The Motion of a Flat-Plate Pendulum in a Viscous Fluid

1969 ◽  
Vol 91 (4) ◽  
pp. 1100-1104
Author(s):  
J. P. Ries ◽  
W. G. Harrach
Keyword(s):  
Viscous Fluid ◽  
Flat Plate ◽  
Amplitude Ratio ◽  
Harmonic Oscillation ◽  
Oscillation Period ◽  
Velocity Amplitude ◽  
Boundary Layer Equations ◽  
Light Oil ◽  
Damped Oscillation ◽  
Predicted Values

The motion of an infinite, flat plate undergoing free oscillations as a submerged pendulum in a viscous fluid is analyzed. An analytical solution has been obtained through a simultaneous solution of the equation of motion for the plate, the drag force relationship, and the boundary-layer equations for the case of laminar, incompressible, unsteady flow. Expressions for the displacement and velocity of the plate appear as the sum of a damped harmonic oscillation and a particular solution which decays asymptotically to zero with increasing time. The period and logarithmic decrement are expressed as functions of a single parameter which contains the physical properties of the fluid and dimensions of the system. Predicted values of plate displacement, plate velocity, amplitude ratio, and damped oscillation period are compared to the results of an experimental investigation performed in water and a light oil.

Skin friction and surface temperature of an insulated flat plate fixed in a fluctuating stream

1971 ◽  
Vol 46 (1) ◽  
pp. 165-175 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Boundary Layer ◽  
Surface Temperature ◽  
Flat Plate ◽  
Skin Friction ◽  
High Frequency ◽  
Energy Equation ◽  
Oscillation Amplitude ◽  
Flow Oscillation ◽  
Velocity Amplitude ◽  
The Mean

The time-mean skin friction of the laminar boundary layer on a flat plate which is fixed at zero incidence in a fluctuating stream is investigated analytically. Flow oscillation amplitude outside the boundary layer is assumed constant along the surface. First, the small velocity-amplitude case is treated, and approximate formulae are obtained in the extreme cases when the frequency is low and high. Next, the finite velocity-amplitude case is treated under the condition of high frequency, and it is found that the formula obtained for the small-amplitude and high-frequency case is also valid. These results show that the increase of the mean skin friction reduces with frequency and is ultimately inversely proportional to the square of frequency.The corresponding energy equation is also studied simultaneously under the condition of zero heat transfer between the fluid and the surface. It is confirmed that the time-mean surface temperature increases with frequency and tends to be proportional to the square root of frequency. Moreover, it is shown that the timemean recovery factor can be several times as large as that without flow oscillation.

A Method of “Separation of Variables” for the Solution of Laminar Boundary-Layer Equations of Narrow-Channel Flows

1992 ◽  
Vol 114 (3) ◽  
pp. 623-629 ◽  
Author(s):  
F. Al-Bender ◽  
H. Van Brussel
Keyword(s):  
Velocity Distribution ◽  
Flow Velocity ◽  
Separation Of Variables ◽  
Internal Flow ◽  
Generalized Solution ◽  
Narrow Channel ◽  
Main Flow ◽  
Velocity Amplitude ◽  
Boundary Layer Equations ◽  
Von Mises

A method of solution for laminar channel flow is established using the von Mises transformation followed by the “separation” of the main flow velocity into amplitude and profile functions. The known boundary conditions on the latter enable a generalized solution that yields, through a parametric relation between auxiliary parameters (the characteristics), a system of ordinary differential equations for the velocity amplitude and the pressure. The result is a powerful semi-analytical method which is very easy to implement for a variety of internal flow configurations. The method is, in essence, a downstream general solution which may be extended upstream to the singular limit of a uniform main flow velocity distribution at the channel entrance. The regular solution for uniform initial velocity distribution cannot thus be obtained. Comparisons with other solutions show only qualitative agreement, for reasons which are discussed, whereas agreement with experimental results, made in a separate publication, is remarkably good.

The slow transverse motion of a flat plate through a non-diffusive stratified fluid

1971 ◽  
Vol 47 (1) ◽  
pp. 171-181 ◽  
Author(s):  
G. S. Janowitz
Keyword(s):  
Viscous Fluid ◽  
Shear Layer ◽  
Flat Plate ◽  
Kinematic Viscosity ◽  
Vertical Plate ◽  
The Body ◽  
Vertical Shear ◽  
Transverse Motion ◽  
Two Dimensional ◽  
Two Dimensional Flow

We consider the two-dimensional flow produced by the slow horizontal motion of a vertical plate of height 2b through a vertically stratified (ρ = ρ0(1 - βz)) non-diffusive viscous fluid. Our results are valid when U2 [Lt ] Ub/ν [Lt ] 1, where U is the speed of the plate and ν the kinematic viscosity of the fluid. Upstream of the body we find a blocking column of length 10−2b4/(Uν/βg. This column is composed of cells of closed streamlines. The convergence of these cells near the tips of the plate leads to alternate jets. The plate itself is embedded in a vertical shear layer of thickness (Uν/βg)1/3. In the upstream portion of this layer the vertical velocities are of order U and in the downstream portion of order Ub/(Uν/βg)1/3 ([Gt ] U). The flow is uniform and undisturbed downstream of this layer.

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