ﺣﻞ ﻋﺪدي ﺟﺪاﯾﺶ ﻻﯾﻪ ﻣﺮزي در ﮐﺎﻧﺎل واﮔﺮ ا ﺳﻪﺑﻌﺪيﺗﺤﺖ ﺗﺄﺛﯿﺮ ﻣﯿﺪان ﻣﻐﻨﺎﻃﯿﺴﯽ ﻏﯿﺮﯾﮑﻨﻮاﺧﺖ

Numerical Investigation of Boundary Layer Separation in a 3-D Divergent Channel under the influence of a non-Uniform Magnetic Field

در اﯾﻦ ﺗﺤﻘﯿﻖ، ﺗﺄﺛﯿﺮ ﻣﯿﺪان ﻣﻐﻨﺎﻃﯿﺴﯽ ﻏﯿﺮﯾﮑﻨﻮاﺧﺖ ﺑﺮ رﻓﺘﺎر ﺟﺮﯾﺎن ﺳﯿﺎل و ﭘﺪﯾﺪه ﺟﺪاﯾﺶ در ﯾﮏ ﮐﺎﻧﺎل واﮔﺮا ﺳﻪﺑﻌﺪي ﺑﻪﺻﻮرت ﻋﺪدي ﺑﺮرﺳﯽ ﺷﺪه اﺳﺖ. ﻣﻌﺎدﻻت ﺣﺎﮐﻢ ﺷﺎﻣﻞ ﭘﯿﻮﺳﺘﮕﯽ و ﻣﻮﻣﻨﺘﻢ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﺑﺮاي ﺟﺮﯾﺎن ﺳﯿﺎل آرام، ﭘﺎﯾﺪار و ﺗﺮاﮐﻢﻧﺎﭘﺬﯾﺮ اﺳﺖ. ﺑﻪﻣﻨﻈﻮر ﻣﺪلﺳﺎزي و ﺣﻞ ﻋﺪدي ﺑﻪ روش ﺣﺠﻢ ﻣﺤﺪود، از ﻧﺮماﻓﺰار ﻣﺘﻦ ﺑﺎز اوﭘﻦﻓﻮم ﺑﺮاي ﮐﺎﻧﺎل واﮔﺮاي ﺳﻪﺑﻌﺪي ﺗﺤﺖ ﺗﺄﺛﯿﺮ ﻣﯿﺪان ﻣﻐﻨﺎﻃﯿﺴﯽ ﻣﺘﻐﯿﺮ اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ. ﺑﺮرﺳﯽ ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽدﻫﺪ در ﻏﯿﺎب ﻣﯿﺪان ﻣﻐﻨﺎﻃﯿﺴﯽ و در رﯾﻨﻮﻟﺪز 250، ﺑﺪون اﻋﻤﺎل ﻣﯿﺪان ﻣﻐﻨﺎﻃﯿﺴﯽ، ﺟﺪاﯾﺶ در دﯾﻮاره ﻫﺎي ﺑﺎﻻ و ﭘﺎﯾﯿﻦ ﮐﺎﻧﺎل واﮔﺮا اﯾﺠﺎد ﻣﯽﺷﻮد. ﺑﺎ اﻋﻤﺎل ﻣﯿﺪان ﻣﻐﻨﺎﻃﯿﺴﯽ ﻣﺸﺎﻫﺪه ﻣﯽﮔﺮدد ﮐﻪ ﺟﺪاﯾﺶ ﻻﯾﻪ ﻣﺮزي ﺑﻪ ﺗﺄﺧﯿﺮ ﺧﻮاﻫﺪ اﻓﺘﺎد. ﻣﺸﺎﻫﺪه ﮔﺮدﯾﺪ ﮐﻪ ﺑﺎ اﻓﺰاﯾﺶ ﻋﺪد ﻫﺎرﺗﻤﻦ ﺗﺎ ﭼﻬﺎر، ﭘﺪﯾﺪه ﺟﺪاﯾﺶ ﮐﺎﻣﻼً ﺣﺬف ﻣﯽ ﺷﻮد و از ﺑﯿﻦ ﻣﯽرود. در ﺷﺮاﯾﻂ ﻣﺸﺎﺑﻪ ﻧﺸﺎن داده ﺷﺪ ﻫﺮاﻧﺪازه ﺑﻪ دﯾﻮاره ﺟﺎﻧﺒﯽ ﻧﺰدﯾﮏ ﺷﻮﯾﻢ، ﺟﺪاﯾﺶ ﻻﯾﻪ ﻣﺮزي زودﺗﺮ رخ ﺧﻮاﻫﺪ داد و ﺑﺎ ﮐﺎﻫﺶ ﻋﺪد رﯾﻨﻮﻟﺪز ﺑﻪ 208 /33، ﺟﺪاﯾﺶ ﻻﯾﻪ ﻣﺮزي ﻧﺴﺒﺖ ﺑﻪ ورودي ﮐﺎﻧﺎل، دﯾﺮﺗﺮ اﺗﻔﺎق ﺧﻮاﻫﺪ اﻓﺘﺎد. ﻫﻤﭽﻨﯿﻦ ﻣﺸﺨﺺ ﮔﺮدﯾﺪ اﮔﺮ ﭘﻬﻨﺎي ﮐﺎﻧﺎل ﺑﯿﺶ از 10 ﺑﺮاﺑﺮ ارﺗﻔﺎع ﮐﺎﻧﺎل در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﻮد، ﺗﺄﺛﯿﺮ دﯾﻮاره ﻫﺎي ﺟﺎﻧﺒﯽ ﻧﺎﭼﯿﺰ اﺳﺖ و ﻧﺘﺎﯾﺞ ﺟﺪاﯾﺶ در ﺟﺮﯾﺎن ﺳﻪﺑﻌﺪي ﻫﻤﺎﻧﻨﺪ ﺟﺮﯾﺎن دوﺑﻌﺪي ﺧﻮاﻫﺪ ﺷﺪ.

In the present research, the non-uniform magnetic field effect on separation phenomenon in divergent channels was investigated numerically. The governing equations, including continuity and momentum equations, were presented and simplified for the laminar, steady, and incompressible flow; then, a non-uniform magnetic field was applied to the flow. Hence, the finite volume method using the OpenFOAM CFD toolbox was employed and a code for 3-D divergent channel flow under a non-uniform magnetic field developed. The effect of non-uniform magnetic field intensity on the boundary layer separation phenomenon on the divergent channel wall was investigated. The results show that the separation in the flow without applying a magnetic field occurs in Re=250 on the channel's upper (lower) wall. By applying the magnetic field and increasing the Hartmann, the boundary layer separation was delayed and in Ha equals 4, the separation is completely deleted and not observed. Under the same conditions, near the sidewalls, the separation occurs sooner than the channel entrance. Furthermore, by reducing the Reynolds to 208.33, the separation occurs late. In a 3-D channel that has a width ten times bigger than its height, the separation points far from the side walls are almost the same as a 2-D channel.