Numerical investigation of supercritical water-cooled nuclear reactor in horizontal rod bundles

The commercial CFD code STAR-CD v4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round rods and rod bundles. Reactors with vertical or horizontal flow in the core can be found. In vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal rods and rod bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with temperature. In the rod bundle simulations, it is found that the geometry and orientation of the rod bundle have strong effects on the wall temperature distributions and heat transfers. In one orientation the square bundle has a higher wall temperature difference than other bundles. However, when the bundles are rotated by 90° the highest wall temperature difference is found in the hexagon bundle. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

竖直上升管中超临界水的宽范围换热关联式

本文针对超临界压力水在竖直上升管内的传热工况,广泛搜集公开文献中的实验数据,建立并整理了宽范围实验数据库;引入两组无量纲数表征超临界流体强烈物性变化及其次级效应对传热的影响,基于无量纲数敏感性分析与多重共线性评估,采用主成分分析回归建立了两种形式的宽范围换热关联式;对两个关联式进行评价,并与其他关联式进行比较,这两个关联式在适用范围、误差大小和准确度方面均优于其他关联式。     

Fluid-to-fluid scaling of heat transfer in circular tubes cooled with supercritical fluids

Experimental investigations of heat transfer at prototypical conditions of supercritical water cooled reactors (SCWRs) are strongly limited due to their huge technical and financial efforts required. One of the possible solutions is the application of model fluids, which have much lower critical pressure and critical temperature. Model fluid technique has been widely applied in the thermal-hydraulic studies of nuclear engineering. In spite of growing activities of heat transfer at supercritical conditions using model fluids, there does still not exist any reliable fluid-to-fluid scaling methods, to transfer the test data in model fluids directly to the conditions of prototype fluid. This paper presents a fluid-to-fluid scaling method for heat transfer in circular tubes cooled with supercritical fluids. Based on conservation equations and boundary conditions, one set of dimensionless numbers and the requirements of a complete scaling are determined. Scaling of pressure and temperature ensures the similarity of thermo-physical properties of various fluids. A new dimensionless number, presenting the product of the so-called pseudo Boiling number, Reynolds number and Prandtl number, is applied to scale heat flux. The distortion approach is used to scale mass flux. The scaling of heat transfer coefficient is based on Nusselt number. In addition, a new approach is introduced to validate the scaling law. The validation results show good feasibility and reasonable accuracy of the proposed scaling law. Assessment of scaling factors of various parameters indicates the high feasibility of Freon-134a as model fluid for SC water. Some guidelines can be derived for the future experimental investigations on heat transfer at supercritical pressures using model fluid techniques.     

Numerical investigation of acceleration effect on heat transfer deterioration phenomenon in supercritical water

It is important to understand the heat transfer deterioration (HTD) phenomenon for specifying cladding temperature limits in the fuel assembly design of supercritical water-cooled reactor (SCWR). In this study, a numerical investigation of heat transfer in supercritical water flowing through vertical tube with high mass flux and high heat flux is performed by using six low-Reynolds number turbulence models. The capabilities of the addressed models in predicting the observed phenomena of experimental study are shortly analyzed. Mechanisms of the effect of flow structures and fluid properties on heat transfer deterioration phenomenon are also discussed. Numerical results have shown that the turbulence is significantly suppressed when the large-property-variation region spreads to the buffer layer near the wall region, resulting in heat transfer deterioration phenomenon. The property variations of dynamic viscosity and specific heat capacity in supercritical water can impair the deterioration in heat transfer, while the decrease of thermal conductivity contributes to the deterioration.     

Single-phase convective heat transfer in rod bundles

The convective heat transfer for turbulent flow through rod bundles representative of nuclear fuel rods used in pressurized water reactors is examined. The rod bundles consist of a square array of parallel rods that are held on a constant pitch by support grids spaced axially along the rod bundle. Split-vane pair support grids, which create swirling flow in the rod bundle, as well as disc and standard support grids are investigated. Single-phase convective heat transfer coefficients are measured for flow downstream of support grids in a rod bundle. The rods are heated using direct resistance heating, and a bulk axial flow of air is used to cool the rods in the rod bundle. Air is used as the working fluid instead of water to reduce the power required to heat the rod bundle. Results indicate heat transfer enhancement for up to 10 hydraulic diameters downstream of the support grids. A general correlation is developed to predict the heat transfer development downstream of support grids. In addition, circumferential variations in heat transfer coefficients result in hot streaks that develop on the rods downstream of split-vane pair support grids.     

Numerical simulation of flows in tight-lattice fuel bundles

The flow in tight rod bundles is characterized by long-term, large-scale coherent patterns in the stream-wise direction.

In the present work, the issue of simulating these structures through unsteady CFD simulations employing periodic boundary conditions in the stream-wise direction, will be addressed. The validity of the approach is assessed through the comparison of a large eddy simulation (LES) for similar flow conditions inside a simplified geometry and experimental data.

A powerful statistical tool (proper orthonormal decomposition) is used to analyze the time varying solution. The flow field has been decomposed into a series of normal modes, identifying the structures responsible for the flow transfer between sub-channels. Additional insights on the physics of these coherent structures are obtained.

An unsteady Reynolds averaged Navier–Stokes simulation (URANS) of the flow in a rod bundle has then been carried out. The comparison between numerical results and experimental results [Krauss, T., Meyer, L., 1998. Experimental investigation of turbulent transport of momentum and energy in a heated rod bundle. Nucl. Eng. Design 180, 185–206] proves that accuracy can be achieved for averaged statistics such as stream-wise velocity, turbulent intensity and wall shear stresses.     

A simplified method for heat transfer prediction of supercritical fluids in circular tubes

This paper presents a new method for heat transfer prediction in supercritical fluids. Emphasis is put on the simplicity of the correlation structure, its explicit coupling with physical phenomena and the selection criteria of the test data. Assessment of qualitative behaviour of heat transfer is carried out based on existing test data and the experience gathered in the open literature. A single dimensionless number, the acceleration number, is introduced to correct the deviation of heat transfer of supercritical fluids from that of conventional fluids. The new correlation structure excludes any direct dependence of the heat transfer coefficient on the wall surface temperature, and eliminates possible numerical instability. The uncertainty analysis of the test data provides information about the sources and the levels of uncertainties of various parameters, and is strongly required for the selection of both the dimensionless parameters implemented into the heat transfer correlation and the test data for the derivation of correlations. Detailed assessment shows that the new correlation gives reasonable prediction accuracy over a wide parameter range and is also capable of predicting heat transfer behaviour in the heat transfer deterioration region.     

Pressure drop and heat transfer in gas-cooled rod bundles

Extensive experimental and analytical investigations of fluid flow and heat transfer in gas-cooled rod bundles have been carried out. Different bundle geometries with partially or fully roughened rod surfaces were tested in a carbon dioxide loop. An advanced and comprehensive measuring control and instrumentation are important design features of this experiment. Comprehensive thermal hydraulic subchannel analysis computer codes have been developed in order to assist fuel element design calculation for gas-cooled reactors. The experiments, codes and their verification procedure are described and the results of comparisons between measured and calculated pressure and temperature distributions are given.     

Critical heat flux prediction in rod bundles under upward low mass flux densities

The analysis of experimental data and results of calculations for heat transfer crisis in heated channels under low upward coolant mass flux densities is presented. This analysis allows the determination of the basic features of the boiling crisis phenomenon. It is shown that the methods currently used for critical heat flux (CHF) prediction have insufficient accuracy in the given range of parameters. A new relationship for the CHF calculation is presented. It should be used for the water–water energy reactor (WWER) and uran–graphite channel reactor—Chernobyl-type (RBMK) rod bundles, and is verified by the test data. The comparison of results obtained by a new CHF correlation and the relationship used in RELAP5/MOD3.1 Code is presented. It is shown that the latter overpredicts the CHF values at atmospheric pressure and for x_cr>0.4 and does not provide conservative estimations for the RBMK fuel bundles.     

CFD investigation of vertical rod bundles of supercritical water-cooled nuclear reactor

The commercial CFD code STAR-CD v4.02 is used as the numerical simulation tool for the supercritical water-cooled nuclear reactor (SCWR). The numerical simulation is based on the real full 3D rod bundles’ geometry of the nuclear reactors. For satisfying the near-wall resolution of y⁺ ≤ 1, the structure mesh with the stretched fine mesh near wall is employed. The validation of the numerical simulation for mesh generation strategy and the turbulence model for the heat transfer of supercritical water is carried out to compare with 3D tube experiments. After the validation, the same mesh generation strategy and the turbulence model are employed to study three types of the geometry frame of the real rod bundles. Through the numerical investigations, it is found that the different arrangement of the rod bundles will induce the different temperature distribution at the rods’ walls. The wall temperature distributions are non-uniform along the wall and the values depend on the geometry frame. At the same flow conditions, downward flow gets higher wall temperature than upward flow. The hexagon geometry frame has the smallest wall temperature difference comparing with the others. The heat transfer is controlled by P/D ratio of the bundles.     

Numerical analysis of heat transfer in supercritical water cooled flow channels

Research activities are ongoing worldwide to develop nuclear power plants with a supercritical water cooled reactor (SCWR) with the purpose to achieve a high thermal efficiency and to improve their economical competitiveness. However, there is still a big deficiency in understanding and prediction of heat transfer in supercritical fluids. In this paper, heat transfer of supercritical water has been investigated in various flow channels using the computational fluid dynamics (CFD) code CFX-5.6 to provide basic knowledge of the heat transfer behaviour and to gather the first experience in the application of CFD codes to heat transfer in supercritical fluids. Three different flow channels are selected, i.e. circular tubes, the sub-channel of a square-array rod bundle and the sub-channel of a triangular-array rod bundle. The effect of mesh structures, turbulence models, as well as flow channel configurations is analysed. Based on the present results, recommendations are made on the application of turbulence models to the heat transfer of supercritical fluids in various flow channels. A new definition for the onset of heat transfer deterioration is proposed. A strong non-uniformity of heat transfer is observed in sub-channel geometries. This non-uniformity has to be taken into account in the design of fuel assemblies of SCWR.     

Experimental investigation of turbulent flow through spacer grids in fuel rod bundles

This paper contains experimental data of pressure, velocity and turbulence intensity in a 24-rod fuel bundle with spacer grids. Detailed pressure measurements inside the spacer grid have been obtained by use of a sliding pressure-sensing rod. Laser Doppler Velocimetry technique was used to measure the local axial velocity and its fluctuating component upstream and downstream of the spacer grid in sub-channels with different blockage ratios. The measurements show a changing pattern in function of radial position in the cross-section of the fuel bundle. For sub-channels close to the box wall, the turbulence intensity suddenly increases just downstream of the spacer and then gradually decays. In inner sub-channels, however, the turbulence intensity downstream of the spacer decreases below its upstream value and then gradually increases until it reaches the maximum value at approximately two spacer heights. The present study reveals that spacer effects, such as local pressure distribution and turbulence intensity enhancement, not only depend exclusively on the local geometry details, but also on the location in the cross-section of the rod bundle.     

Investigation of forced convection heat transfer of supercritical pressure water in a vertically upward internally ribbed tube

In the present paper, the forced convection heat transfer characteristics of water in a vertically upward internally ribbed tube at supercritical pressures were investigated experimentally. The six-head internally ribbed tube is made of SA-213T12 steel with an outer diameter of 31.8 mm and a wall thickness of 6 mm and the mean inside diameter of the tube is measured to be 17.6 mm. The experimental parameters were as follows. The pressure at the inlet of the test section varied from 25.0 to 29.0 MPa, and the mass flux was from 800 to 1200 kg/(m² s), and the inside wall heat flux ranged from 260 to 660 kW/m². According to experimental data, the effects of heat flux and pressure on heat transfer of supercritical pressure water in the vertically upward internally ribbed tube were analyzed, and the characteristics and mechanisms of heat transfer enhancement, and also that of heat transfer deterioration, were also discussed in the so-called large specific heat region. The drastic changes in thermophysical properties near the pseudocritical points, especially the sudden rise in the specific heat of water at supercritical pressures, may result in the occurrence of the heat transfer enhancement, while the covering of the heat transfer surface by fluids lighter and hotter than the bulk fluid makes the heat transfer deteriorated eventually and explains how this lighter fluid layer forms. It was found that the heat transfer characteristics of water at supercritical pressures were greatly different from the single-phase convection heat transfer at subcritical pressures. There are three heat transfer modes of water at supercritical pressures: (1) normal heat transfer, (2) deteriorated heat transfer with low HTC but high wall temperatures in comparison to the normal heat transfer, and (3) enhanced heat transfer with high HTC and low wall temperatures in comparison to the normal heat transfer. It was also found that the heat transfer deterioration at supercritical pressures was similar to the DNB at subcritical pressures.     

Numerical simulation of heat transfer deterioration phenomenon in supercritical water through vertical tube

In this study, a numerical investigation of heat transfer deterioration (HTD) in supercritical water flowing through vertical tube is performed by using six low-Reynolds number turbulence models. All low-Reynolds models can be extended to reproduce the effect of buoyancy force on heat transfer and show the occurrence of localized HTD. However, most k–ε models seriously over-predict the deterioration and do not reproduce the subsequent recovery of heat transfer. The V2F and SST models perform better than other models in predicting the onset of deterioration due to strong buoyancy force. The SST model is able to quantitatively reproduce the two heat transfer deterioration phenomena with low mass flux which have been found in the present study.     

Wall temperature measurement and heat transfer correlation of turbulent supercritical carbon dioxide flow in vertical circular/non-circular tubes

Experimental data are presented which describe heat transfer characteristics of turbulent supercritical carbon dioxide flow in vertical tubes with circular, triangular, and square cross-sections. Experiments are conducted at a constant pressure of 8 MPa under various conditions such as inlet bulk temperatures ranging from 15 to 32 °C, imposed heat fluxes from 3 to 180 kW/m², and mass velocities from 209 to 1230 kg/m² s. The corresponding Reynolds and Grashof numbers are in the range of 3 × 10⁴ to 1.4 × 10⁵, and 5 × 10⁹ to 4 × 10¹¹, respectively. The test section is composed of an entrance region of 0.6 m long and a heating region of 1.2 m long. Wall temperatures are measured by thermocouples installed at the outer surface of the heating region. In order to identify the effect of the cross-sectional shape on the supercritical heat transfer, wall temperature distributions in the streamwise direction are compared at the same heat flux and mass velocity conditions. Based on the wall temperature data, an improved heat transfer correlation, which can be applicable to both forced convection and mixed convection regimes, is proposed, and compared with previous ones.     

Experimental investigation of heat transfer for supercritical pressure water flowing in vertical annular channels

An experiment has recently been completed at Xi’an Jiaotong University (XJTU) to obtain wall-temperature measurements at supercritical pressures with upward flow of water inside vertical annuli. Two annular test sections were constructed with annular gaps of 4 and 6 mm, respectively, and an internal heater of 8 mm outer diameter. Experimental-parameter ranges covered pressures of 23-28 MPa, mass fluxes of 350-1000 kg/m²/s, heat fluxes of 200-1000 kW/m², and bulk inlet temperatures up to 400 °C. Depending on the flow conditions and heat fluxes, two distinctive heat transfer regimes, referring to as the normal heat transfer and deteriorated heat transfer, have been observed. At similar flow conditions, the heat transfer coefficients for the 6 mm gap annular channel are larger than those for the 4 mm gap annular channel. A strong effect of spiral spacer on heat transfer has been observed with a drastic reduction in wall temperature at locations downstream of the device in the annuli. Two tube-data-based correlations have been assessed against the experimental heat transfer results. The Jackson correlation agrees with the experimental trends and overpredicts slightly the heat transfer coefficients. The Dittus-Boelter correlation is applicable only for the normal heat transfer region but not for the deteriorated heat transfer region.     

Investigation on turbulent heat transfer to lead–bismuth eutectic flows in circular tubes for nuclear applications

Since many years, the Forschungszentrum Karlsruhe has been working on the research and development of an accelerator driven sub-critical system (ADS) cooled by lead–bismuth eutectic (LBE). Although various numerical tools for thermal hydraulics have been established at the Forschungszentrum Karlsruhe, reliably validated physical models related to turbulent heat transfer in LBE flows are still missing. Especially, physical models on heat transfer and turbulent Prandtl number have to be re-evaluated in LBE conditions to improve the reliability of numerical tools. In the present paper, review and assessment of the existing physical models are made. Computational fluid dynamics (CFD) analysis is carried out for circular tube geometries. Based on the assessment of the existing models and the CFD results achieved, recommendations are made on correlations of heat transfer and turbulent Prandtl number for numerical applications to LBE flows.     

Analysis of data and recommendations on heat transfer by liquid metals in rod bundles

Translated from Atomnaya Énergiya, Vol. 65, No. 6, pp. 423–426, December, 1988.     

Momentum losses and convective heat transfer in rod bundles — An overview

A critical survey is made of the prediction methods available for analysing the momentum and heat transfer characteristics of axial flow in a clustered rod bundle. The Navier-Stokes and energy equations are presented, their solution procedure is outlined and the boundary layer approximation discussed. Four levels of approximation to these equations, namely, slug flow, integral methods, eddy diffusivity and turbulence energy models are examined and their limitations presented for a simple situation. Consideration is then given to the problem of extending these models to more complex situations such as, variable property flows, rough surfaces and flow blockages.