Local thermal–hydraulic behaviour in tight 7-rod bundles

Advanced water-cooled reactor concepts with tight lattices have been proposed worldwide to improve the fuel utilization and the economic competitiveness. In the present work, experimental investigations were performed on thermal–hydraulic behaviour in tight hexagonal 7-rod bundles under both single-phase and two-phase conditions. Freon-12 was used as working fluid due to its convenient operating parameters. Tests were carried out under both single-phase and two-phase flow conditions. Rod surface temperatures are measured at a fixed axial elevation and in various circumferential positions. Test data with different radial power distributions are analyzed. Measured surface temperatures of unheated rods are used for the assessment of and comparison with numerical codes.In addition, numerical simulation using sub-channel analysis code MATRA and the computational fluid dynamics (CFD) code ANSYS-10 is carried out to understand the experimental data and to assess the validity of these codes in the prediction of flow and heat transfer behaviour in tight rod bundle geometries. Numerical results are compared with experimental data. A good agreement between the measured temperatures on the unheated rod surface and the CFD calculation is obtained. Both sub-channel analysis and CFD calculation indicates that the turbulent mixing in the tight rod bundle is significantly stronger than that computed with a well established correlation.     

Direct numerical simulation of turbulent mixed convection in a vertical channel in a wall-normal magnetic field

Liquid metal coolants have a significant role in the design of advanced fusion reactors. There is a need for an investigation of the thermal behavior of the liquid metal in working reactor environment, such as when fluid flow at low Prandtl number (Pr) with a buoyancy effect, is subjected to a magnetic field. In the present study, a direct numerical simulation (DNS) for a low Pr number fluid flow resulting in turbulent heat transfer with buoyancy effect under a magnetic field has been carried out between two vertical plates kept at different temperatures. In this simulation, the values of the Hartmann number (Ha) were 0 and 6, Pr number was 0.06 and Grashof numbers were 6.4 × 10⁵, 9.6 × 10⁵, and 1.6 × 10⁶. The turbulent quantities of the parameters such as the mean temperature, turbulent heat flux, and temperature variance were obtained by direct numerical simulation (DNS). The Reynolds number (Re) for channel flow based on friction velocity averaged by both walls, viscosity, and channel half-width was set to be constant as Re_τ* = 150. A uniform magnetic field was applied in a direction perpendicular to the walls of the channel. The profiles of mean velocity and velocity fluctuations became asymmetric, and the tendency was enhanced with the increasing buoyancy effect. However, by the application of a magnetic field the tendency decreased. In other words, thermal transport between the walls became weak due to the magnetic effect.     

Critical heat flux prediction in vertical bottom-closed rod bundles

This paper presents the analysis of experimental data and calculational relationships for heat the transfer crisis in LWR rod bundle with closed bottom. A new relationship for critical heat flux prediction in the rod bundle with closed bottom based on the improved drift model is described. The comparison of critical heat flux values given by different correlations (including Groeneveld's algorithm used in RELAP5/MOD3.1 Code) and those obtained from the tests in the wide range of regime and geometric parameters is presented.     

Energy transfer mechanisms in LMR rod bundles under mixed convection conditions

The energy transfer mechanisms operative under mixed convection conditions in heated rod arrays are identified. The relative importance of these various mechanisms of energy transfer has been assessed and is presented in regime maps which allow the designer and experimentalist to rapidly assess the characteristics of an operating regime and the capabilities needed in an analysis tool to treat such a regime. Azimuthal heater rod conduction is important for boron nitride insulated rods typically utilized in out-of-pile sodium tests. Therefore the comparison of energy transfer mechanisms necessitated the development of a correlation for azimuthal heater rod conduction. This correlation has been derived from a physical model formulated to describe this conduction effect. The proposed correlation has been tested against experimental data from out-of-pile tests and has been proven accurate for predicting the azimuthal heater rod conduction effect in LMR rod bundles.     

Cellular convection in vertical annuli of fast breeder reactors

In the pool type fast reactors the roof structure is penetrated by a number of pumps and heat exchangers that are cylindrical in shape. Sandwiched between the free surface of sodium and the roof structure, is stagnant argon gas, which can flow in the annular space between the components and roof structure, as a thermosyphon. These thermosyphons not only transport heat from sodium to roof structure, but also result in cellular convection in vertical annuli resulting in circumferential temperature asymmetry of the penetrating components. There is need to know the temperature asymmetry as it can cause tilting of the components. Experiments were carried out in an annulus model to predict the circumferential temperature difference with and without sodium in the test vessel. Three-dimensional analysis was also carried out using PHOENICS CFD code and compared with the experiment. This paper describes the experimental details, the theoretical analysis and their comparison.     

Effects of mass transfer and free convection currents on MHD Stokes' problem for a vertical plate

An exact analysis is made of the effects of mass transfer and free convection currents on MHD Stokes' (Rayleigh's) problem for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started vertical plate, under the action of a transversely applied magnetic field. The heat due to viscous and Joule dissipation and the induced magnetic field is neglected. During the course of the discussion, the effects of heating (Gr < 0, Gr = Grashof number) or cooling (Gr > 0) of the plate by the free convection currents, Gr_m (modified Grashof number), Sc (Schmidt number) and M (Hartmann number) and the velocity and skin-friction are studied.     

Hydromagnetic free convection effects on the oscillatory flow of an electrically conducting rarefied gas past an infinite vertical porous plate

Unsteady two-dimensional free convection flow of an electrically conducting, viscous, incompressible rarefied gas, past an infinite vertical porous plate in the presence of a transverse magnetic field is studied. The freestream velocity oscillates in time about a constant mean, while the suction velocity, normal to the porous plate, is constant. The magnetic Reynolds number of the flow is not taken to be small enough, so that the induced magnetic field is not negligible. The plate temperature is constant and the difference between the temperature of the plate and the freestream is moderately large causing the free convection currents. The flow field is described by a nonlinear coupled system of equations subjected to the first-order velocity slip and temperature jump boundary conditions. With viscous dissipative heat and Joule heating taken into account, approximate solutions of the problem are obtained for the velocity, temperature and induced magnetic field, as well as, for the related to them quantities of the skin friction, rate of the heat transfer and electric current density.     

Turbulent mixed convection heat transfer experiments in a vertical cylinder using analogy concept

A series of the turbulent mixed convection heat transfer experiments in a vertical cylinder was carried out. In order to achieve high Grashof number easily, the analogy concept was adopted and the heat transfer system was simulated by a mass transfer system. With reasonable facility heights, large Grashof numbers could be achieved using a copper electroplating system. The tests in buoyancy-aided and opposed flow configurations, were performed for Reynolds numbers from 4000 to 10,000 with a constant Grashof number of 6.2 × 10⁹ and Prandtl number of about 2000. The test results reproduced the typical of the mixed convection heat transfer phenomena in a turbulent situation and agreed well with the study performed by Palratan et al. The analogy experimental method simulated the mixed convection heat transfer phenomena successfully and proved itself to be a useful tool for the draft estimation of the heat transfer rate in the highly buoyant systems such as the VHTR.     

A numerical investigation of natural convection heat transfer in horizontal spent-fuel storage cask

Natural convection heat transfer in a horizontally placed dry spent-fuel storage cask is numerical investigated. The commercial computational fluid dynamics (CFD) code, -3.2 is used and the laminar and turbulent model are employed. The numerical predictions obtained are compared with the experimental data reported by Nishimura et al. [J. Nucl. Sci. Technol. 33 (1996) 821]. The computational results corresponding to laminar model agree well with the experimental data, but the calculated results of turbulent model are higher. The velocity pattern and the isotherms are drawn. With the increasing of Rayleigh number, the heat transfer in the cask changes from conduction dominant mode to convection dominant mode. In the condition of Ra_m=1.3×10⁹, turbulent model prevails. The convective heat transfer is so strong that almost all temperature changes take place in the region near the wall of the cask. The Rayleigh number Ra_m and the Nusselt number Nu_m characterized by maximum temperature difference are defined to depict the heat transfer characteristics. It is found laminar and turbulent models predict the same trend but different value. The flow patterns in the cask can be divided to three regimes. In these three regimes, modified Nusselt numbers are proportional to the 0.7, 0.25 and 0 power of the modified Rayleigh number, respectively.     

Development of the finite element method of body fit nodalization for mixed convection analysis in rod bundles

In the reactor rod bundle analysis, mixed convection phenomena are very important after the reactor shutdown. In this paper, the finite element method based on the body fit nodalization are developed to analyze the mixed convection phenomena in a complex geometry. The velocity distribution and the temperature distribution in the reactor rod bundles are obtained using the above two methods. To validate the developed methods, a comparison of the present results with the analytic solutions for a concentric tube is taken. The results show that the mixed convection in a complex geometry can be treated very well with these two methods, and that the finite element method with the body fit nodalization is more efficient than the finite difference method with the body-fitted coordinate system.     

Fluid-to-fluid modeling of critical heat flux in 4 × 4 rod bundles

Fluid-to-fluid modeling of critical heat flux (CHF) is to simulate the CHF behaviors for water by employing low cost modeling fluid, and the flow scaling factor is the key to apply the technique to fuel bundles. The CHF experiments in 4×4 rod bundles have been carried out in Freon-12 loop in equivalent nuclear reactor water conditions (P=10.0–16.0 MPa, G=488.0–2100.0 kg/m² s, X_cr=−0.20–0.30). The models in fluid-to-fluid modeling of CHF is verified by the CHF data for Freon-12 obtained in the experiment and the CHF correlation for water obtained by Nuclear Power Institute of China (NPIC) in the same 4×4 rod bundles. It has been found that the S.Y. Ahmad Compensation Distortion model, the Lu Zhongqi model, the Groeneveld model and Stevens–Kirby model overpredict the bundles CHF values for water. Then an empirical correlation of flow scaling factor is proposed. Comparison of the CHF data in two kinds of test sections for Freon-12, in which the distance of the last grid away the end of heated length is different, shows that the spacer grid, which is located at 20 mm away from the end of the heated length, has evidently influenced on the CHF value in the 4×4 rod bundles for Freon-12. This is different from that for water, and the need for further work is required.     

Temperature distributions in liquid metals for turbulent flow in a horizontal pipe with free convection

A general method is developed for utilizing limited experimental data to obtain velocity or temperature distributions over the cross-section of a heated horizontal pipe, under conditions where distortion occurs due to superimposed free convection effects. The method is applied to available temperature data for five cases of constant-flux heating of liquid metals in turbulent flow, and the resulting isotherms and wall temperature distributions are presented. Substantial asymmetry is demonstrated for Reynolds numbers as high as 10⁵, with a corresponding distortion of the wall temperature distribution, and it is found that local heat transfer coefficients may be as low as 30% of predicted values.     

Analytical prediction of friction factors and Nusselt numbers of turbulent forced convection in rod bundles with smooth and rough surfaces

A simple analytical method was developed for the prediction of the friction factor, f, of fully developed turbulent flow and the Nusselt number, Nu, of fully developed turbulent forced convection in rod bundles arranged in square or hexagonal arrays. The friction factor equation for smooth rod bundles was presented in a form similar to the friction factor equation for turbulent flow in a circular pipe. An explicit equation for the Nusselt number of turbulent forced convection in rod bundles with smooth surface was developed. In addition, we extended the analysis to rod bundles with rough surface and provided a method for the prediction of the friction factor and the Nusselt number. The method was based on the law of the wall for velocity and the law of the wall for the temperature, which were integrated over the entire flow area to yield algebraic equations for the prediction of f and Nu. The present method is applicable to infinite rod bundles in square and hexagonal arrays with low pitch to rod diameter ratio, P/D<1.2.     

Investigation of convection heat transfer to a gas-graphite suspension under conditions of internal flow in vertical channels

The convection heat transfer to the flow of a gas containing graphite dust in cylindrical channels is investigated. A general theoretical dependence is derived. The effect of the basic determining factors on the heat transfer is considered. The experimental results are compared with data given in other papers.     

Simulation of the distribution of flow and phases in vertical and horizontal bundles using the ASSERT-4 subchannel code

ASSERT-4 is a subchannel code based on the non-equilibrium equations of two-fluid flow. The paper briefly describes the equations and constitutive models used in the code, and reviews a number of validation exercises in which code results were compared to measurements in vertical and horizontal two-phase flows.     

Laminar combined convection heat transfer of liquid sodium flowing through a single horizontal row of cooling tubes in the direction of gravity

The laminar combined convection heat transfer of the liquid sodium which flows through a single horizontal row of cooling tubes in the direction of gravity are studied using numerical analysis. The heat transfer characteristics at large Reynolds numbers are improved when Richardson numbers (= GR/Re²) are increased and the improvement rate is enlarged with an increase in value. The temperature field at small Reynolds numbers does not exhibit much change even when the Richardson number reaches a high value. Consequently the Nusselt numbers do not differ from those of forced convection. In other words, in a decay heat removal system at a low velocity, there is a possibility that an improvement in the heat transfer characteristics by combined convection cannot be expected even in a system with a large Richardson number.     

Mixed convection heat transfer to carbon dioxide flowing upward and downward in a vertical tube and an annular channel

This paper addresses three main subjects in supercritical heat transfer: (1) difference in thermal characteristics between upward and downward flows; (2) effect of simulating flow channel shape; (3) evaluation of the existing supercritical heat transfer correlations. To achieve the objectives, a series of experiments was carried out with CO₂ flowing upward and downward in a circular tube with an inner diameter of 4.57 mm and an annular channel created between a tube with an inner diameter of 10 mm and a heater rod with an outer diameter of 8 mm. The working fluid, CO₂, has been regarded as an appropriate modeling fluid for water, primarily because of their similarity in property variations against reduced temperatures. The mass flux ranged from 400 to 1200 kg/m² s. The heat flux was varied between 30 and 140 kW/m² so that the pseudo-critical point was located in the middle of the heated section at a given mass flux. The measurements were made at a pressure of 8.12 MPa, which corresponds to 110% of the critical pressure of CO₂. The difference between the upward and downward flows was observed clearly. The heat transfer deterioration was observed in the downward flow through an annular subchannel over the region beyond the critical point. Several well-known correlations were evaluated against the experimental data, and new correlations were suggested for both a tube and an annular channel.     

A porous body model for predicting temperature distribution in wire-wrapped rod assemblies operating in combined forced and free convection

Based on a model analogous to that of heat transfer in a porous body, a method for predicting temperature distribution in wire-wrapped assemblies operating in forced convection (negligible free convection) was developed in a previous paper. In this paper the method is extended to assemblies operating in mixed convection (combined free and forced convection). The results obtained from this analysis were found to predict available data with a precision equal to that from presently available more complex analysis methods. A new criterion based on the value of a modified Grashof number Gr_c^* has been developed to determine if an assembly with given geometry and operating conditions is in forced convection or in mixed convection.