SIMPLE-like Algorithm Research Articles

Influence of stationary porous media on fluid flow

The work examines the flow of an incompressible fluid containing a porous medium. A porous body is formed through various mechanisms. To describe the flow, a single equation is used that describes the flow of fluid in the porous and free zone. The flow is simulated based on Rakhmatulin’s two-speed model, in a laminar mode with zero speed of a discrete phase. The results of numerical simulation of the hydrodynamic features of a two-dimensional viscous flow are presented. The Kozeny-Karman relation is used as the force of interaction with the porous layer. Computational experimental methods are used to study the effects of nonuniformity of the fluid velocity field arising from a porous body. For the numerical implementation of the resulting equation, which is a generalization of the Navier-Stokes equation, a SIMPLE-like algorithm with corresponding generalizations was used. A single algorithm is used for the entire area, without identifying the free and porous zones.

Modeling the flow in the presence of underwater vegetation

The paper investigates the flow of an incompressible fluid in an open stream with an unequal bottom and slope. The uneven bottom is due to vegetation. The flow is modeled on the basis of the two-velocity Rakhmatulin model, in a laminar regime from zero velocity of the discrete phase. The flow of a viscous fluid in a channel with an open stream with vegetation at the bottom of the stream is considered. The results of numerical simulation of the hydrodynamic features of a two-dimensional viscous flow are presented. The Kozeny-Karman ratio is used as the force of interaction with vegetation. The methods of computational experiment are used to study the effects of non-uniformity of the fluid velocity field, which arise due to vegetation. A qualitative comparison of velocity inhomogeneities is carried out. For the numerical implementation of the resulting equation, which is a generalization of the Navier-Stokes equation, a SIMPLE-like algorithm with appropriate generalizations was used. A single algorithm is applied for the entire area, without highlighting the free and porous zone.

Flow in a channel with porous insert

Filtration of an incompressible liquid (gas) in a non-deformable porou s medium is investigated. The results of numerical simulation of the hydrodynamic features of the flow arising after the passage of the liquid through a layer of an immobile porous medium are presented. An interpenetrating model of multiphase media is used to describe such flows. The porosity and permeability of the porous medium, as well as the force of interfacial interaction, are considered in the framework of compliance with the Kozeny-Karman ratio. The influence of the geometrical shape of the bulk layer on the nature and magnitude of the inhomogeneity of the flow velocity behind the obstacle is shown. Considering the shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The effects of the non-uniformity of the fluid velocity field arising from the curvature of the layer surface and the influence of the arising inhomogeneity on the velocity are investigated by the methods of a computational experiment. A qualitative comparison is made of velocity inhomogeneities when a fluid flows through a porous obstacle. For the numerical implementation of the filtration equation of the interpenetrating model, a SIMPLElike algorithm was used.

Influence of the Form of Porous Insert in the Flow of a Viscous Liquid in a Plane Pipe

Filtration of an incompressible liquid (gas) in a non-deformable porous medium is investigated. The results of numerical simulation of the hydrodynamic features of the flow arising after the passage of the liquid through a layer of an immobile porous medium are presented. An interpenetrating model of multiphase media is used to describe such flows. Kozeny-Karman relations are used as the interaction force. The influence of the geometrical shape of the bulk layer on the nature and magnitude of the inhomogeneity of the flow velocity around the obstacle is shown. The shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The effects of non-uniformity of the fluid velocity field arising due to the shape of the layer surface are investigated by the methods of a computational experiment. A qualitative comparison is made of velocity inhomogeneities when a fluid flows through a porous obstacle. For the numerical implementation of the filtration equation of the interpenetrating model, a SIMPLE-like algorithm was used.

Numerical Study of Pressure Drop and Thermal Characteristics of Al2O3–Water Nanofluid Flow in Horizontal Annuli

In this paper the results of numerical study of the mixed convection heat transfer of Al2O3–water nanofluid in a horizontal annuli are presented. Steady, laminar flows in symmetric configurations are considered. Single-phase fluid approach is adopted for nanofluid modeling. The governing equations are discretized using the finite-volume method. A SIMPLE-like algorithm has been applied for pressure–velocity coupling on the collocated arrangement. In order to validate the code performance, the numerical results are compared with those available in the literature and good agreement is achieved. The effects of some important parameters such as nanoparticle volume fraction, aspect ratio, Grashof number, and heat flux ratio are studied and discussed in detail. In general, it is observed that the local Nusselt number increases with increase in nanoparticle concentration, Grashof number, and radius ratio. However, when increasing the nanoparticle concentration there are considerable increments in pressure drop and pumping power, which are not desirable. On the other hand, changes in the skin friction coefficient are negligible.

Two-phase flow distribution in multiple parallel tubes

This work is focussed on the development of a numerical simulation model that predicts the thermal and fluid-dynamic behaviour of the two-phase flow distribution in systems with multiple branching tubes like manifolds. The geometry of a simulated branching system is represented as a set of tubes connected together by means of junctions. On one side, the in-tube evaporation/condensation phenomena are simulated by means of a one-dimensional two-phase flow model, and on the other side, the splitting/converging flow phenomena occurring at junctions are predicted with appropriate junction models obtained from the technical literature. The global flow distribution is calculated using a semi-implicit pressure based method (SIMPLE-like algorithm) where the continuity and momentum equations of the whole domain are solved and linked with both the in-tube two-phase flow model and the junction models. In the present paper, the flow distribution model is described and its most significant aspects are detailed. Furthermore, the model is validated against experimental and numerical data found in the open literature. The numerical predictions are compared against an adiabatic single-phase flow manifold system working with water and also against a two-phase flow upwardly oriented manifold system working with carbon dioxide. In addition to this, a numerical comparison of a manifold system with two different orientations is carried out. Concluding remarks about the possibilities that this kind of model offers are presented in the last section.

A Fast and Efficient Method for Predicting Fluid Flow and Heat Transfer Problems

A fast and efficient method based on the proper orthogonal decomposition (POD) technique for predicting fluid flow and heat transfer problems is proposed in this paper. POD is first applied to an ensemble of numerical simulation results at design parameters to obtain the empirical coefficients and eigenfunctions, and then the fluid and temperature fields in the range of design parameters are resolved by a linear combination of empirical coefficients and eigenfunctions. The empirical coefficients at off-design parameters are obtained by a cubic spline interpolation method for steady problems and a Galerkin projection method for transient problems. Finally, the efficiency and accuracy of the algorithm are examined by three examples. The POD based algorithm can predict both the velocity and temperature fields in the range of design parameters accurately at a price of a large number of precomputed cases (snapshots). It also brings significant computational time savings for the new cases within the parameter range presimulated compared with the finite volume method with SIMPLE-like algorithm.

Darcy Model for the Study of the Fluid Flow and Heat Transfer Around a Cylinder Embedded in Porous Media

Steady-state convective heat transfer around a circular cylinder embedded in porous media is studied in the range of low and moderate Peclet numbers less than 40. The cylinder is at constant temperature and the Darcy model is used for the analysis of fluid flow and heat transfer in porous media. The governing equations are discretised using finite volume approach based on staggered grids. The powerlaw scheme is used in the numerical solution and a SIMPLE-like algorithm is developed and used in the solution process. It is found that the numerical algorithm is sufficiently efficient in the range of Peclet numbers less than 40. Parametric studies are done for better understanding of the porous media effects on the Nusselt number distribution, pressure distribution, and flow and temperature fields around a circular cylinder. The results are compared with the available numerical data in the literature and have shown good agreements.

Heat transfer and fluid flow in a high-intensity free-burning arc: an improved modeling approach

The high-intensity free-burning arc is modeled using a computational domain including the arc itself and the arc cathode and anode. It is shown that the energy equation with the temperature, instead of the specific enthalpy, as the dependent variable has to be used in order to obtain physically reasonable heat fluxes from the plasma to the electrodes if a SIMPLE-like algorithm is employed in the modeling. New difficulty encountered in the numerical solution of the energy equation is discussed in some detail and has been overcome successfully by use of a `pseudo-density' method and a deferred-correction discretization scheme. A more realistic boundary condition is adopted at the rear face of the anode plate for the solution of the potential equation in order to reveal the effect of electrical collection at the anode on the current density and temperature distributions within the anode plate. Special treatments at the plasma–electrode interfaces are also discussed and adopted in the modeling.

NUMERICAL PREDICTION OF LAMINAR FORCED CONVECTION IN TRIANGULAR DUCTS WITH UNSTRUCTURED TRIANGULAR GRID METHOD

The flow and heat transfer characteristics of smooth triangular ducts with different apex angles of 15, 30, 60, and 90 under the fully developed laminar flow condition were predicted numerically using a finite volume method. The SIMPLE-like algorithm was employed together with an unstructured triangular grid method, where the grid was generated by a Delaunay method. The triangular grid was adopted instead of the traditional rectangular grid to fit better into the triangular cross section of the duct. Two kinds of boundary condition (uniform wall temperature and uniform wall heat flux) were considered. Comparison of the predictions with previous computational results indicated a very good agreement. Both the friction factor and Nusselt number (Nu) showed a strong dependence on apex angle of the triangular duct. When the apex angle was 60, the duct provided the highest steady-state forced convection from its inner surface to the airflow under the laminar flow condition.

An improved numerical algorithm for solution of convective heat transfer problems on nonstaggered grid system

In this paper, a SIMPLE-like algorithm on co-located grid system has been developed. The ability to suppress the spurious pressure field is achieved via introducing the pressure difference between adjacent two grid points into the convection-diffusion finite difference scheme, and the interfacial velocity is obtained by simple linear interpolation. The differencing scheme, discretization of governing equations and solution procedure of the algorithm are described in detail. In order to check the validity of the algorithm, several test cases which have analytical or benchmark solutions are presented. Good agreements are obtained between the numerical and the corresponding analytical or benchmark solutions. The ability of the improved algorithm to suppress the spurious pressure field is demonstrated via a 3-D example.

A PRESSURE-CORRECTION METHOD FOR SOLVING FLUID FLOW PROBLEMS ON A COLLOCATED GRID

A pressure-correction method for the SIMPLE-like algorithm is proposed on a curvilinear collocated grid for the solution of two-dimensional incompressible fluid flow problems, using a vertex-based finite-volume approximation. In the pressure-correction equation, a weighting factor (a fictitious time step) is used as a substitute for the nodal contributions of the momentum equations. It serves as a limiter for the mass imbalance and provides an opportunity to avoid the pressure underrelaxation even when the source term effect in the momentum equations is dominant. The primitive formulation utilizes either the original Rhie-Chow (ORC) or the modified Rhie-Chow (MRC) flux correction at the cell face in discretizing the continuity equation to prevent the pressure oscillations. A comparative evaluation of the ORC and MRC schemes based on the computed results for a buoyancy-driven laminar flow in a half-concentric annulus shows that, on average, the MRC approach produces satisfactory stabilization for the iteration process. The effect of the weighting factor on the convergence of the mass residual is also investigated. The QUICK differencing combined with a deferred correction approach is adopted for the connective fluxes.

Numerical simulation of natural convection in circular enclosures with inner polygonal cylinders, with confirmation by experimental results

Numerical computations are performed for the natural convection in circular enclosures with inner polygonal cylinders. The polygon surface and the outer envelope are at constant but different temperatures. A body-fitted coordinate system is used. The coordinate system is generated via simple algebraic equations. The transformed governing equations are discretized on a control volume basis with power-law finite difference scheme. The SIMPLE-like algorithm is used to deal with the linkage between pressure and velocities. The numerical results are compared with the experimental data available in the literature, and the agreement between the numerical and experimental results are very good.