Potential Flow Solution for Crossflow Impingement of a Slot Jet on a Circular Cylinder

1976 ◽  
Vol 98 (2) ◽  
pp. 249-255 ◽  
Author(s):  
H. Miyazaki ◽  
E. M. Sparrow
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Potential Flow ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stream Velocity ◽  
Cylinder Surface ◽  
Stagnation Region ◽  
Flow Solution

A closed-form solution has been obtained for the potential flow about a circular cylinder situated in an impinging slot jet. Among other results, the potential flow solution yields the free stream velocity for the boundary layer adjacent to the cylinder surface. A basic feature of the solution is the division of the flow field into subdomains, thereby making it possible to employ harmonic functions that are appropriate to each such subdomain. The boundary conditions on the free streamline and the conditions of continuity between the subdomains are satisfied by a combination of least squares and point matching constraints. Numerical evaluation of the solution was carried out for cylinder diameters greater or equal to the nozzle width and for a range of dimensionless separation distances between the nozzle and the impingement surface. Results are presented for the velocity and pressure distributions on the cylinder surface, for the position of the free streamline, and for the velocity gradients at the stagnation point. The latter serve as input information to the Nusselt number and skin friction expressions that are given by boundary layer theory. Comparisons were made with available experimental results for the pressure distribution, velocity gradient, and Nusselt number, and good agreement was found to prevail in the stagnation region.

The flow past a rapidly rotating circular cylinder

1957 ◽  
Vol 242 (1228) ◽  
pp. 108-115 ◽  
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Present Theory ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Rotating Circular Cylinder ◽  
Flow Past ◽  
Separating Flow ◽  
Two Dimensional Flow ◽  
Uniform Stream

This paper considers the two-dimensional flow past a circular cylinder immersed in a uniform stream, when the cylinder rotates about its axis so fast that separation in suppressed. The solution of the flow in the boundary layer on the cylinder is obtained in the form of a power series in the ratio of the stream velocity to the cylinder's peripheral velocity, and expressions are deduced for the value of the circulation and the torque on the cylinder. The terms calculated explicitly are sufficient to give reliable numerical values over the whole range of rotational speeds for which the postulate of non-separating flow is justifiable. The previously accepted theory, due to Prandtl, predicted that the circulation should not exceed a certain limit, while the present theory indicates that the circulation increases indefinitely with increase of rotaional speed. Strong arguments against the older theory are put forward, but the experimental evidence available is inconclusive.

Flow Separation

2009 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Drag Coefficient ◽  
Numerical Solution ◽  
Flow Separation ◽  
Potential Flow ◽  
Experimental Results ◽  
Science Courses ◽  
Boundary Layer Equations ◽  
Solution Of Equations

In thermal science courses, flow over curved objects, like cylinders or spheres are generally discussed qualitatively, followed by the presentation of numerical or experimental results for the drag coefficient, Nusselt number, and flow separation. Rarely, there is much discussion of how solutions are obtained. In this paper the flow separation is first introduced by solving the Falkner-Skan flow. The process for numerical solution of equations is presented to show that the flow separates at a plate angle of about −18°. Comparisons are drawn between this and flow over a cylinder. The non-similar boundary layer equations are then solved flow over a cylinder, using potential flow results for the velocity outside of the boundary layer. This solution shows that the flow separates at 103.5°, which is significantly more than the experimental value of 80°. Using a more realistic velocity for flow outside of the boundary layer, the numerical solution obtained predicts flow separation at an angle of 79°, which is close to the experimental results. All the solutions are obtained using spreadsheets that greatly simplify the analysis.

Velocity Measurements on the Forward Portion of a Cylinder

1990 ◽  
Vol 112 (2) ◽  
pp. 243-245 ◽  
Author(s):  
D. E. Paxson ◽  
R. E. Mayle
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Static Pressure ◽  
Free Stream ◽  
Stream Velocity ◽  
Pressure Measurements ◽  
Velocity Measurements ◽  
Flow Around A Cylinder

Velocity measurements in the laminar boundary layer around the forward portion of a circular cylinder are presented. These results are compared to Blasius’ theory for laminar flow around a cylinder using a free-stream velocity distribution obtained from static pressure measurements on the cylinder. Even though the flow is periodically unsteady as a result of vortex shedding from the cylinder, it is found that the agreement is excellent.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

Note on the Motion Inside a Region of Recirculation (Cavity Flow)

1956 ◽  
Vol 60 (543) ◽  
pp. 203-205 ◽  
Author(s):  
H. B. Squire
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Circular Cylinder ◽  
Maximum Velocity ◽  
Cavity Flow ◽  
Flow Patterns ◽  
Stream Velocity ◽  
Bluff Bodies ◽  
The Core

It is shown that the flow in a region of recirculation may be divided into a core, in which the vorticity may be constant, and a boundary layer surrounding the core. An approximate solution is given for the flow inside a circular cylinder with partly fixed and partly moving walls.Flow patterns which include regions of recirculation occur frequently, for example, behind bluff bodies, in sharp bends, and in sudden expansions in ducts. Little is known about this type of flow, which will be referred to, for brevity, as ‘cavity’ flow. It used to be thought that the velocities in the ‘ cavity ’ were small compared with the stream velocity, but it is now known that the maximum velocity in the cavity may be about 30 per cent. of the stream velocity. This implies that the motion within the cavity cannot be neglected.

A Study of the Relationship Between Free-Stream Turbulence and Stagnation Region Heat Transfer

1987 ◽  
Vol 109 (1) ◽  
pp. 10-15 ◽  
Author(s):  
G. J. VanFossen ◽  
R. J. Simoneau
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Stream ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Cylinder Surface ◽  
Nasa Lewis Research ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Free Stream Turbulence

A study has been conducted at the NASA Lewis Research Center to investigate the mechanism that causes free-stream turbulence to increase heat transfer in the stagnation region of turbine vanes and blades. The work was conducted in a wind tunnel at atmospheric conditions to facilitate measurements of turbulence and heat transfer. The model size was scaled up to simulate Reynolds numbers (based on leading edge diameter) that are to be expected on a turbine blade leading edge. Reynolds numbers from 13,000 to 177,000 were run in the present tests. Spanwise averaged heat transfer measurements with high and low turbulence have been made with “rough” and smooth surface stagnation regions. Results of these measurements show that, at the Reynolds numbers tested, the boundary layer remained laminar in character even in the presence of free-stream turbulence. If roughness was added the boundary layer became transitional as evidenced by the heat transfer increase with increasing distance from the stagnation line. Hot-wire measurements near the stagnation region downstream of an array of parallel wires has shown that vorticity in the form of mean velocity gradients is amplified as flow approaches the stagnation region. Finally smoke wire flow visualization and liquid crystal surface heat transfer visualization were combined to show that, in the wake of an array of parallel wires, heat transfer was a minimum in the wire wakes where the fluctuating component of velocity (local turbulence) was the highest. Heat transfer was found to be the highest between pairs of vortices where the induced velocity was toward the cylinder surface.

Hydrodynamic coefficients of a vertical circular cylinder

1990 ◽  
Vol 17 (3) ◽  
pp. 302-310 ◽  
Author(s):  
Michael Isaacson ◽  
Thomas Mathai ◽  
Carol Mihelcic
Keyword(s):  
Circular Cylinder ◽  
High Frequency ◽  
Closed Form Solution ◽  
Added Mass ◽  
Offshore Structures ◽  
Form Solution ◽  
Ocean Engineering ◽  
Radiation Problem ◽  
The Vertical Distribution ◽  
Linear Radiation

The added mass and the damping coefficient of a large surface-piercing circular cylinder extending to the seabed and undergoing horizontal oscillations are described. A closed-form solution to the corresponding linear radiation problem is obtained by the use of eigenfunction expansions. Attention is given to the vertical distribution of these coefficients and to their high-frequency asymptotic behaviour. Comparisons are made with experimental measurements. The application to typical offshore structures is discussed. Key words: added mass, cylinders, damping, hydrodynamics, ocean engineering.

Selective Roughness in the Boundary Layer to Suppress Flow-Induced Motions of Circular Cylinder at 30,000

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Hongrae Park ◽  
Michael M. Bernitsas ◽  
R. Ajith Kumar
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Passive Control ◽  
Flow Direction ◽  
Water Channel ◽  
Maximum Amplitude ◽  
Cylinder Surface ◽  
Complex Flow ◽  
Strong Suppression ◽  
Wide Range

A passive control means to suppress flow-induced motions (FIM) of a rigid circular cylinder in the TrSL3, high-lift, flow regime is formulated and tested experimentally. The developed method uses passive turbulence control (PTC) consisting of selectively located roughness on the cylinder surface with thickness about equal to the boundary layer thickness. The map of “PTC-to-FIM,” developed in previous work, revealed robust zones of weak suppression, strong suppression, hard galloping, and soft galloping. PTC has been used successfully to enhance FIM for hydrokinetic energy harnessing using the VIVACE Converter. PTC also revealed the potential to suppress FIM to various levels. The map is flow-direction dependent. In this paper, the “PTC-to-FIM” map is used to guide development of FIM suppression devices that are flow-direction independent and hardly affect cylinder geometry. Experiments are conducted in the Low Turbulence Free Surface Water Channel of the University of Michigan on a rigid, horizontal, circular cylinder, suspended on springs. Amplitude and frequency measurements and broad field-of-view visualization reveal complex flow structures and their relation to suppression. Several PTC designs are tested to understand the effect of PTC roughness, location, coverage, and configuration. Gradual modification of PTC parameters, leads to improved suppression and evolution of a design reducing the VIV synchronization range. Over a wide range of high reduced velocities, VIV is fully suppressed. The maximum amplitude occurring near the system’s natural frequency is reduced by about 63% compared to the maximum amplitude of the smooth cylinder.

Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer

1983 ◽  
Vol 126 ◽  
pp. 147-165 ◽  
Author(s):  
Hiroshi Sakamoto ◽  
Mikio Arie
Keyword(s):  
Boundary Layer ◽  
Aspect Ratio ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Vortex Shedding ◽  
Rectangular Prism ◽  
Stream Velocity ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Two Bodies

Measurements of the vortex-shedding frequency behind a vertical rectangular prism and a vertical circular cylinder attached to a plane wall are correlated with the characteristics of the smooth-wall turbulent boundary layer in which they are immersed. Experimental data were collected to investigate the effects of (i) the aspect ratio of these bodies and (ii) the boundary-layer characteristics on the vortex-shedding frequency. The Strouhal number for the rectangular prism and the circular cylinder, defined by S = fcw/U0 and fcd/U0 respectively, was found to be expressed by a power function of the aspect ratio h/w (or h/d). Here fc is the vortex-shedding frequency, U0 is the free-stream velocity, h is the height, w is the width and d is the diameter. As the aspect ratio is reduced, the type of vortex shedding behind each of the two bodies was found to change from the Karman-type vortex to the arch-type vortex at the aspect ratio of 2·0 for the rectangular prism and 2·5 for the circular cylinder.

scholarly journals Magneto-Convective Boundary-Layer Flow of a Nanofluid Past Impulsive Vertical Plate with Inclined Magnetic Field.

2018 ◽  
Vol 7 (4.10) ◽  
pp. 636
Author(s):  
A. G. Vijaya Kumar ◽  
Rahul Gopal Innani ◽  
Yash R. Pawar
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Vertical Plate ◽  
Transverse Velocity ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Fields ◽  
Engine Oil ◽  
Convective Boundary ◽  
Laplace Transform Technique

The following paper is a study of unsteady hydro-magnetic flow on a boundary layer over an impulsive nanofluid vertical plate in the sight of transverse magnetic field inclined at an angle. The considered fluid is a non-scattering medium and pressure gradient is described by Boussinesq’s approximation and radiative heat flux in the equation of energy. Three types of nanofluids containing Al2O3 engine oil, Boron Engine oil and Graphite engine oil are considered by us. The partial differential equations are converted to dimensionless with particular dimensional quantities and then Laplace transform technique is used to get a closed form solution for velocity and temperature fields without any limits. From the obtained graphs, we studied the changes according to given values of nanofluids on the temperature, transverse velocity, skin-friction and the heat transfer rate at the surface of the wall.  

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