Cylinder rolling on a wall at low Reynolds numbers

2011 ◽  
Vol 685 ◽  
pp. 461-494 ◽  
Author(s):  
Alain Merlen ◽  
Christophe Frankiewicz
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Around A Cylinder ◽  
Low Reynolds Numbers ◽  
Initial Location ◽  
Upstream Pressure ◽  
Small Reynolds Numbers ◽  
Onset Of Cavitation

AbstractThe flow around a cylinder rolling or sliding on a wall was investigated analytically and numerically for small Reynolds numbers, where the flow is known to be two-dimensional and steady. Both prograde and retrograde rotation were analytically solved, in the Stokes regime, giving the values of forces and torque and a complete description of the flow. However, solving Navier–Stokes equation, a rotation of the cylinder near the wall necessarily induces a cavitation bubble in the nip if the fluid is a liquid, or compressible effects, if it is a gas. Therefore, an infinite lift force is generated, disconnecting the cylinder from the wall. The flow inside this interstice was then solved under the lubrication assumptions and fully described for a completely flooded interstice. Numerical results extend the analysis to higher Reynolds number. Finally, the effect of the upstream pressure on the onset of cavitation is studied, giving the initial location of the phenomenon and the relation between the upstream pressure and the flow rate in the interstice. It is shown that the flow in the interstice must become three-dimensional when cavitation takes place.

Suppression of vortex shedding behind a circular cylinder by another control cylinder at low Reynolds numbers

2007 ◽  
Vol 573 ◽  
pp. 171-190 ◽  
Author(s):  
A. DIPANKAR ◽  
T. K. SENGUPTA ◽  
S. B. TALLA
Keyword(s):  
Vortex Shedding ◽  
Physical Mechanism ◽  
Grid Method ◽  
Reynolds Numbers ◽  
Accurate Solution ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Control Cylinder

Vortex shedding behind a cylinder can be controlled by placing another small cylinder behind it, at low Reynolds numbers. This has been demonstrated experimentally by Strykowski & Sreenivasan (J. Fluid Mech. vol. 218, 1990, p. 74). These authors also provided preliminary numerical results, modelling the control cylinder by the innovative application of boundary conditions on some selective nodes. There are no other computational and theoretical studies that have explored the physical mechanism. In the present work, using an over-set grid method, we report and verify numerically the experimental results for flow past a pair of cylinders. Apart from providing an accurate solution of the Navier–Stokes equation, we also employ an energy-based receptivity analysis method to discuss some aspects of the physical mechanism behind vortex shedding and its control. These results are compared with the flow picture developed using a dynamical system approach based on the proper orthogonal decomposition (POD) technique.

Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder

1957 ◽  
Vol 2 (3) ◽  
pp. 237-262 ◽  
Author(s):  
Ian Proudman ◽  
J. R. A. Pearson
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Reynolds Numbers ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Past ◽  
Small Reynolds Numbers ◽  
Cylindrical Polar Coordinates ◽  
Flow Past A Sphere

This paper is concerned with the problem of obtaining higher approximations to the flow past a sphere and a circular cylinder than those represented by the well-known solutions of Stokes and Oseen. Since the perturbation theory arising from the consideration of small non-zero Reynolds numbers is a singular one, the problem is largely that of devising suitable techniques for taking this singularity into account when expanding the solution for small Reynolds numbers.The technique adopted is as follows. Separate, locally valid (in general), expansions of the stream function are developed for the regions close to, and far from, the obstacle. Reasons are presented for believing that these ‘Stokes’ and ‘Oseen’ expansions are, respectively, of the forms $\Sigma \;f_n(R) \psi_n(r, \theta)$ and $\Sigma \; F_n(R) \Psi_n(R_r, \theta)$ where (r, θ) are spherical or cylindrical polar coordinates made dimensionless with the radius of the obstacle, R is the Reynolds number, and $f_{(n+1)}|f_n$ and $F_{n+1}|F_n$ vanish with R. Substitution of these expansions in the Navier-Stokes equation then yields a set of differential equations for the coefficients ψn and Ψn, but only one set of physical boundary conditions is applicable to each expansion (the no-slip conditions for the Stokes expansion, and the uniform-stream condition for the Oseen expansion) so that unique solutions cannot be derived immediately. However, the fact that the two expansions are (in principle) both derived from the same exact solution leads to a ‘matching’ procedure which yields further boundary conditions for each expansion. It is thus possible to determine alternately successive terms in each expansion.The leading terms of the expansions are shown to be closely related to the original solutions of Stokes and Oseen, and detailed results for some further terms are obtained.

Three-Dimensional Laminar Wall Jet Flows

2009 ◽  
Author(s):  
Kofi K. Adane ◽  
Mark F. Tachie
Keyword(s):  
Numerical Study ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Jet Flows ◽  
Wall Jet ◽  
Navier Stokes Equation ◽  
Flow Geometry

The present article reports on both experimental and numerical study of three-dimensional laminar wall jet flows. The wall jet was created using a circular pipe of diameter 7 mm and flows into an open channel. The Reynolds numbers based on the pipe diameter and jet exit velocity were varied from 310 to 1300. A particle image velocimetry (PIV) was used to conduct detailed velocity measurements at various streamwise-transverse and streamwise-spanwise planes. A complete nonlinear incompressible Navier-Stokes equation was also solved using a co-located finite volume based in-house computational fluid dynamic (CFD) code. This code was used to compute the experimental flow geometry. From the PIV measurements and CFD results, velocities profiles and jet-half-widths were extracted at selected locations. It was observed that the numerical results are in reasonable agreement with the experimental data. The distributions of the velocities, jet-half-widths and visualisation of the secondary flows were used to provide insight into the characteristics of three-dimensional wall jet flows.

Investigation of radial turbines for wind energy harvesting

2019 ◽  
Vol 233 (5) ◽  
pp. 659-672 ◽  
Author(s):  
M Tayyip Gürbüz ◽  
Menal İlhan ◽  
Sercan Acarer ◽  
Z Haktan Karadeniz
Keyword(s):  
Wind Energy ◽  
Performance Optimization ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
The Body ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Comparable Performance ◽  
Open Rotor ◽  
Low Reynolds

Wind energy has been a research focus of the last few decades, promoting the topic to a much more matured level. However, the body of literature is built around a limited number of turbine types and it is still beneficial to increase turbine diversity for the opportunity to select optimal turbine for a given purpose. The radial (inflow) turbines known in gas and hydro turbine industries for pressurized pipe flows are undiscovered turbines for free-stream wind harvesting both in air and underwater. In such case, the wind tangentially interacts with each blade by an external casing; therefore, all blade angular positions may, at least in theory, contribute equally to power production. Enclosed compact architecture with low rotational speeds and narrow intake ports may possess advantages in enabling the use of much weaker but more recyclable and long-lasting blades and in applications such as integrated wind harvesting for blunt bodies like buildings, vessels and devices or for any application where an open rotor is not feasible. Using experimentally validated Reynolds-averaged Navier–Stokes simulations, mass swallowing capacities and corresponding efficiencies of such turbines are parametrically investigated at low Reynolds numbers, Re chord=11 × 103, and finally enhancement is shown in 88 × 103. Findings provide first insights into such turbines. Considering the investigated very low Reynolds numbers and three-dimensional effects, comparable performance with other small turbines are observed. Moreover, undiscovered potential for performance optimization persists.

Experimental and Numerical Study of Laminar Round Jet Flows Along a Wall

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
K. F. K. Adane ◽  
M. F. Tachie
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Open Water ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Jet Flows ◽  
Wall Jet ◽  
Water Tank ◽  
Navier Stokes Equation ◽  
Image Velocimetry

In the present study, both experimental and numerical techniques were employed to study three-dimensional laminar wall jet flows. The wall jet was created using a circular pipe of diameter 7×10−3 m and flows into an open water tank. The inlet Reynolds numbers based on the pipe diameter and jet exit velocity were 310 and 800. A particle image velocimetry (PIV) was used to conduct detailed measurements at various streamwise-transverse and streamwise-spanwise planes. The complete nonlinear incompressible Navier–Stokes equation was also solved using a collocated finite volume based in-house computational fluid dynamics (CFD) code. The computation was performed for three inlet Reynolds numbers, namely, 310, 420, and 800. From the PIV measurements and CFD results, velocity profiles and jet half-widths were extracted at selected downstream locations. It was observed that the numerical results are in reasonable agreement with the experimental data. The distributions of the velocities, jet spread rates, and vorticity were used to provide insight into the characteristics of three-dimensional laminar wall jet flows.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Sign in / Sign up

Export Citation Format

Share Document