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.     

Experimental study on the Reynolds number dependence of turbulent mixing in a rod bundle

An experimental study for Reynolds number dependence of the turbulent mixing between fuel-bundle subchannels, was performed. The measurements were done on a triangular array bundle with a 1.20 pitch to diameter relation and 10 mm rod diameter, in a low-pressure water loop, at Reynolds numbers between 1.4 × 10³ and 1.3 × 10⁵.The high accuracy of the results was obtained by improving a thermal tracing technique recently developed. The Reynolds exponent on the mixing rate correlation was obtained with two-digit accuracy for Reynolds numbers greater than 3 × 10³. It was also found a marked increase in the mixing rate for lower Reynolds numbers.The weak theoretical base of the accepted Reynolds dependence was pointed out in light of the later findings, as well as its ambiguous supporting experimental data.The present results also provide indirect information about dominant large scale flow pulsations at different flow regimes.     

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.     

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.     

Phenomenological investigations on the turbulent flow structures in a rod bundle array with mixing devices

Detailed turbulent flow profiles have been measured on a square sub-channel geometry with typical mixing devices. For a fine examination of the lateral flow structure on a sub-channel geometry with 2D LDA, a 5 × 5 rod bundle array was fabricated as 2.6 times larger than the real bundle size. The mixing devices used were a typical split type and a swirl type. The experiments were performed at the condition of Re = 48,000 (axial bulk velocity 1.48 m/s) and the water loop was maintained at the conditions of 35 °C and 1.5 bar during an operation. As for the results, distinct intrinsic flow features were observed according to the type of mixing devices. In a typical split type, there was no remarkable swirling flow within a sub-channel and the lateral flow was vigorous in the gaps. In the swirl type, a single swirling flow was dominant within a sub-channel and there were relatively small lateral flows in the gaps.     

A turbulence model study for simulating flow inside tight lattice rod bundles

Performances of various turbulence models are evaluated for calculation of detailed coolant velocity distribution in a tight lattice fuel bundle. The individual models are briefly outlined and compared with respect to the prediction of wall shear stress and velocity field, for a fully developed flow inside a triangular lattice bundle. Comparisons clearly show the importance of proper modeling of the turbulence-driven secondary flows in subchannels. A quadratic k– model, which showed promising capability in this respect, is adjusted in its coefficients, and the adjusted model is applied to fully developed flow in an infinite triangular array, with various Reynolds numbers. The results show that the inclusion of adequate anisotropy modeling enables to accurately reproduce the wall shear stress distribution and velocity field in tight lattice fuel bundles.     

From discovery to recognition of periodic large scale vortices in rod bundles as source of natural mixing between subchannels—A review

The mixing of cooling fluid in rod bundles from one subchannel to another through the gaps between the rods reduces the temperature differences in the coolant as well as along the perimeter of the rods. The phenomenon of natural mixing was first intensively investigated in the 1960s and remains a topic of research up to the present time. The paper describes the main stations on the way to understand the nature of the flow in rod bundles and generally in compound channels with the focus on work performed at Research Center Karlsruhe (FZK).¹Earlier, it was noticed that the mixing rates where higher than could be accounted for by turbulent diffusion alone. For more than 20 years attempts were made to prove experimentally and by code application that secondary flows could account for the measured mixing rates, although the measured secondary flow velocities were much too low. Measurements of the turbulence structure by hot wire anemometry confirmed the existence of cyclic flow pulsations, which had been postulated earlier on the basis of thermocouple measurements. More sophisticated hot wire measurements revealed the nature of these pulsations as periodic, coupled to gap width and Reynolds number. Finally, the extension of the investigation to other compound channel types and flow visualization revealed the true nature of the mixing process as a vortex train moving along the gap between rods or in the narrow part of a compound channel. These findings have been confirmed by LES calculations. Based on these results CFD codes with improved turbulence models calculated successfully the flow in rod bundles including the macroscopic oscillations.     

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.     

The turbulent mixing rate and the fluctuations of static pressure difference between adjacent subchannels in a two-phase subchannel flow

Turbulent mixing rate between adjacent subchannels in a two-phase flow has been known to be strongly dependent on the flow pattern. In this study, flow visualization was made to investigate the mechanism of the turbulent mixing between subchannels in a two-phase flow under hydrodynamic equilibrium conditions. The test channel was a vertical multiple channel consisting of two identical rectangular subchannels, and the working fluids were air and water. It was observed in slug-churn flows that a large scale inter-subchannel liquid flow occurs in front of the nose of a large gas bubble and behind the tail when the bubble axially passes through the subchannel, and thus a high turbulent mixing rate of the liquid phase results. In order to know driving force of such a large scale inter-subchannel flow, measurement of instantaneous static pressure difference between the subchannels was also made. The result showed that there is a close relationship between the liquid phase turbulent mixing rate and the magnitude of the pressure difference fluctuations.     

SIMPLE-2: A computer code for calculation of steady-state thermal behavior of rod bundles with flow sweeping

A computer code has been developed for use in making single-phase thermal hydraulic calculations in rod bundle arrays with flow sweeping due to spiral wraps as the predominant crossflow mixing effect. This code, called SIMPLE-2, makes the assumption that the axial pressure gradient is identical for each subchannel over a given axial increment, and is unique in that no empirical coefficients must be specified for its use. Results from this code have been favorably compared with experimental data for both uniform and highly nonuniform power distributions. Typical calculations for various bundle sizes applicable to the LMFBR program are also included.     

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.     

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.     

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.