Low Reynolds Number Flow Characteristics for Two Side by Side Rotating Cylinders

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
K. Supradeepan ◽  
Arnab Roy
Keyword(s):  
Reynolds Number ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Flow Regimes ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Flux Reconstruction ◽  
Reynolds Number Flow

Numerical simulations were performed for two-dimensional viscous incompressible flow past two stationary side-by-side rotating circular cylinders at Reynolds number (Re) 100 by varying center-to-center distance between the cylinders from 1.1 to 3.5 times the diameter (D) of a cylinder and different rotational speed ratio (α) = 0.5, 1.0, and 1.25. The incompressible Navier–Stokes equations were solved using consistent flux reconstruction (CFR) technique of Roy and Bandyopadhyay (2006, “A Finite Volume Method for Viscous Incompressible Flows Using a Consistent Flux Reconstruction Scheme,” Int. J. Numer. Methods Fluids, 52(3), pp. 297–319). Eight different flow regimes were observed within the investigated parametric space. An attempt has been made to characterize the different flow regimes using vorticity contours, λ2 criterion, and force coefficients. All these above stated methods confirm the existence of eight different regimes in the flow.

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.

Fluid Flow Characteristics Around a Pair of Diamond-Shaped Cylinders in Side-by-Side and Tandem Arrangements

2011 ◽  
Author(s):  
Shuichi Torii ◽  
Noritugu Ueda ◽  
Zijie Lin
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Time History ◽  
Flow Patterns ◽  
Separation Distance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Spacing

The present study deals with unsteady laminar fluid flow phenomena around a pair of diamond-shaped cylinders in free stream. Emphasis is placed on the effects of the Reynolds number, Re, and the ratio of cylinder separation distance to length of diamond-shaped cylinder, s/d, on the flow patterns in side-by-side and tandem arrangements. The Navier-Stokes equations are discretized using finite difference method to determine the time history of velocity vector in the flow field. The Reynolds numbers, Re, is ranged from 30 to 300 and gap spacing, s/d, is varied from 0.0 to 2.5 for side-by-side and 0.0 to 5.0 for tandem, respectively. The results are compared with the experimental results with the aid of flow visualization method. The study discloses that (i) the generations of Karman vortex streets behind the diamond-shaped cylinders are intensified with an increase in the Reynolds number, (ii) the categorized flow patterns in the wake region of the diamond-shaped islands are affected by s/d, and (iii) the vortex shedding frequency in the wake of diamond-shaped cylinders depends on both the gap spacing and the formation of the vortices.

scholarly journals Asymptotic solution of the low Reynolds-number flow between two co-axial cones of common apex

1984 ◽  
Vol 7 (4) ◽  
pp. 765-784 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
Y. K. Gayed
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Asymptotic Series ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Navier Stokes Equations ◽  
Spherical Coordinate ◽  
Flow Solution ◽  
Reynolds Number Flow

The paper is concerned with the axi-symmetrlc, incompressible, steady, laminar and Newtonian flow between two, stationary, conical-boundaries, which exhibit a common apex but may include arbitrary angles. The flow pattern and pressure field are obtained by solving the pertinent Navier-Stokes' equations in the spherical coordinate system. The solution is presented in the form of an asymptotic series, which converges towards the creeping flow solution as a cross-sectional Reynolds-number tends to zero. The first term in the series, namely the creeping flow solution, is given in closed form; whereas, higher order terms contain functions which generally could only be expressed in infinite series form, or else evaluated numerically. Some of the results obtained for converging and diverging flows are displayed and they are demonstrated to be plausible and informative.

Incompressible Flow Between Finite Disks

1982 ◽  
Vol 49 (1) ◽  
pp. 1-9 ◽  
Author(s):  
M. L. Adams ◽  
A. Z. Szeri
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
Parallel Disks ◽  
Rotationally Symmetric ◽  
Number Flow ◽  
High Reynolds ◽  
Multiple Cells

Solutions were developed and are shown here for the primary laminar steady flow field that occurs in an incompressible, isoviscous, Newtonian fluid which is contained between two finite parallel disks. One of the disks is made to rotate at constant velocity and the other is held stationary, and either a source or a sink is located concentric to the axis of rotation. The analysis is general, containing all terms of the Navier-Stokes equations for rotationally symmetric flows, and produces a four-parameter family of solutions. The high Reynolds number flow contains multiple cells, arranged along the radius, and the flow appears to be uniquely defined by the boundary condition and the Reynolds number.

Vortex Formation for Different Geometry of Cavities Using High Reynolds Number

2014 ◽  
Vol 699 ◽  
pp. 416-421
Author(s):  
Mohd Noor Asril Saadun ◽  
Muhammad Zulhakim Sharudin ◽  
Nor Azwadi Che Sidik ◽  
Mohd Hafidzal Mohd Hanafi
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Contaminant Removal ◽  
Navier Stokes Equations ◽  
High Reynolds

A preliminary study of Computational Fluid Dynamics (CFD) on the effect of high Reynolds numbers in the cavity has been carried out. Two dimensional model analysis of the flow characteristics were conducted using the numerical solution of Navier-Stokes equations based on the finite difference method. The flow characteristics in the cavity and the driven flow were modeled via turbulence equation modelling. This paper focuses on the effects of different high Reynolds number on the flow pattern of contaminant removal in the cavity. Different types of geometry and aspect ratio of the geometry were used as the parameters of the cavity in this study. Based on visualization of flows between each model with the different parameters used, the results of a comparison analysis focusing on the behavior of the flow were reported.

scholarly journals Hydrodynamic stability and turbulent transition with the Vreman LES SGS and a modified lattice Boltzmann equation

2018 ◽  
Author(s):  
J. R. Murdock ◽  
S. L. Yang
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Transition To Turbulence ◽  
Scale Model ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
Intermittent Turbulence

For the evaluation of a broad range of Re in incompressible flows, particularly unsteady and transition regimes, the Vreman subgrid scale model is studied within the framework of a modified lattice Boltzmann equation. A unique multiple relaxation time form which recovers the fully incompressible unsteady Navier-Stokes equations is derived for the D3Q19 lattice. Solutions to the 3D-driven cavity are compared to a number of lattice Boltzmann and Navier-Stokes solutions. Initial simulations demonstrate the vanishing nature of eddy viscosity in the steady laminar regime. Onset of unsteadiness is found between Re 1900 and 1950, matching well with the wealth of literature. At Re 6000, velocity history and complex vortex structures show a transition to turbulence near the domain bottom and front walls while the centre of the domain retains laminar characteristics. By Re 8000 intermittent turbulence has progressed to the domain centre. This range of Re for transition and the flow characteristics are in agreement with the general ranges in literature, with further observations being added here. The Vreman model with an incompressible lattice Boltzmann method is found to be a promising tool for laminarto- turbulent simulation.

Three-Dimensional Numerical Simulations of Flows Past Smooth and Rough/Bare and Helically Straked Circular Cylinders Allowed to Undergo Two Degree-of-Freedom Motions

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Juan P. Pontaza ◽  
Raghu G. Menon ◽  
Hamn-Ching Chen
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Degree Of Freedom ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Wall Region ◽  
Roughness Effects ◽  
Two Degree Of Freedom

We simulate the flow past smooth and rough rigid circular cylinders that are either bare or outfitted with helical strakes. We consider operating conditions that correspond to high Reynolds numbers of 105 and 106, and allow for two degree-of-freedom motions such that the structure is allowed to respond to flow-induced cross-flow and in-line forces. The computations are performed using a parallelized Navier–Stokes in-house solver using overset grids. For smooth surface simulations at a Reynolds number of 105, we use a Smagorinsky large eddy simulation turbulence model and for the Reynolds number cases of 106 we make use of the unsteady Reynolds-averaged Navier–Stokes equations with a two-layer k-epsilon turbulence model. The rough surface modifications of the two-layer k-epsilon turbulence model due to Durbin et al. (2001, “Rough Wall Modification of Two-Layer k-Epsilon,” ASME J. Fluids Eng., 123, pp. 16–21) are implemented to account for surface roughness effects. In all our computations we aim to resolve the boundary layer directly by using adequate grid spacing in the near-wall region. The predicted global flow parameters under different surface conditions are in good agreement with experimental data, and significant vortex-induced vibration suppression is observed when using helically straked cylinders.

Low Reynolds-Number Flow in the Vicinity of Axisymmetric Constrictions

1979 ◽  
Vol 21 (2) ◽  
pp. 73-84 ◽  
Author(s):  
N. S. Vlachos ◽  
J. H. Whitelaw
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
Local Shear ◽  
Number Flow ◽  
Recirculation Length

Numerical solutions of the two-dimensional, Navier-Stokes equations are presented for boundary conditions corresponding to the laminar flow of Newtonian and non-Newtonian fluids in a round tube with axisymmetric constrictions. The influence of Reynolds number, blockage diameter ratio and length on the velocity components, streamlines, local shear stress and pressure drop are quantified and, in the case of the first two, shown to be large. The non-Newtonian stress-strain relationship corresponds to that for blood flowing in venules and results in an increased recirculation length and larger regions of high shear stress.

Influence of rotation on the near-wake development behind an impulsively started circular cylinder

1985 ◽  
Vol 158 ◽  
pp. 399-446 ◽  
Author(s):  
Madeleine Coutanceau ◽  
Christian Ménard
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Flow Topology ◽  
Near Wake ◽  
Navier Stokes Equations ◽  
Magnus Effect ◽  
Point Trajectories

The early phase of the establishment of the flow past a circular cylinder started impulsively into rotation and translation is investigated by visualizing the flow patterns with solid tracers and by analysing qualitatively (flow topology) and quantitatively (velocity distributions and singular-point trajectories) the corresponding photographs. The range considered corresponds to moderate Reynolds numbers (Re [les ] 1000). The rotating-to-translating-speed ratio α increases from 0 to 3.25 and the motion covers a period during which the cylinder translates 4.5 or even 7 times its diameter. The details of the mechanisms of the near-wake formation are considered in particular and the increase of the flow asymmetry with increase in rotation is pointed out. Thus the existence of two regimes has been confirmed with the creation or non-creation of alternate eddies after an initial one E1 Furthermore, the new phenomena of saddle-point transposition and intermediate-eddy coalescence have been identified in the formation or shedding of respectively the odd and even subsequent eddies Ei (i = 2,3,…) when they exist. The very good agreement between these experimental data and the numerical results of Badr & Dennis (1985), obtained by solving the Navier-Stokes equations and presented in a parallel paper, confirms their respective validity and permits the determination of the flow characteristics not accessible, or accessible only with difficulty, to the present experiments. These flow properties such as drag and vorticity are capable of providing information on the Magnus effect for the former property and on unsteady separated flows for the latter.

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