Aerodynamics of Harmonically Oscillating Aerofoil at Low Reynolds Number

Transcription

1 doi: 1.58/jatm.v9i1.61 Aerodnamics of Harmonicall Oscillating Aerofoil at Low Renolds Number Aiman Hakim Abdul Rahman 1, Nik Ahmad Ridhwan Nik Mohd 1, Tholudin Mat Lazim 1, Shuhaimi Mansor 1 ABSTRACT: Two-dimensional flows over harmonicall oscillating smmetrical aerofoil at reduced frequenc of.1 were investigated for a Renolds number of 135,, with focus on the unstead aerodnamic forces, pressure and vorte dnamics at post-stall angles of attack. Numerical simulations using ANSYS FLUENT CFD solver, validated b wind tunnel eperiment, were performed to stud the method of sliding mesh emploed to control the wing oscillation. The transport of flow was solved using incompressible, unstead Renolds-Averaged Navier-Stokes equations. The -equation k-ε realizable turbulence model was used as turbulence closure. At large angle of attack, comple flows structure developed on the upper surface of the aerofoil induced vorte shedding from the activit of separated flows and interaction of the leading edge vorte with the trailing edge one. This interaction at some stage promotes the generation of lift force and delas the static stall. In this investigation, it was found that the sliding mesh method combined with the k-ε realizable turbulence model provides better aerodnamic loads predictions compared to the methods reported in literature. Kewords: Aerofoil, Unstead, Low Renolds number, Harmonic oscillation, Post-stall, Computational fluid dnamics. INTRODUCTION Among the earliest documented phenomena of dnamic stall, there is the report of Kramer (193) summarizing his eperimental investigation on the effect of vertical gust on a wing stress. The stud is also the first to recognize the dnamic features associated with the rapid variations of incidence eperienced b an airfoil (Wernert et al. 1996). Nowadas, dnamic stall is commonl recognized as the breakdown of the flow field around an oscillating slender lifting surface operating beond its critical angle of attack (McCroske 1981). Over a past few decades, the dnamic stall event has become one of the major problems in aeronautics and astronautics. Dnamic stall is a condition where the evolution of the flow field is rather different from that obtained for static stall and contains comple unstead flow phenomenon that produces a detrimental effect in man aerodnamic sstems. Maneuvering aircraft, helicopter rotor blades, wind turbines, flapping wing of insect, compressor and turbine blades are some eamples of engineering application involving unstead flow and unstead load during operation. Unstead flow is known to produce a negative effect on aerodnamic load, induced vibration, flutter, buffeting (Kim and Chang 9) and is also known as one of the limiting factors of the aircraft flight speed and operation of mechanical sstem (Lee and Gerontakos 4). Recentl, oscillating wing has gained a particular interest in the field of biomimetic studies aiming at harvesting propulsive force from circulation flow to a small scaled vehicle. The phenomenon of dnamic stall can be categorized into pre- and post-stall depending on the viscous-inviscid interaction (McCroske 1981; Kim and Chang 9; Lee and Gerontakos 4; McCroske et al. 1976). Beond the stall, 1.Universiti Teknologi Malasia Facult of Mechanical Engineering Aeronautical Laborator Skudai/Johor Malasia. Author for correspondence: Nik Ahmad Ridhwan Nik Mohd Universiti Teknologi Malasia Facult of Mechanical Engineering Aeronautical Laborator 8131 Skudai/Johor Malasia ridhwan@utm.m Received: Feb. 1, 16 Accepted: Jul. 18, 16 J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17

2 84 Rahman AHA, Mohd NARN, Lazim TM, Mansor S the separation point moves toward the leading edge forming a complicated flow structure such as leading edge vorte (LEV), free shear laer, and viscous-inviscid interaction that plas an important role in the characteristics of dnamic stall (Kim and Chang 9). In helicopter industr, the development of LEV associated with the increase in the pitching moment of rotor blades is undesirable. However, the dela in the LEV detachment from the aerofoil surface provides an increase in dnamic lift to the aircraft (Lee and Su 11). Accurate prediction of unstead flow and dnamic stall is still one of challenging tasks in eperimental and computational fluid dnamics. Numerous eperimental papers (McCroske 1981; Kim and Chang 9; Lee and Gerontakos 4; McCroske et al. 1976; Panda and Zaman 1994; Coton and Galbraith 1999) and numerical investigations (McCroske and Pucci 198; Ericsson and Reding 197; Gaitonde and Fiddes 1993; Dumlupinar and Murth 11; Barakos and Drikakis 1999) have been carried out and show that the unstead flow can be separating or reattaching over a large portion of the upper surface of an aerofoil, features which reverse flow circulation, formation and shedding of leading and trailing vorte sstem that induces non-linear fluctuating pressure field and produce transient variation in forces and moments that are different to its stead-state conditions (Lee and Gerontakos 4). The flow field of an aerofoil periodicall pitched about a fied-ais is primaril influenced b the amplitude α o, the mean angle α m and the frequenc of oscillation f. The oscillation frequenc is known as the most influential parameter and is often presented in terms of reduced frequenc the ratio of time scales: one imposed b the pitching motion and the other b the free stream velocit and the aerofoil chord (Panda and Zaman 1994). Wang et al. (1), in their stud, emploed the dnamic mesh approach for the simulation of harmonicall pitching aerofoil following Wernert et al. (1996) for moderate Renolds number and Lee and Gerontakos (4) for low Renolds number cases. The used dnamic mesh technique consists of sub-domains that communicate through a pair of circular common interfaces. The commercial ANSYS (13) FLUENT pressure-based solver that solves full unstead Renolds-Averaged Navier-Stokes governing equation for incompressible flow problem was used. The SIMPLE algorithm was used for the pressure-velocit coupling and the nd-order upwind scheme was utilized for the velocit and the turbulence quantities. To accelerate the convergence of the solution, the algebraic multigrid scheme (AMG) with a V-ccle tpe for the pressure and a fleible tpe for the momentum was applied. The turbulence in the flow was calculated using the standard k-ω and shear stress transport (SST) k-ω turbulence models with a modified turbulent viscosit damping. In Gharali and Johnson (13), the instantaneous aerodnamic load of a NACA 1 aerofoil in pure pitching oscillation in a stead freestream was numericall simulated and validated against the eperimental research of Lee and Gerontakos (4), in which the k-ω SST turbulence model with low Renolds correction similar to that of Wang et al. (1) was used. The C-grid topolog was emploed with a total of, cells and 5 nodes wrapped around the aerofoil. The stabilit issue that is ver sensitive to the value of turbulence intensit (Wang et al. 1) and mesh skewness (Gharali and Johnson 13) is also highlighted. In this paper, the challenges and issues of modelling and understanding the unstead aerodnamics of an aerofoil at high incidence angles and highl unstead flow using CFD are investigated and presented. The test case is a -D aerofoil undergoing fast harmonic oscillations. The solution of the CFD using sliding mesh is then compared against dnamic mesh method and available eperimental data. EXPERIMENTAL METHODS Wind tunnel or water tunnel becomes one of standard testing procedures in aerodnamic load measurements. To date, various eperimental studies on oscillating aerofoil were reported from simple to complicated eperimental setup. In this investigation, eperimental data obtained from the McGill Universit s low speed wind tunnel are referred for validation (Gerontakos 4; Lee and Gerontakos 4). In this eperiment, dnamic stall and flow characteristics over an oscillating smmetrical NACA 1 aerofoil at the Renolds number of 135, were investigated. The NACA 1 aerofoil was made of solid aluminum, with a chord length c of 15 cm and a span of 37.5 m. The origin of the coordinate was located at the leading edge of the aerofoil, which was equipped with endplates with a sharp leading edge to eliminate the 3-D effect at the tip of the wing. The aerofoil pitching ais is located at the ¼ chord. In the test section, the measured turbulent intensit was.8% at a free stream velocit u = 35 m/s. A miniature hot wire probe (DISA P11) with a Dantec 56C17 constant-temperature anemometer (CTA) was used for wake measurement. The probe was located at 1-chord J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17

3 Aerodnamics of Harmonicall Oscillating Aerofoil at Low Renolds Number 85 downstream of the trailing edge of the aerofoil. For surface pressure measurement, 61 pressure taps (.35 mm in diameter), in conjunction with 7 fast-response miniature pressure transducers (tpe YQCH-5-1) staggered 1.5 mm apart in the streamwise direction, were used. NUMERICAL SIMULATION In a numerical approach, a similar aerofoil section, as in the wind tunnel eperiment of Lee and Gerontakos (4), was used for validation studies. For unstead, oscillating aerofoil problem, hbrid unstructured mesh was emploed with blocks consisting of stationar and rotating meshes. The Renolds number used in this investigation was 135,. For consistenc, the inlet turbulence intensit in CFD was set at.8%, similarl to the eperiment of Lee and Gerontakos (4). However, as reported b Wang et al. (1), the value of the inlet turbulent intensit has some influence on the stabilit of the solution. Around the aerofoil, the no-slip boundar condition was emploed and wrapped b a boundar laer mesh, which contains 5 laers with the first cell height set at + 1. To ensure that the viscous effect is properl captured, an improved method for calculating turbulent boundar laer based on the reference temperature method for turbulence flow was used, resulting in the 1st cell height of less than m (Meador and Smart 5). In this paper, the ANSYS (13) FLUENT CFD that solves unstead Renolds-Averaged Navier-Stokes equations for incompressible flow problem on unstructured, cell-centered control volume was used. The main purposes of this CFD are the assessment of the sliding mesh method used and blind test for wind tunnel eperiment verification. The used CFD solver takes momentum and pressure as the primar variable and solves pressure correction and momentum sequentiall. This tpe of solver is also known as pressure-based. For timedependent flow problem, the pressure implicit with splitting of operator (PISO) scheme for pressure-velocit coupling was used similarl to the stud of Gharali and Johnson (13). For the selection of turbulence models, similar studies were found in literature using the -equation k-ω turbulent model with the transport of shear stress (Gharali and Johnson 13; Hutchinson et al. 1; Wang et al. 1). In Gharali and Johnson (13), the k-ω turbulence with SST model was used with additional enhancement in the calculation of the turbulent viscosit damping for low Renolds number problem. On the other hand, in this paper, the realizable k-ε turbulent model (Shih et al. 1995) with enhanced wall treatment and mesh with more than 7, points was used and found adequate to resolve the viscous-inviscid interaction as well as able to capture some detail wake structure developed during upstroke and downstroke phases for an aerofoil in post-stall condition. The selection of the realizable k-ε turbulent model was made due to the capabilit of this turbulent model to accuratel predict flows involving rotation, boundar laers under strong adverse pressure gradient, separation and recirculation which often occur around aerofoil undergoing fast dnamic oscillation and deep stall. The schematic of sliding mesh used in the present stud is shown in Fig. 1. The computational domain is divided into blocks. The first contains stationar mesh and the second, a mesh that rotates at the same frequenc as the aerofoil. U ω Figure 1. Schematics of the numerical setup. The harmonic pitching motion of aerofoil is controlled b sliding mesh method that moves rigidl in a dnamic mesh zone (ANSYS 13). For the -D problem, the cell zones are connected each other through non-conformal interfaces. The transport equation for a general scalar quantit (ϕ) in moving boundar is solved according to the following equation: (1) where: ρ is the fluid densit; Γ is the diffusion coefficient; u is flow velocit vector; u is the mesh velocit of the moving g mesh; represents the boundar of control volume V; A is the face area vector; S ϕ is the source term of ϕ. The general scalar transport equation (Eq. 1) is converted into an algebraic equation using control volume method. This method consists of integrating the transport equation about J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17

4 86 Rahman AHA, Mohd NARN, Lazim TM, Mansor S each volume forming a discrete equation that epresses the conservation law on a control volume basis. The update in the change in volume is solved using 1st-order backward difference as: () where: n and n + 1 denote the respective quantit at the current and net time level; dv/dt is the volume-time derivative of the control volume. For sliding mesh approach, the mesh in sliding region remains in its original shape and volume and does not change in time. Thus Eq. can be written as: (3) Using Eq. 3, the 1st term in Eq. 1 can be written as: (4) RESULTS AND DISCUSSION In this section, aerodnamic loads in terms of lift and drag coefficients of a NACA 1 aerofoil undergoing harmonic oscillation at a reduced frequenc, k =.1, are presented with the intention to evaluate the combination of sliding mesh approach and the used k-ε realizable turbulence model. Figures a and b show the comparison of the instantaneous lift and drag coefficients hsteresis calculated for a 1 harmonic oscillation ccle. From these figures, the harmonic motion of the aerofoil in the upstroke phase etends the aerofoil stall angle beond the static stall and up to the angle of attack α = 4.4, as predicted in CFD and the eperiment. The predicted maimum lift coefficient is reported to be C L =.4 at α = 4.43 and.5 times higher than the static stall. The linear lift region also etended up to the angle of attack α = with the gradient of the dc L /dα maintained similar to the static case. In upstroke phase, CFD predicts that there is slightl loss in lift within α(t) 5 ( ). In the dnamic stall region, the wing In order to satisf the mesh conservation law, the volumetime derivative of the control volume is computed from the dot product of mesh velocit and face area vector u A : g The results presented in this paper refer to the aerofoil subjected to a harmonic oscillation which is defined as a function of the angle of attack variation, α(t) = α m + α o sin(ωt), where ω is the oscillation frequenc. In the case of oscillating aerofoils, the unstead motion is characterized b the non-dimensional similarit parameter known as reduced frequenc of oscillation, defined b k = ωc/u, where U is the freestream velocit. The aerofoil ais of oscillation is located at ¼ chord point. The test cases presented are related to aerofoil at post-stall condition with instantaneous angle of attack, α(t) = sin(ωt), and reduced frequenc, k =.1, was chosen. The simulations were run for one and a half ccle with time step dt =.6 s. In later discussion, lift and drag forces on aerofoil are described in terms of the non-dimensionalized unit defined as C L = F /(.5ρU c) and C D = F /(.5ρU c), respectivel, where F and F are the lift and drag forces. (5) Drag coefficient [C D ] Lift coefficient [C L ] Angle of attack [ ] 1 3 Angle of attack [ ] Current CFD upstroke Current CFD downstroke CFD Wang et al. (1) CFD Gharali and Johnson (13) Eperiment Lee and Gerontakos (4) Eperiment Static Figure. Instantaneous aerodnamic loads hsteresis for test case: α(t) = sin(ωt), k =.1. Drag coefficient; Lift coefficient. J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17

5 Aerodnamics of Harmonicall Oscillating Aerofoil at Low Renolds Number 87 stall has a similar pattern and magnitude of loss in lift force to that reported in the eperiment and in Wang et al. (1). However, the dnamic stall event and the loss in the lift force as predicted in Wang et al. (1) showed that there is continuing loss in lift beond the dnamic stall angles as reported in the eperiment. Gharali and Johnson (13), on the other hand, show that the used CFD methods inaccuratel predict the dnamic stall angle, which was found to occur earlier than reported in the eperiment. Similarl to Wang et al. (1), the present CFD analsis predicts a gain in lift as the aerofoil enters in the downstroke phase. Moreover, in Wang et al. (1), the gain in lift appeared to occur at slightl lower incidence angles unlike the present stud. As can be seen in Fig. b, the present analsis shows that the used CFD method slightl underpredicts the drag coefficient within 15 α(t) ( ). A steep increase in the predicted drag can also be seen in the downstroke phase as a result of large increase in the predicted lift (Fig. b) but occurs at lower incidence aerofoil angles as compared to the investigation of Gharali and Johnson (13). Variation in the predicted lift and drag was found to be strongl associated with the change in the local surface pressure with respect to time. Figures 3 and 4 show the instantaneous field pressure near the aerofoil in upstroke and downstroke phases, respectivel. For the purpose of comparison, the field pressures shown in these figures are etracted for the same pressure range. In upstroke phase and at a low angle of attack up to 6, the field pressure (Fig. 3) and the surface pressure (Fig. 5) suggest that the flow is mostl attached to the surface. As the aerofoil continues moving upward, with the incidence angle reaching approimatel 1 (linear region of lift in dnamic condition), the sudden decrease in the suction pressure is apparent on the upper surface, near the leading edge (Fig. 3d). This sudden decrease in the field pressure near the suction area can also be visualized b a large negative pressure gradient near the leading edge of the aerofoil. This phenomenon can also be associated with the generation and propagation of LEV that dominates the upper surface of an aerofoil. As the incidence angle continues to increase, the LEV starts to detach from the surface as well as to propagate and travel downstream towards the trailing edge (Fig. 3e). This LEV carries low pressure field and its close proimit to the surface of an aerofoil greatl alters the value of the aerofoil local surface pressure. As the LEV and trailing edge vorte (TEV) interact with each other, it causes a large drop in field pressure near the trailing edge region (Figs. 3f and 5f). In the transition phase (from upstroke to downstroke), the used method predicts a steep lost in the lift known as dnamic stall. In this transition phase, the primar LEV and (c) (d).4. (e).4. (f) Figure 3. Instantaneous field pressure coefficient in upstroke phase. 4.85, t = 3, s, ; 1.4, t = 1 s, ; (c) 16.99, t = 3 s, ; (d).85, t = 5 s, ; (e) 3.58, t = 7 s, ; (f) 4.98, t = 1, s,. J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17

6 88 Rahman AHA, Mohd NARN, Lazim TM, Mansor S TEV begin to detach from the aerofoil surface, forming vorte shedding in the wake downstream of the aerofoil (Fig. 4a). At this condition, the CFD predicts that a large low pressure area eists on the upper surface of an aerofoil. As the primar (c) (d).4. (e).4. (f) Figure 4. Instantaneous field pressure coefficient in downstroke phase. 3.98, t = 1, s, ;.93, t = 1,3 s, ; (c) 19.84, t = 1,5 s, ; (d) 17.88, t = 1,6 s, ; (e) 11.3, t = 1,9 s, ; (f) 4.99, t =,9 s,. (d) (e) (c) (f) Figure 5. Instantaneous surface pressure coefficient (C P ) distribution in upstroke phase. 4.85, t = 3, s, ; 1.4, t = 1 s, ; (c) 16.99, t = 3 s, ; (d).85, t = 5 s, ; (e) 3.58, t = 7 s, ; (f) 4.98, t = 1, s,. J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17

7 Aerodnamics of Harmonicall Oscillating Aerofoil at Low Renolds Number 89 LEV propagates and travels downward, a secondar LEV is developed due to the downward movement of the aerofoil. The progression of LEV from leading to trailing edge of the aerofoil again develops a low pressure area on the upper surface resulting in an increase in the normal and aial forces. This is clearl visible at an aerofoil incidence angle of approimatel ( ). This is benefited from a large pressure loss because LEV (clockwise rotation) and TEV (anti-clockwise rotation) activities occur on the upper surface of the aerofoil. The surface static pressure coefficients for an aerofoil in downstroke phase are depicted in Figs. 6a to 6f. These figures also show that, even for a geometricall smmetrical aerofoil, the aerodnamics and flow characteristics in the upstroke phase are heterogeneous to the downstroke phase. CONCLUSION The aerodnamic characteristics of a NACA 1 aerofoil in low Renolds number flow (Re = 135,) undergoing harmonic oscillation in a full unstead flow condition were numericall simulated using the sliding mesh method and k-ε realizable turbulent model. The purposes of this research were to investigate the potential of sliding mesh and k-ε realizable turbulent model in the simulation of aerofoil in unstead oscillation, in order to support wind tunnel eperiment, to full understand the aerodnamic behavior of aerofoils in harmonic oscillation and for the design of control sstem for fleible wing. Overall, the cclical forces and flow structure, including LEV and TEV interaction, propagation and shedding, agreed ver well qualitativel and quantitativel with those reported in literature. It can also be concluded that, for low Renolds number problems, the sliding mesh strateg accompanied b the used -equation k-ε realizable turbulence model provides better aerodnamic loads prediction compared to the moving mesh approach using the k-ω SST. The k-ε realizable turbulence model is also found to be adequate in capturing the flow field at high incidence angles and during dnamic stall conditions comparable to the eperiment. In the upstroke ccle and at high aerofoil incidence angles, the propagation and the close proimit of the LEV to the aerofoil surface cause a large drop in the static (d) (e) (c) (f) Figure 6. Instantaneous surface pressure coefficient (C P ) distribution in downstroke phase. 3.98, t = 1, s, ;.93, t = 1,3 s, ; (c) 19.84, t = 1,5 s, ; (d) 17.88, t = 1,6 s, ; (e) 11.3, t = 1,9 s, ; (f) 4.99, t =,9 s,. J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17

8 9 Rahman AHA, Mohd NARN, Lazim TM, Mansor S pressure on the upper surface of the aerofoil, and this is predicted to occur approimatel at ½ of aerofoil chord. The large deficit in static pressure ma cause some influence in the aerofoil pitching moment. For future studies, the detail of LEV-TEV interaction, boundar laer profile, separation and attachment will be investigated to full understand the flow characteristics in the viscous-sublaer region leading to turbulent flow. ACKNOWLEDGEMENTS The authors would like to thank the Universiti Teknologi Malasia, for the financial support to the current stud through Flagship Research Grant No: Q.J G9, as well as Mr. Hasrizam, for preparing mesh and computer setup. AUTHOR S CONTRIBUTION Mohd NARN administered, designed, and made the setup of the numerical simulation as well as wrote the manuscript. Lazim TM and Mansor S provided technical support and conceptual advices. Rahman AHA performed the numerical setup, the data analsis and wrote the manuscript. All authors contributed equall to this paper. REFERENCES ANSYS (13) ANSYS FLUENT theor guide. Canonsburg: ANSYS, Inc. Barakos G, Drikakis D (1999) An implicit unfactored method for unstead turbulent compressible flows with moving boundaries. Comput Fluids 8(8): doi: 1.116/S45-793(98)57-7 Coton FN, Galbraith RA (1999) An eperimental stud of dnamic stall on a finite wing. Aeronaut J 13(13):9-36. doi: 1.117/ S Dumlupinar E, Murth VR (11) Investigation of dnamic stall of airfoils and wing. Proceedings of the 9th AIAA Applied Aerodnamics Conference; Honolulu, USA. Ericsson LE, Reding JP (197) Unstead airfoil stall review and etension. Proceedings of the 8th AIAA Aerospace Sciences Meeting; New York, USA. Gaitonde A, Fiddes S (1993) A moving mesh sstem for the calculation of unstead flows. Proceedings of the 31st Aerospace Sciences Meeting; Reno, USA. Gerontakos P (4) An eperimental investigation of flow over an oscillating airfoil (Master s thesis). Montreal: McGill Universit. Gharali K, Johnson DA (13) Dnamic stall simulation of a pitching airfoil under unstead freestream velocit. J Fluid Struct 4:8-44. doi: 1.116/j.jfluidstructs Hutchinson SR, Brandner PA, Binns JR, Henderson AD, Walker GJ (1) Development of a CFD model for an oscillating hdrofoil. Proceedings of the 17th Australasian Fluid Mechanics Conference; Auckland, New Zealand. Kim DH, Chang JW (9) Renolds number effects on unstead boundar laer of an oscillating airfoil. Proceedings of the 7th AIAA Applied Aerodnamics Conference; San Antonio, USA. Kramer M (193) Increase in the maimum lift of an airplane wing due to sudden increase in its effective angle of attack resulting from a gust. Washington: National Advisor Committee for Aeronautics.Memorandum No.: TM 678. Lee T, Gerontakos P (4) Investigation of flow over an oscillating airfoil. J Fluid Mech 51: doi: 1.117/S Lee T, Su YY (11) Unstead airfoil with a harmonicall deflected trailing-edge flap. Journal of Fluids and Structures 7(8): doi: 1.116/j.jfluidstructs McCroske WJ (1981) The phenomenon of dnamic stall. Moffett Field: NASA Ames Research Center. Memorandum No.: TM McCroske WJ, Carr LW, McAllister KW (1976) Dnamic stall eperiments on oscillating airfoils. AIAA J 14(1): doi: 1.514/ McCroske WJ, Pucci SL (198) Viscous-inviscid interaction on oscillating airfoils in subsonic flow. AIAA J (): Meador WE, Smart MK (5) Reference enthalp method developed from solutions of the boundar-laer equations. AIAA J 43(1): Panda J, Zaman KBMQ (1994) Eperimental investigation of the flow field of an oscillating airfoil and estimation of lift from wake surves. J Fluid Mech 65: doi: 1.117/S Shih TH, Liou W, Shabbir A, Yang Z, Zhu J (1995) A new k - ε edd viscosit model for high Renold number turbulent flows: model development and validation. Comput Fluid 4(3):7-38. Wang S, Toa Z, Ma L, Ingham D, Pourkashanian M (1) Numerical investigation on dnamic stall associated with low Renolds number flows over airfoils. Proceedings of the IEEE nd International Conference on Computer Engineering and Technolog; Reno, USA. Wernert P, Geissler W, Raffel M, Kompenhans J (1996) Eperimental and numerical investigations of dnamic stall on a pitching airfoil. AIAA J 34(5): doi: 1.514/ J. Aerosp. Technol. Manag., São José dos Campos, Vol.9, N o 1, pp.83-9, Jan.-Mar., 17