مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

افزایش دامنه عدد رینولدز در شبیه‌سازی با استفاده از روش المان مرزی

نویسندگان
دانشگاه تربیت مدرس
چکیده
با توسعه روزافزون رایانه‌ها استفاده از روش‌های عددی برای حل مسائل مهندسی کاربرد بسیاری یافته‌است. از جمله‌ی این روش‌ها می‌توان به روشهایی همچون تفاضل محدود، المان محدود، حجم محدود، روش المان مرزی و ... اشاره نمود. در این پژوهش از روش المان مرزی برای شبیه‌سازی عددی استفاده شده‌است. تفاوت روش المان مرزی با روش‌هایی همچون روش المان محدود در ریاضیات حاکم بر مسأله است. در این روش ابتدا از معادله دیفرانسیلی حاکم بر مسأله یک‌بار انتگرال گرفته می‌شود. این انتگرال‌گیری منجر به کاهش یک بعد از ابعاد مسأله می‌گردد و سپس اقدام به شبیه‌سازی می‌شود. در این پژوهش ابتدا با استفاده از یک تغییر متغیر معادله ناویر استوکس به معادله ناویر در الاستواستاتیک تبدیل می‌گردد. سپس از روش‌های پیشنهادی برای مسأله الاستواستاتیک، برای حل جریان سیال لزج استفاده می‌شود. در واقع تفاوت اصلی میان این شیوه و سایر شیوه‌های پیشنهادی در روش المان مرزی در پاسخ بنیادینی است که در این شیوه از آن استفاده شده‌است. در واقع در این پژوهش، برخلاف پژوهش‌های پیشین، از پاسخ بنیادین معادله ناویر استفاده شده است. در پایان با استفاده از ریاضیات حاکم بر مسأله یک برنامه کامپیوتری برای حل جریان سیال لزج نوشته شد. این برنامه برای دو هندسه متفاوت داخل حفره و پشت پله اعمال گردید، که به ترتیب تا اعداد رینولدز 600 و 100 موفق به دست‌یابی به پاسخ‌های همگرا شدیم.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Extending Reynolds Number range in numerical simulation Of fluid flow using Boundary Element Method

نویسندگان English

Ghassem Heidarinejad
amir yousefi
Tehran, Ale Ahmad Ave, Tarbiat Modares University,Faculty of Mechanical Engineering, Room 317
چکیده English

With the development of computers, the application of numerical methods in solving engineering problems has increased considerably. Methods such as Finite Element Method, Finite Volume Method and Finite Difference Method can be mentioned as some. In this research a Boundary Element Method is applied for numerical simulation. The main difference among the Boundary Element method and other numerical methods is the governing mathematics. At first In this method the governing equation is integrated. This leads to a decrease in the dimensions of the problem and then the simulation is performed. In this research, by a change of variable, the Navier Stokes equation is transformed to Navier equation in Elastostatics at first. Subsequently the methods proposed for solving the problems in Elastostatics is utilized to solve the viscous fluid flow. In fact, the applied fundamental solution is the main difference among the proposed method and other Boundary Element Methods. In the proposed method, in contrast to previously proposed methods, the fundamental solution of the Navier equation is utilized for simulation. At last, by considering the governing mathematics a computer code is developed for viscous flow simulation. The code is applied to two different geometries, a lid-driven-cavity and a backward facing step. Convergent solutions is achieved up to Reynolsds numbers equal with 600 and 100 respectively.

کلیدواژه‌ها English

Boundary element method
viscous fluid flow
Navier equation
Cavity
Elastostatics
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