In order to investigate the microbubble drag reduction (MBDR) of ships, numerical studies of MBDR on a low-speed bulk carrier model were conducted based on the two-phase Euler model in OpenFOAM. The governing equations were established for the gas and liquid phases, respectively, considering five kinds of interfacial forces and bubble coalescence and breakup. The modified k-ε turbulence model considering the effects of bubbles was also used, and the superimposed model was adopted to ignore the influence of free surface. The effects of air flow rate, bubble size, ship speed and draft on MBDR of the ship were investigated while the distributions of air volume fraction, turbulent viscosity and bubble size around the ship were analyzed. The numerical results show that: micro bubbles can simultaneously reduce the frictional drag, viscous pressure drag and total drag of the ship; air flow rate can directly influence the drag reduction and more air flow rate can lead to more drag reduction; smaller micro bubbles can lead to higher average volume fraction, more uniform gas distribution and smaller turbulent viscosity, resulting in drag reduction more effectively;bubble coalescence will occur along the direction of the flow and the coalescence effects are more intense for smaller bubbles; higher ship speed and lower draft are more conducive to drag reduction.
| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |