Unsteady compressible second-order boundary layers at the stagnation point of two-dimensional and axisymmetric bodies

1986 ◽  
Vol 20 (4) ◽  
pp. 273-281 ◽  
Author(s):  
R. Vasantha ◽  
G. Nath
Keyword(s):  
Stagnation Point ◽  
Boundary Layers ◽  
Second Order ◽  
Two Dimensional ◽  
Axisymmetric Bodies

Direct numerical simulations of two-dimensional chaotic natural convection in a differentially heated cavity of aspect ratio 4

1995 ◽  
Vol 304 ◽  
pp. 87-118 ◽  
Author(s):  
Shihe Xin ◽  
Patrick Le Quéré
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Boundary Layers ◽  
Travelling Waves ◽  
Outer Edge ◽  
Second Order ◽  
Core Region ◽  
Turbulent Heat ◽  
Two Dimensional

Chaotic natural convection in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is investigated by direct numerical integration of the unsteady two-dimensional equations. Time integration is performed with a spectral algorithm using Chebyshev spatial approximations and a second-order finite-difference time-stepping scheme. Asymptotic solutions have been obtained for three values of the Rayleigh number based on cavity height up to 1010. The time-averaged flow fields show that the flow structure increasingly departs from the well-known laminar one. Large recirculating zones located on the outer edge of the boundary layers form and move upstream with increasing Rayleigh number. The time-dependent solution is made up of travelling waves which run downstream in the boundary layers. The amplitude of these waves grows as they travel downstream and hook-like temperature patterns form at the outer edge of the thermal boundary layer. At the largest Rayleigh number investigated they grow to such a point that they result in the formation of large unsteady eddies that totally disrupt the boundary layers. These eddies throw hot and cold fluid into the upper and lower parts of the core region, resulting in thermally more homogeneous top and bottom regions that squeeze a region of increased stratification near the mid-cavity height. It is also shown that these large unsteady eddies keep the internal waves in the stratified core region excited. These simulations also give access to the second-order statistics such as turbulent kinetic energy, thermal and viscous dissipation, Reynolds stresses and turbulent heat fluxes.

Stagnation Point Flow of a Non-Newtonian Second Order Fluid

1988 ◽  
Vol 12 (2) ◽  
pp. 57-61 ◽  
Author(s):  
I. Teipel
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Stagnation Point ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Equation Of Motion ◽  
Weissenberg Number ◽  
Second Order ◽  
Two Dimensional ◽  
Fourth Order Differential Equation

In this paper the flow near a two-dimensional stagnation point for a particular non-Newtonian fluid has been studied. For a second order fluid the equation of motion for the stream function has been solved by using a similarity approach. A new parameter which is a combination of the Weissenberg number and the Reynolds number characterizes the visco-elastic effects. A fourth order differential equation has to be solved numerically. Only three boundary conditions are necessary. Results for various cases will be shown. In addition an approxamation theory has been derived in order to recognize the influence of the new parameter.

Unsteady flow of a second-order fluid near a stagnation point

1966 ◽  
Vol 24 (1) ◽  
pp. 33-39 ◽  
Author(s):  
A. C. Srivastava
Keyword(s):  
Stagnation Point ◽  
Order Effect ◽  
Second Order ◽  
Two Dimensional ◽  
Shearing Stress ◽  
Harmonic Oscillations ◽  
Phase Lead ◽  
Boundary Layer Region ◽  
Two Dimensional Flow ◽  
Layer Region

Two-dimensional flow of a second-order fluid near a stagnation point occurring on a flat plate which is performing harmonic oscillations in its own plane is considered. The equations have been integrated by the Kármán-Pohlhausen method for small values of ω, the frequency of the oscillation of the plate, and the W.B.K. method is applied to solve the equations for high values of ω. The velocity profile within the boundary-layer region and the shearing stress on the plate have been obtained in both the cases. The oscillation of the shearing stress has a phase lead over the oscillation of the plate. This phase lead decreases with increase of the second-order effect for small values of ω.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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