Local Grid Refinement Technique Research Articles

Analysis and prediction of the gas-liquid interfacial area for droplets impact on solid surfaces

A better understanding of the variation of the gas-liquid interfacial area during droplets impact on solid surfaces in detail is extremely important for process intensification since this can lead to a much-increased efficiency of the heat and mass transfer. At present, experimental observation is the most popular method to investigate the droplet behaviours during the impact of the droplet. However, it is difficult to measure the interfacial areas and observe the transient inner flow field in the droplet. The CFD with VOF model is a powerful and efficient tool for investigating the visual dynamic behaviours, interfacial areas and the detailed inner flow field of droplets. Therefore, effective and efficient CFD models are established to investigate the droplet impact onto solid surfaces through using the VOF model with dynamic contact angle and local grid refinement techniques. The CFD predictions of the dynamic behaviours of the droplets are in reasonable agreement with experimental data over a wide range of surface and liquid properties. The simulation results showed that the gas–liquid interfacial area decreases slightly at the kinematic stage, then increases at the spreading stage, and reaches its maximum at the end of the spreading stage. The hydrophilic surface promotes the increase of gas–liquid interfacial area through releasing the liquid–solid interface energy, while the hydrophobic surface promotes the increase of the gas–liquid interfacial area by promoting droplet breakup. Finally, the energy conversion of the droplet impact on the solid surface is analysed, and a new correlation for predicting the maximum gas–liquid interfacial area of the droplet is proposed.

Numerical simulation of a silicon-based latent heat thermal energy storage system operating at ultra-high temperatures

This study investigates numerically a silicon-based latent heat storage system operating at ultra-high temperatures (∼1410–2000 °C). Owing to the silicon’s high latent heat (1230 kWh·m−3), storage densities of almost an order of magnitude higher than the state-of-the-art molten salt-based systems can be achieved. Prior to fabricating this system, there is a necessity to scrutinize the complex heat transfer mechanisms occurring during silicon phase change and indicate a vessel design that enables quick charge rates. A validated transient computational fluid dynamics model, combining the multiphase volume of fluid method with the enthalpy porosity approach and an adaptive local grid refinement technique is applied. This model simultaneously takes into account the phase-change material (PCM) volumetric change and the effect of dendritic formations and buoyancy-driven natural convection on the melting process. Numerical results reveal that the system charge rate is highly dependent on the PCM permeability, vessel design and operating conditions. Between five shapes investigated, i.e. cube, truncated cone, sphere, cut-off sphere and cylinder of volume V = 3.75E−03 m3, the truncated cone is the most preferable considering both design flexibility- its height can be easily altered, without increasing its volume- and melting rates. Actually, the PCM melting time achieved with the cone is 21% quicker compared to sphere and 6% slower compared to cube. Concerning the vessel size, the melting time increases by almost 28%, when the vessel volume increases to V′ = 2V. Finally, reduction in the silicon melting time, almost by 31%, is achieved by increasing the Stefan number by 35%.

Incomplete mixing in porous media: Todd-Longstaff upscaling approach versus a dynamic local grid refinement method

Field-scale simulation of flow in porous media in presence of incomplete mixing demands for high-resolution computational grids, much beyond the scope of state-of-the-art simulators. Hence, the upscaling-based Todd and Longstaff (TL) approach is typically used, where coarse grid cells are employed with effective mixing fluid properties and parameters found by matching results obtained with fully resolved reference simulations. Dynamic local grid refinement (DLGR) techniques, on the other hand, only employ fine-scale grid resolution where the fully mixed assumption is not valid. The rest of the domain is then solved at coarser resolutions, where the fully mixed assumption is valid. Here, we assess the accuracy and the robustness of DLGR- and TL-based simulations of miscible displacements in homogeneous and heterogeneous porous media. Due to the intrinsic uncertainty within the unstable displacement nature of the studied incomplete mixing processes, the performance of the methods is also investigated based on a range of acceptable solutions rather than relying only on a single reference one. Systematic numerical results illustrate that the DLGR method is much more robust and accurate than the upscaling-based TL approach, and employs only a small fraction of fine-scale reference grids. Especially, the TL upscaling results (though history matched with computationally expensive fine-scale results) are very sensitive to the change of the simulation parameters. Based on this study, we propose a dynamic multilevel simulation strategy for efficient and reliable large-scale simulation of the complex incomplete mixing processes.

Numerical investigation of heavy fuel droplet-particle collisions in the injection zone of a Fluid Catalytic Cracking reactor, part II: 3D simulations

This study investigates the collisions between heavy gasoil droplets and solid catalytic particles taking place at conditions realized in Fluid Catalytic Cracking reactors (FCC). The computational model utilizes the Navier-Stokes equations along with the energy conservation and transport of species equations. The VOF methodology is used in order to track the liquid-gas interface, coupled with a dynamic local grid refinement technique in order to minimize the computational cost. Phase-change phenomena, as well as catalytic cracking surface reactions (2-lump scheme) are taken into account. In this paper, the numerical model is extended to investigate the droplet-particle collision process in three dimensions. In order to save computational resources, only half of the droplet is investigated, by imposing symmetry conditions. Firstly, single droplet-catalyst collisions are simulated and compared against the corresponding ones provided by 2D axisymmetric simulations and afterwards, the model is applied for the characterization of the collision dynamics between a single droplet and a particle cluster, i.e. a realistic 3D particle configuration. As the droplet flows through the space between the catalytic particles, important phenomena are observed, such as a) drop levitation due to the formed vapour layer and b) a thin liquid sheet formation, both of which affect the rate of gasoline production, as well as predictions for liquid pore blocking mechanism; a phenomenon frequently observed industrially. Results indicate that gasoline production decreases when the collision target is a particle cluster, instead of same number (as many as in the cluster) single catalysts, as the corresponding contact area decreases.

Numerical investigation of heavy fuel droplet-particle collisions in the injection zone of a Fluid Catalytic Cracking reactor, Part I: Numerical model and 2D simulations

The present paper investigates the collisions between heavy gasoil droplets and solid catalytic particles taking place at conditions realized in Fluid Catalytic Cracking reactors (FCC). The computational model utilizes the Navier-Stokes equations along with the energy conservation and transport of species equations. The VOF methodology is used in order to track the liquid-gas interface, while a dynamic local grid refinement technique is adopted, so that high accuracy is achieved with a relative low computational cost. Phase-change phenomena (evaporation of the heavy gasoil droplet), as well as catalytic cracking surface reactions are taken into account. Physical properties of heavy and light molecular weight hydrocarbons are modelled by representative single component species, while a 2-lump scheme is proposed for the catalytic cracking reactions. The numerical model is firstly validated for the case of a single liquid droplet evaporation inside a hot gaseous medium and impingement onto a flat wall for droplet heating and film boiling conditions. Afterwards, it is utilized for the prediction of single droplet-catalyst collisions inside the FCC injection zone. The numerical results indicate that droplets of similar size to the catalytic particles tend to be levitated more easily by hot catalysts, thus resulting in higher cracking reaction rates/cracking product yield, and limited possibility for liquid pore blocking. For larger sized droplets, the corresponding results indicate that the production of cracking products is not favored, while solid-liquid contact increases. Hotter catalysts promote catalytic cracking reactions and droplet levitation over the catalytic particle, owed to the formation of a thin vapour layer between the liquid and the solid particle.

A numerical study on droplet-particle collision dynamics

The impact of liquid droplets onto spherical stationary solid particles under isothermal conditions is simulated. The CFD model solves the Navier-Stokes equations in three dimensions and employs the Volume of Fluid Method (VOF) coupled with an adaptive local grid refinement technique able to track the liquid-gas interface. A fast-marching algorithm suitable for the quick computation of distance functions required during the grid refinement in large 3-D computational domains is proposed. The numerical model is validated against experimental data for the case of a water droplet impact onto a spherical particle at low We number and room temperature conditions. Following that, a parametric study is undertaken examining (a) the effect of Weber number (= ρu2Do/σ) in the range of 8 to 80 and (b) the droplet to particle size ratio ranging in-between 0.31 and 1.24, on the impact outcome. This has resulted to the identification of two distinct regimes that form during droplet-particle collisions: the partial/full rebound and the coating regimes; the latter results to the disintegration of secondary satellite droplets from elongated expanding liquid ligaments forming behind the particle. Additionally, the temporal evolution of variables of interest, such as the maximum dimensionless liquid film thickness and the average wetting coverage of the solid particle by the liquid, have been quantified. The present study assists the understanding of the physical processes governing the impact of liquids onto solid spherical surfaces occurring in industrial applications, including fluid catalytic cracking (FCC) reactors.

Predicting the evaporation rate of stationary droplets with the VOF methodology for a wide range of ambient temperature conditions

This paper presents CFD predictions for the evaporation of nearly spherical suspended droplets for ambient temperatures in the range 0.56 up to 1.62 of the critical fuel temperature, under atmospheric pressures. The model solves the Navier-Stokes equations along with the energy conservation equation and the species transport equations; the Volume of Fluid (VOF) methodology has been utilized to capture the liquid-gas interface using an adaptive local grid refinement technique aiming to minimize the computational cost and achieve high resolution at the liquid-gas interface region. A local evaporation rate model independent of the interface shape is further utilized by using the local vapor concentration gradient on the droplet-gas interface and assuming saturation thermodynamic conditions. The model results are compared against experimental data for suspended droplet evaporation at ambient air cross flow including single- and multi-component droplets as well as experiments for non-convective conditions. It is proved that the detailed evaporation process under atmospheric pressure conditions can be accurately predicted for the wide range of ambient temperature conditions investigated.

Numerical investigation of aerodynamic droplet breakup in a high temperature gas environment

The Navier–Stokes equations, energy and vapor transport equations coupled with the VOF methodology and a vaporization rate model are numerically solved to predict aerodynamic droplet breakup in a high temperature gas environment. The numerical model accounts for variable properties and uses an adaptive local grid refinement technique on the gas–liquid interface to enhance the accuracy of the computations. The parameters examined include Weber (We) numbers in the range 15–90 and gas phase temperatures in the range 400–1000K for a volatile n-heptane droplet. Initially isothermal flow conditions are examined in order to assess the effect of Weber (We) and Reynolds (Re) number. The latter was altered by varying the gas phase properties in the aforementioned temperature range. It is verified that the We number is the controlling parameter, while the Re number affects the droplet breakup at low We number conditions. The inclusion of droplet heating and evaporation mechanisms has revealed that heating effects have generally a small impact on the phenomenon due to its short duration except for low We number cases. Droplet deformation enhances heat transfer and droplet evaporation. An improved 0-D model is proposed, able to predict the droplet heating and vaporization of highly deformed droplets.

Selection of voxel size and photon number in voxel-based Monte Carlo method: criteria and applications.

The voxel-based Monte Carlo method (VMC) is now a gold standard in the simulation of light propagation in turbid media. For complex tissue structures, however, the computational cost will be higher when small voxels are used to improve smoothness of tissue interface and a large number of photons are used to obtain accurate results. To reduce computational cost, criteria were proposed to determine the voxel size and photon number in 3-dimensional VMC simulations with acceptable accuracy and computation time. The selection of the voxel size can be expressed as a function of tissue geometry and optical properties. The photon number should be at least 5 times the total voxel number. These criteria are further applied in developing a photon ray splitting scheme of local grid refinement technique to reduce computational cost of a nonuniform tissue structure with significantly varying optical properties. In the proposed technique, a nonuniform refined grid system is used, where fine grids are used for the tissue with high absorption and complex geometry, and coarse grids are used for the other part. In this technique, the total photon number is selected based on the voxel size of the coarse grid. Furthermore, the photon-splitting scheme is developed to satisfy the statistical accuracy requirement for the dense grid area. Result shows that local grid refinement technique photon ray splitting scheme can accelerate the computation by 7.6 times (reduce time consumption from 17.5 to 2.3 h) in the simulation of laser light energy deposition in skin tissue that contains port wine stain lesions.

A multimechanistic multicontinuum model for simulating shale gas reservoir with complex fractured system

Unconventional shale gas reservoirs have become the focus of considerable attention as primary energy resource over the past decades worldwide. Economic gas rate requires the creation of complex fracture networks which could be characterized by the stimulated reservoir volume (SRV) concept. Micro-seismic mapping technique could provide a measurement of the overall SRV and an estimate of the fracture patterns.Accurate and efficient numerical simulation of these reservoirs is challenging. There is substantial physical complexity involving a number of tightly coupled mechanisms in the modeling of gas production. The fabric of shale system with multicontinuum nature comprises organic material, inorganic matrix and natural fracture. The complexity is further amplified by the complex fracture networks with a wide range of fracture length scales and topologies.In this work, we develop a comprehensive physics-based, multicontinuum model to predict shale gas reservoir performance. The model is designed to incorporate the spectrum of known physics inherent in shale system, such as multiphase behavior, desorption, non-Darcy transport in ultra-tight porous media, high-velocity turbulent flow and rock un-consolidation within natural fractures.We also implement a novel hybrid fracture model (UDFM-MINC) that effectively integrates discrete fracture-matrix model (DFM) with continuum type of approach for simulating the multiscaled stimulated shale formations. Primary fractures are described using DFM with unstructured triangular grids (UDFM), and small-scale fractures are handled by the multiple interacting continua (MINC) model in a fully coupled manner. Optimized local grid refinement (LGR) technique is employed to accurately capture the transient flow regime around the primary fractures.We discuss the numerical implementation for the developed model, and present simulation results to demonstrate the model applicability. We also conduct preliminary sensitivity studies to determine the key factors of reservoir and fracture that affect the production performance of unconventional gas wells.

Coupling a local adaptive grid refinement technique with an interface sharpening scheme for the simulation of two-phase flow and free-surface flows using VOF methodology

This study presents the implementation of an interface sharpening scheme on the basis of the Volume of Fluid (VOF) method, as well as its application in a number of theoretical and real cases usually modelled in literature. More specifically, the solution of an additional sharpening equation along with the standard VOF model equations is proposed, offering the advantage of “restraining” interface numerical diffusion, while also keeping a quite smooth induced velocity field around the interface. This sharpening equation is solved right after volume fraction advection; however a novel method for its coupling with the momentum equation has been applied in order to save computational time. The advantages of the proposed sharpening scheme lie on the facts that a) it is mass conservative thus its application does not have a negative impact on one of the most important benefits of VOF method and b) it can be used in coarser grids as now the suppression of the numerical diffusion is grid independent. The coupling of the solved equation with an adaptive local grid refinement technique is used for further decrease of computational time, while keeping high levels of accuracy at the area of maximum interest (interface). The numerical algorithm is initially tested against two theoretical benchmark cases for interface tracking methodologies followed by its validation for the case of a free-falling water droplet accelerated by gravity, as well as the normal liquid droplet impingement onto a flat substrate. Results indicate that the coupling of the interface sharpening equation with the HRIC discretization scheme used for volume fraction flux term, not only decreases the interface numerical diffusion, but also allows the induced velocity field to be less perturbed owed to spurious velocities across the liquid–gas interface. With the use of the proposed algorithmic flow path, coarser grids can replace finer ones at the slight expense of accuracy.

Performance of Shale Gas Reservoirs with Nonuniform Multiple Hydraulic Fractures

Unconventional shale gas resource has become a very significant base throughout the world. Potential shale gas resource is huge and production has increased over the last few years. In this study, extensive numerical simulations were conducted to compare productivity of shale gas reservoirs with nonuniform configuration of hydraulic fractures. Nonuniform multiple hydraulic fractures are characterized by various fracture spacing and half-length. A dual permeability model with logarithmically spaced local grid refinement technique is applied to represent a system of natural fractures, shale matrix, and a hydraulically fractured horizontal well in shale gas reservoirs. Nonuniform fracture spacing leads to the overlap of gas drainage areas and lower productivity. Nonuniform fracture half-length also affects decline of cumulative gas production because pressure drop does not reach tips of long fractures at early time. For best productivity, equally-spaced fractures of uniform half-length are recommended.

Direct Numerical Simulation and Large Eddy Simulation on a Turbulent Wall-Bounded Flow Using Lattice Boltzmann Method and Multiple GPUs

Direct numerical simulation (DNS) and large eddy simulation (LES) were performed on the wall-bounded flow atReτ=180using lattice Boltzmann method (LBM) and multiple GPUs (Graphic Processing Units). In the DNS, 8 K20M GPUs were adopted. The maximum number of meshes is6.7×107, which results in the nondimensional mesh size ofΔ+=1.41for the whole solution domain. It took 24 hours for GPU-LBM solver to simulate3×106LBM steps. The aspect ratio of resolution domain was tested to obtain accurate results for DNS. As a result, both the mean velocity and turbulent variables, such as Reynolds stress and velocity fluctuations, perfectly agree with the results of Kim et al. (1987) when the aspect ratios in streamwise and spanwise directions are 8 and 2, respectively. As for the LES, the local grid refinement technique was tested and then used. Using1.76×106grids and Smagorinsky constant(Cs)=0.13, good results were obtained. The ability and validity of LBM on simulating turbulent flow were verified.

The effect of Weber number on the central binary collision outcome between unequal-sized droplets

The central binary collision of two unequal sized droplets is numerically investigated using the volume of fluid (V.O.F.) methodology. The numerical method based on the solution of the continuity and momentum equations in axi-symmetric formulation is coupled with a recently developed adaptive local grid refinement technique, thus allowing an accurate representation of the interface between the liquid and gas phase. Mass transfer mechanisms are reproduced by solving a transport equation for a colour function representing the mass of one of the colliding droplets before and after collision and mixing. The investigation is performed assuming either constant relative velocity of the colliding droplets or constant total energy of the system, thus creating a combination of the standard non-dimensional parameters affecting the collision process, i.e. Weber (We) and Ohnesorge (Oh) numbers as also droplet diameter ratio (Δ). The reliability of the procedure is first established by comparing predictions with available experimental data. The effect of the above mentioned parameters on ligament’s formation, maximum deformation of the two droplets, the penetration of one droplet into the other and satellite droplet formation is quantified.

Numerical investigation of the evaporation of two-component droplets

A numerical model for the complete thermo-fluid-dynamic and phase-change transport processes of two-component hydrocarbon liquid droplets consisting of n-heptane, n-decane and mixture of the two in various compositions is presented and validated against experimental data. The Navier–Stokes equations are solved numerically together with the VOF methodology for tracking the droplet interface, using an adaptive local grid refinement technique. The energy and concentration equations inside the liquid and the gaseous phases for both liquid species and their vapor components are additionally solved, coupled together with a model predicting the local vaporization rate at the cells forming the interface between the liquid and the surrounding gas. The model is validated against experimental data available for droplets suspended on a small diameter pipe in a hot air environment under convective flow conditions; these refer to droplet’s surface temperature and size regression with time. An extended investigation of the flow field is presented along with the temperature and concentration fields. The equilibrium position of droplets is estimated together with the deformation process of the droplet. Finally, extensive parametric studies are presented revealing the nature of multi-component droplet evaporation on the details of the flow, the temperature and concentration fields.

Performance investigation of 2D lattice Boltzmann simulation of forces on a circular cylinder

The lattice Boltzmann method (LBM) is employed to simulate the uniform flow past a circular cylinder. The performance of the two-dimensional LBM model on the prediction of force coefficients and vortex shedding frequency is investigated. The local grid refinement technique and second-order boundary condition for curved walls are applied in the calculations. It is found that the calculated vortex shedding frequency, drag coefficient and lift coefficient are consistent with experimental results at Reynolds numbers lower than 300. For the high Reynolds number flow, although the simulation by the combined model of LBM and large eddy simulation method is numerically stable, the simulated results deviate from those of experiments, similar to the reported results by conventional numerical methods. It is suggested that this is mainly due to the three-dimensionality of the flow.

The effect of gas and liquid properties and droplet size ratio on the central collision between two unequal-size droplets in the reflexive regime

A numerical investigation of various parameters affecting the collision process of two unequal sized droplets in a gaseous environment in the reflexive regime is presented. The investigation is based on the finite volume numerical solution of the Navier–Stokes equations, in their axial-symmetric formulation, expressing the flow field of the two phases, liquid and gas, coupled with the volume of fluid method (VOF) for tracking the liquid–gas interfaces; a recently developed adaptive local grid refinement technique is used in order to track more accurately the liquid–gas interface with reduced computational cost. A colour function is used in order to follow the mixing process of the two droplets after collision. The reliability of the procedure is first established by comparing predictions with available experimental data and important details as regards the time evolution of the deformed shapes, the ligament formation, the maximum deformation of the droplets and the penetration of one droplet into the other are presented. The collision process and its outcome are investigated having the liquid properties (Ohnesorge number based on the liquid properties), the gas phase properties (Reynolds number based on gas properties) and droplet size ratio as the controlling parameters.

A PARAMETRIC NUMERICAL STUDYOFTHE HEAD-ON COLLISION BEHAVIOR OF DROPLETS

Head-on collision of droplets consisting of different liquids for a wide range of Weber numbers between 25 and 430 is studied numerically using the volume of fluid (VOF) methodology and by adopting an axisymmetric approximation. An adaptive local grid refinement technique is used to capture with precision the liquid–air interface at significantly reduced computational cost relative to a uniformly dense grid. The conditions setting the boundary between permanent coalescence and reflexive separation are defined; in addition, useful relationships determining the ligament’s elongation, the corresponding time of its breakup, the number of satellite droplets formed, the maximum droplet deformation, and the viscous dissipation coefficient are presented. Furthermore, the present study reveals the dependence of collision characteristics not only on Weber number, but also either on Reynolds, capillary, or Ohnesorge numbers.

SINGLE DROPLET IMPACTS ONTO DEPOSITED DROPS. NUMERICAL ANALYSIS AND COMPARISON

The impact of a spherical water droplet onto a stationary sessile droplet lying on a solid wall is studied numerically using the volume-of-fluid methodology. The governing Navier-Stokes equations are solved both for the gas and liquid phase coupled with an additional equation for the transport of the liquid interface. An unstructured numerical grid is used along with an adaptive local grid refinement technique, which enhances the accuracy of the numerical results along the liquid-gas interface and decreases the computational cost. The stationary sessile droplet has been created from the prior impact of one or two water droplets falling onto the solid wall, while two solid walls have been studied−an aluminum substrate and a glass substrate. The material of the wall plays an important role because it has an impact on the droplet's wetting behavior. The numerical model is validated against corresponding experimental data presented in the first part of the present work (Nikolopoulos et al., 2010), showing good agreement. Furthermore, the numerical investigation sheds light on the governing physics of the phenomenon.

Off-centre binary collision of droplets: A numerical investigation

The paper presents results from a numerical investigation of the non-central binary collision of two equal size droplets in a gaseous phase. The flow field is two phase and three dimensional; the investigation is based on the finite volume numerical solution of the Navier–Stokes equations, coupled with the Volume of Fluid Method (VOF), expressing the unified flow field of the two phases, liquid and gas. A recently developed adaptive local grid refinement technique is used, in order to increase the accuracy of the solution particularly in the region of the liquid–gas interface. The reliability of the solution procedure is tested by comparing predictions with available experimental data. The numerical results predict the collision process of the two colliding droplets (permanent coalescence or separation) and in the case of separation the formation and the size of the satellite droplets. The time evolution of the geometrical characteristics of the ligament, for various Weber numbers and impact parameters, is calculated and details are shown of the velocity and pressure fields particularly at the ligament pinch off location not hitherto available. Gas bubbles due to collision are trapped within the liquid phase as it has also been observed in experiments and their volume is calculated.