نویسندگان

دانشکده مهندسی مکانیک، دانشگاه کاشان

چکیده

در این تحقیق برای اولین بار مقایسه ی روش های بولتزمن شبکه ا ی با ضریب تخفیف منفرد، چندتایی و انتروپی بر روی شبکه بندی غیریکنواخت انجام شده و کاربرد این روش ها در شبیه سازی میکروجریان های همدمای دو بعدی در یک حفره، یک کانال و یک کانال با انبساط ناگهانی در محدودهی رژیم لغزشی و تا حدودی رژیم گذار مورد مطالعه قرار گرفته است. در این کار به منظور استفاده از شبکه بندی غی ر یکنواخت از روش بولتزمن شبکه ای مبتنی بر حداقل مربعات و بسط سری تیلور استفاده شده است. همچنین برای در نظر گرفتن لغزش رو ی دیواره ها، از شرایط مرزی پخش مولکولی و روش ترکیبی کمانه کردن و آینه ای و برای محاسبه ی ضرایب تخفیف روش های بولتزمن شبکه ای، از مرتبط کردن آن به عدد نادسن استفاده گردیده است. سپس با تحلیل و بررسی نتایج شبیه سازیها، به مقایسه ی روشها ی بولتزمن شبکه ای مختلف در شبیه سازی میکروجریان ها پرداخته شده است. با مقایسه ی نتایج شبیه سازی های عددی به دست آمده در این کار با نتایج ارائه شده توسط سایر محققین، اعتبار و صحت برنامه های کامپیوتری و دقت جواب ها مورد بررسی قرار گرفته است. نتایج نشان می دهد که روش ها ی بولتزمن شبکه ای با ضریب تخفیف چندتایی نسبت به سایر روش ها قابلیت شبیه سازی میکروجریان ها با عدد نادسن بالاتر را دارد.

کلیدواژه‌ها

عنوان مقاله [English]

Application and Comparison of Different Lattice Boltzmann Methods on Non-Uniform Meshes for Simulation of Micro Cavity and Micro Channel Flow

نویسندگان [English]

  • A. R. Rahmati
  • S. Niazi

چکیده [English]

In this study, for the first time, a comparison of single-relaxation-time, multi-relaxation-time and entropic lattice Boltzmann methods on non-uniform meshes is performed and application of these methods for simulation of two-dimensional cavity flows, channel flows and channel flows with sudden expansion is studied in the slip and near transition regimes. In this work, Taylor series expansion and least squares based lattice Boltzmann method is utilized in order to apply the lattice Boltzmann models on non-uniform meshes. A diffuse scattering boundary condition and a combination of bounce-back and specular boundary conditions are employed to obtain the slip at the walls. Besides, the relaxation times of lattice Boltzmann methods are computed in terms of Knudsen number. Different lattice Boltzmann methods are used to simulate lid-driven micro cavity flows and their results are compared with each other and with those obtained in the literature. Then, the best model in accuracy and stability, i.e. multi-relaxation-time lattice Boltzmann method, is applied to simulate the micro channel flow in different Knudsen numbers. Results show that the proposed method on non-uniform meshes is capable of simulating micro flows problems in the slip and the transition regimes.

کلیدواژه‌ها [English]

  • Taylor series expansion and least squares based lattice Boltzmann method
  • Knudsen number
  • microcavity
  • microchannel
  • sudden expansion
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