Smoothed Particle Hydrodynamics (SPH) is a relatively new meshless numerical approach which has attracted significant attention in the last two decades. Compared with the conventional mesh-based computational fluid dynamics (CFD) methods, the SPH approach exhibits some unique advantages in modeling multiphysic flows and associated transport phenomena due to its capabilities of handling complex boundary evolution as well as modeling complicated physics in a relatively simple manner. On the other hand, as SPH is still a developing CFD method, it is crucial to identify its advantages and limitations in modeling realistic multiphysic flow problems of real life and of industrial interest. Toward this end, this work aims at summarizing the motivations behind utilizing the SPH method in an industrial context, making the state-of-the-art of the present application of this method to industrial problems, as well as deriving general conclusions regarding its assets and limitations and stressing the remaining challenges in order to make it an hand-on computational tool.
In this study MHD effect on natural convection heat transfer in an enclosure filled with nanofluid is investigated. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern, isotherms and concentration. The governing equations are solved via Control Volume based Finite Element Method. The inner and outer circular walls are maintained at constant temperatures while two other walls are thermally insulated. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effect of Hartmann number ( = 0, 30, 60 and 100), buoyancy ratio number ( = 0.1–4) and Lewis number ( = 2, 4, 6 and 8) on streamline, isotherm, isoconcentration and heatline are examined. Also a correlation for Nusselt number corresponding to active parameters is presented. The results indicate that Nusselt number is an increasing function of buoyancy ratio number but it is a decreasing function of Lewis number and Hartmann number. Also it can be concluded that as buoyancy ratio number increases the effects of other active parameters are more pronounced.
The nanofluid boundary layer flow over a rotating disk is the main concern of the present paper. Unlike the traditional Von Karman problem in which a Newtonian regular fluid is assumed, water-based nanofluids containing nanoparticle volume fraction of Cu, Ag, CuO, Al O and TiO are taken into account. The governing equations of motion are reduced to a set of nonlinear differential equations by means of the conventional similarity transformations which are later treated by a spectral Chebyshev collocation numerical integration scheme. The flow and temperature fields as well as the shear stress and heat transfer characteristics are computed for certain values of the nanoparticle volume fraction. A comparative analysis is made in terms of shear stress and cooling properties of considered nanofluids. A mathematical analysis is eventually provided to prove why the nanofluids are advantageous as far as the heat transfer enhancement is concerned. Although the physical features highly rely on the type of the considered nanoparticles, it is found that the heat transfer is greatly enhanced by addition of nanofluid Cu.
► Effects of Brownian motion and thermophoresis are taken into consideration. ► Equations are solved using fourth order Runge–Kutta method with shooting technique. ► Slip boundary conditions for velocity, thermal and concentration boundary condition are used. ► Local Nusselt number decreases with an increase in Brownian motion Nb and thermophoresis parameter Nt. In this analysis, the boundary layer flow and heat transfer over a permeable stretching sheet due to a nanofluid with the effects of magnetic field, slip boundary condition and thermal radiation have been investigated. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. thermal radiation parameter , Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, Eckert number Ec, magnetic parameter and slip parameters. Similarity transformation is used to convert the governing non-linear boundary-layer equations into coupled higher order non-linear ordinary differential equations. These equations are numerically solved using fourth order Runge–Kutta method along with shooting technique. An analysis has been carried out to elucidate the effects of governing parameters corresponding to various physical conditions. Numerical results are obtained for distributions of velocity, temperature and concentration, as well as, for the skin friction, local Nusselt number and local Sherwood number for several values of governing parameters. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nt and Lewis number Le, but it decreases as the values of Nb increase. Besides, it was found that the surface temperature of a sheet increases with an increase in the Eckert number Ec. A comparison with previous studies available in the literature has been done and we found an excellent agreement with it.
The problem of double stratification on boundary layer flow and heat transfer induced due to a nanofluid over a vertical plate is investigated. The transport equations employed in the analysis include the effect of Brownian motion, thermophoresis, thermal stratification and solutal stratification parameters. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms by similarity variables. The resulting systems of equations are then solved numerically using Keller-box method. The solution for the temperature and nanoparticle concentration depends on parameters viz. thermal and solutal stratification parameters, Prandtl number , Lewis number , Brownian motion , buoyancy ratio parameter and the thermophoresis parameter . Numerical results are obtained for velocity, temperature and concentration distribution as well as the local Nusselt number and Sherwood number. It is found that the local Nusselt number and Sherwood number decrease with an increase in stratification parameters and . However, the skin friction coefficient increases with an increase in mass stratification parameter and decreases with an increase in thermal stratification parameter . The obtained results are displayed both graphically tabular form to illustrate the effect of the stratification parameters on the dimensionless velocity, wall temperature and concentration. The numerical results are compared and found to be in good agreement with previous published result on special cases of the problem.
Many boundary-layer flows are governed by one or coupled nonlinear ordinary differential equations (ODEs). Currently, a Mathematica package BVPh 2.0 is issued for nonlinear boundary-value/eigenvalue problems with boundary conditions at multiple points. The BVPh 2.0 is based on an analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM), and is free available online. In this paper, the BVPh 2.0 is successfully applied to solve magnetohydrodynamic (MHD) Falkner–Skan flow of nano-fluid past a fixed wedge in a semi-infinite domain, and the influence of physical parameters on the considered flows is investigated in details. Physically, this work deepens and enriches our understandings about the magnetohydrodynamic Falkner–Skan flows of nano-fluid past a wedge. Mathematically, it illustrates the potential and validity of the BVPh 2.0 for complicated boundary-layer flows.
Many boundary-layer flows are governed by one or coupled nonlinear ordinary differential equations (ODES). Currently, a Mathematica package BVPh 2.0 is issued for nonlinear boundary-value/eigenvalue problems with boundary conditions at multiple points. The BVPh 2.0 is based on an analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM), and is free available online. In this paper, the BVPh 2.0 is successfully applied to solve magnetohydrodynamic (MHD) Falkner-Skan flow of nano-fluid past a fixed wedge in a semi-infinite domain, and the influence of physical parameters on the considered flows is investigated in details. Physically, this work deepens and enriches our understandings about the magnetohydrodynamic Falkner-Skan flows of nano-fluid past a wedge. Mathematically, it illustrates the potential and validity of the BVPh 2.0 for complicated boundary-layer flows. (C) 2015 Elsevier Ltd. All rights reserved.
Summation-by-parts (SBP) operators have a number of properties that make them an attractive option for higher-order spatial discretizations of partial differential equations. In particular, they enable the derivation of higher-order boundary closures leading to provable time stability. When implemented on multi-block structured meshes in conjunction with simultaneous approximation terms (SATs)—penalty terms that impose boundary and interblock-coupling conditions in a weak sense—they offer additional properties of value, even for second-order accurate schemes and steady problems. For example, they involve low communication overhead for efficient parallel algorithms and relax the continuity requirements of both the mesh and the solution across block interfaces. This paper provides a brief history of seminal contributions to, and applications of, SBP-SAT methods followed by a description of their properties and a methodology for deriving SBP operators for first derivatives and second derivatives with variable coefficients. A procedure for deriving SATs is also provided. Practical aspects are discussed, including artificial dissipation, transformation to curvilinear coordinates, and application to the Navier–Stokes equations. Recent developments are reviewed, including a variational interpretation, the connection to quadrature rules, functional superconvergence, error estimates, and dual consistency. Finally, the connection to quadrature rules is exploited to provide a generalization of the SBP concept to a broader class of operators, enabling a unification and rigorous development of SATs for operators such as nodal-based pseudo-spectral and some discontinuous Galerkin operators.
The objectives of this study are to: (1) quantify the influence of sheet/cloud cavitation on the hydrodynamic coefficients and surrounding flow turbulent structures, (2) provide a better insight in the physical mechanisms that govern the dynamics and structure of a sheet/cloud cavity, (3) improve the understanding of the interaction between unsteady cavitating flow, vortex dynamics and hydrodynamic performance. Results are presented for a 3D Clark-Y hydrofoil fixed at an angle of attack of = 8 degrees at a moderate Reynolds number, = 7 × 10 , for both subcavitating ( = 2.00) and sheet/cloud cavitating conditions ( = 0.80). The experimental studies were conducted in a cavitation tunnel at Beijing Institute of Technology, China. The numerical simulations are performed via the commercial code CFX using a transport equation-based cavitation model, the turbulence model utilizes the Large Eddy Simulation (LES) approach with the Wall-Adapting Local Eddy-viscosity model. The results show that numerical predictions are capable of capturing the initiation of the cavity, growth toward the trailing edge, and subsequent shedding, in accordance with the quantitative features observed in the experiment. The detailed analysis of the vorticity transport equation shows strong correlation between the cavity and vorticity structure, the transient development of sheet/cloud cavitation has significantly changed the interaction between the leading edge and trailing edge vortices, and hence the magnitude as well as the frequency of the hydrodynamic load fluctuations. Compared to the subcavitating case, the sheet/cloud cavitation leads to much higher turbulent boundary layer thickness and substantial increase in velocity fluctuation.
A new three-dimensional numerical wave tank is developed for the calculation of wave propagation and wave hydrodynamics by solving the incompressible Navier–Stokes equations. The free surface is modeled with the level set method based on a two-phase flow approximation, allowing for the simulation of complex phenomena such as wave breaking. The convection terms of the momentum and the level set equations are discretized with the finite difference version of the fifth-order WENO scheme. Time stepping is handled with the third-order TVD Runge–Kutta scheme. The equations are solved on a staggered Cartesian grid, with a ghost cell immersed boundary method for the treatment of irregular cells. Waves are generated at the inlet and dissipated at the numerical beach with the relaxation method. The choice of the numerical grid and discretization methods leads to excellent accuracy and stability for the challenging calculation of free surface waves. The performance of the numerical model is validated and verified through several benchmark cases: solitary wave interaction with a rectangular abutment, wave forces on a vertical cylinder, wave propagation over a submerged bar and plunging breaking waves on a sloping bed.
The treatment of inlet conditions for LES is a complex problem, but of extreme importance as, in many cases, the fluid behaviour within the domain is determined in large part by the inlet behaviour. The reason why it is so difficult to formulate inlet conditions is because the inlet flow must include a stochastically-varying component: ideally this component should ‘look’ like turbulence whilst at the same time be as simple as possible to implement and modify. We review methods for accomplishing this reported in the literature, these being ‘precursor simulation’ methods and ‘synthesis’ methods, and implement our own novel versions of these using the code OpenFOAM. Conclusions have been drawn about the relative merits of the different approaches, based on the physical realism of the results and the ease of construction and use.
In this paper, we propose a computational fluid–structure interaction (FSI) framework for the simulations of the interaction between free-surface flow and floating structures, such as offshore wind turbines. The framework is based on a suitable combination of the finite element method (FEM) and isogeometric analysis (IGA), and has good efficiency, accuracy and robustness characteristics. The free-surface phenomena are modeled using the Navier–Stokes equations of incompressible two-fluid flow in conjunction with the level set method. The FEM-based moving-domain ALE-VMS technique is employed to discretize the fluid mechanics equations, while the IGA-based rotation-free shell and beam/cable formulation is employed to model the mechanics of floating structures. The kinematic and traction compatibility at the fluid–structure interface is handled by means of a recently-developed augmented Lagrangian FSI formulation with formal elimination of the Lagrange multiplier variable. A quasi-direct coupling strategy is adopted to handle the large added mass, and implemented by means of a matrix-free technique. The mathematical formulation of the FSI problem and its algorithmic implementation are described in detail, and two numerical test cases are presented. The first case is a free-surface-flow benchmark example of a solitary wave impacting a fixed, rigid platform. The second case is a set of full-scale free-surface-FSI simulations of the OC3-Hywind floating wind turbine design subjected to wave action. The computational results are compared with experimental and simulation data, with good agreement achieved in all cases where such data was available. Wind-turbine computations in the regime of high-amplitude waves are also presented.
This paper presents the results of validation of an open source Direct Simulation Monte Carlo (DSMC) code for general application to rarefied gas flows. The new DSMC code, called , has been written within the framework of the open source C++ CFD toolbox OpenFOAM. The main features of code include the capability to perform both steady and transient solutions, to model arbitrary 2D/3D geometries, and unlimited parallel processing. Test cases have been selected to cover a wide range of benchmark examples from 1D to 3D. These include relaxation to equilibrium, 2D flow over a flat plate and a cylinder, and 3D supersonic flows over complex geometries. In all cases, shows very good agreement with data provided by both analytical solutions and other contemporary DSMC codes.
We quantitatively evaluate the capability and accuracy of the lattice Boltzmann equation (LBE) for modeling flow through porous media. In particular, we conduct a comparative study of the LBE models with the multiple-relaxation-time (MRT) and the Bhatnagar–Gross–Krook (BGK) single-relaxation-time (SRT) collision operators. We also investigate several fluid–solid boundary conditions including: (1) the standard bounce-back (SBB) scheme, (2) the linearly interpolated bounce-back (LIBB) scheme, (3) the quadratically interpolated bounce-back (QIBB) scheme, and (4) the multi-reflection (MR) scheme. Three-dimensional flow through two porous media—a body-centered cubic (BCC) array of spheres and a random-sized sphere-pack—are examined in this study. For flow past a BCC array of spheres, we validate the linear LBE model by comparing its results with the nonlinear LBE model. We investigate systematically the viscosity-dependence of the computed permeability, the discretization error, and effects due to the choice of relaxation parameters with the MRT and BGK schemes. Our results show unequivocally that the MRT–LBE model is superior to the BGK–LBE model, and interpolation significantly improves the accuracy of the fluid–solid boundary conditions.
We present an extensive analysis of the performance of the Volume of Fluid (VOF) method, as implemented in OpenFOAM, in modeling the flow of confined bubbles and droplets (“segmented flows”) in microfluidics. A criterion for having a sufficient grid solution to capture the thin lubricating film surrounding non-wetting bubbles or droplets, and the precise moment of breakup or coalescence is provided. We analyze and propose optimal computational settings to obtain a sharp fluid interface and small parasitic currents. To show the usability of our computational rules, numerical simulations are presented for three benchmark cases, the steady motion of bubbles in a straight two-dimensional channel, the formation of bubbles in two- and three-dimensional T-junctions, and the breakup of droplets in three-dimensional T-junctions. An error analysis on the accuracy of the computations is presented to probe the efficacy of the VOF method. The results are in good agreement with published experimental data and experimentally-validated analytical solutions.
Many natural terrains have complicated surface topography. The simulation of steep-fronted flows that occur after heavy rainfall flash floods or as inundation from dyke breaches is usually based on the non-linear shallow water equations in hyperbolic conservation form. Particular challenges to numerical modellers are posed by the need to balance correctly the flux gradient and source terms in Godunov-type finite volume shock-capturing schemes and by the moving wet–dry boundary as the flood rises or falls. This paper presents a Godunov-type shallow flow solver on adaptive quadtree grids aimed at simulating flood flows as they travel over natural terrain. By choosing the stage and discharge as dependent variables in the hyperbolic non-linear shallow water equations, a new deviatoric formulation is derived that mathematically balances the flux gradient and source terms in cases where there are wet–dry fronts. The new formulation is more general in application than previous approaches. Three benchmark tests are used to validate the solver, and include steady flow over a submerged hump, flow disturbances propagating over an elliptical-shaped hump, and free surface sloshing motions in a vessel with a parabolic bed. The model is also used to simulate the propagation of a flood due to a dam break over an initially dry floodplain containing three humps.
A computational free-surface flow framework that enables 3D, time-dependent simulation of horizontal-axis tidal-stream turbines (HATTs) is presented and deployed using a complex-geometry HATT. Free-surface flow simulations using the proposed framework, without any empiricism, are able to accurately capture the effect of the free surface on the hydrodynamic performance of the turbine, as demonstrated through excellent agreement with the experimental data. To carry out the free-surface computations, we have developed a novel level-set redistancing procedure compatible with the sliding-interface technique used for handling the rotor-stator interaction in the HATT full-machine simulations. To illustrate the versatility of the proposed approach, additional computations are carried out where the HATT is subjected to wave action.
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.