ﺑﺮرﺳﯽ ﻋﺪدي ﻣﻮج اﺳﮑﺎت راﺳﻞ ﺑﺎ اﺳﺘﻔﺎده از روش ﺣﺠﻢ ﻣﺤﺪود و ﺷﺒﮑﻪﺑﻨﺪي روي ﻫﻢروﻧﺪه

Numerical Analysis of Scott Russell’s wave using FVM and Overset Mesh

در اﯾﻦ ﺗﺤﻘﯿﻖ، ﺗﺄﺛﯿﺮ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺨﺘﻠﻒ ﺑﺮ ﯾﮏ ﺳﯿﺴﺘﻢ، ﺷﺎﻣﻞ ﺳﻘﻮط آزاد ﯾﮏ ﺟﻌﺒﻪ داﺧﻞ آب ﻣﻄﺎﻟﻌﻪ ﺷﺪه اﺳﺖ؛ ﻣﺴﺌﻠﻪ ﮐﻼﺳﯿﮑﯽ ﮐﻪ ﺗﻮﺳﻂ اﺳﮑﺎت راﺳﻞ در ﺳﺎل 1844 ﺑﺎ اﺳﺘﻔﺎده از ﺳﻘﻮط آزاد ﺟﺴﻢ ﺳﻨﮕﯿﻦ داﺧﻞ آب و ﺗﺸﮑﯿﻞ و اﻧﺘﺸﺎر ﺗﮏ ﻣﻮج در راﺳﺘﺎي ﻃﻮل ﻣﺤﻔﻈﻪ ﺷﺮح داده ﺷﺪه اﺳﺖ. ﺑﺮاي ﺣﻞ ﻣﺴﺌﻠﻪ، از روش ﺣﺠﻢ ﻣﺤﺪود اﺳﺘﻔﺎده ﺷﺪ. ﺟﻬﺖ ﺑﺮرﺳﯽ ﭘﺮوﻓﯿﻞ ﺳﻄﺢ آب از روش ﺣﺠﻢ ﺳﯿﺎل )VOF( و ﺟﻬﺖ ﺣﺮﮐﺖ ﺟﺴﻢ ﺻﻠﺐ داﺧﻞ آب و ﻫﻮا از ﺷﺒﮑﻪ رويﻫﻢروﻧﺪه ﺑﺮاي ﺗﻮﺻﯿﻒ ﺟﺰﺋﯿﺎت ﺗﺸﮑﯿﻞ ﻣﻮج و ﮔﺮداﺑﻪ اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ. ﺑﺎ ﺳﻘﻮط آزاد ﺟﺴﻢ داﺧﻞ آب، ﻣﻮج و ﮔﺮداﺑﻪاي در زﯾﺮ آن ﺗﺸﮑﯿﻞ ﻣﯽﮔﺮدد. ﮔﺮداﺑﻪي ﺑﻪ وﺟﻮد آﻣﺪه ﺑﻪ ﻫﻤﺮاه ﻣﻮج، در راﺳﺘﺎي ﻃﻮل ﮐﺎﻧﺎل ﻣﻨﺘﺸﺮ ﻣﯽﺷﻮد و ﺳﭙﺲ ﺑﺎ ﻣﺮور زﻣﺎن از ﺑﯿﻦ ﻣﯽ رود. ﺗﺄﺛﯿﺮ ﭘﺎراﻣﺘﺮﻫﺎﯾﯽ ﻣﺎﻧﻨﺪ ﭼﮕﺎﻟﯽ ﺟﻌﺒﻪ، ارﺗﻔﺎع ﺳﻘﻮط ﺟﻌﺒﻪ و ﻋﻤﻖ آب ﺑﺮ ارﺗﻔﺎع ﻣﻮج ﺗﺸﮑﯿﻞ ﺷﺪه ﻣﻮﺛﺮ ﻫﺴﺘﻨﺪ، ﭘﺮوﻓﯿﻞ ﻣﻮج ﺑﻪ دﺳﺖ آﻣﺪه در زﻣﺎن 0/7 ﺛﺎﻧﯿﻪ ﻣﻄﺎﺑﻘﺖ ﺑﺴﯿﺎر ﺧﻮﺑﯽ ﺑﺎ ﻧﺘﺎﯾﺞ ﺗﺠﺮﺑﯽ ﻣﻄﺎﻟﻌﺎت ﭘﯿﺸﯿﻦ ﻧﺸﺎن داد و ﺑﯿﺸﺘﺮﯾﻦ درﺻﺪ ﺧﻄﺎي ﺑﻪ دﺳﺖ آﻣﺪه 4 درﺻﺪ ﮔﺰارش ﮔﺮدﯾﺪ. ﻃﺒﻖ ﻧﺘﺎﯾﺞ ﺑﻪ دﺳﺖ آﻣﺪه، ﺑﺎ اﻓﺰاﯾﺶ ﭼﮕﺎﻟﯽ از 1800 ﺗﺎ 3300 ﮐﯿﻠﻮﮔﺮم ﺑﺮ ﻣﺘﺮ ﻣﮑﻌﺐ و ارﺗﻔﺎع ﺳﻘﻮط ﺟﻌﺒﻪ از 0/4 اﻟﯽ 0/55 ﻣﺘﺮ، ارﺗﻔﺎع ﻣﻮج ﺑﻪ ﺗﺮﺗﯿﺐ 5/3 و 10/2 درﺻﺪ اﻓﺰاﯾﺶ ﯾﺎﻓﺖ. ﻋﻼوه ﺑﺮ اﯾﻦ، ﺑﺎ اﻓﺰاﯾﺶ ﻋﻤﻖ آب از 0/18 اﻟﯽ 0/36 ﻣﺘﺮ، ارﺗﻔﺎع ﻣﻮج 2 درﺻﺪ ﮐﺎﻫﺶ ﯾﺎﻓﺖ و ﻗﻄﺮ ﮔﺮداﺑﻪ اﯾﺠﺎد ﺷﺪه در ﻧﯿﺰ 3/4 درﺻﺪ ﮐﺎﻫﺶ ﯾﺎﻓﺖ. ﻟﺬا اﻫﻤﯿﺖ ﻣﻮجﻫﺎي ﺿﺮﺑﻪاي در ﻣﺨﺎزن ﺳﺪ، ﺑﺎ ﻋﻤﻖ ﭘﺎﯾﯿﻦ و ﺗﭙﻪﻫﺎي ﻣﺸﺮف ﺑﺎ ارﺗﻔﺎع ﻧﺴﺒﺘﺎَ ﺑﺎﻻ، دو ﭼﻨﺪان ﻣﯽﺑﺎﺷﺪ و ﻣﯽﺑﺎﯾﺴﺖ اﯾﻦ ﻧﮑﺎت ﺗﻮﺳﻂ ﻃﺮاﺣﺎن ﻣﺪ ﻧﻈﺮ ﻗﺮار ﮔﯿﺮد.

In this research, the effects of various parameters on system consisting of a heavy box sinking vertically into water have been studied. The classic configuration is due to Scott Russell who used the sinking box in 1844 to illustrate the formation of a solitary wave in a long rectangular tank. A FVM method has been used to solve the problem. The VOF method for wave profile and overset mesh for sinking the box into air and water, is used to clarify details of the wave and vortex formation. It was observed that as the box sinks the water is heaved up to form both the solitary wave and a vortex. This vortex follows the wave down the tank. The effects of box density, height of box and depth of water on the created wave height are effective. The simulation results are in satisfactory agreement with the experiments. The highest verification error was reported at 4 %. According to the results, with increasing density from 1800 to 3300 kg/m3 and box height from 0/4 to 0/55 m, wave height increased by 5/3 % and 10/2 %, respectively. In addition, with increasing water depth from 0/18 to 0/36 m, the wave height decreased by 2 % and the diameter of the resulting vortex decreased by 3/4 %. Therefore, the importance of impulsive waves in dam reservoirs with low depth and overlooking hills with high height is twofold, and these points should be considered by designers