13)

Where τ is the time variable (s).

During off-design operation of the condenser, it is considered that the gas volume space and steam temperature are minimally affected by time and can be neglected. Thus, the above equation simplifies to Equation 14:

d P s = R s T s d M s (14)

According to the principle of mass conservation, the mass balance differential equation for the shell side of the condenser can be derived as follows Equation 15:

d M s d τ = D s t + D o s t + D f − D c (15)

Where D _*st* is the mass flow rate of exhaust steam from the low-pressure cylinder of the turbine (kg/s); D _*ost* is the mass flow rate of non-condensable gases entering the condenser (kg/s); D _*f* is the flash evaporation rate of condensed water (kg/s); and D _*c* is the condensation rate of steam (kg/s).

According to the principle of energy conservation, the energy differential equation for the shell side of the condenser can be expressed as Equation 16:

d M s H s d τ = D s t H s t + D o s t H o s t + D f H s at , v − D c H s (16)

Where H _*s* is the enthalpy of steam (kJ/kg); H _*st* is the enthalpy of the exhaust steam from the low-pressure cylinder of the turbine (kJ/kg); H _*ost* is the enthalpy of non-condensable gases in the condenser (kJ/kg); and H _*sat,v* is the enthalpy of saturated steam at the condenser pressure (kJ/kg).

The mass flow rate of steam condensation in the condenser is calculated based on the heat balance equation as follows Equation 17:

K c A c Δ T m = D c H s − H s a t , w D c = K c A c Δ T H s − H s a t , w (17)

For the tube side of the condenser, a dynamic mathematical model is established using the lumped parameter method. According to the principle of energy conservation, the differential equation for the tube wall in the condenser can be expressed as Equation 18:

M wall , c C p w a l l , c d T w a l l , c d τ = K c A c Δ T m − h w A w , c T w a l l , c − T c 1 + T c 2 2 (18)

Where M _*wall,c* is the mass of the pipe wall (kg); Cp _*wall,c* is the specific heat capacity of the pipe wall (kJ/kg·K); T _*wall,c* is the temperature of the pipe wall (K); h _*w,c* is tube-side single-phase forced-convection heat-transfer coefficient of circulating seawater (kW/m²·K); and T _*c1*, T _*c2* are the inlet and outlet temperatures of the circulating water (K). Two-phase flow does not appear within the circulating-water passage. For fully-developed turbulent flow (Re > 10,000), it is calculated by the Dittus-Boelter correlation given by Equation 19:where Nu is Nusselt number; Re is tube-side Reynolds number; Pr is Prandtl number of seawater; λ is seawater thermal conductivity, W/m·K; d i is inner diameter of condenser tube, m.

h w , c = N u · λ / d i N u = 0.023 R e 0.8 ⁡ Pr 0.4 (19)

Similarly, based on the principle of energy conservation, the energy differential equation for the circulating cooling water side of the condenser is derived as Equation 20:

M w , c C p w d T c 1 + T c 2 / 2 d τ = D w C p w T c 1 − T c 2 − h w A w , c T w a l l , c − T c 1 + T c 2 2 (20)

Where M _*w,c* is the mass of circulating cooling water inside the pipes (kg). The overall heat-transfer coefficient h _*w* of the condenser is calculated according to the 11th-edition HEI Standards for Steam Surface Condensers by Equation 21:

h w = F C K 0 F M F W (21)

• K 0 — uncorrected base heat-transfer coefficient fitted against tube-side flow velocity;
• F C — comprehensive cleanliness coefficient accounting for tube-side fouling;
• F M — correction factor for tube material and wall thickness;
• F W — correction factor for circulating-water inlet temperature.

K 0, F M and F W are obtained from empirical fitting formulas provided in the HEI standard. Two-phase steam condensation occurs only on the shell side of the condenser and is represented by this overall heat-transfer formulation.

For system-level dynamic simulation purposes, the condenser shell-side is treated using the lumped-parameter approach adopted in this work. Consequently, spatial non-uniformity of steam-condensation distribution within the shell side is neglected. It should be noted that the present model is developed for investigating system-scale transient response behaviors, rather than resolving detailed local spatial field features inside the condenser.

2.4 Mechanism of tidal level influence on the performance of OCS

For the circulating water system in power plants, particularly those where the forebay water level is significantly affected by tides, tidal information is a crucial factor in the optimal dispatch of circulating water pumps.

When the outlet siphon well of the seawater once-through circulating water system operates under free outflow conditions, the static head of the circulating water system is determined by the difference between the water level in the intake well and the weir crest level of the siphon well. The total head of the circulating water pump, denoted as H, represents the energy required to transport a unit weight of liquid from the suction pool to the discharge pool. It includes the static head, pressure head, and system resistance losses. If tidal variations are considered, the static head of the system is no longer constant but changes with the tidal level X. In this case, the total head equation of the system can be expressed as Equation 22:

H = c 1 Q 2 + c 2 Q + c 3 H = Z − X + p 2 − p 1 ρ g + ∑ h (22)

Therefore, the empirical equation of the pipeline characteristic curve is a quadratic function of flow rate Q and tide level X, while the head H, flow rate Q, and power P of the circulating water system are all univariate functions of tide level X.

If the pipeline performance curve at the design tide level is expressed as a quadratic parabola of flow rate by Equation 23:

H = c 1 Q 2 + c 2 Q + c 3 (23)

When the tide level changes, the system static head varies accordingly, resulting in a different constant term in the pipeline characteristic curve compared to the design condition.

At the design tide level of 1.36 m, the pipeline characteristic curve is expressed as Equation 24:

H z = 5.18 + 0.0163 Q 2 (24)

The pipeline characteristic curve under different tide levels is expressed as Equation 25:

H z = 6.54 − X + 0.0163 Q 2 (25)

2.5 Condenser fouling thermal resistance model

The growth of fouling undergoes stages of initiation, growth, progressive accumulation, as well as stages of spallation and aging. The increase in fouling is a complex process resulting from the interaction and mutual influence of these two phases. Factors across different stages contribute to the nonlinear growth pattern of fouling. The thermal resistance due to fouling on the water side of the condenser can be calculated using the following Equation 26:

R f i = 1 K p − 1 K ′ (26)

The relationship between fouling thermal resistance, operating time, and other parameters can be analyzed through the following Equation 27:

d m f d t = m d − m r (27)

Where, R _*fi* represents the fouling thermal resistance, K _*p* is the actual heat transfer coefficient, and K′ is the ideal heat transfer coefficient, m _*f* is the mass of fouling deposited per unit heat transfer area (kg/mol); m _*d* is the deposition rate (kg/(m²·s)); m _*r* is the removal rate (kg/(m²·s)); and t is time (s).

The rate of change of fouling thermal resistance is given by the following Equation 28:

R f = m f ρ f λ f (28)

In the equation, R _*f* is the thermal resistance of the fouling deposit layer (m²·K/W), ρ _*f* is the fouling density, and λ _*f* is the thermal conductivity of the fouling.

The deposition rate and removal rate of fouling thermal resistance are expressed as follows Equations 29, 30:

m d = K C − C s n overall rate = k m C − C i mass transfer = k r ′ C i − C s z surface reaction (29)

m r = K 2 τ f σ f ϖ · g ρ 1 / 3 (30)

Where, K is the total deposition coefficient, K _*m* is the mass transfer coefficient, and K _*r* ’ is the surface reaction rate.

2.6 Model validation for steady-state unit performance

Based on the lumped-parameter dynamic models for pipelines, pumps and condenser established in Sections 2.1–2.5, steady-state benchmark verification is carried out to examine the correctness and calculation accuracy of the developed cold-end system model. The simulated results under 100% THA and 100% TRL operating conditions are compared with the official thermal-balance design values of the reference AP1000 unit. Unit net output power, as the most critical indicator reflecting the overall thermal performance, is selected for quantitative comparison, as summarized in Table 2.

TABLE 2. Model error analysis under different operating conditions.

As shown in Table 2, the simulated power values under THA and TRL conditions agree well with the thermal-balance-diagram reference data. The maximum relative error between the model-calculated power and the design value does not exceed 0.3%. Such error magnitude satisfies the accuracy requirement for engineering-oriented system-level transient simulation. Therefore, the present model is qualified to investigate the dynamic response characteristics of cold-end systems under various cold-source disturbances in the subsequent Section 3.

Unlike high-fidelity numerical tools focusing on local three-dimensional flow and phase-change details within individual components, the lumped-parameter model in this work aims at system-level dynamic coupling under diverse cold-source disturbances. Built on mass, momentum and energy conservation, it retains core physical mechanisms with reduced computational burden, enabling efficient transient simulation for numerous combined-disturbance cases and supporting subsequent operational-optimization research.

It should be noted that this work mainly focuses on transient parameter evolution under multi-factor coupled disturbances. Comprehensive comparative analysis covering abundant thermal-hydraulic parameters and wider operating ranges will be further implemented in our future research.

3 Analysis of disturbance parameters

The disturbance factors studied are seawater temperature, tide level, and condenser cleanliness coefficient. The operational parameters of concern are condenser back pressure, circulating water flow rate, net power output, and pump power consumption.

3.1 Seawater temperature disturbance

At the design tide level of 117 cm and design cleanliness coefficient of 0.85, we analyze the dynamic variations of unit back pressure, unit net power output, circulating water outlet temperature, pump power consumption, and condenser heat transfer over time under seawater temperature disturbance.

Figure 7 illustrates that when the seawater temperature rises from 3.8 °C to 3.9 °C, 4.0 °C, 4.1 °C, and 4.2 °C respectively at 100 s, the unit back pressure increases from 0.002399 MPa to 0.002411 MPa, 0.002423 MPa, 0.002436 MPa, and 0.002448 MPa. Meanwhile, the unit net power output decreases from 1,276,442.92 kWh to 1,276,338.71 kWh, 1,276,232.18 kWh, 1,276,123.32 kWh, and 1,276,012.11 kWh. The circulating water outlet temperature rises from 15.54 °C to 15.64 °C, 15.74 °C, 15.84 °C, and 15.94 °C. The condenser heat transfer increases from 1,926,647.27 kW to 1,926,760.44 kW, 1,926,876.40 kW, 1,926,995.27 kW, and 1,927,116.81 kW. The pump power remains constant at 5,417.88 kW.

Figure 7 demonstrates that as seawater temperature increases, the back pressure rises. The increase in back pressure leads to a decrease in unit net power output, an increase in condenser heat transfer, a rise in circulating water flow rate, and an elevation in circulating water outlet temperature. Due to the increase in circulating water volume, the pump power also increases.

3.2 Condenser cleanliness coefficient disturbance

At the design tide level of 117 cm and a seawater temperature of 3.8 °C, we analyze the dynamic variations of unit back pressure, circulating water flow rate, unit net power output, circulating water outlet temperature, pump power, and condenser heat transfer over time under cleanliness coefficient disturbance.

Figure 8 illustrates that when the cleanliness coefficient decreases from 0.85 to 0.845, 0.84, 0.835, and 0.83 respectively at 100 s, the unit back pressure rises from 0.002397 MPa to 0.002401 MPa, 0.002404 MPa, 0.002408 MPa, and 0.002412 MPa; the circulating water flow rate increases from 39.42 m³/s to 39.5 m³/s, 39.6 m³/s, 39.68 m³/s, and 39.76 m³/s; the unit net power output decreases from 1,276,442.99 kWh to 1,276,379.11 kWh, 1,276,314.01 kWh, 1,276,247.66 kWh, and 1,276,180.02 kWh; the circulating water outlet temperature rises from 15.5391 °C to 15.5395 °C, 15.5399 °C, 15.5404 °C, and 15.5408 °C; the pump power increases from 5,433.71 kW to 5,465.47 kW, 5,505.34 kW, 5,537.38 kW, and 5,569.54 kW; and the condenser heat transfer rises from 1,926,647.27 kW to 1,926,717.34 kW, 1,926,789.42 kW, 1,926,863.56 kW, and 1,926,939.83 kW.

As shown in the figure, a decrease in the cleanliness coefficient leads to an increase in the unit’s fouling thermal resistance and a rise in back pressure. The increase in back pressure results in a corresponding decrease in the unit’s net power output. The reduction in net power output, in turn, causes an increase in condenser heat transfer, circulating water flow rate, and circulating water outlet temperature. Furthermore, due to the increase in circulating water flow, the unit’s pump power consumption also rises. Compared to the impact of seawater temperature on the unit, the effect of changes in the cleanliness coefficient is relatively smaller.

3.3 Seawater temperature and tide level coupled disturbance

At the design cleanliness coefficient of 0.85, we analyze the dynamic variations of unit back pressure, circulating water flow rate, unit net power output, circulating water outlet temperature, pump power, and condenser heat transfer over time under coupled disturbances of seawater temperature and tide level.

Figure 9 illustrates that when the seawater temperature rises from 3.8 °C to 3.9 °C, 4.0 °C, 4.1 °C, and 4.2 °C, and the tide level simultaneously drops from 117 cm to 104 cm, 96 cm, 89 cm, and 70 cm at 100 s, the following changes occur:

• The back pressure increases from 0.002397 MPa to 0.002404 MPa, 0.002412 MPa, 0.002419 MPa, and 0.002427 MPa.
• The circulating water flow rate rises from 39.42 m³/s to 39.52 m³/s, 39.62 m³/s, 39.72 m³/s, and 39.82 m³/s.
• The unit net power output decreases from 1,276,442.99 kWh to 1,276,277.95 kWh, 1,276,134.99 kWh, 1,275,995.20 kWh, and 1,275,796.25 kWh.
• The circulating water outlet temperature increases from 15.54 °C to 15.64 °C, 15.74 °C, 15.84 °C, and 15.94 °C.
• The pump power increases from 5,433.71 kW to 5,535.09 kW, 5,613.25 kW, 5,687.04 kW, and 5,818.82 kW.
• The condenser heat transfer rises from 1,926,647.27 kW to 1,926,760.44 kW, 1,926,876.40 kW, 1,926,995.27 kW, and 1,927,116.81 kW.

From the figure, it can be observed that both a drop in tide level and a rise in seawater temperature raise unit back pressure and pump power consumption, while reducing net power output. Tide-level variation exerts only minimal and negligible effects on condenser heat-transfer performance and circulating-water outlet temperature. Under the coupled action of these two disturbances, unit back pressure, circulating-water outlet temperature, pump power consumption and condenser heat transfer all increase, accompanied by a decline in net power output.

When seawater temperature acts as the sole disturbance factor, the circulating-water flow rate rises. By contrast, a tide-level decline tends to reduce the circulating-water flow rate. Nevertheless, the flow-rate modification induced by tide-level drop is substantially weaker than that caused by seawater-temperature elevation. As a result, the overall circulating-water flow rate still shows an upward trend under the combined-disturbance condition. Physically, tide-level change mainly modifies the static head of the circulating-water loop and produces minor deviations in flow rate, but it cannot alter the seawater inlet temperature or the inherent heat-transfer conditions within the condenser. This accounts for its limited direct impact on condenser heat-transfer capacity.

3.4 Seawater temperature and Cleanliness Coefficient Coupled Disturbance

At the design tide level of 117 cm, we analyze the dynamic variations of unit back pressure, circulating water flow rate, unit net power output, circulating water outlet temperature, pump power, and condenser heat transfer over time under coupled disturbances of seawater temperature and cleanliness coefficient.

Figure 10 shows that at 100 s, when the seawater temperature rises from 3.8 °C to 3.9 °C, 4.0 °C, 4.1 °C, and 4.2 °C, and the cleanliness coefficient decreases from 0.85 to 0.845, 0.84, 0.835, and 0.83, respectively, while the tide level remains unchanged, the following changes occur:

• The back pressure increases from 0.002397 MPa to 0.002407 MPa, 0.002418 MPa, 0.002428 MPa, and 0.002439 MPa.
• The circulating water flow rate increases from 39.42 m³/s to 39.62 m³/s, 39.82 m³/s, 40.02 m³/s, and 40.22 m³/s.
• The unit net power output decreases from 1,276,442.99 kWh to 1,276,275.25 kWh, 1,276,103.89 kWh, 1,275,928.85 kWh, and 1,275,750.04 kWh.
• The circulating water outlet temperature rises from 15.54 °C to 15.64 °C, 15.74 °C, 15.84 °C, and 15.94 °C.
• The pump power increases from 5,433.71 kW to 5,513.34 kW, 5,593.75 kW, 5,674.96 kW, and 5,756.97 kW.
• The condenser heat transfer increases from 1,926,647.27 kW to 1,926,832.00 kW, 1,927,024.51 kW, 1,927,224.97 kW, and 1,927,433.21 kW.

From the figure, it can be seen that when seawater temperature rises or the cleanliness coefficient decreases, the unit’s back pressure, circulating water flow rate, pump power, outlet temperature, and heat transfer all increase, while the unit’s net power output decreases. Under the coupled disturbance of temperature and cleanliness coefficient, the variation trends of all unit parameters are consistent with those under single disturbances, but the magnitude of change is significantly greater than under single disturbances, and even exceeds that under the coupled disturbance of temperature and tide level.

3.5 Tide level and cleanliness coefficient coupled disturbance

At a fixed seawater temperature of 3.8 °C, we analyze the dynamic variations of unit back pressure, circulating water flow rate, unit net power output, circulating water outlet temperature, pump power, and condenser heat transfer over time under coupled disturbances of tide level and cleanliness coefficient.

Figure 11 illustrates that at 100 s, when the cleanliness coefficient decreases from 0.85 to 0.845, 0.84, 0.835, and 0.83, and the tide level simultaneously drops from 117 cm to 104 cm, 96 cm, 89 cm, and 70 cm, the following changes occur:

• The back pressure rises from 0.002397 MPa to 0.002402 MPa, 0.002405 MPa, 0.002409 MPa, and 0.002415 MPa.
• The circulating water flow rate increases from 39.42 m³/s to 39.48 m³/s, 39.56 m³/s, 39.64 m³/s, and 39.68 m³/s.
• The unit net power output decreases from 1,276,442.99 kWh to 1,276,317.48 kWh, 1,276,214.22 kWh, 1,276,114.28 kWh, and 1,275,955.48 kWh.
• The circulating water outlet temperature rises from 15.5391 °C to 15.5395 °C, 15.5399 °C, 15.5404 °C, and 15.5408 °C.
• The pump power increases from 5,433.71 kW to 5,519.12 kW, 5,589.13 kW, 5,654.68 kW, and 5,761.67 kW.
• The condenser heat transfer increases from 1,926,647.27 kW to 1,926,717.34 kW, 1,926,789.42 kW, 1,926,863.56 kW, and 1,926,939.83 kW.

When the cleanliness coefficient decreases, the circulating water flow rate tends to increase, whereas a drop in tide level reduces the circulating water flow. However, the effect of tide level on circulating water flow is much smaller than that of the cleanliness coefficient. Therefore, under the coupled influence of both factors, the overall circulating water flow shows an upward trend, although the magnitude of change is smaller compared to that under the coupled disturbances of temperature & cleanliness coefficient and temperature & tide level.

3.6 Temperature, Tide Level, and Cleanliness Coefficient Coupled Disturbance

This section analyzes the dynamic variation patterns of unit back pressure, circulating water flow rate, unit net power output, circulating water outlet temperature, pump power, and condenser heat transfer over time under the coupled disturbance of temperature, tide level, and cleanliness coefficient.

Figure 12 illustrates that at 100 s, when the seawater temperature rises from 3.8 °C to 3.9 °C, 4.0 °C, 4.1 °C, and 4.2 °C, the cleanliness coefficient decreases from 0.85 to 0.845, 0.84, 0.835, and 0.83, and the tide level simultaneously drops from 117 cm to 104 cm, 96 cm, 89 cm, and 70 cm, the following changes occur:

• The back pressure increases from 0.002397 MPa to 0.002408 MPa, 0.002420 MPa, 0.002430 MPa, and 0.002443 MPa.
• The circulating water flow rate rises from 39.42 m³/s to 39.6 m³/s, 39.78 m³/s, 39.98 m³/s, and 40.14 m³/s.
• The unit net power output decreases from 1,276,442.99 kWh to 1,276,213.44 kWh, 1,276,003.52 kWh, 1,275,794.33 kWh, and 1,275,522.962 kWh.
• The circulating water outlet temperature rises from 15.54 °C to 15.64 °C, 15.74 °C, 15.84 °C, and 15.94 °C.
• The pump power increases from 5,433.71 kW to 5,567.13 kW, 5,677.91 kW, 5,793.11 kW, and 5,950.91 kW.
• The condenser heat transfer increases from 1,926,647.27 kW to 1,926,832.00 kW, 1,927,024.51 kW, 1,927,224.97 kW, and 1,927,433.21 kW.

An increase in seawater temperature, a decrease in cleanliness coefficient, and a drop in tide level all lead to an elevation in back pressure. The effect of tide level variation on heat transfer and circulating water outlet temperature is minimal and can be neglected. Under the coupled influence of these three factors, the unit back pressure rises, the circulating water outlet temperature increases, and the unit net power output decreases, while the optimal circulating water flow rate, pump power, and heat transfer also increase. Moreover, the magnitude of change under this coupled condition is greater than in any other operational scenarios.

4 Conclusion

This study systematically analyzes the effects of seawater temperature, tide level, and condenser cleanliness coefficient disturbances on the flow and heat transfer performance of a nuclear power plant’s OCS. The findings are summarized as follows:

• Each disturbance type—increased seawater temperature, decreased tide level, or reduced cleanliness coefficient—elevates unit back pressure, decreases net power output, and increases circulating water flow rate, pump power consumption, and condenser heat transfer.
• Under coupled disturbances, these effects are amplified, with the combination of temperature and cleanliness coefficient having the most significant impact.
• Tide level variations exert minimal influence on condenser heat transfer and outlet temperature but noticeably affect circulating water flow rate and pump power.
• The three-factor coupled disturbance results in the greatest overall system performance variation.

Based on the above dynamic-response characteristics, practical on-site operational recommendations are put forward. Under the coupled disturbance of rising seawater temperature and condenser fouling, condenser back-pressure should be prioritized for monitoring. Once a remarkable back-pressure increment is observed, the operating set-point of circulating-water pumps shall be adjusted promptly, and condenser cleaning maintenance should be scheduled as early as practicable. Since tide-level variation imposes limited impact on heat-transfer performance, it can be regarded as a secondary monitoring indicator.

The above results offer theoretical prerequisites and technical references for cold-end-system regulation under off-design operating conditions. Future work will focus on integrating real-time disturbance prediction and intelligent control strategies to further improve the economic efficiency and operational stability of nuclear-power-plant cold-end systems.

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Footnotes

Edited by: Jiuwu Hui, The Hong Kong Polytechnic University, Hong Kong, China, Hong Kong, SAR, China

Reviewed by: Bo Wang, Harbin Engineering University, China

Danrong Song, Nuclear Power Institute of China (NPIC), China