Towards a multi-scale approach of two-phase flow modeling in the context of DNB modeling

In this article, we present how Direct Numerical Simulation (DNS) is being used in the context of Departure from Nucleate Boiling (DNB) modeling. Two particular applications are analyzed: wall boiling and bubble column flow. An analysis of the relevant length scales involved shows that true DNS, where all the length scales are resolved, is necessarily restricted to flow configurations where one or a few bubbles are involved. In the context of DNB modeling, DNS can thus be used to study (i) the dynamics of the growth of a few bubbles with their eventual spreading and (ii) bubble column flows to predict the void fraction field in the near wall region. To account for collective effects in bubbly flows, we show that it is necessary to develop a new approach where the large turbulence structures and large interface deformations are captured whereas the smallest scales are modeled; this is the Interface and Subgrid Scale (ISS) method. The DNS and ISS methods are presented and preliminary results on the use of DNS for larger scales models are presented.     

Understanding L-H transition in tokamak fusion plasmas

This paper reviews the current state of understanding of the L-H transition phenomenon in tokamak plasmas with a focus on two central issues:(a) the mechanism for turbulence quick suppression at the L-H transition;(b) the mechanism for subsequent generation of sheared flow.We briefly review recent advances in the understanding of the fast suppression of edge turbulence across the L-H transition.We uncover a comprehensive physical picture of the L-H transition by piecing together a number of recent experimental observations and insights obtained from 1D and 2D simulation models.Different roles played by diamagnetic mean flow,neoclassical-driven mean flow,turbulence-driven mean flow,and turbulence-driven zonal flows are discussed and clarified.It is found that the L-H transition occurs spontaneously mediated by a shift in the radial wavenumber spectrum of edge turbulence,which provides a critical evidence for the theory of turbulence quench by the flow shear.Remaining questions and some key directions for future investigations are proposed.     

Revisiting the resolution requirements for turbulence simulations in nuclear heat transfer

Direct numerical simulations (DNSs) require the resolution of all relevant turbulence scales in space and time, whereas large eddy simulations (LESs) need only to resolve the dominant energy carrying large scales. Important influences from physics and numerics on the small-scale resolution are discussed. Quantitative criteria for turbulent flows are re-evaluated. Experience shows, resolving the microscales is usually by far not achieved in DNS; this is less relevant than the adequate resolution of the anisotropic coherent fine flow structures. These structures depend on the flow type, so that general criteria cannot be given. Resolving the large scales is a serious problem. When the computational domain covers only part of the flow domain, the large-scale resolution is coupled to the artificial boundary conditions for open boundaries. Each measure and criteria have to be carefully considered to ensure that the simulations meet the expectations. Special emphasis is given to liquid metal flows because related nuclear applications are often in the transition range between LES and DNS of the temperature field. A new model is given to predict local turbulent Prandtl numbers for subgrid scale heat flux modeling. It covers the required most important influences: local resolution, a local turbulence parameter, and Reynolds and Prandtl numbers.     

Analysis of Unsteady Turbulent Triple Jet Flow with Temperature Difference

Suitable analysis methodology is required to obtain detailed information about magnitude and frequency of temperature variation of flow field for the study of thermal stripping phenomena. The large eddy simulation (LES) is applied to analyze unsteady turbulent triple jet water flow which can be a direct cause of thermal stripping. Current analyses are performed with different sub-grid scale models, number of grids, time increments, and inlet temperature intensities to find the effects of these on prediction. Predicted results of the LES are compared with experimental results. The LES successfully produces a time history of turbulence variables, which can be used to evaluate magnitude and frequency of instantaneous temperature. The LES tends to predict higher levels of root mean square temperatures compared to those of an experiment, indicating very active mixing effect among triple jets. The LES is found to be able to provide reliable frequency information about temperature fluctuation. The different sub-grid scale models show no significant difference in prediction ability and other variations of the LES prediction show no significant difference in prediction either. However, cases using the fine grid and the small time increment are slightly better than others. Further study is desired with different levels of inlet temperature intensities and separate sub-grid scale models for temperature field.     

Numerically simulating the thermal-hydraulic characteristics within the fuel rod bundle using CFD methodology

With the dramatic progress in the computer processing power, computational fluid dynamics (CFD) methodology can be applied in investigating the detailed knowledge of thermal-hydraulic characteristics in the rod bundle, especially with the spacer grid. These localized information, including flow, turbulence, and heat transfer characteristics, etc., can assist in the design and the improvement of rod bundles for nuclear power plants. In this paper, a three-dimensional (3D) CFD model with the Reynolds stresses turbulence model is proposed to simulate these characteristics within the rod bundle and subsequently to investigate the effects of different types of grid on the turbulent mixing and heat transfer enhancement. Two types of grid designs are used herein, including the standard grid and split-vane pair one, respectively. Based on the CFD simulations, the secondary flow can be reasonably captured in the rod bundle with the grid. The split-vane pair grid would enhance both the flow mixing and the heat transfer capability more than the standard grid does, as clearly shown in the simulation results. In addition, compared with the results of experiment and correlation, the present predicted result for the Nusselt (Nu) number distribution downstream the grid shows reasonable agreement for the standard grid design. However, there is discrepancy in the decay trend of Nu number between the prediction and measurement for the split-vane pair gird. This would be improved by adopting the finer mesh (y⁺ < 1) simulation and Low-Reynolds form turbulence model, which is our future research work.     

Computational Fluid Dynamics for nuclear applications: from CFD to multi-scale CMFD

New trends in computational methods for nuclear reactor thermal–hydraulics are discussed; traditionally, these have been based on the two-fluid model. Although CFD computations for single phase flows are commonplace, Computational Multi-Fluid Dynamics (CMFD) is still under development. One-fluid methods coupled with interface tracking techniques provide interesting opportunities and enlarge the scope of problems that can be solved. For certain problems, one may have to conduct “cascades” of computations at increasingly finer scales to resolve all issues. The case study of condensation of steam/air mixtures injected from a downward-facing vent into a pool of water and a proposed CMFD initiative to numerically model Critical Heat Flux (CHF) illustrate such cascades. For the venting problem, a variety of tools are used: a system code for system behaviour; an interface-tracking method (Volume of Fluid, VOF) to examine the behaviour of large bubbles; direct-contact condensation can be treated either by Direct Numerical Simulation (DNS) or by analytical methods.     

Very-Large Eddy Simulation (V-LES) of the flow across a tube bundle

A new turbulence modelling approach (Very-Large Eddy Simulation; V-LES) is developed and compared to conventional RANS and LES for a flow across a tube bundle. The method, which belongs to the large-scale simulation category, represents a good compromise between efficiency and precision, and may thus be used for industrial problems for which LES remains computationally expensive under high to very-high Reynolds number flow conditions. It can also be used for gas-liquid two-phase flows such as pressurized thermal shocks. The method is a sort of blend between U-RANS and LES, in that it resolves very large structures - way larger than the grid size - and models all subscale of turbulence using a two-equation model, by reference to RANS. The original model is shown here to share the same characteristics as the Detached Eddy Simulation (DES) approach, in that when the filter width is smaller than the wall-distance at which viscous effects are negligible (f_μ = 1), the fixed filter width is replaced by the wall distance. First conclusions to be drawn from its extension here is that the flow must be resolved in three-dimensions, under transient conditions, with refined grids. Sensitivity to various computational parameters has been addressed: grid, filter width, domain size, and inflow conditions. This modelling strategy is proved to provide the flow unsteadiness in three-dimensions, while saving computational cost compared to LES. The method is computationally efficient (it can be applied using an implicit solver which permits a higher CFL than with LES; typically 1 versus 0.1), and numerically robust. The computational cost decreases with increasing filter width, though at the expenses of the quality of the results.     

A CFD model for particle dispersion in turbulent boundary layer flows

In Lagrangian particle dispersion modeling, the assumption that turbulence is isotropic everywhere yields erroneous predictions of particle deposition rates on walls, even in simple geometries. In this investigation, the stochastic particle tracking model in Fluent 6.2 is modified to include a better treatment of particle–turbulence interactions close to walls where anisotropic effects are significant. The fluid rms velocities in the boundary layer are computed using fits of DNS data obtained in channel flow. The new model is tested against correlations for particle removal rates in turbulent pipe flow and 90° bends. Comparison with experimental data is much better than with the default model. The model is also assessed against data of particle removal in the human mouth–throat geometry where the flow is decidedly three-dimensional. Here, the agreement with the data is reasonable, especially in view of the fact that the DNS fits used are those of channel flows, for lack of better alternatives. The CFD Best Practice Guidelines are followed to a large extent, in particular by using multiple grid resolutions and at least second order discretization schemes.     

The Effect of Mixing-vane Arrangements in a Subchannel Turbulent Flow

Large eddy simulation (LES) of developed turbulent flows in a rod bundle was carried out for four spacer designs. The mixing-vanes attached at the spacer were inclined at 30° or 20° they were arranged to promote the swirling or convective flow. These arrangements are possible elements to compose an actual rod bundle. Our LES technique with a consistent higher-order immersed boundary method and a one-equation dynamic sub-grid scale model contributed to an efficient treatment of the complex wall configurations of rods and spacers. The computational results reasonably reproduced experimental results for the drag coefficient and the decay rate of swirling flow. The profiles of the axial velocities and the turbulence intensities indicated reasonable trend for the turbulent flow in the rod bundle. The effect of mixing-vane arrangement on the lateral flows was successfully clarified: the cross flow took the longer way on the rod surface than the swirling flow and then was more significantly influenced by momentum diffusion at the no-slip wall. Therefore, the largely inclined mixing-vanes promoted the cross flow only in the neighborhood of the spacer; the swirling flow inside a subchannel could reach farther downstream than the cross flow.     

The SABRE code for fuel rod cluster thermohydraulics

This paper describes the capabilities of the SABRE code for the calculation of single phase and two phase fluid flow and temperature in fuel pin bundles, discusses the methods used in the modelling and solution of the problem, and presents some results including comparison with experiments.The SABRE code permits calculation of steady-state or transient, single or two phase, flows and the geometrical options include general representation of grids, wire wraps, multiple blockages, bowed pins, etc. Transient flows may be calculated using either semi-implicit or fully implicit time solution methods and the temperature distributions within the fuel pins are determined as well as the velocity and temperature of the coolant. Two phase flows are calculated using a homogeneous boiling model, with the possibility of a specified slip between the two phases. General inlet boundary conditions are available (including pressure, velocity, total mass flow) and these may vary linearly with time; the outlet boundary condition is taken as constant pressure. The treatment of grids allows for irreversible head losses at entry and exit. The wire wrap model introduces a grid resistance tensor with its principal axes along and perpendicular to the wire, resulting in a very satisfactory modelling of inducement of swirl.The derivation and solution of the difference equations is discussed. Emphasis is given to the derivation of the spatial differences in triangular subchannel geometry, and the use of central, upwind or vector upwind schemes. The method of solution of the difference equations is described for both steady state and transient problems. Together with these topics we consider the problems involved in turbulence modelling and how it is implemented in SABRE. This includes supporting work with a fine scale curvilinear coordinate programme to provide turbulence source data. The problem of modelling boiling flows is discussed, with particular reference to the numerical problems caused by the rapid density change on boiling.The final part of the paper presents applications of the code to the analysis of blockage situations, the study of flow and power transients and analysis of natural circulation within clusters to demonstrate the scope of the code and compare with available experimental results. The comparisons include the calculation of a flow pressure drop characteristic of a boiling channel showing the Ledinegg instability, examples of overpower and flow rundown transients which lead to coolant boiling, and calculation of natural circulation within a rod cluster.     

Experiment and numerical simulation of bubbly two-phase flow across horizontal and inclined rod bundles

Experimental and numerical analyses were carried out on vertically upward air-water bubbly two-phase flow behavior in both horizontal and inclined rod bundles with either in-line or staggered array. The inclination angle of the rod bundle varied from 0 to 60° with respect to the horizontal. The measured phase distributions indicated non-uniform characteristics, particularly in the direction of the rod axis when the rods were inclined. The mechanisms for this non-uniform phase distribution is supposed to be due to: (1) Bubble segregation phenomenon which depends on the bubble size and shape; (2) bubble entrainment by the large scale secondary flow induced by the pressure gradient in the horizontal direction which crosses the rod bundle; (3) effects of bubble entrapment by vortices generated in the wake behind the rods which travel upward along the rod axis; and (4) effect of bubble entrainment by local flows sliding up along the front surface of the rods. The liquid velocity and turbulence distributions were also measured and discussed. In these speculations, the mechanisms for bubble bouncing at the curved rod surface and turbulence production induced by a bubble were discussed, based on visual observations. Finally, the bubble behaviors in vertically upward bubbly two-phase flow across horizontal rod bundle were analyzed based on a particle tracking method (one-way coupling). The predicted bubble trajectories clearly indicated the bubble entrapment by vortices in the wake region.     

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k—epsilon and the two-phase k—l model is evaluated.     

Linear and Nonlinear Development of the <Emphasis Type="Italic">m</Emphasis> = 0 Instability in Z-Pinch Equilibria with Axial Sheared Flows

The effect of sheared flows on the m = 0 instability development in a z-pinch is numerically investigated using a 2D magnetohydrodynamic (MHD) code. The behavior of both internal and free-boundary modes is studied by using two types of initial configurations: a diffuse Bennett equilibrium and a free-boundary parabolic equilibrium. It was found that sheared flows change the m = 0 development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. Full stability can be obtained for supersonic plasma flows, but a larger shear is needed to obtain stabilization of free-boundary modes.     

Dynamics of oscillatory plasma flows prior to the H-mode in the HL-2A tokamak

This paper discusses edge oscillatory plasma flows, geodesic acoustic mode(GAM) and limit cycle oscillations(LCOs), which have been measured by Doppler reflectometry prior to the high confinement mode(H-mode) in the HL-2A tokamak. The complex relations between the flows and background turbulence have been analyzed. It was observed that the GAM and LCO coexist,and these two flows and turbulence have strong nonlinear interactions during the intermediate confinement phase(I-phase). Dynamics of the shear flows and turbulence prior to the H-mode shows that the oscillatory flows quench the turbulence along with the increase of the mean E × B flow at the early stage of the I-phase, then the oscillatory flows are damped and the further increased mean flow takes over the role in turbulence suppression. The reduced turbulent transport results in the formation of a steep edge transport barrier. It suggests that the oscillatory flows can initiate the L–H transition through providing a positive feedback for the increase of the mean E × B flow strength.     

A two-phase level tracking method

Interfacial closure models in most two-fluid system codes for reactor safety are usually tied to the flow regime map through the mean void fraction in a computational cell. When a void fraction discontinuity exists in a computational volume, neither heat nor momentum exchange at the phase interface for this particular cell can be properly represented in finite-difference equations governing the fluid flow. Moreover, finite-difference methods with a fixed, Eulerian grid will inaccurately predict the cell-to-cell convection of mass, momentum and energy when the mean cell macroscopic variables are convected from the cell containing the void fraction front. The adequate modeling of two-phase mixture levels requires the knowledge of front position and void fractions above and below the front. In order to obtain such information, an efficient and simple tracking method was implemented in the TRAC-BWR code (released April 1984). We have tested this method with a simple problem involving a moving two-phase air/water mixture level. The results revealed inconsistencies in the behavior of velocities, pressures and interfacial friction, and some bounded numerical oscillations. Following our numerical experiment, we developed a systematic approach to improve the two-phase level tracking method. We present this approach and the results of implementation in the TRAC-BWR code.     

CFD analysis of flow field in a triangular rod bundle

The flow field was investigated in subchannels of VVER-440 pressurized water cooled reactors’ fuel assemblies (triangular lattice, P/D = 1.35). Impacts of the mesh resolution and turbulence model were studied in order to obtain guidelines for CFD calculations of VVER-440 rod bundles. Results were compared to measurement data published by Trupp and Azad in 1975. The study pointed out that RANS method with BSL Reynolds stress model using a sufficient fine grid can provide an accurate prediction for the turbulence quantities in this lattice. Applying the experiences of the sensitivity study thermal hydraulic processes were investigated in VVER-440 rod bundle sections. Based on the examinations the spacer grids have important effects on the cross flows, axial velocity and outlet temperature distribution of subchannels therefore they have to be modeled satisfactorily in CFD calculations.     

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.     

Large eddy simulation of rough and smooth liquid plunging jet processes

Large eddy simulation based on the Smagorinsky dynamic sub-grid scale model in combination with the multiphase volume of fluid (VOF) model, was used to simulate the flow of two turbulent plunging water jets. The jets were intended to simulate a weakly disturbed jet with low turbulence content and a highly disturbed jet with a profile almost fully-developed at the exit Reynolds number of 9000. The simulation captured successfully the previous experimentally-observed topological phenomena taking place during the transient impact and continuous-entrainment regime. It showed that surface instabilities in the free jet, due to its turbulence content have remarkable effect on submerged interfacial area, air volume, and air-entrainment rate. The simulation predicted an air entrainment rate within the range of semi-empirical correlations. The calculated mean velocity field exhibited almost identical trends for both. The combination of the LES-VOF models achieved a reasonably good level of agreement with experimental and empirical results.     

Modeling free surface flows relevant to a PTS scenario: Comparison between experimental data and three RANS based CFD-codes. Comments on the CFD-experiment integration and best practice guideline

This paper presents some results concerning a benchmark for stratified two-phase flows conducted in the frame of the European Platform for NUclear REactor SIMulations (NURESIM). This benchmark relies on the FZD slug flow experiment performed in the horizontal air/water channel (HAWAC). For this benchmark special experimental arrangements have been taken in order to be able to properly model the boundary and initial conditions with CFD. A picture sequence recorded with a high-speed camera was used as reference for comparison with the simulations. For this benchmark, three different codes have been tried out. CFX was used with a turbulent two-fluid model in which a special turbulence damping function was implemented in the specific dissipation rate of the turbulent kinetic energy. This allowed a good qualitative representation of the slug dynamics, even though quantitative comparison were less successful because of difficulties in modeling the inlet instabilities. The VOF approach in its laminar and turbulent form was also tried out through the FLUENT code and was found to be inappropriate for those conditions due to the high velocity slip between phases. Moreover, NEPTUNE_CFD was tested with a newly implemented model allowing free surface location and the computation of momentum transfer across this interface. This Large Interface Model (LIM) is able to detect “stratified cells” from the other and so that appropriate closure law can be applied. With this model, the results agreed well with experimental data qualitatively and quantitatively. This benchmark experience also allowed us to draw basis recommendations for a best practice guideline in numerical simulation related to free surface flows in nuclear thermal hydraulics.     

CFD and DNS methodologies development for fuel bundle simulations

Development and application of computational fluid dynamics (CFD) and direct numerical simulation (DNS) approaches to the reproduction of coolant flow inside nuclear fuel bundles are discussed, focusing on the advantages and limitations of the different methodologies and on their synergetic potential. High Reynolds number flow cases are analyzed with the adoption of an improved anisotropic turbulence model, which includes a non-linear stress strain correlation and an enhanced near wall treatment. The capability of the model to predict the coolant flow distribution inside rod bundles is shown and discussed on the base of comparison with experimental data for a variety of geometrical and Reynolds number conditions. In particular predictions for wall shear stresses, velocity, and secondary flow distributions are shown. Moreover, DNS computations are performed adopting an algorithm based on the finite difference method, extended to boundary fitted coordinate systems in order to efficiently concentrate grids near the distorted wall boundaries. The validity and significance of the results is discussed underlying the importance of the insights into the turbulence structure. The calculations are further extended to higher Reynolds numbers, which cannot in general be treated with DNS approach, renouncing to the estimation of the higher-order moments, but limited to the evaluation of the averaged velocity profiles, turbulence intensities and Reynolds stresses.