Steady flow past sudden expansions at large Reynolds number. II. Navier–Stokes solutions for the cascade expansion

1987 ◽  
Vol 30 (1) ◽  
pp. 7 ◽  
Author(s):  
Frank S. Milos ◽  
Andreas Acrivos ◽  
John Kim
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Flow Past

A proposal concerning laminar wakes behind bluff bodies at large Reynolds number

1956 ◽  
Vol 1 (4) ◽  
pp. 388-398 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Bluff Body ◽  
The Body ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Bluff Bodies ◽  
Proper Solution ◽  
Navier Stokes Equation ◽  
Limit Solution

This note advocates a model of the steady flow about a bluff body at large Reynolds number which is different from the classical free-streamline model of Helmholtz and Kirchhoff. It is suggested that, although the free-streamline model may be a proper solution of the Navier-Stokes equation with μ = 0, it is unlikely to be the limit, as μ → 0, of the solution describing the steady flow due to the presence of a bluff body in an otherwise uniform stream. The limit solution proposed here is one which gives a closed wake.A closed wake contains a standing eddy, or eddies, whose general features can be inferred from the results of an earlier investigation of steady flow in a closed region at large Reynolds number. In all cases, the drag (coefficient) on the body tends to zero as the Reynolds number tends to infinity. The proccedure for finding the details of the closed wake behind two-dimensional and axisymmetrical bodies is described, although no particular case has yet been worked out.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

scholarly journals Simulation of flow past two tandem cylinders using deterministic vortex method

2012 ◽  
Vol 16 (5) ◽  
pp. 1460-1464 ◽  
Author(s):  
Guo Huang ◽  
Haiming Huan ◽  
Xiaoliang Xu ◽  
Yu Liu
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Sudden Change ◽  
Vortex Method ◽  
Simulation Method ◽  
Critical Distance ◽  
Navier Stokes ◽  
Tandem Cylinders ◽  
Flow Past

The vortex method is a direct numerical simulation method for solving the Navier-Stokes equations. In order to reveal the influence of Reynolds number and distances between the cylinders, the incompressible flow past a pair of tandem cylinders is solved on the base of the vortex method. The results show that for the flow past two tandem cylinders, there is a critical distance of the tandem cylinders. Over the critical distance, the flow field will have a sudden change, and the drag coefficient, lift coefficient and Strouhal number will also change dramatically. The critical distance will diminish as the Reynolds number rises.

scholarly journals On the uniqueness of steady flow past a rotating cylinder with suction

2000 ◽  
Vol 411 ◽  
pp. 213-232 ◽  
Author(s):  
E. V. BULDAKOV ◽  
S. I. CHERNYSHENKO ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Cross Flow ◽  
Rotation Velocity ◽  
Rotating Cylinder ◽  
Large Reynolds Number ◽  
Order Unity ◽  
Flow Past ◽  
Exponentially Small

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/√Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

Steady flows in rectangular cavities

1967 ◽  
Vol 28 (4) ◽  
pp. 643-655 ◽  
Author(s):  
Frank Pan ◽  
Andreas Acrivos
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Creeping Flow ◽  
Large Reynolds Number ◽  
Steady Flows ◽  
Viscous Effects ◽  
Number Range ◽  
Infinite Depth ◽  
Aspect Ratios ◽  
High Reynolds

This paper deals with the steady flow in a rectangular cavity where the motion is driven by the uniform translation of the top wall. Creeping flow solutions for cavities having aspect ratios from ¼ to 5 were obtained numerically by a relaxation technique and were shown to compare favourably with Dean & Montagnon's (1949) similarity solution, as extended by Moffatt (1964), in the region near the bottom corners of a square cavity as well as throughout the major portion of a cavity with aspect ratio equal to 5. In addition, for a Reynolds number range from 20 to 4000, flow patterns were determined experimentally by means of a photographic technique for finite cavities, as well as for cavities of effectively infinite depth. These experimental results suggest that, within finite cavities, the high Reynolds number steady flow should consist essentially of a single inviscid core of uniform vorticity with viscous effects being confined to thin shear layers near the boundaries, while, for cavities of infinite depth, the viscous and inertia forces should remain of comparable magnitude throughout the whole domain even in the limit of very large Reynolds number R.

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