Browsing by Author "Song, C. S."

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Experimental Investigation of Taylor Instability Using Non-Newtonian Fluids
(St. Anthony Falls Laboratory, 1966-06) Song, C. S.; Tsai, F. Y.
The critical Taylor numbers for five different non-Newtonian solutions were determined experimentally by visual observation using the hydrogen bubble technique. Although three different gap sizes were used, only the data for the smallest size can be considered satisfactorily accurate. Smaller hydrogen bubbles than those used in this experiment are necessary for more aocurate determination. Contrary to a finding by others, the present experiment indicates that the critical Taylor number is decreased as the concentration is increased. The shear on the outer cylinder due to rotation of the inner cylinder was also measured for an intermediate range of Reynolds number, i.e. laminar flow at superoritical Taylor number. Substantial reductions of frictional drag coefficient Were achieved at higher additive concentrations When the comparison was based on equal Reynolds number.
Experimental Studies of Cavitation Noise in a Free-Jet Tunnel
(St. Anthony Falls Hydraulic Laboratory, 1961-07) Song, C. S.; Silberman, Edward
The present paper summarizes the results of experimental studies on cavitation noise generated in the free-jet tunnel at St. Anthony Falls Hydraulic Laboratory in the period October 1960 to June 1961. Two-dimensional test bodies of different shapes, such as a circular cylinder, wedge, and a Tulin-Burkhart hydrofoil were tested. Various types of cavitating flows, namely, transient cavities, steady-state cavities, and non-stationary cavities were covered. Special attention was given to the effect of ventilation on the intensity of cavitation noise. Effects of body size and the presence of a solid boundary were also investigated.
Instability of Ventilated Cavities
(St. Anthony Falls Hydraulic Laboratory, 1959-11) Sliberman, E.; Song, C. S.
Cavitation number σ is defined by σ = (P_o - P_k)/q. It can be controlled by controlling the dynamic pressure q, the ambient pressure P_o, or the internal cavity pressure P_k. The present investigation was undertaken to study methods of controlling P_k by adding air to the wakes of fully submerged bodies. This process has been called ventilation. It was found that with P_o and q fixed, P_k increases, and hence σ decreases, nearly linearly with the rate of air supply. Numerical values are given in the paper for the normal flat plate, circular cylinder, and various hydrofoils, and these values may be extrapolated to other sizes of bodies than those tested. It was also found that once σ was decreased to a certain critical value, further increase in the air supply rate would not produce a continuing linear decrease in σ. Rather, σ remained nearly constant and the cavities began to vibrate. Vibration occurred with one, two, or more waves on the cavity surface. Only by going from a one-wave to a two-wave cavity could σ be reduced further, and the reduction was discontinuous . A detailed description of the vibrating cavities is given. Both two-dimensional and finite aspect-ratio bodies were tested. The tests were conducted in the two-dimensional, vertical, free-jet water tunnel at the St. Anthony Falls Hydraulic Laboratory. All bodies tested, regardless of aspect ratio and whether lifting or nonlifting, behaved quite similarly within both the vibrating and nonvibrating regimes. That the vibration was not peculiar to the vertical free-jet tunnel was demonstrated by comparison with results from a hydrofoil towed in a tank. In the case of lifting bodies of finite span operating near a free surface, air was found to enter, rather than leave, the cavities through the trailing vortexes.
Measurements of the Unsteady Force on Cavitating Hydrofoils in a Free Jet
(St. Anthony Falls Hydraulic Laboratory, 1964-06) Song, C. S.
Experimental data concerning force and other related quantities associated with unsteady super cavitating flow about bodies tested in a free-jet water tunnel are reported herein. Three types of unsteady flows were studied -- those due to pitching oscillation, sudden ventilation, and sudden angle of attack change. All test bodies were of such geometrical configuration that separation could occur only at two or three fixed points. The first type of unsteady flows was subdivided into three categories, each having different characteristics. When a flat plate was oscillated about a large mean angle of attack at small cavitation number and without ventilation, the cavity pressure remained unchanged. When air was supplied to the cavity for ventilation, the cavity pressure oscillated with the same frequency as that of the body oscillation. When the plate was oscillated about a small mean angle of attack, there was a change in the cavity configuration even without ventilation and the resulting flow was quite irregular. The plate was oscillated at the maximum reduced frequency of 0.03. The second phase of the experiment involved measurements of cavity pressure, cavity length, and the force on the body following a sudden ventilation of an otherwise steady cavity. It was found that the change in cavity length and the change in the force lagged behind the cavity pressure change. Furthermore, the rate of cavity increase never exceeded the free-stream speed. An attempt was also made to measure the response of the flow to a sudden angle of attack change. It was concluded that, due to the oscillatory nature of the cavity, a faster angle of attack change than was attained in the experiment is needed to obtain a useful unit function response curve.
A Note on the Linear Theory of Two-Dimensional Seperated Flows about Thin Bodies
(St. Anthony Falls Hydraulic Laboratory, 1962-08) Song, C. S.
By using a generalized method of solution for the mixed boundary value problem of analytic function theory, and by comparing the present method with the method of source-sink distribution and the method of analytic continuation, an attempt is made to unify the seemingly divergent development o the linear theories of thin foils with separating flows. It is shown that most of the mathematical models may be regarded as special cases of generalized Riabouchinsky model.
Pulsation of Ventilated Cavities
(St. Anthony Falls Hydraulic Laboratory, 1961-02) Song, C. S.
The problem of pulsating supercavities under artificial ventilation is analytically treated as a resonance problem of a two-dimensional gas-liquid system using a linearized method. A simple kinematical consideration and a dynamical model of the flow lead to solutions for frequency and amplitude of pulsations. The criteria of pulsation is given in terms of a formula relating σ_v and σ. Maximum air carrying capacities of pulsating cavities are also estimated. Most of the formulas involve an undetermined constant which must be estimated by using experimental data. The analytical results are compared with the experimental data obtained at the St. Anthony Falls Hydraulic Laboratory, and in general, good agreement is obtained. It is found that pulsation is possible only for a two-dimensional cavity or a cavity in which a substantial portion of the span can be regarded as two-dimensional. The existence of a free surface is also essential to pulsation. The strong effect of the free surface suggests that pulsation may become an important problem in the open sea only when submergence is relatively small.
A Quasi-Linear and Linear Theory for Non-Separated and Separated Two-Dimensional, Incompressible Irrotational Flow about Lifting Bodies
(St. Anthony Falls Hydraulic Laboratory, 1963-05) Song, C. S.
A general theory is developed for calculating lift, form drag, and moment applicable to thin bodies at small angles of attack without separation or with separation at an arbitrary number of given points. The separated flows are related to fully cavitated and partially cavitated flows by making use of the concept of free streamlines. The closure condition of free-streamline theory is replaced by a boundedness condition. Unique solutions are thereby obtained for a large variety of problems. The mathematical solution involves a Riemann-Hilbert mixed boundary value problem in an upper-half plane. The general solution for this problem is given in the Appendix and is applied to various kinds of mixed boundary conditions. The method is exemplified by means of four illustrative calculations. As may be expected when the boundary profile is truly linear, the solution agrees with the classic exact solution.
Supercavitating Flat-Plate with an Oscillating Flap at Zero Cavitation Number
(St. Anthony Falls Hydraulic Laboratory, 1965-11) Song, C. S.
The results of experimental and theoretical investigations on a supercavitating flat-plate with an oscillating flap at zero cavitation number are presented. The experiment was carried out in a vertical free-jet water tunnel using 3 in. chord and 2 in. chord flat-plate hydrofoils, both having flap-chord ratios of 0.29. Various relative locations of the free surfaces were used and the reduced frequency range of zero to four was covered. Amplitude and phase angle of lift, drag, and moment as well as the surface wave speed were measured. The problem was also solved, analytically by means of a first order perturbation theory using complex acceleration potential. Numerical values were obtained for the cases of infinite fluid, symmetrical jet, and zero spray thickness using three flap-chord ratios (0.25, 0.30, 0.40). Fairly good agreement between the experimental data and the analytical results was obtained.
Two-Dimensional Supercavitating Plate Oscillating Under a Free-Surface
(St. Anthony Falls Hydraulic Laboratory, 1963-12) Song, C. S.
The problem of a super cavitating flat plate at non-zero cavitation number oscillating under a free surface is analyzed by a linearized method using the acceleration potential. The flow is assumed two-dimensional and incompressible. The flow field is made simply connected by using a cut along the wake. The flow field is then mapped on to an upper half plane and the solution is expressed in an integral form by using Cheng and Rott's method. Equations for the cavity length, total force coefficient, moment coefficient and the frequency response function are expressed in closed form. Numerical results for some special cases are also obtained and presented graphically. When the flow is steady, the present theory agrees with experimental data and other existing theories. For the special case of infinite fluid and infinite cavity the present theory agrees with Parkins' original work. For the special case of zero submergence, the present theory indicates that the total force coefficient is one half that of the value for fully wetted flow in an infinite fluid for both steady and unsteady cases. An alternate analysis is also carried out for the infinite fluid case and the result shows that the effect of the wake assumption is of order of the square of the cavitation number when the cavitation number is small. The effect of the gravity field is also discussed qualitatively. It is also concluded that the effect of the free-surface is to shorten the cavity and to increase the total force coefficient. The steady part of the force coefficient at an arbitrary submergence is obtained by multiplying the value at infinite submergence by a correction factor, whereas the unsteady part is given by a more complicated function. Even with the presence of a free-surface and oscillation of the foil, the total force coefficient at small cavitation number is approximately equal to the corresponding value at zero cavitation number multiplied by a factor (1 + σ).
Unsteady, Symmetrical, Supercavitating Flows Past a Thin Wedge in a Jet
(St. Anthony Falls Hydraulic Laboratory, 1962-01) Song, C. S.
Problems of symmetrical two-dimensional supercavitating flow about a thin wedge in a finite fluid with two free surfaces are solved by means of a linearized method utilizing the complex acceleration potential. Taking advantage of the symmetry, the otherwise doubly connected region is divided into two identical simply connected regions. Conformal mapping technique is then applied to the upper half of the flow region. An oscillatory-type motion as well as general types of unsteady motions are considered. The solution contains no singularity and, as a result, pressure is everywhere finite. The mathematical condition required for the existence of a singularity-free solution leads to an equation which gives the relationship between the cavity length and the cavitation number. The theoretical results are in good agreement with experimental data for the steady-flow case, but data for the unsteady case are not yet available.
Unsteady, Symmetrical, supercavitating Flows Past a Thin Wedge in a Solid Wall Channel
(St. Anthony Falls Hydraulic Laboratory, 1962-06) Song, C. S.; Tsai, F. Y.
Problems of symmetrical two-dimensional supercavitating flow about a thin wedge in a finite fluid with two parallel solid boundaries are solved by means of a linearized method utilizing the complex acceleration potential. The solution contains no singularity and, as a result, pressure is finite everywhere. It is shown that the term indicating the effect of cavity pressure change on the drag which existed in the case of the flows with free boundaries is identical to zero when the boundaries are solid. It is also concluded that, in steady flow cases, the accuracy of the solutions using the linearized method is comparable to that using the linearized velocity potential method. In fact, the two methods give identical solutions cavities are infinitely long.

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