Transverse motion of a disk through a rotating viscous fluid

1995 ◽  
Vol 301 ◽  
pp. 295-324 ◽  
Author(s):  
John P. Tanzosh ◽  
H. A. Stone
Keyword(s):  
Boundary Layer ◽  
Hydrodynamic Force ◽  
Rotation Axis ◽  
Approximate Expression ◽  
Transverse Motion ◽  
Dual Integral Equations ◽  
Plane Flow ◽  
Large Rotation ◽  
Disk Centre ◽  
Drag And Lift

A thin rigid disk translates edgewise perpendicular to the rotation axis of an unbounded fluid undergoing solid-body rotation with angular velocity Ω. The disk face, with radius a, is perpendicular to the rotation axis. For arbitrary values of the Taylor number, [Tscr ] = Ωa2/ν, and in the limit of zero Reynolds number [Rscr ]e, the linearized viscous equations reduce to a complex-valued set of dual integral equations. The solution of these dual equations yields an exact representation for the velocity and pressure fields generated by the translating disk.For large rotation rates [Tscr ] [Gt ] 1, the O(1) disturbance velocity field is confined to a thin O([Tscr ]−1/2) boundary layer adjacent to the disk. Within this boundary layer, the flow field near the disk centre undergoes an Ekman spiral similar to that created by a nearly geostrophic flow adjacent to an infinite rigid plate. Additionally, flow within the boundary layer drives a weak O([Tscr ]−1/2) secondary flow which extends parallel to the rotation axis and into the far field. This flow consists of two counter-rotating columnar eddies, centred over the edge of the disk, which create a net in-plane flow at an angle of 45° to the translation direction of the disk. Fluid is transported axially toward/away from the disk within the core of these eddies. The hydrodynamic force (drag and lift) varies as O([Tscr ]1/2) for [Tscr ] [Gt ] 1; this scaling is consistent with the viscous stresses created in the Ekman boundary layer. Additionally, an approximate expression, suitable for all Taylor numbers, is given for the hydrodynamic force on a disk translating broadside along the rotation axis and edgewise transverse to the rotation axis.

Triple Coordinate Transforms for Prediction of Falling Cylinder Through the Water Column

2004 ◽  
Vol 71 (2) ◽  
pp. 292-298 ◽  
Author(s):  
Peter C. Chu, ◽  
Chenwu Fan, ◽  
Ashley D. Evans, and ◽  
Anthony Gilles
Keyword(s):  
Water Column ◽  
Hydrodynamic Force ◽  
Main Axis ◽  
The Body ◽  
Naval Postgraduate School ◽  
Coordinate Systems ◽  
Buoyancy Forces ◽  
Drag And Lift ◽  
Coordinate Data ◽  
Coordinate Transforms

Triple coordinate systems are introduced to predict translation and orientation of falling rigid cylinder through the water column: earth-fixed coordinate (E-coordinate), cylinder’s main-axis following coordinate (M-coordinate), and hydrodynamic force following coordinate (F-coordinate). Use of the triple coordinate systems and the transforms among them leads to the simplification of the dynamical system. The body and buoyancy forces and their moments are easily calculated using the E-coordinate system. The hydrodynamic forces (such as the drag and lift forces) and their moments are easily computed using the F-coordinate. The cylinder’s moments of gyration are simply represented using the M-coordinate. Data collected from a cylinder-drop experiment at the Naval Postgraduate School swimming pool in June 2001 show great potential of using the triple coordinate transforms.

scholarly journals The effect of wind tunnel interference on the characteristics of an aerofoil

1930 ◽  
Vol 129 (809) ◽  
pp. 135-145 ◽  
Keyword(s):  
Wind Tunnel ◽  
Uniform Distribution ◽  
Infinite Series ◽  
Rectangular Channel ◽  
Approximate Expression ◽  
Point Of View ◽  
Approximate Methods ◽  
Free Jet ◽  
Drag And Lift ◽  
Lift And Drag

The effect of the walls of the enclosure on the measured values of the lift and drag experienced by an aerofoil is quite appreciable and it has been known for a considerable time that correction must be applied to wind tunnel result before they can be applied to free air conditions. Prandtl* investigated the effect on an aerofoil in a free jet or circular tube both in the case where there is a uniform lift distribution, and in the case where there is an elliptic distribution of circulation. The elliptic distribution is of importance because it gives the minimum drag for a given lift. Glauert by means of an approximate method found the induced drag and lift in a rectangular channel when there is a uniform distribution of lift. Terazawa modified Glauert’s method and obtained the exact solution for an aerofoil with uniform distribution of circulation in a rectangular channel. It is The object of this note to extend these results and to obtain the induces drag and lift in a rectangular channel when there is an elliptic distribution of lift. In addition, the discussion of Prandtl is briefly gone through because Prandtl’s results are usually given as the first few terms of an infinite series, and it has not been noticed that the result can be obtained exactly. Glauert’s work on the effect of plane barries is briefly re-examined because, in his analysis, approximate expression were summed over an infinite series of points, and at first glance it appeared that this would introduce some error of the same order as the result. In this note the summation is carried out rigorously and the approximations to the actual values. The small divergences from Glauert’s result obtained by Terazawa in two numerical cases are, in effect, the result of a slightly more accurate approximation. From the practical point of view the results of this paper add little to what is known already, for the major corrections are given by the results of the approximate methods, but this note should fill in some small gaps in the theory of wind tunnel interference.

scholarly journals Numerical Simulation of the Boundary Layer Control on the NACA 0015 Airfoil Through Vortex Generators

2020 ◽  
Author(s):  
Douglas da Silva ◽  
Vinicius Malatesta
Keyword(s):  
Boundary Layer ◽  
Vortex Generator ◽  
Vortex Generators ◽  
Boundary Layer Control ◽  
Recirculation Bubble ◽  
Longitudinal Vortices ◽  
Before And After ◽  
Drag And Lift ◽  
Naca 0015 ◽  
Layer Control

This paper studies the influence caused by a vortex generator (VG) on a wing section with NACA 0015 airfoil when this generator is located before and after a recirculation bubble caused by the boundary layer detachment. The study was numerically carried out and concentrated under conditions of flow with Rec = 2.38 × 105 and angles of attack AoA = 3 and 6, characterized by the fact that they undergo detachment of the boundary layer before and after the location of the VG, respectively. The use of the generator in AoA = 3 strongly influenced the reduction of the recirculation bubble, leading to a drag reduction of 1.43%. In AoA = 6 with a bubble recirculation, the effect was much lower, with no well-defined formation of longitudinal vortices, resulting in increased drag and lift at 0.33 and 0.35%, respectively.

Interference Between Two Circular Cylinders of Finite Height Vertically Immersed in a Turbulent Boundary Layer

1982 ◽  
Vol 104 (4) ◽  
pp. 529-536 ◽  
Author(s):  
S. Taniguchi ◽  
H. Sakamoto ◽  
M. Arie
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Angle Of Attack ◽  
Circular Cylinders ◽  
Wake Region ◽  
Pressure Distributions ◽  
Finite Height ◽  
Drag And Lift ◽  
Circumferential Pressure

Measurements were made of the circumferential pressure distributions around two cylinders of finite height h and diameter d, spaced a distance s apart and vertically immersed in a turbulent boundary layer. The angle of attack φ and the dimensionless spacing s/d were varied. Drag and lift characteristics of both cylinders were classified into three regions divided by two zero-lift lines, namely 0 ≲ φ ≲ 30 deg, 30 ≲ φ ≲ 120 deg, and 120 ≲ φ ≲ 180 deg, in which interference between the two cylinders was found to be almost negligible for s/d ≳ 4.0, except for an influence in the wake region of the upstream cylinder.

scholarly journals Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer

2013 ◽  
Vol 721 ◽  
pp. 155-179 ◽  
Author(s):  
Holger Homann ◽  
Jérémie Bec ◽  
Rainer Grauer
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Spherical Particle ◽  
Drag Force ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
Lift Forces ◽  
Drag And Lift

AbstractThe impact of turbulent fluctuations on the forces exerted by a fluid on a towed spherical particle is investigated by means of high-resolution direct numerical simulations. The measurements are carried out using a novel scheme to integrate the two-way coupling between the particle and the incompressible surrounding fluid flow maintained in a high-Reynolds-number turbulent regime. The main idea consists of combining a Fourier pseudo-spectral method for the fluid with an immersed-boundary technique to impose the no-slip boundary condition on the surface of the particle. This scheme is shown to converge as the power $3/ 2$ of the spatial resolution. This behaviour is explained by the ${L}_{2} $ convergence of the Fourier representation of a velocity field displaying discontinuities of its derivative. Benchmarking of the code is performed by measuring the drag and lift coefficients and the torque-free rotation rate of a spherical particle in various configurations of an upstream-laminar carrier flow. Such studies show a good agreement with experimental and numerical measurements from other groups. A study of the turbulent wake downstream of the sphere is also reported. The mean velocity deficit is shown to behave as the inverse of the distance from the particle, as predicted from classical similarity analysis. This law is reinterpreted in terms of the principle of ‘permanence of large eddies’ that relates infrared asymptotic self-similarity to the law of decay of energy in homogeneous turbulence. The developed method is then used to attack the problem of an upstream flow that is in a developed turbulent regime. It is shown that the average drag force increases as a function of the turbulent intensity and the particle Reynolds number. This increase is significantly larger than predicted by standard drag correlations based on laminar upstream flows. It is found that the relevant parameter is the ratio of the viscous boundary layer thickness to the dissipation scale of the ambient turbulent flow. The drag enhancement can be motivated by the modification of the mean velocity and pressure profile around the sphere by small-scale turbulent fluctuations. It is demonstrated that the variance of the drag force fluctuations can be modelled by means of standard drag correlations. Temporal correlations of the drag and lift forces are also presented.

Experimental Study on the Effect of Vortex Generator on the Aerodynamic Characteristics of NASA LS-0417 Airfoil

2015 ◽  
Vol 758 ◽  
pp. 63-69 ◽  
Author(s):  
S. Sutardi ◽  
Agung E. Nurcahya
Keyword(s):  
Boundary Layer ◽  
Experimental Study ◽  
Wind Tunnel ◽  
Vortex Generator ◽  
Boundary Layer Separation ◽  
Chord Length ◽  
Vortex Generators ◽  
Airfoil Surface ◽  
Freestream Velocity ◽  
Drag And Lift

Boundary layer flow structure developing on an airfoil surfaces strongly affects drag and lift forces acting on the body. Many studies have been done to reduce drag, such as introducing surface roughness on the airfoil surface, gas injection, attachment of vortex generators, or moving surface on the airfoil. Previous results showed that the attachment of vortex generators has potentially been able to control boundary layer separation compared to other controlling devices. This study is focused on the evaluation of the effect of vortex generator attachment on the NASA LS-0417 airfoil profile as this profile is commonly used in wind turbine blade application. The models of this experimental study are NASA LS-0417 profiles, with and without vortex generator. The chord length of the profile is 110 mm, while the span is 210 mm. Profile of the vortex generator is a symmetrical profile of NACA 0012 configured in counter rotating and attached on the upper surface of the main profile. The chord length of the vortex generator is 7 mm with two different values of the height (h): 1 mm and 2 mm. The experiment was conducted in an open loop wind tunnel with maximum attainable freestream velocity of approximately 19 m/s and the turbulence intensity at the tunnel centerline is approximately 0.8%. The wind tunnel cross section is octagonal of 30 cm x 30 cm and of 45 cm to 60 cm adjustable length. The study was performed at two different freestream velocities of 12 m/s and 17 m/s corresponding with Reynolds numbers (Re) of 0.83 x 105 and 1.18 x 105 based on the airfoil chord length and the freestream velocity. Angle of attact (α) was varied from 0o to 24o. Drag and lift were measured using a force balance with measurement uncertainty of approximately 0.77% and 2.47% at measured drag of 0.65N and at measured lift of 0.202N, respectively. A flow visualization study using oil flow method was conducted to obtain qualitaive picture of flow structure on the airfoil surface. Results of this study showed that attachment of the vortex generator on the NASA LS-0417 profile has not been able to improve the profile performance compared to that of unmodified profile. There, however, seems Reynolds number effect on the airfoil performance flow conditions performed in this study. At lager Re, there is an increase in CL/CD of approximately 36% at angle of attack (α) 6o. Next, based on the flow visualization results, attachment of the 2mm vortex generator on the airfoil NASA LS-0417 surface results in an advancement of boundary layer separation at the two Re’s conducted in this study. Finally, the 2mm vortex generator accelerates airfoil stall at approximately 16o, while the 1mm vortex generator is relatively no effect on the airfoil stall angle.

On the analogy between the transport of vorticity and heat in laminar boundary layers

1962 ◽  
Vol 14 (3) ◽  
pp. 399-404 ◽  
Author(s):  
N. Riley
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Energy Equation ◽  
Plane Flow ◽  
Laminar Boundary Layers

The analogy between the transport of heat and vorticity when the Prandtl number is unity is used to provide a simple complementary solution of the boundary-layer energy equation for plane flow. The solution is extended to apply to axisymmetric boundary layers by suitably stretching the co-ordinate normal to the wall. Several applications of the solution are discussed.

Hydrodynamic Force Measurements on a Circular Cylinder Fitted With Peripheral Control Cylinders: Preliminary Results on the Development of VIV Suppressors

2015 ◽  
Author(s):  
Mariana Silva-Ortega ◽  
Gustavo R. S. Assi ◽  
Murilo M. Cicolin
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Drag Reduction ◽  
Vortex Shedding ◽  
Hydrodynamic Force ◽  
Force Measurements ◽  
Number Range ◽  
Preliminary Results ◽  
Reynolds Number Range

Recent achievements in controlling the boundary layer by moving surfaces have been encouraging the development and investigation of passive suppressors of vortex-induced vibration. Within this context, the main purpose of the present work is to evaluate the suppression of vortex shedding of a plain cylinder surrounded by two, four and eight smaller control cylinders. Experiments have been carried out on a fixed circular cylinder to investigate the effect of the control cylinders over drag reduction. Control cylinders with diameter of d/D = 0.06 were tested, where D is the diameter of the main cylinder. The gap between the main cylinder and the control cylinders varied between G/D = 0.05 and 0.15. Experiments with a plain cylinder in the Reynolds number range from 5,000 to 50,000 have been performed to serve as reference. It was found that a cylinder fitted with four control cylinders presented less drag and fluctuating lift than cylinders fitted with two or eight small cylinders.

The Response of a Developed Turbulent Boundary Layer to Local Transverse Surface Motion

1976 ◽  
Vol 98 (3) ◽  
pp. 354-363 ◽  
Author(s):  
R. P. Lohmann
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Turbulent Energy ◽  
Transverse Motion ◽  
Mean Velocity ◽  
Surface Motion ◽  
The Mean ◽  
Structure Lead

Measurements were obtained of the mean velocity, Reynolds stress tensor components and spectral distribution of turbulent energy in a boundary layer that was adjusting spatially from a collateral to a three-dimensional state because of transverse motion of the bounding wall. The results indicate that changes to the turbulent structure lead to a strong coupling between the axial and transverse components of mean velocity. The influence of the imposed motion was found to be confined to a discrete region near the wall over the first ten initial boundary layer thicknesses, after which it became more global in nature.

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