scholarly journals Numerical Flutter Simulation of a High-Aspect-Ratio Swept-Back Wing Based on the Navier-Stokes Equations.

1997 ◽  
Vol 45 (525) ◽  
pp. 615-619
Author(s):  
Hamid Reza KHEIRANDISH ◽  
Goro BEPPU ◽  
Jiro NAKAMICHI
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

1974 ◽  
Vol 65 (2) ◽  
pp. 231-246 ◽  
Author(s):  
D. E. Cormack ◽  
L. G. Leal ◽  
J. H. Seinfeld
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Excellent Agreement ◽  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Shallow Cavity

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6·983, 10 ≤ Gr 2 × 104 and 0·05 [les ] A [les ] 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A [lsim ] 0·1 and Gr2A3Pr2 [lsim ] 105. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

Computation of Incompressible Three-Dimensional Mixed Convection Flows in Long Aspect Ratio Channels Using an Efficient Finite Difference Method for Vectorial Supercomputers

2005 ◽  
Author(s):  
Xavier Nicolas ◽  
Shihe Xin
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Mixed Convection ◽  
Spectral Decomposition ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Factorization Method ◽  
Navier Stokes ◽  
Navier Stokes Equations

Based on Goda’s algorithm and second-order central finite differences, a very efficient vectorized code is tailored to solve 3D incompressible Navier-Stokes equations for mixed convection flows in high streamwise aspect ratio channels. The code takes advantage of incremental factorization method of ADI type, spectral decomposition of the ID Laplace operators and TDMA algorithm. It is validated through experiments of various Poiseuille-Rayleigh-Be´nard flows with steady longitudinal and unsteady transverse rolls.

Precession of a rapidly rotating cylinder flow: traverse through resonance

2015 ◽  
Vol 782 ◽  
pp. 63-98 ◽  
Author(s):  
Francisco Marques ◽  
Juan M. Lopez
Keyword(s):  
Aspect Ratio ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Nonlinear Models ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Small Scale ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Weakly Nonlinear

Recent experiments using a rapidly rotating and precessing cylinder have shown that for specific values of the precession rate, aspect ratio and tilt angle, sudden catastrophic transitions to turbulence occur. Even if the precessional forcing is not too strong, there can be intermittent recurrences between a laminar state and small-scale chaotic flow. The inviscid linearized Navier–Stokes equations have inertial-wave solutions called Kelvin eigenmodes. The precession forces the flow to have azimuthal wavenumber $m=1$ (spin-over mode). Depending on the cylinder aspect ratio and on the ratio of the rotating and precessing frequencies, additional Kelvin modes can be in resonance with the spin-over mode. This resonant flow would grow unbounded if not for the presence of viscous and nonlinear effects. In practice, one observes a rapid transition to turbulence, and the precise nature of the transition is not entirely clear. When both the precessional forcing and viscous effects are small, weakly nonlinear models and experimental observations suggest that triadic resonance is at play. Here, we used direct numerical simulations of the full Navier–Stokes equations in a narrow region of parameter space where triadic resonance has been previously predicted from a weakly nonlinear model and observed experimentally. The detailed parametric studies enabled by the numerics reveal the complex dynamics associated with weak precessional forcing, involving symmetry-breaking, hysteresis and heteroclinic cycles between states that are quasiperiodic, with two or three independent frequencies. The detailed analysis of these states leads to associations of physical mechanisms with the various time scales involved.

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).

Dean vortices in finite-aspect-ratio ducts

2013 ◽  
Vol 716 ◽  
Author(s):  
Philip E. Haines ◽  
James P. Denier ◽  
Andrew P. Bassom
Keyword(s):  
Aspect Ratio ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Curved Channel ◽  
Dean Number ◽  
Element Analysis ◽  
Navier Stokes Equations ◽  
New Class ◽  
Dean Vortices

AbstractWe consider the development of Dean vortices in a curved channel of finite aspect ratio. Solutions to the axisymmetric Navier–Stokes equations are obtained through a finite-element analysis, allowing us to explore the complex and rich bifurcation pattern of the flow as the aspect ratio and Dean number vary. We demonstrate a new class of finite-amplitude vortices and discuss their relationship to similar structures seen in finite-length Taylor–Couette flow.

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