Pressure-velocity Coupling Research Articles

HEAT TRANSFER ENHANCEMENT IN A CHANNEL WITH INCLINED BAFFLES UNDER PULSATING FLOW: A CFD STUDY

This study numerically investigated hydraulic and thermal performance in a channel with inclined baffles under pulsating flow conditions. The baffles were placed in a staggered arrangement. The governing equations were discretized with the finite volume method (FVM), and the pressure-velocity coupling was handled by the SIMPLE algorithm. The Strouhal number (St: 0.5,1, 2, 3, and 4), pulsation amplitude (A: 0.2, 0.5, and 0.8), and Reynolds number (200 ≤ Re ≤ 1000) were changed. The top and bottom surfaces of the channel were kept at <i>T</i><sub>ω</sub> = 350 K, and thermal improvement and friction factor were calculated for a pulsating cycle. The results were given in terms of thermal enhancement (η), relative friction factor (<i>f</i><sub>rel</sub>), and performance evaluation criteria (PEC). The flow and temperature contours were presented to determine the impacts of the pulsation frequency, the pulsation amplitude, and the Reynolds number. The results showed that the pulsation amplitude and the pulsation frequency contributed remarkably to thermal enhancement with increasing Reynolds numbers, while the heat transfer improved significantly depending on pulsation parameters together with a slight rise in friction factor. The highest thermal enhancement achieved was about 1.47 at <i>Re</i> = 1000, <i>A</i> = 0.8, and <i>St</i> = 4. The highest PEC obtained was approximately 1.12 at <i>Re</i> = 1000, <i>A</i> = 0.2, and <i>St</i> = 4.

Influence of the Inclination Angle on Mixed Convection and Heat Transfer in a “T” Shaped Double Enclosure

The effect of the tilt angle on mixed convection and related heat transfer in a “T” shaped double enclosure with four heated obstacles on the bottom surface is numerically investigated. The considered obstacles are constantly kept at a relatively high (fixed) temperature, while the cavity’s upper wall is cooled. The finite volume approach is used to solve the mass, momentum, and energy equations with the SIMPLEC algorithm being exploited to deal with the pressure-velocity coupling. Emphasis is put on the influence of the tilt angle on the solution symmetry, flow structure, and heat exchange through the walls. The following parameters and related ranges are considered: Rayleigh number 104 ≤ Ra ≤ 5.105, tilt angle 0° ≤ φ ≤ 90°, Reynolds number 100 ≤ Re ≤ 1000, Prandtl number Pr = 0.72, block height B = 0.5, opening width C = 0.15, and distance between blocks D = 0.5. The results reveal different branches of solutions on varying Re and φ . They also show that the symmetry of the solution regarding the P2 axis is retained for all cases with no tilt and for values of Re between 100 and 1000.

NUMERICAL STUDY OF TURBULENT HEAT TRANSFER PROCESS IN DIFFERENT WAVY CHANNELS WITH SOLID AND PERFORATED BAFFLES

This study numerically investigated the effects of different baffle arrangements on heat transfer enhancement and flow in channels with different wave profiles. Four different wave profiles - rectangular, trapezoidal, triangular, and circular - were considered for the wavy channels. Analyses were made on the solid and perforated baffles that were installed vertically in the channel's central area to determine their hydrodynamic performance and convective heat transfer. Pressure-velocity coupling in discretized equations was handled with the SIMPLE algorithm, and analyses were carried out using the ANSYS Fluent solver. The standard <i>k-ε</i> turbulence model was used to solve the simulations. In this study, the channel geometry, the baffle arrangement, and the Reynolds number (4000 ≤ Re ≤ 12,000) were changed. The wavy surfaces were preserved at <i>T<sub>ω</sub></i> = 360 K. The results were presented with different dimensionless parameters such as Nusselt number (Nu), friction factor (<i>f</i>), and thermal performance factor (TPF). Analyses indicated that the Nu number increased with increasing Re in all channel flows. In all wave profiles, the highest heat transfer was obtained in the solid baffle arrangement. The heat transfer increased by 2.12 times in the rectangular channel with solid baffle at Re = 4000 compared to the channel without a baffle. The highest average Nusselt number and relative friction factor were obtained about 143.34 and 1.24, respectively, in rectangular profile with solid baffle at Re = 12,000. The variation of the friction factor differed according to the wave profile and the baffle arrangement. The triangular profile with two-perforation baffles had the lowest TPF value, 1.09, and the rectangle profile with a solid baffle had the highest TPF value, 2.02. The results of the present study showed that the flow and heat transfer behaviors were similar in trapezoidal and circular channels.

Numerical Assessment of Nanofluid Natural Convection Using Local RBF Method Coupled with an Artificial Compressibility Model

In this paper, natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function (RBF). The nanofluids used were Cu-water or -water mixture with nanoparticle volume fractions range of . A system of continuity, momentum, and energy partial differential equations was used in modeling the flow and temperature behavior of the fluids. Partial derivatives in the governing equations were approximated using the RBF method. The artificial compressibility model was implemented to overcome the pressure velocity coupling problem that occurs in such equations. The main goal of this work was to present a simple and efficient method to deal with complex geometries for a variety of problem conditions. To assess the accuracy of the proposed method, several test cases of natural convection in square and triangular cavities were selected. For Rayleigh numbers ranging from to , a validation test of natural convection of Cu-water in a square cavity was used. The numerical investigation was then extended to Rayleigh number , as well as -water nanofluid with a volume fraction range of . In a second investigation, the same nanofluids were used in a triangular cavity with varying volume fractions to test the proposed meshless approach on non-rectangular geometries. The numerical results appear to be in agreement with those from earlier investigations. Furthermore, the suggested meshless method was found to be stable and accurate, demonstrating that it may be a viable alternative for solving natural heat transfer equations of nanofluids in enclosures with irregular geometries.

Thermal evaluation of a room coated by thin urethane nanocomposite layer coating for energy-saving efficiency in building applications

Today, it is common to use thin-layer nanocomposite coatings as insulation to reduce heat loss through building walls. One of the important advantages of these coatings is preventing energy loss as a thermal barrier in low thicknesses and with high efficiency. Investigations on the energy loss and saving of coated buildings are often practiced using numerical and experimental approaches. In this study, numerical simulation and experimental evaluation consisting of modification of nanoparticles and preparation powder coating nanocomposite, are used to study the effects of coated polyurethane nanocomposite containing nano Al2O3 and nano ZrO2 on both sides of the walls of a sample room on temperature distribution and heat transfer. For this purpose, a three-dimensional enclosure was assumed as a room having a radiant cooling panel, which is modeled under various features of the walls' interior and exterior coating. To determine the flow and temperature fields, the governing equations that include the continuity, momentum, turbulence, and energy equations, which are coupled through the buoyancy term, have been solved using the Fluent software. The SIMPLE algorithm to accommodate the pressure-velocity coupling, the k-ε model for turbulence modeling, the Boussinesq approximation for buoyancy term modeling, and the DO model for radiation simulation, are employed. The results of the thermography of the samples showed that the temperature reduction in the samples containing zirconium oxide compared to aluminum oxide had a better performance in the thermal insulation of the coating and the lowest temperature was observed in the nanocomposite containing 3% zirconium oxide. Numerical studies showed that this thin layer nanocomposite coating reduces energy consumption by 4% and 13%, respectively, compared to pure polyurethane coatings and acrylic paints.

Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation

A novel numerical model was developed to investigate air entrapment in binary droplet impact with solidification microstructure formation under practical plasma spraying conditions. The evolving liquid–gas interface was tracked by the explicit finite difference solution to the Cahn–Hilliard equation, coupled with the Navier–Stokes equations. Another diffuse interface model was invoked to trace solid–liquid and grain–grain boundaries. The model was discretized using an explicit finite difference method on a half-staggered grid. The velocity pressure coupling was decoupled with the projection method. The in-house code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. The time duration over which gas compressibility matters was estimated. Typical cases with air entrapment were studied with the model. The effect of droplet porosity on air entrapment was probed into as well: the larger the porosity of a droplet, the bigger the trapped air bubble. The grain growth near the air bubble is skewed. Moreover, a case without air entrapment was also shown herein to stress that air bubbles could be suppressed or even eliminated in plasma spraying by adjusting the landing positions of successive droplets.

Investigating the characteristics of flow past an elliptic moving belt

Laminar flow past a bluff body includes various physical aspects that can be important in engineering applications. In the present article, a numerical investigation of the laminar flow around an elliptic moving belt with a fixed axis ratio (minor to major diameter ratio) of 0.25 was carried out. The studied parameters were the angle of attack (α) and speed ratio (ratio of belt's speed to free stream velocity, k) ranging from 0o to 30o, and 0 to 4, respectively. The Reynolds numbers based on the major diameter of the belt were 200 and 500. To obtain the objective parameters such as the aerodynamic coefficients, flow patterns, pressure and skin friction distributions, the two-dimensional incompressible Navier-Stokes equations were numerically solved using an in-house, high-order, pressure-velocity coupling algorithm. Based on the results achieved by this study, the belt's motion caused the reduction of the viscous effects on the upper surface. as the speed ratio increased, the skin friction coefficient on the upper surface of the belt was reduced. Three flow patterns as: steady flow without vortex, steady flow with stationary vortex, and unsteady flow with vortex shedding were formed in the considered problem. Moreover, the aerodynamic investigation of the moving belt indicated that the belt's motion enhanced the lift coefficient and decreased the drag coefficient. At the higher Reynolds number, the drag coefficients were less than that of the lower one, while the Reynolds number variation had a little effect on the lift coefficients.

Mixed convection from two horizontally aligned hot and cold circular cylinders in a vented square enclosure

The mixed convection heat transfer from two horizontally aligned cylinders with one hot and one cold cylinder inside a vented square enclosure with openings on the upper and lower surfaces has been numerically investigated. The simulated behaviour of heat and flow fields has acquired the solutions using the Navier-Stokes equation and energy equation for steady, laminar and incompressible flow properties. Considering a diverse range of opening sizes O = 0.125–1, spacing sizes S = 0.3–0.45, Richardson number Ri = 0.1–10 and Reynolds number Re = 50–400 were covered with fixed Prandtl number Pr = 0.72. Velocity contours and isotherms with the average and local Nusselt numbers (Nu) have been displayed with various parameters. The method of solution uses the finite volume method (FVM). Pressure–velocity coupling and the SIMPLE method were used to solve the momentum and energy equation via the CFD software ANSYS/ FLUENT 2021 R1. The numerical solution shows the linear relationship between increasing the average Nu value with increasing Ri, Re and opening sizes O of the vents.Moreover, the increasing of spacing size to S = 0.375 positively enhances the value of average Nu around the hot cylinder. The best increase in value of average Nu resulted in S = 0.375 and O = 0.375 with 36.8 %. The average increase in Nu ranged from 10 % to 38 %.

Numerically investigation of Flow and Heat Transfer in differentially heated enclosures

In this research work natural convection in two dimensional cavity is studied numerically for differently heated air filled square and rectangular cavity. Vertical cavity with two adiabatic and hot and cold wall with different aspect ratio of 1, 2.5, 5, 7.5 and 10 has taken for investigation. the heat transfer was investigated over the wide range of Rayleigh number from 103 to 106 . Solutions are obtained for several Rayleigh numbers with Prandtl number Pr = 0.70 and aspect ratio 1, 2.5, 5, 7.5 and 10. The Pressure-Velocity Coupling Method used with Non-Iterative Time Advancement (NITA) scheme used to solve the problem. Flow patterns and isotherm plots were used to display the results, and for every case, local and mean Nusselt values were also produced. The results show that an increase in Rayleigh numbers greatly increases heat transfer, natural convection intensity, and average Nusselt number at a particular aspect ratio. The distribution of temperature and stream function are taken as a function of thermal and geometrical output parameter for given problem. Two stage investigations have been performed to find out the variation in the result between different approaches. Keyword: ANN (average Nusselt number), AR (aspect ratio), LNN (local Nusselt number), Nu (Nusselt number), Pr (Prandtl number), Ra (Rayleigh number).

A Conservative Level Set Approach to Non-Spherical Drop Impact in Three Dimensions.

A recently developed conservative level set model, coupled with the Navier-Stokes equations, was invoked to simulate non-spherical droplet impact in three dimensions. The advection term in the conservative level set model was tackled using the traditional central difference scheme on a half-staggered grid. The pressure velocity coupling was decoupled using the projection method. The inhouse code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. Before conducting extensive simulations, the model was tested on meshes of varied resolutions and validated against experimental works, with satisfyingly qualitative and quantitative agreement obtained. The model was then employed to predict the impact and splashing dynamics of non-spherical droplets, with the focus on the effect of the aspect ratio. An empirical correlation of the maximum spread factor was proposed. Besides, the number of satellite droplets when splashing occurs was in reasonable agreement with a theoretical model.

A novel high-order solver for simulation of incompressible flows using the flux reconstruction method and lattice Boltzmann flux solver

In this paper, a novel high-order solver using the flux reconstruction (FR) method and the lattice Boltzmann flux solver (LBFS) is proposed for accurately and efficiently simulating nearly incompressible flows. The existing LBFSs are all based on the finite volume (FV) scheme. The present work extends the application of the LBFS for the first time by combining the high-order FR scheme. Compared with the traditional high-order incompressible Navier-stokes (N-S) solvers, no particular techniques are needed for the current FR-LBFS to overcome the difficulty of the pressure-velocity coupling since the present method is a weakly compressible model. Moreover, unlike the traditional N-S solvers where the inviscid and viscous terms are treated separately, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly in FR-LBFS. In the present method, the common inviscid and viscous fluxes at the cell interface of the FR scheme are evaluated simultaneously by the local reconstruction of lattice Boltzmann equation (LBE) solution from macroscopic flow variables at solution points. Thus the discretization of the second-order partial derivative term is avoided. Compared with the high-order off-lattice Boltzmann methods (OLBM), the FR-LBFS is more stable, efficient and low-storage. No special techniques are needed to remove the stiffness of the governing equations which existing in the discrete velocity Boltzmann equation (DVBE). Compared with the high-order FV-LBFS, the FR-LBFS is compact for parallel computing by avoiding wide stencils on meshes. In addition, the present scheme has lower dissipation and can be more flexible to increase accuracy order. Numerical validations of the proposed method are implemented by simulating (a) Taylor-Green vortex problem, (b) steady plane Poiseuille flow, (c) lid-driven cavity flow, (d) laminar boundary layer and (e) flow past a square cylinder.

Low Reynolds Number Flow Past Square Cylinder in the Vicinity of a Plane Wall

The characteristics of flow over a square cylinder in the vicinity of a plane stationary wall have been numerically investigated. 2D time-dependent incompressible flow at low-Reynolds numbers of 100 and 200 has been calculated using the finite volume method. CFRUNS scheme is used for pressure-velocity coupling in numerical calculation. The authors have tried to make an attempt to analyze the features of the complex flow field through flow streamlines and the vorticity contours. The impact of the gap between the cylinder and the plane wall upon flow pattern behavior is also studied. An intense interaction between vorticity in the boundary layer generated over the plane wall and the vorticity associated with the shear layer emanating from the separation points on the cylinder surface has been observed producing a very complex flow field in the cylinder wake and the gap between the cylinder and the wall.

Effect of Magnetic Baffles and Magnetic Nanofluid on Thermo-Hydraulic Characteristics of Dimple Mini Channel for Thermal Energy Applications

The combined effect of a magnetic baffle and a dimple turbulator on the heat transfer and pressure drop is investigated computationally in a mini channel. Fe3O4 magnetic nanofluid is used as a working fluid. The Reynolds number (Re) is varied from 150 to 210 and the magnetic field intensities range from 1200 G to 2000 G. Finite-volume based commercial computational fluid dynamics (CFD) solver ANSYS-Fluent 18.1 was used for the numerical simulations. A laminar viscous model is used with pressure-velocity coupling along with second-order upwind discretization and QUICK scheme for discretizing the momentum and energy equations. The results show that there is an increase of 3.53%, 10.77%, and 25.39% in the Nusselt numbers when the magnetic fields of 1200 G, 1500 G and 2000 G, respectively, are applied at x = 15 mm, as compared to the flow without a magnetic field when the pitch = 10 mm. These values change to 1.51%, 6.14% and 18.47% for a pitch = 5 mm and 0.85%, 4.33%, and 15.25% for a pitch = 2.5 mm, when compared to the flow without a magnetic field in the respective geometries. When the two sources are placed at x = 7.5 mm and 15 mm, there is an increase of 4.52%, 13.93%, and 33.08% in the Nusselt numbers when magnetic fields of 1200 G, 1500 G, and 2000 G are applied when the pitch = 10 mm. The increment changed to 1.82%, 8.16%, and 22.31% for a pitch = 5 mm and 1.01%, 5.96%, and 21.38% for a pitch = 2.5 mm. This clearly shows that the two sources at the front have a higher increment in the Nusselt numbers compared to one source, due to higher turbulence. In addition, there is a decrease in the pressure drop of 10.82%, 16.778%, and 26.75% when magnetic fields of 1200 G, 1500 G, and 2000 G, respectively, are applied at x = 15 mm, as compared to flow without magnetic field when the pitch = 10 mm. These values change to 2.46%, 4.98%, and 8.54% for a pitch = 5 mm and 1.62%, 3.52%, and 4.78% for a pitch = 2.5 mm, when compared to flow without magnetic field in the respective geometries. When two sources are placed at x = 7.5 mm and 15 mm, there is an decrease of 19.02%, 31.3%, and 50.34% in the pressure drop when the magnetic fields of 1200 G, 1500 G and 2000 G are applied when the pitch = 10 mm. These values change to 4.18%, 9.52%, and 16.52% for a pitch = 5 mm and 3.08%, 6.88%, and 14.88% for a pitch = 2.5 mm. Hence, with the increase in the magnetic field, there is a decrease in pressure drop for both the cases and the pitches. This trend is valid only at lower magnetic field strength, because the decrease in the pressure drop dominates over the increase in pressure drop due to turbulence.

Volume-of-Fluid Based Finite-Volume Computational Simulations of Three-Phase Nanoparticle-Liquid-Gas Boiling Problems in Vertical Rectangular Channels

This study develops robust numerical algorithms for the simulation of three-phase (solid-liquid-gas) boiling and bubble formation problems in rectangular channels. The numerical algorithms are based on the Finite Volume Methods (FVM) and implement both the volume-of-fluid (VOF) methods for liquid-gas interface tracking as well as the volume-fraction methods to account for the concentration of embedded solid nano-particles in the liquid phase. Water is used as the base-liquid and the solid phase is modelled via metallic nano-particles (both aluminium oxide and titanium oxide nano-particles are considered) that are homogeneously mixed within the liquid phase. The gas phase is considered as a vapour arising from the bolling processes of the liquid-phase. The finite volume methodology is implemented on the OpenFOAM software platform, specifically by careful modification and manipulation of existing OpenFOAM solvers. The governing fluid dynamical equations, for the three-phase boiling problem, take into account the thermal conductivity effects of the solid (nano-particle), the momentum and energy equations for both the liquid-phase and the gas-phase, and finally the decoupled mass conservation equations for the liquid- and gas- phases. The decoupled mass conservation equations are specifically used to model the phase change between the liquid- and gas- phases. In addition to the FVM and VOF numerical methodologies for the discretization of the governing equations, the pressure-velocity coupling is resolved via the PIMPLE algorithm, a combination of the Pressure Implicit with Splitting of Operator (PISO) and the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithms. The computational results are presented graphically with respect to variations in time as well as in the nano-particle volume fractions. The simulations and results accurately capture the formation of vapour bubbles in the two-phase (particle-free) liquid-gas flow and additionally the computational algorithms are similarly demonstrated to accurately illustrate and capture simulated boiling processes. The presence of the nano-particles is demonstrated to enhance the heat-transfer, boiling, and bubble formation processes.

An implicit Cartesian cut-cell method for incompressible viscous flows with complex geometries

A versatile conservative three-dimensional Cartesian cut-cell method for simulation of incompressible viscous flows over complex geometries is presented in this paper. The present method is based on the finite volume method on a non-uniform staggered grid together with a consistent mass and momentum flux computation. Contrary to the commonly cut-cell methods, an implicit time integration scheme is employed in the present method, which avoids numerical instability without any additional small cut-cell treatment. Strict conservation of the mass and momentum for both fluid and cut cells is enforced through the PISO algorithm for the pressure–velocity coupling. The versatility and robustness of the present cut-cell method are demonstrated by simulating various two- and three-dimensional canonical benchmarks (flow over a circular cylinder, airfoil, sphere, pipe, and heart sculpture) and the computed results agree well with previous experimental measurements and various numerical results obtained from the boundary-fitted, immersed boundary/interface, and other cut-cell methods, verifying the accuracy of the proposed method.

Numerical investigations on the difference between aiding and opposing flows in the developing regime of laminar mixed convection in vertical tubes

The present article discusses the numerical simulation results of laminar mixed convection flow in vertical tubes. A comparative analysis of the thermal and hydrodynamic features of both buoyancy-assisted and opposed flows was performed for Reynolds number (), Grashof number () and Richardson number () with uniform heat flux boundary condition. 2-D axisymmetric steady state simulations were carried out for a length-to-diameter () ratio of with water as the working fluid. Numerical simulations were performed by employing SIMPLE scheme for pressure–velocity coupling in momentum equations and second order UPWIND scheme for solving energy equations. In case of assisting flow (), at fully developed state the centerline velocity decreases, and velocity is increased near the tube wall due to heat flux induced free convection. With increasing heat flux, the decrement in centerline velocity compared to the no-heat flux condition increases. Further, with increasing heat flux, the increase in friction factor and Nusselt number was observed. Therefore, at the same the variation of heat flux led to unique velocity profiles and temperature gradients. The variation of centerline velocity and temperature in developing region was also studied. While centerline temperature was monotonically increasing with length, the centerline velocity increased up to a maximum in the developing region and then attained the steady state at a lower value in the fully developed state. Subsequently we studied the dependence of on the hydrodynamic and thermal features. For constant friction factor and Nusselt number was observed to increase with increase in from 0.1 to 1.5 range. At fixed variation of heat flux leads to variation of or Hence, the buoyancy effect has a significant role in the entrance length development. The hydrodynamic entry length after an initial increase, attained an almost constant value with increasing On the other hand, the thermal entry length exhibited a decreasing trend with increasing Similarly, at constant Nusselt number increased with increasing for a range of 100–1000. It was evident that for a given and the heat transfer in the developing flow is always higher as that of the fully developed flow. Contrasting observations were observed for buoyancy-opposed flow. Velocity is accelerated at the center as compared to the tube wall in case of opposing flow for same and For a fixed the friction factor and Nusselt number decreased with increasing the Both the hydrodynamic and thermal entry length increases for opposing flows. Finally, we have developed correlations for fully developed friction factor () with as well as and Nusselt number () with for buoyancy-assisting and buoyancy-opposing flows. Two independent correlations are also produced for with Graetz number () for developing and fully developed regimes in both assisting as well as opposing flows.

Discrete adjoint momentum-weighted interpolation strategies

This Technical Note outlines an adjoint complement to a critical building block of pressure-based Finite-Volume (FV) flow solvers that employ a collocated variable arrangement to simulate virtually incompressible fluids. The focal point is to strengthen the adjoint pressure-velocity coupling by using an adjoint Momentum-Weighted Interpolation (MWI) strategy. To this end, analogies of established primal MWI techniques are derived and investigated. The study reveals the merits of an adjoint MWI but also highlights the importance of its careful implementation.

Numerical simulation of three-fluid Rayleigh-Taylor instability using an enhanced Volume-Of-Fluid (VOF) model: New benchmark solutions

The main objective of the present study is to introduce two novel benchmark solutions namely: two-dimensional three-fluid Rayleigh-Taylor Instability problems, aiming to provide an up-to-date data set and a unique fundamental insight into morphology and hydrodynamic behavior of coupled Rayleigh-Taylor-Kelvin-Helmholtz instability phenomenon. To this end, the Volume-Of-Fluid (VOF) model is adopted to probe the complex configurations and kinetic processes of highly nonlinear multi-fluid flow problems with large topological changes and moving interfaces. However, to improve the performance and accuracy of the classical VOF model and preserve monotonicity for the density and viscosity, a novel high-order bounded advection scheme is first proposed in the context of the Total Variation Diminishing and Normalized Variable Diagram (TVD-NVD) constraints and then is utilized for the discretization of the convection terms in the Navier-Stokes and transport equations. To further increase the accuracy of the numerical simulations, the second-order PLIC-ELVIRA is implemented for the reconstruction of the physical discontinuity between phases and the determination of its curvature. Furthermore, to enhance the consistency and stability of the classical VOF model in handling incompressible multi-fluid flows, a novel semi-iterative pressure-velocity coupling algorithm is constructed by the combination of the standard PISO and SIMPLEC algorithms and is then applied to ensure mass conservation in each grid cell. To demonstrate the versatility and robustness of the proposed model in dealing with the multiphase flows involving large interface deformation and breaking phenomena, a series of canonical test cases such as dam-break over a dry bed with and without stationary obstacle, 2D three-fluid rising bubble, two-fluid and three-fluid Rayleigh-Taylor Instability are adopted. In the last stage, an improved VOF model is applied to solve two new three-fluid Rayleigh-Taylor Instability benchmark problems on a staggered grid system. The results of this study can provide a wide panorama on the improvements of standard VOF model and may be utilized as benchmark solutions for validation of various CFD tools or simply to understand more complex related multi-fluid flows.

A meshless solution of the compressible viscous flow in axisymmetric tubes with varying cross-sections

The meshless Diffuse Approximate Method (DAM) is for the first time formulated and applied to simulate the compressible Newtonian flow of an ideal gas in an axisymmetric tube with varying cross-sections. The problem is structured by coupled partial differential equations for conservation of mass, momentum and energy, and the equation of state closure. These equations are solved in primitive variables and strong form. DAM is formulated on irregular node arrangement by using the second and third-order polynomial shape functions and Gaussian weights, leading to weighted least squares approximation on overlapping local subdomains. Pressure-velocity coupling is performed by the Pressure Implicit with Splitting of Operators (PISO) scheme. The solution of the represented novel application of DAM is verified by matching the meshless results with the fine-mesh finite-volume method results. The characteristics of meshless DAM for this kind of problem are systematically assessed by a detailed investigation of the varying node density, shape function order, Gaussian weight's shape, and the number of nodes in a local subdomain. The sensitivity study of DAM parameters shows that for the tested problems, the most suitable values of the Gaussian weight function and the number of nodes in a local subdomain are 5.0 and 13, respectively. Third-order convergence rate with better results is observed while using third-order polynomial shape functions.

Open-source finite volume solvers for multiphase (n-phase) flows involving either Newtonian or non-Newtonian complex fluids

Two new control volume solvers multiFluidInterFoam and rheoMultiFluidInterFoam are presented for the simulation of Newtonian and non-Newtonian n-phase flows (n≥2), respectively, fully accounting for interfacial tension and contact-angle effects for each phase. The multiFluidInterFoam solver modifies certain crucial aspects of the regular multiphaseInterFoam solver provided by OpenFOAM for Newtonian flows, improving its efficiency and robustness, but most importantly improving considerably its accuracy for surface tension driven flows. The new solver uses the volume-of-fluid (VOF) method based on the MULES method and artificial interface compression for the interface capturing, in combination with a suitable continuum surface force model; i.e. the interfacial tension coefficient decomposition method is employed to treat pairings of interfacial tension between the phases. VOF smoothing is also implemented by applying a Laplacian filter on the distribution of volume fractions, and the SIMPLEC algorithm is employed for the velocity–pressure coupling. The above algorithm has also been extended with the development of the rheoMultiFluidInterFoam solver which is capable of fully taking into account complex non-Newtonian effects (e.g. yield stress, viscoelasticity, etc.) of the involved liquids. To this end, the developed solver incorporates the RheoTool toolbox (Pimenta and Alves, 2017), utilizing a wealth of constitutive equations suitable for modeling different types of fluids with complex rheology. Our solvers are tested for both the implementation of the surface tension and of the constitutive equations in a wide range of different flow setups, considering typical benchmark two-phase and three-phase flows, such as the cases of dam break with an obstacle, spreading of a floating lens, a levitating drop, and a bubble rising in an ambient fluid; flows involving Newtonian, viscoplastic and viscoelastic liquids have been considered. Comparisons against analytical solutions or previously published numerical data are performed clearly demonstrating the capability of the new solvers to efficiently and accurately simulate interfacial tension dominated three-phase flows (and n-phase flows in general) for both simple and complex liquids.