Coupled Solvers for Gas-Solids Flows

2010 ◽  
pp. 204-220
Author(s):  
Berend van Wachem
Keyword(s):  
Stokes Equations ◽  
Volume Fraction ◽  
Linear Equations ◽  
Computational Cost ◽  
Navier Stokes ◽  
Source Terms ◽  
Navier Stokes Equations ◽  
Coupled Solvers ◽  
Multi Phase ◽  
Fully Coupled

In recent years, the application of coupled solver techniques to solve the Navier-Stokes equations has become increasingly popular. The main reason for this, is the increased robustness originating from the implicit and global treatment of the pressure-velocity coupling. The drawback of a coupled solver are the increase in memory requirement and the increased complexity of implementation. However, fully coupled methods are reported to have an overall favorable computational cost when a suitable pre-conditioner and algorithm for solving the resulting set of linear equations are employed. In solving multi-phase flow problems, the coupled solver approach is even more advantageous than in single-phase, due to the presence of large source terms arising from the coupling of the phases. In this chapter, various strategies for the fully coupled approach are discussed. These strategies include employing artificial compressibility, applying physically consistent cell face interpolation, and applying momentum weighted cell face interpolation. The idea behind the strategies is outlined and their advantages and disadvantages are discussed. The treatment of source terms and volume fraction in coupled methods is also shown. Finally, a number of examples of implementations and calculations are presented.

Iterative method for solving fully-coupled fluid solid systems

2010 ◽  
pp. 653-670
Author(s):  
Elisabeth Longatte
Keyword(s):  
Stokes Equations ◽  
Cross Flow ◽  
Elastic Cylinder ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Ale Formulation ◽  
Volume Method ◽  
Fully Coupled ◽  
Solid System

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in the presence of axial or cross-flow. A partitioned procedure is involved to perform the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by a finite element method in the linear elasticity framework and a fixed point method is used for the fluid solid system computation. In the present work two examples are presented to show the method robustness and efficiency.

Combined Marangoni and buoyancy convection in a porous annular cavity filled with Ag-MgO/water hybrid nanofluid

2021 ◽  
Vol 17 ◽  
Author(s):  
B. Kanimozhi ◽  
M. Muthtamilselvan ◽  
Qasem M. Al-Mdallal ◽  
Bahaaeldin Abdalla
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Axial Magnetic Field ◽  
Vertical Wall ◽  
Navier Stokes ◽  
Hybrid Nanofluid ◽  
Radial Magnetic Field ◽  
Navier Stokes Equations ◽  
Buoyancy Convection

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for other two boundaries. The effect of magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows.Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

Magnetic field effects on the slip velocity and temperature jump of nanofluid forced convection in a microchannel

2015 ◽  
Vol 230 (11) ◽  
pp. 1921-1936 ◽  
Author(s):  
Arash Karimipour ◽  
Masoud Afrand
Keyword(s):  
Magnetic Field ◽  
Forced Convection ◽  
Slip Velocity ◽  
Temperature Jump ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Computer Code ◽  
Navier Stokes ◽  
Magnetic Field Effects ◽  
Navier Stokes Equations

Forced convection of water–Cu nanofluid in a two-dimensional microchannel is studied numerically. The microchannel wall is divided into three parts. The entry and exit ones are kept insulated while the middle one has more temperature than the inlet fluid. The whole of microchannel is under the influence of a magnetic field with uniform strength of B0. Slip velocity and temperature jump are involved along the microchannel walls for different values of slip coefficient such as B = 0.001, B = 0.01, and B = 0.1 for Re = 10, Re = 50, and Re = 100. Navier–Stokes equations are discretized and numerically solved by a developed computer code in FORTRAN. Results are presented as the velocity, temperature, and Nusselt number profiles. Moreover, the effect of magnetic field on slip velocity and temperature jump is investigated for the first time in the present work. Larger Hartmann number, Reynolds number, and volume fraction correspond to more heat transfer rate; however, the effects of Ha and ϕ are more significant at higher Re.

scholarly journals Fast solvers for finite difference approximations for the stokes and navier-stokes equations

1996 ◽  
Vol 38 (2) ◽  
pp. 274-290 ◽  
Author(s):  
Dongho Shin ◽  
John C. Strikwerda
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Linear Equations ◽  
Computational Effort ◽  
Navier Stokes ◽  
Fast Solvers ◽  
Navier Stokes Equations ◽  
Finite Difference Approximations ◽  
Grid Points ◽  
First Time

AbstractWe consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The two best methods, one presented here for the first time, apparently, and a second, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes equations and incompressible Navier-Stokes equations at low Reynolds number.

scholarly journals Natural convection melting of nano-enhanced phase change material in a cavity with finned copper profile

2018 ◽  
Vol 240 ◽  
pp. 01006 ◽  
Author(s):  
Nadezhda Bondareva ◽  
Mikhail Sheremet
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Melting Process ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Dimensional Approximation ◽  
Change Material

Present study is devoted to numerical simulation of heat and mass transfer inside a cooper profile filled with paraffin enhanced with Al2O3 nanoparticles. This profile is heated by the heat-generating element of constant volumetric heat flux. Two-dimensional approximation of melting process is described by the Navier-Stokes equations in non-dimensional variables such as stream function, vorticity and temperature. The enthalpy formulation has been used for description of the heat transfer. The influence of volume fraction of nanoparticles and intensity of heat generation on melting process and natural convection in liquid phase has been studied.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

scholarly journals Sound generation in a mixing layer

1997 ◽  
Vol 330 ◽  
pp. 375-409 ◽  
Author(s):  
TIM COLONIUS ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Acoustic Field ◽  
Stokes Equations ◽  
Near Field ◽  
Mixing Layer ◽  
Navier Stokes ◽  
Far Field ◽  
Source Terms ◽  
Acoustic Analogy ◽  
Navier Stokes Equations ◽  
Acoustic Sources

The sound generated by vortex pairing in a two-dimensional compressible mixing layer is investigated. Direct numerical simulations (DNS) of the Navier–Stokes equations are used to compute both the near-field region and a portion of the acoustic field. The acoustic analogy due to Lilley (1974) is also solved with acoustic sources determined from the near-field data of the DNS. It is shown that several commonly made simplifications to the acoustic sources can lead to erroneous predictions for the acoustic field. Predictions based on the quadrupole form of the source terms derived by Goldstein (1976a, 1984) are in excellent agreement with the acoustic field from the DNS. However, despite the low Mach number of the flow, the acoustic far field generated by the vortex pairings cannot be described by considering compact quadrupole sources. The acoustic sources have the form of modulated wave packets and the acoustic far field is described by a superdirective model (Crighton & Huerre 1990). The presence of flow–acoustic interactions in the computed source terms causes the acoustic field predicted by the acoustic analogy to be very sensitive to small changes in the description of the source.

Development of a Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbomachinery Applications

2014 ◽  
Author(s):  
Luca Mangani ◽  
Marwan Darwish ◽  
Fadl Moukalled
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Computational Cost ◽  
Simple Algorithm ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Analysis And Design ◽  
Flow Problems ◽  
Matrix Coefficients

In this paper we present a fully coupled algorithm for the resolution of compressible flows at all speed. The pressure-velocity coupling at the heart of the Navier Stokes equations is accomplished by deriving a pressure equation in similar fashion to what is done in the segregated SIMPLE algorithm except that the influence of the velocity fields is treated implicitly. In a similar way, the assembly of the momentum equations is modified to treat the pressure gradient implicitly. The resulting extended system of equations, now formed of matrix coefficients that couples the momentum and pressure equations, is solved using an algebraic multigrid solver. The performance of the coupled approach and the improved efficiency of the novel developed code was validated comparing results with experimental and numerical data available from reference literature test cases as well as with segregated solver as exemplified by the SIMPLE algorithm. Moreover the reference geometries considered in the validation process cover the typical aerodynamics applications in gas turbine analysis and design, considering Euler to turbulent flow problems and clearly indicating the substantial improvements in terms of computational cost and robustness.

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