Flows In Complex Geometries Research Articles

Eulerian-Eulerian large eddy simulation of two-phase dilute bubbly flows

An efficient mathematical model is presented for conducting large eddy simulation (LES) of turbulent bubbly flows at low gas hold-ups. The mathematical model is based on the filtered multi-fluid equations derived by application of the component-weighted volume-averaging process of each phase. A two-fluid model is applied to the filtered set of equations, yielding a more computationally tractable set of filtered equations. The filtered equations are formulated in generalized curvilinear coordinates to simulate turbulent gas-liquid bubbly flows in complex geometries. The Germano model is used to account for sub-grid turbulent stresses. The gas and liquid momentum equations are discretized with the hybrid staggered/non-staggered method. The performance of the developed mathematical model is demonstrated by simulating the benchmark test case of a turbulent gas-liquid bubbly flow in a rectangular bubble column. The accuracy of the proposed method is assessed via comparison with the experimental data and other numerical results in the literature.

Numerical simulation of a turbulent Lead Bismuth Eutectic flow inside a 19 pin nuclear reactor bundle with a four logarithmic parameter turbulence model

Computational Fluid Dynamic allows scientists and engineers to investigate fluid flow in complex geometries and evaluate heat transfer between a solid body and a fluid. In the present paper we study the heat transfer of a Lead Bismuth Eutectic (LBE) turbulent flow in a bare 19 pin nuclear reactor bundle. When dealing with low Prandtl number fluids, like LBE for which Pr = 0.025, proper turbulence models are needed to improve the prediction of heat transfer. We use here a four logarithmic parameter turbulence model in order to calculate Reynolds stresses and turbulent heat flux. In particular, an equation for temperature fluctuations and one for their dissipation are solved. These variables are used to model thermal characteristic time scales. The results are reported for different values of the Peclet number and a fixed value of the pitch to diameter ratio. The obtained values of the Nusselt number are compared with experimental correlations, that can be found in literature, and with the ones obtained using a Simple Eddy Diffusivity model, where the eddy thermal diffusivity is calculated as proportional to eddy viscosity through a modeled turbulent Prandtl number.

Lattice Boltzmann Method Simulations of High Reynolds Number Flows Past Porous Obstacles

Lattice Boltzmann Method (LBM) simulations for turbulent flows over fractal and non-fractal obstacles are presented. The wake hydrodynamics are compared and discussed in terms of flow relaxation, Strouhal numbers and wake length for different Reynolds numbers. Three obstacle topologies are studied, Solid (SS), Porous Regular (PR) and Porous Fractal (FR). In particular, we observe that the oscillation present in the case of the solid square can be annihilated or only pushed downstream depending on the topology of the porous obstacle. The LBM is implemented over a range of four Reynolds numbers from 12,352 to 49,410. The suitability of LBM for these high Reynolds number cases is studied. Its results are compared to available experimental data and published literature. Compelling agreements between all three tested obstacles show a significant validation of LBM as a tool to investigate high Reynolds number flows in complex geometries. This is particularly important as the LBM method is much less time consuming than a classical Navier–Stokes equation-based computing method and high Reynolds numbers need to be achieved with enough details (i.e., resolution) to predict for example canopy flows.

Analysis of local wear variables for high-precision erosion modelling in complex geometries

Particle-laden flows in complex geometries often require a more robust performance from erosion models in order to obtain accurate prediction of wear. Most erosion models developed over the last six decades have not been able to achieve the desired accuracy needed for these complex systems, primarily because they are based on single particle-wear material interactions, experimental correlations, and often do not capture the full physics of the erosion process. Recently, the capability of computational fluid dynamics (CFD) in resolving fluid-particle-wall interactions more realistically has been shown to have great potential in the development of high-performance erosion models, especially when combined with experimental data analysis. This paper adopts this combined CFD-experimental methodology to improve the prediction performance of some selected erosion models. Experimental data for the wear of an elbow in gas-solid flow from a previous study was combined with new CFD predictions of local wear variables such as particle impact angle, particle impact velocity, and particle mass rate. A geometric function is developed which can be combined with some common erosion models to significantly improve their wear prediction accuracy for gas-solid elbows. Also, the effects of target material surface roughness and particle rotation on local wear variables are investigated numerically. The simulation results reveal an increased dispersion of particles and a more even distribution of local wear variables at the elbow. In conclusion, this paper presents a method for improving performance of erosion models, and potentially a method to translate wear data between complex geometries.

Bernaise: A Flexible Framework for Simulating Two-Phase Electrohydrodynamic Flows in Complex Domains

Bernaise (Binary ElectRohydrodyNAmIc SolvEr) is a flexible high-level finite element solver of two-phase electrohydrodynamic flow in complex geometries. Two-phase flow with electrolytes is relevant across a broad range of systems and scales, from 'lab-on-a-chip' devices for medical diagnostics to enhanced oil recovery at the reservoir scale. For the strongly coupled multi-physics problem, we employ a recently developed thermodynamically consistent model which combines a generalized Nernst-Planck equation for ion transport, the Poisson equation for electrostatics, the Cahn-Hilliard equation for the phase field (describing the interface separating the phases), and the Navier-Stokes equations for fluid flow. As an efficient alternative to solving the coupled system of partial differential equations in a monolithic manner, we present a linear, decoupled numerical scheme which sequentially solves the three sets of equations. The scheme is validated by comparison to limiting cases where analytical solutions are available, benchmark cases, and by the method of manufactured solution. The solver operates on unstructured meshes and is therefore well suited to handle arbitrarily shaped domains and problem set-ups where, e.g., very different resolutions are required in different parts of the domain. Bernaise is implemented in Python via the FEniCS framework, which effectively utilizes MPI and domain decomposition, and should therefore be suitable for large-scale/high-performance computing. Further, new solvers and problem set-ups can be specified and added with ease to the Bernaise framework by experienced Python users.

A Lagrangian-Eulerian framework for simulation of transient viscoelastic fluid flow

A novel framework for simulation of transient viscoelastic fluid flow is proposed. The viscoelastic stresses are calculated at Lagrangian nodes which are distributed in the computational domain and convected by the fluid. The coupling between the constitutive equation and the fluid momentum equations is established through robust interpolation with radial basis functions.The framework is implemented in a finite volume based flow solver that combines an octree background grid with immersed boundary techniques. Since the distribution of the Lagrangian node set is performed entirely based on spatial information from the fluid solver, the ability to simulate flows in complex geometries is therefore as general as for the fluid solver itself.In the Lagrangian formulation the discretization of the convective terms in the constitutive equations is avoided. No re-formulation of the constitutive equation is required for stable solutions. Numerical experiments are performed of UCM and Oldroyd-B fluids in a channel flow and of a four mode PTT fluid in a confined cylinder flow. The computed flow quantities consistently converge and agree excellently with analytical and numerical data for fully developed and transient flow.

The shallow water equations and their application to realistic cases

The numerical modelling of 2D shallow flows in complex geometries involving transient flow and movable boundaries has been a challenge for researchers in recent years. There is a wide range of physical situations of environmental interest, such as flow in open channels and rivers, tsunami and flood modelling, that can be mathematically represented by first-order non-linear systems of partial differential equations, whose derivation involves an assumption of the shallow water type. Shallow water models may include more sophisticated terms when applied to cases of not pure water floods, such as mud/debris floods, produced by landslides. Mud/debris floods are unsteady flow phenomena in which the flow changes rapidly, and the properties of the moving fluid mixture include stop and go mechanisms. The present work reports on a numerical model able to solve the 2D shallow water equations even including bed load transport over erodible bed in realistic situations involving transient flow and movable flow boundaries. The novelty is that it offers accurate and stable results in realistic problems since an appropriate discretization of the governing equations is performed. Furthermore, the present work is focused on the importance of the computational cost. Usually, the main drawback is the high computational effort required for obtaining accurate numerical solutions due to the high number of cells involved in realistic cases. However, the proposed model is able to reduce computer times by orders of magnitude making 2D applications competitive and practical for operational flood prediction. Moreover our results show that high performance code development can take advantage of general purpose and inexpensive Graphical Processing Units, allowing to run almost 100 times faster than old generation codes in some cases.

Numerical simulation to investigate the induced buoyant flow characteristics caused by intensive heat in complex curvilinear geometries

AbstractThe buoyancy‐induced turbulent flows in complex geometries with internal heat source have important application in enclosure fire dynamics, for example, smoke movement in the situation of fire in tunnels. The majority of computational works studying the fire‐induced hot air movement in such cases use a Cartesian coordinate system. Hence, to simulate curved geometries, the Cartesian grid should be refined so that it comparatively matches the geometry. In the present work, a three‐dimensional numerical method using nonorthogonal curvilinear coordinate system was developed. Numerical simulations were performed to study the flow structures and the heat transfer characteristics of fire‐induced buoyant flow and the effects of using curvilinear coordinates on the result's accuracy and the computational cost. Numerical results were compared with the available experimental data and the results obtained by fire dynamics simulator (FDS) software. The results of the present method showed better agreement with the experimental results when compared with the FDS results.

Coupled level-set and immersed-boundary method for simulation of filling in a complex geometry based mold

A coupled level-set and immersed-boundary-method (CLSIBM) is proposed for simulation of liquid and gas phase flow during filling of a complex geometry based mold using a modified cut-cell technique. The CLSIBM uses Cartesian computational domain, with two level-set functions: for liquid-metal and gas interface and ϕf,s for liquid-metal/gas and solid (mold box) interface. The cut-cell based immersed boundary method enable us to handle any internal two-phase flow in complex geometry using a Cartesian grid. Numerical results are presented for filling in four different tanks/molds, demonstrating the robustness of the proposed method during mold filling in complex geometry mold box.

Full-scale smoke tests in a three-storey residential building

This work presents summarized results based on three real-scale tests carried out on a three-story building. The main purpose of these tests is to get some information on how the smoke flows in a building with floors connected with a staircase in order to assess the ability of numerical codes to simulate the smoke flow in complex geometries with multiple rooms.During these tests, a well-controlled source fire was used and measurements of temperatures and velocities were made all over the different stairs and rooms into the building. The heat release rate in the fire room was deduced from the measured mass loss rate and gas analysis. A comparison between numerical results using the two zones model CFAST [5] and the experimental results was also made.The current work will provide a large database to evaluate software programs used in fire safety engineering.

Nanofluid Flow in Complex Geometries—A Review

Nanofluid Flow in Complex Geometries—A Review

Scaling law for slip flow of gases in nanoporous media from nanofluidics, rocks, and pore-scale simulations

In unconventional reservoirs, as the effective pore size becomes close to the mean free path of gas molecules, gas transport in porous media begins to deviate from Darcy’s law. The objective of this study is to explore the similarities of gas flows in nanochannels and core samples as well as those simulated by direct simulation BGK (DSBGK), a particle-based method that solves the Bhatnagar-Gross-Krook (BGK) equation.Due to difficulties in fabrication and experimentation, previous study on gas flow experiments in nanochannels is very limited. In this work, steady-state gas flow was measured in reactive-ion etched nanochannels with a controlled channel size on a sillicon wafer. A core-based permeability measurement apparatus was used to perform steady-state gas flow measurements on carbonate and shale samples. Klinkenberg permeability was obtained under varying pore pressures but constant temperature and effective stress. Methane was used in nanofluidic and rock experiments, making them directly comparable. Results from both experiments were then compared to gas flow simulations by DSBGK method carried out on several independently constructed geometry models. DSBGK uses hundreds of millions of simulated molecules to approximate gas flow inside the pore space. The intermolecular collisions are handled by directly integrating the BGK equation along each molecules trajectory, rather than through a sampling scheme like that in the direct simulation Monte-Carlo (DSMC) method. Consequently, the stochastic noise is significantly reduced, and simulation of nano-scale gas flows in complex geometries becomes computationally affordable.The slippage factors obtained from these independent studies varied across three orders of magnitude, yet they all appear to collapse on a single scaling relation where the slippage factor in the slip flow regime is inversely proportional to the square root of intrinsic permeability over porosity. Our correlation could also fit the data in the literature, which were often obtained using nitrogen, after correcting for temperature and gas properties. This study contributes to rock characterization, well testing analysis as well as the understanding of rarefied gas transport in porous media.

Numerical investigation on the phase change process of different shaped macro encapsulated PCM

Latent heat energy storage using macro encapsulated phase change material is an emerging technique for thermal energy storage applica- tions. The main aim of the present investigation is to investigate the melting process of phase change material filled in different shaped configurations. The selected different cavities are square, circular and triangular. A mathematical model based on convection dominated melting is required to be developed, especially in view of the complex flow geometries encountered in such problems. Thus, an attempt has been made to develop a model using ANSYS Fluent 16.2 to investigate the heat transfer rate and solid-liquid interface visualization of PCM filled in different shapes of cavity. It is found that triangular shaped macro encapsulated PCM melts faster than square and circu- lar shaped encapsulated PCM.

Nodal integral method for convection-diffusion transport using linear and higher order quadrilateral elements

Generic nodal integral method (NIM) based scheme, utilizing nine noded 2D quadratic elements along with four noded 2D linear elements, is developed to solve the fluid flow and heat transfer equations in complex geometries. Non-linear (quadratic) quadrilateral elements are used for discretization of boundary region and linear quadrilateral elements are used for interior region. Lagrange interpolation functions are used to map both type of elements to corresponding square computational elements. The scheme for Neumann and mixed type of boundary conditions are also developed for quadratic elements. C1 type continuity condition is imposed at the interfaces of adjacent elements. Numerical results are compared with analytical solutions for diffusion and advection-diffusion equations. Results for Navier–Stokes equations in curved domain are compared with previously reported experimental as well as numerical results. The comparative study has also been done between presently developed scheme using quadratic and linear elements (referred as scheme-1) and scheme based on complete discretization with linear elements (referred as scheme-2). The comparison shows that both the schemes are of nearly second order accurate while the scheme-1 is more accurate than scheme-2. The results show that the efficient mapping of curved surface with quadratic elements improves the accuracy of NIM schemes.

An improved k-ε turbulence model for FENE-P fluids capable to reach high drag reduction regime

An improved k-ε turbulence model for viscoelastic fluids is developed to predict turbulent flows in complex geometries, with polymeric solutions described by the finitely extensible nonlinear elastic-Peterlin constitutive model. The k-ε model is tested against a wide range of direct numerical simulation data, with different rheological parameters combinations, and is capable to capture the drag reduction for all regimes of low, intermediate and high, with good performance. Two main contributions are proposed, one through the viscoelastic closures present in the turbulent kinetic energy and dissipation equations, and the other, by modifying eddy viscosity model damping function to incorporate the viscoelastic effect close to the wall, especially at the buffer layer. In addition, improvements have been made to the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors present in the Reynolds-averaged transport equation for the conformation tensor. The main advantage is the capacity to predict all components of the tensor with good performance.

Two-Phase Flow In Mini-Scale Complex Geometry

Heat-transfer coefficients are reported for one surface, a plain surface, with 50 mm square base area. Parallel channel test piece has one mm by one mm, 25 channelsThe data were produced while boiling R113 at atmospheric pressure. For this surface, the mass flux range was 200 – 600 kg/m2s and the heat flux range was 5 - 80 kW/m2. The results obtained have been compared with standard correlations for tube bundles. The measured heat-transfer coefficients for the parallel micro-channel surface are slightly bigger for any plate channel surface. It is dependent on heat flux and reasonably independent of mass flux and vapor quality. Thus, heat transfer is probably dominated by nucleate boiling. The parallel channel heat transfer coefficients were typically bigger than other plate -channel values.

Interpretation of Heat‐Pulse Tracer Tests for Characterization of Three‐Dimensional Velocity Fields in Hyporheic Zone

AbstractHeat‐pulse tracers are a promising field method to measure Darcy flux in the hyporheic zone. Interpretation of data collected from such tests typically assumes knowledge of the direction of local Darcy flux (vertical) and relies on simplified heat transport models with one‐dimensional fluid flow and heat transfer. These assumptions are seldom valid due to complex flow geometry, heterogeneity, and the presence of localized heat sources. We derive a set of analytical expressions that obviate the need for these simplifying assumptions, thus substantially improving the capabilities of existing field instruments without requiring additional measurements. These closed‐form solutions account for tensorial nature of heat‐transfer parameters, and are obtained by using Green's functions and rotational coordinate transformations. The approach simplifies data collection, estimates three‐dimensional Darcy flux, relates fluid flow to heat‐transfer properties of the host medium, and can facilitate inverse modeling. Field applications of our solutions and their ramifications for data collection and analysis are discussed.

Simulation of a multistage fractured horizontal well in a water-bearing tight fractured gas reservoir under non-Darcy flow

Reservoir development for unconventional resources such as tight gas reservoirs is in increasing demand due to the rapid decline of production in conventional reserves. Compared with conventional reservoirs, fluid flow in water-bearing tight gas reservoirs is subject to more nonlinear multiphase flow and gas slippage in nano/micro matrix pores because of the strong collisions between rock and gas molecules. Economic gas production from tight gas reservoirs depends on extensive application of water-based hydraulic fracturing of horizontal wells, associated with non-Darcy flow at a high flow rate, geomechanical stress sensitivity of un-propped natural fractures, complex flow geometry and multiscale heterogeneity. How to efficiently and accurately predict the production performance of a multistage fractured horizontal well (MFHW) is challenging. In this paper, a novel multicontinuum, multimechanism, two-phase simulator is established based on unstructured meshes and the control volume finite element method to analyze the production performance of MFHWs. The multiple interacting continua model and discrete fracture model are coupled to integrate the unstimulated fractured reservoir, induced fracture networks (stimulated reservoir volumes, SRVs) and irregular discrete hydraulic fractures. Several simulations and sensitivity analyses are performed with the developed simulator for determining the key factors affecting the production performance of MFHWs. Two widely applied fracturing models, classic hydraulic fracturing which generates long double-wing fractures and the volumetric fracturing aimed at creating large SRVs, are compared to identify which of them can make better use of tight gas reserves.

Lattice Boltzmann model for three-phase viscoelastic fluid flow.

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

A coupled lattice Boltzmann method and discrete element method for discrete particle simulations of particulate flows

Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle–particle and particle–fluid interactions require an adequate representation but the computational cost has to be kept low. In this work, we present a novel coupling approach for such simulations. A lattice Boltzmann formulation of the generalized Navier–Stokes equations is used to describe the fluid motion. This promises efficient simulations suitable for high performance computing and, since volume displacement effects by the solid phase are considered, our approach is also applicable to non-dilute particulate systems. The discrete element method is combined with an explicit evaluation of interparticle lubrication forces to simulate the motion of individual submerged particles. Drag, pressure and added mass forces determine the momentum transfer by fluid–particle interactions. A stable coupling algorithm is presented and discussed in detail. We demonstrate the validity of our approach for dilute as well as for dense systems by predicting the settling velocity of spheres over a broad range of solid volume fractions in good agreement with semi-empirical correlations. Moreover, the accuracy of particle–wall interactions in a viscous fluid is thoroughly tested and established. Finally, simulations of mono- and bi-disperse fluidized beds highlight the capability of our new approach to handle configurations with large particle numbers.