Laminar free convection in open-ended vertical 7-rod bundles: experiments and porous model

The flow of ambient air induced solely by buoyancy, through a vertical rod bundle has been modelled as a phenomenon in a porous medium. The rods are at uniform heat flux condition and the circular shell adiabatic. The induced flow rate was found to be controlled by a parameter ψ dependent on the heat flux, rod diameter, length, fluid properties and the bundle permeability. Measurements performed on two 7-rod bundles corroborate the theoretical predictions. Longitudinally averaged heat transfer rates from the central and peripheral rods have also been measured and average information generated for the bundle.     

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.     

7棒束紧密栅元流体流动传热数值研究

紧密栅元内的流体流动传热研究对高转化比反应堆燃料组件的优化有十分重要的意义。本文采用CFD方法对7棒束紧密栅元棒束通道内流体流动传热现象进行了数值模拟,并与7棒束紧密栅元内氟利昂流体传热的实验结果进行对比分析,详细分析了定位格架对棒束内流体传热流动的影响。结果表明：数值计算所得的非加热棒的壁面温度和实验吻合良好,定位格架的存在对其下游流体流动、棒束最高温度分布及交混系数有明显的影响,棒束某些位置因流动滞止导致温度大幅上升,在设计中应加以注意。     

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.     

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.     

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.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 2: Correlations for horizontal rod bundles based on theoretical results

Natural convection heat transfer from horizontal rod bundles in N_xm × N_ym arrays (N_xm, N_ym = 5–9) in liquid sodium was numerically analyzed for three types of the bundle geometry (in-line rows, staggered rows I and II). The unsteady laminar two-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, R_f, ranging from 0.0637 to 63.1 (q = 1×10⁴ to 7×10⁶ W/m²). S_x/D and S_y/D for the rod bundle, which are the ratios of the distance between center axes on the abscissa and the ordinate to the rod diameter, respectively, were ranged from 1.6 to 2.5 on each bundle geometry. The spatial distribution of Nusselt numbers, Nu, on horizontal rods of a bundle was clarified. The average value of Nusselt number, Nu_av, for three types of bundle geometry with various values of S_x/D and S_y/D were calculated to examine the effect of the array size, S/D and R_f on heat transfer. The bundle geometry for the higher Nu_av value under the condition of S_x/D×S_y/D = 4 was examined by changing the ratio of S_x/S_y. A correlation for Nu_av for the three types of bundle geometry above mentioned including the effects of S_x/D and S_y/D was developed. The correlation can describe the theoretical values of Nu_av for the three types of bundle geometry in N_xm × N_ym arrays (N_xm, N_ym = 5–9) for S_x/D and S_y/D ranging from 1.6 to 2.5 within 10% difference.     

Laminar convection in wall sub-channels and transport rates for finite rod-bundle assemblies by superposition

Finite rod-clusters in circular, square and hexagonal shells have been divided along the symmetry lines into a number of interior, wall and corner subchannels. Laminar fluid flow and heat transfer results have been generated for these subchannels with varying pitch-to-diameter and wall distance-to-diameter ratios. Wall shear stress and temperature variations for typical wall subchannels are presented. Friction factor values for finite bundles are then obtained by superposing the results of the subchannels that constitute the bundles. The values so generated are in excellent agreement with previous work in the literature obtained by the method of symmetry sectors. Considerable disagreements were, however, observed in the superposed values of Nusselt number, apparently due to conduction effects.     

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.     

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.     

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.     

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.     

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.     

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.     

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.