Intelligent computing and simulation of magnetic field influence on Casson fluid flow in complex geometries

HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries

The generation of an orthogonal grid by the use of a boundary integral technique

Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical solver is developed employing the meshless framework to efficiently compute the hydrodynamic stability of fluid flows in complex geometries. The developed method is tested on two cases of Taylor–Couette flows. The concentric case represents the parallel flow assumption incorporated in the Orr–Sommerfeld model and the eccentric Taylor–Couette flow incorporates a non-parallel base flow with separation bubbles. The method was validated against earlier works by Marcus [“Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment,” J. Fluid Mech. 146, 45–64 (1984)], Oikawa et al. [“Stability of flow between eccentric rotating cylinders,” J. Phys. Soc. Jpn. 58, 2355–2364 (1989)], Leclercq et al. [“Temporal stability of eccentric Taylor–Couette–Poiseuille flow,” J. Fluid Mech. 733, 68–99 (2013)], and Mittal et al. [“A finite element formulation for global linear stability analysis of a nominally two-dimensional base flow,” Numer. Methods Fluids 75, 295–312 (2014)]. The results for the two cases and the effectiveness of the method are discussed in detail. The method is then applied to Taylor–Couette flow in an elliptical enclosure and the stability of the flow is investigated.

The BEACON code is a Best Estimate Advanced Containment code which being developed by EG and G, Idaho, Inc., at the Idaho National Engineering Laboratory. The program is designed to perform a best estimate analysis of the flow of a mixture of air, water, and steam in a nuclear reactor containment system under loss-of-coolant accident conditions. The code can simulate two-component, two-phase fluid flow in complex geometries using a combination of two-dimensional, one-dimensional, and lumped-parameter representations for the various parts of the system. The current version of BEACON, which is designated BEACON/MOD2A, contains mass and heat transfer models for wall film and for wall conduction. It is suitable for the evaluation of short term transients in PWR dry containment systems. This manual describes the models employed in BEACON/MOD2A and specifies code implementation requirements. It provides application information for input data preparation and for output data interpretation.

The spectral-element method (SEM), is a high-order numerical method with the ability to accurately simulate fluid flows in complex geometries. SEM has opened the possibility to study – in great detail – fluid phenomena known to be very sensitive to discretization errors, e.g. flows undergoing pressureinduced separation [4]. Recently, Cherry et al. [1] performed experiments using Magnetic Resonance Velocimetry (MRV) of turbulent diffuser flow exhibiting unsteady three-dimensional separation at Re = 10 000 based on bulk velocity and height of the inflow duct. Two geometries with different opening angles were investigated and it was found that the flow was extremely sensitive to slight changes in the geometrical setup. To understand this sensitivity and to analyze its causes, we present a direct numerical simulation (DNS) of one of these cases (denoted by “Diffuser 1“ in [1]) by means of the SEM. Here, we focus on careful analysis of mean flow results in order to assess the quality of the simulation data.KeywordsDirect Numerical SimulationDiscretization ErrorGeometrical SetupMagnetic Resonance VelocimetryFriction Reynolds NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

ABSTRACTThis article presents a new element-based finite-volume discretization approach for the solution of incompressible flow problems on co-located grids. The proposed method, called the method of proper closure equations (MPCE), employs a proper set of physically relevant equations to constrain the velocity and pressure at integration points. These equations provide a proper coupling between the nodal values of pressure and velocity. The final algebraic equations are not segregated in this study and are solved in a fully coupled manner. To show the applicability and performance of the method, it is tested on several steady two-dimensional laminar-flow benchmark cases. The results indicate that the method simulates the fluid flow in complex geometries and on nonorthogonal computational grids accurately. Also, it is shown that the method is robust in the sense that it does not require severe underrelaxation even at relatively high Reynolds numbers. In each test case, the required underrelaxation parameter, the number of iterations, and the corresponding CPU time are reported.

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

PurposeThe present investigation aims to deal with the study of unsteady, heat-generating/-absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium in the presence of cross-diffusion effects.Design/methodology/approachA numerical computation for the governing equations has been performed using implicit finite difference method of Crank–Nicolson type.FindingsThe influence of various physical parameters on velocity, temperature and concentration distributions is illustrated graphically, and the physical aspects are discussed in detail. Numerical results for average skin-friction, Nusselt number and Sherwood number are tabulated for the pertaining physical parameters. Results indicate that Soret and Dufour effects have notable influence on heat and mass transfer characteristics of the fluid when the temperature and concentration gradients are high. It is also observed that the consideration of heat generation/absorption plays a vital role in predicting the heat transfer characteristics of moving fluids.Research limitations/implicationsConsider a two-dimensional, unsteady, free convective flow of an incompressible Casson fluid over a vertical cone and a flat plate saturated with non-Darcy porous medium. The fluid properties are assumed to be constant except for density variations in the buoyancy force term. The fluid flow is moderate and the permeability of the medium is assumed to be low, so that the Forchheimer flow model is applicable.Practical implicationsThe flow of Casson fluids (such as drilling muds, clay coatings and other suspensions, certain oils and greases, polymer melts and many emulsions), in the presence of heat transfer, is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs.Social implicationsIn the heat and mass transfer investigations, the Casson fluid model is found to be accurately applicable in many practical situations in the wings of polymer processing industries and biomechanics, etc.; some prominent examples are silicon suspensions, suspensions of bentonite in water and lithographic varnishes used for printing inks.Originality/valueThe motivation of the present study is to bring out the effects of heat source/sink, Soret and Dufour effects on chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium. The flow of Casson fluids (such as certain oils and greases, polymer melts and many emulsions) in the presence of heat transfer is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. A numerical computation for the governing equations has been performed using implicit finite difference method of the Crank–Nicolson type.

Prediction of Heat and Fluid Flow in Complex Geometries Using General Orthogonal Coordinates

Large scale unsteady motions in many practical engineering flows play a very important role and it is very unlikely that these unsteady flow features can be captured within the framework of Reynolds averaged Navier–Stokes approach. Large‐eddy simulation (LES) has become, arguably, the only practical numerical tool for predicting those flows more accurately since it is still not realistic to apply DNS to practical engineering flows with the current and near future available computing power.Numerical methods for the LES of turbulent flows in complex geometry have been developed and applied to predict practical engineering flows successfully. The method is based on body‐fitted curvilinear co‐ordinates with the contravariant velocity components of the general Navier–Stokes equations discretized on a staggered orthogonal mesh. For incompressible flow simulations the main source of computational expense is due to the solution of a Poisson equation for pressure. This is especially true for flows in complex geometry. A multigrid 3D pressure solver is developed to speed up the solution. In addition, the Poisson equation for pressure takes a simpler form with no cross‐derivatives when orthogonal mesh is used and hence resulting in increased convergence rate and producing more accurate solutions. Copyright © 2004 John Wiley & Sons, Ltd.

An immersed boundary method for direct and large eddy simulation of stratified flows in complex geometry

A strongly conservative finite-volume procedure is presented for flows in complex geometries. The technique is based on a complete transformation of the governing equations, and physical velocity components, rather than the traditionally used Cartesian velocity components, are used as primitive variables. It was found that projecting the discretized vector transport equation in the direction of the covariant base vectors eliminated two substantial difficulties associated with flows in complex geometries. These difficulties stem from the presence of cross-pressure gradient terms and the need for a transformation between the different types of curvilinear velocity components in the mass conservation equation. It is shown that the present formulation ensures that the computational scheme is diagonally dominant. It was found that partially implicit treatment of nonorthogonal diffusion terms improved the convergence rate primarily for high-cell-Reynolds-number values. For nonstaggered grids, a new sol...

The stability of buoyant flow in an infinite extended vertical fluid layer bounded by impermeable conducting isothermal rigid walls, known as magnetic field influence on Casson fluid flow in rotating convection, is investigated. A system of governing equations (Navier–Stokes, heat, and induction ones) is solved with isothermal rigid boundary conditions. When the majority of electrically conducting fluids are extremely small, the stability of governing equations can be simplified by taking the smallness of magnetic Prandtl number into account. In linear stability, the Chebyshev collocation method is used to solve numerically the system of eigenvalue problems. The Casson fluid parameter, Chandrasekhar number, magnetic Prandtl number, and Taylor number all have destabilizing effects on the system's basic velocity and basic magnetic field, resulting in instability. The critical Rayleigh number (Rc), critical wave number (ac), and critical wave speed (cc) are calculated using the influence of governing parameters. The Casson fluid parameter and magnetic Prandtl number were found to stabilize stationary disturbances in neutral stability curves.

In the present study, the dynamic Vreman model based on the global equilibrium between the subgrid-scale dissipation and the viscous dissipation with a global model coefficient are applied to large eddy simulation of turbulent flow in complex geometries. Distributions of pressure, velocity and vorticity as well as some flow structure are gained, which is helpful to examine the performance of SGS model and understand the flow characters in complex geometries.

A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows