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.     

Unsteady numerical simulations of the single-phase turbulent mixing between two channels connected by a narrow gap

This paper focuses on the unsteady numerical simulation of the turbulent flow in two types of geometry containing a narrow gap with the explicit algebraic Reynolds stress model. The model was first validated through the comparison of simulation results inside a rectangular channel containing a cylinder and the corresponding experimental data. The structures of the oscillation were correctly reproduced. Simulation of turbulent mixing between circular channels connected by a narrow gap was carried out with the validated model. Because of the influence of the strong anisotropic turbulent flow in the gap region, the mixing rate was dramatically enhanced by the cyclic and almost periodic flow pulsation. The calculation results of the turbulent mixing rate showed good agreement with the experiment and the maximum error was less than 15%.     

Prediction of turbulent mixing rates of both gas and liquid phases between adjacent subchannels in a two-phase slug-churn flow

This paper presents a slug-churn flow model for predicting turbulent mixing rates of both gas and liquid phases between adjacent subchannels in a BWR fuel rod bundle. In the model, the mixing rate of the liquid phase is calculated as the sum of the three components, i.e. turbulent diffusion, convective transfer and pressure difference fluctuations between the subchannels. The components of turbulent diffusion and convective transfer are calculated from Sadatomi et al.'s [Nucl. Eng. Des. 162 (1996) 245–256] method, applicable to single-phase turbulent mixing, by considering the effect of the increment of liquid velocity due to the presence of gas phase. The component of the pressure difference fluctuations is evaluated from a newly developed correlation. The mixing rate of the gas phase, on the other side, is calculated from a simple relation of mixing rate between gas and liquid phases. The validity of the proposed model has been confirmed with the turbulent mixing rates data of Rudzinski et al. [Can. J. Chem. Eng. 50 (1972) 297–299] as well as the present authors.     

The effect of turbulent mixing models on the predictions of subchannel codes

In this paper, the predictions of the COBRA-IV and ASSERT-4 subchannel codes have been compared with experimental data on void fraction, mass flow rate, and pressure drop obtained for two interconnected subchannels. COBRA-IV is based on a one-dimensional separated flow model with the turbulent intersubchannel mixing formulated as an extension of the single-phase mixing model, i.e. fluctuating equal mass exchange. ASSERT-4 is based on a drift flux model with the turbulent mixing modelled by assuming an exchange of equal volumes with different densities thus allowing a net fluctuating transverse mass flux from one subchannel to the other. This feature is implemented in the constitutive relationship for the relative velocity required by the conservation equations. It is observed that the predictions of ASSERT-4 follow the experimental trends better than COBRA-IV; therefore the approach of equal volume exchange constitutes an improvement over that of the equal mass exchange.     

Investigations on mixing phenomena in single-phase flow in a T-junction geometry

The paper deals with T-junction mixing experiments carried out with wire-mesh sensors. The mixing of coolant streams of different temperature in pipe junctions leads to temperature fluctuations that may cause thermal fatigue in the pipe wall. This is practical background for an increased interest in measuring and predicting the transient flow field and the turbulent mixing pattern downstream of a T-junction. Experiments were carried out at a perpendicular connection of two pipes of 51 mm inner diameter. The straight and the side branches were supplied by water of different electrical conductivity, which replaced the temperature in the thermal mixing process. A set of three wire-mesh sensors with a grid of 16 × 16 measuring points each was used to record conductivity distributions downstream of the T-junction. Besides the measurement of profiles of the time averaged mixing scalar over extended measuring domains, the high resolution in time and space of the mesh sensors allow a statistic characterization of the stochastic fluctuations of the mixing scalar in a wide range of frequencies. Information on the scale of turbulent mixing patterns is obtained by cross-correlating the signal fluctuations recorded at different locations within the measuring plane of a sensor.     

New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations

The determination of single-phase friction factor of pipe flow is essential to a variety of industrial applications, such as single-phase flow systems, two-phase flow systems and supercritical flow systems. There are a number of correlations for the single-phase friction factor. It still remains an issue to examine similarities and differences between them to avoid misusing. This paper evaluates the correlations for the single-phase friction factor against the Nikuradse equation and the Colebrook equation, respectively. These two equations are the base for the turbulent portion of the Moody diagram, and are deemed as the standard to test the explicit counterparts. The widely used correlations for smooth pipes, the Blasius correlation and the Filonenko correlation, have big errors in some Re ranges. Simpler forms of the single-phase friction factor covering large ranges are needed. For this reason, two new correlations of single-phase friction factor for turbulent flow are proposed, one for smooth pipes and the other for both smooth and rough pipes. Compared with the Nikuradse equation, the new correlation for smooth pipes has the mean absolute relative error of 0.022%, with the maximum relative error of −0.045% in the Reynolds number (Re) range from 3000 through 10⁸. It is an idea replacement of the correlations of Blasius and Filonenko. The new correlation for both smooth and rough pipes has the mean absolute relative error of 0.16% and the maximum relative error of 0.50% compared with the Colebrook equation in the range of Re = 3000-10⁸ and Rr = 0.0-0.05, which is the most simplest correlation in that error band.     

Simulations of turbulence, heat transfer and mixing across narrow gaps between rod-bundle subchannels

Turbulent flow and temperature fields were determined numerically in a rectangular duct containing a heated rod. As the spacing δ between the rod and the duct wall decreased from 0.10D (D is the rod diameter) to 0.03D, coherent turbulent kinetic energy and temperature fluctuations dramatically increased in the gap region, but, for δ = 0.01D, coherent fluctuations essentially disappeared. As δ/D → 0, the frequency of coherent fluctuations decreased and cross-gap mixing weakened, contrary to predictions based on extrapolated available empirical correlations.     

The structure of turbulent flow through a wall subchannel of a rod bundle

An experimental investigation was performed to establish reliable information on the transport properties of turbulent flow through subchannels of rod bundles. Detailed data were measured of the distributions of the time-mean velocity, the turbulence intensities in all directions and hence, the kinetic energy of turbulence, of the shear stresses in the directions normal and parallel to the walls and of the wall shear stresses for a wall subchannel of a rod bundle of four parallel rods. The pitch to diameter ratio of the rods equal to the wall to diameter ratio was 1.07, the Reynolds number of this investigation was Re = 8.7 × 10⁴.On the basis of the data measured the eddy viscosities in the directions normal and parallel to the walls were calculated. Thus, detailed data of the eddy viscosities in direction parallel to the walls in rod bundles were obtained for the first time. The experimental results were compared with predictions by the VELASCO code. There are considerable differences between calculated and measured data of the time-mean velocity and the wall shear stresses. Attempts to adjust the VELASCO code against the measurements were not successful. The reasons of the discrepancies are discussed.     

Assessment of the interchannel mixing model with a subchannel analysis code for BWR and PWR conditions

The influence of the interchannel mixing model employed in a traditional subchannel analysis code was investigated in this study, specifically on the analysis of the enthalpy distribution and critical heat flux (CHF) in rod bundles in BWR and PWR conditions. The equal-volume-exchange turbulent mixing and void drift model (EVVD) was embodied to the COBRA-IV-I code. An optimized model of the void drift coefficient has been devised in this study as the result of the assessment with the two-phase flow distribution data for the general electric (GE) 9-rod and Ispra 16-rod test bundles. The influence of the subchannel analysis model on the analysis of CHF was examined by evaluating the CHF test data in rod bundles representing PWR and BWR conditions. The CHFR margins of typical light water nuclear reactor (LWR) cores were evaluated by considering the influence on the local parameter CHF correlation and the hot channel analysis result. It appeared that the interchannel mixing model has an important effect upon the analysis of CHFR margin for BWR conditions.     

Large eddy simulation of subchannels using the lattice Boltzmann method

Large eddy simulation results of a subchannel of a rod bundle with triangular rod arrangement are presented. The simulations have been carried out using the lattice Boltzmann method. The simulation results are compared with the measurements of (Trupp and Azad, 1975) [Trupp, A.C., Azad, R.S., 1975. The structure of turbulent flow in triangular array rod bundles. Nucl. Eng. Des. 32, 47]. The mean axial velocity profile shows good agreement with the measurement data. Secondary flow has been deduced from the measurements and it has been observed directly in the simulation results. Reasonable agreement has been achieved for most Reynolds stresses. Nevertheless, the calculated normal stresses show small, but systematic deviation from the measurement data.     

Large-Eddy Simulation study of turbulent mixing in a T-junction

A potential cause of thermal fatigue failures in energy cooling systems is identified with cyclic stresses imposed on a piping system. These are generated due to temperature changes in regions where cold and hot flows are intensively mixed together. A typical situation for such mixing appears in turbulent flow through a T-junction, which is investigated here using Large-Eddy Simulations (LES). In general, LES is well capable in capturing the mixing phenomena and accompanied turbulent flow fluctuations in a T-junction. An assessment of the accuracy of LES predictions is made for the applied Vreman subgrid-scale model through a direct comparison with the available experimental results. In particular, an estimation of the minimal mesh-resolution requirements for LES is examined on the basis of the complementary RANS simulations. This estimation is based on the characteristics turbulent scales (e.g., Taylor micro-scale) that can be computed from LES or RANS simulations.     

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.     

Simulation of gas mixing and transport in a multi-compartment geometry using the GOTHIC containment code and relatively coarse meshes

The recently concluded OECD SETH project included twenty-four experiments on basic flows and gas transport and mixing driven by jets and plumes in two, large, connected vessels of the PANDA facility. The experiments featured injection of saturated or superheated steam, or a mixture of steam and helium in one vessel and venting from the same vessel or from the connected one. These tests have been especially designed for providing an extensive data base for the assessment of three-dimensional codes, including CFD codes. In particular, one of the goals of the analytical activities associated with the experiments was to evaluate the detail of the model (mesh) necessary for capturing the various phenomena. This work reports an overview of the results obtained for these experimental data using the advanced containment code GOTHIC and relatively coarse meshes, which are coarser than the ones typically used for the simulation with commercial CFD codes, but are still representative of the models which are currently affordable for a full containment analysis. In general, the phenomena were correctly represented in the simulations with GOTHIC, and the agreement of the results with the data was in most cases pretty good, in some cases excellent. Only for a few tests (or particular phenomena occurring in some tests) the simulations showed noticeable discrepancies with the experimental data, which could be referred to either an insufficiently detailed mesh or to lack of specialized models for local effects.     

Flow redistribution due to void drift in two-phase flow in a multiple channel consisting of two subchannels

Void drift in two-phase flow is studied experimentally using a geometrically simple, vertical channel consisting of two interconnected subchannels. Data on the flow redistributions of both air and water along the channel axis are obtained and presented for the following two multiple channels: one with two circular subchannels of different cross-sectional area and the other with two identical circular subchannels. The data are analysed by a simple one-dimensional subchannel code taking account of the effects of void drift and turbulent mixing between subchannels, i.e. incorporating both the void-settling model of Lahey et al. and a term similar to that in the COBRA code in the momentum equation. The flow redistribution process can be explained by the analysis.     

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.     

Ex-vessel transport and mixing of a deborated slug in a PWR primary geometry

The transport and mixing of a slug of deborated water in a lowered loop PWR is modeled by partitioning the volumes of the primary system according to chemical rector theory. Piping is modeled as plug flow volumes while the steam generator outlet plenum and the reactor coolant pumps are modeled as backmixed volumes. This simple approach provides a good representation of the transport and mixing phenomena outside the reactor vessel. The proposed methodology can be used to generate initial and boundary conditions for separate effects tests and CFD computations for the reactor vessel complex geometry. The decoupling of the ex-vessel primary system greatly enhances the resolution of boron dilution transient issue.     

Thermal-hydraulic performance analysis of a subchannel with square and triangle fuel rod arrangements using the entropy generation approach

The present paper discusses entropy generation in fully developed turbulent flows through a subchannel,arranged in square and triangle arrays. Entropy generation is due to contribution of both heat transfer and pressure drop. Our main objective is to study the effect of key parameters such as spacer grid, fuel rod power distribution,Reynolds number Re, dimensionless heat power ω, lengthto-fuel-diameter ratio λ, and pitch-to-diameter ratio ξ on subchannel entropy generation. The analysis explicitly shows the contribution of heat transfer and pressure drop to the total entropy generation. An analytical formulation is introduced to total entropy generation for situations with uniform and sinusoidal rod power distribution. It is concluded that power distribution affects entropy generation.A smoother power profile leads to less entropy generation.The entropy generation of square rod array bundles is more efficient than that of triangular rod arrays, and spacer grids generate more entropy.     

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.     

Numerical methods for the prediction of thermal fatigue due to turbulent mixing

Turbulent mixing of hot and cold flows is one of the possible causes of thermal fatigue in piping systems. Especially in primary pipework of nuclear power plants this is an important, safety related issue. Since the frequencies of the involved temperature fluctuations are generally too high to be detected well by common plant instrumentation, accurate numerical simulations are indispensable for a proper fatigue assessment. In this paper, a link is made between two such numerical methods: a coupled CFD-FEM model and a sinusoidal model. By linking these methods, more insight is obtained in the physical phenomenon causing thermal fatigue due to turbulent mixing. Furthermore, useful knowledge is acquired on the determination of thermal loading parameters, essential for reducing overconservatism, as currently present in simplified fatigue assessment methods.     

Simulation of turbulent and thermal mixing in T-junctions using URANS and scale-resolving turbulence models in ANSYS CFX

Being of importance for turbulent and thermal mixing and consequently for thermal striping and thermal fatigue problems in nuclear power plants, the turbulent isothermal and thermal mixing phenomena have been investigated in two different testcase scenarios. First testcase scenario as proposed by ETHZ (Zboray et al., 2007) comprises of turbulent mixing of two water streams of equal temperature in a T-junction of 50 mm pipes in the horizontal plane and thereby excluding any buoyancy effects. The second testcase is based on the Vattenfall test facility in the Älvkarleby laboratory and has been proposed by Westin (2007) where water of 15 K temperature difference mixes in a T-junction in vertical plane, provoking thermal striping phenomena. ANSYS CFX 11.0 with Reynolds averaging based (U)RANS turbulence models (SST and BSL RSM) as well as with scale-resolving SAS-SST turbulence model has been applied to both test cases. CFD results have been compared to wire-mesh sensor, LDV and thermocouple measurements. While the turbulent mixing in the ETHZ testcase could be reproduced in good quantitative agreement with data, the results of the LES-like simulations were not yet fully satisfying in terms of the obtained accuracy in comparison to the detailed measurement data, also the transient thermal striping phenomena and large-scale turbulence structure development was well reproduced in the simulations.