Determination of angle of attack for rotating blades

Transcription

1 Determato of agle of attack for rotatg blades Hora DUMITRESCU 1, Vladmr CARDOS*,1, Flor FRUNZULICA 1,, Alexadru DUMITRACHE 1 *Correspodg author *,1 Gheorghe Mhoc-Caus Iacob Isttute of Mathematcal Statstcs ad Appled Mathematcs of Romaa Academy Calea 13 Septembre No. 13, Sector 5, , Bucharest, Romaa v_cardos@yahoo.ca Departmet of Aerospace Sceces, POLITEHNICA Uversty of Bucharest Splaul Idepedeţe 313, 06004, Bucharest, Romaa ffruz@yahoo.com DOI: / Abstract: For a rotatg blade the flow passg by a blade secto s beded due to the rotato ad the local flow feld s flueced by the boud crculato o the blade. As a further complcato, 3-D effects from tp ad root vortces do a precse defto of the agle of attack (AOA) a dffcult task. Two methods for determg the AOA o rotatg blade from velocty ad pressure measuremets are preseted. Key Words: Wd turbe; 3-D rotatoal effects; Numercal smulato, blade secto 1. INTRODUCTION Durg the desg process of a wd turbe blade, accurate ad able predcto methods are requred for the mache s full rage of operatg codtos. As egeerg methods, blade elemet mometum (BEM) ad vortex lattce (VL) methodologes have bee wdely used for rotor desg ad aalyss. However, the accuracy of these methods s lmted by the qualty of employed arfol data, whch s usually gve as tabulated lft ad drag coeffcets as fucto of attack agle ad Reyolds umber. The arfol characterstcs used BEM code usg arfol data obtaed drectly from - D wd tuel measuremets wll ot yeld the correct loadg ad power. Owg to the 3-D ature of the flow over wd turbe blades, the measured arfol characterstcs wll be dfferet from the real characterstcs. The flow wll be altered partly due to the 3-D propertes of the blade geometry, whch s most proouced at the thck root secto ad ear the blade tp, ad partly because of rotatoal effects the 3-D twstg boudary layer. As a cosequece, -D arfol characterstcs have to be corrected before they ca be used a BEM code. Varous models for correctg the data for the fluece of Corols ad cetrfugal forces have bee developed by Sel et al. [1], Du ad Selg [], ad Chavaropoulos ad Hase [3]. Arfol data ca also be extracted drectly from pressure o the blades obtaed by CFD rotor computatos [4], [5]. A geeral method for determg the AOA was recetly developed by She et al. [6]. The dea of ths techque s to employ the Bot-Savart law to determe the fluece of boud vortcty o the local velocty feld. The ma objectve of the preset paper s to show that the local AOA ad atve velocty at hgh wd speed (TSR 3.0) have the eglgble wake terferece factors ad a, pp ISSN

2 Hora DUMITRESCU, Vladmr CARDOS, Flor FRUNZULICA, Alexadru DUMITRACHE 38 mportat cotrbuto from the boud vortex that makes the local axal velocty equal or eve bgger tha the wd speed. At hgh tp speed rato (TSR > 3.0) the terferece factor becomes mportat ad the local axal velocty s smaller tha the wd speed.. METHODS OF DETERMINATION OF AOA For a -D arfol the agle of attack (AOA) s defed as the geometrcal agle betwee the flow drecto ad the chord. For a rotatg blade the flow passg by a blade secto s beded due to the rotato of the rotor ad the local flow feld s flueced by the boud crculato o the blade ad the 3-D effects from the tp ad root vortces. Two smple methods are proposed to compute correctly the agle of attack for wd turbes stadard operatos ad geeral flow codtos. Method 1 Method cossts of sx steps ad uses the measured or estmated veloctes to a umber of cross-sectos of the blade. Step 1: Determg the tal flow agles usg the velocty at every motor pot [1, N]. 0 1 z,, ta V / V, (1) 0 V, Vz, V,, () where Vz,, V, are the velocty compoets the axal ad azmuth drectos, respectvely ad N s the umber of cross sectos. Step : Estmatg the lft ad drag forces usg the prevous agles of attack ad the local blade forces Fz,, F, from the measured pressure data at each cross-secto: L Fz, cos F, s where F, pedl, Ft, j pedl, dl s the cross-secto crcut elemet ad s the umber of terato. Step 3: Computg assocated the boud crculatos from the estmated lft forces by usg the Kutta-Joukowsky theorem at each cross-secto, (3) D Fz, s F, cos, (4) L / V, (5), Step 4: Computg the duced velocty created by the boud vortces usg the Bot-Savart law u y x y u u u dr, (6) B R 1 j j j d x r,, z 3 4 j1 0 x y j where R ad B are the rotor radus ad umber of blades, respectvely. x deotes the posto of the motor pot ad y s the posto of the boud vortex whch s located at 0.5 chord from the leadg-edge; thus (x y) s the dstace from the source to the motor pot.

3 39 Determato of agle of attack for rotatg blades Step 5: Computg the ew flow agle ad the ew atve velocty by subtractg the duced velocty from the cyldrcal coordate velocty V, V, V ud r,, z, ta 1 1 V V u z, z,, u,, (7) 1, z, z,,, V V u V u, (8) Step 6: If s ot covergece go to Step. Whe the covergece s reached, the agle of attack ad lft ad drag coeffcets ca be foud at all radal cross-sectos:, (9) C L / V c, (10) l,, C D / V c, (11) d,, where s the sum of ptch ad twst agles ad c s the chord legth. Method cosst of the followg 4 steps ad uses the measured chordwse pressure dstrbutos to a umber of cross-sectos. Step 1: Determe the edge velocty o the whole blade surface from the measured pressure p p0 coeffcet C p usg the steady Beroull equato (assumed to be true) at edge U of the boudary layer 1 1 p u p U, (1) U U 1 C x/ c. (13) Step : Determe the local boud crculato o the cross secto as the velocty jump over the boudary layer wth the sg based o the edge velocty, U wall r p γ x e O e. (14) Step 3: Compute the self ducto at a motor pot the cross-secto from the local boud crculato u x u, u, u U B γ y x y 3 1 surface x y r 1 ddr, (15) 4 r z where,r are coordates the tagetal ad radal drectos, respectvely, of the local coordate system, y, o the blade surface. Step 4: Compute the flow agle a secto from the velocty measured/estmated at the motor pot whch the self ducto from the boud vortces s subtracted

4 Hora DUMITRESCU, Vladmr CARDOS, Flor FRUNZULICA, Alexadru DUMITRACHE 40 V u V u, (16) 1 ta z z / z z V V u V u. (17) The agle of attack ad force coeffcets are the determed as L D, Cl, C. (18) V c V c d The techques were appled to determe the AOA usg the data of Naver-Stokes computatos o flows past the 10/10 NREL wd turbe from the Usteady Aerodyamcs Expermetal (UAE) at the NASA Ames wd tuel [6]. 3. RESULTS AND DISCUSSION I ths work, comparso wth expermetal data measured o a two-bladed 10.1 m dameter wd turbe s made. Ths test seres was ru the NASA Ames wd tuel for NREL usteady aerodyamcs phase VI expermet [6]. The turbe used was stall regulated, ts blades were twsted ad tapered ad the sectoal geometry was that of the S809 arfol. Measuremets were performed a flow wth less tha 1% turbulece, ad the data obtaed are arguably the most able ad comprehesve avalable ths day. Tests were performed the dowwd ad upwd cofguratos, for a wde rage of yaw agles, wd speeds, coe ad ptch agles, at a costat rotatoal speed of 71.6 rpm. Ths study wll cocetrate o the zero yaw agle upwd basele cofgurato, whch the loadg was almost uform for every azmuth agle. Such codtos are optmal to solated stall delay, ad 3-D effects geeral. They are the also deal to perform tests o dfferet stall delay models. Ths cofgurato also has a zero degree coe agle, ad a global ptch of 3 degrees, defed as the agle betwee the chord at the tp of the blade ad the rotatoal plae. Fg. 1 Arfol secto force coeffcets I Fgure 1, the coveto used for the dfferet forces coeffcets ad agles s show. As o coe agle was used, the studed cofgurato, (all the quattes see ths fgure are the same plae). Local tagetal ad axal forces ca be obtaed drectly from pressure measuremets/cfd computatos gorg the local flow drecto, whereas lft ad drag

5 41 Determato of agle of attack for rotatg blades coeffcets requre kowledge about the local AOA ad atve velocty. Ths s see Fg. 1 from whch the followg atoshps are obtaed betwee ormal ad tagetal F force compoets, N F CN, ad C T T, ad assocated lft ad drag coeffcets, cv cv C C cosc s, (19) L N T C C s C cos, (0) DP N T where ρ s desty of ar, V s the local velocty ad α deotes the AOA. Fg. Comparso of CFD extracted lft ad drag curves Fgure shows the comparso of CFD computatos extracted aerodyamc coeffcets (secod method) wth those of -D expermet for V 11 m/s. Sce the stall delay effects are most evdet the board rego, comparso of CFD extracted curves wth those of -D data, ad Dumtrescu-Cardoş model correcto [7] oly at these sectos are preseted ths fgure. Here, the data from [8] s also added for comparso. I Ref. [7], the agles of attack at the varous radal sectos for each wd speed were calculated usg a lftg surface code based o the measuremets of the UAE. Though the geeral tedecy s smlar, great devatos do exst betwee dfferet methods. To determe the effectve agle of attack expermetally or umercally s stll a challegg task ad there eeds a lot to do for better dervato of the agles of attack for 3- D rotatg blades.

6 Hora DUMITRESCU, Vladmr CARDOS, Flor FRUNZULICA, Alexadru DUMITRACHE 4 4. CONCLUSIONS A seres of a computatos of the rotatg NREL blade wth the commercal code FLUENT [10] have bee performed. The cofgurato was smlar to the o-yaw S-seres measuremets of the UAE carred out the NASA Ames wd tuel. To derve the lft ad drag coeffcets a agle of attack s requred combato wth the ormal ad tagetal force coeffcets. A proper flow agle of attack s ot drectly avalable ad two smple methods have bee proposed to compute correctly the agle of attack for wd turbes. The frst method usg the measured/ computed veloctes requres a teratve calculato, whle the secod techque usg measured/computed pressures o terato s requred ad the motor pots ca be chose to be closer to the blade surface. O the other had, the dffculty of usg the pressure-method s to fd the separato pot where the local crculato chages sg, ad the dstrbuto of sk frcto should be determed from CFD solutos. Therefore, how to determe the effectve agle of attack s a key factor to uderstad the stall flow. Dumtrescu-Cardoş (D-C) model ca correct stall delay to a extet, however, the actual flow s more complex. REFERENCES [1] H. Sel, R. Houwk ad T. Bosscher, Sectoal predcto of lft coeffcets o rotatg wd turbe blades stall 1994 ECN Report: ECN-C [] Du Z ad Selg M S The effect of rotato o the boudary layer of a wd turbe blade 000 Reewable Eergy [3] P. K. Chavaropoulos ad M.O. L. Hase, Ivestgatg three-dmesoal ad rotatoal effects o wd turbe blades by meas of a quas-3-d Naver-Stokes solver, Joural of Fluds Egeerg, vol. 1, pp , 000. [4] M. O. L. Hase, N. N. Sørese, N. J. Sørese ad J. A. Mchelse, Extracto of lft, drag ad agle of attack from computed 3-D vscous flow aroud a rotatg blade, EWEC, Dubl, Iad, pp , [5] J. Johase ad N. N. Sørese, Arfol characterstcs from 3-D CFD rotor computatos, Wd Eergy, vol. 7, pp , 004. [6] W. Z. She, M. O. L. Hase ad J. N. Sørese, Determato of the agle of attack o rotor blades, Wg Eergy, vol. 1, pp , 009. [7] D. Smms, S. Schreck, M. Had ad L. J. Fgersh, NREL usteady aerodyamcs expermet the NASA- Ames wd tuel: a comparso of predctos to measuremets, NREL/TP , NREL, Golde, CO, 001. [8] H. Dumtrescu ad V. Cardoş, New model for board stall-delay, Caus Iacob Coferece o Flud Mechacs ad ts Techcal Applcatos, Sept. 9-30, Bucharest, Romaa, 011. [9] J. L. Tagler, Isght to a wd turbe stall ad post-stall aerodyamcs, Wd Eergy, vol. 7, pp.47-60, 004. [10] ANSYS Fluet Commercally avalable CFD software package based o the Fte Volume method.