Semi-implicit Method For Pressure-linked Equations Research Articles

Two-Dimensional Numerical Simulation of Gas–Solid Reactive Flow with Moving Boundary

In order to combine the advantages of both the Lagrangian and Eulerian algorithm for a moving boundary, this work presents a two-dimensional axisymmetric computational model in ALE (arbitrary Lagrangian–Eulerian) forms for the gas–solid transient reacting flow with a moving boundary of the interior ballistic process. A two-phase flow model is established to describe the complex physical process based on a modified two-fluid theory, which takes into account gas production, interphase drag, intergranular stress, and heat transfer between two phases. The governing equations are discretized with the TVD-type MUSCL scheme to obtain a second-order accurate numerical method in finite volume form and solved by the semi-implicit method for pressure-linked equations with density corrections. A dynamic self-adapting mesh update method is developed to expand the computational domain for projectile motion and reduce the computational cost. Several verification tests demonstrate the accuracy and reliability of this approach. A pressure-driven projectile case is used to demonstrate the coupling of the moving projectile with gas dynamics. The application on a real gun shows an excellent agreement between numerical simulation and experimental measurements. Numerical results provide a deeper understanding of the interior ballistic process, including gas production, flame spreading, and pressure wave developing, etc. By applying the ALE technique to two-phase reactive flows with moving boundary, it is be able to take advantage of the best aspects of both Lagrangian and Eulerian approaches. This new method is reliable as a predictive tool for the study of the physical phenomenon and can therefore be used as an assessment tool for future interior ballistics studies.

Numerical Study on Flow Field for a Solar Collector at Various Inflow Incidence Angles

Previous studies on solar water heaters (SWHs) have primarily focused on the thermal efficiency of a solar collector and structural safety. This study applied a numerical simulation method to examine the characteristics of flowfield. In addition, a solar collector of a SWH was employed to investigate the distribution of average surface pressure and vortex structure for various inflow incidence angles as well as the influence of two types of spoiler. This study adopted a computational fluid dynamics fluid mechanics method, an incompressible flow algorithm (i.e., semi-implicit method for pressure-linked equation [SIMPLE]), to simulate the flow field of the solar collector. A turbulence model (realizable k-e model) was adopted. The obtained numerical values were compared with the experimental results. Because the simulation data were approximated to the experimental results, the turbulence strength and length were set as 11.7% and 0.12, respectively. The parameter for this study was inflow angle (θ = 15°, 22.5°, 30°, 37.5°, and V = 35m/s). The characteristics of the flow field for various spoilers at inflow angle (θ) = 22.5° were examined. According to the numerical simulation results, the low-pressure area on the upper surface of the solar collector first enlarged and then diminished as the inflow angle increased. The largest low-pressure area occurred at the wind incidence angle (θ)=30°. Because the cross-sectional aspect ratio in the frontal view changed, the overall lift force increased as the angle θ increased. Because the vertical inflow cross-sectional area changed, air resistance gradually reduced. After spoilers of various sizes were installed, inflow airflow directly hit the solar collector, thereby reducing the pressure difference between the upper and lower surfaces of the solar collector. When the length of the spoiler increased, the shielding effect was enhanced; therefore, the increased size of the spoiler gradually reduced the lift force.

A Nonequilibrium Thermal Model for Direct Metal Laser Sintering

A three-dimensional numerical model based on nonequilibrium thermal effect for direct metal laser sintering (DMLS) with a moving laser beam is developed. The effects of surface tension, buoyancy force, and permeability as well as volume shrinkage are taken into account. The nonequilibrium model is discretized by the finite volume method and solved numerically using the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm with power-law scheme in staggered mesh. The surface temperature distribution and shapes of top surface and liquid–mushy and mushy–solid interfaces are investigated. The results show that mushy zone and heat-affected zone are formed during DMLS, and the melting pool size is dominated mainly by surface tension and buoyancy force. The parametric study shows that the top surface and liquid–mushy and mushy–solid interfaces become lower with increasing laser intensity, increasing initial porosity, or decreasing scanning velocity.

English

In this project we describe the complete process of modeling and simulation of computational fluid dynamics (CFD) problems that occur in engineering practice. We focus mainly on the simulation of the airflow around the aircraft. The fluid flow simulations are obtained with the CFX software package ANSYS. We use the solver based on the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE). The important part is the preparation of the model with the software ANSYS. We will describe the preprocessing including the creation and modification of the surface mesh in ANSYS and the three-dimensional volume grid generation. We discuss the generation of the threedimensional grid by the snappy Hex Mesh tool, which is included in the ANSYS package. Further, we present a way of analyzing the results and some of the outputs of the simulations and following analysis. The CFD simulations were performed on the computational model of the commercial aircraft. The computations were performed for different model settings and computational grids. It means that we considered laminar and turbulent flow and several combinations of the angle of attack and inlet velocity. This case study aims to perform a CFD analysis on an aircraft model using CFX solver. While performing the simulations, meshing techniques, pre-processing and post processing sections and evaluation of a simulation is being learnt. Coefficient of lift and drag were also recorded as a user input data. These values were also compared by running two different simulations with one change of input parameter i.e. angle of attack and inlet velocity

Parallel domain decomposition method with non-blocking communication for flow through porous media

This paper introduces a domain decomposition method for numerically solving the Stokes equation for very large, complex geometries. Examples arise from realistic porous media. The computational method is based on the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm which uses a finite-differences approach for discretizing the underlying equations. It achieves comparable speed and efficiency as lattice Boltzmann methods. The domain decomposition method splits a large three-dimensional region into slices that can be processed in parallel on multi-processor computation environments with only minimal communication between the computation nodes. With this method, the flow through a porous medium with grid sizes up to 20483 voxel has been calculated.

Passive Laminar Heat Transfer Across Porous Cavities Using the Thermal Non-Equilibrium Model

This work presents a study on laminar free convection within a square cavity filled with a fluid saturated porous medium. Macroscopic flow equations are obtained by volume-averaging local instantaneous continuity and momentum equations. The so-called “two-energy equation model” is used, in which distinct macroscopic equations are applied to the working fluid and the solid material. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. The effect of Ram on Nuw correctly predicted the enhancement of passive heat transfer across the cavity for increasing Ram. Increasing ks/kf enhances the conduction transport through the solid material and, consequently, dampens the overall Nusselt number, defined here as the ratio between conduction and convection mechanisms over conduction transport only. Further, results indicate that by increasing the void space within the porous material the overall Nusselt number is reduced rather than increased. Individual contributions to the average Nusselt number indicate that, although convection is enhanced with increasing porosity, the reduction of conduction heat transfer through the solid material is the controlling mechanics for Nuw as porosity increases. The results herein might contribute to design and optimization of passive heat transfer systems.

Heat transfer and fluid flow analysis of an artificially roughened solar air heater: a CFD based investigation

In this paper, the effect of rib (circular sectioned) spacing on average Nusselt number and friction factor in an artificially roughened solar air heater (duct aspect ratio, AR = 5:1) is studied by adopting the computational fluid dynamics (CFD) approach. Numerical solutions are obtained using commercial software ANSYS FLUENT v12.1. The computations based on the finite volume method with the semi-implicit method for pressure-linked equations (SIMPLE) algorithm have been conducted. Circular sectioned transverse ribs are applied at the underside of the top of the duct, i.e., on the absorber plate. The rib-height-to-hydraulic diameter ratio (e/D) is 0.042. The rib-pitch-to-rib-height (P/e) ratios studied are 7.14, 10.71, 14.29 and 17.86. For each rib spacing simulations are executed at six different relevant Reynolds numbers from 3800 to 18000. The thermo-hydraulic performance parameter for P/e = 10.71 is found to be the best for the investigated range of parameters at a Reynolds number of 15000.

A NOVEL PRESSURIZED ZONAL MODEL USING THE MOMENTUM EQUATION

Zonal models combine the simplicity of single and multi-zone models with the comprehensiveness of Computational Fluid Dynamics (CFD) models and thus become a better substitute to predict detailed thermal and airflow behaviors in building. Based on a geometric partitioning of a room into a number of subzones, these models give more accurate and detailed results than the single or multi-zone modeling approaches and use less computer resource than CFD models. Nevertheless, most of the zonal models have to face a difficulty involving the limits of the simplification that need to be considered without losing accuracy and comprehensiveness. A new zonal model, called Pressurized zOnal Model using the Momentum Equation (POMME), has been developed, in which a simplified numerical model, representing various heat and mass transfer conservation equations is used. The program solver is similar to those used for CFD programs and is based on the finite-volume numerical techniques, the staggered grid formulation, the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm and other methods. The validation of this new zonal model has been accomplished by comparing its results with those obtained from the CFD software: PHOENICS. The results demonstrate not only the strength of the zonal model POMME in predicting the indoor airflow and thermal conditions, without the involvement of additional sub-models, but also its ability to provide relatively accurate results for building enclosures.

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re) 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK) is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe) numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies.

Drag of contaminated bubbles in power-law fluids

Flow and drag phenomena of spherical bubbles in contaminated power-law fluids are numerically investigated using the spherical stagnant cap model over the range of conditions as the Reynolds number (Re: 0.1–200), the power-law index (n: 0.2–1.6) and the degree of contamination (α: 0–180°). The conservation equations of mass and momentum are solved using the semi-implicit method for pressure-linked equations (SIMPLE) algorithm along with the quadratic upstream interpolation for convective kinematics (QUICK) scheme for momentum terms. The solver has been thoroughly validated with the existing literature results over wide range of pertinent conditions. The new results show that for Re>20 and α≥60°, a recirculation wake behind the contaminated bubble is observed for all values of power-law index; and the size of the recirculation wake is found to decrease with the increasing power-law index. Furthermore, a crossover Reynolds number (at Re≈5) exists for drag coefficient vs. Reynolds number behavior with respect to the power-law index; and it is found to be independent of the degree of contamination. Below this crossover Reynolds number, compared to Newtonian fluid results, the normalized drag coefficients are large for shear-thinning fluids (n<1) and are smaller for shear-thickening fluids; and opposite trends are observed beyond the crossover Reynolds number.

Numberical Simulation of Labyrinth Screw Pump with Separated Structure by Fluent

3D model and grid was conducted in Gambit,while single-phase flow field in the pump was simulated in CFD code-Fluent,by means of multiple reference frame (MRF) method, Renormalization group k-ε two-equation turbulence model (RNG k-εmodel) and Semi-Implicit Method for Pressure-Linked Equations (SIMPLEC) algorithm. Aim at problems generated by pump body such as body length limitation on pressure increasing, three new structure of labyrinth screw pumps,rotor separated LSP,stator separated LSP and rotor stator all separated LSP, were put forward in this paper.The analytical results got by contrasted pump hydraulic performance of different structure models indicated that pressure increasing magnitude and pressure increasing rate of the three separated pumps is larger compared to the unseparated pumps,and the conclusion was achieved that pump performance can be optimized through separating rotor or stator into sections by making ring slots on screw body.

Numerical Simulation of Multi-Layer Rectangle Micro-Channel Heat Sink for Single-Phase Flow and Heat Transfer

The single-phase flow and heat transfer for multi-layer rectangle micro-channel heat sink are numerically simulated. During the simulation, Finite Volume Method (FVM) was used to solve Computational Fluid Dynamics (CFD) problem. First order upwind scheme was used to discrete control equations, and semi-implicit method for pressure-linked equations was used to solve discretization equations. The maximum temperature difference is 76.2362 °C, and the total thermal resistance is 0.4765 °C/W, which agrees well with the result of analysis result 0.5145 °C/W. The corresponding pressure drop is about 54.1360 N/m2.

Preliminary Hydrodynamic Modeling of Fluidized Beds of Single Component and Binary Particle System in Compartmented Gasifier

In the present study, three-dimensional simulation using computational fluid dynamics (CFD, FLUENT 6.3.26) and experiments were conducted on a transparent cold-flow gas-solid bubbling compartmented fluidized bed gasifier (CFBG) model with identical diameter as the pilot-scaled CFBG. Using Eulerian-Eulerian granular model with closure laws according to the kinetic theory of granular flow that based on modified drag model simulations were conducted to model the hydrodynamics of CFBG in terms of gas-solid flow pattern, bed expansion ratio, bed pressure drop and bubble diameter. The model was resolved by semi-implicit method for pressure-linked equation (SIMPLE) algorithm in CFD. Different inerts like river sand, quartz sand, and alumina were used to examine the hydrodynamics behaviors both in single component and binary system where biomass, palm shell, was mixed with river sand. The modeling predictions compared reasonably well with experimental bed expansion ratio measurements and qualitative gas-solid flow patterns. Pressure drops predicted by the simulations were in relatively close agreement with experimental measurements. Furthermore, the simulated bubble diameters showed similarities with the Darton et al., bubble size equation.

Drag of Tandem Spheroids in Power-Law Fluids at Moderate Reynolds Numbers

The relative motion between a power-law fluid and two tandem spheroid particles was investigated numerically. The field equations that govern this problem were solved using a commercial computational-fluid-dynamics-based solver. The semi-implicit method for pressure-linked equations (SIMPLE) algorithm and the quadratic upstream interpolation for convective kinematics (QUICK) scheme for convective terms were used. The solver was thoroughly benchmarked through domain and grid studies. Further, extensive new results are presented for the following ranges of conditions: Reynolds number (Re), 1–200; particle aspect ratio (e), 0.5–2; power-law index (n), 0.4–1.6; and interparticle distance (S), 2–5. The main focus of this work was to report the effects of these parameters on the streamlines, surface viscosity, and drag coefficients of the tandem particles. The dependence of the average drag coefficient on the power-law index and Reynolds number had a crossover Reynolds number that was found to be a strong function of the particle aspect ratio and the interparticle distance. Below this crossover Reynolds number, the average drag coefficient increased with decreasing power-law index, whereas for Reynolds numbers greater than the crossover Reynolds number, the average drag coefficient decreased with decreasing power-law index.

Turbulent flow and heat transfer enhancement of forced convection over heated baffles in a channel

PurposeThe purpose of this paper is to examine the turbulent fluid flow and heat transfer characteristics for rectangular channel provided with solid plate baffles which are arranged on the bottom and top channel walls in a periodically staggered way.Design/methodology/approachThe turbulent governing equations are solved by a finite volume method with the second‐order up winding scheme and the k‐ω turbulence model to describe the turbulent structure. The velocity and pressure terms of momentum equations are solved by SIMPLE (semi‐implicit method for pressure‐linked equation) algorithm. The parameters studied include the entrance Reynolds number Re (5.103‐2.104), the baffles height are fixed at (h=0.08 m); whereas three different baffle spacing were considered S1 = D, S2 = D/2 and S3=3D/2 and the working medium is air.FindingsIn this work, it is found that vortex shedding generated by the baffle on the upper wall can additionally enhance heat transfer along the baffle surfaces. The wavy flow significantly changes the recirculating zone behind the last baffle. Finally, changing the baffles spacing seemed to reduce to changing the heat transfer surface between the solid and the fluid in the sense that higher heat transfer is obtained for lower spacing between baffles.Originality/valueThe results of the numerical calculations of the flow field indicate that the flow patterns around the solid baffles depending on the spacing of the baffles and it significantly influences the local heat transfer coefficient distributions. The problem is inversely proportional for the friction factor.

Acceleration of iterative Navier-Stokes solvers on graphics processing units

While new power-efficient computer architectures exhibit spectacular theoretical peak performance, they require specific conditions to operate efficiently, which makes porting complex algorithms a challenge. Here, we report results of the semi-implicit method for pressure linked equations (SIMPLE) and the pressure implicit with operator splitting (PISO) methods implemented on the graphics processing unit (GPU). We examine the advantages and disadvantages of the full porting over a partial acceleration of these algorithms run on unstructured meshes. We found that the full-port strategy requires adjusting the internal data structures to the new hardware and proposed a convenient format for storing internal data structures on GPUs. Our implementation is validated on standard steady and unsteady problems and its computational efficiency is checked by comparing its results and run times with those of some standard software (OpenFOAM) run on central processing unit (CPU). The results show that a server-class GPU outperforms a server-class dual-socket multi-core CPU system running essentially the same algorithm by up to a factor of 4.

Effects of material properties on heating processes in two-layered porous media subjected to microwave energy

Microwave heating of double-layer porous medium is numerically investigated using a proposed numerical model. A two-dimensional domain composed of two porous layers is considered. The two porous layers have different particle sizes, porosities, thermal and dielectric properties. The generalized non-Darcian model developed takes into account of the presence of a solid drag and the inertial effect. The transient Maxwell’s equations are solved by using the finite difference time domain (FDTD) method to describe the electromagnetic field in the waveguide and in the media. The temperature profile and velocity field within the media are determined by solution of the momentum and energy equations given by the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. This study focuses on effects of diameter, porosity, position and types of particles that have different thermal and dielectric properties. The computed results agree well with the experimental results. While the particle size and porosity mainly affect fluid flow within porous media, the thermal and dielectric properties strongly influence heat transfer mechanism in each layer of porous media.

Mass deposition and fluid flow in stenotic arteries: Rectangular and half-circular models

Mass deposition inside the artery wall may play a significant role in the development of the disease atherosclerosis. Locally elevated concentrations of LDL in the arterial wall are considered to be the initiator of atherosclerotic plaque formation. In this study, an attempt has been made to study initially the effect of fluid dynamic parameters on the disease and finally proposed a concept, from the idea of basic flow characteristics in constricted arteries, for the assessment of mass deposition in the arterial wall to some extent for rectangular as well as half circular stenosed models. Reynolds numbers are chosen as 100, 200, 300 and 400 and percentage of restrictions as 30%, 50%, 70% and 90% respectively. The governing Navier-Stokes and continuity equations are solved in the artery lumen with the commercial CFD code ANSYS 12.1. The pressure-velocity coupling equations are solved by SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. The studies on pressure drop at stenosis zone and flow separation zone reveal that the effect of percentage of restriction is more dominant than Reynolds number on the progression of the disease, atherosclerosis for any shaped restriction. The mass deposition results of rectangular and half circular stenotic models motivate to conclude that the effect of percentage of restriction is more prone to the disease than that of Reynolds number. Half circular stenotic shape insists for the less chance of mass deposition in the arterial wall compared to rectangular shaped restriction.

Numerical Study of Turbulent Periodic Flow and Heat Transfer in a Square Channel with Different Ribs

A numerical investigation has been carried out to examine turbulent flow and heat transfer characteristics in a three-dimensional ribbed square channels. Fluent 6.3 CFD code has been used. The governing equations are discretized by the second order upwind differencing scheme, decoupling with the SIMPLE (semi-implicit method for pressure linked equations) algorithm and are solved using a finite volume approach. The fluid flow and heat transfer characteristics are presented for the Reynolds numbers based on the channel hydraulic diameter ranging from 104 to 4 ′ 104. The effects of rib shape and orientation on heat transfer and pressure drop in the channel are investigated for six different rib configurations. Rib arrays of 45° inclined and 45° V-shaped are mounted in inline and staggered arrangements on the lower and upper walls of the channel. In addition, the performance of these ribs is also compared with the 90° transverse ribs.

Fourier Analysis of the Effect of Non-Constant Terms on the Convergence Properties of SIMPLE Algorithm Formulated on a Staggered Grid

The Fourier analysis is employed to study the effect of non-constant terms on the convergence properties of SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm formulated on a staggered grid in two-dimension. The results indicate the non-constant items can broaden the convergence range of pressure relaxation factor for a given velocity under-relaxation factor. What’s more, the non-constant items do well to the damping of the lowest error and can accelerate the convergence rate.