scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

A Conceptual Model of Flapping-Wing Mechanism Inspired from the Results of Numerical Study

2013 ◽  
Vol 397-400 ◽  
pp. 783-788
Author(s):  
Xing Wei Zhang ◽  
Chao Wang ◽  
Hang Liu
Keyword(s):  
Conceptual Model ◽  
Power Efficiency ◽  
Stokes Equations ◽  
Numerical Study ◽  
Flapping Wing ◽  
Numerical Results ◽  
Navier Stokes ◽  
Active Deformation ◽  
Navier Stokes Equations ◽  
Wing Model

This paper investigates the aerodynamic forces of several plunging wing models by means of computational fluid dynamics. A finite volume method was used to solve the two-dimensional unsteady incompressible Navier-Stokes equations. The forces and power efficiency have been calculated and compared between sets of different models. Current work found that the nonsymmetrical moving can enhance the lift and thrust forces. The numerical results also prove that the flexible wing model can be use to improve the efficiency and reduce the input. Additionally, a new conceptual model for flapping wing mechanism with active deformation and adaptive nonsymmetrical driving motion is proposed base on the numerical results.

Axisymmetric Inertial Oscillations in Transient Rotating Flows in a Cylinder

1997 ◽  
Vol 119 (2) ◽  
pp. 390-396
Author(s):  
Jae Won Kim ◽  
Jae Min Hyun
Keyword(s):  
Large Time ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Experimental Studies ◽  
Numerical Results ◽  
Navier Stokes ◽  
Inertial Oscillations ◽  
Time Duration ◽  
Navier Stokes Equations

A numerical study is made of axisymmetric inertial oscillations in a fluid-filled cylinder. The entire cylinder undergoes a spin-up process from rest with an impulsively started rotation rate Ω(t) = Ω0 + εω cos(ωt). Numerical solutions are obtained to the axisymmetric, time-dependent Navier-Stokes equations. Identification of the inertial oscillations is made by inspecting the evolution of the pressure difference between two pre-set points on the central axis, Cp. In the limit of large time, the inertial frequency thus determined is in close agreement with the results of the classical inviscid theory for solid-body rotation. As in previous experimental studies, the t* − (Ω0/ω) plots are constructed for inertial oscillations, where t* indicates the time duration until the maximum Cp is detected. These detailed numerical results are in broad agreement with the prior experimental data. Flow intensifications under the resonance conditions are illustrated based on the numerical results. Depictions are made of the increase in the amplitude of oscillating part of the total angular momentum under the resonance conditions. Also, the patterns of t* − (Ω0/ω) curves are displayed for different inertial frequency modes.

Three-dimensional natural convection in a box: a numerical study

1977 ◽  
Vol 83 (1) ◽  
pp. 1-31 ◽  
Author(s):  
G. D. Mallinson ◽  
G. De Vahl Davis
Keyword(s):  
Natural Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aspect Ratios ◽  
Inertial Interaction ◽  
Longitudinal Temperature

The solution of the steady-state Navier–Stokes equations in three dimensions has been obtained by a numerical method for the problem of natural convection in a rectangular cavity as a result of differential side heating. In the past, this problem has generally been treated as though it were two-dimensional. The solutions explore the three-dimensional motion generated by the presence of no-slip adiabatic end walls. For Ra = 104, the three-dimensional motion is shown to be the result of the inertial interaction of the rotating flow with the stationary walls together with a contribution arising from buoyancy forces generated by longitudinal temperature gradients. The inertial effect is inversely dependent on the Prandtl number, whereas the thermal effect is nearly constant. For higher values of Ra, multiple longitudinal flows develop which are a delicate function of Ra, Pr and the cavity aspect ratios.

scholarly journals A SEMI-IMPLICIT SCHEME FOR SOLVING INCOMPRESSIBLE VISCOUS FREE SURFACE FLOWS

2005 ◽  
Vol 4 (2) ◽  
Author(s):  
C. M. Oishi ◽  
J. A. Cuminato ◽  
V. G. Ferreira ◽  
M. F. Tomé ◽  
A. Castelo ◽  
...  
Keyword(s):  
Free Surface ◽  
Numerical Method ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Numerical Results ◽  
Navier Stokes ◽  
Variable Order ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
The Stability

The present work is concerned with a numerical method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in the primitive variables formulation. The diffusive terms are treated by Implicit Backward and Crank-Nicolson methods, and the non-linear convection terms are, explicitly, approximated by the high order upwind VONOS (Variable-Order Non-Oscillatory Scheme) scheme. The boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical method is then applied to the simulation of free surface and confined flows. The numerical results show that the present technique eliminates the stability restriction in the original explicit method. For low Reynolds number flow dynamics, the method is robust and produces numerical results that compare very well with the analytical solutions.

scholarly journals A SEMI-IMPLICIT SCHEME FOR SOLVING INCOMPRESSIBLE VISCOUS FREE SURFACE FLOWS

2005 ◽  
Vol 4 (2) ◽  
pp. 106
Author(s):  
C. M. Oishi ◽  
J. A. Cuminato ◽  
V. G. Ferreira ◽  
M. F. Tomé ◽  
A. Castelo ◽  
...  
Keyword(s):  
Free Surface ◽  
Numerical Method ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Numerical Results ◽  
Navier Stokes ◽  
Variable Order ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
The Stability

The present work is concerned with a numerical method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in the primitive variables formulation. The diffusive terms are treated by Implicit Backward and Crank-Nicolson methods, and the non-linear convection terms are, explicitly, approximated by the high order upwind VONOS (Variable-Order Non-Oscillatory Scheme) scheme. The boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical method is then applied to the simulation of free surface and confined flows. The numerical results show that the present technique eliminates the stability restriction in the original explicit method. For low Reynolds number flow dynamics, the method is robust and produces numerical results that compare very well with the analytical solutions.

scholarly journals Effect of Uniform and Non-Uniform Hot Wall Temperature on Species Separation in a Tilting Cell

2020 ◽  
Vol 307 ◽  
pp. 01035
Author(s):  
Mouna Touiker ◽  
Abdeslam Omara
Keyword(s):  
Aspect Ratio ◽  
Stokes Equations ◽  
Liquid Mixture ◽  
Lewis Number ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Tilting Angle ◽  
The Right ◽  
Volume Method

This work deals with the Soret separation of a binary liquid mixture (Water 60 wt %-Ethanol 40 wt %). The studied configuration is a tilted rectangular cavity of large aspect ratio A. It is assumed that the right wall is heated uniformly or non-uniformly, while the left wall is maintained at a constant cold temperature. The top and bottom walls are well insulated. A developed program (based on the finite-volume method and the semi-implicit method for pressure-linked equations algorithm) was utilized to numerically solve the governing Navier–Stokes equations, the energy and the species equations with the associated boundary conditions. The relevant parameters in this study are the tilting angle (α), the aspect ratio (A), the mass Rayleigh number (Ram) and the Lewis number (Le).

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

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