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.     

The flow and heat transfer characteristics of turbulent flow in typical rod bundles in ocean environment

The flow and heat transfer characteristic of turbulent flow in typical 4 and 7 rod bundles in ocean environment is investigated theoretically. In ocean environment, the periodic variation of secondary flow in 7 rod bundles is not obvious. Because of the velocity oscillation, there is a periodic heat accumulation on the tube wall. And the restriction of the channel wall on the rolling motion is considerable. In 7 rod bundles, because of the restriction of the channel wall, the effect of the additional force perpendicular to flowing direction is limited, and the turbulent flowing and heat transfer is mainly determined by the axial turbulent intensity and inlet velocity. However, in the 4 rod bundles, the restriction of the channel wall is small. The effect of the additional force perpendicular to flowing direction on the flowing and heat transfer is significant. And the additional force perpendicular to flowing direction can also affect the Reynolds stress.     

The structure of turbulent flow in triangular array rod bundles

A wind tunnel study of fully developed uniform-density turbulent flow through triangular array rod bundles is described. Measurements were made for three tube spacings (

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) over a Reynolds number range of 12 000–84 000. The data include friction factors, local wall shear stresses, and the distributions of mean axial velocity, Reynolds stresses and eddy diffusivities. The secondary flow pattern is from the available evidence.     

The prediction of fully developed axial turbulent flow in rod bundles

Results are presented from the application of a finite-volume calculation method to fully-developed axial turbulent flow in various smooth rod bundle arrangements. Simplified algebraic versions of the Reynolds stress transport equations are used in the calculation of the full three dimensional velocity field, without any special adjustments for each geometry. The predictions obtained for different rod spacings compare favourably with experiment and reveal the significant role of the cross-plane turbulence-driven secondary flow in shaping the mean flow and turbulence distributions. The success of the results obtained establish the effectiveness of the method and encourage further applications and development.     

Heat transfer in turbulent longitudinal flow through unbaffled assemblies of fuel rods

A numerical analysis of heat transfer in turbulent longitudinal flow through assemblies of unbaffled fuel rods is presented. The solution applies to triangular or rectangular arrays of fuel rods with fully developed velocity and temperature profiles, for fluids with Prandtl number 1 and « 1. In the case of liquid metals, the thermal resistance of the cladding and bond are considered, but the turbulent heat transport component is neglected. For common liquids the circumferential turbulent heat transfer is considered. Results are compared in the range of dimensionless rod spacing of 1.0–1.6. Theoretical predictions and experimental results of other authors dealing with the problem show relatively good agreement.     

Calculated effect of radially asymmetric heat generation on temperature and heat flux distribution in a fuel rod

The effect of radially asymmetric heat generation on the temperature and heat flux distribution in a fuel rod is evaluated. Based on practical assumptions, the temperature distribution in power reactor fuel can be obtained between reasonable limits by solving the steady-state heat conduction equation with asymmetric heat generation.     

Measurements of turbulent velocity and temperature in axial flow through a heated rod bundle

Fully developed turbulent air flow in a heated 37-rod bundle with a pitch to diameter ratio of 1.12 has been investigated. Measurements were performed with a hot-wire probe with x-wires and a temperature wire. Besides the distributions of the mean velocity, mean fluid temperature, the wall shear stress and wall temperature, the turbulent quantities such as the turbulent kinetic energy, the Reynolds-stresses and the turbulent heat fluxes were measured and compared with data from isothermal flow and heated flow in pipes.     

An experimental study of turbulent flow through a square-array rod bundle

Using laser-Doppler anemometry and calibrated Preston tubes, experiments were performed in water (80°C, 0.6 MPa) to obtain information on the distributions of wall shear stresses, mean axial velocities and turbulence intensities for fully developed adiabatic flow through a six-rod bundle at a Reynolds number of 5 × 10⁵. The rods were arranged in a square array with a pitch to a diameter ratio of 1.15 and a wall-distance to diameter ratio of 0.62. The core flow in the central subchannel appears to be similar to pipe flow, but in the gap regions much higher turbulence intensities are encountered. The skewed wall shear stress profiles together with the deformed constant-velocity lines suggest the presence of secondary flows in the corner subchannels.     

LES and URANS simulations of turbulent flow in 4 rod bundles in ocean environment

The flow and heat transfer of turbulent flow in typical 4 rod bundles in rolling motion is investigated with LES and URANS. The effect of rolling motion consists of two parts, the axial additional force which causes velocity oscillation and the radial additional force. The effect of rolling motion on the flowing similarity is considerable. The effect of radial additional force on the flow should not be neglected. In ocean environment, the effect of radial additional force on the flow should not be neglected. The average parameters are determined by the drive force and axial additional force, but the parameter profiles in the cross section are mainly determined by the radial additional force.     

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.     

Experimental and analytical studies on turbulent heat transfer performance of a fuel rod with spacer ribs for high temperature gas-cooled reactors

Turbulent heat transfer performance of a fuel rod with three-dimensional trapezoidal spacer ribs for high temperature gas-cooled reactors was studied for various Reynolds numbers using an annular channel at the same coolant condition as the reactor operation, maximum outlet temperature of 1000 °C and pressure of 4 MPa, and analytically by a numerical simulation using the k- turbulence model. The turbulent heat transfer coefficients of the fuel rod were 18–80% higher than those of a concentric smooth annulus at a region of Reynolds number exceeding 2000. On the other hand, the predicted average Nusselt number of the fuel rod agreed well with the empirical correlation obtained from the experimental data within a relative error of 10% with Reynolds number of more than 5000. It was verified that the numerical analysis results had sufficient accuracy. Furthermore, the numerical prediction could clarify quantitatively the effects of the heat transfer augmentation by the spacer ribs and the axial velocity increase due to a reduction in the annular channel cross-section.     

A scale analysis of the turbulent mixing rate for various Prandtl number flow fields in rod bundles

The turbulent mixing rate is a very important variable in the thermal–hydraulic design of nuclear reactors. In this study, the turbulent mixing rate for the flow through rod bundles is estimated with the scale analysis on the flow pulsation generated by periodic vortices that is pointed out as a main cause of the mixing in rod bundles. Based upon the assumption that turbulent mixing is composed of molecular motion, isotropic turbulent motion (turbulent motion without the flow pulsation), and flow pulsation, the scale relation is derived as a function of P/D, Re, and Pr. The derived scale relation is compared with the published experimental results and shows good agreement. Since the scale relation is applicable to various Prandtl number fluid flows, it is expected to be useful for the thermal–hydraulic analysis of liquid metal coolant reactors as well as moderate Prandtl number coolant reactors.     

Tabular method of calculating the critical heat flux in water-cooled triangular rod assemblies

A new method of calculating the critical heat flux in fuel-rod assemblies is presented. The method is based on a generalization of the experimental data in tabular form. The table for the critical heat fluxes is constructed for the correct macrocells of triangular bundles with relative rod spacing s/d=1/4 and a 9.36 mm heat diameter of a microcell for the following conditions: no effect due to peripheral zones and unheated rods; turbulizing influence of the entrance conditions and spacers; and, the heating along the length and across assemblies is uniform. To use the table for other, quite wide regions of the determining parameters, relations are presented for calculating the effect of the important parameters: heating diameter, relative rod spacing in the assembly, distance to the entrance (heated length), turbulizing influence of the spacers, and others. 1 figure, 1 table, 9 references. State Science Center of the Russian Federation—A. I. Leipunskii Physics and Power-Engineering Institute. Translated from Atomnaya énergiya, Vol. 87, No. 1, pp. 17–24, July, 1991.     

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.     

A critical heat flux approach for square rod bundles using the 1995 Groeneveld CHF table and bundle data of heat transfer research facility

The critical heat flux (CHF) approach using CHF look-up tables has become a widely accepted CHF prediction technique. In these approaches, the CHF tables are developed based mostly on the data bank for flow in circular tubes. A set of correction factors was proposed by Groeneveld et al. [Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. 1986 AECL-UO Critical Heat Flux lookup table. Heat Transf. Eng. 7(1–2), 46] to extend the application of the CHF table to other flow situations including flow in rod bundles. The proposed correction factors are based on a limited amount of data not specified in the original paper. The CHF approach of Groeneveld and co-workers is extensively used in the thermal hydraulic analysis of nuclear reactors. In 1996, Groeneveld et al. proposed a new CHF table to predict CHF in circular tubes [Groeneveld, D.C., et al., 1996. The 1995 look-up table for Critical Heat Flux. Nucl. Eng. Des. 163(1), 23]. In the present study, a set of correction factors is developed to extend the applicability of the new CHF table to flow in rod bundles of square array. The correction factors are developed by minimizing the statistical parameters of the ratio of the measured and predicted bundle CHF data from the Heat Transfer Research Facility. The proposed correction factors include: the hydraulic diameter factor (K_hy), the bundle factor (K_bf), the heated length factor (K_hl), the grid spacer factor (K_sp), the axial flux distribution factors (K_nu), the cold wall factor (K_cw) and the radial power distribution factor (K_rp). The value of constants in these correction factors is different when the heat balance method (HBM) and direct substitution method (DSM) are adopted to predict the experimental results of HTRF. With the 1995 Groeneveld CHF Table and the proposed correction factors, the average relative error is 0.1 and 0.0% for HBM and DSM, respectively, and the root mean square (RMS) error is 31.7% in DSM and 17.7% in HBM for 9852 square array data points of HTRF.     

Turbulent velocity and temperature distribution in the central subchannel of rod bundles

In this paper a method is given for solving the momentum and heat transfer equations for the central subchannel of a reactor subassembly in general curvilinear orthogonal coordinates. For turbulent flow, the eddy diffusivities are determined by Prandtl's ‘mixing length’ hypothesis. A new method is proposed to determine eddy diffusivities parallel to the wall. The eddy diffusivities of heat are calculated from those of momentum using the relations obtained by various authors, and the results are compared in the case of sodium. To show the capability of the computer codes developed, the three-dimensional temperature field is calculated in the central subchannel of a fuel element cooled by sodium and helium. The agreement between calculated and experimental results is satisfactory.