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ارزیابی روشی سریع مبتنی بر تجزیه متعامد بهینه برای مطالعه انتقال حرارت تابشی در محیط فعال | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 10، دوره 54، شماره 9، آذر 1401، صفحه 2175-2174 اصل مقاله (2.12 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2022.21069.7377 | ||
| نویسندگان | ||
| محسن نیکنام شارک1؛ علی صفوی نژاد* 1؛ محمد کاظم مویدی2 | ||
| 1دانشکده مهندسی مکانیک، دانشکده مهندسی، دانشگاه بیرجند، بیرجند، ایران. | ||
| 2دانشکده مهندسی مکانیک، دانشکده مهندسی، دانشگاه قم، قم، ایران. | ||
| چکیده | ||
| برای مطالعه انتقال حرارت تابشی در محیط فعال، باید معادله انتقال تابش حل شود. جز در مواردی خاص، حل تحلیلی برای این معادله وجود ندارد. حل آن با روش های عددی نیز معمولاً زمانبر است. در مسائل انتقال حرارت ترکیبی تابش-هدایت یا تابش-جابهجایی، و مسائل معکوس انتقال حرارت، معادله انتقال تابش باید چندین بار حل شود. بنابراین، زمان حل این معادله مهم است. در این تحقیق، روشی سریع مبتنی بر تجزیه متعامد بهینه برای حل معادله انتقال تابش ارائه میگردد. تعدادی از خواص (مانند: گسیلندگی مرزها، ضریب جذب و انحراف محیط) به عنوان پارامترهای مستقل انتخاب می شوند. معادله انتقال تابش برای حالتهای خاصی از این پارامترها، با استفاده از روش راستاهای مجزا حل شده، و پاسخهای سیستم، ماتریس نمایه را تشکیل می دهند. با استفاده از تجزیه مقادیر تکین، این ماتریس به صورت حاصلضرب سه ماتریس تجزیه می گردد. با توجه به بزرگی مقادیر تکین، فقط ستونهای خاصی از این ماتریسها، انتخاب می شوند. در نتیجه، درجات آزادی سیستم اصلی کاهش یافته و یک مدل رتبهکاسته ایجاد می گردد. با استفاده از درونیابی توابع پایه شعاعی به ازای هر بردار ورودی دلخواه (شامل پارامترهای مستقل)، می توان پاسخ سیستم را با سرعت بالایی تقریب زد. نتایج نشان میدهد مدل رتبهکاسته در مقایسه با حل عددی دقت بالایی دارد. پیچیدگی های سیستم در مدل رتبهکاسته تأثیری نداشته، و فارغ از ویژگیهای محیط (مقدار پارامترهای مستقل)، زمان حل از مرتبه 0/02 ثانیه است. | ||
| کلیدواژهها | ||
| معادله انتقال تابش؛ محیط فعال؛ مدلسازی رتبهکاسته؛ تجزیه متعامد بهینه؛ توابع پایه شعاعی | ||
| عنوان مقاله [English] | ||
| Evaluating the fast method based on proper orthogonal decomposition for radiative heat transfer in a participating medium | ||
| نویسندگان [English] | ||
| Mohsen Niknam Sharak1؛ Ali Safavinejad1؛ Mohammad Kazem Moayyedi2 | ||
| 1Department of Mechanical Engineering, Faculty of Engineering, University of Birjand, Birjand, Iran | ||
| 2Department of Mechanical Engineering, Faculty of Engineering, University of Qom, Qom, Iran | ||
| چکیده [English] | ||
| The radiative transfer equation models the thermal radiation in a participating medium. Except in specified cases, there is no analytical solution for this equation. Solving the radiative transfer equation with numerical methods is usually time-consuming. This work presents a fast method based on proper orthogonal decomposition to solve the radiative transfer equation. Some variables are selected as independent parameters. The radiative transfer equation for the specified value of these parameters is solved using the discrete ordinates method, and the system responses form the snapshot matrix. The matrix is decomposed singular value decomposition as a product of three matrices. Due to the magnitude of singular values, only a few first columns of these matrices are selected. As a result, the degrees of freedom of the original system are decreased, and a reduced-order model is created. Employing the radial basis functions, the system response, corresponding to any arbitrary input vector (independent parameters), can be approximated with high speed. The results show that the reduced-order method has high accuracy compared to the numerical solution. The complexities of the system do not affect the reduced-order method. Regardless of the characteristics of the medium (the value of independent parameters), the solution time is the order of 0.02 seconds. | ||
| کلیدواژهها [English] | ||
| Radiative heat transfer, Participating medium, Reduced-order modeling, Proper orthogonal decomposition, Radial basis functions | ||
| مراجع | ||
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