Analytical prediction of turbulent friction factor for a rod bundle

An analytical calculation has been performed to predict the turbulent friction factor in a rod bundle. For each subchannel constituting a rod bundle, the geometry parameters are analytically derived by integrating the law of the wall over each subchannel with the consideration of a local shear stress distribution. The correlation equations for a local shear stress distribution are supplied from a numerical simulation for each subchannel. The explicit effect of a subchannel shape on the geometry parameter and the friction factor is reported. The friction factor of a corner subchannel converges to a constant value, while the friction factor of a central subchannel steadily increases with a rod distance ratio. The analysis for a rod bundle shows that the friction factor of a rod bundle is largely affected by the characteristics of each subchannel constituting a rod bundle. The present analytic calculations well predict the experimental results from the literature with rod bundles in circular, hexagonal, and square channels.     

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.     

Two-phase turbulent mixing and buoyancy drift in rod bundles

This paper describes the development of generalized relationships for single- and two-phase intersubchannel turbulent mixing in vertical and horizontal flows, and lateral buoyancy drift in horizontal flows.The relationships for turbulent mixing, together with a recommended one for void drift, have been implemented in a subchannel thermalhydraulics code, and assessed using a range of data on enthalpy migration in vertical steam–water flows under BWR and PWR diabatic conditions. The intent of this assessment was to optimize these relationships to give the best agreement with the enthalpy migration data for vertical flows. The optimized turbulent mixing relationships were then used as a basis to benchmark a proposed buoyancy drift model to give the best predictions of void and enthalpy migration data in horizontal flows typical of PHWR CANDU¹ reactor operation under normal and off-normal conditions.Overall, the optimized turbulent mixing and buoyancy drift relationships have been found to predict the available data quite well, and generally better and more consistently than currently used models. This is expected to result in more accurate calculations of subchannel distributions of phasic flows, and hence, in improved predictions of critical heat flux (CHF).     

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.     

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.     

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.     

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.     

CFD application to prediction of void distribution in two-phase bubbly flows in rod bundles

This paper is concerned with the prediction of the void fraction distribution in two-phase bubbly flows in fuel rod bundles. Special attention has been devoted to the phenomena which govern the void fraction distribution in the lateral direction of a channel. A two-fluid model of two-phase flow has been formulated and implemented into a commercial computational fluid dynamics (CFD) code. The model has been used for the prediction of the void distribution in three different channels: a circular channel (inside diameter (ID), 34.5 mm) with a single heated rod of 13.9 mm outside diameter (OD), and circular channels (ID, 71 mm) with six heated rods (13.8 and 13.9 mm OD each). The predicted axial and lateral avoid fraction distributions in subcooled and bulk boiling regions have been area averaged in three lateral zones and compared with experimental data: in all cases, satisfactory agreement between the predictions and measurements has been obtained.     

A design guide for calculating liquid-metal turbulent forced convection heat transfer with non-uniform heat fluxes and transients

Calculation of turbulent forced convection heat transfer in ducts during non-uniform wall heat fluxes and transients is of interest to the national liquid-metal fast breeder nuclear reactor program. This paper presents an improved method whereby such heat transfer can be determined during analysis and design. Since the method involves the use of fully developed, steady-state heat transfer coefficients, several dimensionless coefficients and selected physical properties, tables, graphs, or equations are included for the convenience of the designer. Application of the improved method is specialized to four geometries of interest: circular tube, parallel-plate channel, annular space, and approximation of pin or rod bundle.     

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 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.     

An analytical method of evaluating the effect of rod displacement on circumferential temperature and heat flux distributions in turbulent flow through unbaffled rod bundles

An analytical method of evaluating the circumferential variations of temperature and heat flux fields inside and around a displaced fuel rod in triangular rod bundles in turbulent flow is presented with illustrative examples. The analysis consists mainly of the derivation of the simultaneous solutions of a set of heat conduction equations for fuel, cladding and coolant under the assumption of fully developed flow and heat transfer conditions. The local coolant velocity distribution, which is necessary for deriving the temperature field in coolant, is determined by solving the Navier-Stokes equation and the turbulent mixing of coolant is taken into consideration. The results show how the circumferential variations in the temperature and heat flux fields on the outer surface of the cladding increase the lower the ratio and the larger the fuel rod displacement due to thermal conduction and peripheral coolant flow velocity distribution.     

Pressure drop and velocity distribution in rod bundles with spacer grids

The paper contains experimental data and analysis of the pressure drop of turbulent flow through rod bundles. For laminar flow the dependence of the pressure drop on the pitch-to-diameter and wall-to-diameter ratios is discussed on the basis of theoretical analysis. In addition, correlations for the calculation of the pressure loss due to spacer grids are presented and compared with experimental data.Detailed measurements of the velocity distribution in a full bundle of 19 rods are compared with predictions for fully developed turbulent flow. Moreover, detailed measurements of the velocity distributions upstream and downstream of spacer grids typical for LMFBRs are discussed together with the mass flow separation and redistribution between the subchannels. The mass flow distribution found experimentally is compared with the predictions by a subchannel code. The status of experimental knowledge is shown.     

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.     

Transient friction and form loss factors in turbulent and laminar flow; a brief review

During pump coastdown steady state friction and form loss factors are currently used to calculate pressure drop. Both transient turbulent and laminar flow can exist in a typical LMFBR during the transition to natural convection and circulation. Existing transient friction and form loss data are very sparse. Nevertheless when existing deceleration rates in an LMFBR were compared with transient friction factor data it was concluded that use of steady state friction and form loss correlations is valid during pump coastdown.     

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.