{"id":151,"date":"2025-03-08T14:01:53","date_gmt":"2025-03-08T14:01:53","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/e265438\/?p=151"},"modified":"2025-04-17T09:04:09","modified_gmt":"2025-04-17T09:04:09","slug":"su2da-discrete-adjoint-yontemi-ile-tasarim-optimizasyonu-yapmak","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/e265438\/su2da-discrete-adjoint-yontemi-ile-tasarim-optimizasyonu-yapmak\/","title":{"rendered":"SU2’da Discrete Adjoint Y\u00f6ntemi ile Tasar\u0131m Optimizasyonu Yapmak"},"content":{"rendered":"\n


SU2 \u00e7\u00f6z\u00fcc\u00fcs\u00fc, yo\u011funluk-tabanl\u0131 (density-based) ak\u0131\u015flarda, \u00f6ncelikle aerodinamik tasar\u0131m optimizasyonu ve genel HAD \u00e7\u00f6z\u00fcmleri i\u00e7in geli\u015ftirilmi\u015ftir. Bu kapsamda SU2 i\u00e7erisinde e\u011fim(gradyan)-tabanl\u0131 Continous ve Discrete Adjoint y\u00f6ntemleri bulunmaktad\u0131r. [1] Bu y\u00f6ntemlerin zamana-ba\u011fl\u0131 \u00e7\u00f6z\u00fcm yapabilmesi i\u00e7in gerekli eklemeler daha \u00f6nce yap\u0131lm\u0131\u015ft\u0131r.

\u00dczerinde \u00e7al\u0131\u015f\u0131lan fenomen, do\u011fas\u0131 gere\u011fi zamana-ba\u011fl\u0131 olarak \u00e7\u00f6z\u00fclmelidir. Tasar\u0131m optimizasyonu i\u015fleminde kullan\u0131lan Discrete adjoint y\u00f6ntemi genel olarak zamandan-ba\u011f\u0131ms\u0131z tasar\u0131m optimizasyon problemleri i\u00e7in kullan\u0131lmaktad\u0131r. SU2 \u00e7\u00f6z\u00fcc\u00fcs\u00fcnde ise bu y\u00f6ntem zamana-ba\u011fl\u0131 problemler i\u00e7in de \u00e7\u00f6z\u00fclebilmektedir. Genel olarak zamana-ba\u011fl\u0131 adjoint optimizasyon y\u00f6ntemi a\u00e7\u0131k-kaynak kodlu ve ticari yaz\u0131l\u0131mlarda bulunmamaktad\u0131r. Bu sebepler SU2 \u00e7\u00f6z\u00fcc\u00fcs\u00fcn\u00fcn do\u011fru bir tercih oldu\u011funu \u00f6nermektedir. Ayr\u0131ca, SU2 yaz\u0131l\u0131m\u0131nda zamana-ba\u011fl\u0131 optimizasyon y\u00f6nteminin sadece bir kanat profili \u00fczerinde kullan\u0131ld\u0131\u011f\u0131 bilinmektedir. [2]<\/p>\n\n\n\n


Tasar\u0131m optimizasyonu i\u015flemine ba\u015flarken ilk olarak geometride de\u011fi\u015fiklik yap\u0131lmas\u0131 planlanan alan ve bu alanda geometri\/mesh deformasyonu yapacak y\u00f6ntem do\u011fru se\u00e7ilmelidir. SU2 i\u00e7erisinde Free-Form Deformation (FFD) kutusu denilen bir y\u00f6ntem ile deformasyon yap\u0131lacak kat\u0131 y\u00fczey bir kutu i\u00e7ine al\u0131n\u0131r. Bu kutu y\u00fczeyinde baz\u0131 kontrol noktalar\u0131 tan\u0131mlanmaktad\u0131r. Bu kontrol noktalar\u0131 daha sonra tasar\u0131m de\u011fi\u015fkenleri olarak da tan\u0131mlanmaktad\u0131r ve bu noktalar hareket ederek kat\u0131 y\u00fczeyin, ayn\u0131 zamanda \u00e7\u00f6z\u00fcm a\u011f\u0131n\u0131n, \u015feklini kontrol etmektedir. Olu\u015fturulan FFD kutu geometrisi g\u00f6rsel 1\u2019de g\u00f6r\u00fclebilir.<\/p>\n\n\n

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G\u00f6rsel 1 <\/strong>FFD Kutusu<\/figcaption><\/figure>\n<\/div>\n\n\n

FFD kutusu olu\u015fturulduktan sonra tasar\u0131m optimizasyonu i\u00e7in gerekli parametreler SU2 konfig\u00fcrasyon dosyas\u0131nda tan\u0131mlanmaya ba\u015flanabilir. \u00d6ncelikle adjoint denklemleri zamana-ba\u011fl\u0131 \u00e7\u00f6z\u00fclece\u011fi i\u00e7in adjoint \u00e7\u00f6z\u00fcm\u00fc zaman-iterasyon ad\u0131m\u0131 say\u0131s\u0131 ve hedef fonksiyonu (objective function) belirlenmi\u015ftir. Bu tan\u0131mlamalardan sonra hedef fonksiyonun ne olaca\u011f\u0131 ve nerede hesaplanaca\u011f\u0131 tan\u0131mlanmal\u0131d\u0131r. Hedef fonksiyonu olarak roket geometrisi \u00fczerinde, g\u00f6rsel 2\u2019te g\u00f6sterilen y\u00fczeyde, bas\u0131n\u00e7 de\u011ferlerinin ortalamas\u0131 al\u0131nm\u0131\u015ft\u0131r.<\/p>\n\n\n\n

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G\u00f6rsel 13<\/strong> Detayl\u0131 geometri<\/figcaption><\/figure>\n\n\n\n

Adjoint y\u00f6ntemi ile zamana-ba\u011fl\u0131 tasar\u0131m analizi yapmak hem \u00e7ok fazla CPU zaman\u0131 hem de \u00e7ok fazla depolama alan\u0131 gerektirmektedir. Bu sebeple d\u00fc\u015f\u00fck zaman-ad\u0131ml\u0131 sonu\u00e7lar almak uzun s\u00fcrmektedir. Adjoint y\u00f6nteminde hassasl\u0131k (sensitivity) hesaplamalar\u0131, HAD ile elde edilen direkt \u00e7\u00f6z\u00fcmde bulunan veriler kullan\u0131larak geriye do\u011fru iterasyonlar halinde yap\u0131lmaktad\u0131r. G\u00f6rsel 2\u2019te g\u00f6r\u00fclen sar\u0131 renkli roket duvar \u00fczerindeki bas\u0131nc\u0131 minimuma indirmek i\u00e7in hedef fonksiyon a\u011f\u0131rl\u0131\u011f\u0131 -1 olarak tan\u0131mlanm\u0131\u015ft\u0131r. Herhangi bir s\u0131n\u0131r fonksiyonu (constraint function) tan\u0131mlanmam\u0131\u015ft\u0131r. Tasar\u0131m optimizasyon sonucu olarak al\u0131nan \u00e7\u0131kt\u0131 a\u015fa\u011f\u0131daki \u015fekildedir.<\/p>\n\n\n\n

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KAYNAKLAR<\/strong><\/h4>\n\n\n\n[1] Palacios, F., Colonno, M. R., Aranake, A. C., Campos, A., Copeland, S. R., Economon, T. D., Lonkar, A. K., Lukaczyk, T. W., Taylor, T. W. R., and Alonso, J. J., \u201cStanford University Unstructured (SU2): An Open-Source Integrated Computational Environment for Multi-Physics Simulation and Design,\u201d 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition<\/em>, Grapevine, TX, Jan. 7\u201310, 2013. AIAA 2013-0287.
https:\/\/doi.org\/10.2514\/6.2013-0287<\/a>
[2] Schotth\u00f6fer, S., Zhou, B. Y., Albring, T., and Gauger, N. R., \u201cRegularization for Adjoint-Based Unsteady Aerodynamic Optimization Using Windowing Techniques,\u201d AIAA Journal<\/em>, Vol. 59, No. 7, 2021, pp. 2517\u20132531. https:\/\/doi.org\/10.2514\/1.J059377<\/a>
<\/p>\n","protected":false},"excerpt":{"rendered":"

SU2 \u00e7\u00f6z\u00fcc\u00fcs\u00fc, yo\u011funluk-tabanl\u0131 (density-based) ak\u0131\u015flarda, \u00f6ncelikle aerodinamik tasar\u0131m optimizasyonu ve genel HAD \u00e7\u00f6z\u00fcmleri i\u00e7in geli\u015ftirilmi\u015ftir. Bu kapsamda SU2 i\u00e7erisinde e\u011fim(gradyan)-tabanl\u0131 Continous ve Discrete Adjoint y\u00f6ntemleri bulunmaktad\u0131r. [1] Bu y\u00f6ntemlerin zamana-ba\u011fl\u0131 \u00e7\u00f6z\u00fcm yapabilmesi i\u00e7in gerekli eklemeler daha \u00f6nce yap\u0131lm\u0131\u015ft\u0131r. \u00dczerinde \u00e7al\u0131\u015f\u0131lan … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":9337,"featured_media":80,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[6],"tags":[],"class_list":["post-151","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sayisal-sonuclar"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/posts\/151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/users\/9337"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/comments?post=151"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/posts\/151\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/media\/80"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/media?parent=151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/categories?post=151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/e265438\/wp-json\/wp\/v2\/tags?post=151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}