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| Numerical simulation of fluid phenomena observed in living things |
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Dolphins can swim at an extremely high speed as compared to that expected from the muscular power of dolphins. This marvelous power of dolphins is generally attributed to a small deformation in its flexible-skin-compliant surface (i.e., viscoelastic membrane). A compliant surface can be deformed by pressure variations in the ambient fluid without external energy input. By using this effective mechanism investigated in living things, compliant surfaces can be used as promising fluid control devices. Compliant surfaces are considered to exhibit a turbulent transition delay and turbulent drag reduction effects. In the former case, the turbulent transition delay effect increases the transition Reynolds number; this has been proved by experiments and numerical calculations using a linear disturbance equation. In the latter case, however, the validity and mechanism of the turbulent drag reduction effect have not been clarified thus far. Attempts to conduct further experiments have been unsuccessful because of the difficulty in the experimental measurement of the near-wall flow at a deformable boundary.
In recent years, computer performance has improved by leaps and bounds, and a direct numerical simulation of the flow field near complex boundaries can be performed. By using this numerical calculation, the details of the physical quantities in the near-wall flow can be obtained, although they cannot be measured by experiments. In addition, we can conduct a virtual experiment in which the physical properties of a compliant surface can be conveniently determined by assigning data ranging from realistic to virtual values of the parameters. Therefore, numerical simulation is expected to become an effective tool for elucidating the flow control mechanism using compliant surfaces. |
This study aims to investigate the validity of the turbulent drag reduction effect and the optimum values of the physical properties of a compliant surface for reducing frictional drag (--> see References (1) and (2)). First, we developed a direct numerical simulation code of the turbulent flow between parallel plates with a compliant surface. To simplify this problem, the compliant surface is represented by a model of a spring-mass-damper system, as shown in Fig. 1. For wall-turbulent flows typified by the flow between the parallel plates, the near-wall quasi-streamwise vortex structure is known to significantly contribute toward the turbulent drag reduction effect and Reynolds stress. It is considered that the turbulent drag can be reduced by suppressing the rotational motion of the quasi-streamwise vortex structure.
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| Fig. 1 Schematic model of a compliant surface. |
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| The quasi-streamwise vortex structure is closely related with the wall-pressure variation (Fig. 2). Hence, we conducted a flow field simulation involving this structure. In the simulation, the physical properties of the compliant surface were selected such that the time dependence of the wall-pressure variation is in phase with the deformation speed of the compliant surface. Figures 3 (a) and (b) show the top views of the near-wall turbulent quasi-ordered structure at the initial stage of the compliant surface deformation and that after a sufficiently elapsed time, respectively. As evident from these figures, the rotational motion of the quasi-streamwise vortex structure is retarded and the fluctuation in the low-speed streaks is suppressed. As a result, the turbulent flow gets inactivated, resulting in approximately 3% reduction in frictional drag (--> see Reference (4)). |
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| Fig. 2 Schematic of the flow field near the streamwise vortices, and the desired wall velocity of the compliant surface to suppress the vortices. |
Fig. 3 Instantaneous flow field of the compliant channel flow.
(a) t^ += 4.86
(b) t^ += 301. Blue: u'^ += -3.5, red: u'^+=+3.5, and white: II^ += -0.03. |
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In technical applications, compliant surfaces can be used as covering materials for the surfaces of airplanes and large ships to reduce the frictional drag forces exerted by the external fluid flow. For this application, this study developed a numerical simulation code for solving the problem of external flow around the compliant surface of an object. Simple models of a cylinder and sphere were selected, and the effect of a compliant surface on the frictional drag, pressure drag, and lift were investigated. As shown in Figs. 4 and 5, Karman vortices alternately appear in the wake of the compliant cylinder and sphere; both these surfaces exhibit a small deformation. The shape of the compliant cylinder/sphere becomes flat in the vicinity of their stagnation points located upstream This indicates the possibility of a reduction in the frictional drag, although the pressure drag increases with an increase in the area projected from the upstream flow (--> see References (7) and (8)).
This result demonstrates that the frictional drag of a device is reduced by using a compliant surface for large ships and airplanes against which the frictional drag occurs at a ratio of more than 90% of the entire drag value.
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| Fig. 4 Instantaneous flow field around a compliant cylinder. |
Fig. 5 Instantaneous flow field around a compliant sphere. |
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