Prediction of inception of sheet cavitation on solid walls has been recognized to be very difficult, since it is significantly affected by the boundary layer flow characteristics, the population of free nuclei, the nu...Prediction of inception of sheet cavitation on solid walls has been recognized to be very difficult, since it is significantly affected by the boundary layer flow characteristics, the population of free nuclei, the nuclei held in the wall roughness, the amount of dissolved air in liquid and so on. It has not sufficiently been made clear how the inception is affected by the conditions of water qualities and background flow characteristics. In this study, high speed observation of inception of sheet cavity from free nuclei is conducted for a two-dimensional convergent-divergent nozzle flow, where the sheet cavity forms just downstream of the nozzle throat. The effects of the amount of dissolved air and the free stream velocity on the inception process of sheet cavitation is examined. In addition, the bubble nuclei density, which is well known to be important factor for cavitation inception, is passively controlled by the filter installed in the tunnel. From the observations, it is confirmed that the nuclei number density significantly affects the formation of sheet cavity rather than the other two parameters. In conditions with large nuclei number density, the sheet cavity does not form, and bubbly cavitation appears instead. In the case with small nuclei number density, the sheet cavity forms from a single flowing nucleus and develops streamwisely and spanwisely. In the conditions with medium nuclei number density, the sheet cavity also forms but is shorter/narrower streamwisely/spanwisely, due to interaction of other nuclei flowing near the formed sheet cavity.展开更多
Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 ...Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 is an associative submanifold of R^7 if and only if M is almost complex in S^6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S^6 are the equation for primitive maps associated to the 6-symmetric space G2/T^2, and use this to explain some of the known results. Moreover, the equation for S^1-symmetric almost complex curves in S^6 is the periodic Toda lattice, and a discussion of periodic solutions is given.展开更多
文摘Prediction of inception of sheet cavitation on solid walls has been recognized to be very difficult, since it is significantly affected by the boundary layer flow characteristics, the population of free nuclei, the nuclei held in the wall roughness, the amount of dissolved air in liquid and so on. It has not sufficiently been made clear how the inception is affected by the conditions of water qualities and background flow characteristics. In this study, high speed observation of inception of sheet cavity from free nuclei is conducted for a two-dimensional convergent-divergent nozzle flow, where the sheet cavity forms just downstream of the nozzle throat. The effects of the amount of dissolved air and the free stream velocity on the inception process of sheet cavitation is examined. In addition, the bubble nuclei density, which is well known to be important factor for cavitation inception, is passively controlled by the filter installed in the tunnel. From the observations, it is confirmed that the nuclei number density significantly affects the formation of sheet cavity rather than the other two parameters. In conditions with large nuclei number density, the sheet cavity does not form, and bubbly cavitation appears instead. In the case with small nuclei number density, the sheet cavity forms from a single flowing nucleus and develops streamwisely and spanwisely. In the conditions with medium nuclei number density, the sheet cavity also forms but is shorter/narrower streamwisely/spanwisely, due to interaction of other nuclei flowing near the formed sheet cavity.
文摘Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 is an associative submanifold of R^7 if and only if M is almost complex in S^6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S^6 are the equation for primitive maps associated to the 6-symmetric space G2/T^2, and use this to explain some of the known results. Moreover, the equation for S^1-symmetric almost complex curves in S^6 is the periodic Toda lattice, and a discussion of periodic solutions is given.
