Διερεύνηση Διαφορετικών Διατυπώσεων της Συνεχούς Συζυγούς Μεθόδου για τον Υπολογισμό Παραγώγων Ευαισθησίας στην Αεροδυναμική Βελτιστοποίηση με Ακρίβεια. Εφαρμογές

Γκαραγκούνης, Κωνσταντίνος; Gkaragkounis, Konstantinos

dc.contributor.author	Γκαραγκούνης, Κωνσταντίνος	el
dc.contributor.author	Gkaragkounis, Konstantinos	en
dc.date.accessioned	2016-07-13T07:50:01Z
dc.date.available	2016-07-13T07:50:01Z
dc.date.issued	2016-07-13
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/43082
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.12557
dc.rights	Default License
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	en
dc.subject	Συνεχής συζυγής μέθοδος	el
dc.subject	Αεροδυναμική	el
dc.subject	Βελτιστοποίηση	el
dc.subject	Παράγωγοι	el
dc.subject	Continuous adjoint method	en
dc.subject	E-SI	en
dc.subject	Sensitivities	en
dc.subject	Optimisation	en
dc.title	Διερεύνηση Διαφορετικών Διατυπώσεων της Συνεχούς Συζυγούς Μεθόδου για τον Υπολογισμό Παραγώγων Ευαισθησίας στην Αεροδυναμική Βελτιστοποίηση με Ακρίβεια. Εφαρμογές	el
dc.title	The Assessment of Different Formulations of the Continuous Adjoint Method for the Computation of Exact Sensitivity Derivatives in Aerodynamic Optimisation. Applications	en
heal.type	bachelorThesis
heal.classification	Αεροδυναμική βελτιστοποίηση μορφής	el
heal.language	el
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2016-07-08
heal.abstract	Στην αεροδυναμική Βελτιστοποίηση μορφής, βασικό ζήτημα είναι το πώς υπολογίζονται οι παράγωγοι μιας αντικειμενικής συνάρτησης ως προς τις μεταβλητές σχεδιασμού με ακρίβεια και χαμηλό υπολογιστικό κόστος. Η μορφή της παραγώγου αυτής σχετίζεται με διαφορετική διατύπωση της συζυγούς μεθόδου. Μέχρι πρότινος, στη βιβλιογραφία υπήρχαν δύο διατυπώσεις (FI και SI), ενώ πρόσφατα στο πλαίσιο διδακτορικής διατριβής που εκπονήθηκε στη ΜΠΥΡ&Β ΕΜΠ στο Εργαστήριο Θερμικών Στροβιλομηχανών της Σχολής Μηχανολόγων Μηχανικών από τον Ιωάννη Καββαδία, παρουσιάστηκε τρίτη (E-SI) που συνδυάζει τα πλεονεκτήματα των προηγούμενων 2. Σε αυτήν τη διπλωματική εργασία μέσα από εφαρμογές συγκρίνονται οι διατυπώσεις της συζυγούς μεθόδου και παρουσιάζονται τα συμπεράσματα.	el
heal.abstract	This diploma thesis aims at assessing di erent formulations of the continuous adjoint method, in the eld of aerodynamic shape optimization, for computing the sensitivity derivatives (SDs) of any objective function given, w.r.t the design variables. The goal is not just the accurate computation of the SDs but also the reduction of the computational cost. Until recently, two formulations of the continuous adjoint method could be found in the literature, namely the Field Integral (FI) and the Surface Integral Formulation (SI). The FI formulation leads to SD expressions which include eld integrals of the derivatives of displacement of the grid nodes, w.r.t. the design variables (the coordinates of NURBS control points, for instance). Its main advantage is that a high level of accuracy in the computed SDs is achieved, in comparison with nite di erences. However, the need of computing, with nite di erences, terms associated with the displacement of the grid nodes, in the whole computational domain, per design variable and in each cartesian direction, results in high computational cost. On the other hand, the second formulation leads to SDs which include exclusively surface integrals and is merited for its low computational cost. However, this formulation often leads to lower accuracy, in the SDs. This is because, until recently in literature, a speci c term of the full expression of the derivative was omitted. This term will be referred to as the 'Leibniz term', since it comes from the application of the Leibniz rule of di erentiation under the integral sign. This term was omitted, because it was assumed to be close to zero at boundaries, at least in ner grids. However, the omission of this term in general is not as harmless as believed, yet leading to inaccuracies in the computation of SDs. Very lately, in the Parallel CFD & Optimization Unit of the Lab. of Thermal Turboma- viii chines of NTUA (PCopt/NTUA), within the PhD thesis by I. Kavvadias [3, 15], a new formulation was developed, namely the Enhanced-Surface Integral Formulation (E-SI). This formulation combines the advantages of the two previous ones, i.e. the low compu- tational cost of the SI Formulation and higher accuracy in computing the SDs o ered by the FI formulation. The rst one is attributed to the fact that the SD expression includes only surface integrals, similarly to the standard SI Formulation. The second one results from the substitution of the Leibniz term with a surface integral. This integral comes from the inclusion of a volume integral in the augmented objective function, which is associated with the grid displacement law, and its di erentiation. The fact that, through E-SI, low computational cost along with higher accuracy in SD computation are achieved is of great importance, particularly in industry, where the number of the design variables could reach the order of millions, such as when a sensitivity map has to be computed. In such cases, the high computational cost of the FI formulation makes their use almost prohibitive. using it. As a result, until recently, only the SI formulation could be implemented, despite its issues with lower accuracy (which are frequently overcome by using excessively stretched meshes). In the present diploma thesis, the characteristics of each formulation are assessed, through simulations pertinent to the steady 1D Burgers equation, the shape optimization (of just the computation of SDs) of two isolated airfoils and a cascade airfoil. Furthermore, a term-by-term analysis in derivatives is performed, in order to explain the observed di erences between the FI and SI formulations and quantify the importance of the omitted Leibniz term, in the SI formulation. Finally, the frozen-turbulence assumption is assessed, because, in turbulent ows, this may lead to inaccuracies in the computation of SDs.	en
heal.advisorName	Γιαννάκογλου, Κυριάκος	el
heal.committeeMemberName	Αρετάκης, Νικόλαος	el
heal.committeeMemberName	Μαθιουδάκης, Κωνσταντίνος	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Μηχανολόγων Μηχανικών. Τομέας Ρευστών. Εργαστήριο Θερμικών Στροβιλομηχανών	el
heal.academicPublisherID	ntua
heal.numberOfPages	102 σ.
heal.fullTextAvailability	true