ارزیابی روشی سریع مبتنی بر تجزیه متعامد بهینه برای مطالعه انتقال حرارت تابشی در محیط فعال

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشکده مهندسی، دانشگاه بیرجند، بیرجند، ایران.

2 دانشکده 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

موضوعات

عنوان مقاله [English]

Evaluating the fast method based on proper orthogonal decomposition for radiative heat transfer in a participating medium

نویسندگان [English]

  • Mohsen Niknam Sharak 1
  • Ali Safavinejad 1
  • Mohammad Kazem Moayyedi 2
1 Department of Mechanical Engineering, Faculty of Engineering, University of Birjand, Birjand, Iran
2 Department 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

[1] M.F. Modest, S. Mazumder, Radiative heat transfer, Academic press, 2021.
[2] J.R. Howell, M.P. Mengüç, K. Daun, R. Siegel, Thermal radiation heat transfer, CRC press, 2020.
[3] R.-R. Zhou, B.-W. Li, The modified discrete ordinates method for radiative heat transfer in two-dimensional cylindrical medium, International Journal of Heat and Mass Transfer, 139 (2019) 1018-1030.
[4] Q. Nguyen, M.H. Beni, A. Parsian, O. Malekahmadi, A. Karimipour, Discrete ordinates thermal radiation with mixed convection to involve nanoparticles absorption, scattering and dispersion along radiation beams through the nanofluid, Journal of Thermal Analysis and Calorimetry, 143(3) (2021) 2801-2824.
[5] F. Asllanaj, S. Contassot-Vivier, O. Botella, F.H. França, Numerical solutions of radiative heat transfer in combustion systems using a parallel modified discrete ordinates method and several recent formulations of WSGG model, Journal of Quantitative Spectroscopy and Radiative Transfer, 274 (2021) 107863.
[6] Z. Sun, C.D. Hauck, Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport, SIAM Journal on Scientific Computing, 42(4) (2020) B869-B893.
[7] S. Gugercin, A.C. Antoulas, A survey of model reduction by balanced truncation and some new results, International Journal of Control, 77(8) (2004) 748-766.
[8] G. Scarciotti, A. Astolfi, Nonlinear model reduction by moment matching, Foundations and Trends® in Systems and Control, 4(3-4) (2017) 224-409.
[9] M. Billaud-Friess, A. Nouy, Dynamical model reduction method for solving parameter-dependent dynamical systems, SIAM Journal on Scientific Computing, 39(4) (2017) A1766-A1792.
[10] M.C. Varona, R. Gebhart, J. Suk, B. Lohmann, Practicable Simulation-Free Model Order Reduction by Nonlinear Moment Matching, arXiv preprint arXiv:1901.10750,  (2019).
[11] N. Faedo, F.J.D. Piuma, G. Giorgi, J.V. Ringwood, Nonlinear model reduction for wave energy systems: a moment-matching-based approach, Nonlinear Dynamics, 102(3) (2020) 1215-1237.
[12] G. Scarciotti, A.R. Teel, On moment matching for stochastic systems, IEEE Transactions on Automatic Control, 67(2) (2021) 541-556.
[13] Y. Liang, H. Lee, S. Lim, W. Lin, K. Lee, C. Wu, Proper orthogonal decomposition and its applications—Part I: Theory, Journal of Sound and vibration, 252(3) (2002) 527-544.
[14] J. Zhou, X. Wu, L. Kang, M. Wang, J. Huang, An adaptive proper orthogonal decomposition method for evaluating variability bounds of antenna responses, IEEE Antennas and Wireless Propagation Letters, 18(9) (2019) 1907-1911.
[15] K. Li, Z. Sha, W. Xue, X. Chen, H. Mao, G. Tan, A fast modeling and optimization scheme for greenhouse environmental system using proper orthogonal decomposition and multi-objective genetic algorithm, Computers and Electronics in Agriculture, 168 (2020) 105096.
[16] Y. Liang, X.-W. Gao, B.-B. Xu, Q.-H. Zhu, Z.-Y. Wu, A new alternating iteration strategy based on the proper orthogonal decomposition for solving large-scaled transient nonlinear heat conduction problems, Journal of Computational Science, 45 (2020) 101206.
[17] G. Jiang, H. Liu, K. Yang, X. Gao, A fast reduced-order model for radial integral boundary element method based on proper orthogonal decomposition in nonlinear transient heat conduction problems, Computer Methods in Applied Mechanics and Engineering, 368 (2020) 113190.
[18] Q.-H. Zhu, Y. Liang, X.-W. Gao, A proper orthogonal decomposition analysis method for transient nonlinear heat conduction problems. Part 2: Advanced algorithm, Numerical Heat Transfer, Part B: Fundamentals, 77(2) (2020) 116-137.
[19] K.-J. Bathe, Computational fluid and solid mechanics, Elsevier, 2001.
[20] B. Xu, A. Yebi, M. Hoffman, S. Onori, A rigorous model order reduction framework for waste heat recovery systems based on proper orthogonal decomposition and galerkin projection, IEEE Transactions on Control Systems Technology, 28(2) (2018) 635-643.
[21] V. Shinde, E. Longatte, F. Baj, Y. Hoarau, M. Braza, Galerkin-free model reduction for fluid-structure interaction using proper orthogonal decomposition, Journal of Computational Physics, 396 (2019) 579-595.
[22] A. Towne, Space-time Galerkin projection via spectral proper orthogonal decomposition and resolvent modes, in:  AIAA Scitech 2021 Forum, 2021, pp. 1676.
[23] B. Koo, H. Kim, T. Jo, S. Kim, J.Y. Yoon, Proper orthogonal decomposition–Galerkin projection method for quasi-two-dimensional laminar hydraulic transient flow, Journal of Hydraulic Research, 59(2) (2021) 224-234.
[24] M. Dehghan, M. Abbaszadeh, An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation, Engineering Analysis with Boundary Elements, 92 (2018) 244-256.
[25] S. Wang, S. Khatir, M.A. Wahab, Proper Orthogonal Decomposition for the prediction of fretting wear characteristics, Tribology International, 152 (2020) 106545.
[26] H. Wang, W. Li, Z. Qian, G. Wang, Reconstruction of wind pressure fields on cooling towers by radial basis function and comparisons with other methods, Journal of Wind Engineering and Industrial Aerodynamics, 208 (2021) 104450.
[27] M. Mendez, M. Balabane, J.-M. Buchlin, Multi-scale proper orthogonal decomposition of complex fluid flows, Journal of Fluid Mechanics, 870 (2019) 988-1036.
[28] S.D. Muralidhar, B. Podvin, L. Mathelin, Y. Fraigneau, Spatio-temporal proper orthogonal decomposition of turbulent channel flow, Journal of Fluid Mechanics, 864 (2019) 614-639.
[29] L.I. Abreu, A.V. Cavalieri, P. Schlatter, R. Vinuesa, D.S. Henningson, Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows, Journal of Fluid Mechanics, 900 (2020).
[30] L. Shen, K.-Y. Teh, P. Ge, F. Zhao, D.L. Hung, Temporal evolution analysis of in-cylinder flow by means of proper orthogonal decomposition, International Journal of Engine Research, 22(5) (2021) 1714-1730.
[31] J. Novo, S. Rubino, Error analysis of proper orthogonal decomposition stabilized methods for incompressible flows, SIAM Journal on Numerical Analysis, 59(1) (2021) 334-369.
[32] A. Antoranz, A. Ianiro, O. Flores, M. García-Villalba, Extended proper orthogonal decomposition of non-homogeneous thermal fields in a turbulent pipe flow, International Journal of Heat and Mass Transfer, 118 (2018) 1264-1275.
[33] J. Tencer, K. Carlberg, M. Larsen, R. Hogan, Accelerated solution of discrete ordinates approximation to the boltzmann transport equation for a gray absorbing–emitting medium via model reduction, Journal of Heat Transfer, 139(12) (2017).
[34] L. Soucasse, A.G. Buchan, S. Dargaville, C.C. Pain, An angular reduced order model for radiative transfer in non grey media, Journal of Quantitative Spectroscopy and Radiative Transfer, 229 (2019) 23-32.
[35] M. Tano, J. Ragusa, D. Caron, P. Behne, Affine reduced-order model for radiation transport problems in cylindrical coordinates, Annals of Nuclear Energy, 158 (2021) 108214.
[36] H. Amiri, S. Mansouri, A. Safavinejad, Combined conductive and radiative heat transfer in an anisotropic scattering participating medium with irregular geometries, International Journal of Thermal Sciences, 49(3) (2010) 492-503.
[37] Z. Ostrowski, R. Białecki, A.J. Kassab, Solving inverse heat conduction problems using trained POD-RBF network inverse method, Inverse Problems in Science and Engineering, 16(1) (2008) 39-54.
[38] D.R. Rousse, G. Gautier, J.-F. Sacadura, Numerical predictions of two-dimensional conduction, convection, and radiation heat transfer. II. Validation, International journal of thermal sciences, 39(3) (2000) 332-353.
نشریه مهندسی مکانیک امیرکبیر
دوره 54، شماره 9
آذر 1401
صفحه 2175-2174

فایل ها

هم رسانی

ارجاع به این مقاله

آمار