an author's https://oatao.univ-toulouse.fr/20807 https://doi.org/10.1016/j.jweia.2018.08.008 Fiumara, Alessandro and Gourdain, Nicolas and Chapin, Vincent and Senter, Julien Aerodynamic analysis of a C- class-like catamaran in simplified unsteady wind conditions using LES and URANS modeling. (2018) Journal of Wind Engineering and Industrial Aerodynamics, 180. 262-275. ISSN 0167-6105 Aerodynamic analysis of a C-class-like catamaran in simplified unsteady wind conditions using LES and URANS modeling Alessandro Fiumara a,*, Nicolas Gourdain b, Vincent Chapin b, Julien Senter c a Assystem Technologies and ISAE-Supaero, Toulouse, France b ISAE-Supaero, Toulouse, France c Assystem Technologies, Toulouse, France 1. Introduction shapes in unsteady flow conditions, like flapped wings, and are largely exploited by insects and flying animals to enhance their flying capa- The interest for wingsails has grown since their introduction on bilities (Maxworthy, 1979; Ellington et al., 1996; Muijres et al., 2008). America's Cup catamarans in 2013. Wingsails enhance the yacht per- On bat wings, the increase in lift due to the LEV is of 40% (Muijres formance thanks to the achievement of larger lift-to-drag ratio and et al., 2008). LEVs are also exploited in the aeronautic field to increase maximum lift coefficients with respect to soft sails. However, the the lift of delta wings. In the naval domain, (Viola and larger aerodynamic forces acting on the wingsail can compromise the Arredondo-Galeana, 2017), performing PIV experimental tests, stability of the yacht during navigation especially in unsteady condi- observed and analyzed the formation of LEV on a soft spinnaker tions, e.g. during maneuvers or under the effect of gusts. Since this estimating the LEV contribution to the sail global lift at more than instability can easily bring the yacht to capsize, a research of the effect 10%. of the flow unsteadiness is necessary to prevent the occurring of such The aim of this study is then to detail the influence of the wind un- an event. steadiness on the flow physics and on the wingsail performances of a C- Though similar to aeronautical wings (two-element slotted wing), class catamaran-like geometry. Two complementary numerical ap- wingsailshavesomespecific features (e.g. the use of symmetric air- proaches have been exploited, LES and URANS with two different foils, the low Reynolds number as well as its use in highly unsteady solvers. The LES is indeed more adapted to compute separated flow in flow conditions) that complicate flow analysis with respect to the highly turbulent environments. However, due to the huge computational aeronautical domain. The aerodynamic studies on wingsails are indeed requirements, LES is used, even in the aeronautical domain, in the not numerous with some experimental campaigns performed to char- analysis of multi-element wings only on extruded airfoil geometries acterize the wingsail performance without focusing on the flow (Deck, 2005), (Deck and Laraufie, 2013) rather than on full physics around the rig (Magherini et al., 2014), (Blakeley et al., 2012) three-dimensional wings. In the naval domain, except the DES approach and (Blakeley et al., 2015)). (Fiumara et al., 2016a) carried out wind used by (Viola et al., 2014) to analyze high separated regions on soft sails, tunnel tests analyzing the flow physics, particularly in the wingsail slot LES has never been exploited for the analysis of a full three-dimensional zone, deepening the study of (Chapin et al., 2015). (Fiumara et al., wingsail. The comparison between the LES and URANS solutions on a 2016b) also described the strong influence of the slot size on the stall given wingsail geometry can give an indication of the actual capabilities behavior of a scale wingsail performing URANS simulations. All these of the URANS to predict the flow influence on a wingsail in unsteady studies were however performed in steady flow conditions without wind conditions. taking into account the sea boundary layer and wind unsteadiness. The flow variations can lead to significant modifications of the operating 2. Numerical methodology point of the slot and hence of the aerodynamic forces acting on the wingsail. One of the causes of the increase of the aerodynamic forces is 2.1. Geometry the onset of leading-edge vortices (Anderson, 2005), (Breitsamter, 2008). These flow structures typically take place over thin airfoil A C-class hull catamaran was designed based on the overall length * Corresponding author. E-mail addresses: afi[email protected], afi[email protected] (A. Fiumara), [email protected] (N. Gourdain), [email protected] (V. Chapin), [email protected] (J. Senter). https://doi.org/10.1016/j.jweia.2018.08.008 Nomenclature k Turbulent kinetic energy (m2/s2) L.E. Leading edge α Wingsail local angle of attack () LEV Leading Edge Vortex δ Flap deflection angle () m Exponent of the power law for velocity profile AW Apparent Wind o Overlap of the flap with the main AWA Apparent Wind Angle () Re Reynolds number AWS Apparent Wind Speed (m/s) Rec2 Reynolds number referred to the flap chord BS Boat speed (m/s) S Wingsail surface (m2) Cμ Momentum coefficient SC Stall cell c Total chord of the wingsail (m) t Time (s) c1 Main chord (m) T.E. Trailing Edge c2 Flap chord (m) Tu Turbulence intensity CD Drag coefficient TW True Wind CF Skin friction coefficient TWA True Wind Angle ( ) CL Lift coefficient TWS True Wind Speed (m/s) Cp Pressure coefficient u, v, w Velocity components on the steady wind axis (m/s) þ F Non-dimensional wind frequency (fgc2/V∞) V Velocity magnitude (m/s) fg Wind frequency (Hz) V∞ Freestream velocity magnitude (m/s) g Gap dimension of the slot (mm) WG-URANS URANS simulation without wind unsteadiness G-LES LES simulation in unsteady wind x, y, z Axes of the wingsail reference system G-URANS URANS simulation in steady wind xs,ys,zs Axes of the sea reference system H Wingsail height (m) xrot x-coordinate of the flap rotation axis Hc Catamaran hull height (m) xw,yw,zw Steady wind axes Hh Hull elevation from the sea surface (m) yF Transversal distance between the flap L.E. and the main T.E href Reference height of the atmospheric boundary layer (m) z* Normalized height position z/H and beam dimensions imposed by the class rule (Fig. 1). The trampoline Cup Class Rule, 2015). These wingsails have similar design and features was also modeled with a solid platform. The rig is the two-element to the ones used on the C-class catamarans. The flap deflection of 35 is a wingsail analyzed by (Chapin et al., 2015) and scaled in a way to ach- setting used by sailors during navigation along the downwind leg. ieve a surface close to the maximal one imposed by the class rules 2 (27.87 m ). 2.2. Computation domain The gap distance between the trampoline and the wingsail is of 0.03H. Usually, sailors introduce a twist to adjust the heeling moment of A box domain with a squared section was used for the numerical the wing to the wind conditions. However, since the wingsail twist is analyses. The side length is of 47croot while the height is of 2H (Fig. 2). fi variable according to sailing conditions and considering the dif culty to The catamaran was located in the middle of the box domain with the fi nd a twist distribution along the wingspan compatible with real utili- hull rotated with respect to the inlet wall normal of À41.4 . Port side is zation, it was decided to use an untwisted wingsail to reduce the number then oriented toward the inlet wall. The wingsail is instead rotated by fl fl of parameters in the geometry. The ap is also not twisted and de ected À8 with respect to the inlet wall normal. Furthermore, the hull of the δ by an angle ( )of35 after a rotation about the hinge line located at 90% catamaran is not in contact with the box bottom surface, but a distance of of the main root chord and parallel to the main T.E. The gap (g) between Hh ¼ 0.94Hc was imposed to simulate the catamaran elevation from the fl fl the two elements is of 0.6%c1root when the ap is not de ected. The sea surface introduced by the hydrofoils. geometrical values of the gap and the hinge line position were drawn on The wingsail and wind reference frames are represented in Fig. 3 the wingsail schemes in the America's Cup AC 50 class rules (America's together with the scheme of the catamaran. The wingsail reference frame (x, y, z) has the origin located on the L.E. of the wing root section with the x-axis directed towards the T.E. and the z-axis directed upwards. The wind reference frame (xw, yw, zw) has the origin translated of À2.65Hc in the z-direction (zw ¼ z À 2.65Hc). The xw and yw axes are respectively orthogonal and parallel to the apparent inlet wall of the box domain (i.e. Fig. 1. Geometry of the catamaran with its main parameters. Fig. 2. C-class catamaran inside the computation domain. Table 2 Apparent wind characteristics at different heights. zw (m) z* ¼ z/H TWS (m/s) AWS (m/s) AWA ( ) α ( ) 0.000 À0.112 0 6.17 0 À33.4 1.000 À0.026 2.62 5.19 24.8 À8.6 1.300 0.00 2.74 5.17 26.1 À7.3 4.195 0.250 3.33 5.12 32.6 À0.8 7.090 0.500 3.63 5.12 36.0 2.6 9.985 0.750 3.85 5.13 38.4 5.0 12.880 1.000 4.01 5.15 40.3 6.9 15.000 1.183 4.11 5.16 41.4 8.0 Fig.