Calculaton of Aerodynamc Characterstcs of NACA 2415, 23012, 23015 Arfols Usng Computatonal Flud Dynamcs (CFD) Hmanshu Parashar Abstract A method of solvng the flow over arfols of Natonal Advsory Commttee for Aeronautcs (NACA) seres - 2415, 23012 & 23015 s proposed usng the assstance of commercal CFD package s such as Gambt and Fluent. The flow was obtaned by solvng the steady-state governng equatons of contnuty, momentum, and energy conservaton combned wth standard k- turbulence model. NACA arfols wth angle of attack from -15 to +15 degrees wth an nterval of 5 degrees are analyzed. Calculatons were made for constant ar velocty alterng only the angle of attack for each arfol. Varous meshes were generated to check grd dependency. The aerodynamc characterstcs of the arfols calculated n Fluent software by the frst-order quantty wth two dmensonal double precson solver. It s shown that the effects on the aerodynamc characterstcs such as lft and drag coeffcents of arfols are assocated wth ther shapes. The NACA 4 dgt and 5 dgt arfols behaves dfferently n same flow felds whch n turn change the lft, drag and moment of arfols. Index Terms Aerodynamcs characterstcs, NACA arfols, Lft and Drag, Turbulence model I. INTRODUCTION The flow around arfols or cascade of arfols s known to be hghly three dmensonal, unsteady, & turbulent, makng the modelng of the flow very demandng n terms of computatonal resources. Some of the mportant factors to be consdered n the analyss of the flow are the adverse pressure gradent and the presence of hgh turbulence stress. When smulatng the flow over arfols, transton from lamnar to turbulent flow plays an mportant role n determnng the flow features and n quantfyng the arfol performance such as lft and drag. Hence, the proper modelng of transton, ncludng both the onset and extent of transton wll defntely lead to a more accurate drag predcton. If a number of flow stuatons are to be consdered, a number of physcal geometres are to be created and then tested. Ths ncreases tme and expense of testng. The development of hgh speed dgtal computng durng the last few decades has brought the great mpact on the way a physcal stuaton s modeled and analyzed. Speed of modern computng and prncples from the scence of flud mechancs, heat transfer, and combuston are appled to engneerng desgn practce. Numercal methods have emerged as a powerful method and have overcome the restrctons n both expermental and analytcal methods. They solve the dscretzaton of the governng mathematcal equatons n a way such that the numercal solutons can be obtaned. Ths approach forms the core of Computatonal Flud Dynamcs. II. NUMERICAL METHOD AND TURBULENCE MODELING In the present study the numercal smulaton was carred out usng the fnte volume based CFD code FLUENT for solvng the Reynolds-averaged Naver Stokes (RANS) equatons. The mass conservaton equaton, the full Naver stokes equaton, and energy equatons are the governng equatons used n ths study. The equaton for conservaton of mass or contnuty equaton can be wrtten as follows: Contnuty Equaton Equaton (1) s the general form of the mass conservaton equaton and s vald for ncompressble as well as compressble flows. D Dt x 0 Momentum Equaton Conservaton of momentum s descrbed by Equaton (2). P g t x V I Where U II x III IV 2 3 x k k (1) (2) Manuscrpt receved March 16, 2015. Frst Author name, Hmanshu Parashar, Student of Internatonal Masters n Turbulence, École Centrale de Llle, France I: Local change wth tme 610
II: Momentum convecton III: Surface force IV: Molecular-dependent momentum exchange (dffuson) V: Volume force Energy Equaton Conservaton of energy s descrbed by Equaton (3). 2 T T T c c U P (3) 2 t I Where II I : Local energy change wth tme II: Convectve term III: Pressure work IV: Heat flux (dffuson) V: Irreversble transfer of mechancal energy nto heat The second order upwnd scheme has been used to solve the flow varables. The pressure based Naver-Stokes solver s used for the analyss of the problem. The smplest "complete models'' of turbulence are two equaton models n whch the soluton of two separate transport equatons allows the turbulent velocty and length scales to be ndependently determned. The standard k- model falls wthn ths class of turbulence model and has been used n present case. III. PHYSICAL MODEL AND BOUNDARY CONDITIONS The 2-Dmensonal arfol geometres were created n CAD (CATIA) envronment usng the control pont of the camber profle and meshng was done n Gambt software. A Ptch - Chord rato of 0.5 C was mantaned n all cases. The arfol s assumed to have a chord length of 1.0 meters (all dmensons are n standard SI system of unts), wth the front-most part of the arfol at (0, 0, and 0) and the tralng edge at (1, 0, 0). III IV V Fg. 1 Computatonal Doman IV. GRID GENERATION In order to adequately resolve the boundary layer along the arfol wall, grd ponts are clustered near the wall. Far away from walls, where the flow does not have large velocty gradents, the grd ponts are kept a bt apart. A hybrd grd was used n ths problem. An unstructured quad-pave mesh was generated over arfol. Grd dependency was checked and found there was no change n result when total no of cells were around 15,000. The governng equatons are dscretzed and solved at these grd ponts. V. RESULTS The numercal smulatons are performed and results are reported for NACA 2415, 23012, 23015 arfols. The angle of attack s n degrees for all the fgures. Fg. 2-4 shows the varaton of coeffcent of lft wth angle of attack. It can be seen that C l vares lnearly wth α over a large range of angle of attack. The lft s showng a negatve trend as α s gong below 0 degrees and a upward trend as angle of attack s ncreased above 0 degrees for all three arfols. When α = 0, there s stll a postve value of C l, that s, there s stll some lft even when the arfol s at zero angle of attack to the flow. Ths s due to postve camber of the arfol. NACA 2415 arfol gves the maxmum lft compared to the NACA 23012 and 23015 arfols rrespectve of α. NACA 23012 and 23015 arfol shows more or less same characterstcs. The computatonal doman extends far upstream of the arfol where the boundary condton are defned as velocty nlet and outlet was defned as pressure outlet. Inlet velocty was set to 50 m/s and outlet pressure was set to atmospherc pressure. The perodc boundary condtons were defned on lower and upper sde of the doman. On all the sold boundares, the condtons nvoked are the No-slp condton and heat flux normal to the wall, q = 0. Computatonal doman s shown n fg 1. 611
Lft and drag vares wth the angle of attack. In fact, drag s the prce for generatng the lft. Thus, although t s desrable to obtan as much lft as possble, ths cannot be done wthout ncreasng the drag. It s therefore necessary to fnd the best compromse. Fg. 5-7 represents the plot of coeffcent of drag and ther correspondng angle of attack. The maxmum or peak drag s encountered when α= 0. Drag dmnshes as α ncreases or decreases. NACA 23015 and 2415 arfol have same drag when α = 0. NACA 23012 arfol have least drag at extreme values of angle of attack than that of the NACA 2415 and 23015. Fg. 2 C l Vs α Plot for NACA 2415 Fg. 5 C d Vs α Plot for NACA 2415 Fg. 3 C l Vs α Plot for NACA 23012 Fg. 6 C d Vs α Plot for NACA 23012 Fg. 4 C l Vs α Plot for NACA 23015 612
Fg. 7 C d Vs α Plot for NACA 23015 The "drag polar" specfes the drag coeffcent C d for a gven lft coeffcent C l (and vce versa). Ths s often the most mportant part of the results and can be used to fnd the best clmb or snk rate as well as the optmum glde angle deally possble wth the arfol. The reason for usng the drag polar format s that when evaluatng the aerodynamc performance of an arfol, the α values are not really relevant. All that matters s the drag and how t compares to lft. The drag polar format compares these drectly, and hence summarzes the most mportant features of the arfol s drag characterstcs n one plot. The drag polar curve s shown n fg. 8-10 for NACA arfols. These two parameters are of paramount mportance snce they are used to calculate aerodynamc effcency. NACA 23012 arfol has least drag compare to NACA 2415 and 23015 when C l = 0. The NACA 23012 has maxmum C l at the least expense of mmum drag.hence, ts much better than rest two arfols. Fg. 9 C l Vs C d Plot for NACA 23012 Fg. 10 C l Vs C d Plot for NACA 23015 The lft-drag rato reaches ts maxmum at 0 degrees angle of attack, meanng that at ths angle we obtan the most lft for the least amount of drag. VI. CONCLUSION Fg. 8 C l Vs C d Plot for NACA 2415 Numercal smulatons have been carred out for NACA 2415, 23012 & 23015 arfol seres. The smulaton captures all the mportant features of the flow. A specal care was taken to buld good qualty mesh wth grd clusterng to capture flow separaton and adverse pressure gradent as much closely as possble. At a fxed freestream velocty wth varyng angle of attack rangng from -15 to +15 degrees, two man aerodynamc parameters C l and C d are calculated and plotted for all three NACA arfols. A far agreement s acheved between the avalable theory from Abbott et al and numercal smulaton results for all the NACA arfol. 613
ACKNOWLEDGMENT I am greatly ndebted to my esteemed nsttuton Malla Reddy College of Engneerng and Technology, Hyderabad, Inda. I extend my grattude for the assstance provded by department faculty. The prvlege of workng on ths proect usng CAD/CFD lab facltes remans memorable. REFERENCES [1] Abbott IH, Von Doenhoff AE (1959). Theory of Wng Sectons. Dover Publshng, New York. [2] Bacha WA, Ghaly WS (2006). Drag Predcton n Transtonal Flow over Two-Dmensonal Arfols, Proceedngs of the 44th AIAA Aerospace Scences Meetng and Exhbt, Reno, NV. [3] Badran O (2008). Formulaton of Two-Equaton Turbulence Models for Turbulent Flow over a NACA 4412 Arfol at Angle of Attack 15 Degree, 6th Internatonal Colloquum on Bluff Bodes Aerodynamcs and Applcatons, Mlano, 20-24 July. [4] Fluent Inc. (2006), Fluent 6.3 User s Gude. [5] Fluent Inc.(2007), Gambt 2.4 User s Gude [6] Johansen J (1997). Predcton of Lamnar/Turbulent Transton n Arfol Flows. Rsø Natonal Laboratory, Rosklde, Denmark. [7] Menter FR (1994). Two-Equaton Eddy-Vscosty Turbulence Models for Engneerng Applcatons. AIAA J., 32: 1598-1605. [8] McCroskey WJ (1987). A Crtcal Assessment of Wnd Tunnel Results for the NACA 0012 Arfol. U.S. Army Avaton Research and Technology Actvty, Nasa Techncal Memorandum, 42: 285-330. 1) Frst Author: Hmanshu Parashar has done Aeronautcal Engneerng from Malla Reddy College of Engneerng and Technology, Hyderabad, Inda n the year 2010. He has worked as a Sr. CFD-Engneer n CSM Software Pvt. Ltd., Bangalore, Inda from 2010-2014. Presently he s pursung Masters n Turbulence from École Centrale de Llle, France. 614