Turbulent Buoyant Flows Research Articles

High-Fidelity Velocity and Concentration Measurements of Turbulent Buoyant Jets

Accurate models of turbulent buoyant flows are essential for the design of the cooling circuit of nuclear reactors and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We analyze experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous particle image velocimetry and laser-induced fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The refractive index matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy-driven flows (e.g. natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in a uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as a basis for the development of a new model that captures turbulent mixing.

Large-eddy-simulation of turbulent buoyant flow and conjugate heat transfer in a cubic cavity with fin ribbed radiators

Turbulent convective flow in a cubic cavity is a fundamental model observed in various processes that appeared in environmental and industrial applications. The turbulent fluctuations in the flow field, fluid-solid interaction/coupling, and the transient nature of the problem make it challenging to establish numerical modeling. The turbulent flow and convective heat transfer in a cubic cavity fixed with three fins are studied here. The numerical solutions are obtained through large-eddy simulation with Smagorinsky subgrid-scale model combined with conjugate heat transfer to incorporate temperature distribution in solid fins. The upper and lower walls of the enclosure are differently heated, while the lateral walls are adiabatic, and equally spaced conductive fins are located at the bottom surface. The solutions are initially compared with the numerical and experimental results for validation purposes. Successively, the model is applied to explore the impact of a material (copper) that makes up the horizontal wall on the flow field. We found that the heat transfer essentially alters the turbulent field, and the flow field becomes less homogeneous along the vertical direction. A number of streaky and coherent turbulent structures are found with varying magnitudes. The Q-criterion, second-invariant of the velocity-gradient tensor, predicted that strong vortices occur near the fins and in the surrounding regions of the cavity. Moreover, the energy (entropy) spectral, which plays a crucial role in engineering applications and turbulent theory, is also presented, showing the contribution of each frequency component to the velocity (temperature) variance at a given point. The velocity and temperature fields are found to be anti-symmetric, except close to the front and back walls. The major cause for this is the conducting bottom and fins, which produces thermal stratification in the cavity. The conducting bottom induces the locally unstable thermal stratification in the vicinity of the wall, which intensifies the turbulence as the flow advances toward the temperature-controlled boundaries. Further, the turbulent exchange in the central region is more responsible for the heat transfer than convection that occurs due to the differentially heated walls.

Large-eddy simulation of turbulent heat transfer in negative buoyant fountain

This paper presents the results of large-eddy simulation (LES) of a downward wall jet that encounters an upward flow in a vertical rectangular channel, named negative buoyant fountain (NBF). The downward jet fluid has higher temperature than the opposing upward stream so that the influence of the buoyancy force on the physics of the mixing process can be investigated. Two subgrid-scale models available in the OpenFOAM platform, i.e. the dynamic k-equation model (DKM) and the wall-adapting local eddy-viscosity (WALE) model, are used for cross-comparison. The numerical results of the time-averaged and fluctuating velocity fields agree satisfactorily with the experimental data. The LES results form an accurate, high-resolution, three-dimensional database of buoyant turbulent mixing, which has expanded the sparse flow field measurements provided by the experiment, hence the numerical database could be used to validate the Reynolds-averaged Navier–Stokes (RANS) simulation method and to contribute to the turbulence modeling. In particular, the statistics of turbulent heat flux have been analyzed and various turbulent heat flux models have been a priori tested based on the LES numerical database. Such information could be useful for RANS simulation guidelines or for deriving anisotropic turbulent heat flux models applicable for turbulent buoyant flows sharing the similar principal flow structures in complex geometries.

Assessment of turbulent heat flux models for URANS simulations of turbulent buoyant flows in ROCOM tests

Turbulent mixing in buoyant flows is an essential mechanism involved in many scenarios related to nuclear safety in nuclear power plants. Comprehensive understanding and accurate predictions of turbulent buoyant flows in the reactor are of crucial importance, due to the function of mitigating the potential detrimental consequences during postulated accidents. The present study uses URANS methodology to investigate the buoyancy-influenced flows in the reactor pressure vessel under the main steam line break accident scenarios. With a particular focus on the influence of turbulent heat flux closure models, various combinations of two turbulence models and three turbulent heat flux models are utilized for the numerical simulations of three ROCOM tests which have different characteristic features in terms of the flow rate and fluid density difference between loops. The simulation results are compared with experimental measurements of the so-called mixing scalar in the downcomer and at the core inlet. The study shows that the anisotropic turbulent heat flux models are able to improve the accuracy of the predictions under conditions of strong buoyancy whilst in the weak buoyancy case, a major role is played by the selected turbulence models with essentially a negligible influence of the turbulent heat flux closure models.

Analysis of adaptive mesh refinement in a turbulent buoyant helium plume

AbstractThe study evaluates OpenFOAM's adaptive mesh refinement (AMR) capabilities and accuracy when applied to numerical simulations of turbulent buoyant flows. To this purpose, large eddy simulations of Sandia's turbulent helium plume test case are considered, a scenario with similar characteristics (in terms of air entrainment and vortex shedding) to those encountered in large‐scale fires. Comparison is made of the relative accuracy (in terms of both first and second order statistics), the predicted puffing frequencies and the computing times of numerical simulations using AMR and static meshes. Additionally, a sensitivity study on different AMR parameters is conducted and an evaluation of the performance of the dynamic Smagorinsky model when combined with AMR is made. Overall, the predictions of AMR are very satisfactory, in terms of both accuracy and computing times, compared to the use of static meshes of different sizes. Nevertheless, it is observed that a careful choice of a static mesh can result in equally accurate predictions with comparable, or even smaller, computing times than AMR for the case at hand. Additionally, the use of AMR slightly modified the entrainment characteristics in the near‐field region of the plume and (significantly) altered some of the, dynamically determined, turbulence model parameters.

Explicit Algebraic Stress Model for Three-Dimensional Turbulent Buoyant Flows Derived Using Tensor Representation

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.

Large-Eddy-Simulation of Turbulent Buoyant Flow and Conjugate Heat Transfer in a Cubic Cavity with Fin Ribbed Radiators

Large-Eddy-Simulation of Turbulent Buoyant Flow and Conjugate Heat Transfer in a Cubic Cavity with Fin Ribbed Radiators

Velocity Field and Scalar Field Measurements of Turbulent Buoyant Round Jets in a Two-Layer Stratified Environment

Results reported in the literature have shown that the turbulence models currently implemented in computational fluid dynamics (CFD) commercial codes (e.g., ANSYS-CFX, STAR-CCM+, and FLUENT) have a tendency to overestimate thermal stratification and underestimate turbulent mixing when buoyancy effects become dominant with respect to momentum effects. Also, standard large eddy simulation models cannot fully capture the behavior of jets interacting with stratified environments because the assumption of turbulence isotropy of the smaller scales breaks down. Because of light diffraction and image distortion, it is challenging to apply nonintrusive optical flow measurements, like particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF), to get experimental data for CFD validations when there are density variances involved in the flow. However, a refractive index matching (RIM) technique that has been recently developed in our Experimental and Computational Multiphase Flow Laboratory allows us to perform high-resolution measurements of velocity fields and scalar fields for turbulent buoyant jet flow in the presence of density differences as high as 8.6%. To form a fully turbulent round free jet, an experimental facility was designed with a jet nozzle diameter of 2 mm, located at the bottom of a cubic tank with 30-cm side length. The jet flow is established by a servo-engine-driven piston to eliminate possible fluctuations introduced by the motor. A high-fidelity synchronized PIV/PLIF system was utilized in conjunction with RIM to measure the velocity and concentration fields in the self-similar regions of a jet flow with a density difference of 3.16% for aqueous solutions. With Reynolds numbers of 4000 and 10 000, the jet impinging with a two-layer stably stratified environment is compared to the positively buoyant jet with lighter fluid injected into denser surroundings. Detailed quantifications of the measurement uncertainties are also carried out. The experimental results are presented in terms of turbulent statistics and the analysis of jet penetration depths.

On the use of dynamic turbulence modelling in fire applications

In an attempt to make a step forward towards predictive fire modelling, the application of turbulence modelling approaches, calculating the sub-grid scale viscosity, kinetic energy, turbulent Prandtl and Schmidt numbers based on a dynamic procedure, has been tested on a wide range of pool fire scenarios (i.e., MaCFP workshop test cases). Through the use of Large Eddy Simulations, it is investigated whether the applied modelling approaches can accurately predict the pool fire dynamics on different grid sizes and result in improved predictions compared to models using constant parameters. Additionally, it is evaluated whether the theoretical constants related to turbulence modelling, derived from isotropic decaying turbulence scenarios, are justified in turbulent buoyant flows.

A Review of the CFD Modeling Progress Triggered by ISP-47 on Containment Thermal Hydraulics

The Organisation for Economic Co-operation and Development (OECD)/Nuclear Energy Agency International Standard Problem 47 (ISP-47) was aimed at assessing the predictive capabilities of computational fluid dynamics (CFD) and lumped-parameter codes regarding hydrogen mixing under representative thermal-hydraulic conditions of a loss-of-coolant-accident. The benchmark consisted of two systematic steps. The first step was a fundamental model assessment based on quasi-steady-state separate-effects tests in the French TOSQAN facility (7 m3, IRSN, Saclay) and MISTRA facility (100 m3, CEA, Saclay) regarding steam condensation, buoyant turbulent flows, and mixed atmospheric conditions. The second step was based on a more realistic experimental transient in the multicompartmented German Thermal-hydraulics, Hydrogen, Aerosols and Iodine (THAI) facility (60 m3, Becker Technologies, Eschborn). At that time, the blind and open analysis revealed that CFD codes needed further improvement regarding modeling of turbulence in buoyant flows, steam condensation, temperature and species concentration, and stratification buildup as well as their dissolution. This result triggered a comprehensive experimental and analytical effort, e.g., within the German national THAI, the OECD-THAI, and the OECD-SETH-1 and OECD-SETH-2 projects. Now, 10 years later, this paper aims to benchmark the state-of-the-art containment CFD model, developed at Forschungszentrum Juelich and RWTH Aachen University, and to highlight the progress made and the remaining open issues.

A new numerical scheme for using the two-energy equation model for turbulent buoyant flow in a composite enclosure

Walls made of layers of different materials and sizes, including empty spaces, can be used for modulating energy transfer across such composite structures. By changing layer thicknesses and by using distinct porous and solid materials, the overall cavity Nusselt number can be modified in regard to its traditional behavior found in cavities fully fitted with porous materials or with no obstructions. Numerical simulations of transport equations for such composite systems poses an additional difficulty if one considers the different layers, appropriate interface conditions between them and the need to use one single computational domain for simplicity. Motivated by such engineering application and numerical need, this work presents the analysis about natural convection in a two-dimensional horizontal composite square cavity, using laminar and k-ε turbulence models. Both the one energy equation (1EEM) and two energy equation (2EEM) closures are applied. The composite square cavity is equally divided and formed by three distinct regions. Non-dimensional temperatures are proposed such that the entire computational domain is handled in a single numerical scheme. It was found that the fluid begins to permeate the porous medium for values of Ra greater than 106. Nusselt number values show that for the range of Ra analyzed there are no significant variation between the laminar/turbulent and 1EEM/2EEM model solution. When comparing the effects of Ra, thermal conductivity ratio and Da on Nu, results indicate that has a greater influence in controlling heat transfer rates across the composite cavity.

Effect of heat source aspect ratio on turbulent thermal stratification in a naturally ventilated enclosure

The turbulent buoyant flows generated from a heat source block in a naturally ventilated cubical enclosure with vertical and horizontal openings are numerically investigated. Turbulence is modeled with large eddy simulation (LES) and the filtered governing equations are solved using an in-house code based on finite difference method (FDM). The time dependent flow characteristics are analyzed by varying the heat source aspect ratio (ϕ) in the range 0.25 ≤ϕ≤ 4.0 and the Grashof numbers (Gr) are varied between 107≤ Gr ≤ 1011. A chaotic flow behavior is observed inside the enclosure and the bidirectional exchange across the openings increases linearly with Grashof number. The results indicate that the heat source aspect ratio significantly impacts the thermal buoyancy force with the formation of multi-recirculating vortex cells inside the enclosure. A significant enhancement in the heat transfer rate and mass flow rates are observed after increasing the heat source aspect ratio. The results also indicate that the flow instabilities that develop across the vertical opening exceeded those across the horizontal opening. The present numerical results are in good agreement with the benchmark results reported in literature.

Application of a parallel solver to the LES modelling of turbulent buoyant flows with heat transfer

An existing fully implicit, non-dissipative direct numerical simulation (DNS) algorithm is reformulated to utilise the sub-grid scale (SGS) models in large eddy simulation (LES). The Favre-filtered equations with low-Mach number scaling are derived. The wall-adapting local eddy-viscosity (WALE) is used as SGS model. A fully parallel, finite volume solver is developed based on the resulting LES algorithm using PETSc library and applied to buoyancy- and thermally-driven transitional/turbulent flows in Rayleigh-Taylor instability and turbulent Rayleigh-Benard convection. Results verify that the proposed low-Mach number LES approach, which is physically more accurate than pure incompressible methods for flows with variable properties, perfectly captures the evolution and complex physics of turbulent buoyant flows with or without heat transfer by taking the effects of density and viscosity changes into account without the Oberbeck-boussinesq (OB) assumption even at large temperature differences with uniform accuracy and efficiency.

Application of a Parallel Solver to the LES Modeling of Turbulent Buoyant Flows with Heat Transfer

An existing fully implicit, non-dissipative direct numerical simulation (DNS) algorithm is reformulated to utilise the sub-grid scale (SGS) models in large eddy simulation (LES). The Favre-filtered equations with low-Mach number scaling are derived. The wall-adapting local eddy-viscosity (WALE) is used as SGS model. A fully parallel, finite volume solver is developed based on the resulting LES algorithm using PETSc library and applied to buoyancy- and thermally-driven transitional/turbulent flows in Rayleigh-Taylor instability and turbulent Rayleigh-Bénard convection. Results verify that the proposed low-Mach number LES approach, which is physically more accurate than pure incompressible methods for flows with variable properties, perfectly captures the evolution and complex physics of turbulent buoyant flows with or without heat transfer by taking the effects of density and viscosity changes into account without the Oberbeck-Boussinesq (OB) assumption even at large temperature differences with uniform accuracy and efficiency.

Large eddy simulation of turbulent buoyant flow in a confined cavity with conjugate heat transfer

Turbulent natural convection in enclosure is a paradigmatic case for wide class of processes of great interest for industrial and environmental problems. The solid-fluid thermal interaction, the anisotropy of the turbulence intensity in the flow field along with the transient nature of heat transfer processes, pose challenges regarding the numerical modeling. The case of a square cavity with differently heated vertical walls and two horizontal conductive plates is studied at Ra = 1.58 × 109. The study is carried out numerically, using large-eddy simulation together with a dynamic Lagrangian turbulence model and a conjugate heat transfer method to take into account heat transfer at the solid surfaces. First, validation is carried out against the literature experimental and numerical data. The results of validation tests evidence the limitations of using the adiabatic conditions as a model for reproducing an insulator. In fact, the adiabatic condition represents the asymptotic behavior which is often difficult to reach in real conditions. Successively, the model is used to investigate the effect on the flow field of different materials composing the horizontal walls. Initial conditions representative of physical experiment are used. In order to reduce the computational time required for a simulation with insulating materials at the walls, a four-step temperature advancement strategy is proposed, based on the artificial reduction-first and recover-later of the specific heat coefficient Cp of the materials at different stages of the simulation. The conductivity of the solid media is found to influence the flow configuration since heat transfer at the solid walls substantially modifies the turbulent field and makes the flow field less homogeneous along the horizontal direction.

Non-Boussinesq approach for turbulent buoyant flows in enclosure with horizontal vent and forced inlet port

The effects of forced ambient velocity on thermal plume behavior in a ceiling vented square enclosure are numerically investigated. Turbulence is modeled by unsteady Favre-averaged Navier–Stokes (UFANS) equation with Lam Bremhorst low Reynolds number k−ɛ turbulence model. A non-Boussinesq variable density approach is used to model the density variations. Simplified Marker and Cell (SMAC) algorithm is used to solve the governing equations on collocated grid with high accuracy compact finite difference schemes. The pressure Poisson equation is solved by bi-conjugate gradient algorithm and time integration is performed with four stage Runge–Kutta method (Rk-4). The results are presented for Grashof number Gr = 1011 and 1012 and Gay-Lussac number Ga = 0.2 and 2. The present model is valid when buoyancy effects are significant in comparison with forced convection effects. The heat transfer characteristics are analyzed by varying forced inlet velocity, inlet port size and inlet port location. The assisting flow enhances plume discharge rate and increases convective heat loss from cavity. The opposing flow weakens thermal buoyancy and minimizes convective heat loss from cavity. The present mathematical model and numerical method are in good agreement with the existing results available in the literature.

A new framework for simulating forced homogeneous buoyant turbulent flows

This work proposes a new simulation methodology to study variable density turbulent buoyant flows. The mathematical framework, referred to as homogeneous buoyant turbulence, relies on a triply periodic domain and incorporates numerical forcing methods commonly used in simulation studies of homogeneous, isotropic flows. In order to separate the effects due to buoyancy from those due to large-scale gradients, the linear scalar forcing technique is used to maintain the scalar variance at a constant value. Two sources of kinetic energy production are considered in the momentum equation, namely shear via an isotropic forcing term and buoyancy via the gravity term. The simulation framework is designed such that the four dimensionless parameters of importance in buoyant mixing, namely the Reynolds, Richardson, Atwood, and Schmidt numbers, can be independently varied and controlled. The framework is used to interrogate fully non-buoyant, fully buoyant, and partially buoyant turbulent flows. The results show that the statistics of the scalar fields (mixture fraction and density) are not influenced by the energy production mechanism (shear vs. buoyancy). On the other hand, the velocity field exhibits anisotropy, namely a larger variance in the direction of gravity which is associated with a statistical dependence of the velocity component on the local fluid density.

The effect of density pulsations in the field of a buoyancy force on heat transfer and turbulent fluid flow in a vertical pipe at supercritical pressures

Regimes of deteriorated (with peaks of the wall temperature) heat transfer are calculated for a turbulent buoyant flow and down flow of carbon dioxide under supercritical pressure in a vertical pipe, as well as in a horizontal round pipe. The calculations involve a system of motion, continuity, and energy equations written in the narrow channel approximation. These equations are solved by the finite difference method. A model of turbulent stress and turbulent thermal flow takes into account the influence of density pulsations in the field of the buoyancy force and in the presence of thermal acceleration of the flow. Regimes with a small influence of the buoyancy force are considered. The calculation results for the variation in the wall temperature and resistance coefficients along the pipe agree well with the experimental data. An explanation for the appearance of a peak in the wall temperature distribution along the pipe in the region where the fluid temperature is close to the pseudocritical temperature is presented.

OpenFOAM applied to the CFD simulation of turbulent buoyant atmospheric flows and pollutant dispersion inside large open pit mines under intense insolation

The particular conditions of air circulation inside large open pit mines under intense insolation, dominated by mechanical and buoyant effects, are crucial when studying the dispersion of pollutants inside and outside the pit. Considering this, we study this problem using CFD tools able to include the complex geometry characterizing it and the different processes affecting circulation: flow interaction with obstacles, buoyancy, stratification and turbulence. We performed simulations using a previously developed OpenFOAM solver, focusing in the particular case of Chuquicamata, a large open pit mine (∼1km deep) located in northern Chile. Both idealized and real topographies were used. Given the importance of turbulence in this type of large-scale flows we have used LES to incorporate it in the calculation, using a DES approach to solve the flow near walls.The results from the idealized cases support the idea that buoyant currents foster the exit of particles from the pit and increase the turbulence inside its atmosphere, modifying the purely mechanical recirculatory flow inside the cavity. Differences in the air circulation and dispersion of particles between idealized and non-idealized cases are reported. In particular, there are changes in the intensity and location of the recirculation inside the pit due to variations in the aspect ratio (length/depth) of the cavity along the axis perpendicular to the main flow. Also, the topography surrounding the mine affects the main flow that sweeps the cavity, channeling it along the main axis of the pit and forcing it to enter the cavity through the lower level of the top edge. As a consequence, the patterns of pollutant transport observed in the idealized cases, dominated by near-wall upward currents, are different than those observed in the cases with complex topography, where the dispersion is dominated by internal buoyant upward currents. Anyhow, whether by internal or near wall upward currents, in all buoyant cases considered a large percentage of the particles injected inside the pit leaves the cavity.Further experiments studying the effect of 3D aspect ratio over the mechanically forced internal flow are needed to fully understand the effect of the internal geometry of the pit over the flow.

Simple lattice Boltzmann approach for turbulent buoyant flow simulation

In the present work, a simple large eddy simulation (LES)-based lattice Boltzmann model (LBM) is developed for thermal turbulence research. This model is validated by some benchmark tests. The numerical results demonstrate the good performance of the present model for turbulent buoyant flow simulation.