Yoshiaki Takahashi

Simple Lagrangian formulation of bubbly flow in a turbulent boundary layer (bubbly boundary layer flow)

For the theoretical consideration of a system for reducing skin friction, a mathematical model was derived to represent, in a two-phase field, the effect on skin friction of the injection of micro air bubbles into the turbulent boundary layer of a liquid stream. Based on the Lagrangian method, the equation of motion governing a single bubble was derived. The random motion of bubbles in a field initially devoid of bubbles was then traced in three dimensions to estimate void fraction distributions across sections of the flow channel, and to determine local bubble behavior. The liquid phase was modeled on the principle of mixing length. Assuming that the force exerted on the liquid phase was equal to the fluid drag generated by bubble slip, an equation was derived to express the reduction in turbulent shear stress. Corroborating experimental data were obtained from tests using a cavitation tunnel equipped with a slit in the ceiling from which bubbly water was injected. The measurement data provided qualitative substantiation of the trend shown by the calculated results with regard to the skin friction ratio between cases with and without bubble injection as function of the distance downstream from the point of bubble injection.

Dynamic control of a remotely operated vehicle using a neural network

The control of a remotely-operated underwater vehicle to maintain a prescribed depth in shallow water under irregular surface waves is realized through the application of the Robust Adaptive Neuro Controller, a composite control system incorporating—together with the conventional control algorithm—a neural network controller. This network bestows a learning capability on the system, allowing it to deal with unanticipated disturbances that would otherwise cause erroneous behavior of the vehicle. The effectiveness of this application is verified through mathematical simulation of a model vehicles behavior, through experiment in a model basin, and through simulation of the behavior of an actual remotely operated vehicle in shallow water under irregular surface waves. Graphic data representing the learning process undergone by the neural network distinctly indicate the rising output from the network with the progression of learning, and the vehicles depth variation traced in terms of the mean square error vividly show the diminution of deviation from the prescribed depth obtained with application of the neural network. Thus controlled to maintain constant depth, under-water vehicles with power supplied externally through a tether for propulsion and for heavy-duty operations should consolidate their advantage for such activities as maintenance of submarine structures and surveys in deep or hazardous water.

Distribution of void fraction in bubbly flow through a horizontal channel: Bubbly boundary layer flow, 2nd report

A method of enveloping the hull with a sheet of microbubbles is discussed. It forms part of a study on means of reducing the skin friction acting on a ships hull. In this report, a bubble traveling through a horizontal channel is regarded as a diffusive particle. Based on this assumption, an equation based on flow flux balance is derived for determining the void fraction in approximation. The equation thus derived is used for calculation, and the calculation results are compared with reported experimental data. The equation is further manipulated to make it compatible with a mixing length model that takes into account the presence of bubbles in the liquid stream. Among the factors contained in the equation thus derived, those affected by the presence of bubbles are the change of mixing length and the difference in the ratio of skin friction between cases with and without bubbles. These factors can be calculated using the mean void fraction in the boundary layer determined by the rate of air supply into the flow field. It is suggested that the ratio between boundary layer thickness and bubble diameter could constitute a significant parameter to replace the scale effect in estimating values applicable to actual ships from corresponding data obtained in model experiments.