machine design, Vol.6(2014) No.3, ISSN pp

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1 machine design, Vol.6(2014) No.3, ISSN pp Original scientific paper DETERMINATION OF AERODYNAMIC CHARACTERISTICS OF A LIGHT AIRCRAFT USING VISCOUS CFD MODELING Zoran STEFANOVIĆ 1 - Ivan KOSTIĆ 1, * - Olivera KOSTIĆ 1 1 University of Belgrade, Faculty of Mechanical Engineering, Belgrade, Serbia Received ( ); Revised ( ); Accepted ( ) Abstract: The CFD calculations with included viscous effects represent the latest analyses, aimed for the assessment of aerodynamic characteristics of a new light airplane. During the evolution of such an aircraft, appropriate calculation methods should be applied at the different design development stages. The general trend is application of fairly simple, but reliable analytical and semi-empirical methods at the initial stages, combined with simplified - inviscid CFD computational models, and complex viscous CFD analyses at its final design levels. At the present stage of light aviation development, it is assumed that the contemporary design tools for each of those steps should be appropriate enough, so that they actually verify and additionally fine-tune each other's results. Here presented viscous CFD calculations have been based on the application of unstructured meshes with reasonably small number of elements, combined with robust physical model, involving RANS k- SST turbulence treatment, which has enabled analyses at around-critical and post-stall angles of attack. These calculations have provided very useful, both quantitative and qualitative aerodynamic data, while the results for aerodynamic coefficients have shown fair agreements with those obtained by methods at previous design levels Key words: light aircraft, aerodynamic design, viscous CFD calculations, unstructured mesh, RANS k- SST 1. INTRODUCTION This paper is primary focused on the latest stage of the aerodynamic analyses of a new light aircraft (NLA), designed at the Innovation Centre of the Faculty of Mechanical Engineering, University of Belgrade. This is a two-seat, single piston-engine trainer, of metal primary structure, with plastic composite engine cowling, wing and tail tips, aimed for primary and advanced flight training under VFR and IFR conditions, aerobatic training, sport flying, etc. (see Fig. 1.). From the historical perspective, in the initial stages of the aerodynamic computational analyses of NLA, a fairly simple CFD model based on 3D vortex lattice method (VLM) was used [1, 2]. Such inviscid calculation model inherently neglected boundary layer influence and separation effects, so the effectiveness of the flaps and control surfaces were overestimated at moderate and higher deflection angles, and parasite drag components could not be determined. Also, the lift and moment curves could have been determined only in their linear domains, and just induced drag polars could be calculated. In order to overcome these problems and obtain complete final diagrams, the authors have applied the hybrid method approach, developed in two directions. First, to obtain proper effectiveness of flaps and control surfaces within the CFD calculations, the non-linear calibration factors had been successfully derived, from wind tunnel test data of a domestic aircraft of similar category. They also included the additional circulation correction parameters, which took into account the different lifting characteristics and influences of applied slotted flaps, instead of the plane flaps simulated by VLM [3, 4]. Second, the parasite drag components, which can not be obtained by the applied VLM calculations, were determined using reliable analytical and semi-empirical methods. These results have been superimposed with the induced drag values, which VLM successfully calculates for many combinations of flaps and elevator deflections, and angles of attack [5]. On the other hand, these methods also have some inevitable inherent shorcomings: The VLM (also called the "inviscid CFD") omits viscous effects and can not verify analytically determined aerodynamic predictions at arround-critical angles of attack; obtained parabolic polars give minimum drag at zero lift, while actual minimums are at some small positive lift coefficients, etc. Due to that, at the final stage of aerodynamic design, with general aircraft configuration finally "frozen" (Fig. 2.), aerodynamic analysis required the application of the CFD model with includes viscous effects, taking into account both micro and macro-vorticity influences on the flowfield around the airplane. This way, the whole range of angles of attack could have been investigated, including deep stall (beyond critical) angles. Considering control surfaces, in this paper only flaps deflection cases have been considered, and all results have been compared with those obtained by previously applied methods. *Correspondence Author s Address: University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade 35, Serbia, ikostic@mas.bg.ac.rs

2 relevant details have been omitted (like spaces between shock absorber struts and torque arms, etc.). In cases with flaps deflected the accurate 3D geometry of the convergent slot between the single-slotted flaps and the wing structure had to be modeled (more detailed information about applied flaps type can also be found in [3] and [6]). On the NLA, flaps extend from the ailerons to the trapezoidal centerplane segments of the wing (see Fig (3) and Fig. 2.). Fig.2. Loft for CFD calculations, flaps deflection = 30 o Fig.1. The NLA development: (1) initial conceptual design sketch, (2) 3D CAD model, (3) loft for viscous CFD analyses, (4) airframe used in structural tests, and (5) completely equipped full size airplane mockup 2. THE CFD CALCULATION MODEL WITH VISCOUS EFFECTS To generate tree airplane lofts, necessary for the CFD analyses, the CAD model (Fig (2)) has been used, with flaps deflections of = 0 o, = 20 o and = 30 o. All other undeflected control surface gaps on the airplane have been "sealed", in order to reduce the complexity of the analyses, without any substantial penalties considering the overall accuracy of the results. Also, some less The selection of the meshing method and the applied physical model complexity was based on an optimum compromise, dictated by the available hardware resources. After a certain number of test runs, the optimum choice, which gave satisfactory outcomes, was based on the following: (A) Application of a mesh with reasonably small number of elements, in this case of the order of tetrahedral elements for half-model calculations (Fig. 3.), the exact numbers vary slightly for different flaps configurations. It should be noted that for very large and complex configurations, the fine meshes can exceed tens of millions of elements, but even with very powerful hardware, the CPU time for a single run might be measured in hundreds of hours. 72

3 per one angle of attack had been reduced to only 1 2 hours (longer time required for higher angles of attack). 3. DISCUSSION OF THE RESULTS The CFD aerodynamic analyses have been performed for angles of attack [ o ] ranging from negative, to positive post-stall values, at Reynolds number MRe 5.3 calculated with respect to the wing chord, for all flaps positions (to retain full compatibility of the results, although such MRe value would be a bit too high for operational flaps applications). The analyses have provided very useful quantitative and qualitative results Quantitative Assessments Fig.3. Mesh applied for CFD calculations, in the vicinity of the model (B) Application of a very sophisticated calculation method, capable of dealing with separation effects at high angles of attack, fully taking into account compressibility effects (for example, as for transonic 3D flow calculations, although compressibility influence at the NLA's cruising Mach number of M = 0.15 is rather small), etc. Calculation of angles of attack around and beyond critical has become possible after the RANS (Reynolds-Averaged Navier-Stokes) k- SST (Shear- Stress Transport) turbulent model [7], [8], [9] has been applied, so this model has been adopted as standard for all calculations. Since only symmetrical cases have been analyzed, another reasonable simplification was the analysis of half-models, instead of full (also see Fig. 3.), while for the visual presentations, the images were generated using mirroring option with respect to the plane of symmetry. The solution convergence had been boosted by the initial optimum reordering of the mesh domain using the Reverse Cuthill-McKee method [10], the application of FMG - the Full Multi-Grid solution initialization at 4 levels [9], [10], and by active solution steering, applying the automatic optimization of Courant number for the achieved solution convergence stage. It had been assumed that the solution for the given angle of attack has converged when the solution monitors for lift, drag, and pitching moment coefficients show no change (constant values) within the last 100 iterations. By this approach, with the available hardware, the required CPU time for the convergence of the solutions Obtained numerical results can generally be divided into global and detailed, where the most important global assessments imply the lift coefficient C L, drag coefficient C D and pitching moment coefficient C M about the nominal CG (center of gravity) position, for the entire airplane configuration, with flaps at three characteristic positions (retracted, i.e. = 0 o, and deflected to = 20 o and = 30 o ). The results are graphically shown in Fig.'s 4. and 5, and in Tables Fig.4. Diagrams of lift and moment coefficients for three flaps positions Presently it has been assumed that these two flaps positions would satisfy their purpose for take-off and landing applications, on such a light aircraft (although with their electric actuator, any angle can be established). 73

4 flaps deflection, CFD calculations indicate rather abrupt stall, which presents no particular problem at normal flying altitudes. On the other hand, during the landing phase, flaps deflections change it to smooth and sustained stall behavior, specially at = 30 o. This is of primary importance in case of student pilots, whose judgment of ground proximity before touch down might be poor - even when at minimum speed, the airplane will smoothly glide towards the ground. Table 3. Calculated aerodynamic coefficients for = 30 o Fig.5. Polar curves for three flaps positions Table 1. Calculated aerodynamic coefficients for = 0 o [ o ] C D C L C M C L / C D Table 2. Calculated aerodynamic coefficients for = 20 o [ o ] C D C L C M C L / C D Presented results, obtained by CFD analyses, show moderate increase in maximum lift coefficient with flaps deflection. With the applied flaps design and deflections, the configuration fully satisfies the EASA CS-23 regulation requirements considering minimum speeds. The influence of flaps is more important considering the airplane's stall characteristics (Fig. 4.). Namely, without [ o ] C D C L C M C L / C D The assessed maximum value of (C L / C D ) max 11 is quite realistic and satisfactory for light aircraft of metal design (values in the range of are most commonly reported by pilots in operational use, for such airplane category). The detailed numerical results imply that each of the coefficients shown in Tables can be divided into separate contributions of the airplane loft members, also called the zones, or "named selections". Table 4. provides an example of the detailed contributions to the drag coefficient C D = , obtained for = 30 o and angle of attack = 12 o (see also Table 3.). Table 4. Detailed contributions to total drag coefficient, for = 12 o and = 30 o (number of decimal digits is shown as provided by the software) Zone Pressure Viscous Total flap wing nose leg e main leg fuselage horiz. tail vert. tail Total Qualitative assessments The most relevant qualitative characteristics of the airplane design have been obtained using flow pattern (represented by eddy viscosity) and pressure distribution visualization tools (Fig. 6.). 74

5 Fig.6. Examples of flow pattern (eddy viscosity - left), and pressure (right) visualizations, = 6 o and = 0 o In this sense, the CFD post-processing tools provide information which are, at least, of the same relevance as those obtained by the wind tunnel visualization techniques. It must be kept in mind that the applied CFD calculation method had previously been thoroughly tested and verified by comparisons with the relevant experimental data, used for the so called software parameter calibration purposes. Figure 7. shows the flow field pattern development for flaps-retracted configuration, and angles of attack 10 o. The eddy, or vortex generated viscosity visualization gives the most relevant insight in the flow characteristics around, and behind the airplane. Small red colored domains in Fig. 7. (3) indicate initial separation, which occurs close to the wing roots (also see point 3 on C L diagram), at the critical angle of attack of cr = 15 o, where maximum lift coefficient is achieved. One degree more, at = 16 o, the separated flow intensity obviously drastically increases, indicating the airplane s tendency of rather abrupt stall with flaps retracted. Only three degrees beyond critical angle of attack, at = 18 o, the airplane is in a deep stall condition, with very massive separation, which is clearly identified by dark-red and yellow domains, looking like fire coming out of the wings (actually, these are the zones of very intensive air turbulence). Very important is the fact that, at this angle of attack, the bottom side of horizontal tail is out of the turbulent domain (see Fig. 7. (5) right). This contributes to the airplane s natural tendency for stall recovery, by pitching the nose down towards smaller, sub-critical angles of attack, which is very important for training airplanes. Also, up to about = 14 o, the horizontal tail is also out of the turbulent flow generated by the wing (see Fig. 7. (2) left). This way, flow visualization has confirmed the appropriate positioning of the tail. Fig.7. Quite abrupt stall, occurring with flaps retracted 75

6 Figure 8. shows quite different behavior of the airplane in landing configuration, with flaps deflected to = 30 o. The maximum lift coefficient is reached at about = 12 o, and this value remains practically constant until = 15 o (Fig (2) (5)), and after that the airplane drops into a deep stall (Fig (6)). During such sustained stall behavior, the flow separation, which laterally occurs at the wingcenterplane junction (flaps root section, see Fig. 8.), longitudinally slowly moves from the trailing edge, for some 40% chord forward, within 3 o of domain. That keeps most of the wing area still "flyable" in this range, and as already mentioned, helps student pilots to perform smoother landings, considering their limited flying experience during the initial flight training stages. Fig.8. Sustained stall with flaps deflected to = 30 o Fig.9. Pressure distribution, flaps at = 30 o, = 12 o 76

7 This phenomenon can directly be attributed to the applied slotted flaps type. Through the convergent gap, generated by their deflection (again see Fig. 2.), a certain amount of air is accelerated towards the upper flaps surfaces, where the initial stall begins. This air energizes the flow in the domains where it tends to separate, suppresses the abrupt stall tendency, and prolongs the generation of maximum lift. A benefit of the presented visualization procedure, which should be additionally emphasized, is the detection of lateral spanwise position of initial flow separation. It is obvious that in both cases, without and with flaps deflected, it occurs close to the wing root, at the junction of the outer rectangular wing and the trapezoidal centerplane sections. Another requirement for primary flight training airplanes is that the initial stall should appear as close to the wing root as possible. In case of asymmetric stalling conditions, where flow over one side of the wing separates before the other (in sideslip, with sideways wind gusts, etc.), such an airplane will show little tendency to roll-over and fall into a spin, after stall. Figure 9. shows the pressure distribution over the loft with flaps fully deflected, calculated with respect to the ambient atmospheric pressure at the cruising altitude, taken as zero reference. By this approach, the underpressure is quantified by negative, and over-pressure by positive values. The under-pressure, seen as bright yellow domain over the upper wing surface overflows the fuselage in the domain of the canopy, by which this part of the fuselage additionally contributes to a certain extent to the overall lift. It is known that in the presence of wing, the fuselage generates more lift than the same fuselage shape as an isolated body. In the domain of profiled wing tips, which could be treated as very small winglets, the same low pressure extends all the way to the trailing edge, also improving lift in that part of the wing, etc Comparisons with previous results The results calculated by here presented CFD model are compared in Fig.'s 10. and 11. with those obtained by methods applied in previous design steps [3, 4, 5]. Keeping in mind the fact that several principally different calculation methods have been applied during three consecutive design development stages, the obtained results for the NLA s aerodynamic characteristics show quite fair agreements. Lift coefficient curves give very close values for lift curve slopes for all three configurations. Viscous CFD calculations provide more optimistic assessments of maximum lift coefficient values (higher in all three cases than obtained by Datcom). The only principal difference is in stall characteristics unlike Datcom, the viscous CFD has predicted abrupt stall with flaps retracted, and slow and sustained stall with full flaps extended. Considering pitching moment characteristics, the VLM and viscous CFD results coincide well for all three configurations, where slopes of moment curves define the measure of airplane s longitudinal static stability (pitching moment had not been analyzed by Datcom). Finally, certain differences in polar curves are readily expected. Namely, in hybrid method calculations, polars are obtained in simplified parabolic forms of the type C D = A + B CL 2, suitable for performance calculations, which give minimum drag at zero lift coefficient. In reality, minimum drag is achieved at certain small positive lift coefficients, as predicted by viscous CFD calculations. On the other hand, the order of drag values at lift coefficients used in standard operational flying conditions has been mutually confirmed by all methods. Fig.10. Comparisons of lift and moment curves 77

8 while the range of angles of attack had been extended to the post-stall values, compared with methods applied at previous design steps. Calculations have provided a vast scope of very useful quantitative and qualitative data. Results obtained by all methods during the aerodynamic development of NLA, including the latest CFD calculations, have shown fair agreements for practical engineering purposes. This way, the requirement posted in contemporary airplane design, that the calculation tools and methods applied at all different design levels should generally confirm, supplement and fine-tune each-other, has been satisfied. REFERENCES 4. CONCLUSION Fig.11. Comparisons of drag polars Aerodynamic analyses presented in this paper have been performed using a CFD method which takes into account viscous, but also compressibility effects (no matter how small in case of light aircraft). The calculation model uses mesh with a reasonably small number of elements, and a very sophisticated physical model, based on the RANS k- SST equations for turbulence. By this, and applying the half-model analysis, the CPU time for calculations of different angles of attack had been substantially reduced, [1] Bertin, J., Smith, M. (1989). Aerodynamics for engineers, Prentice - Hall International Editions, ISBN: , Englewood Cliffs, NJ [2] Katz, J., Plotkin, A. (1991). Low Speed Aerodynamics - From Wing Theory to Panel Methods, McGraw-Hill, ISBN: , New York [3] Stefanović, Z. & Kostić, (2010). A Vortex Lattice Method Application in Aerodynamic Analysis and Design of Light Aircraft, Proceedings of the Sixth International Symposium about Forming and Designin in Mechanical Engineering, KOD 2010, Palić - Serbia, ISBN: , University of Novi Sad - Faculty of Technical Sciences, pp , Graphic Center GRID, Novi Sad [4] Stefanović, Z.; Kostić, I. & Kostić, O. (2011). Efficient Evaluation of Preliminary Aerodynamic Characteristics of Light Trainer Aircraft, Proceedings of the International Conference of Innovative Technologies, IN-TECH 2011, Bratislava, ISBN: , World Association for Innovative Technologies, pp , Tisk AS, Jaromer [5] Stefanović, Z.; Kostić, I. & Kostić, O. (2012). Primary Aerodynamic Analysis of a New Light Aircraft in Symmetrical Flight Cinfigurations, Proceedings of the Seventh International Symposium - Machine and Industrial Design in Mechanical Engineering, KOD 2012, Balatonfured - Hungary, ISBN: , University of Novi Sad - Faculty of Technical Sciences, Slovak University of Technology in Bratislava - Faculty of Mechanical Engineering, ADECO, pp , FTS Graphic Center GRID, Novi Sad [6] Stefanović, Z. (2005) Aeroprofili (Airfoils), University of Belgrade, Faculty of Mechanical Engineering, ISBN: , Belgrade [7] Wilcox, D. C. (2006) Turbulence Modeling for CFD, DCV Industries, Inc. ISBN , San Diego, California [8] ANSYS FLUENT 14.0 (2011): Theory Guide, ANSYS, Inc., Canonsburg, PA [9] ANSYS FLUENT 14.0 (2011): User's Guide, ANSYS, Inc., Canonsburg, PA [10] ANSYS FLUENT 14.0 (2011): Tutorial Guide, ANSYS, Inc., Canonsburg, PA 78