Details of the Computed Flowfield Over a Circular Cylinder at Reynolds Number 1200

1988 ◽  
Vol 110 (4) ◽  
pp. 446-452 ◽  
Author(s):  
C. L. Rumsey
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Local Maximum ◽  
Flow Region ◽  
Rapid Onset ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Approximate Factorization ◽  
Start Up

The application of an upwind-biased implicit approximate factorization Navier-Stokes algorithm to the unsteady impulsive start-up flow over a circular cylinder at Reynolds number 1200 is described. The complete form of the compressible Navier-Stokes equations is used, and the algorithm is second-order accurate in both space and time. The drag on the cylinder is computed for early times in the start-up flow. The value of the local maximum drag as well as the time at which it occurs are predicted and compared to another computational result and experiment. The development with time of the shape and size of the separated vortical flow region is computed, as well as the time-variation of several boundary layer parameters and profile shapes. Computations, in general, show excellent agreement with experiment, although the present method predicts a more rapid onset of reversed flow on the cylinder than evidenced in experiment. The effect of grid density on the development of the unsteady flow is also shown.

Fine Structure of Vortex Sheet Rollup by Viscous and Inviscid Simulation

1991 ◽  
Vol 113 (1) ◽  
pp. 31-36 ◽  
Author(s):  
G. Tryggvason ◽  
W. J. A. Dahm ◽  
K. Sbeih
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Large Scale ◽  
Stokes Equations ◽  
Flow Region ◽  
Vortex Sheet ◽  
Navier Stokes ◽  
Vortex Sheets ◽  
Limiting Behavior ◽  
High Reynolds

Numerical simulations of the large amplitude stage of the Kelvin-Helmholtz instability of a relatively thin vorticity layer are discussed. At high Reynolds number, the effect of viscosity is commonly neglected and the thin layer is modeled as a vortex sheet separating one potential flow region from another. Since such vortex sheets are susceptible to a short wavelength instability, as well as singularity formation, it is necessary to provide an artificial “regularization” for long time calculations. We examine the effect of this regularization by comparing vortex sheet calculations with fully viscous finite difference calculations of the Navier-Stokes equations. In particular, we compare the limiting behavior of the viscous simulations for high Reynolds numbers and small initial layer thickness with the limiting solution for the roll-up of an inviscid vortex sheet. Results show that the inviscid regularization effectively reproduces many of the features associated with the thickness of viscous vorticity layers with increasing Reynolds number, though the simplified dynamics of the inviscid model allows it to accurately simulate only the large scale features of the vorticity field. Our results also show that the limiting solution of zero regularization for the inviscid model and high Reynolds number and zero initial thickness for the viscous simulations appear to be the same.

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.

Stokes flow between two intersecting circular arcs

1965 ◽  
Vol 61 (1) ◽  
pp. 271-274 ◽  
Author(s):  
K. B Ranger
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
Circular Arcs ◽  
Converging Flow ◽  
Point Of Intersection

This paper considers a family of viscous flows closely related to the exact Jeffery-Hamel solution ((l), (2)) of the two-dimensional Navier-Stokes equations, for diverging or converging flow in a channel. It is known that if the walls of the channel intersect at an angle less than π then there is a unique solution of the Navier-Stokes equations in which the streamlines are straight lines issuing from the point of intersection of the walls and the flow is everywhere diverging or everywhere converging. The flow parameters depend on the total fluid mass M emitted at the point of intersection and the angle 2α between the walls. By taking the Reynolds number R = M/ν, where v is the kinematic viscosity, the stream function can be expanded in a power series in R in which the leading term is a Stokes flow. Alternatively the solution can be developed by perturbing the Stokes flow and is one of very few examples known in which a Stokes flow can be regarded as a uniformly valid first approximation everywhere in an infinite fluid region. The class of flows to be considered is a generalization of the Jeffery–Hamel flow by taking the flow region to be finite and bounded by two circular arcs which intersect at an angle less than π At one point of intersection fluid is forced into the region and an equal amount is absorbed out at the other point. It is found to the first order that the flow at the two points of intersection corresponds to the zero Reynolds number limit for diverging and converging flow, respectively. Now since the flow at these points can be developed by perturbing the Stokes flow solution it is reasonable to assume that the zero Reynolds number flow in the entire finite region bounded by the arcs is a Stokes flow since the most likely region in which this approximation becomes invalid is locally at the points of intersection but here the validity of the approximation is ensured. A comparison of the convection terms with the viscous terms verifies that this conclusion is borne out.

Viscous and inviscid simulations of the start-up vortex

2017 ◽  
Vol 813 ◽  
pp. 53-69
Author(s):  
Paolo Luchini ◽  
Renato Tognaccini
Keyword(s):  
Reynolds Number ◽  
Large Time ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Vortex Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Spiral Vortex ◽  
Start Up

Inviscid, unsteady simulations of the roll up of the start-up vortex issuing from a semi-infinite plate are compared with previous simulations of the viscous flow. The inviscid equations were solved by a lumped-vortex method, the two-dimensional, incompressible Navier–Stokes equations in the vorticity–streamfunction formulation modelled the viscous problem. The purpose is to verify whether the irregular behaviour found by the inviscid solution well approximates the unstable evolution of the viscous spiral vortex in the limit of infinitely large time (or equivalently Reynolds number).

Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil

1996 ◽  
Vol 308 ◽  
pp. 195-217 ◽  
Author(s):  
P. Ghosh Choudhuri ◽  
D. D. Knight
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Stokes Equations ◽  
Leading Edge ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Approximate Factorization ◽  
Simultaneous Formation ◽  
Pitching Airfoil

The effects of compressibility, pitch rate and Reynolds number on the initial stages of two-dimensional unsteady separation of laminar subsonic flow over a pitching NACA-0012 airfoil have been studied numerically. The approach involves the simulation of the flow by solving the two-dimensional unsteady compressible laminar Navier-Stokes equations employing the implicit approximate-factorization algorithm of Beam & Warming and a boundary-fitted C-grid. The algorithm has been extensively validated through comparison with analytical and previous numerical results. The computations display several important trends for the ‘birth’ of the primary recirculating region which is a principal precursor to leading-edge separation. Increasing the non-dimensional pitch rate from 0.05 to 0.2 at a fixed Reynolds number and Mach number delays the formation of the primary recirculating region. The primary recirculating region also forms closer to the leading edge. Increasing the Mach number from 0.2 to 0.5 at a fixed Reynolds number and pitch rate causes a delay in the formation of the primary recirculating region and also leads to its formation farther from the airfoil top surface. The length scale associated with the recirculating regions increases as well. Increasing the Reynolds number from 104 to 105 at a fixed Mach number and pitch rate hastens the appearance of the primary recirculating region. A shock appears on the top surface at a Reynolds number of 105 along with the simultaneous formation of multiple recirculating regions near the leading edge.

Three-dimensional pressure- and shear-driven flow phenomena in a circular recess of a hydrostatic rotary table

2013 ◽  
Vol 228 (6) ◽  
pp. 989-1004
Author(s):  
Feng Shen ◽  
Cong-Lian Chen ◽  
Zhao-Miao Liu
Keyword(s):  
Reynolds Number ◽  
Vector Fields ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Region ◽  
Numerical Control ◽  
Navier Stokes ◽  
Rotary Table ◽  
Flow Phenomena ◽  
Flow States

The three-dimensional pressure- and shear-driven flow phenomena in a circular recess of hydrostatic rotary table in heavy-duty computer numerical control machines is very complicated and has not been fully explored. Navier–Stokes equations have been applied through the whole flow region using a finite volume approach to explore this complicated flow phenomena, including the influences of feeding Reynolds number ( Rei), sliding Reynolds number ( Res) and the recess geometry on flow behaviors. A test rig based on a particle image velocimetry was built to compare experimental and numerical results, finding a good agreement for stationary cases. The results show that the flow patterns in the recess are very complex and four three-dimensional vortices exist at Rei = 448 and Res = 74.6. Four flow states are defined according to the structure of the vortices. Different sectional profiles of the streamlines and velocity vector fields are examined to reveal the mechanism of pressure- and shear-driven flow interactions. The results of influences of recess geometry on flow states and pressure patterns are intended to contribute to represent a database in view of the hydrostatic rotary table theoretical modeling.

scholarly journals Axisymmetric travelling waves in annular sliding Couette flow at finite and asymptotically large Reynolds number

2013 ◽  
Vol 720 ◽  
pp. 582-617 ◽  
Author(s):  
K. Deguchi ◽  
A. G. Walton
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Equilibrium Solutions ◽  
Specific Flow

AbstractThe relationship between numerical finite-amplitude equilibrium solutions of the full Navier–Stokes equations and nonlinear solutions arising from a high-Reynolds-number asymptotic analysis is discussed for a Tollmien–Schlichting wave-type two-dimensional vortical flow structure. The specific flow chosen for this purpose is that which arises from the mutual axial sliding of co-axial cylinders for which nonlinear axisymmetric travelling-wave solutions have been discovered recently by Deguchi & Nagata (J. Fluid Mech., vol. 678, 2011, pp. 156–178). We continue this solution branch to a Reynolds number $R= 1{0}^{8} $ and confirm that the behaviour of its so-called lower branch solutions, which typically produce a smaller modification to the laminar state than the other solution branches, quantitatively agrees with the axisymmetric asymptotic theory developed in this paper. We further find that this asymptotic structure breaks down when the disturbance wavelength is comparable with $R$. The new structure which replaces it is investigated and the governing equations are derived and solved. The flow visualization of the resultant solutions reveals that they possess a streamwise localized structure, with the trend agreeing qualitatively with full Navier–Stokes solutions for relatively long-wavelength disturbances.

Flow Around a Suddenly Start Rotating Circular Cylinder and Introduce a New Paradox

2007 ◽  
Author(s):  
Baku M. Nagai ◽  
Muhammed Sohel Rana ◽  
Kazumasa Ameku ◽  
Junji Chinen
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Velocity Distribution ◽  
Analytic Solution ◽  
Stokes Equations ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotating Circular Cylinder ◽  
Theoretical Results

There have been many misunderstanding about the flow around vortices for example a stationary and/or moving vortex pair. The authors have pointed out that no fluid dynamics textbooks have accepted the existence of stationary or arbitral speed moving vortices. About the vortex flow, recently the authors have found a new analytic solution of the Navier-Stokes equations for two-dimensional flow around a suddenly start rotating circular cylinder. This analytic solution explains the velocity distribution, vorticity distribution with change in time, and boundary layer thickness close to a vortex filament because of the action of viscosity. The resulting solutions are involved simple exponential function. Authors present a new construction for the solution of the Navier-Stokes equations for suddenly start rotating circular cylinder. New solution is based on the concept of the similarity solution approach using similarity variable, dimensional analysis, initial, & boundary conditions. A brief theoretical discussion is presented about the suddenly start rotating circular cylinder. The second part of the paper deals with the analytic solution being compared with experimental results in various Reynolds number. A typical measurement is that of relaxation of rotational velocities when the cylinder is subjected only to the viscous resistance. To measure the velocity distribution of the flow the experiments were made with the help of tracer particle (aluminum powder and 150-grain diameter meshes) for water and oil (Super Mulpus 68). The effects of the Reynolds number on the laminar asymmetric flow structure in the flow region are studied. The induced speed distribution in the rotation of cylinder (diameter 10 mm) circumference has examined about the Reynolds number from 26 to 522 for water consequent cylinder rpm 10, 25, 50, 75, 100 and 0.12 to 2.32 for Super Mulpus 68 Oil consequent cylinder rpm 5, 10, 25, 50, 75, 100. The relation between the induced speeds after the time had passed enough and the various cylinder rotational speeds for both analytical and experimental results are shown. At lower Reynolds number experimental results are closer to theoretical results for a finite time condition, at that time there is exist vorticity around the cylinder. We can also establish that more difference between experimental and theoretical results with higher Reynolds number. An interesting phenomenon has been observed in the flow patterns at various Reynolds number and is discussed. Finally, authors have explained the significant difference between experimental and theoretical results and a new paradox has been introduced.

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