The thermal-hydraulics program in support of the development of the Canadian supercritical water-cooled reactor (SCWR) concept has undergone several phases. It focused on key parameters such as heat transfer, critical flow, and stability of fluids at supercritical pressures. Heat-transfer experiments were performed with tubes, annuli, and bundles in water, carbon dioxide (CO2), or refrigerant flows. Data from these experiments have led to enhancement in understanding of the phenomena, improved prediction methods, and verified analytical tools. In addition, these experiments facilitated the investigation of separate effects on heat transfer (such as geometry, diameter, spacing device, and transient). Chocking flow characteristics were studied experimentally with sharp-edged nozzles of two different sizes of opening. Experimental data have been applied in improving the critical-flow correlation in support of accident analyses. A one-dimensional (1D) analytical model for instability phenomena has been developed and assessed against the latest experimental data for quantifying the prediction capability and applicability.
Canada is developing a pressure-tube-type supercritical water-cooled reactor (SCWR) concept with enhanced safety, proliferation resistance, and sustainability characteristics at compatible costs to current fleet of nuclear reactors . It joined the Generation-IV International Forum for cooperative research and development (R&D) with the international community and is currently collaborating with researchers in China, European Union, Japan, and the Russian Federation in developing SCWR concepts. Despite differences in core configuration of SCWR concepts being pursued in various countries, technical issues encountered in several technology areas are common and are addressed collectively .
Thermal-hydraulics at supercritical pressures has been identified as one of the critical technology areas in the development of the SCWR concept . It affects the operating power and the safety margin of the SCWR concept and also has an impact on the selection of cladding material and neutronic design. Canada has initiated a national program in support of R&D for the SCWR. Thermal-hydraulics studies have been performed at federal laboratories, federal agencies, Canadian Nuclear Laboratories, and Canadian universities [3,4]. A number of joint projects were established to extend the thermal-hydraulics R&D effort through bilateral collaborations between Canadian Nuclear Laboratories and researchers in China, the Russian Federation, and the United Kingdom. The objective of this paper is to present the latest advancement in thermal-hydraulics studies of the Canadian Gen-IV National Program supporting the development of the Canadian SCWR concept.
Canadian Supercritical Water-Cooled Reactor Concept
The Canadian SCWR concept is evolved from the heavy-water reactor, which is based on the modular fuel-channel configuration that separates the coolant from the moderator . Its core consists of an inlet plenum, where 366 fuel channels are installed through the bottom tubesheet (see Fig. 1). The outlet of each fuel channel is connected to an outlet header installed inside the inlet plenum to minimize the pressure and temperature gradients and in turn the thickness of the header wall. Light-water coolant from the feedwater pump is injected into the inlet plenum through four water lines. It travels around the outlet header to the fuel-channel openings just above the tubesheet. After entering the fuel channel, the coolant travels into the fuel assembly through four nozzles and flows down the central-flow tube (see Fig. 1). The flow direction of the coolant reverses at the bottom of the flow tube and the coolant travels upward through the fuel rods. After exiting the fuel rods, the steamlike coolant travels to the outlet headers and is discharged to the high-pressure turbine through the steam pipes (direct thermodynamics cycle). The fuel channels are submerged in the low-pressure heavy-water moderator housed inside the Calandria below the tubesheet. A recirculation system is installed to cool the moderator both actively and passively.
The fuel assembly consists of a “flasklike” structure housing a 64-rod fuel bundle. A layer of yttria stabilized zirconia is installed inside the structure wall to insulate the zirconium pressure tube, which contacts directly the moderator, from the high-temperature coolant (Fig. 2). It is cladded both sides to maintain its structure.
The fuel bundle consists of two rings of 32 fuel rods around the central-flow tube. Each fuel rod contains mix thorium and plutonium (13 wt % on average) pellets over a 5 m active length inside an Alloy 800H cladding tube. End caps are welded to the ends of the tube. Wire-wrapped spacers are installed to maintain the spacing between rods and minimize vibration.
The Canadian SCWR concept is developed to generate 2540 MW of thermal power and operate at the pressure of 25 MPa and core outlet temperature of 625 °C, matching closely the advanced supercritical pressure turbine. Its gross thermal efficiency is 48% (compared to 33–35% for the current generation of nuclear reactors) resulting in 1200 MW electric power. Cogeneration is feasible for producing hydrogen, steam, heat, and fresh water (through the desalination process).
Thermal-Hydraulics Studies in Canada's National Gen-IV Program
Canada established the Generation-IV National Program to coordinate R&D effort among federal laboratories and agency in developing the SCWR concept . The program was managed at the Natural Resources Canada and was carried out in phases; the first phase was started in 2008 and completed in 2011 and the second phase was initiated in 2012 and completed in 2015. A separate program was managed at the Natural Science and Engineering Research Council to coordinate effort among academia . It was initiated in 2009 and completed in 2016 (also in two phases).
The first phase of the program focused on the fundamental R&D work in material, chemistry, thermal-hydraulics, and safety to support the development of the Canadian SCWR concept. Several literature reviews were carried out to understand the phenomena and large amount of experimental data were compiled for development of prediction methods and establishment of future experimental programs. New facilities were constructed to enhance the infrastructure and R&D capabilities of the federal laboratories and universities. Fundamental experiments were performed to provide supplemental data for enhancing the understanding and knowledge base.
The second phase of the program aimed at applied R&D work covering mechanical components, reactor physics, fuel, and fuel channel, in addition to material, chemistry, thermal-hydraulics, and safety. Further in-depth studies were carried out to complete the development of the Canadian SCWR concept.
Thermal-hydraulics studies in the program covered both experimental and analytical work. Heat-transfer experiments were performed with water through vertical annuli of two different gap sizes and with carbon dioxide (CO2) or Refrigerant-134a (R-134a) through vertical tubes in the first phase. Data obtained from these experiments have been applied in assessing and validating tube-data-based prediction methods. In phase II, heat-transfer experiments were performed with a three-rod bundle in CO2 flow, a four-rod bundle in water flow, and a seven-rod bundle in R-134a flow. Data from these experiments are being applied in validating subchannel codes and computational fluid dynamics (CFD) tools. Table 1 summarizes all the heat-transfer experiments in the Canadian Program. Experiments studying the critical-flow phenomena were also performed using two sharp-edge orifices. Data were applied in assessing and updating the current critical-flow models (which were developed for subcritical pressures) in support of the analysis of the postulated large-break loss-of-coolant accident or the design of the pressure-relieve valve. Experiments and analytical studies were carried out to study static and oscillatory instabilities in natural circulation flow under supercritical conditions.
As mentioned earlier, studies in phase I of the Gen-IV National Program focused on compilation of experimental data to understand the phenomena. An extensive database has been compiled on heat transfer in tubes, annuli, and bundles cooled with water, CO2, or refrigerant flows at supercritical pressures. This database was applied in assessing tube-data-based prediction methods for incorporation into the subchannel code. Furthermore, it was used to develop a transcritical heat-transfer look-up table for water flow in tubes improving the prediction accuracy. Through the comparison of heat-transfer behaviors for different fluids, a set of fluid-to-fluid modeling parameters were developed for heat transfer at supercritical pressures. In phase II, experimental data obtained with bundles were applied in assessing the prediction accuracy of the subchannel code and CFD tool. This has improved the confidence in applying these tools to derive a heat-transfer correlation for the Canadian SCWR fuel assembly. Based on the critical-flow measurements obtained in phase I experiments, a critical-flow model has been derived and incorporated into the reactor-safety code for safety analyses.
Heat Transfer in Tubes and Annuli
Heat-transfer experiments using simple geometry (such as tubes and annuli) provide data to understand the fundamental phenomena, derive correlations, and validate CFD tools. Tube-data-based correlations have been incorporated into subchannel codes for assessing heat-transfer behaviors in bundles. It is premature to perform experiments with a full-scale fuel assembly at the conceptual design phase. Therefore, bundle-specific heat-transfer correlations are unavailable. Tube-data-based correlations have been applied in safety analyses for SCWR concepts.
An extensive heat-transfer database has been compiled through collaboration with other research organizations . The latest set of data was contributed from Nuclear Power Institute of China and was obtained with water or CO2 flow in tubes. Including these data, the database contains over 26,000 data points for water flow and close to 20,000 data points for CO2 flow in tubes. Additional data from recent experiments are being compiled and would further expand the database.
The database has been applied in assessing the prediction accuracy of 18 heat-transfer correlations . Overall, the correlation of Chen and Fang  provides the best prediction accuracy for both water and CO2 flows. Correlations of Bishop et al. , Wang and Li , and Mokry et al.  also agree with the water-flow data reasonably well. Figure 3 compares predicted wall temperatures and heat-transfer coefficients of various correlations against experimental data of Nuclear Power Institute of China , which were obtained with water flow in a 6 mm ID tube and CO2 flow in an 8 mm ID tube. The correlation of Chen and Fang  follows closely the experimental data, while the other correlations overpredict the heat-transfer coefficients (hence underpredicting wall temperatures). Similar trends were observed for CO2 data. The correlation of Chen and Fang  agrees closely with the experimental data compared to the correlations of Wang et al.  and Watts and Chou .
The majority of heat-transfer correlations are expressed as a function of fluid properties at the wall. Previous assessments implemented the experimental information in establishing the goodness-to-fit of the available data. From the application point of view where wall temperature is not known a priori, an iterative approach is required. It has been applied with the Chen and Fang correlation  for a selected set (8373 data points) of water data. The iteration was not converged for 110 data points. Overall, the wall-temperature measurements have been overpredicted by about 5% with a standard deviation of 10% for 8263 data points.
Heat Transfer in Bundles
The heat-transfer behavior in rod bundles is more complex than simple channels such as tubes and annuli. It is attributed to the geometry configuration and power distributions that lead to enthalpy and flow imbalances in subchannels of the bundle. As the development of SCWRs is still at the conceptual phase, experiments using full-scale bundles are premature. Heat-transfer behaviors have been investigated using subassemblies at supercritical pressures [16–18].
Canadian Nuclear Laboratories collaborated with Xi'an Jiaotong University in investigating the heat-transfer characteristics in a 2 × 2 rod bundle with and without the wire-wrapped spacers [16,17]. Nonuniform circumferential wall-temperature distributions were observed around the uniformly heated rods. Peak temperatures were measured at the narrow-gap region between the rod and the unheated ceramic square enclosure and minimum temperatures at the central subchannel between all the four heated rods. Differences between peak and minimum wall temperatures depend on the flow conditions. Heat-transfer enhancement was observed for the bundle equipped with the wire-wrapped spacers. It is, however, relatively small.
The 2 × 2 rod bundle data have been applied in assessing the tube-data-based heat-transfer correlations based on cross-sectional averaged conditions. This assessment provides the general view on the applicability of these correlations for bundles. Figure 4 compares the predictions of three correlations (which have been shown to provide the best overall prediction accuracy) against experimental heat-transfer coefficients and measured wall temperatures. Correlations of Chen and Fang , Bishop et al. , and Griem  agree closely with experimental values for the bundle without the wire-wrapped spacers. However, only the correlation of Chen and Fang  follows closely the experimental values for the bundle with the wire-wrapped spacers. Correlations of Wang et al.  and Jackson  underpredict the wall temperatures at subcritical bulk-fluid temperatures but the differences reduce as the bulk-fluid temperature approaches the pseudocritical temperature.
The effect of spacer configuration on heat transfer has been examined in a three-rod bundle cooled with CO2 at supercritical pressures . Wire-wrapped or grid spacers were installed onto the heated rods. Figure 5 illustrates axial wall-temperature distributions and calculated heat-transfer coefficients along one heated rod. Overall, there are not much differences in wall temperatures between wire-wrapped and grid spacers. However, the variation in wall temperature at various circumferential positions of the heat rod is smaller for the wire-wrapped spacer than the grid spacers at the subcritical temperature region. This may be attributed to the improved mixing between subchannels of the wire-wrapped spacer reducing the flow and enthalpy imbalances. Localized heat-transfer enhancement has been observed at the grid spacer locations but decayed over a short distance from the spacer.
A reduction in wall temperature has also been observed at the inlet region of the bundle with the wire-wrapped or grid spacer. This is attributed to the development of the thermal-boundary layer. Similar trend was shown for the 8 mm tube at the same flow conditions. The region of wall-temperature reduction appears to be shorter for the wire-wrapped spacer than the grid spacer. This could be attributed to the improved mixing that enhances the development of the thermal-boundary layer.
Assessment of Subchannel Code
As indicated previously, it is premature to perform heat-transfer experiments on the simulator of full-scale fuel assembly at the conceptual phase. The current approach in establishing the heat-transfer characteristics of the proposed SCWR fuel assembly has been based on predictions of subchannel codes coupling with CFD tools . Several assessments against bundle subassemblies were performed to quantify the prediction accuracy of the subchannel and improve the confidence of the fuel assembly concept. One of the assessments applied the Jackson correlation  in predicting the heat-transfer coefficient in the subchannel .
Another assessment was carried out to compare the prediction accuracies of other correlations. Figure 6 compares the predicted wall temperatures using the ASSERT-PV  subchannel code with six different correlations (including the Jackson correlation). Overall, applying the correlation of Mokry et al.  resulted in overprediction of the circumferential wall temperature distribution while using the Dittus–Boelter correlation  and Swenson et al. correlation  has led to underprediction. The Jackson correlation  provides reasonably close predictions of the circumferential wall temperature but the Kurganov correlation  agrees well with the experimental data, especially at the near pseudocritical bulk-fluid temperature.
Modeling of the flasklike fuel assembly configuration is challenging for the subchannel code (see Fig. 2). While walls of the pressure tube and the central-flow tube are insulated, heat is transferred from the high-temperature coolant in the fuel-rod region to the inlet coolant inside the central-flow tube and the moderator outside the pressure tube. The ASSERT-PV's heat-transfer algorithm has been improved to model the heat losses to the moderator and another algorithm was developed to model the heat transferred to the inlet coolant inside the central-flow tube. An assessment of the improved algorithm showed a reduction in the maximum cladding temperature prediction .
Assessment of Turbulent Models in the star ccm+ Computational Fluid Dynamics Tool
Subchannel codes are mainly valid for cases corresponding to implemented models (such as heat transfer, hydraulics resistance, and mixing). From the heat transfer point of view, these codes are valid mainly for uniformly (both axially and circumferentially) heated bare subchannels since all the heat-transfer correlations implemented into the codes were based on data of uniformly heated bare tubes. As the fuel assemblies may encounter a variety of scenarios during operations, heat-transfer characteristics for different configurations (such as spacers, nonuniform axial and radial powers, and rod deformation) are required and could not be quantified using the subchannel codes.
Computational fluid dynamics tools have been applied in quantifying various separate effects on heat transfer and mixing at supercritical pressures. Attributed to the complexity of heat-transfer characteristics at subcritical, pseudocritical, and supercritical temperatures, it has been demonstrated that a single turbulent model or a set of modeling parameters is inappropriate for all the regions. Figure 7 compares predictions of the star ccm+ CFD tool against circumferential wall-temperature distributions over a rod of the 2 × 2 bare-rod bundle . Changing the turbulent model provides better agreement over various regions.
The star ccm+ tool was then applied in predicting the effect of wire-wrapped spacers on heat transfer in the 2 × 2 rod bundle . Figure 8 compares the predictions against the measured circumferential wall-temperature distribution at the supercritical bulk-fluid temperature. Despite the reasonably close predictions for the bare-rod bundle, the tool underpredicts the wall temperature by about 10 °C. In addition, the peak temperature location has been shifted away from the narrow-gap location between the heated rod and the ceramic shroud by about 45 deg. Examining closer the axial wall temperature distribution (left-side figure), wall temperatures were predicted higher at upstream than downstream locations of the wire-wrapped spacer. This seems to be an exaggeration of the heat transfer enhancement over the wire.
Wall-temperature measurements obtained from the 2 × 2 bundle were relatively sparse and might not have provided the full picture. Detailed measurements in wall temperature were obtained with CO2 flow through a three-rod bundle equipped with wire-wrapped spacers . The heat-transfer characteristics were presented in the Heat Transfer in Bundles section. The prediction capability of the star ccm+ tool was assessed against the experimental wall temperature measurements . Figure 9 shows the mesh configuration in the simulation and the comparison of measured and predicted axial wall temperature distributions. The tool provides good predictions at the inlet region (subcritical bulk-fluid temperature) but deviates from the measurements at downstream locations with increasing bulk-fluid temperature. These simulations were based on the same turbulent model, which might not be applicable for the pseudocritical or supercritical regions.
Chocking Flow Studies
An important step in the design and safety analysis of a nuclear reactor is the understanding and modeling of chocking flow, as it is used for pressure-relief valve design and/or selection as well as for modeling accident scenarios, such as a large-break loss-of-coolant accident. Although the choking flow phenomenon has been extensively studied, there is limited information and knowledge under supercritical conditions. Critical-flow experiments were carried out at upstream pressures ranging from 22.1 MPa to 32.1 MPa, flow temperatures between 50 °C and 502 °C, and discharge pressures between 0.1 MPa and 3.6 MPa. A total of 545 data points were obtained (Fig. 10 shows a comparison of chocking flow data). These data were applied in assessing the homogeneous-flow and separated-flow models. Both models have been shown inadequate to capture the phenomena at supercritical pressures. The homogeneous-flow model was modified to improve the prediction accuracy .
A significant variation in density is encountered over the fuel assembly in SCWRs, similar to the boiling-water reactors. It has a strong implication to the neutronic of the core and could lead to instability. Analytical models and experiment studies were performed to improve the understanding of flow stability phenomena at supercritical pressures [32,33]. Flow stability boundaries were derived for water flow in single and parallel channels at supercritical pressures. In addition, stability in a two-dimensional axisymmetric pipe with upward flow of supercritical water was modeled using the CFD tool “ANSYS cfx v14.5” with various Reynolds-averaged Navier–Stokes turbulent models  and compared against that predicted using an one-dimensional (1D) analytical model. Good agreement in predicted boundaries was observed between the CFD tool and the one-dimensional analytical model for both static and oscillatory instabilities.
Two phases of Canada's Generation-IV National Program have provided crucial R&D support for developing the Canadian SCWR concept. Thermal-hydraulics and safety projects have led to enhanced understanding of the complexity in heat transfer, hydraulics resistance, stability, and critical flow for developing the fuel assembly and safety system concepts. Large amount of experimental data on thermal-hydraulics parameters have been obtained for verifying and validating prediction methods and analytical tools. Analyses of these data facilitate development or improvement of prediction methods. Verification and validation of analytical tools have strengthened the confidence on the current fuel assembly and reactor-safety system concepts. Benchmarking of CFD tools and subchannel codes against experimental data obtained with bundles showed that these analytical tools provide reasonably close predictions. In addition, turbulent models in CFD tools may not be universally applicable for all the heat-transfer regimes. Further studies are recommended to improve the prediction capability of these tools.
Large amount of experimental data were obtained for chocking flow at upstream supercritical pressures. A new critical-flow model, based on a modification of the homogeneous model, has been derived. Implementing this model facilitates the design of pressure-relief valves and the safety analysis of a large-break loss-of-coolant accident.
A one-dimensional analytical model has been developed for predicting the instability boundaries of water flow in tubes at supercritical pressures. These boundaries were supported with the CFD tool using the Reynolds-averaged Navier–Stokes models.
The authors thank Professor Q. C. Bi and Dr. H. Wang of Xi'an Jiantong University, Professor S. Tavoularis and Mr. A. Eter of University of Ottawa for providing the experimental data, Professor A. Teyssedou and A. Muftuoglu of École Polytechnique de Montréal, and Professor V. Chatoorgoon of University of Manitoba for sharing their results as well as Dr. H. Zahlan and Dr. K. Podila for sharing their analytical results. Financial support of the Canadian Gen-IV National Program has been provided by the Office of Energy Research and Development (OERD) at Natural Resources Canada, the Natural Sciences and Engineering Research Council (NSERC), and Canadian Nuclear Laboratories.
- D =
- DTpc =
temperature difference between the pseudocritical temperature and fluid temperature, °C
- G =
mass flux, kg/m2 s
- hb =
bulk enthalpy, J/kg
- H =
heat-transfer coefficient, W/m K
- P =
- Pc =
critical pressure, Pa
- Q =
heat flux, W/m2
- Tb =
bulk temperature, °C
- Tin =
inlet temperature, °C
- Tw =
wall temperature, °C