Workflow- Based Shape Optimization of Airfoils and Blades using Chained Bezier Curves

Transcription

1 Workflow- Based Shape Optmzato of Arfols ad Blades usg Chaed Bezer Curves Igor Pehec, Damr Vuča, Želja Loza Faculty of Electrcal Egeerg, Mechacal Egeerg ad Naval Archtecture FESB, Uversty of Splt, Croata Summary Ths paper gves a ew method for 2D ad 3D shape optmzato as a fucto of prescrbed crtera wth referece to cost fucto. Such optmzato techques ca be used for geeratg ew ad optmzato of exstet shapes ad geometres. The troduced optmzato tool s developed geeral terms ad ca wth slght modfcatos be used for shape recogto ad damage detfcato. The procedure allows sgfcat desg freedom creatg shapes at the cost of umercal testy. Keywords Shape optmzato, Workflow, Bezer curve, Arfols Itroducto, Shape optmzato modefrontier tools The correct defto of shape varables s of utmost mportace the layout of a optmzato problem. As the varables are charge of chagg geometry, t s ecessary to flter out all the satsfactory geometrc shapes ad to fd the best soluto amogst those. The tred owadays s towards reverse egeerg, where the techcal desg of a product s a cosequece of requred fuctos ad costrats. So, we are tryg to determe the shape varables whch gve the most acceptable soluto, depedg o the requested accuracy. I evolutoary optmzato, the tal shape optmzato s absolutely radom, ad the subsequet chage s partally radom. Therefore the shape to be subjected to aalyss s ot kow advace, sce t s geerated based o requred fuctoalty, verfed ad optmzed usg techcal crtera. The umber of optmzato varables for shape defto must be small due to lmted computer resources ad CPU tme. Usg adequate parameterzatos, we descrbe the geometry wth a reduced umber of varables. Ths paper develops a 2D parameterzato usg chaed pecewse Bezer curves. Chaed Bezer curves wth low umbers of cotrol pots are capable of descrbg complcates geometrc shapes, but we have to esure cotuty at jots. The Bezer curve polyomal form s gve as: P( u) = 0 B 1, ( u) P = u ( 1 ) P = u 1 0 0! ( )!! ( ) 1 P, where: degree of Bezer curves, takes values 0 to u parameter for approxmato pots from P 1 to P 4 wth radom dvso.

2 I ths paper the arfol for wd turbe blades s studed as a test case. The am s fdg the respectve optmal shape. Pcture 1.1 shows a process dagram for the correspodg shape optmzato. Iput CFD aalyzes Output Optmzer Bezer Arfol cotrol pots Calculatg lft ad drag Calculatg excellece Pcture 1.1. Block dagram of geometry optmzato pla usg chaed pecewse Bezer curves wth ADINA tool. To perform such a optmzato process, several applcatos are requred. The optmzer, modefrontier, vares the shape varables ad sed the curret shape to ADINA (CFD) that calculates load o 2D arfol. The the results from ADINA are read by aother -house developed program from the respectve output fle, whch the calculates drag ad lft coeffcets. These drag ad lft coeffcets represet elemets for the crtero of the arfol s excellece. As ADINA s a o-stadard applcato for modefrontier, t was eeded to develop a ow applcato to execute ad cotrol ADINA. The applcatos used ths optmzato workflow process are: modefrontier, MATLAB, Vsual Basc, Vsual C ad ADINA-F. Pcture 1.2. presets a block dagram of the arfol shape optmzato workflow for wd turbe arfol shape optmum desg wth the modefrontier evromet. Pcture 1.2. Dagram of arfol shape optmzato process modefrontier.

3 The process starts from a radomly geerated populato of 2D arfols. The shape varables are data arrays that defe arfol geometres. The array sze depeds o the requred precso of geometry represetato ad complexty of shape. Sx pots are typcally suffcet to defe a 2D geometry, but order to allow for more freedom shapg the geometry t s defed wth 10 Bezer cotrol pots. Costrats are mposed to lmt the scope of the shape varables. A small scrpt s wrtte MATLAB that geerates the cotour pots alog the arfol whch s gve by the respectve shape varables (cotrol pots) data array. The requred cotuty betwee chaed pecewse Bezer curves s mposed umercally. The aerofol shape pots are essetal for aerodyamc aalyss ad resultg force calculatos o the aerofol. The flow smulato ad optmzato are lked wth data mg modefrontier. The data mg provdes for the exchage of data durg the process of chagg the geometry shape optmzato. The flow smulato (fte elemets) provdes the elemetary forces actg o the aerofol. These forces are the bass for the calculato of lft ad drag coeffcets usg MATLAB scrpts. The flow s smulated usg ADINA. The data mg process s used to trasfer the geometrc data betwee the optmzer ad ADINA. ADINA s started from MATLAB usg a -house scrpt wrtte Vsual Basc. The scrpt cludes system commads such as shell, sedkey, etc, that allow t to commucate wth other applcatos wth Wdows. Also, t was ecessary to set delays (watg tmes) betwee such system operatos, allowg them to be completed before subsequet system calls are lauched. Ths s ecessary because of problems that otherwse appear usg ADINA batch mode. Two typcal cases appear durg the course of the process: ADINA provdes a good soluto, ad ADINA does ot provde a proper soluto or breaks. The secod case s caused by mproper (vald) geometry geerated by the optmzer. Whch of the cases has occurred s detected by verfyg the ADINA output fle exstece ad completeess. I the secod case, the correspodg caddate shape s dsmssed sce ADINA could ot produce a complete aalyss output fle. The exstece ad completeess of the output fle s checked by a separate route. The optmzato method used ths paper s the geetc algorthm, coveet for ths mult-objectve desg problem. The optmzato method s set wth the modefrontier tool cludg all the parameters such as the umber of geeratos, parameters of cross-over, selecto (the best uts for cloe), mutato, etc. The followg pctures llustrate the optmzato progress: Pcture 1.3. Arfols optmzato progress.

4 Pcture 1.4. Pressure ad velocty dstrbutos aroud arfols. 1,6 1,4 1,2 1 Cl / Cd 0,8 0,6 0,4 0, Agle of Attack Pcture 1.4 Lft ad drag coeffcet for NACA 4415 arfol wd tuel (Abbo blue Cl ad gree Cd curve) ad ADINA smulato (red Cl ad yellow Cd curve) Coclusos Ths paper presets a approach of geeratg object geometres by optmzato of shape varables, applcable to 2D ad 3D cases. Pecewse curves are employed ad cotuty at jots s esured by addg extra pots. Ths approach s appled to arfols for wd turbe blades. Correspodg CFD smulato results ad expermetal wd tuel values geerally agree shape, but the respectve lft ad drag coeffcets dffer somewhat. The dfferece values ca be attrbuted to the complexty of umercal flow smulatos ad correspodg assumptos as well as the fact that lmted computer resources ad CPU tme are avalable for the fte elemet model. O the other had, expermetal graphs are also obtaed by expermets where the codtos ca ot be cotrolled fully. Ayway, the degree of agreemet ad the evoluto of shape from the radom tal to the NACA- smlar fal shapes make the shape optmzato process as proposed here successful.

5 Lterature: [1] J.A. Samareh, A Survey of Shape Parameterzato Techques, CEAS/AIAA/ICASE/NASA Lagley Iteratoal Forum o Aeroelastcty ad Structural Dyamcs, 1999, Wllamsburg, VA, Also, NASA/CP , Jue 1999, pp [2] V. Brabat, C. Fleury, Shape Optmal Desg Usg B-Sples, Computer Method Appled Mechacs ad Egeerg, Vol. 44, Aug. 1984, pp [3] M. Pourazady, Z. Fu, A Itegrated Approach to Structural Shape Optmzato, Computers & Structures, Vol 60. No 2. pp [4] D. Vuča, Z. Loza, Multobjectve Desg Optmzato wth Aggregate Ftess Fucto based o Total Lfecycle Cost, WSEAS Trasactos o Systems. 5 (2006), 7; [5] J.A. Samareh, Geometry Modellg ad Grd Geerato for Desg ad Optmzato, ICASE/LaRC/NSF/ARO Workshop o Computatoal Aerosceces the 21st Cetury, 1998, pg.1-19 [6] J.A. Samareh, Use of CAD Geomery MDO, 6th AIAA/USAF/NASA/ISSMO Symposum o Multdscplary Aalyss ad Optmzato, 1996, Bellevue, WA, Also, AIAA [7] M. Zhou, N. Pagaldpt, H.L. Thomas, Y.K. Shyy, A tegrated approach to topology, szg, ad shape optmzato, Struct Multdsc Optm 26, (2004) [8] Far, G., Curves ad Surfaces for CAGD (2002) Berkeley, Calfora. [9] G. Chaduss, G. Bugeda, ad E. Oate: Shape varable defto wth C 0, C 1 ad C 2 cotuty fuctos, (1999), Barceloa, Spa. [10] Vuča, D., Prmjea račuala u žejerskoj aalz (2007) Faculty of Electrcal Egeerg, Mechacal Egeerg ad Naval Archtecture FESB, Uversty of Splt, Croata. [11] Vuča, D., Metode žejerske umerčke optmzacje (2005) Faculty of Electrcal Egeerg, Mechacal Egeerg ad Naval Archtecture FESB, Uversty of Splt, Croata. [12] Ira H. Abbott, A. E vo Doehoff, Theory of Wg Sectos: Icludg a Summary of Arfol Data (1959) [13] Ada, ADINA TM 8.3 User terface ad commad referece maual, Ada R&D Ic, (2005). [14] Matlab, MATLAB User's Gude: The Mathworks, (2003). [15] [16] Polo C. Mosett G., Aerodyamc Shape Optmzato by Meas of Hybrd Geetc Algorthm, ZAMM- Zetscrft für Agewadte Mathematk ud Mechak 76 3 (1996), pp ISBN , ISSN.