Method for designing leading edges and supporting structure provided with said edge

Abstract

The invention relates to a method for producing or designing a leading edge of a lifting structure, wherein starting at the midpoint of the base (0,0), a curve is applied to the profile of the structure, the length L.sub.1 of which is according to the maximum thickness of the NACA section in the base of the profile H.sub.0 in the base and is defined by the equation L.sub.1=0.0510H.sub.0.sup.20.0790H.sub.0+15.5790, and the maximum height of which on the x-axis is located at point L.sub.1/2 and defined by means of the relationship x=0.0137(L.sub.1).sup.1.4944, the shape of said curve being defined by means of the equation: (yy.sub.0)=0.0000000107x.sup.6+0.0000016382x.sup.50.0000794412x.sup.4+0.0010194142x.sup.3+0.0097205322x.sup.2+0.0136993913x, and the rest of the curve being calculated by means of an iterative process according to the above.

Claims

1. A method for producing or designing a leading edge of a lifting structure, the method including the following steps: a. establishing a coordinate system with an x-axis in the base of the profile of the lifting structure and a y-axis orthogonal thereto and extending from the midpoint of the base to the vertex of the structure b. identifying a maximum thickness of a National Advisory Committee for Aeronautics (NACA) section in the base of the profile H.sub.0 and starting to modify the surface profile at coordinate (0,0) by applying a curve, the length L.sub.1 of which, according to the maximum thickness H.sub.0 in the base, is defined by the equation L.sub.1=0.0510H.sub.0.sup.20.0790H.sub.0+15.5790, and the maximum height of which on the x-axis, which is located at point y.sub.1/2, is defined by means of the relationship x=0.0137(L.sub.1).sup.1.4944, the shape of said curve being defined by means of the equation: (yy.sub.0)=0.0000000107x.sup.6+0.0000016382x.sup.50.0000794412x.sup.4+0.0010194142x.sup.3+0.0097205322x.sup.2+0.0136993913x, c. repeating step b using the thickness H.sub.1 of the profile at the height y.sub.1 to calculate the new length L.sub.2such that y.sub.2=L.sub.1+L.sub.2-, the maximum height on the x-axis, which is located at point L.sub.1+L.sub.2/2, being defined by means of the relationship x=0.0137(L.sub.2).sup.1.4944, the shape of said curve being defined by means of the equation: (yy1)=0.0000000107x.sup.6+0.0000016382x.sup.50.0000794412x.sup.4+0.0010194142x.sup.3+0.0097205322x.sup.2+0.0136993913x, and d. repeating step b for additional segments.

2. The method for producing or designing a leading edge of a lifting structure according to claim 1, wherein a depth of impact D, calculated from the leading edge of the profile, ranges from a maximum value at point y=0 to a value equal to zero at point y.sub.max; and wherein D.sub.0 is in the range of 0.25% to 0.31% of the chord length of a first NACA section P.sub.max of the structure to be modified.

3. Aero/hydrodynamic lifting structure provided with a leading edge designed according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) For the purpose of aiding to better understand the features of the invention according to a preferred practical embodiment thereof, the following description of a set of drawings in which the following has been depicted with an illustrative character is attached:

(2) FIG. 1 is a depiction of the profile of the lifting surface and the initial reference points (coordinates) for defining the first and successive curves that define the leading edge of this model.

(3) FIG. 2 shows the profile, elevational, perspective, and side views of a surface according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

(4) The leading edge is designed in several iterative steps. First, a coordinate system is established with an x-axis in the base of the profile of the lifting structure and a y-axis orthogonal thereto and extending from the midpoint of the base of the profile to the vertex of the structure. The curve starts at point (0,0), the length L.sub.1 of which, according to the maximum thickness H.sub.0 in the base, is defined by the equation L.sub.1=0.0510H.sub.0.sup.20.0790H.sub.0+15.5790.

(5) The shape of the curve is obtained by means of the equation:
(yy.sub.0)=0.0000000107x.sup.6+0.0000016382x.sup.50.0000794412x.sup.4+0.0010194142x.sup.3+0.0097205322x.sup.2+0.0136993913x
such that y.sub.0=0

(6) The maximum height on the x-axis of said curve is reached at point y.sub.1/2 and has a value of x=0.0137(L.sub.1).sup.1.4944.

(7) This polynomial function is obtained from studying the caudal fins of sharks in 3D format with the help of Plot Digitizer software, obtaining the values of the points on the x-axis and y-axis of a graph from the image of the curve. The inventors then performed fitting with respect to the polynomial function which better assured a reduction in the coefficient of friction (see below).

(8) Once the first segment of the curve has been calculated, the second one is calculated in a similar manner, where H.sub.1 is the thickness of the profile at the height y.sub.1 at which the first curve ends, such that L.sub.2=0.0510H.sub.1.sup.20.0790H.sub.1+15.5790.

(9) The shape of the curve being that indicated by the equation:
(yy.sub.1)=0.0000000107x.sup.6+0.0000016382x.sup.50.0000794412x.sup.4+0.0010194142x.sup.3+0.0097205322x.sup.2+0.0136993913x

(10) The maximum height on the x-axis in that second segment, which is reached at point L.sub.1+L.sub.2/2, has a value of x=0.0137(L.sub.2).sup.1.4944.

(11) As can be seen in FIG. 2, the elevation of the lifting structure is not modified, although a transverse sectioning thereof will obviously show the difference in depth between different segments.

(12) The depth of impact D measured with respect to the leading edge of the profile is dynamically calculated from a maximum value at point y=0 to a value equal to zero at point y.sub.max. The maximum value of D, i.e., D.sub.0, is in the range of 0.25% to 0.31% of the chord length of the first NACA section P.sub.max of the structure to be modified. Said range is obtained from the most preferred Pmax value of 0.28% to which a correction factor of 10% is applied.

(13) The edge is scalable to any size and can be applied to airborne or waterborne lifting structures.

(14) In the experimental results shown below, the edge of the invention applied to a hydrodynamic stabilizer has shown a reduction in the drag coefficient of 1% compared with an identical model with the smooth leading edge (see Table 1 below).

(15) The hydrodynamic efficiency of the models has been evaluated as follows: a model with an edge according to the aforementioned invention and a model with a smooth edge were reconstructed by means of software. Next, by means of a computational fluid dynamics (CFD) analysis using the ANSYS Fluent software, the drag coefficients (Cd), velocity field, and pressures were compared with the surface the leading edge of which is smooth. The comparison was carried out for two velocities (2 and 5 m/s) and three different angles of attack (0, 15, and 45).

(16) To that end, the CAD file of the hydrodynamic stabilizer was supplied in the IGS/STEP format and the CFD model was generated based on said file. The CAD of the geometry was also supplied in the same format with the smooth leading edge.

(17) The study conditions were first established, defining: a) the geometry of the virtual control volume in which analyses were performed (7 meters long, 3 meters wide, and 1.5 meters tall; b) the most suitable meshing characteristics to be used in the models. In this last case, a mesh sensitivity analysis was included for selecting the ideal number of cells for the purpose of optimizing computational effort.

(18) Thereafter, a layer of cells was established around the hydrodynamic stabilizer which allows capturing the boundary layer around same (with special care in the area of the leading edge) and moderate mesh growth towards the outside was then applied.

(19) Three parameters were analyzed for the influence thereof on the drag coefficient Cd: the velocity, the angle of attack, and the profile of the leading edge.

(20) The drag coefficient is defined as:

(21) $C_d=\frac{2F_d}{.Math.u_{\mathrm{aux}}^2.Math.A}$
where F is the force component in the direction of the flow velocity; is the fluid density, u is the flow velocity, and A is the reference surface which, for submerged hydrodynamic bodies, is the surface in contact with the fluid.

(22) The results of the CFD analysis indicate that the proposed leading edge has a smaller drag coefficient than its smooth counterpart in all the studied configurations and that the average reduction in the resistance of the leading model with a curved edge is 1.1%. Table 1 shows the percentage of reduction in the drag coefficient (Cd) of the stabilizer with a curved profile with respect to the wing with a smooth profile (1(Cd of curved profile/Cd of smooth profile)100) in the different cases of study: two velocities (2 and 5 m/s) and three different angles of attack (0, 15, and 45).

(23) TABLE-US-00001 Angle v (m/s) 0 15 45 1 (Cd of curved 2 3.7% 1.0% 0.6% profile/Cd of smooth 5 0.2% 0.9% 0.2% profile) 100

(24) On the other hand, the velocity fields for the type of curved profile are also more developed and have less impact on the downstream flow than in the case of a smooth profile.