Fig 3 - uploaded by Igor Nesteruk
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Vertical velocities on the water surface upstream of the body with a convex nose at different depths of steady motion.
Source publication
A streamlined shape of the best swimmers removes the boundary-layer separation and ensures a laminar flow pattern. The fastest fish have a very sharp convex nose (rostrum), the purpose of which remains unclear. The bodies of revolution similar to their shapes are analyzed in steady underwater and floating motion. The sources and sinks were located...
Contexts in source publication
Context 1
... depth h with the use of Eq. (7) and are shown in Fig. 6 (upstream of the body). The downstream vertical velocities are very close to the case of the convex nose body shown in Fig. 4 . Figure 6 illustrates that for small depths of motion ( h < 0 . 1 ), the values of v y ( x, h, 0 ) are much lower in comparison with the convex nose case shown in Fig. 3 . This fact can be explained by the absence of the bow stagnation point and the low values of pressure near the nose shown in Fig. 5 . Thus, we can conclude that special shaped bodies of revolution with sharp concave noses are expected to have smaller wave drag in a floating mode of ...
Context 2
... proposed shapes can be recommended for the underwater hulls of SWATH ships (see, e.g., Ref. [31] ), since the disturbances of the water surface and corresponding wave drag reduce at rather small values of h (see the black lines in Figs. 3 , 4 and 6 ). The total drag on such hulls can be estimated with the use of Eqs. (11) or (13) ...
Citations
... Due to the high Reynolds numbers many important inverse problems of high-speed hydromechanics (in particular, supercavitating flows, ) can be solved with the use of the ideal fluid approach. In particular, for axisymmetric elongated bodies and cavities (with high values of length to diameter ratio L/D), the asymptotical series for flow potential of sources and sinks located on the axis of symmetry can be used [15][16][17][18][25][26][27][28][29][30][31][32][33]. In the case of unbounded flow of incompressible fluid, exact solutions of Euler equations were obtained [30][31][32][33]. ...
... In particular, for axisymmetric elongated bodies and cavities (with high values of length to diameter ratio L/D), the asymptotical series for flow potential of sources and sinks located on the axis of symmetry can be used [15][16][17][18][25][26][27][28][29][30][31][32][33]. In the case of unbounded flow of incompressible fluid, exact solutions of Euler equations were obtained [30][31][32][33]. ...
... To avoid separation of the boundary layer and reduce the drag, axisymmetric and 2D shapes with negative pressure gradients on their surfaces were calculated, [31][32][33]. On some bodies, the absence of separation was confirmed by experiments in the wind tunnels [31,34]. ...
High Reynolds numbers allow solving many important inverse problems of high-speed hydromechanics with the use of the ideal fluid approach. The shapes of elongated axisymmetric cavities and bodies of revolution with the prescribed pressure distribution were calculated with the use of asymptotical series for flow potential and exact solutions of Euler equations. In particular, axisymmetric and 2D shapes with negative pressure gradients on their surfaces were proposed in order to avoid separation of the boundary layer and reduce the drag. Wind tunnel experiments have confirmed the absence of separation on some bodies of revolution similar to the trunks of aquatic animals. The proposed shapes with sharp concave noses (similar to the rostrum of the fastest fish) have no stagnation points, pressure and temperature peaks. These special shaped bodies moving near the water surface cause much lower vertical velocities on its surface and can have a low wave resistance. These facts open prospects of using corresponding hulls for underwater and floating vehicles. In supersonic flows, they can reduce overheating of the noses.
... A very sharp nasal rostrum of these animals probably allows them to remove the boundary layer separation and avoid high pressures on the body surface as well as reduce the wave resistance when moving near the water surface. The corresponding axisymmetric bodies with concave noses have no pressure peaks on their shape and have much lower values of the vertical velocity on the water surface [6]. Since the reason for the waves on the water surface is the high pressure on the vessel bow and stern [7][8][9][10], these special-shaped bodies could be used to reduce wave resistance. ...
... Small disturbances of the water surface caused by the special-shaped bodies of a revolution with concave noses (similar to the rostrums of the fastest fish) [6] open prospects of their use for floating vehicles. The volumetric Reynolds number for Explorer-1 is approximately 1.3 million. ...
... Let us calculate the values of function f (h) for the body of revolution obtained in [6] with the use of sources and sinks located on the axis of symmetry. Their intensity is given by: ...
The popularity of modern water bikes increases due to the relatively high speed developed with the use of a human muscle power only. For example, the maximum speed of prototypes reaches the value 3 m/s. Similar vehicles can be used not only for recreation and fitness, but also for transportation. To increase their speed and tonnage, we recommend improving the pontoon shape and using electrical power. The underwater part of the pontoon shape was recommended to be similar to the body shape of the fastest fish in order to decrease the wave resistance and total drag. The optimal depth of the movement of corresponding shapes was calculated. The total drag and maximum speeds of the vehicles with the human muscle and electrical power are estimated. Expected success in improving the pontoon shape opens wide prospects for the use of these special-shaped hulls in shipbuilding.
... and to reduce the wave resistance when moving near the water surface. The corresponding axisymmetric bodies with concave noses have no pressure peaks on their shape [6] and much lower values of the vertical velocity on the water 2 surface [7]. Since the reason of the waves on the water surface is the high pressure on the vessel bow and stern [8][9][10][11], these special shaped bodies could be used to reduce the wave resistance. ...
... Simulation with the use of sources and sinks. Source: [7]. ...
... The values of parameters c , d, 1 a , and x * were adjusted to remove the stagnation point on the nose. The absence of the very small velocities near this point allows reducing the maximal pressure on the body surface and the wave drag [7]. Black solid line in Figure 4 represents an example of such body of revolution with a sharp concave nose, similar to shape of sailfish. ...
Rather high speed of modern water bikes that they develop using only human muscle power increases their popularity. For example, the maximum speed of prototypes reaches the value 3 m/s. Similar vehicles can be used not only for recreation and fitness, but also for transportation. To increase their speed and tonnage, we recommend improving the pontoon shape and using electrical power. The total drag and maximal speeds of the vehicles with the human muscle and electrical power are estimated. Expected success in improving the pontoon shape opens wide prospects for the use of these special shaped hulls in shipbuilding.
