|Hydrodynamic forces and ship motions induced by surges in a navigation lock|
Kalkwijk, J.P. Th. (1973). Hydrodynamic forces and ship motions induced by surges in a navigation lock. Communications on Hydraulics, 73-1. Delft University of Technology: Delft. 195 pp.
Deel van: Communications on Hydraulics. Delft University of Technology. Department of Civil Engineering: Delft
Motion > Ship motion
Physics > Mechanics > Fluid mechanics > Hydrodynamics
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This thesis treats the fluid and ship motion in a navigation lock and their mutual interaction as caused by surges, which occur in the chamber during filling or emptying. The other phenomena, which possibly play a role during these processes are ignored. The considerations of this treatise hold good for one ship in the chamber of the navigation lock, which is moored off such, that its displacement in the horizontal plane is negligible. The first simplification is less essential; with regard to the second simplification the theory presented can be extended relatively simply for longitudinal displacement of the ship. Furthermore no attention is devoted to various filling and emptying systems and their possible consequences for the theory; at any instant a practically homogeneous horizontal velocity distribution is assumed at the doors.
After an introduction, chapter 1, in which the present computational methods are described, it is pointed out in chapter 2, that the wave phenomena in the case under consideration are of the shallow water type, since the ratio of a characteristic depth and wave length will be generally small. This fact is used in chapter 3, in which simpler equations are derived from the more complicated equations, which describe the fluid motion in three dimensions, by using a series expansion in terms of a small corresponding parameter. In principle this is carried out for a channel with ship having both arbitrary cross-sections, for which the characteristic widths are small with respect to the characteristic wave length. The derivation is proceeded up to the first order of approximation of each variable. Finally the long wave equations (Boussinesq equations) arise, in which the equation of motion contains two extra terms, which allow for the deviation of the hydrostatic pressure distribution. This deviation is caused by the acceleration of fluid particles in directions perpendicular to the longitudinal direction.
At the transition of the section of the channel with ship to a section without ship it is assumed, that the adaptation of the flow patterns takes only a small distance. Therefore, such a transition is schematized to a vertical plane, where the laws of conservation of mass, momentum and energy can be applied. This is carried out in chapter 4. In chapter 5 the various hydrodynamic forces acting on the ship are derived by means of the results of the preceeding chapters. A result of the higher order approximation is, that apart from a longitudinal force cross-forces can be expected as a consequence of translatory waves.
The various coefficients in the chapters 3, 4 and 5, which result from the higher order approximation, are evaluated for some configurations in appendix A.
In order to examine the applicability of the theory derived, the harmonic solution of the linearized equations is determined in chapter 6; the analytical results are checked by means of experimental data. Before doing so, a naval methodology is examined to determine its applicability in the present case. In general this methodology proves to be applicable and therefore it has been used, where it was needed to explain certain phenomena. The general harmonic solution is condered in greater detail for a channel with infinite length, in which a ship is moored; an incoming harmonic translatory wave causes the ship to oscillate. The corresponding experiments are described ~n appendix B. The theoretical and experimental results generally show good agreement for the ship and wave motion and the longitudinal force; the theory proved to yield better results for these responses in the range of the higher frequencies than the theory, in which all dynamic effects in the vertical plane are disregarded. In contrast the results for the cross forces were less satisfactory, since cross oscillation of the fluid next to and underneath the ship proved to have a detrimental effect. Therefore, extension of the theory is attempted in chapter 7 in order to take into account this phenomenon. In fact the approach used in this chapter is no longer consistent with the theory as derived in chapter 3. For sufficiently low frequencies, however, it can be shown theoretically that the results obtained are identical to those of chapter 3. Furthermore, it is shown in this chapter that the cross-oscillation itself has little influence on the main motion, so that the theory derived in chapter 3 can be used with sufficiently great accuracy as to this aspect. The theoretical results for the cross-forces, however have been improved substantially. In the frequency range considered they obtain the same order of magnitude as the longitudinal force; in the neighbourhood of the resonance frequency of the cross-oscillation they can become considerably greater. On the basis of the results obtained in the chapters 6 and 7, it can be concluded, that for the higher frequencies, which can occur in a navigation lock, the theory derived in chapter 3 means an improvement with respect to the approach now in use. Moreover using the results of chapter 7 a reasonable approximation to the cross-forces can be found.
The harmonic solutions, given in the chapters 6 and 7, cannot be used for the computation of a concrete case. This is caused by the quasilinear character of the various equations due to the continuously changing water level in a ship lock. Therefore, in chapter 8 the integration of the equations is carried out in a numerical way. In the integration it is assumed, that the velocities remain small, so that some quadratic terms in the equations of motion can be neglected. The computational scheme is chosen such, that the detrimental effect of the truncation error is eliminated; its stability is investigated in appendix C. The program is tested by means of the results of an experiment with a transient with arbitrary shape. Finally the program is used for a specific case. In this case the cross-forces as caused by the translatory waves proved to be an order of magnitude smaller than the longitudinal force.