ANALYSIS OF FORCE DYNAMICS FOR AIRFOIL IN THE WAKE OF DIFFERENT GRIDS

Transcription

1 ANAYSIS OF FORE YNAMIS FOR AIRFOI IN THE WAKE OF IFFERENT GRIS Mhammad Ramzan hr*, Abdl atif Manganhar**, Shahid Hssain Siyal***, Khalid Hssain Solangi**** ABSTRAT This paper presents the lift and drag force dynamics for an airfoil FX 79-W-151A nder trblent wind inflows generated with fractal and classical sqare grids. The force measrements were performed in a wind tnnel in the wake of these grids. The measred force dynamics is analyzed sing classical averaging procedre and a angevin approach. The comparison of lift and drag dynamics achieved in the wake of fractal and classical sqare grids, sggests that the fractal sqare grid contribtes significantly extended lift and drag dynamics in terms of standard deviation from the mean as well as short-time local dynamics extracted by angevin approach. Even at low trblence level, the fractal sqare grid wake contribtes mch higher force flctations than the classical sqare grids. Key words: Wind tnnel measrements, force dynamics, airfoil, trblent inflows, fractal sqare grid, classical sqare grid. 1. INTROUTION Wind trbines operate in dynamic wind fields, which contribte dynamic forces on wind trbine rotor blades. These blades are designed sing airfoils that are commonly characterized by static lift and drag forces at fix angles of attack (AOAs) nder steady low-trblence flow [1, 2, 3]. However, in reality, most of the time, wind trbines enconter trblent inflows de to grond bondary layer effects [4, 5, 6]. The trblent inflows case fast variations in AOA [7], which reslt sbstantial enlargement in lift and well-known dynamic stall effect [8, 9, 10], leading to large and rapid changing forces on the airfoil. In order to investigate the dynamic behavior of forces on airfoils, different grids are designed to generate mltiscale trblent inflows in wind tnnels. These mainly inclde the classical grids [11, 12, 13] and the fractal grids [14]. Recently, a type of an active grid has also been reported for mlti-scale trblence generation [15]. The classical grids se rectanglar arrays of bars and fractal grids se geometric patterns repeated at smaller scales. The type of fractal sqare grid is experienced to generate more similar wind flctations to atmospheric wind than the classical grids [16, 17]. The fractal sqare grid prodces small scale wind statistics similar to those observed in open-air [16]. The aim of this contribtion is to provide insight on force dynamics achieved in the wake of fractal sqare grid and the classical sqare grids, in particlar the comparison of local force flctations on short-time scales (highfreqency) obtained with these grids. The paper is organized as follows. Section 2 describes the measrement details and the analysis approach applied. Section 3 presents the comparison of reslts from the described grids. The last Section 4 concldes the otcome. 2. METHOOOGY 2.1. Experimental ata The force measrements were performed in a wind tnnel for an airfoil FX 79-W-151A at University of Oldenbrg Germany [16]. The airfoil was installed in vertical position in closed-loop test section of wind tnnel as shown in Figre 1. The test section has dimensions of 1 m wide, 0.8 m high and 2.6 m long. The mean wind inflow velocity was 50 m/s approximately. The airfoil chord length was 0.2 m leading to Reynolds nmber of 7x10 5. Figre 1: View of the wind tnnel test section. The black arrows indicate the installed position of strain gage force sensors and the vertical airfoil [16]. * Ph researcher, ForWind-entre for Wind Energy Research, University of Oldenbrg, Germany. ** Assistant Professor, Qaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Pakistan. *** Ph Researcher, Royal Institte of Technology (KTH), Stockholm, Sweden. **** Ph Researcher, University of Malaya, Kala mpr, Malaysia. QUAI-E-AWAM UNIVERSITY RESEARH JOURNA OF ENGINEERING, SIENE & TEHNOOGY, VOUME 13, No. 2, JU-E

2 The trblent inflows were generated sing fractal and classical sqare grids as shown in Figre 2. The sed grids inclde; a 5-cm sqare mesh grid, a 10-cm sqare mesh grid and a fractal sqare grid yielding the trblence intensity of 3.6%, 6.7% and 4.6%, respectively. The trblence intensity is estimated sing the relation. σ T i = (1) Where is the mean wind inflow and σ the standard deviation of wind inflow. All three (two different mesh size classical sqare grids of type as shown in Figre 2 and one fractal sqare grid as shown in Figre 2) grids had a blockage ratio of 25%. Figre 2: Types of grids. lassical sqare mesh grid and fractal sqare grid. The forces were measred for AOAs 0 o -25 o at sampling freqency of 1 khz sing two strain gage force sensors installed at the end points of airfoil in span-wise direction; see Figre 1. The sensors measre the forces parallel and perpendiclar to the wind inflow, which represent the drag and lift forces, respectively. Before measrements, the force sensors were calibrated via balances Analysis Approach The measred forces are analyzed sing classical averaging method and a angevin approach. The approaches are applied on lift and drag force coefficients obtained sing the relations [17] Where F = q. A F = q. A F and (2) (3) F are the measred lift and drag forces respectively, q the dynamic pressre of wind inflow and A the airfoil area. The classical averaging procedre is applied on and time series at each AOA to estimate the respective mean and standard deviation. Frther, to extract more detailed information on force dynamics from this complex trblence driven system, a angevin approach [18] is applied in the form of drift fnction. The drift fnction in angevin approach is a deterministic fnction, also known as first Kramers-Moyal coefficient, which provides fll response map of local dynamics of a system. The angevin approach based on drift fnction reads [19, 20, 21]. ( α) ( X ( t+ τ) X ( t) ) ( ) X, = lim τ 0 X t = X, α τ Where X represents the or (4), and α the fix AOA. The approach is applied directly on and times series at each AOA to evalate the respective mean time derivative of and time series. Additionally, for better nderstanding of meaning of drift fnction and comparison of strength in local dynamics in each grid case, a drift potential is estimated sing the relation [17]. (, ) = X (, ) 0 φ X α X α dx Eqation (5) describes the potential in local force dynamics of a system. 3. RESUTS The lift and drag force measrements performed in the wake of fractal and classical sqare grids are analyzed sing the approaches described in Section 2.2. The reslts are presented in terms of static and crves with local dynamics at each AOA. Here, Figre 3 shows the reslts for fractal sqare grid, Figre 4 for 5-cm sqare grid and Figre 5 for 10-cm sqare grid. In Figres, the mean (solid line) and standard deviation (dashed lines) for and are obtained sing classical averaging method, whereas the short-time local dynamics (red and green arrows with black crosses) by angevin approach sing Eqation (4). The drift potential is achieved throgh Eqation (5) for AOA 24 o in each case. The AOA 24 o represents the deep stall regime, which gives better nderstanding of drift potential with wide local force dynamics compared to drift potential at smaller AOAs. omparing the reslts from Figres 3, 4 and 5, the grid with higher trblence level (10-cm sqare grid) shows an increase in maximm with slight shift to higher AOAs. Similar behavior was observed for measrements on NAA airfoil by Amandolése and Széchényi [22], and on FX 79-W-151A airfoil by Schneemann et al. [17]. The flctations in terms of standard deviation are very small in case of both classical sqare grids in pre-stall regime and rise gradally as stall (5) QUAI-E-AWAM UNIVERSITY RESEARH JOURNA OF ENGINEERING, SIENE & TEHNOOGY, VOUME 13, No. 2, JU-E

3 regime starts. In comparison to this, the standard deviations in case of fractal sqare grid are significantly higher in both regimes despite the lower trblence level and lower maximm lift than the 10-cm sqare grid case. The short-time local dynamics based on angevin approach also show mch higher flctations with larger potential in case of fractal sqare grid than both the classical sqare grids. The angevin crves consisting of stable fix points (black crosses where drift fnction is zero) of the local dynamics match almost perfectly with respective mean crves in all three cases. Again, comparing the case of from Figres 3, 4 and 5, the grid with lower trblence level (5-cm sqare grid) shows an increase in maximm at higher AOAs compared to fractal and 10-cm sqare grid cases. However, the standard deviation in pre-stall regime is slightly lower than both the fractal and 10-cm sqare grids de to its low trblence intensity. The standard deviations in the wake of fractal sqare grid in stall regime are mch higher than the classical sqare grids. Similarly, as in case, the short-time local dynamics of shows remarkable flctations with larger potential in case of fractal sqare grid compared to both classical sqare grids. The angevin crves consisting of stable fix points of the local dynamics have almost absolte matching with respective mean crves. Figre 3: Static and crves with local dynamics measred in the wake of fractal sqare grid. verss AOA, where solid ble line represents the mean crve and dashed lines the standard deviation from mean. The red arrows indicate the deterministic increase in and green the deterministic decrease in towards the stable points; the black crosses, where drift fnction is zero. The black arrow points ot the potential in drift fnction for AOA 24 o. verss AOA and same explanation like applies for. Figre 4: Static and crves with local dynamics measred in the wake of 5-cm sqare mesh grid. verss AOA, where solid ble line represents the mean crve and dashed lines the standard deviation from mean. The red arrows indicate the deterministic increase in and green the deterministic decrease in towards the stable points; the black crosses, where drift fnction is zero. The black arrow points ot the potential in drift fnction for AOA 24 o. verss AOA and same explanation like applies for. QUAI-E-AWAM UNIVERSITY RESEARH JOURNA OF ENGINEERING, SIENE & TEHNOOGY, VOUME 13, No. 2, JU-E

4 The comparison sggests that the trblent inflow generated with fractal sqare grid contribtes remarkable extended and dynamics in terms of standard deviation from the mean as well as short-time local dynamics than the classical sqare grids even at low trblence intensity. Figre 5: Static and crves with local dynamics measred in the wake of 10-cm sqare mesh grid. verss AOA, where solid ble line represents the mean crve and dashed lines the standard deviation from mean. The red arrows indicate the deterministic increase in and green the deterministic decrease in towards the stable points; the black crosses, where drift fnction is zero. The black arrow points ot the potential in drift fnction for AOA 24 o. verss AOA and same explanation like applies for. 4. ONUSIONS The and dynamics measred in the wake of fractal and classical sqare grids have been analyzed sing classical averaging method and a angevin approach. The comparison sggests that the fractal sqare grid wake contribtes remarkable extended and dynamics in terms of standard deviation from the mean and shorttime local dynamics extracted by angevin approach. Even at low trblence level, the fractal sqare grid wake contribtes mch higher force flctations than the classical sqare grids. Frther, the variation of AOA has significant effect on and dynamics. AKNOWEGEMENTS Athors wold like to thank Jörge Schneemann for access to his measred data. REFERENES [1] W. A. Timmer and R. P. J. O. M. van Rooij. Smmary of the elft University wind trbine dedicated airfoils. Jornal of Solar Energy Engineering, Vol. 125, No. 4, pp , [2] P. Fglsang, K. S. ahl and I. Antonio. Wind tnnel tests of the Risø-A1-18, Risø-A1-21 and Risø-A1-24 airfoils. Scientific report Risø-R-1112(EN), Risø National aboratory, Jne QUAI-E-AWAM UNIVERSITY RESEARH JOURNA OF ENGINEERING, SIENE & TEHNOOGY, VOUME 13, No. 2, JU-E [3] P. Fglsang, I. Antonio, K. S. ahl and H. A. Madsen. Wind tnnel tests of the FFA-W3-241, FFA-W3-301 and NAA airfoils. Scientific report Risø-R- 1041(EN), Risø National aboratory, ecember [4] J. Vindel,. Yage and J. M. Redondo. Strctre fnction analysis and intermittency in the atmospheric bondary layer. Nonlinear Processes in Geophysics, Vol. 15, pp , [5] N. Troldborg, J. N. Sørensen, R. Mikkelsen and N. N. Sørensen. A simple atmospheric bondary layer model applied to large eddy simlations of wind trbine wakes. Wind Energy, [6] J.. Kaimal and J. J. Finnigan. Atmospheric Bondary ayer Flows Their Strctre and Measrement. Oxford University Press, pp. 287, New York, [7] B. Stoevesandt and J. Peinke. hanges in Angle of Attack on Blades in the Trblent Wind Field. In Proceedings of the EWE, [8]. M. Eggleston and F. S. Stoddard. Wind trbine engineering design. Van Nostrand Reinhold ompany, New York, USA, [9] J. G. eishman. Principles of Helicopter aerodynamics- ambridge Aerospace Series (2nd edn). ambridge University Press, ambridge, [10] G. Wolken-Möhlmann, P. Knebel, S. Barth and J. Peinke. ynamic lift measrements on a FX 79-W-151A airfoil via pressre distribtion on the wind tnnel walls. Jornal 4

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