**2. Heat transfer at supercritical conditions**

Heat transfer at supercritical conditions is characterized by changes in the thermophysical properties of the fluid specifically at pseudocritical points. A pseudocritical point exists at a pressure above the critical pressure of a fluid and at a temperature corresponding to the maximum value of the specific heat for this particular pressure (Pioro and Duffey, 2007). The increase in the specific heat reaches its maximum at the critical point and then decreases as the pressure increases. Furthermore, the pseudocritical temperature increases as the pressure increases. For instance, the corresponding pseudocritical temperatures of lightwater at 23 and 25 MPa are approximately 377.5 and 384.9°C, respectively. Nevertheless, as the temperature passes through the pseudocritical temperature, the specific heat increases. This increase in the specific heat of the fluid allows for the deposition of a significant

<sup>1</sup>Currently, such option is used in CANDU-6 reactors.

Thermal Aspects of Conventional and Alternative Fuels

reactors (Pioro and Duffey, 2007).

SCW NPPs.

**2.1 Heat-transfer correlations** 

be used (Bae and Kim, 2009).

efficiencies compared to those of the current NPPs.

in SuperCritical Water-Cooled Reactor (SCWR) Applications 127

a b

In terms of the operating conditions of the coolant, these reactors are all categorized as subcritical. PWRs have the highest operating pressure approximately at 15 MPa followed by CANDU reactors and BWRs, which operate at a pressure of 11 and 7 MPa, respectively. The outlet temperature of the coolant depends on the operating pressure of the reactor. In PWRs and CANDU reactors, the outlet temperature of the coolant is slightly below the saturation temperature of their corresponding operating pressures in order to avoid boiling of the coolant inside the reactor and achieve a high enthalpy rise across the reactor core. In addition, it is necessary to maintain the pressure within an operational margin due to pressure fluctuation during operation. As a result, the thermal efficiency of NPPs is limited by operating at subcritical pressures. Consequently, the operating pressure must be increased to pressures above the critical pressure in order to achieve higher thermal

As shown in Fig. 3b, SCWRs operate at pressures and temperatures above the critical pressure and temperature of water. These high temperatures and pressures make it possible to use supercritical "steam" turbines, which have led to high thermal efficiencies when used in coal-fired power plants. As a result, SCWRs will use a proven technology, which has been examined over 50 years of operation in coal-fired power plants. The use of such technology minimizes the technological barriers for the development of suitable turbines for use in the

The development of SCWRs requires an intensive study of convective heat transfer at supercritical pressures. Heat transfer at a supercritical pressure is different from that of a subcritical pressure because the thermophysical properties of a light-water coolant undergo significant variations as the temperature of the coolant passes through the pseudocritical point. Therefore, the traditional Nusselt number and other related non-dimensional parameters developed at subcritical pressures based on the bulk-fluid temperature cannot

Fig. 3. a) Density of water at 7, 11, and 15 MPa and b) Operating parameters of several

amount of heat into the fluid. Eventually, this deposited heat can be converted into mechanical energy in steam turbines.

In addition to the specific heat, other thermophysical properties of a fluid undergo significant changes at the pseudocritical point. These changes affect the heat transfer capabilities of the fluid. Therefore, it is important to ensure that the thermophysical properties of a supercritical fluid are determined with accuracy. Figure 2 shows density and specific heat of water at 22.064 and 25 MPa. These thermophysical properties of water have been determined using the NIST REFPROP software.

Fig. 2. a) Density and b) specific heat of water at 22.064 and 25 MPa.

In general, all thermophysical properties experience considerable changes near the critical and pseudocritical points. These changes are the greatest near the critical point; whereas, they become more gradual in the vicinity of the pseudocritical point. This gradual change in the thermophysical peroperties of fluids results in asingle-phase flow at supercritical conditions. In contrast, at subcritical conditions, a two-phase flow exists as the temperature of the fluid reaches the saturation temperature corresponding to the operating pressure. At the saturation tempertaure, the fluid undergoes a phase change from liquid to vapor when heat is added to the fluid. As a result of this phase change, there is a discontinuity in the variation of the thermophysical properties of the fluid. Figure 3a shows the density of water at 7, 11, and 15 MPa pressures, which correspond to the operating pressures of BWRs, CANDU reactors, and PWRs. As shown in Fig. 3a, there is a sharp drop in the density of water as the saturation temperatures of the corresponding pressures are reached.

The thermal efficiency of a Nuclear Power Plant (NPP) to a large extent depends on the pressure and temperature of the steam at the inlet to the turbine when the Rankine cycle is considered. In the case of either a direct cycle or an indirect cycle, the physical properties of the steam at the inlet of the turbine depend on the operating temperature and pressure of the reactor coolant. Figure 3b shows the operating pressures and temperatures of BWRs, PWRs, and PHWRs (e.g., CANDU reactors), which comprise the vast majority of the currently operating NPPs.

amount of heat into the fluid. Eventually, this deposited heat can be converted into

In addition to the specific heat, other thermophysical properties of a fluid undergo significant changes at the pseudocritical point. These changes affect the heat transfer capabilities of the fluid. Therefore, it is important to ensure that the thermophysical properties of a supercritical fluid are determined with accuracy. Figure 2 shows density and specific heat of water at 22.064 and 25 MPa. These thermophysical properties of water have

a b

In general, all thermophysical properties experience considerable changes near the critical and pseudocritical points. These changes are the greatest near the critical point; whereas, they become more gradual in the vicinity of the pseudocritical point. This gradual change in the thermophysical peroperties of fluids results in asingle-phase flow at supercritical conditions. In contrast, at subcritical conditions, a two-phase flow exists as the temperature of the fluid reaches the saturation temperature corresponding to the operating pressure. At the saturation tempertaure, the fluid undergoes a phase change from liquid to vapor when heat is added to the fluid. As a result of this phase change, there is a discontinuity in the variation of the thermophysical properties of the fluid. Figure 3a shows the density of water at 7, 11, and 15 MPa pressures, which correspond to the operating pressures of BWRs, CANDU reactors, and PWRs. As shown in Fig. 3a, there is a sharp drop in the density of

water as the saturation temperatures of the corresponding pressures are reached.

The thermal efficiency of a Nuclear Power Plant (NPP) to a large extent depends on the pressure and temperature of the steam at the inlet to the turbine when the Rankine cycle is considered. In the case of either a direct cycle or an indirect cycle, the physical properties of the steam at the inlet of the turbine depend on the operating temperature and pressure of the reactor coolant. Figure 3b shows the operating pressures and temperatures of BWRs, PWRs, and PHWRs (e.g., CANDU reactors), which comprise the vast majority of the

Fig. 2. a) Density and b) specific heat of water at 22.064 and 25 MPa.

mechanical energy in steam turbines.

currently operating NPPs.

been determined using the NIST REFPROP software.

Fig. 3. a) Density of water at 7, 11, and 15 MPa and b) Operating parameters of several reactors (Pioro and Duffey, 2007).

In terms of the operating conditions of the coolant, these reactors are all categorized as subcritical. PWRs have the highest operating pressure approximately at 15 MPa followed by CANDU reactors and BWRs, which operate at a pressure of 11 and 7 MPa, respectively. The outlet temperature of the coolant depends on the operating pressure of the reactor. In PWRs and CANDU reactors, the outlet temperature of the coolant is slightly below the saturation temperature of their corresponding operating pressures in order to avoid boiling of the coolant inside the reactor and achieve a high enthalpy rise across the reactor core. In addition, it is necessary to maintain the pressure within an operational margin due to pressure fluctuation during operation. As a result, the thermal efficiency of NPPs is limited by operating at subcritical pressures. Consequently, the operating pressure must be increased to pressures above the critical pressure in order to achieve higher thermal efficiencies compared to those of the current NPPs.

As shown in Fig. 3b, SCWRs operate at pressures and temperatures above the critical pressure and temperature of water. These high temperatures and pressures make it possible to use supercritical "steam" turbines, which have led to high thermal efficiencies when used in coal-fired power plants. As a result, SCWRs will use a proven technology, which has been examined over 50 years of operation in coal-fired power plants. The use of such technology minimizes the technological barriers for the development of suitable turbines for use in the SCW NPPs.

#### **2.1 Heat-transfer correlations**

The development of SCWRs requires an intensive study of convective heat transfer at supercritical pressures. Heat transfer at a supercritical pressure is different from that of a subcritical pressure because the thermophysical properties of a light-water coolant undergo significant variations as the temperature of the coolant passes through the pseudocritical point. Therefore, the traditional Nusselt number and other related non-dimensional parameters developed at subcritical pressures based on the bulk-fluid temperature cannot be used (Bae and Kim, 2009).

Thermal Aspects of Conventional and Alternative Fuels

2010). Figure 4 shows a single-reheat cycle for SCW NPPs.

Fig. 4. Single-reheat cycle for SCW NPPs (Naidin et al., 2009).

**3.1 Thermal cycles** 

in SuperCritical Water-Cooled Reactor (SCWR) Applications 129

The use of supercritical "steam" turbines in NPPs leads to higher thermal efficiencies compared to those of the current NPPs. There are several design options of Rankin cycles in order to convert the thermal energy of the supercritical "steam" into mechanical energy in a supercritical turbine. These design options include direct, indirect, and dual cycles. In a direct cycle, supercritical "steam" from the reactor passes directly through a supercritical turbine eliminating the need for the steam generators. This elimination reduces the costs and leads to higher thermal efficiencies compared to those produced in indirect cycles. In an indirect cycle, the supercritical coolant passes through the heat exchangers or steam generators to transfer heat to a secondary fluid, which passes through the turbine(s). The advantage of an indirect cycle is that potential radioactive particles would be contained inside the steam generators. On the other hand, the temperature of the secondary loop fluid is lower than that of the primary loop (e.g., reactor heat transport system loop). As a result, the thermal efficiency of an indirect cycle is lower than that of a direct cycle (Pioro et al.,

With direct cycles, the thermal efficiency can be increased further through a combination of reheat and regeneration options. As shown in Fig. 4, in a single-reheat cycle, supercritical "steam" from the reactor passes through a high pressure turbine where its temperature and pressure drop. Then, the steam from the outlet of the high pressure turbine is sent through the SRH fuel channels inside the reactor core, but at a lower pressure. As the steam passes through the SRH fuel channels its temperature increases to an outlet temperature of 625°C at a pressure between 3 and 7 MPa (Pioro et al., 2010). At the outlet of the SRH channels, SHS passes through the intermediate pressure turbines. When a regenerative option is

At a supercritical pressure, the thermophysical properties of a coolant at the sheath-wall temperature differ significantly from those at the bulk-fluid temperature. Although, a fluid does not undergo a phase change at a supercritical pressure, a low-density fluid separates the sheath-wall from a high-density fluid at high heat fluxes and low mass fluxes. This results in a reduction in the convective Heat Transfer Coefficient (HTC). Consequently, the sheath-wall temperature increases. This phenomenon is known as the Deteriorated Heat Transfer (DHT) regime. Therefore, the sheath-wall temperature must be reflected in a correlation, which is used to study the heat transfer at supercritical conditions.

Many correlations have been developed for the calculation of HTC at supercritical conditions. The most widely used correlations include those developed by Bishop et al. (1964); Swenson et al. (1965); Krasnoscheckov et al. (1967); Jackson (2002); and Mokry et al. (2009). Zahlan et al. (2011) compared the prediction capabilities of sixteen correlations including the aforementioned correlations. The conclusion of the Zahlan et al. (2011) comparison study showed that the Mokry et al. (2009) correlation resulted in the lowest Root-Mean-Square (RMS) error within the supercritical region compared to all other examined correlations.
