A stochastic Lamb–Oseen vortex solution of the 2D Navier–Stokes equations

2009 ◽  
Vol 26 (12) ◽  
pp. 1756-1763 ◽  
Author(s):  
J. L. Sereno ◽  
J. M. C. Pereira ◽  
J. C. F. Pereira
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vortex Solution ◽  
Oseen Vortex

An unsteady two-cell vortex solution of the Navier—Stokes equations

1970 ◽  
Vol 41 (3) ◽  
pp. 673-687 ◽  
Author(s):  
P. G. Bellamy-Knights
Keyword(s):  
Radial Flow ◽  
Stokes Equations ◽  
Circumferential Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Radial Flux ◽  
Vortex Solution ◽  
Flow Systems ◽  
Vortex Solutions

The steady two-cell viscous vortex solution of Sullivan (1959) is extended to yield unsteady two-cell viscous vortex solutions which behave asymptotically as certain analogous unsteady one-cell solutions of Rott (1958). The radial flux is a parameter of the solution, and the effect of the radial flow on the circumferential velocity, is analyzed. The work suggests an explanation for the eventual dissipation of meteorological flow systems such as tornadoes.

Complex solutions of the Dean equations and non-uniqueness at all Reynolds numbers

2017 ◽  
Vol 818 ◽  
pp. 241-259 ◽  
Author(s):  
F. A. T. Boshier ◽  
A. J. Mestel
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Vortex Solution ◽  
Vortex Solutions ◽  
Complex Solutions ◽  
Unknown Solution

Steady incompressible flow down a slowly curving circular pipe is considered, analytically and numerically. Both real and complex solutions are investigated. Using high-order Hermite–Padé approximants, the Dean series solution is analytically continued outside its circle of convergence, where it predicts a complex solution branch for real positive Dean number, $K$. This is confirmed by numerical solution. It is shown that other previously unknown solution branches exist for all $K>0$, which are related to an unforced complex eigensolution. This non-uniqueness is believed to be generic to the Navier–Stokes equations in most geometries. By means of path continuation, numerical solutions are followed around the complex $K$-plane. The standard Dean two-vortex solution is shown to lie on the same hypersurface as the eigensolution and the four-vortex solutions found in the literature. Elliptic pipes are considered and shown to exhibit similar behaviour to the circular case. There is an imaginary singularity limiting convergence of the Dean series, an unforced solution at $K=0$ and non-uniqueness for $K>0$, culminating in a real bifurcation.

Bifurcation in steady laminar flow through curved tubes

1982 ◽  
Vol 119 ◽  
pp. 475-490 ◽  
Author(s):  
K. Nandakumar ◽  
Jacob H. Masliyah
Keyword(s):  
Stokes Equations ◽  
Outer Wall ◽  
Dual Solutions ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Vortex Solution ◽  
Duct Geometry ◽  
Flow Through ◽  
Curved Ducts

The occurrence of dual solutions in curved ducts is investigated through a numerical solution of the Navier-Stokes equations in a bipolar-toroidal co-ordinate system. With the shape of duct being the region formed by the natural co-ordinate surfaces, it was possible to alter the duct geometry gradually and preserve the prevailing form of the velocity field, in a manner suggested by Benjamin (1978).In addition to the Dean number Dn = Re/Rc½, a geometrical parameter that defines the shape of the duct was also varied systematically to study the bifurcation of a two-vortex solution into a two- and four-vortex solution. Dual solutions have been found for all geometrical shapes investigated here. Of particular interest are the shapes of a full circle and a semicircle with a curved outer wall.

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.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations
Sign in / Sign up

Export Citation Format

Share Document