Modeling of Airfoil Trailing Edge Flap with Immersed Boundary Method

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1 Downloaded from orbt.dtu.dk on: Sep 27, 2018 Modelng of Arfol Tralng Edge Flap wth Immersed Boundary Method Zhu, We Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær Publshed n: ICOWEOE-2011 Publcaton date: 2011 Document Verson Publsher's PDF, also known as Verson of record Lnk back to DTU Orbt Ctaton (APA): Zhu, W. J., Shen, W. Z., & Sørensen, J. N. (2011). Modelng of Arfol Tralng Edge Flap wth Immersed Boundary Method. In ICOWEOE-2011 (Vol. Paper 07) General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts. Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research. You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan You may freely dstrbute the URL dentfyng the publcaton n the publc portal If you beleve that ths document breaches copyrght please contact us provdng detals, and we wll remove access to the work mmedately and nvestgate your clam.

2 1 ICOWEOE MODELING OF AIRFOIL TRAILING EDGE FLAP WITH IMMERSED BOUNDARY METHOD We Jun Zhu, Wen Zhong Shen and Jens Nørkær Sørensen Department of Mechancal Engneerng, Techncal Unversty of Denmark, DK-2800 Lyngby, Denmark Abstract The present work consders ncompressble flow over a 2D arfol wth a deformable tralng edge. The aerodynamc characterstcs of an arfol wth a tralng edge flap s numercally nvestgated usng computatonal flud dynamcs. A novel hybrd mmersed boundary (IB) technque s appled to smulate the movng part of the tralng edge. Over the man fxed part of the arfol the Naver-Stokes (NS) equatons are solved usng a standard body-ftted fnte volume technque whereas the movng tralng edge flap s smulated wth the mmersed boundary method on a curvlnear mesh. The obtaned results show that the hybrd approach s an effcent and accurate method for solvng turbulent flows past arfols wth a tralng edge flap and flow control usng tralng edge flap s an effcent way to regulate the aerodynamc loadng on arfols. A C l f f k v U P t x t Nomenclature ampltude lft coeffcent frequency volume force knetc energy / frequency forcng cell velocty flow velocty components pressure tme coordnates angle of attack / ptch angle tralng edge angle knematc vscosty eddy vscosty Acronyms specfc dsspaton rate densty CFD computatonal flud dynamcs IB mmersed boundary LES large eddy smulaton NS Naver-Stokes RANS Reynolds averaged Naver-Stokes RHS rght hand sde Introducton The IB method has been developed to handle flows over complex wall geometres or movng geometres. The mmersed boundary method s deally desgned for Cartesan grd solvers [1, 2]. The wall surface s represented wth forcng terms whch are added as addtonal terms n the NS equatons. The sgnfcant advantage of usng such technque s the great smplfcaton of grd regeneraton around the movng objects. The IB method provdes an alternatve numercal method to solve complex flow problems, such as flow over arfol wth deformable tralng edge. By combnng the IB model nto the exstng n-house flow solver, t s expected that the detaled flow feld around a deformable tralng edge can be acheved wth standard computatonal effort. Such a numercal tool wll also have potental value for dfferent applcatons other than modelng arfol flow problems. The IB method s namely that the sold boundares are mmersed on grds that normally don t conform to the shape. Ideally, the IB approach requres only smple Cartesan grd 1

3 2 nstead of body conformal grd. For numercal smulatons, the requred nput data s the prescrbed IB surface shape. To smulate dfferent body geometres, the only change s the IB surface data and the computatonal mesh s not modfed. In other words, the IB surface movement has to be prescrbed as preprocessng. For a gven IB surface, the grd does rarely conform to the IB surface. In case that the IB surface cuts through the grd lnes, the IB surface would be represented by the neghborng grd ponts. Therefore the ssue of mposng wall boundary condtons at IB surface s the key factor. Ths would requre modfyng the NS equatons n the vcnty of the IB surface. Detaled dscussons of wall treatment are presented n the followng sectons n ths paper. To apply the IB technque n turbulent flow condtons, the partcular challenge s to model the wall turbulence boundary layer at hgh Reynolds numbers. It turns out that the wall model both affects the accuracy of the solver and the soluton convergence. Kaltzn and Iaccarno [3, 4] appled one equaton [5] and two equatons [3] turbulence models together wth the IB method. The turbulence models have zero wall boundary condtons for all turbulence varables. They proposed look-up tables to model turbulence varables such as eddy vscosty. LES model s the other opton of turbulence modelng. Tesscn et al. [6] modeled a hydrofol tralng edge flow usng the IB method n conjuncton wth LES where a near-wall model s nvestgated. In Esenbach and Fredrch [7], arfol flow at hgh angle of attack s smulated n the framework of IB method for LES where they ntroduced the block cell nterface concept. Comparng the RANS and LES turbulence models, the LES model s more straghtforward to be used snce t does not requre any wall functons but only senstve to mesh densty. The RANS turbulence model produces averaged flow solutons whch s more feasble for the present study. From the control pont of vew, the LES turbulence model wll gve much dffculty snce all flow quanttes are fluctuatng around the mean value. Here we proposed a hybrd method that combnes wall-bounded flow solver together wth IB technque. In ths manner, only the movng part of the sold body s modeled by IB method. Ths ensures much better accuracy at the statc part of sold body and also enhanced the mesh densty at the movng part. The paper s organzed as followng: secton 2 ntroduces the governng equatons that combned wth the IB technology; secton 3 presents the classcal result of lamnar flow over a cylnder usng both standard CFD n curvlnear mesh and the IB method n a Cartesan grd system; secton 4 focuses on turbulent flow over a NACA 0012 arfol wth a combned moton of ptch and tralng edge flap; secton 5 shows an actve control case usng tralng edge flap. A concluson n gven n the fnal secton. Numercal method The present verson of the IB technque s based on the Reynoldsaveraged ncompressble NS equatons and the contnuty equaton, U ( UU j) 1 ( P t xj U U ( t) x j xj x U 0 x 2 / 3k) x j f (1) where the body force f creates the desred velocty feld along the sold boundary; P s the pressure, ρ s the densty of ar, and U j denotes the velocty components. ν s the knematc vscosty, ν t s the turbulent eddy vscosty and k s the turbulent knetc energy,

4 3 obtaned from the turbulence model. In the IB method, the forcng term f s determned from a tme dscretzaton of Equaton (1), U n 1 U t n RHS n 1 / 2 n 1 / 2 f (2) where the RHS results from the dscretzaton of the convectve, vscous and pressure-gradent terms at tme level n+1/2. The notaton of f at n+1/2 means drect forcng,.e. the forcng term s beng computed before the velocty but at the same tme step. From Equaton (2), the volume force f whch yelds the desred velocty v n+1 smply s wrtten as [2, 8, 9] f n v U RHS. (3) t n1 / 2 1/2 n1 Solvng the flow equaton wth the forcng terms determnes the velocty on the wall represented by n 1 the IB. The velocty v on the forcng cells s determned by lnear nterpolaton between the wall surface and the neghbourng grd ponts. In the present work, the IB methodology s adapted to the k-ω turbulence model of Menter [10]. To employ the k-ω model n the framework of the IB method, the wall normal dstance to the IB surface y b s ntroduced such that y b y mn y,. (4) n turbulent knetc energy, k, s set to zero nsde the body and on the IB surface. The ω-values on the IB surface are calculated usng the local normal dstance from the forcng cells to ther nearest IB surface. For stablty reasons, the ω values nsde the body can not be attrbuted a constant value, as t creates a dscontnuty when gong from the sold body to the flow regon. A practcal way to crcumvent ths problem s to apply Equatons (4) and (5) also nsde the sold body. Ths ensures a smooth dstrbuton of ω-values everywhere n the computatonal doman. In the case of a movng body, the dstance y b needs to be re-calculated at each tme-step and compared wth the dstance from sold walls. To locate the cells that defne the mmersed boundary, the method of ray tracng s appled. Ths s llustrated n Fgure 1, whch depcts the IB surface, the body cells and the outsde cells around a sold body. Applyng ray tracng to determne the locaton of ponts A and B, t s observed that the ray startng from pont A has crossed the IB surface two tmes, whereas the one startng at pont B has three cross ponts. The general rule s that a pont s located outsde the sold body f the ray emanatng from t has zero or an even number of cross ponts wth the IB surface. Therefore, the wall dstance functon s determned ether from the sold wall or from the IB surface. Thus, the near wall boundary condtons on IB cells are gven as k w b 0 60 y 2 b (5) To satsfy the boundary condtons of the turbulent quanttes, the Fgure 1. Locaton of body cells (open crcles) usng ray tracng method.

5 4 Lamnar flow over a cylnder As the IB method s ntally desgned for low Reynolds number flows wth Cartesan grd, we start wth lamnar flow over cylnder as the frst test case. The flow Reynolds number s set at 100. In ths case, the equal spacng Cartesan mesh s used such as shown n Fgure 2. The sold boundary s represented by the sold lne whch s mmersed n the grd. Knowng all the cells cut though the IB lne, the cylnder geometry s fnally represented by the cell center ponts near the IB lne as shown n Fgure 2. (a) (b) Fgure 3. Curvlnear (a) and IB (b) smulatons. Fgure 2. Cartesan mesh for IB smulaton. To compare the qualty of IB technque, the same flow s performed by standard curvlnear mesh. Fgure 3 shows the flow vortcty of two methods at same tme nstant. As t s seen, the two smulatons yeld smlar flow feld. Although very coarse grd s appled, the present IB smulaton stll provdes good accuracy. The more detaled comparson s gven n Fgure 4 where the pressure coeffcents of the two smulatons are compared. There s good general agreement wth two methods. The soluton can be further mproved f fner mesh s ntroduced. Fgure 4. Comparson of the Cp dstrbuton along the cylnder surface. Complex turbulent flow case In ths secton, turbulent flow past an arfol that combnes ptchng and tralng edge flappng s consdered. Prevous expermental nvestgatons [11] showed that ths moton s assocated wth a complex flow behavour due to the phase lag between the ptch and flap angles. In such a case, the unsteady aerodynamc load s dependent on the combnaton of the ptch and flap

6 5 angles. In the followng the IB method wll be valdated for ths combned moton by comparng numercal smulatons wth expermental results [11]. Fgure 5. Mesh near the tralng edge part. Fgure 6. Sketch of arfol subject to combned ptchng and flappng movement wth nstantaneous plots of stream-wse velocty contours and stream-lnes. The arfol under study s the NACA 0012 and the mesh confguraton s shown n Fgure 5. The tralng edge flap s 22.6% percent of the arfol chord length. The grd lnes are clustered along the vrtual tralng edge whch s now represented by IB. In order to utlze a smlar setup as n the experment, the numercal tralng edge flap has rgd movement as well. It should be noted that long tralng edge flaps manly are amed for hgh lft devces, such as wngs of arcraft. However, t s stll a good reference for wnd turbne blade applcatons. The arfol ptchng axs s located at a chord wse poston of 35% percent of the arfol chord measured from the leadng edge, as depcted n Fgure 6. In the fgure, the ptch and flap angles are referred to as α and, respectvely. The arfol movement s gven as α(t) = α 0 +A sn(2k 1 t) and (t) = 0 +B sn(2k 2 t -), where denotes the phase shft between the two oscllatons. The arfol s ptchng at a mean angle α 0 =4 o, an ampltude A=6 o, and a reduced frequency k 1 = The flap has a smlar moton wth 0 =0 o, an ampltude B=5.4 o, and a reduced frequency k 2 =0.042 (k 2 =2k 1 ). The flow s smulated at a Reynolds number of , wth an ntal angle of attack α 0 =4 o. A snapshot of the stream-wse velocty contours and stream lnes s shown n Fgure 6. Snce the ptchng moton of the arfol s performed by oscllatng the computatonal grd nstead of movng the arfol, the ptch angle s observed as a drectonal change of the stream lnes. The results are here compared to experments [11] at dfferent phase lags between the flap and the arfol ptchng movements. The tme hstory of the ptch and flap angles, and assocated lft curves, are shown for =148 o, 294 o, and 357 o n Fgures (7), (8) and (9), respectvely. As seen n the fgures, the arfol ptch and flap motons n the experment do not exactly correspond to snusodal shapes. Due to mechancal oscllatons n the model system, measurement errors exst for both ptch and flap motons. The numercal results, however, are generally n very good agreement wth the expermental data, demonstratng that the IB technque has the flexblty of dealng wth complex arfol moton. The advanced numercal tool also provdes a much better accuracy than the smplfed tools used n [11]. The dfferent shapes of the loops presented n

7 6 Fgures (7)-(9) are due to the dfferent phase angles between the flap and arfol motons. For a ptchng arfol wth a fxed flap, one would expect an open 'o'-lke loop. By combnng the flap movement wth arfol ptchng, the unsteady aerodynamcs becomes more complcated. The effect caused by the flap movement s smlar to a smultaneously alterng of the arfol shape, correspondng e.g. to a camberng or a de-camberng of the arfol shape. In Fgure 7, at a tme nstant t 0.065, the ptch and flap angles attan approxmately ther maxmum value at the same tme. Ths corresponds to a maxmum camberng effect, and a maxmum lft value s seen to occur at α 0 =10 o. A smlar tendency s shown n Fgure 8 at a tme nstant t 0.055, where the flap angle attans ts mnmum value at the same tme as the ptch angle attans a maxmum value. Due to the maxmum de-camberng effect from the flap, the maxmum lft s decreased, as compared to Fgure 7. (a) (b) Fgure 8. (a) Moton of the ptch and flap angles. (b) Comparson of the computed lft coeffcent wth experment at a phase lag of 298 o. (a) (a) (b) Fgure 7. (a) Moton of the ptch and flap angles. (b) Comparson of the computed lft coeffcent wth experment at a phase lag of 148 o. (b) Fgure 9. (a) Moton of the ptch and flap angles. (b) Comparson of

8 7 the computed lft coeffcent wth experment at a phase lag of 357 o. Flow control study In ths secton we consdered a flow control case usng NACA arfol wth a 15%-chord adaptve tralng edge. The purpose of ths study s to show the ablty of usng tralng flap to control the loadng on a wnd turbne arfol. The numercal calculaton wll also gve some gude lnes for the smlar experments that wll be carred out at DTU/MEK wnd tunnel. Therefore, the smulaton uses nearly the same geometrc confguratons as the expermental setup. Fgure 10 llustrates some features of the numercal mesh confguratons. The velocty at nlet s V = 10 m/s, the test secton has dmenson of 0.5m x 0.5m, the arfol chord s 0.2m and the tralng edge flap s 0.03m. Two small arfols are placed n front of the man arfol. The small arfols have a chord of 0.1 m and they are located at the postons of A(-0.1,0.1) and B(-0.1,-0.1), where the leadng edge of the man arfol s located at (0,0). The task of the two small arfols above and below the man arfol s to snusodally ptch the nflow and therefore change the angle of attack at the man arfol. The two arfols are modeled by addng two pont forces n the momentum equatons of NS equatons Lft 0. 5 sn( 2ft). (6) By applyng such a prescrbed force at pont A and B, the desred velocty feld s obtaned whch yelds the change of angle of attack at the man arfol. Fgure 10. Mesh confgureaton The flow vortcty s shown n Fgure 11 where the effect at the two forcng ponts s observed as votcty. For flow at zero angle of attack, the steady lft s acheved at C l = 0.18 for NACA arfol. If we start to ptch the small arfols and wth the purpose to stll mantan the steady lft at C l = 0.18, a correspondng moton of the tralng edge flap of NACA arfol shall be prescrbed. Here, a P-controller s appled to control the flap angle, e.g., β = k*(c l ) where k s a constant to adjust the angular speed of the tralng edge. The lft coeffcent from the man arfol s shown n Fgure 12 as functon of smulaton tme. At the tme nterval of t = [0,10], the smulaton was only performed for the man arfol. It s seen that flow s quckly stablzed at C l = At the second tme nterval of t = [10, 12], the two small arfols start to ptch n the same manner as n Equaton (6) wth a frequency of 1. The perodc lft curve s created as t s expected. At the thrd tme nterval t = [12, 20], the control of the tralng edge s actvated by usng the P-controller. It s see that for the present case, the smple P-controller s suffcent to mantan the man arfol at a desred constant value.

9 8 Fgure 11. Vortcty contour plot wth the two oscllatng arfols and the man arfol. been adapted to a k-ω turbulence model. The IB method combnes the advantages of the IB technque wth the effcency of applyng a standard CFD method on a structured mesh. In the case of a combned ptchng and flappng moton smulatons were compared to exstng experments. The tme behavour of the computed lft coeffcent was n excellent agreement wth measured values. The smulatons clearly demonstrated the robustness and accuracy of treatng complex arfol movements by the IB formulaton. Furthermore, an nvestgaton of load control wth tralng edge flap has shown great potental even wth a smple control method. Acknowledgements The authors would lke to acknowledge the Dansh Natonal Advanced Technology Foundaton (Højteknologfonden) and Vestas Wnd Systems A/S for supportng ths research work. The numercal smulatons were carred out on a cluster sponsored by the Dansh Centre for Scentfc Computng. Fgure 12. Tme seres lft coeffcent at controlled and uncontrolled perod. Concluson The present paper descrbed the development of a hybrd mmersed boundary method. The method s developed wth the am of controllng aerodynamc loadng for turbulent flows past wnd turbne arfols. The prncple of the new IB method s to employ a standard CFD on a structured mesh over most of the arfol and utlze the IB technque to model the movement of the tralng edge flap. The model s mplemented nto an exstng ncompressble Reynolds-averaged Naver-Stokes code. Specal attenton was pad to turbulent flows, where the IB methodology has References [1] Mttal, R., and Iaccarno, G., Immersed Boundary Methods, Annual Revew of Flud Mechancs, Vol. 37, 2005, pp do: /annurev.flud [2] Mohd-Yosuf J., Combned mmersed boundary/b-splne methods for smulaton of flow n complex geometres, Annu. Res. Brefs, Cent. Turbul. Res., pp [3] Georg Kaltzn and Ganluca Iaccarno, Turbulence modelng n an mmersed-boundary RANS method, Center for Turbulence Research Annual Research Brefs [4] Georg Kaltzn and Ganluca Iaccarno, Toward mmersed boundary smulaton of hgh

10 Reynolds number flows, Center for Turbulence Research Annual Research Brefs [5] Spalart, P. R. and Allmaras, S. R., A one-equaton tubulence model for aerdynamc flows, La Recherche Aerospatale, 1994, Vol. 1, [6] F. Tesscn y, G. Iaccarno, M. Fatca, M. Wang AND R. Verzcco, Wall modelng for large-eddy smulaton usng an mmersed boundary method, Center for Turbulence Research Annual Research Brefs [7] Sven Esenbach and Raner Fredrch, Large-eddy smulaton of flow separaton on an arfol at a hgh angle of attack and Re = 10 5 usng Cartesan grds,theoretcal and Computatonal Flud Dynamcs, Volme 22, Numbers 3-4/May, 2008, , /s z. [8] E.A. Fadlun, R. Verzcco, P. Orland, J. Mohd-Yusof, Combned mmersedboundary/fnte-dfference methods for three-dmensonal complex flow smulatons, J. Comput. Phys. 161 (2000) [9] M. Uhlmann, An mmersed boundary method wth drect forcng for the smulaton of partculate flows, J. Comput. Phys. 184 (2003) [10] F.R. Menter, Two-equaton eddy-vscosty turbulence models for engneerng applcatons, AIAA J. 32(8) (1994) [11] A. Krzysak, J. Narkewcz, Aerodynamc loads on arfol wth tralng-edge flap ptchng wth dfferent frequences, Journal of Arcraft, 43(2) (2006)