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A BOUNDARY ELEMENT FORMULATION USING THE simple METHOD

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1993年第7期16卷 549-579页

作者： GRIGOREV, MM Department of Mechanical Engineering Chemical Technology Institute of Kazan K. Marx Street 68 Kazan 420015 Russia

A new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well-known simple algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and Spalding.32 However, the new method demands a much larger computer storage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two-dimensional domain are found analytically. To preserve the stability in the iteration process, under-relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates at Re = 20 and Re = 200, the flows in a square cavity with a moving upper lid at Re - 1 and Re = 100 and the flow in a plane channel with sudden symmetric expansion at Re = 46.6.

关键词： BOUNDARY INTEGRAL EQUATION BOUNDARY ELEMENT METHOD simple algorithm 2-DIMENSIONAL LAMINAR FLOW

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A two-dimensional finite volume hydrodynamic model for coastal areas: Model development and validation

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OCEAN ENGINEERING 2008年第1期35卷 150-164页

作者： Daoud, A. H. Rakha, K. A. Abul-Azm, A. G. Suez Canal Author Suez Canal Res Ctr Ismailia Egypt Cairo Univ Fac Engn Dept Irrigat & Hydraulics Giza Egypt

A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous terms are discretized using a second order central difference approximation. The simple (Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for coupling the velocity components and the water elevation gradient for the water level correction. The system of equations is solved sequentially using the Strongly Implicit Procedure (SIP). To simulate wave driven current, a phase averaged wave model is used first to simulate wave transformation and calculate radiation stresses. The performance of the developed model is validated for different sources of external forces and different combinations of boundary conditions. The validation cases include tidal circulation in a harbor and wave induced currents behind a breakwater parallel to the coastline. The model is finally applied to simulate the flow pattern in a closed artificial lagoon and along the coastline near Damietta Port located along the Northern coast of Egypt. Results of the developed model agree well with the published results for the considered cases. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： finite volume simple algorithm nearshore hydrodynamics shallow water equations tidal circulation wave induced current

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Three dimensional, two phase flow mathematical model for PEM fuel cell: Part I. Model development

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ENERGY CONVERSION AND MANAGEMENT 2004年第11-12期45卷 1861-1882页

作者： Hu, MR Gu, AZ Wang, MH Zhu, XJ Yu, LJ Shanghai Jiao Tong Univ Inst Refrigerat & Cryogen Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Inst Fuel Cell Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn Dept Energy Shanghai 200240 Peoples R China

A full three dimensional PEM fuel cell model is developed, which considers not only the rib resistance to the species but both the single and two phase flow and transport in the gas channels and diffusers at both the anode and cathode sides of the PEM fuel cell. Two sets of boundary conditions, one for a conventional flow field and the other for an interdigitated one, are presented. A detailed discussion of the numerical techniques for the PEM fuel cell model is given with a flow diagram to provide an overview of the solution procedure using the FORTRAN language. A rigorous validation method is used to show good agreement between our predicted results and the experimental data. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： PEM fuel cell two phase flow model conventional flow field interdigitated flow field simple algorithm

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Partitioning of solar still for performance recovery: Experimental and numerical investigations with cost analysis

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SOLAR ENERGY 2017年 153卷 41-50页

作者： Rashidi, Saman Esfahani, Javad Abolfazli Rahbar, Nader Ferdowsi Univ Mashhad Dept Mech Engn Mashhad 917751111 Iran Islamic Azad Univ Semnan Branch Energy & Sustainable Dev Res Ctr POB 35196-97951 Semnan Iran Islamic Azad Univ Young Researchers & Elite Club Semnan Branch POB 35196-97951 Semnan Iran

In this paper, the effects of partitioning in solar still on performance recovery are investigated experimentally and numerically. Two single slope solar stills containing conventional and modified by installing a partition are fabricated and tested, simultaneously. Two stills have a same basin area. All experiments were performed in Semnan with geographical coordinates of 35 degrees 33' N, 53 degrees 23' E, Iran. Hourly temperature, productivity, and efficiency for the modified and conventional stills are obtained and compared. Moreover, a numerical simulation based on simple algorithm is utilized and different contours are drawn to more discuss about the physics of this problem. Finally, a cost analysis is performed to investigate the modified still, economically. It is found that the partitioned still works at much higher temperature difference between water and the condensing area especially for afternoon hours. Moreover, the productivity increases by installing the partition in the still. These enhancements are about 4.81%, 4.82%, 5.62%, and 8.16% for first, second, third, and fourth days of the experiment, respectively. Finally, the cost analysis studies reveal that the costs per liter of the fresh water production for the conventional and modified stills are 0.0096 and 0.0104 $/L/m(2), respectively. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Partition Single slope solar still simple algorithm Cost analysis

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Starting Flow by Pitch Acceleration of Flat-Plate Foil

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AIAA JOURNAL 2020年第10期58卷 4287-4303页

作者： Yu, Huai-Te Natl Def Univ Dept Mech & Aerosp Engn Chung Cheng Inst Technol Taoyuan 33551 Taiwan

This paper presents the investigation of the starting flow in association with pitch acceleration using transient laminar-flow computation and an unsteady inviscid-flow theory. A thin flat-plate foil pitched at the leading edge is modeled in a two-dimensional incompressible fluid at chord Reynolds numbers of the order of 10(3). Several acceleration amplitudes (1.1 <= alpha(m)'' t(c)(2) <= 17.0) and acceleration durations (0.0693 <= beta = Delta alpha/alpha(m) = Delta t/t(p) <= 0.5) are maneuvered using a modified canonical kinematic equation at reduced pitch rates from 0.196 to 0.763. Comparisons between computational and theoretical data reveal that the formation of the starting vortex is determined by the acceleration amplitude scaled by the square of the convective time. The corresponding starting force coefficient that scales with the dimensionless acceleration amplitude is proportional to the acceleration angle Delta alpha, which decreases with increasing reduced pitch rate. The starting vortex, once formed at the trailing edge, is shed at the end of the acceleration period. The quasi-steady theory that includes only pitch motion as the strength of the dipolar sheet for apparent-mass flow can also yield an acceptable approximation to capture the apparent-mass force coefficient spike in acceleration.

关键词： Trailing Edges Vortex Shedding Phenomena Freestream Conditions Incompressible Flow Mass Flow Lift Coefficient Pressure Coefficient simple algorithm Thin Airfoil Theory Particle Image Velocimetry

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Mathematical modelling and numerical simulation of CO₂/CH₄ separation in a polymeric membrane

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APPLIED MATHEMATICAL MODELLING 2015年第21期39卷 6599-6611页

作者： Gilassi, Sina Rahmanian, Nejat Univ Teknol PETRONAS Dept Chem Engn Bandar Seri Iskandar 31750 Perak Malaysia Univ Bradford Fac Engn & Informat Sch Engn Chem Engn Programme Bradford BD7 1DP W Yorkshire England

CO2 capture from natural gas was experimentally and theoretically studied using a dead-end polymeric permeation cell. A numerical model was proposed for the separation of CO2/CH4 using Polytetrafluoroethylene (PTFE) in a flat sheet membrane module and developed based upon the continuity, momentum and mass transfer equations. The slip velocity condition was considered to show the reflection of gas flow in contact with the membrane surface. The solution method was based on the well-known simple algorithm and implemented using MATLAB to determine the velocity and concentration profiles. Due to change in velocity direction in the membrane module, the hybrid differencing scheme was used to solve the diffusion-convection equation. The results of the model were compared with the experimental data obtained as part of this work and good agreement was observed. The distribution of CO2 concentration inside the feed and permeate chambers was shown and the velocity profile at the membrane surface was also determined using reflection factor for polymeric membrane. The modelling result revealed that increasing the amount of CO2 in gas feed resulted in an increase in the CO2 in the permeate stream while the gas feed pressure increased. By changing the permeability, the model developed by use of the solution-diffusion concept could be used for all polymeric membranes with flat sheet modules. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Mathematical modelling Solution-diffusion model PTFE membrane simple algorithm CO2/CH4 separation Cross flow membrane cell

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Numerical analysis of the buckling and recuperation dynamics of flexible filament using an immersed boundary framework

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INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW 2019年 77卷 256-277页

作者： Kanchan, Mithun Maniyeri, Ranjith NITK Biophys Lab Dept Mech Engn Mangalore 575025 Karnataka India

The dynamics of flexible filaments in viscous shear flow is of interest to biologists and engineers in a wide variety of applications involving folding and unfolding sequence of long-chain biomolecules like DNA, non-motile sperm and microalgae. It is also helpful in understanding the deformation of natural and synthetic fibers which can be applied in areas such as biotechnology. In the present work, deformation and migration behavior of non-motile unicellular phytoplankton diatoms subjected to viscous shear flow are considered. These unicellular diatoms develop into colonies which are made up of linked chains. The complex fluid-structure interaction is solved by developing a two-dimensional numerical model with an immersed boundary framework. The simulation consists of suspending an elastic filament mimicking a diatom chain in a shear flow at low Reynolds number. The governing continuity and Navier-Stokes equations are solved on a Cartesian grid arranged in a staggered manner. A forcing term is added to the momentum equation that incorporates the presence of flexible filament in the fluid domain. The discretization of the governing equation is based on a finite volume method, and a simple algorithm is used to compute pressure and velocity. A computer code is developed to perform numerical simulations, and the model is first verified with the deformation study of a tethered flexible filament in uniform fluid flow. Next, the shape deformations for flexible filament placed freely in shear flow are compared with the studies of previous researchers. Further, the present results are validated with Jeffery's equation for particles immersed in shear flow along with classification plot for filament orbit regimes. All of these comparisons provide a reasonable validity for the developed model. The effect of bending rigidity and shear rate on the deformation and migration characteristics is ascertained with the help of parametric studies. A non-dimensional parameter called Visc

关键词： Diatom chains Finite volume method Immersed boundary method Low Reynolds number Viscous flow forcing simple algorithm

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Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method

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JOURNAL OF COMPUTATIONAL PHYSICS 2008年第6期227卷 3358-3382页

作者： Hua, Jinsong Stene, Jan F. Lin, Ping Inst High Performance Comp Singapore 117528 Singapore Natl Univ Singapore Dept Math Singapore 117543 Singapore

The rise of bubbles in viscous liquids is not only a very common process in many industrial applications, but also an important fundamental problem in fluid physics. An improved numerical algorithm based on the front tracking method, originally proposed by Tryggvason and his co-workers, has been validated against experiments over a wide range of intermediate Reynolds and Bond numbers using an axisymmetric model [J. Hua, J. Lou, Numerical simulation of bubble rising in viscous liquid, J. Comput. Phys. 22 (2007) 769-795]. In the current paper, this numerical algorithm is further extended to simulate 3D bubbles rising in viscous liquids with high Reynolds and Bond numbers and with large density and viscosity ratios representative of the common air-water two-phase flow system. To facilitate the 3D front tracking simulation, mesh adaptation is implemented for both the front mesh on the bubble surface and the background mesh. On the latter mesh, the governing Navier-Stokes equations for incompressible, Newtonian flow are solved in a moving reference frame attached to the rising bubble. Specifically, the equations are solved using a finite volume scheme based on the Semi-Implicit Method for Pressure-Linked Equations (simple) algorithm, and it appears to be robust even for high Reynolds numbers and high density and viscosity ratios. The 3D bubble surface is tracked explicitly using an adaptive, unstructured triangular mesh. The numerical model is integrated with the software package PARAMESH, a block-based adaptive mesh refinement (AMR) tool developed for parallel computing. PARAMESH allows background mesh adaptation as well as the solution of the governing equations in parallel on a supercomputer. Further, Peskin distribution function is applied to interpolate the variable values between the front and the background meshes. Detailed sensitivity analysis about the numerical modeling algorithm has been performed. The current model has also been applied to simulate a number o

关键词： computational fluid dynamics incompressible flow multiphase flow bubble rising simple algorithm front tracking method adaptive mesh refinement moving reference frame

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Numerical investigation and characteristic analysis of the swirl meter with different swirlers

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MEASUREMENT & CONTROL 2020年第7-8期53卷 1122-1130页

作者： Chen, Desheng Lin, Zhe Liu, Qi Wang, Yanping Wu, Fei Wu, Dongyang Zhejiang Sci Tech Univ Key Lab Fluid Transmiss Technol Zhejiang Prov Second Ave 928 Hangzhou 310018 Zhejiang Peoples R China Zhejiang Testing & Inspect Inst Mech & Elect Prod Hangzhou Peoples R China Hangzhou Oxygen Plant Grp Co Ltd Hangzhou Peoples R China

The swirl meter is one of the gas flow meters used in the industry. Its advantages are as follows: a strong signal level, easy maintenance, and stable performance. Hence, it has become widely accepted for natural gas metering. In this study, the numerical computation of the three-dimensional unsteady flow in a swirl meter was conducted using the renormalization group k-epsilon turbulence model and simple algorithm. The internal flow fields were analyzed in detail, wherein the velocity and pressure distributions were discussed under six flow rates (6, 15, 25, 40, 70, and 100 m(3)/h) and three swirl cone angles (11 degrees, 20 degrees, and 30 degrees). The obtained results are reported and discussed as follows: the stable performance of the swirl meter was due to its capacity to maintain its internal characteristics over a large flow range. Also, it was detected that though the pressure decrease was gradual on the wall, an opposite tendency was shown at the center. On the other hand, the swirler structure was crucial to the metering capacity of the swirl meter, and the swirler cone angle influenced the pressure and velocity.

关键词： Swirl meter numerical simulation simple algorithm swirler cone angle pressure distribution

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Numerical simulation of oscillating lid driven square cavity

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ALEXANDRIA ENGINEERING JOURNAL 2018年第4期57卷 2609-2625页

作者： Indukuri, Jagadeesh Varma Maniyeri, Ranjith Natl Inst Technol Karnataka Dept Mech Engn Mangalore 575025 Karnataka India

This paper aim to develop a two-dimensional computational model to study the fluid dynamic behaviour in a square cavity driven by an oscillating lid using staggered grid based finite volume method. Firstly the developed computational model is validated with that of other researcher's results for the case of finite wall motion. Later the numerical simulations are performed for the case of top wall oscillations for various combinations of Reynolds number and frequencies. From these simulations an optimum frequency is chosen and then with the optimum frequency the simulations are carried out to explore the vortex behaviour for the cases of parallel wall oscillations (both top and bottom walls moving in the same direction) and anti-parallel wall oscillations (both top and bottom walls moving in the opposite direction). From these simulations it may be concluded that Re = 1000 is medium range of operation for better mixing inside the cavity for the cases of parallel and anti-parallel wall oscillations. (C) 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Finite volume method First order upwind scheme Oscillating lid driven cavity simple algorithm

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