Implementation of the renormalization group (RNG) k–ε turbulence model in GOTHIC/6.lb: solution methods and assessment

In GOTHIC, the standard k–ε model is used to model turbulent flow. In an attempt to enhance the turbulence modelling capabilities of the latest 6.1b version of the code for simulation of mixing driven by highly buoyant discharges, we implemented the renormalization group (RNG). This model, which is only implemented in the “gas” phase, was tested with different simple test-problems and its predictions were compared to the corresponding ones obtained when the standard k–ε model was used. As expected, the RNG model is less dissipative than the standard k–ε model. However, comparison of code predictions with experimental measurements show that the predictions of the RNG model are better only near the source. Finally, we show how in the framework of this latest code version, one can implement higher-order non-linear turbulence models.     

CFD simulations of light gas release and mixing in the Battelle Model-Containment with CFX

In this validation work two turbulence models (k– and SST model) and two grids (a finer hybrid grid and a tetrahedral coarser grid) are considered in order to model helium release and dispersion. Simulation results are compared against an experiment of jet release phenomena in the Battelle Model Containment facility (BMC), a multi-compartment facility with a total volume of about 560 m³. In the selected test, HYJET Jx7, helium was released into the containment at a speed of 42 m/s over a time of 200 s. Although the k– model is the most commonly used turbulence model in most Computational Fluid Dynamics (CFD) applications, it does not provide the most accurate predictions for this application. Alternatively the SST turbulence model has been employed giving more accurate results. This investigation provides a further confirmation that the validation of commercial CFD codes is always required in order to select the more suitable physical models and computational grids for each specific application.     

Computations of post-trip reactor core thermal hydraulics using a strain parameter turbulence model

Coolant flows in the cores of nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be modified strongly from the forced convection condition by the action of buoyancy, in particular exhibiting impaired levels of heat transfer with respect to corresponding forced convection cases. The heat transfer performance of these ‘mixed convection’ flows is investigated here using two physically distinct eddy viscosity turbulence models: the recent ‘strain parameter’ (or k––S) model of Cotton and Ismael [A strain parameter turbulence model and its application to homogeneous and thin shear flows. Int. J. Heat Fluid Flow 19 (1998) 326] is examined against the benchmark low-Reynolds-number k– model of Launder and Sharma [Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1 (1974) 131]. Comparison is made with three sets of heat transfer data for ascending mixed convection flows, and it is demonstrated that both turbulence models are generally successful in resolving the Nusselt number distributions occurring along the lengths of mixed convection flow passages. The mechanisms by which the strain parameter model generates reduced turbulence levels, and hence impaired heat transfer rates, is explored in comparison with a fourth set of experimental data for mixed convection flow profiles.     

Two phase flow 1D turbulence model for poly-disperse upward flow in a vertical pipe

A 1D test-solver was developed in recent years for modeling of two phase bubbly flows in pipe geometry. The solver considers a number of bubble classes and calculates bubble-size resolved void fraction profiles in the radial direction. A successful implementation was achieved regarding bubble forces models (non-drag forces). Discrepancies appeared when coalescence and breakup rates were significant. These rates depend upon local turbulence quantities, which are possible reason for discrepancies. Originally the test-solver is equipped by Sato model (Sato, Y., Sadatomi, M., Sekoguchi, K., 1981. Momentum and heat transfer in two-phase bubble flow. I. International Journal Multiphase Flow 7, 167–177 .) which accounts for turbulence via shear- and bubble-induced viscosities calculated out of empirical correlations. One equation for the turbulent kinetic energy was solved, while the dissipation rate was calculated out of a correlation. In order to improve calculation of the local turbulence parameters, a two-phase k– turbulence model was adopted instead. The account for the bubble-induced turbulence was made via a source term taken out of literature. Comparisons between new and old turbulence modeling against experimental data showed better agreement for the new model. The experiments covered a wide range of water and air superficial velocities for upward bubbly flow in two pipe's diameters: 50 and 200 mm. The main feature of the new model is providing more reliable values of turbulence parameters for application in coalescence and breakup models. A comparison with CFX 5.7 calculations in a 50 mm pipe showed better calculation results when the source term was considered in the k– equations. An implementation into CFX is planned.     

Two fluid model for two-phase turbulent jets

Eulerian two-fluid models are widely used in nuclear reactor safety and CFD. In these models turbulent diffusion of a dispersed phase must be formulated in terms of the fluctuating interfacial force and the Reynolds stresses. The interfacial force is obtained using the probability distribution function approach by Reeks (1992). This paper is the first application of this force to a case of engineering interest outside homogeneous turbulence. An Eulerian multidimensional two-fluid model for a cylindrical two-phase dispersed particle jet is proposed and compared with experimental data. The averaged conservation equations of mass and momentum are solved for each phase and the turbulent kinetic energy equation is solved for the continuous phase. The turbulent diffusion force and the Reynolds stresses are constituted within the context of the k- model of turbulence. A dissipation term has been added to the k- model for the turbulence modulation by the particles. Once the constitutive relations have been defined, the two-fluid model is implemented in a computational fluid dynamics code. It is shown that when the particles are very small the model is consistent with a convection-diffusion equation for particle transport where the diffusivity is defined according to Taylor's model (Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math. Society, A20, pp. 196–211). The two-fluid model is also compared against two experimental data sets. Good agreement between the model and the data is obtained. The sensitivity of the results to various turbulent mechanisms is discussed.     

The effect of turbulence modeling on hydrogen jet dispersion inside a compartment space using the HYDRAGON code

The mitigation of hydrogen in the containment of nuclear reactor after the Loss of Coolant Accident is essential to preserve the structural reliability of the containment. This paper presents the results of the systematic work done by using the HYDRAGON code to investigate the effect of turbulence models on the concentration distribution of hydrogen and to determine the HYDRAGON code thermal-hydraulic simulation capability during a severe accident at the nuclear power plant. The HYDRAGON code is developed by the Department of Engineering Physics, Tsinghua University, which is an independent research program. The influence of various types of turbulence models, i.e. a standard k ? ? model, a re-normalized group (RNG) k ? ? model, and a realizable k ? ? model were analyzed and the simulation results were compared with the experimental data. When simulation results were compared to experimental data, it was found that, in most compartments, the standard k ? ? model generally yielded reasonable agreement with the experimental results as compared to RNG k ? ? and realizable k ? ? models; however, for probes P7 and P12, better trend was captured by RNG k ? ? and realizable k ? ? models, respectively.     

Investigation of turbulence modelling in thermal stratification analysis

In-vessel thermal stratification analysis was carried out using a multidimensional thermohydraulic analysis code, in which a higher-order finite difference scheme was applied to the convection terms. Discussions centred on the buoyancy modelling in the vicinity of the stratification interface through comparisons between experiment and calculation.Computational results were obtained from the following three turbulence models: (i) the k−ε model with a constant turbulent Prandtl number Pr_t, (ii) the k−ε model with the turbulent Prandtl number being dependent on the local Richardson number Ri, and (iii) the algebraic stress model. Numerical analysis of the stratification phenomena using the higher-order scheme showed that, in general, the modelling of the buoyancy terms appearing in the turbulence transport equations was the most important key to successful results. When the k−ε model was used, it was pointed out that a dependence on the local Richardson number must be carefully included in the turbulent Prandtl number. In this case, however, the range of applicability was limited to the phenomena observed in the water system in general because the model was constructed and calibrated for water experiments. Overall it was found that the calculated stratification interface rise agreed well with experimental results in water and sodium insofar as the algebraic stress model was utilized. As a conclusion, in predicting the behaviour of the thermal stratification phenomena in liquid metal cooled reactors, the coupled use of the higher-order difference scheme and the algebraic stress model was most appropriate and recommended.     

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.     

Experimental and numerical investigation of counter-current stratified flows in horizontal channels

Counter-current flow regimes of air and water are investigated in the WENKA test facility at the Forschungszentrum Karlsruhe. With the fluorescent-particle image velocimetry (PIV) measurement technique, velocity and velocity fluctuations are measured up to the free surface. A statistical model is presented to correlate the measured void fraction with the turbulent kinetic energy calculated from the measured velocity fluctuations. The experimental data are used to develop a phase interaction model to simulate stratified flows. Two different approaches are compared for turbulence modelling. The Prandtl mixing length model and an extended k–ω model for the two-phase region are applied to supercritical flow conditions.     

Experimental investigation and CFD simulation of horizontal stratified two-phase flow phenomena

For the investigation of stratified two-phase flow, two horizontal channels with rectangular cross-section were built at Forschungszentrum Dresden-Rossendorf (FZD). The channels allow the investigation of air/water co-current flows, especially the slug behaviour, at atmospheric pressure and room temperature. The test-sections are made of acrylic glass, so that optical techniques, like high-speed video observation or particle image velocimetry (PIV), can be applied for measurements. The rectangular cross-section was chosen to provide better observation possibilities. Moreover, dynamic pressure measurements were performed and synchronised with the high-speed camera system.CFD post-test simulations of stratified flows were performed using the code ANSYS CFX. The Euler–Euler two fluid model with the free surface option was applied on grids of minimum 4 × 10⁵ control volumes. The turbulence was modelled separately for each phase using the k–ω-based shear stress transport (SST) turbulence model. The results compare very well in terms of slug formation, velocity, and breaking. The qualitative agreement between calculation and experiment is encouraging and shows that CFD can be a useful tool in studying horizontal two-phase flow.     

Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles

Heat transfer in upward flows of supercritical water in circular tubes and in tight fuel rod bundles is numerically investigated by using the commercial CFD code STAR-CD 3.24. The objective is to have more understandings about the phenomena happening in supercritical water and for designs of supercritical water cooled reactors. Some turbulence models are selected to carry out numerical simulations and the results are compared with experimental data and other correlations to find suitable models to predict heat transfer in supercritical water. The comparisons are not only in the low bulk temperature region, but also in the high bulk temperature region. The two-layer model (Hassid and Poreh) gives a better prediction to the heat transfer than other models, and the standard k– high Re model with the standard wall function also shows an acceptable predicting capability. Three-dimensional simulations are carried out in sub-channels of tight square lattice and triangular lattice fuel rod bundles at supercritical pressure. Results show that there is a strong non-uniformity of the circumferential distribution of the cladding surface temperature, in the square lattice bundle with a small pitch-to-diameter ratio (P/D). However, it does not occur in the triangular lattice bundle with a small P/D. It is found that this phenomenon is caused by the large non-uniformity of the flow area in the cross-section of sub-channels. Some improved designs are numerically studied and proved to be effective to avoid the large circumferential temperature gradient at the cladding surface.     

Thermal hydraulic analysis compared with tests of full-scale concrete casks

To develop a thermal analysis method for the concrete cask, numerical calculation based on thermal hydraulic phenomena was performed. In the present calculation model, calculation area was divided into two parts. One is inside of the canister and the other is outside of the canister. These two parts were combined at the surface of the canister. In the model of the outside, k– turbulence model was adopted for air flow region. Comparing calculation results with test results, it was found that the analysis method was valid for normal and accident conditions of the storage.     

On turbulence models for rod bundle flow computations

In commercial computational fluid dynamics codes there is more than one turbulence model built in. It is the user responsibility to choose one of those models, suitable for the problem studied. In the last decade, several computations were presented using computational fluid dynamics for the simulation of various problems of the nuclear industry. A common feature in a number of those simulations is that they were performed using the standard k–ε turbulence model without justifying the choice of the model. The simulation results were rarely satisfactory. In this paper, we shall consider the flow in a fuel rod bundle as a case study and discuss why the application of the standard k–ε model fails to give reasonable results in this situation. We also show that a turbulence model based on the Reynolds stress transport equations can provide qualitatively correct results. Generally, our aim is pedagogical, we would like to call the readers attention to the fact that turbulence models have to be selected based on theoretical considerations and/or adequate information obtained from measurements.     

Modified k-ε model for two-phase turbulent jets

A modified k-ε model is proposed for two-phase turbulent jets which takes into account the additional dissipation of turbulent kinetic energy by the dispersed phase. Within the context of the two-phase averaged equation for the turbulent kinetic energy of the continuous phase, a constitutive relation is proposed for the additional dissipation of turbulence. The additional dissipation effect was modeled using a transfer function, which relates the fluctuations of the dispersed phase with the fluctuations of the continuous phase, integrating over the turbulence energy spectrum. A further improvement to the theory considers that dissipation only occurs when the eddies are bigger than the particles. Therefore a cutoff frequency is proposed and for big particles or bubbles dissipation may become negligible. The model is inserted in an Eulerian computational fluid dynamics code. The results are compared with data available in the literature for an air-particle jet. The results agree with the data within the range of experimental error. Comparisons were also made without including dissipation effects and it was concluded that the dissipation due to eddy-particle interactions is significant and should be included in a general two-phase k-ε model.     

Numerical study of a bubble plume generated by bubble entrainment from an impinging jet

The current paper presents the prediction results of a bubbly flow under plunging jet conditions using multiphase mono- and poly-dispersed approaches. The models consider interfacial momentum transfer terms arising from drag, lift, and turbulent dispersion force for the different bubble sizes. The turbulence is modeled by an extended k–? model which accounts for bubble induced turbulence. Furthermore in case of a poly-dispersed air–water flow the bubble size distribution, bubble break-up and coalescence processes as well as different gas velocities in dependency on the bubble diameter are taken into account using the Inhomogeneous MUSIG model. This model is a generalized inhomogeneous multiple size group model based on the Eulerian modeling framework which was developed in the framework of a cooperative work between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf (FZD). The latter is now implemented into the CFD code CFX.According to the correlation on the lateral lift force obtained by Tomiyama (1998); this force changes its sign in dependence on the bubble size. Consequently the entrained small bubbles are trapped below the jet. They can escape from the bubble plume only by turbulent fluctuations or by coalescence. If the size of the bubbles generated by coalescence exceeds the size at which the lift force changes its sign these large bubbles go out from the plume and rise to the surface.A turbulent model based on an additional source term for turbulence kinetic energy and turbulence eddy dissipation equation is compared to the common concept for modeling the turbulence quantities proposed by Sato et al. (1981). It has been found that the large bubble distribution is slightly affected by the turbulence modeling which affects particularly the bubble coalescence and break-up process.     

CFD simulation of bubble column

Three-dimensional simulations of gas-liquid flow in the bubble column using the Euler-Euler approach is presented. The attempt is made to assess the performance and applicability of different turbulence models namely, k-?, k-? RNG, k-ω, Reynolds stress model (RSM) and large eddy simulation (LES) using a commercial code (ANSYS-CFX). For this purpose, the predictions are compared against the experimental data of Kulkarni et al. (2007). Performance of the turbulence models is assessed on basis of comparison of axial liquid velocity, fractional gas hold-up, turbulent kinetic energy and turbulent eddy dissipation rate. All the non-drag (turbulent dispersion, virtual mass and lift force) and drag force were incorporated in the model. The low-Reynolds number treatment of the k-ω yields a better qualitative prediction than the k-? model. The RSM predictions are comparable with LES results and seemed to give better prediction near the sparger, where the flow is more anisotropic and gives a clue why RANS approaches fails to predict the flow in this region. However, the large eddy simulations showed good agreement with the experimental data, but requires higher computational time than RSM.     

A covariance model for Markov statistics

We propose a model to compute the variances for the ensemble average material fluxes in line Markov statistics. The model is exact at the limit of collisionless transport. The calculation of the material flux variances needs the determination of the covariances (in μ and μ′) and we have developed a system of coupled equations and made the usual heuristic extension to the case with collisions. A simple numerical solution, based on the standard discrete ordinates approximation with the diamond discretization, is proposed in 1D slabs. Numerical applications are given for bimaterial homogeneous statistics. The results are encouraging but further research is needed in this area. This will involve a modification of the standard Levermore–Pomraning model.     

Numerical Simulation of Heat Transfer of Supercritical Fluids in Circular Tubes Using Different Turbulence Models

In this study, the heat transfer of supercritical fluids in vertical and horizontal circular tubes has been investigated numerically to understand the thermal-hydraulic behavior of supercritical fluids. The simulations are carried out using different turbulence models and the numerical results are compared with the experimental data to evaluate the accuracy and applicability of those turbulence models. Six turbulence models are used in this study, the LB low-Re k-? model, the LS low-Re k-? model, the RNG k-? model, the realizable k-? model, the standard k-? model, and the Reynolds stress model. The comparison shows that the Reynolds stress model gives better agreement with the experimental data than other turbulence models studied in this work.     

Magnetohydrodynamically enhanced heat transfer in a liquid metal system

The phenomena of liquid metal flow under the influence of magnetic and electric fields are important in the development and design of nuclear and metallurgical plants, such as the blanket cooling systems of fusion or fast breeder reactors and electromagnetic stirring devices. In this study, a computer code that models recirculating flows in two dimensions using a k − ε turbulence model is expanded to include the magnetohydrodynamic (MHD) effects of applied electric and magnetic fields. This modified code is then used to examine the effect of MHD stirring on the heat transfer characteristics of a liquid metal cooling system. Using liquid sodium properties, various thermophysical properties are investigated. The results indicate that a significant increase in the rate of heat transfer is obtainable when the heat transfer system is operated in the presence of MHD stirring.     

Thermal hydraulic study on detection of random failure of fuel by delayed neutron detection system

During a fuel element failure in a liquid metal cooled fast breeder reactor, the fission products originating from the failed pins mix into the sodium pool. Delayed neutron detectors are provided in the sodium pool to detect such failures by way of detection of delayed neutrons emitted by delayed neutron precursors present in the fission products. The transient evolution of precursor concentration is governed by the sodium flow distribution in the pool. Transient thermal hydraulic analysis of precursor concentration evolution in the hot pool of a 500 MWe fast reactor has been carried out using the computational fluid dynamics code PHOENICS to estimate the time at which the failures of various fuel subassembly are detected. Standard k– turbulence model is used to take care of turbulence in conjunction with the precursor concentration equation. It has been found that in order to effectively detect the failure of all fuel SA in the core, a minimum of eight detectors are essential to be provided in the hot pool.