Pressure Implicit With Splitting Of Operators Research Articles

Numerical simulation of the movement of the water surface with macroscopic particles during a partial dam break for various complex reliefs

In this paper, it was considered a numerical simulation of the water surface movement during the partial collapse of the destruction of a dam with complex terrain. The numerical simulations took into account debris after a partial collapse of the dam, which imitates debris and moves downstream with the water flow. Carrying out these calculations brings the results closer to the real scenario. The mathematical model was based on the Navier–Stokes equations and uses the turbulent large eddy method (LES) model describing the flow of an incompressible viscous fluid. To describe the movement of a two-phase fluid, the volume of fluid (VOF) methods for the phase were used, and the Discrete Phase Model (DPM) and Macroscopic Particle Model (MPM) were used to describe the movement of particles. For the numerical solution of this system of equations, the Pressure Implicit Split Operator (PISO) numerical algorithm was chosen. The results show that the model is accurate and capable of handling very complex interactions such as particle transport or hydrodynamic actions on structures if the appropriate scales are reproduced. Also in this work, a three-dimensional (3D) model of the flow of a dam break on uneven terrain was considered and combined problems were performed that are closer to real conditions. For combined problems, flood zones and flood times were determined, knowledge of which will help evacuate people from dangerous areas. The accuracy of the 3D model and the selected numerical algorithm were verified using two natural measurements.

Computational fluid dynamics (CFD) simulation modeling for the cultivation of microalgal monoculture in axenic enclosed bubble column photobioreactor (BCPBR)

Researchers are more concerned with axenic-enclosed PBRs, where there is less or no chance of contamination during the production of biochemical and highly valuable metabolites, and monocultures of microalgae are being grown more frequently. It is a closed, manufactured vessel that aids in the photosynthesis of microalgal cells using artificial light or sunlight as the energy source. In this study, the bubble column PBR (BCPBR) was selected because it possessed some advantages over other PBRs for the growth of Chlorella vulgaris. The BCPBR system prevents contact between the enclosed microalgal cells and the environment, allowing the culturing of microalgae species that are difficult to grow in open pond systems. To compare BCPBR performance quantitatively, the efficient mixing expected in BCPBR, as discussed in the literature, was applied to the CFD model. The experimental results observed during the cultivation of C. vulgaris with restaurant wastewater (RWW) in BCPBR clearly showed better mixing, high growth, and improved treatment efficiency. CFD analysis was conducted on the evolution of bubbles in the BCPBR. The Pressure-Implicit with Splitting of Operators (PISO) pressure correction method is used for velocity and pressure coupling. A geo-reconstruct approach is used to construct the interface, and a second-order upwind calculation technique is used to determine the flow parameters. Therefore, CFD simulation in this study will contribute to the following aspects: (i) the volume fraction contours and velocity contours are going to validate the experimental study as the homogenous mixing favors the growth and productivity, (ii) To study how the size of the nozzle and inlet velocity affect the turbulence generated by bubbles in a BCPBR to identify the optimal nozzle size and velocity for the required turbulence.

Phase-field formulated meshless simulation of axisymmetric Rayleigh-Taylor instability problem

A formulation of the immiscible Newtonian two-liquid system with different densities and influenced by gravity is based on the Phase-Field Method (PFM) approach. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in all the terms. The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in Cartesian and axisymmetric coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. This solution procedure has improved stability compared to Chorin's pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the authors’ previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris, Open-source Field Operation and Manipulation (OpenFOAM®) code and previously existing results.

Phase-field formulated meshless simulation of Rayleigh-Taylor instability problem

The interface between two immiscible Newtonian liquids with different densities and the same viscosity, influenced by gravity, is based on the Phase-Field Method (PFM) formulation. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in the inertial and buoyancy terms (non-Boussinesq formulation). The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in two-dimensional Cartesian coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. Implicit time discretisation is performed for the NS and CH equations in the momentum predictor and Phase-Field (PF) variable corrector steps of PISO, while the momentum corrector steps solve the NS equation explicitly. This solution procedure has improved stability compared to Chorin’s pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the author’s previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris.

Implementation and Validation of Explicit Immersed Boundary Method and Lattice Boltzmann Flux Solver in OpenFOAM

In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems.

WELL-BALANCED ALGORITHM AND HEIGHT FUNCTION METHOD FOR DYNAMIC CONTACT ANGLE IN TWO-PHASE SYSTEMS

The well-balanced algorithm combined with dynamic contact angle was well studied in the literature but was never implemented with the pressure-implicit with splitting of operators (PISO) algorithm in a collocated grid commonly used in an incompressible, transient simulation. This article presents a well-balanced algorithm for PISO schemes coupling with the height function method for curvature estimation. The dynamic contact angle model from Kistler and Cox is also integrated to improve the modelling of the curvature at the wall boundary. In collocated finite volume schemes, the well-balanced PISO algorithm is developed by modifying both the calculation of the gradients in the momentum equation and the Rhie and Chow algorithm. This new gradient calculation method ensures that surface tension force and pressure gradient are identically discretized at the same location. The Rhie and Chow algorithm is also modified by adding the surface tension force to balance the pressure forces. The stationary droplet case in two-dimensions is presented first to validate the proposed methodology. The well-balanced algorithm coupling with the height function method shows its benefits by damping spurious currents by two to three orders of magnitude. The 3D surface-driven flow and water-spreading droplets are then simulated; the results show that the new scheme coupled with dynamic contact angle model outperforms the unbalanced scheme of the smooth void fraction method for theoretical and experimental comparisons.

Optimization of Co-Flow Jet Parameters for Ahmed Body Application

This study evaluates the drag reduction strategy of suction and blowing on idealize automotive vehicle, Ahmed Body. Optimization approach is adapted in order to analyse the effect of slot location, momentum coefficient and slot angle on the vehicle which experiencing drag. Despite all the efforts that have been done to reduce the Ahmed body drag using various active flow control system, most of the drag reduction were only less than 15%. A 25° Ahmed body with build in co-flow jet is modelled using a CAD software. The flow around the Ahmed body is simulated at Reynolds number based on length Re = 4.29 × 106. The governing equation were solve using an open source software package, which has been validated against experimental data. Pressure Implicit with Splitting of Operator (PISO) algorithm is applied to solve the equation. The outcome of the simulation are varies depending on the variables. Some show a decrease in drag while there are also that actually increase the drag of the system. This are caused by the suction and blowing slots that effect the surrounding air flow whether it is reducing or increasing the wake size downstream of the body. The result shows the momentum coefficient and location of both suction and blowing jet played an important role of manipulating the flow around the body and reducing the drag. The velocity contours indicated that the key to drag reduction is by using 40 m/s jet velocity, placement of suction and blowing away from each other.

Determination of forced convection effects on the response of membrane-based ion-selective electrodes via numerical solution to the Navier-Stokes-Nernst-Plank-Poisson equations

Ion selective electrodes (ISEs) enable measurements via the build-up of a phase boundary potential at the surface of a sensing membrane. While a framework exists to understand the performance of ISEs in stagnant samples, the influences of fluid flow on ISEs are less studied. We model the transport of ions in solution occurring near interfaces between ISE membranes and aqueous samples when subject to an external flow. We developed a numerical model extending the Pressure-Implicit with Splitting of Operators (PISO) algorithm to incorporate the Navier-Stokes-Nernst-Plank-Poisson system of equations. We find that external flow distorts the aqueous side of the formed double layer at the ISE membrane and aqueous sample interface, leading to an increase in the phase boundary potential. The change in potential is shown to be a function of a novel set of dimensionless numbers, most notably the Debye Length Reynolds number, i.e., the Reynolds number with the Debye Length as the system dimension.

Instabilities in tidal turbine wakes

We report on the observation of vortex instabilities in the wake of a tidal turbine undergoing harmonic unsteady axial inflow (e.g. due to surface waves). The work was carried out using unsteady RANS (URANS) modelling using the open-source CFD software OpenFOAM, using the `pimpleDyMFoam' solver. The PIMPLE algorithm used in the URANS solver is a combination of the PISO (Pressure Implicit with Splitting of Operator) and SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithms. URANS simulations usually have a limitation on the time step set by the Courant number (C = u (delta t)/(delta x), where delta x is the minimum cell length and u the local velocity. In the PISO algorithm, C<1 is usually required. However, the PIMPLE algorithm allows stable transient simulations at C>>1 by applying under-relaxation to each time-step until a convergence criterion is met, before allowing the time-step to complete with no applied relaxation factors. The turbulence model used was komega-SST, which has been used extensively in tidal turbine modelling.
 As with a wind turbine, the response of a tidal turbine to unsteady flow is heavily influenced by the behaviour of the helical wake that returns in close proximity to the turbine blades times per revolution ( – number of blades). Unsteady inflow causes the blades to shed vorticity into the wake, which in turn leads to a spatial variation in wake vortex strength, such that the vorticity of adjacent returning wake segments can differ, and thus there is a spatially varying velocity deficit in the wake. This spatial variation in velocity deficit triggers instability in the blade tip vortices, the emergence of which we demonstrate is governed by the non-dimensional group relating the blade passing frequency to the gust frequency. If the ratio between these two frequencies is an integer, the wake is stable. If not, the tip vortices exhibit various forms of instability. If the wake is unstable, adjacent wake segments will eventually coalesce as they move downstream, such that the wake consists of larger regions of vorticity with lower spatial frequency, compared to the wake immediately behind the turbine. There is also some indication that these unstable, coalesced wakes persist further downstream, compared with stable wakes. This has implications for wind and tidal farm design, where interaction of a row of turbines with the wakes of upstream turbines is an important consideration.

NUMERICAL SIMULATION OF A FLUID FLOW IN THE CYLINDRICAL DUCT CONTAINING TWO DIAPHRAGMS WITH ORIFICES OF DIFFERENT DIAMETERS

The flow of a viscous incompressible fluid in a cylindrical duct with two serial diaphragms with orifices of different diameters was studied based on the numerical solution of the unsteady Navier-Stokes equations. The solution algorithm was based on the finite volume method using second-order accurate difference schemes in both space and time. The TVD (Total-Variation Diminishing) form of a central-difference scheme with a flux limiter was used for the interpolation of the convective terms. The combined evaluation of the velocity and pressure fields was carried out using the PISO (Pressure Implicit Split Operator) procedure. The problem was solved using OpenFOAM (Open-source Field Operation And Manipulation) open-source toolkit libraries using the computing power of the cluster supercomputer of the V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine. It was shown that within a certain range of the diameter ratio of the orifices of the diaphragms, a circulation movement is established in the cavity between the diaphragms. The boundary layer breaks off from the surface of the first diaphragm and forms an annular shear layer. When approaching the second diaphragm, a sequence of ring vortices is formed in it, which interact with the surface of the diaphragm and lead to the emergence of tonal sound. When the ratio of the orifice diameter of the second diaphragm to the first decreases, the share of the jet’s kinetic energy, which participates in the circulation in the middle of the cavity between the diaphragms, increases. As a result, the amplitude of velocity fluctuations in the orifice of the second diaphragm decreases. When the ratio of the diameters of the orifices increases, the share of energy involved in the circulation decreases, and when a certain value of the ratio is reached, the interaction between the vortices in the shear layer and the surface of the diaphragm does not occur. As a result, the excitation of the tonal sound stops. The Strouhal number of self-oscillations practically does not change when the diameter ratio of the orifices changes. During the calculations, two different modes of self-oscillation were obtained, which is consistent with previous works.

MATHEMATICAL MODELING OF WATER MOVEMENT DURING A DAM BREAK USING THE VOF METHOD

River valleys in mountainous areas are often subject to heavy rains and melting glaciers, resulting in the risk of mudflows and the destruction of hydraulic protective structures. In order to minimize the potential risk and negative outcomes of a disaster, both on an individual and environmental scale, it is crucial to possess essential information. This includes understanding the timing, location, and extent of flooding, as well as comprehending the force of water flow impact on protective structures. In the research, the numerical process of the movement of the water flow caused by the breakthrough of the dam is investigated. A two-dimensional numerical model of water flow during a dam break was constructed using the VOF method to describe the described process. With the help of the VOF method, the movement of the water surface is captured, while maintaining the law of conservation of mass. The mathematical model consists of Reynolds-averaged incompressible Navier-Stokes equations and includes the interphase equation. The turbulent k-e model was used to close the system of equations. The numerical algorithm used is PISO (Pressure-Implicit with Splitting of Operators). The obtained numerical results agree with the experimental data, indicating the developed algorithm’s reliability and accuracy. The results are presented as comparative graphs and images showing the contour of the free surface movement along the experimental reservoir. A numerical model that has been tested in this way can provide significant support in preventing the devastating consequences of a dam break and providing timely assistance during the evacuation of the population.

Numerical analysis of air entrapment during water droplet impact on a substrate

As a liquid droplet impact on a substrate, it spreads flattens, and air may become trapped between the droplet and the substrate. This trapped air first evolves into an air film, which passes through many stages before eventually becoming an air bubble through retraction, contraction, toroid creation, pinching off, and so forth. The droplet cools while spreading across the substrate and finally freezes to create a splat. In most thermal spray coating applications, this phenomena is seen in the individual droplet solidification. The major purpose of this research is to develop an OpenFOAM solution that can model the effect of molten droplets on solid surfaces using free surface evolution. The PIMPLE algorithm, which is used in this solution, combines the PISO (Pressure Implicit with Splitting of Operators) and SIMPLE (Semi Implicit Method for Pressure-Linked Equations) approaches. In this approach, pressure–velocity equations are resolved, and the continuous surface flow model is used to simulate the surface tension force. Furthermore, the solution incorporates the dynamic contact angle. An enthalpy-based formulation that takes solidification into account is used to simulate the energy equation. The solver is validated with the aid of the available experimental results. Hydrodynamics can be used to properly simulate the various stages of air entrapment.

Influences of Liquid Viscosity and Relative Velocity on the Head-On Collisions of Immiscible Drops

Many researchers have devoted themselves to the collision processes of binary droplets of the same liquid. However, the liquids used in their study were limited, and the phase diagram of the collision outcome was depicted in terms of the Weber and the non-dimensional impact parameter. In this research, the variety of liquid was broadened, and the phase diagram characterized by the Weber number and the Ohnesorge number for head-on collisions of immiscible drops was provided. First, a ternary flow model of binary collision of immiscible drops in quiescent ambient air was proposed. Second, the three-phase fluid interface was tracked and updated by iterating the VOF (Volume of Fluid) functions. The flow field was also updated with the PISO (Pressure-Implicit with Splitting of Operators) algorithm. Finally, the effects of the impact velocity and the viscosities of the liquids on the deformation degree of droplets were analyzed.

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.

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.

Counter-flow phenomena studied by nuclear magnetic resonance (NMR) velocimetry and flow simulations

Flow patterns including counter-flow and flow reversal effects have been studied by a combination of nuclear magnetic resonance flow imaging and numerical modeling using the finite volume method in the open-source computational fluid mechanics package OpenFOAM. Two cylindrical geometries have been used: In a concentric double-cylinder system the flow reversal under oscillatory rotation of the inner cylinder has been followed, and the time evolution of the flow reversal has been studied. We find extended periods of counter-rotating flow in the gap where fluid in the inner part of the gap follows the new direction of the rotor, while the outer part takes a longer time until the viscous forces transmit the reverted flow direction outwards. The radial position of the reversal of flow direction has been monitored as a function of the oscillation angle after the turning point. In the second cylindrical geometry, the rotating bob is placed off the center and a counter-rotating vortex is detected in the wider part of the gap. At constant viscosity and eccentricity, the position of the center of the vortex was found to depend on the rotation frequency of the bob. Qualitative and quantitative agreement between experiment and laminar (nonturbulent) flow simulations has been obtained for both steady-state flow using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm and time-dependent flow using the Pressure Implicit with Splitting of Operators (PISO) algorithm.

CoronaChargingFoam: An OpenFOAM based solver for multi-physical simulations of direct unipolar diffusion charging of aerosol particles

Diffusion charging of ultrafine aerosol particles is widely used in various fields and understanding the multi-physical phenomena during the charging processes is critical to the optimization of chargers and prediction of particle evolution in particulate systems. In this work, a numerical algorithm of unipolar aerosol diffusion charging is coupled with corona discharge, a combination of electric field, current continuity and heat transfer, and fluid flow enabling the modelling of multi-physics in direct charging processes. The governing equations are discretized based on the finite volume schemes. Methods of numerically calculating the ion-particle attachment coefficients are proposed and a class named niMixedFvPatchField describing the boundary condition of ion injection on the anode is defined on the basis of OpenFOAM libraries. Iteratively strategies are applied to uncouple the governing equations and the PISO (Pressure Implicit with Splitting of Operators) algorithm is used to solve the aerosol flow equations. A new solver labelled as coronaChargingFoam in the OpenFOAM framework is developed to implement the numerical algorithm and it is further validated by comparing four test cases: Laplacian electric field, electric field-charge coupling effect, ion-particle attachment coefficients, and charging efficiencies. Acceptable agreement level in all these comparisons verifies the fidelity of the solver implementation. Program summaryProgram Title: coronaChargingFoamCPC Library link to program files:https://doi.org/10.17632/vrfky24b8m.1Licensing provisions: GNU General Public License (either version 3 or any later version)Programming language: C++External routines/libraries: OpenFOAM (http://www.openfoam.org)Nature of problem: coronaChargingFoam solves the problem of aerosol charging dynamics in direct unipolar diffusion chargers in which the equations of diffusion charging are coupled with corona discharge, a combination of electric field, current continuity and heat transfer, and fluid flow enabling the modelling of multi-physics in direct charging processes.Solution method: coronaChargingFoam employs the Finite-volume method to discretize the governing equations. Iteratively strategies are applied to uncouple the multi-physical equations and the PISO algorithm is used to solve the flow fields. Simpson method and Fibonacci approach are employed in the calculation of ion-particle attachment coefficients. A new class, niMixedFvPatchField, is defined to describe the ion-injection boundary condition on the anode.Additional comments including restrictions and unusual features: The current version of the solver can only be applied in diffusion charging for monodisperse aerosol particles. This restriction will be relaxed in near future by adopting models for polydisperse particles and incorporating field charging mechanism.

Blade-resolved numerical simulations of the NREL offshore 5 MW baseline wind turbine in full scale: A study of proper solver configuration and discretization strategies

This paper presents a blade-resolved numerical investigation of the NREL 5 MW baseline wind turbine for offshore applications including blade-tower interference, analyzing the solver configuration and its influence on the results accuracy and computational costs. The wind turbine was analyzed considering its full dimensions under the operating condition of optimal wind-power conversion efficiency for a wind speed of 10 m/s at hub height. The power production, generated thrust, and forces distribution along the blade span were estimated. The computational analyses were carried out using a Computational Fluid Dynamics (CFD) methodology employing the Finite Volume Method (FVM) implemented in the OpenFOAM software considering different approaches of the Pressure Implicit Split Operator (PISO) solver and different mesh refinement strategies for the spatial discretization process, which resulted in two different meshes being investigated. For one of the meshes, a temporal discretization analysis was performed for three different CFL numbers. The iterative form of the PISO algorithm was considered in its generic form and with an extra step to correct the pressure before the beginning of the iterative process in each time step. Both approaches can be accomplished in OpenFOAM through the PIMPLE solver facilities for the treatment of the pressure-velocity coupling in unsteady problems. The analysis of the transient incompressible turbulent flow was conducted considering the same turbulence model for all CFD investigations, the URANS k − ω SST. A numerical verification was conducted in each analysis by comparing the CFD results against values obtained using the blade element momentum theory, implemented in OpenFAST. To conclude each analysis, a computational cost investigation was carried out. Finally, for the spatial and temporal discretization investigation, detailed information regarding the flow characteristics is presented. According to the accuracy of the results obtained through the CFD simulations, the best numerical arrangement is given by the iterative PISO with face flux correction as pressure-based solver and a temporal discretization which employs lower values of CFL, such as 1 or 2.

Development and verification of meshless diffuse approximate method for simulation of compressible flow between parallel plates

A meshless numerical model is developed to simulate single-phase, Newtonian, compressible flow in the Cartesian coordinate system. The coupled set of partial differential equations, i.e., mass conservation, momentum conservation, energy conservation, and equation of state is solved by using Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO) pressure correction algorithm on an irregular node arrangement. DAM is structured by using the second-order polynomial basis functions and the Gaussian weight function, leading to the weighted least squares approximation on overlapping sub-domains. Implicit time discretization is performed for the predictor step of PISO, while in the corrector steps the equations are discretized explicitly. The numerical model is validated for flow between parallel plates with helium obeying ideal gas law. The solver’s accuracy is assessed by investigating the shape of the Gaussian weight and the number of the nodes in the local subdomains. The calculated velocity, temperature and pressure fields are compared with the Finite Volume Method (FVM) results obtained by OpenFOAM software and show a reasonably good agreement.

Numerical study on multiple bubbles condensation in subcooled boiling flow based on CLSVOF method

Numerical studies are performed to investigate the condensation behavior of single and multiple bubbles in subcooled boiling flow. An open-source code is developed to model the dynamic behavior of the bubbles in real-time. The Newtonian flow is considered and relative equations are solved employing a coupled Level Set (LS) and Volume of Fluid (VOF) method known as CLSVOF model according to the Pressure Implicit with Splitting of Operators (PISO) algorithm. Initially, the numerical findings were compared and verified by available experimental data. The result of a single bubble condensation revealed that the initial bubble size, the subcooling of liquid, and the velocity of the flow not only significantly affect the bubble deformation behavior, but also the rate of condensation. For multiple bubbles, the results revealed that due to interaction between bubbles, bubbles' dynamic condensation behavior is more complex compared to a single one. Due to this interaction, it is found that the rate of bubble condemnation and condensation process vary. Furthermore, the effects of the gradient velocity, gradient temperature, and gap between multiple bubbles on the rate of mass transfer through the condensation are studied. A critical gap between multiple bubbles is introduced. It is found that when (H∗=H/D≥2) for different bubble diameters, the effect of bubbles interaction can be ignored. Here H∗ is a dimensionless gap of center-to-center of bubbles.