Pressure-velocity Coupling Research Articles

RK-SIMPLER: Explicit Time-Accurate Algorithm for Incompressible Flows

The SIMPLE family of algorithms has popularized the pressure-based schemes for incompressible flows and is the basis of many commercial codes. The influence of pressure on velocity is of primary importance in incompressible flows. The continuity equation implicitly dictates the pressure field, yet pressure is not a variable of the mass conservation equation. The pressure term that appears in the momentum equations is often treated as a source term. Thus, there is no explicit conservation equation for pressure. This predicament, and its remedy well known by the name “pressure–velocity coupling,” is resolved in SIMPLE and its variants by obtaining an approximate pressure correction field, which is used iteratively to correct the velocity field and/or the pressure field, seeking an overall satisfaction of the conservation equations. The approximate nature of the pressure correction equation often causes convergence issues. A new algorithm is presented here, eliminating the need for the pressure correction equation, based on the fact that if the pressure field is known, the momentum equations can be solved in any number of ways to obtain the velocity field correctly. An exact equation for the pressure field is obtained by manipulating the discretized mass and momentum equations based on SIMPLER, which is the only nonlinear equation solved iteratively in the new algorithm (RK-SIMPLER). The momentum equations are cast in the form of an ordinary differential equation suitable for time integration using Runge–Kutta stages. Once the pressure field is known, the velocity field is updated explicitly every time step without iteratively solving the momentum equations. This also means that there are no subiterations within a time step. In addition, there are no corrections for the pressure or the velocity field, and hence there is no need for the approximate pressure correction equation. The RK-SIMPLER algorithm proves that, for incompressible flows, the fundamental equation is the pressure–velocity coupled exact equation for pressure and that there is no need for the nonlinear velocity equations to be solved iteratively. Also, the new algorithm presented here uses only exact equations and requires neither underrelaxation for any of the discretized quations nor subiterations for the time integration. The only approximation is that the pressure field is held constant through the Runge–Kutta update of the velocity field. The RK-SIMPLER algorithm converges well and captures the unsteady flow features for the cases analyzed. In contrast, for steady flows, the algorithm is stable but less competitive compared to unsteady flow simulations in terms of CPU time, due to the restrictions on the allowable time step.

Устойчивость контура морского судна к опрокидыванию "волной-убийцей"

The topic of the article is the computational fluid dynamics method for investigation of the contour stability in the rogue waves. Sampling of the Reynolds-averaged Navier-Stokes (RANS) equations was done by the method of the control volumes. In order to solve the linear system of the scalar equations, an implicit Gauss-Seidel method was used. Pressure-velocity coupling was achieved by using the Pressure-Implicit with Splitting of Operators (PISO) algorithm. The volume of the fluid (VOF) model was used to solve a single set of the momentum equations and tracking of the volume fraction of each of the fluids throughout the domain. A geometric reconstruction scheme was implemented to represent the interface between the fluids using a piecewise-linear approach. In order to compute the translational and angular motion of the center of gravity of the vessel contour, the three degrees of freedom (3DOF) solver was used. Variable sampling in the time domain was used to ensure stability of the solution. A rogue wave with a single high central peak and two small side elevations was used in a numerical wave tank, which met most of the marine observations. The wavelength of the 30-meter high rogue waves, which can capsize marine vessels of a big displacement, was calculated. On the basis of the spatial spectrum of the rogue wave, equations of the velocity of the fluid flowing into the numerical wave tank were obtained. Due to the non-linear processes the rogue wave height reached its maximum and then collapsed to form a plunging breaker. The contour was positioned at a predetermined distance from the initial position of the rogue wave and when the contour met with the rogue wave, the heeling angle of the contour was calculated. On the basis of a series of numerical experiments, the distances and the wavelengths of the rogue waves capsizing the contours of the fishing vessels were calculated. It was discovered that the rogue waves with the length of 120-140 meters and high steepness capsize the contours of the fishing vessels with displacement up to 9260 tons.

Numerical modeling of non-Fourier heat transfer and fluid flow during plasma arc welding of AISI 304 stainless steel

ABSTRACTThis paper is an attempt to study the evolution of temperature profiles and weld pool geometry during plasma arc welding (PAW) by solving the transient Navier–Stokes and Energy equations. The analysis for an AISI 304 stainless steel rectangular plate was carried out using a flexible written program in Fortran. Due to the low accuracy of the Fourier heat transfer equation for short times and large dimensions, a non-Fourier form of heat transfer equation was used. Gaussian heat source is considered as the heat source model. The fluid flow in the molten pool is of interest because it can change the temperature distribution in and around the molten zone. The governing equations for fluid flow were solved by the finite-volume method in which the SIMPLE method was utilized for pressure–velocity coupling. The effects of heat conduction, fluid flow, and force actions at the weld pool were considered. Thermo-physical properties such as thermal conductivity, specific heat, and dynamic viscosity vary as a function of temperature. There are two mechanisms involved which actively cause heat transfer to the surroundings: radiation and convection heat transfer. The numerical results are compared to the experimental data. The results corroborate that the weld pool thickness in the cross section of PAW and the time taken by molten metal to reach the end of thick metal are in good agreement with the experimental measurements. Finally, the results obtained from the assumed Fourier heat transfer are compared for the same study.

Improved PISO algorithms for modeling density varying flow in conjugate fluid–porous domains

Two modified segregated PISO algorithms are proposed, which are constructed to avoid the development of spurious oscillations in the computed flow near sharp interfaces of conjugate fluid-porous domains. The new collocated finite volume algorithms modify the Rhie-Chow interpolation to maintain a correct pressure-velocity coupling when large discontinuous momentum sources associated with jumps in the local permeability and porosity are present. The Re-Distributed Resistivity (RDR) algorithm is based on spreading flow resistivity over the grid cells neighboring a discontinuity in material properties of the porous medium. The Face Consistent Pressure (FCP) approach derives an auxiliary pressure value at the fluid-porous interface using momentum balance around the interface. Such derived pressure correction is designed to avoid spurious oscillations as would otherwise arise with a strictly central discretization. The proposed algorithms are successfully compared against published data for the velocity and pressure for two reference cases of viscous flow. The robustness of the proposed algorithms is additionally demonstrated for strongly reduced viscosity, i.e., higher Reynolds number flows and low Darcy numbers, i.e., low permeability of the porous regions in the domain, for which solutions without unphysical oscillations are computed. Both RDR and FCP are found to accurately represent porous media flow near discontinuities in material properties on structured grids. Two modified segregated PISO algorithms are proposed.The Rhie-Chow interpolation is modified to maintain a correct pressure-velocity coupling when large discontinuous momentum sources are present.The proposed algorithms are successfully compared against published data for the velocity and pressure for two reference cases of viscous flow.The robustness of the proposed algorithms is additionally demonstrated for high Reynolds number flows and low Darcy numbers.

Numerical analysis of effect of magnetic field on combined surface tension and buoyancy driven convection in partially heated open enclosure

Purpose – The purpose of the paper is to investigate the effects of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillary flow in an open enclosure with localized heating from below and symmetrical cooling from the sides. Design/methodology/approach – The governing equations are discretized by the control volume method with power-law scheme and solved numerically by SIMPLE algorithm for the pressure-velocity coupling together with under-relaxation technique. Findings – In this work, it is observed that, the average Nusselt number, decreases with an increase of Hartmann number Ha, and increases with increase of Prandtl and Grashof number. At large Marangoni number Ma, a prominent secondary eddies are observed at the top of the enclosure due to the effect of surface tension. Originality/value – The study combines many external forces on thermocapillary flow.

The influence of the fabric filter layout of in a flow mass filtrate

Nowadays, more and more companies are forced to control particulate emissions to the atmosphere, due to economic reasons, legal aspects or simply the change in policy that favors ecological commitment. This new trend induces the necessity for better particle capture equipment and has made the environmental control equipment market increase by 20% in the last few years (Rocha et al., 2012). The dry capture of fine particles is carried out by filtration, and the fabric filter has become a very popular equipment because of its high efficiency and low operational cost. In the other hand, this efficiency is dependent upon proper design and layout, and the particle–filter interactions greatly influence the filtration results and the overall efficiency.In this context, this article presents the computational fluid dynamic (CFD) simulation of the airflow inside an industrial fabric filter with a set of 49 bags and a total surface area of 75 m2. The simulations were performed using the ANSYS FLUENT v13.0. This package applies the Finite Volumes Method, using the URANS approach, as well as the realizable k–ε model for the turbulence and the SIMPLE algorithm for the pressure–velocity coupling (Miltner et al., 2015). Four inlet positions were analyzed in order to determine how the internal flow profile and the equipment filtering performance depends on the inlet position. The simulations allowed concluding that the simple and double inverted feed positions led to a more satisfactory flow, considering not only the overall efficiency but also the bag's useful lifespan.

Solving turbulent diffusion flame in cylindrical frame applying an improved advective kinetics scheme

In this work, we derive a few new advective flux approximation expressions, apply them in a hybrid finite-volume-element (FVE) formulation, and solve the turbulent reacting flow governing equations in the cylindrical frame. To derive these advective-kinetic-based expressions, we benefit from the advantages of a physical influence scheme (PIS) basically, extend it to the cylindrical frame suitably, and approximate the required advective flux terms at the cell faces more accurately. The present numerical scheme not only respects the physics of flow correctly but also resolves the pressure–velocity coupling problem automatically. We also suggest a bi-implicit algorithm to solve the set of coupled turbulent reacting flow governing equations, in which the turbulence and chemistry governing equations are solved simultaneously. To evaluate the accuracy of new derived FVE–PIS expressions, we compare the current solutions with other available numerical solutions and experimental data. The comparisons show that the new derived expressions provide some more advantages over the past numerical approaches in solving turbulent diffusion flame in the cylindrical frame. Indeed, the current method and formulations can be used to solve and analyze the turbulent diffusion flames in the cylindrical coordinates very reliably.

Validation of OpenFOAM numerical methods and turbulence models for incompressible bluff body flows

A verification and validation study was performed using the open source computational fluid dynamics solver OpenFOAM version 2.0.0 for incompressible bluff body fluid flows. This includes flow over a backward facing step, a sphere in the subcritical regime, and delta wing with sharp leading edge. The study investigates solver scalability, and accuracy of numerical methods and turbulence models available in the solver. Grid verification study shows mostly monotonic convergence with averaged grid uncertainty <5% for integral quantities and up to 10% for local variables. The solver shows good strong scalability up to 192 processors on a mesh with 11M cells. The study identifies that the 2nd order linear upwind scheme is most efficient and accurate for Reynolds Averaged Navier Stokes (RANS) simulations, while the 1st/2nd order blended limited linear scheme is best for simulations employing hybrid RANS/Large Eddy Simulation (HRL). PIMPLE and SIMPLE pressure–velocity coupling methods are identified to be best for HRL and RANS simulations, respectively. The validation study showed that drag and mean velocity predictions compared within 5% of the experimental data, whereas larger errors were predicted for turbulent kinetic energy and instability frequency predictions. OpenFOAM predictions compared within 6% of FLUENT results for backward facing step and sphere cases, and performed better than the latter for the delta wing vortex breakdown predictions. Overall, OpenFOAM is found to be a reliable research solver; however, it is more sensitivity to grid quality than FLUENT, which needs to be further investigated.

Simulation of Unsteady Flow Around a Cylinder

In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.&#x0D; The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re&gt;60. The results have been compared with the available experiments and a good agreement has been found between them

A two-phase flow model for three-dimensional breaking waves over complex topography

A two-phase flow model has been developed to study three-dimensional breaking waves over complex topography, including the wave pre-breaking, overturning and post-breaking processes. The large-eddy simulation approach has been adopted in this study, where the model is based on the filtered Navier–Stokes equations with the Smagorinsky sub-grid model being used for the unresolved scales of turbulence. The governing equations have been discretized using the finite volume method, with the PISO algorithm being employed for the pressure–velocity coupling. The air–water interface has been captured using a volume of fluid method and the partial cell treatment has been implemented to deal with complex topography in the Cartesian grid. The model is first validated against available analytical solutions and experimental data for solitary wave propagation over constant water depth and three-dimensional breaking waves over a plane slope, respectively. Furthermore, the model is used to study three-dimensional overturning waves over three different bed topographies, with three-dimensional wave profiles and surface velocities being presented and discussed. The overturning jet, air entrainment and splash-up during wave breaking have been captured by the two-phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems over complex topography.

Numerical Investigation of Heat Transfer by CuO–Water Nanofluid in Rectangular Enclosures

This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO–water nanofluid and differentially heated. Conservation of mass, momentum, and energy equations are solved numerically by a control volume finite-element method using the SIMPLER algorithm for pressure–velocity coupling. The Prandtl number is fixed at 7.02, corresponding to water. Aspect ratio and solid volume fraction are varied from 0.5 to 4 and from 0% to 4%, respectively. The inclination angle is varied from 0° to 90° and used as a control parameter to investigate flow mode-transition and the accompanying hysteresis phenomenon (multi-steady solutions). It is found that the efficiency of heat transfer is improved by the addition of nanoparticles into base fluid; however, there is an optimum solid volume fraction that maximizes the heat transfer rate. Numerical results show also that the diameter of solid particle is an important parameter that affects the heat transfer efficiency; its impact is more important than the concentration itself. Effects of inclination angle on streamlines and on thermal boundary layer are presented. Combined effects of aspect ratio and inclination angle on heat transfer and hysteresis region are analyzed.

A pressure–velocity coupling approach for high void fraction free surface bubbly flows in overset curvilinear grids

SummaryA methodology for improved robustness in the simulation of high void fraction free surface polydisperse bubbly flows in curvilinear overset grids is presented. The method is fully two‐way coupled in the sense that the bubbly field affects the continuous fluid and vice versa. A hybrid projection approach is used in which staggered contravariant velocities at cell faces are computed for transport and pressure–velocity coupling while the momentum equation is solved on a collocated grid arrangement. Conservation of mass is formulated such that a strong coupling between void fraction, pressure, and velocity is achieved within a partitioned approach, solving each field separately. A pressure–velocity projection solver is iterated together with a predictor stage for the void fraction to achieve a robust coupling. The implementation is described for general curvilinear grids detailing particulars in the neighborhood to overset interfaces or a free surface. A balanced forced method to avoid the generation of spurious currents is extended for curvilinear grids. The overall methodology allows simulation of high void fraction flows and is stable even when strong packing forces accounting for bubble collisions are included. Convergence and stability in one‐dimensional (1D) and two‐dimensional (2D) configurations is evaluated. Finally, a full‐scale simulation of the bubbly flow around a flat‐bottom boat is performed demonstrating the applicability of the methodology to complex problems of engineering interest. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Effects of Number of Porous Insert, Spindle Speed and Gap Thickness on Characteristics of a Partially Porous Aerostatic Journal Bearing

The effects of the rotating speed of the spindle, the number of the porous medium inserted into the partially porous aerostatic journal bearing and the thickness of the bearing gap on the characteristics of the bearing such as the pressure distribution, the load carrying capacity and the stiffness of the bearing were studied. Based on the finite volume method and the pressure-velocity coupling scheme of the SIMPLE algorithm with the standard k-ε turbulent model, the CFD software was used to solve the Navier-Stokes equations to calculate the pressure field in the bearing gap. The computed results revealed the faster the spindle rotated, the higher the gap pressure. As the gap thickness increased, the gap pressure, the load carrying capacity and the stiffness of the bearing decreased. The more the porous inserts, the higher the gap pressure and the load carrying capacity, but the less the bearing stiffness would be.

Natural convection in an inclined rectangular enclosure filled by CuO–H2O nanofluid, with sinusoidal temperature distribution

A two-dimensional steady laminar natural convection in an inclined rectangular enclosure filled with CuO–water nanofluid is investigated numerically. The horizontal walls are thermally insulated and the left vertical side wall is heated by a spatial temperature distribution. Mass Conservation, momentum, and energy equations are solved numerically by the finite volume element method using the SIMPLER algorithm for pressure–velocity coupling. This study has been carried out for the pertinent parameters in the following ranges: inclination angle ω = 0°–90°, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (Ar = 0.25, 0.5, 1 and 2). These simulations are performed at constant Rayleigh and Prandtl numbers, they are fixed at Ra = 105and Pr = 7.02. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first, then decreases with increasing the inclination of the enclosure for aspect ratio (Ar ≥ 1) and increases with increasing the inclination angle for Ar < 1. The rate of heat transfer increases with increasing of volume fraction of nanoparticles.The subject of this paper is to study the effect of nanoparticles on heat transfer, together with the effect of the tilt angle and the aspect ratio.

Large eddy simulation of incompressible free round jet with discontinuous Galerkin method

SummaryIn the paper, discontinuous Galerkin method is applied to simulation of incompressible free round turbulent jet using large eddy simulation with eddy viscosity approach. The solution algorithm is based on the classical projection method, but instead of the solution of the Poisson equation, a parabolic equation is advanced in pseudo‐time, which provides the pressure field ensuring the proper pressure–velocity coupling. For time and pseudo‐time integration, explicit Runge–Kutta method is employed. The computational meshes consist of hexahedral elements with flat faces. Within a given finite element, all flow variables are expressed with modal expansions of the same order (including velocity and pressure). Discretisation of the viscous terms in the Navier–Stokes equations and Laplacian in the Poisson equation is stabilised with mixed finite element approach. The correctness of the solution algorithm is verified in a commonly used test case of laminar flow in 3D lid‐driven cavity. The results of computations of the free jet are compared with experimental and numerical reference data, the latter obtained from the high‐order pseudospectral code. The statistics of centerline flow velocity – mean velocity and its fluctuations – show satisfactory agreement with the reference data. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Conjugated heat transfer analysis of a film cooling passage with different rib configurations

Purpose – The purpose of this paper is to analyze the effect of thermal conductivity on gas turbine blades, and to investigate the contribution of different rib configurations to the heat flux and the film cooling effectiveness. Design/methodology/approach – The Renormalization Group (RNG) model with enhanced wall treatment was used for the turbulence modeling, and the SIMPLE algorithm was used to handle the pressure-velocity coupling. Findings – A flame-shape distribution on the internal wall provides high heat flux compared to a hawk-shape distribution; the film cooling effectiveness on the external wall is enhanced for the lateral film cooling effectiveness by heat conduction and film cooling (convection); by comparing the square-rib and pin-rib configurations, the circular-rib configuration offers a higher film cooling effectiveness on the Aluminum wall. Research limitations/implications – In the present research, the combination of internal cooling and external cooling is used to predict cooling effectiveness on film-cooled flat plate; two kinds of different plate materials are used to obtain the influence of the thermal conductivity. The successful computational method should give guidelines for potential CFD users in engineering sciences. Practical implications – The results of the paper are of engineering interest where film cooling and ribbed surfaces are applied. The successful computational method will also serve as guidelines for potential users of CFD in design as well as research and development work. Originality/value – In the present research, the combination of internal cooling and external cooling is used to predict cooling effectiveness on film-cooled flat plate; two kinds of different plate materials are used to obtain the influence of the thermal conductivity.

A numerical benchmark test for continuous casting of steel III

This paper represents a continuation of numerical results regarding the recently proposed industrial benchmark test [1], obtained by a meshless method. A part of the benchmark test, involving turbulent fluid flow with solidification in two dimensions, was elaborated in [2]. A preliminary macrosegregation upgrade was presented in [3], and in [4], a first three dimensional test was performed. Previous tests were bound to calculations in mold and sub-moldregions only. In the present paper, reference calculations in two dimensions are presented for the entire strand. The physical model is established on a set of macroscopic equations for mass, energy, momentum, species, turbulent kinetic energy, and dissipation rate. The mixture continuum model is used to treat the solidification system. The mushy zone is modeled as a Darcy porous media with Kozeny-Karman permeability relation, where the morphology of the porous media is modeled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number k-ε turbulence model, closed by the Abe-Kondoh-Nagano closure coefficients and damping functions. Lever microsegregation model is used. The numerical method is established on explicit time-stepping, collocation with scaled multiquadrics radial basis functions with adaptive selection of its shape on non-uniform five-nodded influence domains. The velocity-pressure coupling of the incompressible flow is resolved by the explicit Chorin'sfractional step method. The advantages of the method are its simplicity and efficiency, since no polygonisation is involved, easy adaptation of the nodal points in areas with high gradients, almost the same formulation in two and three dimensions, high accuracy and low numerical diffusion.

A multiple marker level-set method for simulation of deformable fluid particles

A novel multiple marker level-set method is introduced for Direct Numerical Simulation of deformable fluid particles (bubbles and droplets), which is integrated in a finite-volume framework on collocated unstructured grids. Each fluid particle is described by a separate level-set function, thus, different interfaces can be solved in the same control volume, avoiding artificial and potentially unphysical coalescence of fluid particles. Therefore, bubbles or droplets are able to approach each other closely, within the size of one grid cell, and can even collide. The proposed algorithm is developed in the context of the conservative level-set method, whereas, surface tension is modeled by the continuous surface force approach. The pressure–velocity coupling is solved by the fractional-step projection method. For validation of the proposed numerical method, the gravity-driven impact of a droplet on a liquid–liquid interface is studied; then, the binary droplet collision with bouncing outcome is examined, and finally, it is applied on simulation of gravity-driven bubbly flow in a vertical column.

Prediction–Correction Method for Parallelizing Implicit 2D Hydrodynamic Models. I: Scheme

AbstractParallel solutions of linear systems arising from velocity–pressure coupling in implicit two-dimensional (2D) hydrodynamic models are usually difficult and inefficient. Using domain decomposition, a prediction–correction parallelization method is proposed to solve such systems in parallel. It is proposed as a special method for parallelizing simulations of free-surface flows in alluvial rivers. Rather than solving a large-scale global linear system over the whole domain, the method solves sub linear systems for subdomains in two steps, prediction and correction. For free-surface flows in alluvial rivers, the gravity wave propagation over subdomains is divided into internal and external parts, moving within a subdomain and across its boundaries, respectively. The external part is assumed to be well solved at the prediction step; the whole wave propagation is then solved at the correction step using updated boundary values and initial estimates. A theoretical analysis is conducted to derive the comp...

Investigation on the relative performance of various low-Reynolds number turbulence models for buoyancy-driven flow in a tall cavity

The present study deals with the numerical investigation of turbulent buoyancy driven flow in a differentially heated rectangular cavity with adiabatic horizontal walls. The aspect ratio of cavity is 5 and the Rayleigh number based on the cavity height is 4.56 × 1010. The computations have been carried out using the finite volume method on a staggered grid and SIMPLEC algorithm for pressure–velocity coupling. The low-Reynolds number \(k-\epsilon\) model proposed by Yang and Shih (YS), low-Reynolds number \(k-\omega\) model proposed by Wilcox, and \(k-\omega\) shear stress transport (SST) model of Menter have been applied for turbulence closure. The performance comparison of different models have been carried out using the experimental, LES and various RANS results available in the literature. The computation of turbulent natural convection flow is numerically challenging due to complex flow involving laminar, transition and turbulent regions, coupling of velocity with the energy equation, and some other problems reported in literature e.g. grid dependency of solution, numerical stability problem, etc. The flux Richardson number is calculated to get an estimate of relative importance of buoyancy and shear force in different regions of flow. The shearing and swirling zones have been identified in the entire flow domain using the \(\lambda _{2}\) criterion. Based on the comparison of mean flow, heat transfer and turbulence characteristics with the available results, it has been found that YS model performs better. The better performance obtained from YS model may be due to peculiarity of model that takes into account the Kolmogorov time scale near the wall and the conventional time scale \((k/\epsilon )\) away from the wall.