Artificial Compressibility Algorithm Research Articles

Hydrothermal and entropy generation analyses of natural convection of nano-encapsulated phase change materials suspension in a cavity subjected to the localized heating

Being heated electronic components significantly reduces their efficiency, and thus requiring high-efficient cooling strategies to keep such devices operating at an optimal temperature level. The present study is devoted to investigating the cooling performance of water-based nano-encapsulated phase change materials (NePCMs) suspension in the presence of a heat source with uniform temperature. The nano-sized PCM capsules are constructed by n-nonadecane as the core and polyurethane for the protective shell. The n-nonadecane is capable of absorbing/releasing a significant quantity of latent heat in the process of its phase transition, which is actually beneficial for improving the heat transfer performance. The home developed FORTRAN program based on the finite volume method (FVM) combined with the artificial compressibility algorithm is employed to solve the nonlinear coupled equations for fluid flow and heat transfer. The influences of the Rayleigh number (103≤Ra≤105), the Stefan number (0.1≤Ste≤0.9), the volume fraction of the nano-capsules (0≤ϕ≤0.04), and the heating position (0.25≤a≤0.75) on the hydrothermal behavior and entropy generation are explored. The findings reveal that there exists a capsule loading interval wherein the heat transfer enhancement can be achieved, but beyond that range, the deterioration of cooling performance may occur. Moreover, the contribution of suspending NePCMs to the heat transfer improvement is greatly more noticeable at low Rayleigh number, and particularly for the arrangement of upper heating. The average Nusselt number decreases with the increment of the Stefan number, and the variation approximately follows an exponential change for all considered Rayleigh numbers and heating positions. Concerning the entropy generation, it is essentially contributed by the heat transfer irreversibility, and the region with high irreversibility is always located around the intersection of the heated surface and the insulated vertical wall. This research can provide theoretical guidance for cooling the electronic components by utilizing the NePCMs suspension.

Two- and three-dimensional simulation of natural convection flow of CuO-water in a horizontal concentric annulus considering nanoparticles’ Brownian motion

A numerical study of two- and three-dimensional natural convection flows of copper oxide water-based nanofluid in a horizontal concentric annulus has been conducted to investigate the influence of Rayleigh number () and nanoparticles volume fraction () on both hydrodynamic and thermal behaviors, and further to examine the difference between two- and three-dimensional simulations. The Brownian motion of nanoparticles is considered in evaluating the effective thermal conductivity and dynamic viscosity of nanofluid. The mass, momentum and energy conservation equations are solved numerically by the finite volume method together with the artificial compressibility algorithm for pressure-velocity coupling. The obtained results indicate that the addition of nanoparticles in water leads to an existence of the general flow structure, but causes more complicated changes in flow intensity. The thermal performance of the nanofluid increases with increment of nanoparticles volume fraction up to a critical particle loading at which the maximum heat transfer occurs. The corresponding maximum heat transfer enhancement, at three different Rayleigh numbers (), is approximately 17.2% (19.0%), 11.2% (11.1%), and 13.6% (12.8%) for 2-D (3-D) configuration.

An upwind vertex centred finite volume algorithm for nearly and truly incompressible explicit fast solid dynamic applications: Total and Updated Lagrangian formulations

This paper presents an explicit vertex centred finite volume method for the solution of fast transient isothermal large strain solid dynamics via a system of first order hyperbolic conservation laws. Building upon previous work developed by the authors, in the context of alternative numerical discretisations, this paper explores the use of a series of enhancements (both from the formulation and numerical standpoints) in order to explore some limiting scenarios, such as the consideration of near and true incompressibility. Both Total and Updated Lagrangian formulations are presented and compared at the discrete level, where very small differences between both descriptions are observed due to the excellent discrete satisfaction of the involutions. In addition, a matrix-free tailor-made artificial compressibility algorithm is discussed and combined with an angular momentum projection algorithm. A wide spectrum of numerical examples is thoroughly examined. The scheme shows excellent (stable, consistent and accurate) behaviour, in comparison with other methodologies, in compressible, nearly incompressible and truly incompressible bending dominated scenarios, yielding equal second order of convergence for velocities, deviatoric and volumetric components of the stress.

A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics

In previous work (Lee et al., 2016, 2017), Lee et al. introduced a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics with special emphasis on the treatment of near incompressibility. A first order system of hyperbolic equations was presented expressed in terms of the linear momentum and the minors of the deformation, namely the deformation gradient, its co-factor and its Jacobian. Taking advantage of this representation, the suppression of numerical deficiencies (e.g. spurious pressure, long term instability and/or consistency issues) was addressed through well-established stabilisation procedures. In Lee et al. (2016), the adaptation of the very efficient Jameson–Schmidt–Turkel algorithm was presented. Lee et al. (2017) introduced an adapted variationally consistent Streamline Upwind Petrov–Galerkin methodology. In this paper, we now introduce a third alternative stabilisation strategy, extremely competitive, and which does not require the selection of any user-defined artificial stabilisation parameter. Specifically, a characteristic-based Riemann solver in conjunction with a linear reconstruction procedure is used, with the aim to guarantee both consistency and conservation of the overall algorithm. We show that the proposed SPH formulation is very similar in nature to that of the upwind vertex centred Finite Volume Method presented in Aguirre et al. (2015). In order to extend the application range towards the incompressibility limit, an artificial compressibility algorithm is also developed. Finally, an extensive set of challenging numerical examples is analysed. The new SPH algorithm shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding second order of convergence for velocities, deviatoric and volumetric components of the stress.

Numerical analysis of three-dimensional MHD natural convection flow in a short horizontal cylindrical annulus

A numerical study of three-dimensional (3D) MHD laminar flow in a short horizontal cylindrical annulus has been performed to characterize the impacts of a uniform axial magnetic field on both hydrodynamic and thermal behaviors. This configuration corresponds to a horizontal annular mold containing molten iron or low carbon steel in electromagnetic casting (EMC). Complex nonlinear governing equations are solved numerically by means of the finite volume method based on artificial compressibility algorithm. The induced electric potential caused by the magnetic field is considered. Results show that a typical 3D steady spiral flow arises and the symmetry breaking occurs under a weak magnetic field of Ha < 10. As the Hartmann number increases, the spiral flow is distinctly suppressed, and then it changes to a helical flow with two transverse cells adjacent to each of the end walls. Correspondingly, the flow patterns and isotherms of fluid become symmetric with respect to the mid-axial plane of the annulus. Further increasing the Hartmann number, the fluid particle trajectories essentially lie in the cross-section of the annulus, as for two-dimensional solutions, with an extremely small axial dependency. In addition, both the values of local Nusselt number at the isothermal walls and its axial dependency, mainly in the upper region (−38π≤φ≤38π), are significantly affected by the magnetic field. The results of the present work can be useful in producing high-quality products by magnetic control.

Instability investigation of creeping viscoelastic flows between the rotating cylinders

In this paper, instability in the creeping viscoelastic flow between the rotating cylinders is investigated numerically. Due to the low speed of flow field, the second order fluid (SOF) model is used as the constitutive equation and the governing equations are solved by a second order finite difference method based on the artificial compressibility algorithm in a staggered mesh. The effects of normal stress differences on the flow stability are investigated for a wide range of gap ratios. Unlike the previous studies, the origin and mechanism of flow instability resulted from normal stress differences are investigated in detail. Numerical results indicate that the hoop stress and radial-normal stress components are appeared in viscoelastic flows between the rotating cylinders and they have an important role on the flow stability.

On the origin of viscoelastic Taylor-Couette instability resulted from normal stress differences

In this paper, the effect of normal stress differences on the viscoelastic Taylor-Couette instability is studied numerically. The governing equations are discretized using FTCS finite difference method on a staggered mesh based on the artificial compressibility algorithm. Using the CEF model as the constitutive equation and the Carreau-Yasuda model as the viscometric functions, the flow between rotating cylinders has been studied for a range of radius ratios, Taylor numbers and rheological properties. It is shown that increasing the first normal stress difference destabilizes the flow field while increasing the negative second normal stress difference stabilizes the flow field. The main contribution of the current study is an answer to this question: How do the first and second normal stress differences affect the stability of viscoelastic flow between rotating cylinders? For this reason, we used the order of magnitude technique to obtain a force balance relation in the core region of flow. Based on this relation and numerical simulation, the origin of viscoelastic Taylor-Couette instability resulted from normal stress differences are studied in detail. Furthermore, a two dimensional analytical solution for the main flow velocity component between finite rotating cylinders is carried out considering the end effect of stationary walls.

Effects of optical parameters on fluid flow and heat transfer of participating magnetic fluid

Effects of optical parameters on fluid flow and heat transfer of participating magnetic fluid are investigated in this work. Instead of Rosseland approximation, the source term of radiative flux is obtained by solving radiative transfer equation (RTE). In the physical model, all walls of a square cavity are defined as opaque and diffusively reflection. The fluid in the cavity has characteristics of gray, absorbing, emitting, scattering and electrically conducting. The continuity equation and momentum equation are solved by artificial compressibility algorithm based on finite volume method (FVM). FVM is also used to solve the energy equation, and the RTE is solved by discrete ordinates method (DOM) with SSDN quadrature scheme to discretize the solid angle. The results are presented in graphical. Streamlines, isotherms and comparative results of heat transfer rate show the effects of optical parameters on fluid flow and heat transfer.

Instability investigation of creeping viscoelastic flow in a curved duct with rectangular cross-section

In this paper, instability in the creeping viscoelastic flow inside a curved rectangular duct is investigated numerically for the first time. Using the Criminale–Eriksen–Filbey (CEF) model as the constitutive equation, the governing equations are solved by a second order of finite difference method based on the artificial compressibility algorithm in a staggered mesh. The effects of normal stress differences on the flow stability are investigated. The numerical results obtained indicate that the increase of the negative second normal stress difference of viscoelastic fluid causes stability in the creeping flow in curved ducts, however, the increase of the first normal stress difference intensifies the instability. Furthermore, at the special value of Ψ 2/ Ψ 1=−0.5, the interaction of the two normal stress differences results in a stable flow field.

An artificial compressibility algorithm for modelling natural convection in saturated packed pebble beds: A heterogeneous approach

AbstractThis work is concerned with the modelling of heat and fluid flow through saturated packed pebble beds. A volume‐averaged set of local thermal disequilibrium governing equations is employed to describe the latter as a heterogeneous porous medium with porosity varying from 0.39 to 0.99. The thermal disequilibrium approach, together with stated porosity upper limit, allows for the modelling of wall effects such as wall channeling and wall–bed radiative heat transfer. The resulting set of coupled non‐linear partial differential equations is solved via a locally preconditioned artificial compressibility method, where spatial discretization is effected with a compact finite volume edge‐based discretization scheme. The latter was done in the interest of accuracy. Stabilization is effected via JST scalar‐valued artificial dissipation. This is the first instance in which an artificial compressibility algorithm is applied to modelling heat and fluid flow through heterogeneous porous materials. For this reason, special attention was given to the calculation of acoustic velocities, stabilization scaling factors, as well as allowable time‐step sizes. The developed technology is validated by application to the modelling of a number of benchmark test cases. Copyright © 2008 John Wiley &amp; Sons, Ltd.

A cut‐cell non‐conforming Cartesian mesh method for compressible and incompressible flow

AbstractThis paper details a multigrid‐accelerated cut‐cell non‐conforming Cartesian mesh methodology for the modelling of inviscid compressible and incompressible flow. This is done via a single equation set that describes sub‐, trans‐, and supersonic flows. Cut‐cell technology is developed to furnish body‐fitted meshes with an overlapping mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. Spatial discretization is effected via an edge‐based vertex‐centred finite volume method. An alternative dual‐mesh construction strategy, similar to the cell‐centred method, is developed. Incompressibility is dealt with via an artificial compressibility algorithm, and stabilization achieved with artificial dissipation. In compressible flow, shocks are captured via pressure switch‐activated upwinding. The solution process is accelerated with full approximation storage (FAS) multigrid where coarse meshes are generated automatically via a volume agglomeration methodology. This is the first time that the proposed discretization and solution methods are employed to solve a single compressible–incompressible equation set on cut‐cell Cartesian meshes. The developed technology is validated by numerical experiments. The standard discretization and alternative methods were found equivalent in accuracy and computational cost. The multigrid implementation achieved decreases in CPU time of up to one order of magnitude. Copyright © 2007 John Wiley &amp; Sons, Ltd.

A modification of the artificial compressibility algorithm with improved convergence characteristics

AbstractThe artificial compressibility algorithm has a significant drawback in the difficulty of choosing the artificial compressibility parameter, improper choice of which leads either to slow convergence or divergence. A simple modification of the equation for pressure in the artificial compressibility algorithm which removes the difficulty of choosing the artificial compressibility parameter is proposed. It is shown that the choice of the relaxation parameters for the new algorithm is relatively straightforward, and that the same values can be used to provide robust convergence for a range of application problems. This new algorithm is easily parallelized making it suitable for computations such as direct numerical simulation (DNS) which require the use of distributed memory machines. Two key benchmark problems are studied in evaluating the new algorithm: DNS of a fully developed turbulent channel flow, and DNS of a driven‐cavity flow, using both explicit and implicit time integration schemes. The new algorithm is also validated for a more complex flow configuration of turbulent flow over a backward‐facing step, and the computed results are shown to be in good agreement with experimental data and previous DNS work. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Numerical simulation of cavitating two-phase gas-liquid three-dimensional flow in a duct of varying cross-section based on homogenous mixture model

The paper presents a numerical method to simulate two-phase turbulent cavitating flows in ducts of varying cross-section usually faced in engineering. The method is based on solution of two-phase Reynolds-averaged Navier-Stokes equations of two-phase mixture. The numerical method uses artificial compressibility algorithm extended to unsteady flows with dual-time technique. The discreted method employs an implicit, characteristic-based upwind differencing scheme in the curvilinear grid systems. Numerical simulation of an unsteady three-dimensional two-phase cavitating flow in a duct of varying cross-section with available experiment was performed. The unsteady important characteristics of the unsteady flow can be observed in results of numerical simulation. Comparison of predicted results with experimental data for time-averaged velocity and phase fraction are provided.

Computation for Unsteady Incompressible Flow on Unstructured Grid.

The artificial compressibility algorithm for incompressible flows is applied to an unstructured grid method. It is based on a finite volume cell-vertex upwind technique and uses a time-marching procedure to efficiently solve the continuity equations as well as the momentum equations. The Lower-Upper Symmetric Gauss-Seidel(LU-SGS)approximate factorization scheme is implemented with the Navier-Stokes solver on arbitrary three-dimensional unstructured grid. Numerical simulation is performed for steady and unsteady incompressible flow problems, 2-D wake of cylinder, 3-D stenosed tube and branched tube.

Validation of Unstructured Grid Method for Incompressible Flows using Artificial Compressibility Method.

The artificial compressibility algorithm for incompressible flows is applied to an unstructed grid method. It is based on a finite volume cell-vertex upwind technique and uses a time-marching procedure to efficiently solve the continuity equation as well as the momentum equations. The Lower-Upper Symmetric Gauss-Seidel (LU-SGS) approximate factorization scheme is implemented with the Navier-Stokes solver on arbitrary three-dimensional unstructured grid. The LU-SGS algorithm provides a significant enhancement of the convergence rate. The accuracy of the method is validated by applying the method to incompressible flow problems of a 2-D cavity and 3-D duct.

Strongly-Coupled Multigrid Method for 3-D Incompressible Flows Using Near-Wall Turbulence Closures

An efficient artificial compressibility algorithm is developed for solving the three-dimensional Reynolds-averaged Navier-Stokes equations in conjunction with the low-Reynolds number k-ω turbulence model (Wilcox, 1994). Two second-order accurate central-differencing schemes, with scalar and matrix-valued artificial dissipation, respectively, and a third-order accurate flux-difference splitting upwind scheme are implemented for discretizing the convective terms. The discrete equations are integrated in time using a Runge-Kutta algorithm enhanced with local time stepping, implicit residual smoothing, and V-cycle multigrid acceleration with full- and semi-coarsening capabilities. Both loosely and strongly-coupled strategies for solving the turbulence closure equations are developed and their relative efficiency is evaluated. Calculations are carried out for turbulent flow through a strongly-curved 180 deg pipe bend discretized with fine, highly-stretched and skewed meshes. It is shown that the strongly-coupled multigrid algorithm, with semi-coarsening in the transverse plane, is an efficient approach for simulating flows of practical interest with advanced near-wall turbulence closures.