Takao Inui

Nonlinear Ship Waves

Publisher Summary This chapter discusses about nonlinear ship waves. The waves generated by ships advancing steadily in deep water have been considered as typical linear dispersive ones. Many wave-making resistance theories have been proposed by mathematicians and naval architects, most of which are based on this linear postulation. Miyata and co-workers supposed that the complicated nonlinear free surface phenomena called breakdown of waves or necklace vortices were consequent results of nonlinear wave making in the near field, and over a period of five years they carried out experimental investigations into the characteristics and structure of nonlinear waves, as well as numerical analyses of nonlinear wave formation by a finite-difference method. The chapter deals with the studies they made at the experimental tank of the University of Tokyo. In Section II of the chapter, characteristics of nonlinear waves around ship models are experimentally studied, and in Section III more detailed characteristics and structure are clarified with simple wedge models. A numerical method of simulating nonlinear wave formation around the bow is described in Section IV, and the computed results are discussed and compared with experimental results in Section V.

Flat Bottom Effects on Wave-Making Resistance (the Second Report)

In the previous paper the flat bottom effects on wave-making resistance was investigated with respect to the non-bulbous Pienoid models.This paper is an extension to the similar problems of designing the bulbous Pienoids with least wave resistance.The essential conclusion of the previous report is the fact that the observed free wave amplitude due to the additional bottom doublet is as small as nearly half of the corresponding linear theory.For the purpose of ascertaining the adaptability of this conclusion to the case of bulbous forms, three bulbous Pienoid models M 23, M 24 and M 25 are designed and tank-tested as follows : M 23 (αB=0, where αB denotes the reduction factor of the bottom doublet wave), i. e. the bottom doublet is completely neglected.M 24 (αB=1), i. e. the bottom doublet wave is assumed as large as the linearized theoryM 25 (αB=0.4).Based on each assumption, the optimum combination of the side source and the bulb singularity is obtained at Fn=0.277 (K0L=13) for the described draught and displacement.In this procedure, so-called μ-correction (μS) to the side source ought to be taken into account adequately. However, herein as the preliminary step, no correction was applied to the side source (μS=0), which resulted in some confusion as follows.Experimental results show that the first medel M 23 (αB=0) is the best among the three tested models.However, this fact does not necessarily conclude that the first assumption αB=0 is correct, because the present assumption μS=0 is not acceptable.To ascertain this, the fourth model MTM-4 is redesigned (but not tank-tested) by adopting the side source correction μS=0.4 as well as the bottom doublet correction μB=0.4.The obtained lines of MTM-4 is found as very much the same with those of M 23 (Fig. 13).This may suggest that the optimum bulbous Pienoid with a flat bottom can be designed by applying μS=0.4 and μB=0.4 with no correction for the bulb singularity.

Wave Analysis of Simple Hull Forms

A set of 2 m models are wave-analyzed. Importance is placed on the bow wave analysis (Part I) rather than in the resultant wave analysis (Part II). The Part I measured bow wave patterns show not only parallel shift but also the local distortion in co-ordination to the calculated wave patterns. Measured bow wave amplitude is found smaller than the calculated amplitude through certain ranges. The comparison among the three models tested shows that the linearized theory does not work so far as frameline effect is concerned. This may suggest some type of empirical correction factor. The Part II resultant wave analysis of bow and stern waves of Model M-8 shows Newmans truncation formula is not valid with one exception. The effect of finite transverse separation is of less importance than the truncation error. A discrepancy is observed between measured and calculated wave amplitudes of the transverse wave component. Besides viscosity effect, sheltering effect is supposed to be the cause for this discrepancy.

Influence of Designed Waterline and Frameline Forms on Wave-Making Characteristics of Ships (The Second Report)

This paper is the second report on the subject that the authors studied and reported at the Society in 1966. The previous paper deals with the tank experiments of three symmetrical models, UU-, VU- and VV-types, all of which are derived from a certain prescribed sectional area curve with block coefficient CB=0.55. The present paper deals with the further symmetrical models, newly envisaged, UU- and ∧U-types, under the same configuration with block coefficient CB=0.52.The main object of this second report is to appraise the validity and usefulness of the slender ship theory which is to be applied to the preliminary stage of the hull form design procedure, i. e., the determination of the sectional area curve. The effectiveness of the so-called “Pienoid” method is also verified concerning the final stage of the determination of the detailed hull form characteristics such as the waterline-and frameline-forms.In this connection, the authors prepared some mathematical tables to be applied to the slender ship theory calculation of the wave-making resistance.

The New Carriage and Facilities of the Experimental Tank of the University of Tokyo

For the past decade not a few test facilities have been introduced at the Experimental Tank of the University of Tokyo, especially corresponding to the recent theoretical advances in ship hydrodynamics. These are illumination technique of water surface by aluminium powder coating, facilities for photogrammetry using sub-carriage with the stereo plotter of double projection type, and the digitally controlled speed regulator system most of which we owed to Toyo Rayon Science Foundation.Following these developments, we decided to build the new towing carriage with the innovation of motor generator and trolley wire into rigid type of square section provided that speed regulator system should be remained. The design of new carriage was started on Sept. 1965 under the works of “TCG” and completed on Feb. 1967. As shown in Fig. 12 (b), the resistance test is now performed with high accuracy and other capabilities of flow & waves photographing equipments are working successfully. This paper describes the experiences of these design and construction.

Wave Profile Measurements Along Some Mathematical Models by the Benzoic Acid Film Method

The wave profile measurements are made with two wall-sided, deep-drafted mathematical models (S-103, S-203) by applying the chemical film method, where the Benzoic Acid is effectively used for the first time, and found as pre-eminently suited to contrasting the flow phenomena on ship models such as wave profiles, initial still water lines, stream lines, and laminar flow area.Comparisons are also made between the calculated and the observed wave profiles.Coincidence is good along the models, but is unsatisfactory in the rear.The principal cause might be safely ascribed to the fact that the wake intesity is always extinguishedly strong just on the narrow band in the vertical symmetrical plane (y=0).Conclusions are then drawn that the present field of the mentioned comparisons between the theory and the observation must be extended from one dimension (on the line y=0, exclusively) to two dimensions, to which the photographic measurements by stereograph might be expected as essential.

On A Resistance Dynamometer for A Submerged Body-Its Details and Applications to Form Drag Measurements

The study of the viscous drag of ships in model basins can be promoted in the following two steps : (1) First, to study turbulent, smooth, and rectangular plane surfaces with varying aspect : ratios, (2) Second, to investigate ship hull forms with varying particulars.With respect to the first of the above, quite recently an almost fully satisfactory solution has been found by Dr. G. Hughes (1952 ·1954).However, the second and consequently the final step still remains unsolved, and the need is emphasized of the adoptation of submerged double models by the Skin Friction Committee at the Seventh International Conference on Ship Hydrodynamics (1954).The first part of this report gives a short description of a resistance dynamometer to be used for a submerged body, which was designed at the Tokyo University Tank during the years 1952-1953.In the second part, form factors are directly deduced according to various hull forms through the use of the above-mentioned dynamometer.Further, a possibility is also suggested of indirect estimation of form factors by applying wave-making theory to ordinary resistance tests of surface models.