Effect of cluster eccentricity on longitudinal laminar flow in finite bundles of rods

Cluster eccentricity effects on longitudinal flow in finite bundles are analyzed theoretically by the method of superposition. Two displacements were studied: (1) along the line joining the centers of one peripheral rod and the cluster, and (2) along the line between two peripheral rods passing through the cluster center. The differences between the friction factors were negligible. Friction factors were obtained for five-, seven- and nine-rod clusters with various eccentricities, and were found to decrease steadily with eccentricity, while flow area and hydraulic diameter remained unchanged.     

Computational analysis of two-phase flow in horizontal bundles

Phase distribution during boiling flow in horizontal channels and fuel bundles tends to be asymmetric, particularly at low flows, due to gravity induced separation of the phases. Standard models and computational techniques developed for flow on vertical rod bundles cannot adequately simulate this tendency in horizontal flows, so more advanced techniques involving thermal and mechanical disequilibrium between phases are required.The paper describes the development and application of a drift flux code ASSERT (Advanced Solution of Subchannel Equations in Reactor Thermalhydraulics) which models departure from mechanical and thermal equilibrium between phases. Details of the model and computational technique are given, and parametric studies are shown to illustrate the capability of the code to simulate two-phase flow in horizontal bundles.Fundamental to the successful application of such a code are phenomenological studies aimed at the quantification of the empirical relationships selected for use. The paper concludes with a detailed study of mechanisms governing two-phase flow between neighbouring horizontal channels, isolating the driving effects of pressure gradient, gravity head and turbulent interchange by means of comparison with available experimental data.     

Reversal of laminar flow in a circular pipe

In the analysis of the loss of coolant accident (LOCA) in water reactors, the frictional resistance is treated in a one-dimensional sense using the quasi-steady state approximation for evaluation of the friction factor. The calculation has predicted one or more flow reversals. The present paper examines the limits of validity of the quasi-steady approximation by comparing with a new exact solution assuming no flow separation. Radial velocity distributions, mean flowrate and friction coefficients are compared for the specific case of a ramp change in pressure gradient including the limiting step. For low ramp rates with transient laminar flow in circular pipes the quasi-steady approximation is found valid; for high ramp rates the time to zero bulk flow is underestimated by 22.2%.     

Annular flow experiments in rod bundles with spacers

Measurements of pressure drop, film flow rate and film thickness have been made on a special test section modelling the four subchannels between ten fuel rods in a LWR geometry. Tests were carried out with air/water at 2.5–3-bar (a). Measurements were made with and without spacer grids inserted in the channel. In the former case, the measurements were made upstream and downstream of the spacers. In the case without spacers, the results show similar trends to data from tubular geometries with a similar hydraulic diameter. The two spacers tested both showed similar pressure losses. There was an increase in film flow rate and film thickness downstream of the ULTRAFLOW spacer. For a conventional egg-crate spacer there was a small change, with in some cases a decrease in film flow rate.     

Effects of ship motions on laminar flow in tubes

The thermal–hydraulics of barge-mounted floating nuclear desalination plants is the incentive for this study. Laminar flow in tubes in heaving motion is modeled. The friction factor and heat transfer coefficient are obtained. All the equations of laminar flow in steady state are applicable for heeling motion. The effect of ship motions on the laminar developing region is also analyzed. The ship motions can weaken the boundary layer in the laminar developing region and strengthen the laminar frictional resistance. The effect of ship motions on the instability of laminar flow is also investigated. The ship motions do not affect the instability point, but they can shorten the distance between the instability point and the transition point, and cause the transition from laminar flow to turbulent flow to occur earlier.     

Numerical calculations for two-phase flow analyses in pin bundles

Two-phase flow equation systems, in which equations are defined for each phase, are discussed for use in analyzing coolant behaviors in LMFBR pin bundles. These equation systems have not yet consolidated, because of theoretical and experimental difficulties and complexities.One of the problems is the equation systems' stability. This paper shows the stability for the low Reynolds number (O(1)) system, using a one dimensional linear equation system. Based on this fact, a two-phase flow equation system is numerically solved by using the subchannel method for 19- and 37-pin bundles. The calculational examples are LOF and TOP conditions with/without the blockage, and fission gas release.     

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.     

Theoretical analysis of phase-lag in low frequency laminar pulsating flow

The phase-lag between pressure gradient and flow rate in laminar pulsating flow in circular pipes and parallel-plate channels are studied theoretically. It is found that the phase-lag between pressure gradient and flow rate in low frequency (f < 0.5 Hz) pulsating laminar flow exists both in circular pipes and parallel-plate channels. The phase-lag increases with the increase of pulsating frequency, radius of the pipe and the height of the channel, however, it decreases with increase of the fluid viscosity. In addition, the phase-lag is not related to the pulsating amplitude. The analytical results show that velocity radial distribution does not affected by the low frequency pulsation and the value of phase-lag depends on the ratio of the acceleration pressure drop to the total pressure drop.     

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.     

The model of laminar pulsatile flow in tubes in rolling motion

The laminar pulsatile flow in tubes in rolling motion is investigated theoretically. The theoretical model of laminar flow in rolling motion is developed and the velocity correlation is also derived. The effect of rolling motion on velocity and frictional resistance factor is analyzed. The rolling motion mainly affects on the laminar flow by the tangential force. The centrifugal force does not affect on the flow. The tangential force affects on the flow in axial direction, its radial effect is very weak and could be omitted. There are two critical rolling points in rolling motion. After the first critical rolling point, the flowing velocity next to the wall reverses. Moreover, the flow rate at the tube cross-section becomes negative after the second critical rolling point. The buoyancy force is only one part of the effects that affects on the average velocity of a natural circulation system in rolling motion. The effect of Womersley number on the velocity is significant, which can not only affect on the average velocity but also on the oscillating period and velocity amplitude. The rolling motion does not affect on the average frictional resistance of laminar pulsatile flow. If the rolling motion is very serious, the flow is at a transitional or turbulent flow state, in this case the effect of rolling motion on the average frictional resistance is considerable.     

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.     

Evaluation of conduction mixing lengths for subchannel analysis of finite LMFBR bundles

An analytical, two-dimensional, multi-region, multi-cell technique was developed for the thermal analysis of LMFBR rod bundles. Local temperature fields of various unit cells were obtained for seven- and nineteen-rod bundles of different geometries and power distributions. The validity of the technique was verified by its excellent agreement with the THTB calculational result. By comparing the calculated fully-developed circumferential cladding temperature distribution with those of the experimental measurements, an axial correction factor has been derived to account for the entrance effect under practical conditions.A scheme was also developed to couple the two-dimensional distributed analysis and lumped parameter calculation such that the entrance effect can be implanted into the distributed parameter analysis. The technique has demonstrated its applicability for a seven-rod bundle. The results of calculation were compared to those of three-dimensional analysis.     

Liquid solidification in laminar tube flow with internal heat sources

The effect of liquid solidification (freezing) on the heat transfer characteristics for laminar flow of a heat-generating fluid in a cooled circular tube is investigated analytically. Steady-state conditions and a uniform wall temperature, which is lower than the liquid freezing temperature, are assumed. The radius of the liquid-solid interface and local Nusselt number are determined as a function of position along the tube for several different values of the wall temperature and internal heat-generating rate. The thickness of the solid-phase shell increases with distance down the tube and approaches to its fully developed value depending upon a single dimensionless freezing parameter which measures the relative rate of external cooling and internal heating. The local Nusselt number, however, first decreases rapidly, attains a minimum and then increases toward its fully developed value, which is identical with 6.