بهبود عملكرد روش شبكه‌ي بولتزمن به منظور مطالعه عددي جريان گاز در محيط‌هاي متخلخل نانو مقياس

Improving the performance of lattice Boltzmann method in order to numerical study of gas flows in nano scale porous media

روش شبكه بولتزمن متداول (استاندارد) صرفاً قادر است نتايج جريان در مقياس ميكرو را -كه معمولاً منطبق بر رژيم جريان لغزشي است- بخوبي پيش‌بيني نمايد اما براي جريان در مقياس نانو –كه معمولاً منطبق بر رژيم گذرا است- از دقت كافي برخوردار نيست. در اين مقاله با انجام اصلاحاتي در روش شبكه بولتزمن، جريان در نانو كانال حاوي محيط متخلخل در بازه وسيعي از رژيم‌هاي جريان، شامل رژيم لغزشي و گذرا، به كمك روش مذكور مدلسازي شده است. همچنين براي اولين مرتبه پديده مينيمم نادسن در ميكرو و نانو‌كانال‌هاي حاوي محيط متخلخل مشاهده شده و مورد ارزيابي قرار گرفته است.

The standard Lattice Boltzmann Method, LBM, is usually able to predict the results of micro scale flows which are corresponding to the slip flow regime, while it has not sufficient accuracy for nano scale flows which are corresponding to the transition flow regime. In this paper, by improving the lattice Boltzmann method, pressure driven flow through non-porous nano channels and nano channels filled with porous media has been modeled for wide range of Knudsen numbers, Kn, covering the slip and transition regimes. The results show that the presented lattice Boltzmann model is able to predict the flow features in micro and nano scales for wide range of Knudsen numbers by modifying the relaxation time. In the presented research, the effects of the Knudsen number and porosity on the flow rate, Darcy number and pressure drop are reported. Also, for the first time, the Knudsen’s minimum effect for micro/nano channels filled with porous media is observed and evaluated. For the pressure driven flows in non-porous channels this effect occurs at Kn=1, while the results show that for the nano channels filled with porous media this effect occurs at Kn=0.1 because of the tortuosity effects.