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## ‣ Instabilidade hidrodinâmica linear do escoamento compressível em uma cavidade; Linear hidrodinamic instability of compressible lid-driven cavity flow

Bergamo, Leandro Fernandes
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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## ‣ Análise de escoamentos não-isotérmicos, incompressíveis, utilizando simulação de grandes escalas e o método de elementos finitos; Analysis of non-isotheemal,incompressible flows, using large eddy simulation and finite element method

Santos, Elizaldo Domingues dos
Tipo: Dissertação Formato: application/pdf
Português
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## ‣ Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

Yapici,K.; Uludag,Y.
Fonte: Brazilian Society of Chemical Engineering Publicador: Brazilian Society of Chemical Engineering
Tipo: Artigo de Revista Científica Formato: text/html
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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.

## ‣ Characterization of oscillatory instability in lid driven cavity flows using lattice Boltzmann method

Anupindi, Kameswararao; Lai, Weichen; Frankel, Steven
Tipo: Artigo de Revista Científica
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In the present work, lattice Boltzmann method (LBM) is applied for simulating flow in a three-dimensional lid driven cubic and deep cavities. The developed code is first validated by simulating flow in a cubic lid driven cavity at 1000 and 12000 Reynolds numbers following which we study the effect of cavity depth on the steady-oscillatory transition Reynolds number in cavities with depth aspect ratio equal to 1, 2 and 3. Turbulence modeling is performed through large eddy simulation (LES) using the classical Smagorinsky sub-grid scale model to arrive at an optimum mesh size for all the simulations. The simulation results indicate that the first Hopf bifurcation Reynolds number correlates negatively with the cavity depth which is consistent with the observations from two-dimensional deep cavity flow data available in the literature. Cubic cavity displays a steady flow field up to a Reynolds number of 2100, a delayed anti-symmetry breaking oscillatory field at a Reynolds number of 2300, which further gets restored to a symmetry preserving oscillatory flow field at 2350. Deep cavities on the other hand only attain an anti-symmetry breaking flow field from a steady flow field upon increase of the Reynolds number in the range explored. As the present work involved performing a set of time-dependent calculations for several Reynolds numbers and cavity depths...

## ‣ Numerical study of forced convection lid-driven cavity flows using LES (Large Eddy Simulation)

Santos, Elizaldo Domingues dos; Petry, Adriane Prisco; Rocha, Luiz Alberto Oliveira; França, Francis Henrique Ramos
Tipo: Artigo de Revista Científica
Português
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This study presents the LES (large eddy simulation) of forced convection in laminar and two dimensional turbulent flows when the flow reaches the steady state. The main purpose is the evaluation of a developed numerical methodology for the simulation of forced convection flows at various Reynolds numbers (100 ≤ ReH ≤ 10,000) and for a fixed Prandtl number (Pr = 1.0). The hexahedral eight-node FEM (finite element method) with an explicit Taylor-Galerkin scheme is used to obtain the numerical solutions of the conservation equations of mass, momentum and energy. The Smagorinsky model is employed for the sub-grid treatment. The time-averaged velocity and temperature profiles are compared with results of literature and a CFD (computational fluid dynamics) package based on finite volume method, leading to a highest deviation of nearly 6%. Moreover, characteristics of the forced convection flows are properly obtained, e.g., the effect of the Reynolds number over the multiplicity of scales.

## ‣ Simulação de escoamentos não-periódicos utilizando as metodologias pseudo-espectral e da fronteira imersa acopladas; Simulation of non-periodics flows using the fourier pseudo-spectral and immersed boundary methods

Mariano, Felipe Pamplona
Tipo: Dissertação
Português
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Para compreender fenômenos relacionados à combustão, aeroacústica, transição a turbulência entre outros, a Dinâmica de Fluídos Computacional (CFD) utiliza os métodos de alta ordem. Um dos mais conhecidos é o método pseudo-espectral de Fourier, o qual alia: alta ordem de precisão na resolução das equações, com um baixo custo computacional. Este está ligado à utilização da FFT e do método da projeção do termo da pressão, o qual desvincula os cálculos da pressão da resolução das equações de Navier-Stokes. O procedimento de calcular o campo de pressão, normalmente é o mais oneroso nas metodologias convencionais. Apesar destas vantagens, o método pseudo-espectral de Fourier só pode ser utilizado para resolver problemas com condições de contorno periódicas, limitando o seu uso no campo da dinâmica de fluídos. Visando resolver essa restrição uma nova metodologia é proposta no presente trabalho, que tem como objetivo simular escoamentos não-periódicos utilizando o método pseudo-espectral de Fourier. Para isso, é utilizada a metodologia da Fronteira Imersa, a qual representa as condições de contorno de um escoamento através de um campo de força imposto nas equações de Navier-Stokes. Como teste...

## ‣ The lid-driven square cavity flow : From stationary to time periodic and chaotic

Tipo: Artículo de Revista
Português
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Ranging from Re=100 to Re=20,000, several computational experiments are conducted, Re being the Reynolds number. The primary vortex stays put, and the longterm dynamic behavior of the small vortices determines the nature of the solutions. For low Reynolds numbers, the solution is stationary; for moderate Reynolds numbers, it is time periodic. For high Reynolds numbers, the solution is neither stationary nor time periodic: the solution becomes chaotic. Of the small vortices, the merging and the splitting, the appearance and the disappearance, and, sometime, the dragging away from one corner to another and the impeding of the merging - these mark the route to chaos. For high Reynolds numbers, over weak fundamental frequencies appears a very low frequency dominating the spectra - this very low frequency being weaker than clear-cut fundamental frequencies seems an indication that the global attractor has been attained. The global attractor seems reached for Reynolds numbers up to Re=15,000. This is the lid-driven square cavity flow; the motivations for studying this flow are recalled in the Introduction.

## ‣ Compressible modes in a square lid-driven cavity

Bergamo, Leandro Fernandes; Gennaro, Elmer Mateus; Theofilis, Vassilis; Medeiros, Marcello Augusto Faraco
Fonte: Elsevier B.V. Publicador: Elsevier B.V.
Tipo: Artigo de Revista Científica Formato: 125-134
Português
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); This paper studies the effect of compressibility on the linear stability of a two-dimensional lid-driven cavity flow in the subsonic regime. The base flow is generated by high fidelity direct numerical simulation and a biglobal mode instability analysis is carried out by a matrix forming approach. The eigenvalue problem is discretized by high-order finite differences and Arnoldi algorithm is used to reduce the size of the problem. The solution procedure uses sparse matrix techniques. Influence of Mach number on the modes known from incompressible calculations is presented, showing that compressibility has a stabilizing effect. New modes that appear only for compressible flows are presented and their relationship with duct acoustics is investigated.

## ‣ Proper general decomposition (PGD) for the resolution of Navier–Stokes equations

DUMON, Antoine; ALLERY, Cyrille; AMMAR, Amine
Português
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In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.; Région Poitou-Charentes

## ‣ Modelagem mecânica e investigação numérica de escoamentos de fluidos SMD empregando um método multi-campos de galerkin mínimos-quadrados

Santos, Daniel Dall'Onder dos
Tipo: Dissertação Formato: application/pdf
Português
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## ‣ Flujo de Poiseuille y la cavidad con pared móvil calculado usando el método de la ecuación de lattice Boltzmann; Poiseuille flow and the lid-driven cavity calculate using the Lattice Boltzmann equation method

Elkín G. Flórez S.; Grupo de Investigación ECOMMFIT, profesor asistente, Programa de Ingeniería Mecánica, Universidad de Pamplona.; Ildefonso Cuesta; Grupo de Investigación ECOMMFIT, Universidad Rovira i Virgili.; Clara Salueña; Grupo de Investigac
Tipo: article; publishedVersion Formato: application/pdf
Português
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## ‣ Driven cavity flow: from molecular dynamics to continuum hydrodynamics

Qian, Tiezheng; Wang, Xiao-Ping
Tipo: Artigo de Revista Científica
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Molecular dynamics (MD) simulations have been carried out to investigate the slip of fluid in the lid driven cavity flow where the no-slip boundary condition causes unphysical stress divergence. The MD results not only show the existence of fluid slip but also verify the validity of the Navier slip boundary condition. To better understand the fluid slip in this problem, a continuum hydrodynamic model has been formulated based upon the MD verification of the Navier boundary condition and the Newtonian stress. Our model has no adjustable parameter because all the material parameters (density, viscosity, and slip length) are directly determined from MD simulations. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations, from the molecular-scale structure to the global flow. The main discovery is as follows. In the immediate vicinity of the corners where moving and fixed solid surfaces intersect, there is a core partial-slip region where the slippage is large at the moving solid surface and decays away from the intersection quickly. In particular, the structure of this core region is nearly independent of the system size. On the other hand, for sufficiently large system, an additional partial-slip region appears where the slippage varies as $1/r$ with $r$ denoting the distance from the corner along the moving solid surface. The existence of this wide power-law region is in accordance with the asymptotic $1/r$ variation of stress and the Navier boundary condition.; Comment: 28 pages...

## ‣ Flow in the Driven Cavity Calculated by the Lattice Boltzmann Method

Miller, W.
Tipo: Artigo de Revista Científica
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The lattice Boltzmann method with enhanced collisions and rest particles is used to calculate the flow in a two-dimensional lid-driven cavity. The abilitity of this method to compute the velocity and the pressure of an incompressible fluid in a geometry with Dirichlet and Neumann boundary conditions is verified by calculating a test-problem where the analytical solution is known. Different parameter configurations have been tested for Reynolds numbers from $Re=10$ to $Re=2000$. The vortex structure for a more generalized lid-driven cavity problem with a non-uniform top speed has been studied for various acpect ratios.; Comment: post-script-file text without figures. figures can be asked from the Author

## ‣ Investigations of the NS-alpha model using a lid-driven cavity flow

Scott, K. A.; Lien, F. S.
Tipo: Artigo de Revista Científica
Português
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In this paper we investigate a subgrid model based on an anisotropic version of the NS-$\alpha$ model using a lid-driven cavity flow at a Reynolds number of 10,000. Previously the NS-$\alpha$ model has only been used numerically in the isotropic form. The subgrid model is developed from the Eulerian-averaged anisotropic equations [Holm, \textit{Physica D}, v.133, pp 215-269, 1999]. It was found that when $\alpha^{2}$ was based on the mesh numerical oscillations developed which manifested themselves in the appearance of streamwise vortices and a `mixing out' of the velocity profile. This is analogous to the Craik-Leibovich mechanism, with the difference being that the oscillations here are not physical but numerical. The problem could be traced back to the discontinuity in $\alpha^{2}$ encountered when $\alpha^{2}=0$ on the endwalls. An alternative definition of $\alpha^{2}$ based on velocity gradients, rather than mesh spacing, is proposed and tested. Using this definition the results with the model shown a significant improvement. The splitting of the downstream wall jet, rms and shear stress profiles are correctly captured a coarse mesh. The model is shown to predict both positive and negative energy transfer in the jet impingement region...

## ‣ Experimental observation of the steady - oscillatory transition in a cubic lid-driven cavity

Liberzon, A.; Feldman, Y.; Gelfgat, A. Yu.
Tipo: Artigo de Revista Científica
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Particle image velocimetry is applied to the lid-driven flow in a cube to validate the numerical prediction of steady - oscillatory transition at lower than ever observed Reynolds number. Experimental results agree with the numerical simulation demonstrating large amplitude oscillatory motion overlaying the base quasi-two-dimensional flow in the mid-plane. A good agreement in the values of critical Reynolds number and frequency of the appearing oscillations, as well as similar spatial distributions of the oscillations amplitude are obtained.; Comment: 14 pages, 6 figures, submitted to Phys. Fluids

## ‣ The secondary flow in a short aspect ratio circular lid driven cavity at small but finite Reynolds number

Muite, Benson K.
Tipo: Artigo de Revista Científica
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Regular perturbation solutions are obtained for the Stokes flow field, the first order effects of inertia on the flow field, and the primary and secondary pressure fields in the circular lid driven cavity. The physical mechanism that causes vortex breakdown exists at small Reynolds number; it is a stagnation of the secondary flow by an adverse pressure gradient. The discontinuity between the rotating lid and the stationary sidewall has negligible influence on the flow field provided that the inertial forcing of the secondary flow is not localized near the boundary discontinuity, and the Reynolds number is small.; Comment: 18 pages, 20 figures, submitted to Physics of Fluids

## ‣ Sheared stably stratified turbulence and large-scale waves in a lid driven cavity

Cohen, N.; Eidelman, A.; Elperin, T.; Kleeorin, N.; Rogachevskii, I.
Tipo: Artigo de Revista Científica
Português
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We investigated experimentally stably stratified turbulent flows in a lid driven cavity with a non-zero vertical mean temperature gradient in order to identify the parameters governing the mean and turbulent flows and to understand their effects on the momentum and heat transfer. We found that the mean velocity patterns (e.g., the form and the sizes of the large-scale circulations) depend strongly on the degree of the temperature stratification. In the case of strong stable stratification, the strong turbulence region is located in the vicinity of the main large-scale circulation. We detected the large-scale nonlinear oscillations in the case of strong stable stratification which can be interpreted as nonlinear internal gravity waves. The ratio of the main energy-containing frequencies of these waves in velocity and temperature fields in the nonlinear stage is about 2. The amplitude of the waves increases in the region of weak turbulence (near the bottom wall of the cavity), whereby the vertical mean temperature gradient increases.; Comment: 11 pages, 14 figures, REVTEX4-1

## ‣ Oscillatory instability of fully 3D flow in a cubic diagonally lid-driven cavity

Feldman, Yuri
Tipo: Artigo de Revista Científica
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A transition to unsteadiness of a flow inside a cubic diagonally lid-driven cavity with no-slip boundaries is numerically investigated by a series of direct numerical simulations (DNS) performed on 100^3 and 200^3 stretched grids. It is found that the observed oscillatory instability is setting in via a subcritical symmetry-breaking Hopf bifurcation. The instability evolves on two vortices in a coupled manner. Critical values of Reynolds number Recr=2320 and non-dimensional angular oscillating frequency omegacr=0.249 for transition from steady to oscillatory flow are accurately estimated. Characteristic patterns of the 3D oscillatory flow are presented.

## ‣ Large-eddy simulation of the flow in a lid-driven cubical cavity

Bouffanais, Roland; Deville, Michel O.; Leriche, Emmanuel
Tipo: Artigo de Revista Científica
This paper presents the large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method (SEM) using the dynamic model. Two spectral filtering techniques suitable for these simulations have been implemented. Numerical results for Reynolds number $\text{Re}=12'000$ are showing very good agreement with other experimental and DNS results found in the literature.