Finite Element Solution of Inertia Influenced Flow in Thin Fluid Films

2007 ◽  
Vol 129 (4) ◽  
pp. 876-886 ◽  
Author(s):  
Noël Brunetière ◽  
Bernard Tournerie
Keyword(s):  
Finite Element ◽  
Numerical Model ◽  
Fluid Flows ◽  
Mesh Size ◽  
The Finite Element Method ◽  
Fluid Films ◽  
Inertia Effects ◽  
Continuity Equations ◽  
Numerical Precision ◽  
Incompressible Fluid Flows

The aim of this paper is to present a numerical model to compute laminar, turbulent, and transitional incompressible fluid flows in thin lubricant films where inertia effects cannot be neglected. For this purpose, an averaged inertia method is used. A numerical scheme based on the finite element method is presented to solve simultaneously the momentum and continuity equations. The numerical model is then validated by confronting it with previously published analytical, experimental, and numerical results. Particular attention is devoted to analyzing the numerical conservation of mass and momentum. The influence of mesh size on numerical precision is also analyzed. Finally, the model is applied to a misaligned hydrostatic seal. These seals operate with a substantial leakage flow, where nonlaminar phenomena occur. The influence of inertia and misalignment of the faces on the seal behavior is analyzed through a comparison with an inertialess solution. Significant differences are observed for high values of the tilt angle when the flow is nonlaminar. Inertia effects increase when the flow is laminar.

Physical statement of the problem for a numerical model of soil freezing and heaving taking into account heat and mass transfer

2021 ◽  
pp. 244-256
Author(s):  
Виктор Григорьевич Чеверев ◽  
Евгений Викторович Сафронов ◽  
Алексей Александрович Коротков ◽  
Александр Сергеевич Чернятин
Keyword(s):  
Finite Element Method ◽  
Mass Transfer ◽  
Finite Element ◽  
Numerical Model ◽  
Boundary Conditions ◽  
Heat And Mass Transfer ◽  
Soil Freezing ◽  
The Finite Element Method ◽  
Freezing Front ◽  
Element Method

Существуют два основных подхода решения задачи тепломассопереноса при численном моделировании промерзания грунтов: 1) решение методом конечных разностей с учетом граничных условий (границей, например, является фронт промерзания); 2) решение методом конечных элементов без учета границ модели. Оба подхода имеют существенные недостатки, что оставляет проблему решения задачи для численной модели промерзания грунтов острой и актуальной. В данной работе представлена физическая постановка промерзания, которая позволяет создать численную модель, базирующуюся на решении методом конечных элементов, но при этом отражающую ход фронта промерзания - то есть модель, в которой объединены оба подхода к решению задачи промерзания грунтов. Для подтверждения корректности модели был проделан ряд экспериментов по физическому моделированию промерзания модельного грунта и выполнен сравнительный анализ полученных экспериментальных данных и результатов расчетов на базе представленной численной модели с такими же граничными условиями, как в экспериментах. There are two basic approaches to solving the problem of heat and mass transfer in the numerical modeling of soil freezing: 1) using the finite difference method taking into account boundary conditions (the boundary, for example, is the freezing front); 2) using the finite element method without consideration of model boundaries. Both approaches have significant drawbacks, which leaves the issue of solving the problem for the numerical model of soil freezing acute and up-to-date. This article provides the physical setting of freezing that allows us to create a numerical model based on the solution by the finite element method, but at the same time reflecting the route of the freezing front, i.e. the model that combines both approaches to solving the problem of soil freezing. In order to confirm the correctness of the model, a number of experiments on physical modeling of model soil freezing have been performed, and a comparative analysis of the experimental data obtained and the calculation results based on the provided numerical model with the same boundary conditions as in the experiments was performed.

Stratification and Buoyancy Effect of Heat Transportation in Magnetohydrodynamics Micropolar Fluid Flow Passing Over a Porous Shrinking Sheet Using the Finite Element Method

2019 ◽  
Vol 8 (8) ◽  
pp. 1640-1647 ◽  
Author(s):  
Shahid Ali Khan ◽  
Yufeng Nie ◽  
Bagh Ali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Mesh Size ◽  
Stratified Medium ◽  
Shrinking Sheet ◽  
The Finite Element Method ◽  
Nonlinear Odes ◽  
Micropolar Fluid Flow ◽  
Element Method

The current study investigates the numerical solution of steady heat transportation in magnetohydrodynamics flow of micropolar fluids over a porous shrinking/stretching sheet with stratified medium and buoyancy force. Based on similarity transformation, the partial differential governing equations are assimilated into a set of nonlinear ODEs, which are numerically solved by the finite element method. All obtained unknown functions are discussed in detail after plotting the numerical results against different arising thermophysical parameters namely, suction, magnetic, stratification, heat source, and buoyancy parameter. Under the limiting case, the numerical solution of the velocity and temperature is compared with present work. Better consistency between the two sets of solutions was determined. To verify the convergence of the numerical solution, the calculation is made by reducing the mesh size. The present study finds applications in materials processing and demonstrates convergence characteristics for the finite element method code.

scholarly journals NUMERICAL MODEL OF AVIATION GEARBOX TEST RIG IN A CLOSED LOOP CONFIGURATION

Aviation ◽  
2010 ◽  
Vol 14 (1) ◽  
pp. 3-11 ◽  
Author(s):  
Tadeusz Markowski ◽  
Stanislaw Noga ◽  
Stanislaw Rudy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Model ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Closed Loop ◽  
Free Vibration Analysis ◽  
The Finite Element Method ◽  
Test Rig ◽  
Element Method

The development of computer techniques and computational systems based on the finite element method allows one to conduct a free vibration analysis of large systems like an aviation gearbox test rig. The object of this paper is to present a free vibration analysis of a gear fatigue test rig working in a closed loop configuration. A numerical model of the test rig based on the finite element method is presented in this paper. The base model contains all the essential structures of the real system. After the numerical results of the natural frequencies of the rig were obtained, they were then verified by the experimental results on a real object. Numerical analysis was performed using the ANSYS code. Santrauka Baigtiniu elementu metodu paremtas kompiuterines technikos ir kompiuteriniu sistemu kūrimas leidžia atlikti laisvuju svyravimu analize tokios dideles sistemos, kaip aviacines pavaru dežes, testavimo irenginys. Šio darbo tikslas buvo atlikti pavaru dežes nuovargio bandymu irenginio, veikiančio uždaro kontūro konfigūracijoje, laisvuju svyravimu analize. Taip pat pateikiamas testavimo irenginio skaitinis modelis, kurio veikimas yra pagristas baigtiniu elementu metodu. Pagrindinis modelis turi visas tikrosios sistemos svarbiausias struktūras. Gavus irenginio savuju dažniu kiekybinius rezultatus, buvo patikrinti realaus objekto eksperimentiniai rezultatai. Naudojantis ANSYS sistema buvo atlikta skaitine analize.

The Low Reynolds Number Limit of Vortex and Wake-Induced Vibrations

2010 ◽  
Author(s):  
Ste´phane E´tienne ◽  
Dominique Pelletier
Keyword(s):  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
Hopf Bifurcation ◽  
Numerical Model ◽  
Structural Damping ◽  
The Finite Element Method ◽  
Structure Interaction ◽  
Transverse Vibrations ◽  
Fully Coupled

Vortex and wake induced vibrations (VIV/WIV) of a circular cylinder at low values of the Reynolds number (Re) are simulated by means of a fully coupled fluid-structure interaction numerical model based on the finite element method. It is shown that VIV/WIV could occur far below the first Hopf bifurcation (Re <47). The main objective of this study is to determine the limiting Reynolds-Reduced velocity (Ur) curve that separates the non-vibrational area from the possible vibrations occurrence area. We assume that by taking a zero mass cylinder and zero structural damping we will obtain the low limit of vibrations in terms of Re and Ur. It is shown in particular that transverse vibrations could occur for reduced velocities larger than 40 and not below 3.5.

scholarly journals LARGE EDDY SIMULATION OF TURBULENT INCOMPRESSIBLE FLUID FLOWS BY A NINE-NODES CONTROL VOLUME-FINITE ELEMENT METHOD

2005 ◽  
Vol 4 (2) ◽  
pp. 173
Author(s):  
J. B. C. Silva ◽  
S. S. Mansur ◽  
R. C. Lima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Control Volume ◽  
Fluid Flows ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Turbulent Incompressible Fluid ◽  
Incompressible Fluid Flows ◽  
Control Volume Finite Element

The main purpose of this work is the numerical computation of turbulent incompressible fluid flows by a nine-node control volume finite element method (CVFEM) using the methodology of large-eddy simulation.. The domain is discretized using nine nodes finite elements and the equations are integrated into control volumes around the nodes of the finite elements. The Navier?Stokes equations are filtered for simulation of the large scales variables and the sub-grid scales stress appearing due to the filtering process are modeled through the eddy viscosity model of Smagorinsky. The two-dimensional benchmark problem of the lid-driven cavity flow is solved to validate the numerical code and preliminary results for the horizontal and vertical velocity profiles at the centerlines of the cavity and the stream functions are presented and compared with available results from the literature.

scholarly journals Finite Element Modelling of the Residual Stresses Induced in Thermally Deposited Coatings

2014 ◽  
Vol 59 (2) ◽  
pp. 593-599 ◽  
Author(s):  
J. Zimmerman
Keyword(s):  
Finite Element ◽  
Numerical Model ◽  
Deposition Process ◽  
Titanium Coating ◽  
The Finite Element Method ◽  
Second Stage ◽  
Residual Stress State ◽  
Detonation Method ◽  
Progressive Growth ◽  
Good Agreement

Abstract A numerical model based on the finite element method has been constructed with the aim to examine the residual stress state induced during thermal deposition of coatings on various substrates. The first stage of the modelling was designed to solve the problem of the high-velocity impact of a single spherical particle on a substrate using the “dynamics-explicit” module of the FEM ADINA software. In the second stage, the deposition process was simulated as a progressive growth of the coating until it achieved the desired thickness, and then the entire system was cooled to the ambient temperature. This problem was assumed to be thermo-mechanical and was also solved with the use of the FEM ADINA software. The samples assumed in the computations were cylindrical in shape and were built of a titanium coating, with three different thicknesses, deposited on an Al2O3 ceramic substrate by the detonation method. The numerical model was verified experimentally by measuring the deflection of the samples after their cooling. The computed values appeared to be in good agreement with those obtained experimentally.

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