Identyfikacja i optymalne projektowanie kształtu wyrobów i konstrukcji włókienniczych przewodzących ciepło

Korycki, R.

Artykuł - szczegóły

Tytuł artykułu

Identyfikacja i optymalne projektowanie kształtu wyrobów i konstrukcji włókienniczych przewodzących ciepło

Autorzy

Korycki R.

Identyfikatory

Warianty tytułu

Identification and optimal design of the shape of the heat conducting textile products and structures

Języki publikacji

Abstrakty

Podjęte w pracy problemy identyfikacji i optymalnego projektowania kształtu wyrobów i konstrukcji włókienniczych przewodzących ciepło mają bardzo duże znaczenie praktyczne. Wynika ono ze znacznej liczby rzeczywistych problemów wymiany ciepła i różnorodności ich przebiegu, niewystarczającej prezentacji w literaturze, narastającej tendencji do numerycznego modelowania przepływu ciepła w wyrobach i konstrukcjach włókienniczych oraz spodziewanych efektów ekonomicznych dzięki podwyższeniu ich wartości użytkowej i handlowej. Praca została poprzedzona wstępem, zawierającym motywacje jej podjęcia, elementy oryginalności według oceny autora oraz tezę. Kolejny rozdział - przegląd literatury - zawiera omówienie pozycji literatury związanej z pracą. W następnej kolejności omówiliśmy homogenizację wyrobów włókienniczych w problemach przewodzenia ciepła. W pracy zostały zdefiniowane problemy proste i odwrotne przewodzenia ciepła. Rozwinięciem tego jest charakterystyka problemów identyfikacji i optymalnego projektowania, co pozwala zapisać ogólne algorytmy ich rozwiązania. Jako pierwszy został określony nieustalony problem przewodzenia ciepła w termicznie anizotropowym, stałym wyrobie lub konstrukcji włókienniczej. Należy go zapisać za pomocą równania przewodzenia, warunków brzegowych Dirichleta, Neumanna, Henkela oraz warunku początkowego. Wrażliwość pierwszego rzędu została obliczona przy wykorzystaniu koncepcji pochodnej materialnej. Przy założeniu dowolnego funkcjonału zdefiniowanego w przestrzeni i czasie, jego wrażliwość pierwszego rzędu względem parametrów projektowania została określona przy użyciu metod bezpośredniej i układów sprzężonych. Należało również znaleźć równania przewodzenia i warunki brzegowe charakteryzujące oba układy - bezpośredni i sprzężony. Następnie zostały przedyskutowane najczęściej stosowane funkcjonały identyfikacji i optymalizacji, a ponadto scharakteryzowane warunki stacjonarności niezbędne podczas identyfikacji oraz warunki optymalności dla optymalnego projektowania. Dalej przedyskutowaliśmy cztery najczęściej stosowane metody modyfikacji kształtu brzegu oraz opisaliśmy nieskończenie małe transformacje obszaru podczas ich stosowania. Zostały przedyskutowane trzy metody dyskretyzacji obszaru, z których metoda elementów skończonych została przyjęta jako podstawowa do przeprowadzanych obliczeń. Dla zilustrowania efektywności i możliwości obliczeniowych w prezentowanych problemach zostały rozwiązane trzy przykłady numeryczne dwuwymiarowej identyfikacji i optymalizacji kształtu. W dalszej kolejności został zaprezentowany problem promieniowania cieplnego jako jeden z najbardziej znaczących mechanizmów przekazywania ciepła w wysokich temperaturach i przedyskutowane parametry charakteryzujące promieniowanie cieplne (przede wszystkim emisyjność). Warunek promieniowania na brzegu wewnętrznym został zapisany w postaci równania całkowego według Białeckiego. Do analizy wrażliwości i obliczeń został przyjęty przypadek pochłaniającego czynnika izotermicznego o stałym współczynniku absorpcji. Warunek promieniowania można rozwiązać przy użyciu metody reszt ważonych według Finlaysona, przy czym określamy strumień ciepła w kierunku normalnym do brzegu. Ustalony problem przewodzenia ciepła w termicznie anizotropowym stałym wyrobie lub konstrukcji włókienniczej został opisany za pomocą równania przewodzenia, warunków Dirichleta, Neumanna, Henkela na brzegu zewnętrznym oraz warunku promieniowania według Białeckiego na powierzchni wewnętrznej. Wykorzystując analizę wrażliwości problemu metodami bezpośrednią i układów sprzężonych, otrzymujemy wyrażenia wrażliwości pierwszego rzędu dowolnego funkcjonału względem parametrów projektowania. Została również zamieszczona implementacja numeryczna problemu, w postaci dwóch przykładów dwuwymiarowego projektowania kształtu. Ostatnie rozdziały pracy zawierają wnioski i zestawienie cytowanej literatury.

In view of the practical importance we have presented and discussed the identification and optimal design of the shape of the heat conducting textile products and structures. First, the direct and inverse heat conduction problems were defined. The identification and optimal design problems were formulated and the general algorithms shown. A transient heat conduction problem within a thermal anisotropic solid textile product or structure was introduced. The conduction equation, Dirichlet. Neumann, Henkel and initial conditions were defined. The first-order sensitivity was calculated using material derivative concept. Considering an arbitrary behavioral functional defined over space and time domains, its first-order sensitivity operators with respect to design parameters were derived using the direct and adjoint approaches. Conduction equations and boundary conditions characterizing both direct and adjoint approaches were also obtained. Next, we have discussed the identification and optimization functionals. Stationarity conditions necessary for identification and optimality conditions for optimal design were introduced. Then, four modiflcation methods of the boundary shape were discussed and the associated infinitesimal domain transformation processes were described. Three numerical methods of the domain discretization were discussed, however, in the performed calculations only the Finite Element Method was used. Three numerical examples of the two-dimensional shape identification and optimization are solved to illustrate the effectiveness and computational efficiency of the presented problems. Next, the thermal radiation problem was presented as one of the most important mechanisms of the heat transfer in high temperatures. The radiation parameters were discussed (first of all the emissivities). The radiation condition on the internal boundary was introduced according Bialecki as an integral equation. The case of isothermal, participating medium of constant absorption coefficient within the hole was assumed to the analysis. Radiation condition was solved using the Weighted Residual Method according Finlayson and the normal heat flux is calculated. A steady heat conduction problem within a thermal anisotropic solid textile product or structure was considered as the conduction equation, Dirichlet, Neumann, Henkel conditions on the external boundary and Bialecki condition on the internal surface. First-order sensitivities of an arbitrary behavioral functional with respect to design parameters were obtained using the direct and adjoint approaches. The obtained equations were incorporated into the stationarity and optimality conditions, respectively. The numerical implementation of the problems was also given and two examples of two-dimensional optimal shape design included. Finally, the conclusions and the references are given.

Słowa kluczowe

wyroby włókiennicze przewodzenie ciepła metoda elementów skończonych MES

textiles thermal conduction finite elements method FEM

Wydawca

Wydawnictwo Politechniki Łódzkiej

Czasopismo

Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka

Rocznik

2003

Tom

Z. 326

Strony

7--170

Opis fizyczny

Bibliogr. 211 poz.

Twórcy

autor

Korycki R.

Katedra Mechaniki i Informatyki Technicznej, Politechnika Łódzka

Bibliografia

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