Triangular Rod Research Articles

Assessment of the RANS Turbulence Models for a Turbulent Flow and Heat Transfer in a Rod Bundle

A computational fluid dynamics (CFD) analysis has been performed to assess the Reynolds Average Navier-Stokes (RANS) turbulence models to predict a turbulent flow and heat transfer in a triangular rod bundle with pitch-to-diameter ratios (P/Ds) of 1.06 and 1.12. The CFD predictions using various turbulence models were compared with experimental results. Anisotropic turbulence models such as the nonlinear k - [curly epsilon] and the second-order closure models predicted the turbulence-driven secondary flow in the triangular channel and the distributions of the time mean velocity and temperature showing significantly improved agreement with the measurements from the linear standard k - [curly epsilon] model. The anisotropic turbulence models predicted the turbulence structure for a rod bundle with a large P/D fairly well but could not predict the very high turbulence intensity of the azimuthal velocity observed in the narrow flow region (gap) for a rod bundle with a small P/D.

Cross-section structure functions in terms of the three-dimensional structure functions of infinitely long cylinders

Integral transformations are presented for determining structure functions of the maximum cross-section of infinitely long cylinders in terms of the structure functions of the cylinder. This includes the determination of the chord length distribution density (CLD) P(x) of the plane cross-section figure of the cylinder. P(x) is completely defined in terms of the first derivative A′(r) of the chord length distribution density A(r) of the three-dimensional rod. The general result is exemplified for the case of a triangular rod.

1638 擬似直接数値計算法を用いた高燃焼度燃料集合体内詳細熱流動解析

The pseudo direct numerical simulation, extended to boundary fit coordinate, has been carried out for fully-developed turbulent flow though triangular rod bundle, on the assumption of infinite array. The purpose of this work is to verify the method to be applied for rod bundle thermal hydraulic analysis. The turbulent Reynolds number, based on the friction velocity and the hydraulic equivalent diameter, is 600. The good results for the mean velocity profile, and the wall shear stress distribution are obtained.

The Development of Blanking System with the Fail-Safe Teaching Function.

This paper introduces a new safety system of power press for the aluminum sash processing. Common photo-electric safety devices are not available to this work because the aluminum sash obstructs some light beams. In order to solve this problem, a blanking system with the fail-safe teaching function was developed. It permits the slide actuation only when the specified light beams are obstructed by the sash and the other reaches to optical detectors. Experimental results are described as follows; 1) The smallest detection diameter became worst value when the gap between material and human body were 1 or 2 millimeters. 2) When the material was a square bar, the smallest detection diameter might be larger than the physical resolution (14 mm) of safety device, as the reflection of the light beam occured in the surface of the square bar. 3) When the material was the round bar or the triangular rod etc., the smallest detection diameter was also larger than the physical resolution (14 mm), as the blind area for detecting human body existed. 4) The human body detection might be impossible when the shape of human body was intentionally taught, or the shape of human body and the material were simultaneously taught by mistake.

The chord length distribution of a triangular rod

A triangular rod (edge length of the basic triangle is a) is considered. Analytic expressions of the chord length distribution density A( l, a) and other structure functions of small-angle scattering are calculated. Applications of A( l, a) in the field of SAS are discussed. The three-dimensional correlation function and the asymptotic behaviour of the SAS intensity I( h) are analyzed. Here, the Kirste–Porod term is missing which correlates with the fact that parallel interfaces do not exist.

The chord length distributions of selected infinitely long geometric figures – connections to the field of small-angle scattering

Analytic expressions are summarized and the intrinsic behaviour of the chord length distribution and the small-angle scattering correlation function are investigated for the following eight infinitely long geometric figures: S. plane stripe; Q. square rod; R. rectangular rod; N. elliptic needle; C. circular rod; O. hollow cylinder; H. hemicircular rod; T. triangular rod. There does not exist a power series expansion of the scattering intensity in the origin of any infinitely long figure, because of I(0) → ∞ . On the other hand, the asymptotic behaviour of the SAS intensities for large scattering vectors is clearly defined by the shape parameters. This can be analysed by the use of so-called normalized Porod-plots P 1( h), which can be approximated by their asymptotic expansion P 1∞( h). Deciding formulas for practical application in materials science are summarized in simple Mathematica patterns.

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.

Numerical Analysis of Developing Turbulent Structure in Triangular Array Rod Bundles.

Numerical analysis has been performed on developing turbulent flow in triangular array rod bundles. The ratio of pitch represented by two rod centers to rod diameter is 1.2 and Reynolds number is 4.9×104. In calculation, an algebraic stress model was adopted in order to predict Reynolds stresses precisely, and a boundary-fitted coordinate system was introduced to set boundary conditions easily. Calculated results were compared with the experimental data. The calculated profiles of secondary flow and Reynolds stresses in rod bundles are shown in this study. As a result of this calculation, it was found that the calculated intensity of the secondary flow is about 0.6% of bulk velocity. This calculated intensity of secondary flow coincides with the evaluated value from the experimental data measured by several researchers. Judging from this calculated value, it is very difficult to measure the secondary flow in rod bundles. The present method predicts larger the turbulent enregy and primary velocity fluctuation in the vicinity of the wall than the experimental data.

Thermal-hydraulic study on a double-flat-core high-conversion light water reactor

Research and developmental work on the high-conversion light water reactor (HCLWR) at JAERI aims at attractive design in terms of energy source and economy to ensure a safety level equal to or higher than that of current LWRs. In thermal hydraulics, efforts are being devoted to understand the phenomena in a tight lattice core and to develop analytical methods for optimum design. In critical heat flux (CHF) experiments, several existing CHF correlations were evaluated. It was found that the KfK correlation can be applied to the triangular tight lattice rod array used for the experiment reported here. In the hydraulic experiment the core pressure drop was investigated with existing correlations in various types of core geometries. It was found that Rehme's correlation for spiral wire and integral spiral rib can be applied and that the drag coefficient of grid spacers is noticeably affected by the height of spacers. On the basis of these experiments, the thermal-hydraulic characteristic was investigated for the double-flat-core HCLWR, which potentially has advantages such as negative void reactivity coefficient, high conversion ratio, and high burnup. It was found that the double-flat-core HCLWR is highly feasible, having enough margin in CHF, a core pressure drop comparable to current PWRs, and a fairly low peak clad temperature in LOCA reflood as calculated by REFLA code.

Evaluation of DNBR under operational and accident conditions for double-flat-core type HCLWR.

A double-flat-core type high conversion light water reactor (HCLWR) has been developed at JAERI to improve fuel utilization. Experimental and analytical studies on the departure from nucleate boiling ratio (DNBR) under operational and accident conditions for the HCLWR have been performed. It was found by comparing several critical heat flux (CHF) correlations with the CHF data obtained at JAERI and Bettis Atomic Power Laboratory that the KfK correlation has the most promising features for the application to the triangular tight lattice rod array. The minimum allowable DNBR (MDNBR) for the HCLWR was determined to be 1.28 by comparing the Bettis CHF data with the KfK correlation. The best-estimate code J-TRAC was used for system transient calculations under the primary coolant pump trip and locked rotor accident conditions. The subchannel code COBRA-IV-I was then used to obtain local flow conditions and fuel rod surface heat flux. The analytical results indicated that an enough safety margin was assured und...

Heat conduction in an equilateral triangular rod under a step-change wall temperature

This paper examines the steady state heat conduction in an equilateral triangular homogenous rod of infinite length. The rod is composed of an isotropic heat conducting material and is subjected to a step wall temperature change on all three faces with no heat source or sink. The temperature field in the equilateral triangular rod is obtained by an approximate analytic method using Fourier integral transforms and a numerical scheme. The temperature variations in the transverse direction at various longitudinal sections are plotted, along with the temperature variations in the longitudinal direction for various points in the transverse coordinate. Also, for the same wall temperature condition, the generating lines of isothermal surfaces, which are symmetrical, are plotted. The wall heat flux variation along the longitudinal direction is obtained and plotted against the longitudinal coordinate. To present the total heat flow, a dimensionless heat flow coefficient at the cross section corresponding to the wall temperature discontinuity is defined and its value is found to be 1.83850.

The French Thermal-Hydraulic Program Addressing the Requirements of Future Pressurized Water Reactors

In the framework of feasibility studies of future pressurized water reactors, a thermal-hydraulic program has been established in order to qualify computer codes in three fields: critical heat flux and reflooding heat transfer in triangular rod bundle arrays with tight lattices and the coolability of movable fertile rods in their guide tubes. Tests carried out at the Commissariat a l'Energie Atomique in cooperation with Electricite de France and Framatome are now in progress, and preliminary results are shown for these three studies.

Distributed resistance modeling of wire-wrapped rod bundles

Three-dimensional flow hydrodynamic distributed resistance models for rod bundles were developed. The models specifically account for the presence of the wire-wrap spacer and may be used for any lumped parameter thermohydraulic analysis numerical program. Validation studies of the hydrodynamic resistance models were also performed using a subchannel code ASFRE. The models were tested against subchannel velocity and temperature data taken from bundles of triangular rod array configurations with wire-spacers. Overall the models performed satisfactorily predicting the most important qualitative trends for flows in wire-wrapped rod bundles.

A Simplified Finite Element Model for Fully Developed Axial Turbulent Flow in Rod Bundles

A simplified computational scheme that can be efficiently applied to predict fully developed axial flow in rod bundle subchannels is presented and compared with experimental results for different flow conditions. Galerkin's finite element method and the physical model of turbulence proposed by Roco and Zarea (1978) are used in this approach. The flow in the corner, wall, and central subchannels for both triangular and square rod bundles is investigated. Different values of the subchannel pitch-to-diameter ratio and various Reynolds numbers are considered. In all these cases, the present computational scheme gives the correct qualitative trends for the distributions of the axial velocity and wall shear stress. The comparison performed with current measurements in the subchannels of a 3 x 6 rectangular rod bundle and with other available experimental and analytical results taken from the literature shows good agreement.

Effect of gas phase on heat transfer in turbulent water flow in a model of a compact triangular rod bundle

Results are presented from an experimental study of the effect of a gas phase on temperature fields in a flow and a wall and on the mean heat-transfer coefficient in the flow of a water-gas mixture. It is shown that the effect is substantial.

Turbulence Modeling of Axial Flow in a Bare Rod Bundle

Temperature distribution within the rod bundle of a nuclear reactor is of major importance in nuclear reactor design. However temperature information presupposes knowledge of the hydrodynamic behavior of the coolant which is the most difficult part of the problem due to the complexity of the turbulence phenomena. In the present work a two equation turbulence model—a strong candidate for analyzing actual three dimensional turbulent flows—has been used to predict fully developed flow of infinite bare rod bundle of various aspect ratios (P/D). The model has been modified to take into account anisotropic effects of eddy viscosity. Secondary flow calculations have been also performed although the model seems to be too rough to predict the secondary flow correctly. Heat transfer calculations have been performed to confirm the importance of anisotropic viscosity in temperature predictions. Experimental measurements of the distribution of axial velocity, turbulent axial velocity, turbulent kinetic energy and radial Reynolds stresses were performed in the developing and fully developed regions. A two channel Laser Doppler Anemometer working in the reference mode with forward scattering was used to perform the measurements in a simulated interior subchannel of a triangular rod array with P/D = 1.124. Comparisons between the analytical results and the results of this experiment as well as other experimental data in rod bundle arrays available in the literature are presented. The predictions are in good agreement with the results for high Reynolds numbers.

Predicted Secondary Flows in Triangular Array Rod Bundles

A one-equation turbulence model was applied to forecast the main features of fully-developed turbulent flow through infinite equilateral triangular arrays of parallel rods having pitch-to-diameter ratios of 1.12 – 1.35 and Reynolds numbers of (2.7 – 25) × 104. For all cases, the secondary flow was found to be a single cell of circulation for each primary flow cell of a subchannel. The strength of the secondary flow increased with Reynolds number but decreased with rod spacing. The numerical results (which included friction factors, wall shear stress variations and axial velocity distributions) are shown to be in reasonable agreement with published experimental data.

A Note on Turbulent-Laminar Transition for Flow in Triangular Rod Bundles

The Ramm-Johannsen correlation of eddy diffusivity for momentum is used to compute the onset and growth of flow laminarization in triangular rod bundles. The laminarization is indicated by Reynolds numbers based on the bulk flow condition in the coolant channel. Simple correlations that qualitatively estimate the transition Reynolds numbers are developed for applications in the safety analysis of liquid-metal fast breeder reactors.

Experimental and Analytical Study of Axial Turbulent Flows in an Interior Subchannel of a Bare Rod Bundle

Reactor fuel elements generally consist of rod bundles with the coolant flowing axially through the bundles in the space between the rods. Heat transfer calculations form an important part in the design of such elements, which can only be carried out if information of the velocity field is available. A one-equation statistical model of turbulence is applied to compute the detailed description of velocity field (axial and secondary flows) and the wall shear stress distribution of steady, fully developed turbulent flows with incompressible, temperature-independent fluid, flowing through triangular arrays of rods with different aspect ratios (P/D). Also experimental measurements of the distributions of the axial velocity, turbulence kinetic energy, and Reynolds stresses were performed using a laser Doppler anemometer (LDA), operating in a “fringe” mode with forward scattering, in a simulated interior subchannel of a triangular rod array with P/D = 1.123 and L/DH = 77. From the experimental results, a new mixing length distribution is proposed. Comparisons between the analytical results and the results of this experiment as well as other experimental data available in the literature are presented. The results are in good agreement.

Prediction of Local and Integral Turbulent Transport Properties for Liquid-Metal Heat Transfer in Equilateral Triangular Rod Arrays

A theoretical method based on a phenomenological turbulence model has been applied to evaluate turbulent transport properties for liquid-metal heat transfer in bare equilateral triangular rod bundles. Results obtained for local distributions of thermal eddy diffusivity in the various directions are presented in terms of correlations. From a subsequent solution of the three-dimensional heat transfer problem between two characteristic interior subchannels under conditions characteristic for tracer-type mixing experiments, integral thermal mixing coefficients and thermal length scales have been evaluated. Results demonstrate that the basic concept of subchannel analysis treating molecular conduction and turbulent transport independently of each other tends to underestimate intersubchannel transport. The uncertainties which are involved in principal assumptions of the turbulence-model as well as in the available empirical results are discussed in some detail.