WO2023242858A1

WO2023242858A1 - "external attachment to increase aerodynamic efficiency of a wing applicable for aeroplanes, turbines, and fans"

Info

Publication number: WO2023242858A1
Application number: PCT/IN2023/050381
Authority: WO
Inventors: Rinku Mukherjee; Aritras Roy
Original assignee: INDIAN INSTITUTE OF TECHNOLOGY MADRAS (IIT Madras)
Priority date: 2022-06-16
Filing date: 2023-04-20
Publication date: 2023-12-21

Abstract

The present invention discloses wing (100) having improved aerodynamic performance characteristics. The wing (100) with an airfoil section (102), which may be symmetric/cambered comprises an external skin (104) attached to a leading edge (102-1) for morphing at least some airfoils (102) along wing span, and a plurality of micro fiber composite (MFC) strips (202) attached at pre-defined locations of the external skin (104). Electrical actuation of one or more of the plurality of MFC strips (202) changes at least one of a curvature of the external skin (104) with respect to the leading edge (102-1) and lift of the wing (100), thereby changing an aerodynamic shape of the airfoil (102) for controlling flow separation at pre-defined angles of attack (α) of the wing (100).

Description

EXTERNAL ATTACHMENT TO INCREASE AERODYNAMIC EFFICIENCY OF A WING APPLICABLE FOR AEROPLANES, TURBINES, AND FANS FIELD OF INVENTION [0001] The present invention generally relates to modifying the shape of a 3- dimensional wing. More specifically, this is done using a simple external attachment, almost like a prosthetic, which improves its aerodynamic performance. BACKGROUND OF THE INVENTION [0002] Aircrafts typically include a variety of devices for improving their aerodynamic performance during different phases of flight. For example, an aircraft may include leading edge devices mounted on leading edges of its wings and which may be deployed during takeoff, approach, and/or landing phase of a flight, and may be retracted during cruise phase of the flight. Some of these devices are used at landing and take-off, where an aircraft operates at the maximum possible lifting force and hence very close to the maximum allowable angle of attack. The corresponding drag force is also maximum, which is beneficial during landing. For take-off, on the other hand, other movable parts of an aircraft are also used to overcome the high drag to utilize the high lift. [0003] The wing of an aircraft may be adapted to modify its shape, providing it with increased adaptability to various air flow conditions. As an example, during its flight regime, an aircraft’s wings need to accommodate two extreme conditions. During cruise, lift-to-drag ratio of the aircraft should be maximized to allow flying for the longest range. During landing, a significantly higher drag is required to bring the aircraft to a standstill within the length of a runway. In order to satisfy these disparate requirements of the high lift-to-drag ratio at cruise and the high maximum lift coefficient at landing, aircrafts are generally equipped with high lift devices such as leading and trailing edge flaps and/or slats. However, such high lift devices rely heavily on complex mechanisms that consist of thousands of individual parts and heavy actuators to displace and/or rotate the whole assembly. [0004] Examples of aerodynamic applications of wings include aircraft wings, rudders, rocket fins, turbine blades, fan blades, etc. Any given shape of a wing has a working limit beyond which it fails or its efficiency is not maintained. Such a wing is also designed to get maximum benefits within the set limits. However, flow conditions encountered in actual flight do not always adhere to the set limits for which the airfoil member is designed and may therefore lead to malfunction or decreased efficiency. [0005] Apart from applications in the civilian sector, this invention has immense applicability in the defense sector, for example on rockets, missiles, torpedoes, morphing aircrafts etc., where maneuverability at high angles of attack is not a choice but requirement. Therefore, there exists a need in the art for a wing that addresses the above mentioned deficiencies/requirements and encounters adverse flow conditions during flight, without altering shape of the base wing/blade. OBJECTS OF THE INVENTION [0006] An object of the present invention is to provide a wing having improved aerodynamic performance characteristics. [0007] Another object of the present invention is to provide a wing employing an external attachment for morphing the shape of a base wing/blade. [0008] Yet another object of the present innovation is to provide a wing with improved aerodynamic efficiency without the requirement of altering shape of the base wing/blade. [0009] Yet another object of the present invention is to provide a wing capable of performing efficiently at high angles of attack including post-stall angles without flow separation or loss in lift or significant drag penalty, or at user-defined aerodynamic characteristics at lower angles of attack with enhanced lift and reduced drag penalty. [0010] Still another object of the present invention is to provide a wing capable of being retrofitted with existing wing. SUMMARY OF THE INVENTION [0011] The summary is provided to introduce aspects related to a wing, including aircraft wings, rudders, rocket fins, turbine blades, fan blades, etc. This summary is not intended to identify essential features of the claimed subject matter nor is it intended for use in determining or limiting the scope of the claimed subject matter. [0012] An aspect of the present invention relates to a wing including an external skin attached to the leading edge of the wing for morphing a portion or the complete wing, and a plurality of micro fiber composite (MFC) strips attached to the external skin at pre-defined locations. When not in operation, the external skin takes the shape of the wing. Electrical actuation of one or more of the plurality of MFC strips changes the curvature of the external skin at one or more sections along the wing span and hence, the corresponding aerodynamic characteristics of the wing., This change in the shape of the external skin is then used for controlling flow separation at high angles of attack or more efficient flight performance at lower angles of attack. [0013] Electrical actuation of the plurality of MFC strips adjusts the curvature of the external skin in such a way to correspond to the shape of the boundary layer during flight. [0014] The plurality of MFC strips are connected to a power amplifier configured to regulate electrical power supplied to the plurality of MFC strips, for changing the curvature and the lift of the aircraft. [0015] The plurality of MFC strips are calibrated to change the lift and the curvature of the external skin during flight. [0016] According to an embodiment of the present invention, the change of the curvature of the external skin is determined by a de-cambering method for known 2D/airfoil aerodynamic characteristics to prevent span-wise flow separation and improve stalling characteristics. Stall is associated with large increase in drag and loss in lift. The change of the curvature is specifically analyzed by the de-cambering method for the angle of attack in the range of 0 ≤ α ≤ 17°, wherein it prevents flow separation with and without improving its lift-to-drag ratio. [0017] The external skin is attached to a wing, which has a symmetric section or a cambered section. In other words, the 2D section or airfoil of the wing is symmetric or cambered in shape.. The external skin is formed of a metal sheet of a ductile material. [0018] The gap between the external skin and the body of the wing is filled with plasticine to prevent flow leakage during wind tunnel experiments. BRIEF DESCRIPTION OF THE DRAWINGS [0019] The accompanying drawings constitute a part of the description and are used to provide further understanding of the present invention. Such accompanying drawings illustrate the embodiments of the present invention which are used to describe the principles of the present invention. The embodiments are illustrated by way of example and not by way of limitation in the figures of the accompanying drawings in which like references indicate similar elements. It should be noted that references to “an” or “one” embodiment in this invention are not necessarily to the same embodiment, and they mean at least one. [0020] Fig. 1 illustrates a 3D wing, the airfoil being the 2D section, an external skin attached to the leading edge of the wing, in accordance with an embodiment of the present invention. [0021] Fig.2 illustrates a power amplifier, electrical signal output/input switch used for actuating a single MFC strip from a plurality of micro fiber composite (MFC) strips pasted on to the external skin attached at the leading edge of the wing, in accordance with an embodiment of the present invention. [0022] Fig.3 illustrates actuation of the external ^skin by the ^{MFC strips} at a root/middle section of the wing, in accordance with an embodiment of the present invention. [0023] Fig.3(a) illustrates an MFC not in operation and external skin taking the shape of the baseline wing, in accordance with an embodiment of the present invention. [0024] Fig.3(b) illustrates an MFC in operation, and the external skin having developed a new shape compared to the baseline wing, in accordance with an embodiment of the present invention. [0025] Fig.3(c) illustrates further change in shape of the external skin actuated by MFC strip, in accordance with an embodiment of the present invention. [0026] Figs. 4A to 4C illustrate an overview of two-dimensional (2D) de-cambering method used for morphing an airfoil, in accordance with an embodiment of the present invention. [0027] Figs.5A to 5C illustrate implementation of the de-cambering method on a three- dimensional (3D) wing, in accordance with an embodiment of the present invention. [0028] Figs.6A and 6B illustrate components used in experimental setup of wind tunnel testing for morphing of the 3D wing, in accordance with an embodiment of the present invention. [0029] Figs.7A and 7B illustrate graphs showing variation of coefficient of lift (C_L) and coefficient of moment (CM) with respect to different angles of attack (α) on morphed and base wings for a symmetric 2D section (Fig.7A) and a cambered/curved 2D section (Fig. 7B) of the base wing, in accordance with an embodiment of the present invention. [0030] Fig. 8 illustrates a graph showing drag polars (C_L vs C_D) used to calculate the efficiency of two rectangular wings at Reynolds number (R) = 0.1 × 10⁶, in accordance with an embodiment of the present invention. [0031] Fig. 9 illustrates a graph showing the shape of the baseline wing at the root/middle section and a comparison of the morphed shapes generated using two linear functions and δ2 obtained from residuals ΔCL and ΔCM generated from numerical analysis and wind tunnel experiments in accordance with an embodiment of the present invention. [0032] Figs. 10A and 10B illustrate graphs showing variation of the coefficient of lift (C_L), coefficient of moment (C_M) and coefficient of drag (C_D) with respect to angles of attack (α) in the range of 0° ≤ α ≤ 9° on morphed and base wings for a user-defined 10%, 20% and 30% increase in baseline operating CL at α = 5^o, in accordance with an embodiment of the present invention. [0033] Figs. 11A and 11B illustrate graphs showing variation of the coefficient of lift (CL), the coefficient of moment (CM) and the coefficient of drag (CD) with respect to angles of attack (α) in the range of 0° ≤ α ≤ 17° on morphed and base wings for a user-defined 10%, 20% and 30% increase in baseline operating C_L at α=15^o, in accordance with an embodiment of the present invention. [0034] Figs. 12A and 12B illustrate graphs for numerically morphed surfaces of different wings at angle of attack (α) = 5° and pre-defined increments in the coefficient of lift (C_L), in accordance with an embodiment of the present invention. [0035] Figs. 13A and 13B illustrate graphs for numerically morphed surfaces of different wings at angle of attack (α) = 15° and pre-defined increments in the coefficient of lift (C_L), in accordance with an embodiment of the present invention. [0036] Figs. 14A and 14B illustrate graphs showing variation of the coefficient of lift (CL), the coefficient of moment (CM) and the coefficient of drag (CD) with respect to angles of attack (α) in the range of 0° ≤ α ≤ 17° on the morphed and base wings with a pre-defined 10%, 20% and 30% increment in the baseline operating coefficient of lift (C_L) over the entire α range. i.e.0° ≤ α ≤ 17°, in accordance with an embodiment of the present invention. [0037] Figs. 15A and 15B illustrate graphs for numerically morphed surfaces of the wing at a pre-stall angle of attack of 5° for pre-defined increments in the coefficient of lift (CL) over the entire α range. i.e. 0° ≤ α ≤ 17°, in accordance with an embodiment of the present invention. [0038] Figs. 16A and 16B illustrate graphs for numerically morphed surfaces of the wing at a post-stall angle of attack of 15° for pre-defined increments in the coefficient of lift (CL) over the entire α range. i.e. 0° ≤ α ≤ 17°, in accordance with an embodiment of the present invention. [0039] Fig.17 illustrates oil flow visualisations on surface of the wing at different angles of attack (α), in accordance with an embodiment of the present invention. [0040] Fig. 18 illustrates a schematic representation of a rectangular wing, in accordance with an embodiment of the present invention. [0041] Figs.19A and 19B illustrate graphs for the comparison of the morphed surfaces of wings with a symmetric (NACA0012) vs cambered/curved (NACA4415) 2D sections at angle of attack (α) = 14°, in accordance with an embodiment of the present invention. [0042] Figs. 20A and 20B illustrate graphs for the morphed surfaces of a wing with cambered/curved 2D sections at various angles of attack (α), in accordance with an embodiment of the present invention. [0043] Figs. 21A and 21B illustrate graphs showing variation of the coefficient of lift (CL), the coefficient of moment (CM) and the coefficient of drag (CD) with respect to angles of attack (α) in the range of 0° ≤ α ≤ 17° on the morphed and base wings with a symmetric (NACA0012) 2D section for a pre-defined increment in the coefficient of lift (C_L) over the entire α range. i.e.0° ≤ α ≤ 17°, in accordance with an embodiment of the present invention. [0044] Figs.22A and 22B illustrate graphs for the morphed surfaces of the wing with a symmetric (NACA0012) 2D section at a pre-stall angle of attack of 5° and pre-defined increments in the coefficient of lift (C_L), in accordance with an embodiment of the present invention. [0045] Figs.23A and 23B illustrate graphs for the morphed surfaces of the wing with a symmetric (NACA0012) 2D section at a post-stall angle of attack of 15° and pre-defined increments in the coefficient of lift (CL), in accordance with an embodiment of the present invention. [0046] Figs. 24A and 24B illustrate contours of the morphed surfaces of the wing, in accordance with an embodiment of the present invention. [0047] Figs. 25A and 25B illustrate graphs representing traces of maximum camber locations along span-wise direction over the morphed surfaces of the wing for 20% increment in design C_L at α = 5° and at α = 15°, respectively, in accordance with an embodiment of the present invention. [0048] Figs. 26A and 26B illustrate graphs representing traces of maximum camber locations along span-wise direction over the morphed surfaces of the wing for 30% increment in design CL at α = 5° and at α = 15°, respectively, in accordance with an embodiment of the present invention. [0049] Fig.27A illustrates upper surface of the base wing with an oil flow visualization thereof, in accordance with an embodiment of the present invention. [0050] Fig.27B illustrates the upper surface of the wing morphed with an external skin and an oil flow visualization thereof, in accordance with an embodiment of the present invention. [0051] Fig. 28A illustrates surface flow of air up to mid-span on the upper surface of the rectangular wing with the external skin at α = 14° and without the external skin at α = 11°, in accordance with an embodiment of the present invention. [0052] Fig.28B illustrates aerodynamic characteristics of the surface flow of air on the upper surface of the rectangular wing, showing variation between the aerodynamic characteristics on the morphed wing and the base wing, in accordance with an embodiment of the present invention. [0053] Figs.29A and 29B illustrate time history of pressure coefficient (Cp) at different locations on suction side of the base wing and corresponding aerodynamic characteristics at Re = 0.1 × 10⁶, in accordance with an embodiment of the present invention. [0054] Figs.30A and 30B illustrate graphs representing unsteady CL of the base wing and the numerically morphed wing, in accordance with an embodiment of the present invention. [0055] Fig. 31 illustrates graphs representing unsteady CL of the base wing and the physically morphed wing, in accordance with an embodiment of the present invention. [0056] Figs.32A to 32C illustrate graphs representing transient nature of the morphing at the root/middle section of the wing at different time instances, in accordance with an embodiment of the present invention. [0057] Fig. 33 illustrates graphs representing the transient nature of section CL characteristics at different time instances, in accordance with an embodiment of the present invention. [0058] Fig. 34 illustrates graphs representing transient aerodynamic characteristics to implement different design CL conditions, in accordance with an embodiment of the present invention. [0059] Fig. 35 illustrates graphs representing section C_L characteristics to implement different design CL conditions, in accordance with an embodiment of the present invention. [0060] Figs.36A to 36D illustrate graphs representing the morphed surfaces of the wing at different design C_L conditions, in accordance with an embodiment of the present invention. [0061] Fig.37 illustrates a table representing unsteady flow separation behavior of the morphed wing during a Computational Fluid Dynamics (CFD) experiment at different time instances, in accordance with an embodiment of the present invention. [0062] Fig.38 illustrates separation lines from experiments conducted at root section of the wing at α = 14°, in accordance with an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION [0063] The detailed description set forth below in connection with the appended drawings is intended as a description of various embodiments of the present invention and is not intended to represent the only embodiments in which the present invention may be practiced. Each embodiment described in this invention is provided merely as an example or illustration of the present invention, and should not necessarily be construed as preferred or advantageous over other embodiments. The detailed description includes specific details for the purpose of providing a thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced without these specific details. [0064] Fig. 1 illustrates a 3D wing 100 having an airfoil 102 and an external 3D skin 104 attached to the leading edge 102-1 of the wing 100, in accordance with an embodiment of the present invention. The airfoil 102 may be any of an aircraft wing, a rudder, a rocket fin, a turbine blade, a fan blade and the likes. In one implementation, as shown in Fig.1, the airfoil 102 is the 2D section of a wing of an aircraft. The 3D skin 104 is an external attachment adapted to morph at least one airfoil section 102. The 3D skin 104 may be attached to a 3D wing with any of a symmetric 2D section or a cambered 2D section of the airfoil 102. The 3D skin 104 may be made up of a metal sheet of a ductile material, such as Aluminium, or an alloy thereof. A gap between the 3D skin 104 and the baseline surface of the 3D wing 100 may be filled with plasticine to prevent flow leakage. [0065] The 3D wing 100 also includes a plurality of power-actuated micro fiber composite (MFC) strips 202 attached to the 3D external skin 104 at pre-defined locations. Fig. 2 illustrates an implementation of a single power-actuated MFC strip 202 attached to the external skin 104. However, more than one MFC strips 202 may be attached to the 3D external skin 104 at discrete locations, while the 3D external skin 104 cover an entire span of the 3D wing 100. One or more of the MFC strips 202 may be electrically actuated to change or deflect curvature of the external skin 104 and hence change the lift force of the 3D wing 100, at a pre-defined degree. This change in curvature of the external skin 104 leads to change in aerodynamic shape of the 3D wing 100 and control of flow separation at pre-defined angles of attack of the 3D wing 100. [0066] Fig.3 illustrates changing of curvature of the 3D external ^{skin 104} by the ^MFC ^strips 202 at a root section/airfoil 102 at the middle of the 3D wing 100, thereby also changing its lift force, in accordance with an embodiment of the present invention. The change in the aerodynamic shape of the 3D wing 100 may be implemented, in real-time during flight, using the power-actuated MFC strips 202 attached to the 3D external skin 104, as shown in Figs.3(b) and 3(c). When not in operation, the 3D external skin 104 may simply take the shape of the base wing 100, as shown in Fig.3(a), and thereafter change its shape during the flight to change the aerodynamic shape of the 3D wing 100 to better adjust flight performance characteristics. The change in curvature of the external skin 104 is devised/predicted in real-time by numerical analysis of a de-cambering method at pre- determined flow conditions to prevent span-wise flow separation and improve stalling characteristics at the pre-defined angles of attack of the 3D wing 100. The change is curvature of the 3D wing 100 may also be analyzed by the de-cambering method at different flow conditions to operate at a user-defined enhanced coefficient of lift of the 3D wing 100 for the angle of attack in the range of 0 ≤ α ≤ 17 °, during flight. [0067] The power-actuated MFC strips 202 may also be configured to adjust lift of the 3D wing 100, upon electrical actuation thereof, to enable the aerodynamic shape of the airfoil 102 to correspond to a shape of boundary layer during flight. [0068] The MFC strips 104 may be calibrated to change or adjust the lift and/or the curvature of the 3D external skin 104 with respect to the leading edge 102-2 of the 3D wing 100, during flight. [0069] The MFC strips 202 may be connected to a power amplifier 204 configured to modulate/adjust voltage supplied to the MFC strips 202, to enable control over the change in the lift and the curvature of the 3D external skin 104 with respect to the leading edge 102- 2 of the 3D wing 100. The power amplifier 204 may be a high voltage power amplifier, such as microHVA-2, connected to a regulated DC power supply unit, as shown in Fig.2. Input voltages for the power-actuated MFC strips 202 may be user-defined, which are obtained from numerical analysis of the degree of deployment of the 3D external skin 104. Supply of the input voltages to the power-actuated MFC strips 202 may be controlled by NI DAQ (National Instruments data acquisition system). Once power is supplied to one or more of the MFC strips 202 with a pre-defined voltage, the MFC strips 202 change the curvature of the 3D external skin 104 over the wing 100 and take shape of the separated boundary layer, as shown in Fig.3. [0070] The MFC strips 202 are also configured to delay or control the flow separation at high angles of attack of the 3D wing 100. Therefore, a number of power-actuated MFC strips 202 may be attached to the entire 3D external skin 104, which enable morphing of the 3D external skin 104 to a desired shape that is different from the shape of a base upper surface of the 3D wing 100. To this effect, the 3D wing 100 is able to perform efficiently at high angles of attack including post-stall angles without any flow separation, or at user- defined aerodynamic characteristics at lower angles of attack. Further, the MFC strips 202 control the change in curvature of the 3D external skin 104 and lift of the 3D wing 100 to prevent flow separation at high angles of attack, while providing an aerodynamic advantage at lower angles of attack without flow separation. [0071] Figs. 4A to 4C illustrate an overview of two-dimensional (2D) de-cambering method used for morphing the wing 100, in accordance with an embodiment of the present invention. Fig.4A illustrates a plot representing slope of coefficient of lift (C_L) – angle of attack (α) curve with flow visualization as shown in Figs. 4A(b) and 4A(c). Fig. 4B illustrates the basic idea behind the decambering approach showing that the real separated flow shown in Fig.4B(a) is estimated numerically using two linear decambering functions δ1 and δ2 shown in Figs.4B(b) and 4b(c), where: ∆ ^^ ^^ δ2 = ^^ ^^ ^^2 ^^2−1 ^^ ^^ ^^ ^^2 , and (1)

[0072] Fig. 4(C) shows the definition of the residuals ΔCL and ΔCM used in the de- cambering approach, where Fig.4(c)(a) illustrates a CL – α curve for potential and viscous flows, the residual ΔC_L being the difference between the two, and Fig.4(c)(b) illustrates a Coefficient of Moment (Cm) – α curve for potential and viscous flows, the residual ΔCM being the difference between the two. [0073] The surface of the rectangular wing 102 is morphed at high angles of attack such that the wing 102 is capable of operating at a reduced/enhanced coefficient of lift (CL) at which the base wing operates but without flow separation. Therefore, unlike the base wing, where the flow is separated, the flow remains attached on the wing 102 morphed by the external skin 104. [0074] A morphed surface is numerically generated to operate at a local design 2D CL, which is obtained by incrementing the base CL by a percentage at pre-stall and post-stall angles of attack. The morphed surface is generated numerically using a de-cambering technique, which accounts for deviation of the coefficients of lift and pitching moment from that predicted by potential flow, analytically, using Computational Fluid Dynamics (CFD) and implemented experimentally by attaching the external skin 104 to the leading edge 102- 1 of the wing 100. [0075] Two different wing sections, NACA0012 corresponding to symmetric section of the wing 102 and NACA4415 corresponding to cambered section of the wing 102, were tested on a rectangular planform. The effect of morphing on aerodynamic performance was observed, and aerodynamic characteristics were studied. Results indicate that significant improvement in aerodynamic performance is achieved at high angles of attack, especially at post-stall through morphing of the wing 100 by the external skin 104. [0076] The experiment was intended to identify variable camber morphing approach of rectangular wings. In this experiment, a simple active morphed flow surface technique using a de-cambering approach was applied to prevent span-wise flow separation and improvement in stalling characteristics at high angles of attack α. The experiments were also aimed to investigate the span-wise variations of effective camber morphing on three- dimensional (3D) rectangular planforms especially at post-stall stages. Results indicate that morphing of the wing 100 by the external skin 104 not only helps to control the 3D flow separation but also aids in operating at design CL conditions for any given angle of attack. The experiments were carried out using a low speed, subsonic wind tunnel. [0077] It was observed that boundary layer separates from upper surface of a wing at high angles of attack, and the corresponding viscous C_L and C_m deviate from potential flow theory predictions. This deviation also results in an effective loss in the chord-wise camber distributed along the span of the wing. If this effective loss in camber distribution along span is accounted for, then a potential flow prediction for the de-cambered wing closely matches the section viscous CL and Cm for high angle of attack (α) flow past the base wing. Specifically, the effective de-cambering for a particular α and at a particular wing-section using two linear functions,

and δ₂ as shown in Figs.4B(b) and 4B(c) is computed using the deviations of the viscous Cl and Cm, that is residuals denoted by ∆CL and ∆Cm respectively from the potential-flow predictions. [0078] Fig. 5A illustrates implementation of the de-cambering method on a three- dimensional (3D) wing with a symmetric/cambered section by a basic vortex lattice method for a range of angles of attack. Figs. 5B and 5C illustrate 2D and 3D plots indicating aerodynamic characteristics of the de-cambered wing, respectively. For a 3D wing, changing a δ (δ = δ1 or δ2) on one section has a significant effect on the neighboring sections and on the sections of downstream lifting surfaces. A 2N-dimensional Newton iteration was used to predict the local de-cambering to account for these cross-coupling effects. A 2N × 2N matrix equation was solved as shown in equation (4) below such that right-hand side thereof consisting of the residuals approaches zero. [ _^^][ _{^^ ^^}] _{= −[ ^^]}, where (4) J=Jacobian (degree), shown in equation (5) below. It is a matrix showing the change in residuals ∆C_L and ∆C_m due to a change in δ₁ and δ₂. δx are the unknowns

and δ2 (degree). F is forcing function, (∆C_L)_viscous - (∆C_L)_potential, and (∆CM)viscous - (∆CM)potential [0079] The Jacobian is partitioned into four sub matrices as shown in equation (5) below:

^^∆ ^^ ^^ ^^ (Jm2)i, j = ^^ ^^2, ^^ , where l, m = 1:N N= number of discrete sections the 3D wing span 100 is divided into. J_l1 (degree) = change in ∆C_L due to change in δ₁ Jl2 (degree) = change in ∆CL due to change in δ2 Jm1 (degree) = change in ∆CM due to change in δ1 J_m2 (degree) = change in ∆C_M due to change in δ₂ i, j = 1:N i = location of section on 3D wing span 100 where δ1 and δ2 is changed j = location of section on 3D wing span 100 where the change in residual is calculated [0080] The iteration procedure is summarized as follows: 1. Assume starting values of δ1 and δ2 for each section of the two wings. 2. Compute the wing aerodynamic characteristics for both wings using the Vortex Lattice Method (VLM) code. 3. Compute local section effective angles of attack α_sec using the local section coefficient of lift, C_lsec as shown in equation (7) below. 4. Compute the residuals ∆Cl = (Cl)visc - (Cl)sec and ∆Cm = (Cm)visc - (Cm)sec. The (Cl)visc and (Cm)visc are obtained from the known section data for the angle of attack corresponding to α_sec. 5. Calculate the Jacobian matrix considering both wings together for Newton iteration which is a numerical technique to implement the steps of the iteration procedure using a computer program. 6. Solve the matrix equation (4) to obtain the perturbations to δ1 and δ2 at each section of both wings and update values of δ1 and δ2 on each wing. 7. Repeat steps 2 to 6 until ∆C_l and ∆C_m on each section of both wings are close to zero within a specified tolerance.

[0081] Figs.6A and 6B illustrate components used in experimental setup of wind tunnel testing for morphing of the airfoil, in accordance with an embodiment of the present invention. Experiments were conducted in a subsonic, open circuit wind tunnel with a test- section of size 0.5m × 0.5m × 2m, as shown in Fig.6A(a). Turbulence intensity at a free- stream location was approximately 0.50%, as reported by manufacturer of the tunnel and uncertainty in experimental results were calculated as shown in Table 1 below. The uncertainty in the angle of attack was determined to be in the order of 0.3° – 0.4°.

Table 1: Uncertainty analysis [0082] Direct loads were measured using a 3-component load-balance system. Two separate 3D wing models were used with an aspect ratio, AR = 6.4, chord length, c = 6.3cm, span, b = 40cm, and the section profiles NACA4415 and NACA0012. Pressure was measured using 22 pressure ports distributed around root section of the wing 102 using Scanivalve pressure transducer, which has a resolution of 0.1% of full-scale reading. An area blockage ratio was less than 5% of cross-sectional area of the test section during entire pitching motion of the wing 100. [0083] All wings tested were held at a quarter-chord point. An origin of coordinates was located at the leading edge 102-1 of the wing 100. A sting was covered by a streamlined sting cover. It was also necessary to account for interference and tare effects of the sting, which has its direct aerodynamic drag effects on the wing 100. Before performing wing tests, sting tares were taken at different test Reynolds numbers, and corrections were applied by subtracting from the corresponding measurements. [0084] A three-component load-balance was used to measure lift and drag forces and pitching moment. The angle of attack (α) measurements were taken by an angular measurement scale attached with the force balance itself. The zero α of wings tested was set by aligning a wing reference chord line to centerline of the tunnel. Besides, model span fraction which is ratio of the wingspan to width of the test section, of all the wings tested was 0.8. Normally, the maximum model span should be equal to or less than 0.8 of the tunnel width for a full model to apply standard wind tunnel corrections. [0085] A six-component force balance system was used to measure aerodynamic loads and moments directly, as shown in Figs.6B(a) to 6B(c). This force balance transducer has a high signal-to-noise ratio and typically provides a signal 75 times stronger than conventional gauges needed for such an unsteady high angle of attack study (α). The force balance transducer was attached to a wing mounting mechanism so that for every α, a line of action was the same for the wing 100 and balance centerline (see Fig. 6B(b)). A Scanivalve pressure transducer with a resolution of 0.1% of full-scale reading was used to measure pressure on the wing models using 22 pressure ports distributed around the root section of the wing 100. [0086] The wing reference chord line was aligned to centreline of the tunnel to set α = 0° of the wing model to set up the reference for the corresponding α range. After that, an external algorithm was designed and attached to NI DAQ (National Instruments data acquisition system) for measuring real-time α in a particular unsteady motion. Hence, spatial and temporal information of the unsteady motions was recorded simultaneously along with force and moment readings. Data was collected at an effective sampling rate of 1 kHz using the NI DAQ, which is accurate up to ±0.5% of full-scale reading. Instantaneous force data were subsequently ensemble-averaged over a sufficient period of time to obtain the average value. [0087] A 3D base wing model with the symmetric section NACA4415 of the wing 100 and aspect ratio, AR = 6.4, chord length, C = 6.3cm was used. During the entire pitching motion of the wing 100, the area blockage ratio was less than 5% of cross-sectional area of the test section. The span fraction, which is the ratio of the wing-span to the width of the test section, was found to be 0.8 for all the wing models. Typically, to apply standard wind tunnel corrections, the maximum model span should be ≤ 0.8 of the width of the tunnel for a full-scale model. [0088] Smoke flow visualization experiments were also performed using a smoke generator system located at inlet of the tunnel. The smoke fluid used was of type A with a particle size of 0.2-0.3 micron (mass mean diameter). The flow was illuminated with remotely triggered strobe light arrangements, and the images were acquired with a digital camera with 1028 × 1024 px resolution. The measurement plane was selected precisely at close to the root section of the wing 100. [0089] Wind Tunnel tests were conducted on two wings 100 of the same aspect ratio, AR = 6.4, and two different airfoil sections, NACA0012 corresponding to the symmetric section of the wing 102, and NACA4415 corresponding to the cambered section of the wing 102, without any physical morphing. In-house numerical code, VLM3D (Vortex lattice method) was used to analyze the same wings 100 morphed such that they prevent flow separation while operate at design C_L conditions. An analytical approach was also employed to generate the morphed surfaces, and analysis using Computational Fluid Dynamics (CFD) was carried out. [0090] Figs.7A and 7B illustrate graphs showing variation of coefficient of lift (C_L) and coefficient of moment (C_M) with respect to different angles of attack (α) on morphed wing sections and base wing sections. For two rectangular wings 100, both of aspect ratio, AR = 6.4 with the different airfoil sections, i.e. NACA0012 and NACA4415, the CL − α at two different Reynolds number (Re), i.e. Re ≈ 0.045 × 10⁶ and Re ≈ 0.1 × 10⁶ and the CM − α at Re ≈ 0.1 × 10⁶ are shown in Figs.7A and 7B. Experiments were conducted on the base wing model without any physical morphing of the wing surface. On the other hand, the numerical analysis was carried out on a morphed wing surface, such that the morphed wing surface prevents flow separation at post-stall angles of attack. In other words, at a post-stall angle of attack, e.g. α = 15°, it was observed that the numerical CL closely resembles the experimental value. However, unlike in the experiment, where the flow is separated on the base wing at this angle of attack, it was found that the flow remains attached in the numerical analysis conducted on the morphed wing 100. [0091] Fig. 8 illustrates a graph showing drag polars of two rectangular wings at Reynolds number (R) = 0.1 × 10⁶, in accordance with an embodiment of the present invention. The numerical method predicts only induced drag, hence as expected, it is lesser than the total drag obtained from experiments. It was observed that for a given coefficient of drag (C_D), implemented morphed surfaces result in higher C_L for both base wings. The numerical morphing was generated using the de-cambering method, which involves accounting for the difference between viscous and potential flow solutions at a post-stall angle of attack, as shown graphically in Fig. 4A(a). The residuals calculated using Thin Airfoil Theory, as shown in Figs. 4B(b) and 4b(c) and in accordance with the above equations (1) to (3), were calculated for a wing with the cambered airfoil section NACA4415, where the viscous result was obtained from both the present experiment and as predicted by the in-house code, VLM3D. The specific values of the residuals and the corresponding morphing at the root section of the wing 100 at α = 14° and Re = 0.1 × 10⁶ are shown in Table 2 and also graphically represented in Fig.9.

Table 2: Root Section of Wing of section NACA4415 at α = 14° and Re = 0.1 × 10⁶ [0092] Fig.9 illustrates a graph for variation in morphing of the cambered airfoil section NACA4415 using the two linear functions δ₁ and δ₂, in accordance with an embodiment of the present invention. The experimental CL and Cm were obtained by consolidating pressures at the root section of the wing 100 obtained from the 22 pressure ports on the wing model. The numerical C_L and C_m on the other hand, were obtained directly by calculating the section CL and Cm at the root section of the wing 100. The morphing was then calculated using the residuals as described above and as shown in Figs.4A and 4B at the root section of the wing 100. The resulting morphed surfaces along with the base airfoil at the root section of the wing 100 are shown in Fig.9. [0093] Figs. 10A and 10B illustrate graphs showing variation of the coefficient of lift (CL), coefficient of moment (CM) and coefficient of drag (CD) with respect to angles of attack (α) in the range of 0° ≤ α ≤ 9° on morphed wing sections and base wing sections, in accordance with an embodiment of the present invention. Morphed surfaces were generated using the de-cambering method at different post-stall flow conditions to prevent flow separation at the same reduced C_L at which the base wing operates. Hence, the operating aerodynamic characteristics were not improved although flow separation was prevented, which has distinct advantages in operation and control at high angles of attack. [0094] Using the same approach, it was attempted to generate a morphed wing surface such that its 2D wing section can operate at a design C_L, which is larger than the operating CL of the base wing 102. Design CL of the airfoil member 102 was decided in two ways, namely, locally at a particular α, and for a range of α including post-stall. For both these ways, a percentage increment of 10%, 20% and 30% in the input C_L − α was implemented for the wings (AR = 6.4) with two different airfoil sections, NACA0012 and NACA4415. [0095] Figs. 11A and 11B illustrate graphs showing variation of CL, CM and CD with respect to angles of attack in the range of 0° ≤ α ≤ 17° on morphed wing sections and base wing. The base 2D C_L was chosen at a specific pre-stall and post-stall angle of attack, i.e. α = 5° and 15° respectively and the design CL was then obtained as 10%, 20% and 30% increment of the base 2D C_L as shown in Figs. 10A(a) and 11A(a). The aerodynamic coefficients as well as the morphed surface for 10% increment in base C_L is shown in Figs. 10A, 10B, 11A and 11B. It is important to note that when the design 2D CL is considered at α = 5°, the 3D wing angle of attack is 0° ≤ α ≤ 9° shown in Figs.10A and 10B, and when the design 2D C_L is considered at α = 15°, the 3D wing angle of attack is 0° ≤ α ≤ 17° as shown in Figs.11A and 11B. For the design CL at α = 5°, an increase in the CL − α slope was observed starting at α = 3° along with an increase in the wing 3D CL for 3° < α ≤ 9° as shown in Fig.10B(a). In other words, although the design C_L value increased only at α = 5° but for the 3D wing, there is an increment in the CL for other angles of attack as well. This was observed as an advantage in terms of more efficient operation at low angles of attack of an aircraft employing the morphed wing. Besides, no significant increase in induced drag was observed even for an increment of 30% of the base C_L as shown in Fig.10B(b), which was observed as an advantage of pre-stall flying and operations conditions. It was also observed that the CM − α slopes increased with increase in the design CL as shown in Fig. 10B(c), which in turn affects stability of operations of the aircraft. [0096] Unlike the design CL at α = 5°, the wing aerodynamic characteristics change locally for the design CL at α = 15° as shown in Figs. 11A and 11B. It was observed that with an increase in the design input 2D C_L, the output 3D C_L, C_Di and C_M also increased as shown in Figs. 11B(a)-11B(c). A maximum of approximately 16.66% increase in CDi was observed compared to base wing for a design CL of 30% increment of the base airfoil member 102. The morphed surfaces required to implement the design C_L at pre-stall and post-stall are shown in Fig.12A, 12B, 13A and 13B, respectively. [0097] Figs. 12A and 12B illustrate graphs for numerically morphed surfaces of different wing sections at α = 5° and pre-defined increments CL. Figs.13A and 13B illustrate graphs for numerically morphed surfaces of different wing sections at α = = 15° and pre- defined increments in CL. During the numerical analysis, while most of the morphed surfaces appeared reasonable enough for physical implementation, two cases needed attention. For a 30% increment of the base C_L at pre-stall angle of attack shown in Fig. 12A(c), the morphed surface near the root was nearly 90°. It was noted that this could be a limiting case, and further hike in CL may result in an unreasonable morphed surface. For a similar increment at post-stall shown in Fig. 13A(c), two of the morphed surfaces make obtuse angles. It was noted that this morphed structure may be deemed unreasonable and not fit for physical implementation. [0098] Figs. 14A and 14B illustrate graphs showing variation of CL, CM and CD with respect to angles of attack in the range of 0° ≤ α ≤ 17° on the morphed wing sections and the base wing with a pre-defined increment in CL, in accordance with an embodiment of the present invention. In this case, the design 2D CL is obtained by an increment of 10%, 20% and 30% of the base 2D C_L for every angle of attack in the range 0° ≤ α ≤ 17° as shown in Fig. 14A(a). The aerodynamic coefficients as well as the morphed surface for 10% increment in base CL are shown in Figs. 14A and 14B. It was observed from Fig. 14B(a) that α stall increases with increase in percentage of design C_L without significant increase in C_Di as shown in Fig.14B(b). It is also observed from Fig.14B(c) that increase in design C causes a shift of the kink in post-stall region to deep-stall reg

L ion, where the factor

is maximum and the wing experiences a positive C_M. Large change in C_L means it will also cause large tilting motion of the leading edge 102-1, i.e. moment = lift force X lever arm. Hence, for a small change in angle of attack, there is a large change in C_M. Hence, this factor also has a large value. Hence, this morphed surface provides an increased zone of control at high angles of attack by avoiding instability. [0099] Figs. 15A and 15B illustrate graphs for numerically morphed surfaces of different wing sections at angle of attack in the range of 0° ≤ α ≤ 17° and a pre-stall angle of attack of 5° and pre-defined increments in C_L. Figs. 16A and 16B illustrate graphs for numerically morphed surfaces of different wing sections at angle of attack in the range of 0° ≤ α ≤ 17° and a post-stall angle of attack of 15° and pre-defined increments in C_L, in accordance with an embodiment of the present invention. The morphed surfaces required to implement the design 2D CL over 0° ≤ α ≤ 17° at two specific wing angles of attack, pre- stall at α = 5° is shown in Figs.15A and 15B and post-stall at α = 15° is shown in Figs.16A and 16B. The patch-wise effective morphed surfaces for the pre-stall angle of attack shown in Figs. 15A and 15 look reasonably similar across span-wise directions and fit for implementation. This adaptive morphed flow surfaces was observed to behave analogously from a tip section to the root section of the wing 100. On the other hand, for the post-stall angle of attack, i.e. α = 15°, the orientation of most of the effective morphed surfaces shown in Figs.16A and 16B were observed to be equivalent to the increase in span-wise sectional camber distribution to generate more lift, which is maximum at the root section of the wing 100. This may be explained by the root stalling behavior of the rectangular wing 100 where flow starts separating from the span-wise mid-section or root section, as also seen from Fig. 17 which illustrates oil flow visualisations on surface of the wing 100 at different angles of attack. Hence, the morphed root section’s effective deflection was higher to achieve a particular design of CL. [0100] The significantly different morphed surfaces at α = 5° and 15° were due to the difference in flow pattern from pre-stall to the post-stall region as shown using oil flow visualization on the base wing with cambered airfoil section NACA4415 in Fig.17. At α = 5°, flow was observed to be almost attached everywhere except a narrow region of laminar separation bubble around the leading edge 102-1 of the wing 100, whereas at α close to 15°, flow was fully separated from the wing surface. Therefore, to get higher CL at α = 15° as a design approach, a higher degree of camber morphing is required compared to at α = 5°. It was also seen that the root section of the wing 100 experiences a strong span-wise undulation of 3D separated flow structures at a higher α. [0101] Fig. 18 illustrates a schematic representation of the rectangular wing 102, in accordance with an embodiment of the present invention. Figs. 19A and 19B illustrate graphs for the aerodynamic characteristics for morphed surfaces of different wing sections at α = 14°. The rectangular wing 100 was divided into 12 sections/patches along the span as shown in Fig. 18 and each section/patch is morphed as shown in the implementation illustrated in Figs. 1 to 3. Half the upper surface of the wing 100 is shown here since the morphing is symmetric. Therefore, morphing on 6 patches on half the wing are shown in Figs. 19A and 19B for the two different wing sections, NACA0012 corresponding to the symmetric section of the wing 100 and NACA4415 corresponding to the cambered section of the wing 100, respectively, at a post-stall α = 14° at Re = 0.045 × 10⁶. It was observed that both the base wing and the morphed wing have the same CL and CM at a given post- stall angle of attack. However, while the flow stalls on the base wing, it is un-stalled on the morphed wing. It was also seen in Figs.19A and 19B, for the wing with section, NACA0012, morphing is almost greater than 10% along with different chord-wise locations than the wing 100 with section, NACA4415 to prevent flow separation at post-stall α = 14°. However, it was interesting to note that the extent of morphing required to control the flow separation increases towards root section along different patches for the wing with section NACA0012, whereas the extent of morphing is almost similar for the wing 100 with section NACA4415. [0102] Figs.20A and 20B show change in the morphed surfaces for change in the angle of attack for the wing 100 with aspect ratio (AR) = 6.4 and section NACA4415 at Re ≈ 0.045 × 10⁶. Both 3D and 2D views are shown in Figs.20A and 20B. The change in the morphing parameters due to wing section is studied by analysing the parameters on the wing 100 of section NACA0012 as shown in Figs.21A and 21B, where variation of C_L, C_M and C_D with respect to angles of attack in the range of 0° ≤ α ≤ 17° on the morphed wing sections are shown. The morphing is implemented for an increment of the base 2D CL over 0° ≤ α ≤ 17°. It was observed that both the slope of C_L - α curve as well as α stall increase with increase in design C_L as shown in Fig. 21B(a). Corresponding to the significant increase in a maximum coefficient of lift (CLmax), there was no significant increase in the induced drag as shown in Fig. 21B(b). A kink in the CM − α curve, where the factor ^{^^ ^^} _^^ ^^ ^^ is greatest was observed at α ≈ 8°. It was also observed that the kink does not change with hike in design C_L as shown in Fig.21B(c). [0103] The numerically generated morphed surfaces to implement the 2D design C_L conditions specifically for a pre-stall and post-stall angle of attack, i.e. α = 5° and 15° are shown in Figs. 22A-22B and 23A-23B, respectively, for a wing of section NACA0012. Using the second method of implementing morphing, a comparison of aerodynamic characteristics of the morphed rectangular wing 100 with AR = 6.4 and the base wing for the two different wing sections, NACA0012 and NACA4415 are shown in Table 3.

Table 3: Effect of Wing Section on Aerodynamic Characteristics of Wing with Morphed Surface [0104] It was observed that with an increase in percentage of design 2D C_L, α stall increases, and for the wing of cambered section NACA4415, this increase was 3° more than that of the wing of the symmetric section, NACA0012. The CLmax for the wing with the symmetric section was observed to increase by ≈ 53% when the design 2D C_L is increased to 20% from 10% and by ≈ 60% when the design 2D CL is increased to 30% from 20%. This corresponding increase is ≈ 259% and ≈ 65% for the wing with the cambered section. Similarly, the maximum coefficient of drag (C_Dimax) for the wing with the symmetric section NACA0012 was observed to increase by ≈ 94% when the design 2D C_L is increased to 20% from 10% and by ≈ 45% when the design 2D CL was increased to 30% from 20%. This corresponding increase was observed to be ≈ 21% and ≈ 82% for the wing with a cambered section NACA4415. Therefore, when the design 2D C_L was increased from 10% to 20%, the 3D CLmax achieved for a morphed wing of the cambered section NACA4415 was ≈ 200% more than the morphed wing of the symmetric section NACA0012. [0105] The corresponding increase in C_Dimax for the morphed wing of the cambered section NACA4415 was observed to be ≈ 75% less than the morphed wing of the symmetric section NACA0012. Also, for 10%, 20% and 30% increase in design 2D CL, the CLmax was ≈ 0.8, ≈ 0.9 and ≈ 1.0 for the symmetric section NACA0012 and ≈ 1.1, ≈ 1.3 and 1.4 for the cambered section NACA4415. In other words, the maximum C_L that was achieved by morphing the wing of the symmetric section NACA0012 to implement 30% increase in design 2D CL was 10% less than that achieved by morphing the wing of the cambered section NACA4415 to implement 10% increase in the design 2D C_L. [0106] Figs.24A and 24B illustrate contours of the morphed surfaces of the wing 100, in accordance with an embodiment of the present invention. The morphed wing surfaces were generated numerically for several strips along the span of the wing 100. In order to get a better picture of the complete morphed wing, a contour plot of the morphing was generated as shown in Figs.24A and 24B for the two different sections of the wing 100, one with the symmetric section NACA0012 and the other with the cambered section NACA4415, which is essentially re-drawing of camber line at several sections along the span of the wing 100. The angle of attack of the wing was at post-stall, α = 15°, and the morphing is shown for two cases, namely, morphed wing surface to prevent flow separation, and morphed wing surface to achieve 20% increase in design 2D C_L over 0° ≤ α ≤ 17°. [0107] Figs. 25A and 25B illustrate graphs representing traces of maximum camber locations along span-wise direction over the morphed surfaces of the wing for 20% increment in design C_L at α = 5° and at α = 15°, respectively. It was observed for the wing 100 with the symmetric section NACA0012, that its morphed surface is undulated with several changes in slope along the wingspan along with distinct changes in slope along the chord. For the wing 100 with the cambered section NACA4415, on the other hand, the morphed surface was observed to be more gradual without distinct or sharp changes in the slope. Hence, it was expected that the morphed surface of the wing 100 with the cambered section NACA4415 will experience gradual rolling moments without resulting in any adverse stability conditions. Therefore, it was observed that the physical implementation of the morphing on the wing 100 with the cambered section NACA4415 was safer and better feasible, and a sufficiently ductile material of average thickness of the external skin 104 would suffice. [0108] Figs.26A and 26B show traces of maximum camber locations along with span- wise directions of the morphed wing surface at two design CL conditions, i.e. local hike and overall hike for α = 5° and 15°. It was observed that, changes in maximum camber locations was more gradual from the tip section to the root section of the wing 100 in an overall hike in design CL conditions for both α = 5°and 15°. Significant upstream movement was observed towards the leading edge 102-1 of the wing 100 at α = 15⁰, which essentially describes the higher-order morphing of the root section in order to operate at the design C_L. In order to make a better and correct assessment of the morphed surfaces, the change in the y − offset along wing span, i.e. in z direction is tabulated for two locations along the chord, x = 0.4c and x = 0.8c at α = 5° and 15° for both morphing approaches. [0109] These two chord-wise locations were selected as they are susceptible to maximum deflection with respect to the base configuration. The specific locations (patches) and the axes system (separate zoomed in inset) are shown in Fig. 18, and the changes are tabulated in Tables 4(a) and 4(a), provided below.

Table 4(a): Change in slope along wing span for 20% hike in base CL at (a) α = 5°

Table 4(b): Change in slope along wing span for 20% hike in base CL at (a) α = 15° [0110] The change in slope between, for instance, the patch at the tips, P1 and the patch ^^ ^^ ^^ o it, P2 was calculated as ₂− ^^ adjacent t ₁ ^^ ^^ = ^^₂− ^^₁, and the y values were calculated at two locations, e.g. (y2)x = 0.4C and (y2)x = 0.8C at several z locations, i.e. along the wing span. Tip Clearance was simply the y − offset of the morphed surface at the tips. It was therefore assessed that some specific cases, e.g. as shown in Fig. 26B cannot be implemented but overall a fair possibility of the practical implementation of the method exists for a range of angles of attack including the post-stall angles of attack. [0111] Surface oil flow visualizations for the base rectangular wing 100 of the cambered section NACA4415 as well as the same wing morphed with the external skin 104 to prevent flow separation at α = 14° and Re = 0.045 × 10⁶ are shown in Figs. 27 A and 27B. An aluminium alloy sheet is used as the external skin 104 because of its ductile nature and moderate mechanical strength to morph the surface of the base wing100 to prevent flow separation. [0112] Fig. 28A illustrates surface flow of air up to mid-span on the upper surface of the rectangular wing 100 with the airfoil skin at α = 14° and without the external skin at α = 11°, in accordance with an embodiment of the present invention. The orientation of the external skin 104 was as per the numerical morphing shown in Fig. 30A(b). When the external skin 104 is employed, the space between the skin 104 and the surface of the base wing 100 was filled with plasticine to prevent flow leakage, as shown in Fig. 27B(a). For the surface oil flow visualization, a proportionate mixture of vacuum pump oil, titanium dioxide, and Oleic acid was spray-coated uniformly as a thin layer on the surface of the wing model, as shown in Figs.27A(b) and 27B(b) and Figs.28A(a) and 28A(b). [0113] At α = 14°, the surface oil flow visualization for the base wing shows almost even distribution of oil over the entire wing surface indicated by the white ‘lumps’ as shown in Fig.27A(b) except around the top right, right edge and bottom right, which is the region around tip section of the wing 100, where the white is more dispersed and the painted black wing surface shows through. This suggests that flow was not significantly attached to the surface near the root section of the wing 100 and hence does not disturb the oil-coated surface while the flow was more attached near the tip section of the wing 100, and pushes the oil coating away for the black painted wing surface. In other words, the flow stalls near the root section of the wing 100. [0114] The surface oil flow visualization for the morphed wing surface, on the other hand, shows significant areas of attached flow indicated by the black color beginning at the tip section and extending partially into the root section of the wing 100 as shown in Fig. 27B(b) and Fig. 28A(a). The remaining white area is also smudged, indicating a partially attached flow. To support this surface flow visualisation study, force and moment data were also recorded and compared with the base wing which is shown in Table 5, and also plotted in Fig.28B(a), 28B(b) and 28B(c). Location of moment center was not determined for the morphed structure separately and the C_M was calculated at C/4, since for traditional airfoil shapes, the location where lift force is calculated and hence the moment calculated using this force multiplied by the distance from this location to the leading edge 102-1 is C/4. It is important to note here that α = 14° is a post-stall angle of attack and flow separates on the base wing. On the wing with the external skin 104 however, the flow remains attached, which is corroborated by the surface flow visualisation experiments. As observed from Table 5 below, the aerodynamic characteristics are comparable, which is expected and as per the numerical de-cambering technique.

Table 5: Comparison on aerodynamic coefficients of wing with & without external skin at α = 14° [0115] It was observed that the surface flow patterns of the wing with the external skin 104 at α = 14° shown in Fig.28A(a) is comparable with the flow structures of the base wing at α = 11° shown in Fig. 28A(b), suggesting that at a higher angle of attack the morphed wing 100 has more attached flow compared to the base wing. This is also reflected in the C_L − α curve shown in Fig.28B(a), where the morphed wing 100 performs better than the base wing. Notably, there is negligible change in the C_M shown in Fig. 28B(b), so that no additional stability criteria have to be addressed. It was also observed that there was an enhancement in CD but the ratio of CL/CD is still greater for the morphed structure, and importantly at the post-stall angle of attack, α = 14°, flow was attached. [0116] Figs.29A and 29B illustrate time history of pressure coefficient (C_p) at different locations on suction side of the base wing and corresponding aerodynamic characteristics at Re = 0.1 × 10⁶, in accordance with an embodiment of the present invention. Flow separates around the root section of the rectangular wing 100. Surface pressure measurements were carried out at the root section of the wing 100 to throw light on the beginning of flow separation at high angles of attack. The time histories of Cp at different chord-wise locations on the suction side, x/c around the root section of the base wing at Re = 0.1 × 10⁶ are shown in Figs.29A and 29B. A scan valve pressure transducer with a resolution of 0.1% of full- scale reading was used to measure surface pressure signals of the wing model through 22 pressure ports. [0117] The corresponding local C_L and C_m at the root section of the wing 100 were directly calculated by integrating the pressures and also obtained directly from force measurements in the wind tunnel experiment. A comparison of these for a wing of aspect ratio (AR) = 6.4, and the cambered airfoil section NACA4415 is shown in Figs.29B(b) and 29B(c). The C_L obtained from direct load measurements was higher than that obtained by integrating the pressure at pre-stall, but showed reasonable agreement in predicting the stall and post-stall regimes. [0118] Figs.30A and 30B illustrate graphs representing unsteady C_L of the base wing and the numerically morphed wing, in accordance with an embodiment of the present invention. The present transient behaviour of the base CL at high angles of attack measured using experiments was compared with unsteady numerical analysis of the same using the in-house code, Unsteady Vortex Lattice Method (UVLM3D) and CFD commercial code at Re = 0.1 × 10⁶ as shown in Figs.30A and 30B. Three angles of attack were chosen to be at the onset of stall, i.e. at α = 11°, around stall at α = 14° and at post-stall at α = 18° at Re = 0.1 × 10⁶. Detached Eddy Simulation (DES) turbulence model was used for the unsteady simulations in CFD analysis. A higher initial CL value was observed for both UVLM3D and CFD analysis at all angles of attack. However, it was observed that the experimental results agree well with the numerical approach and the CFD analysis except at deep stall, i.e. α = 18°, where larger degree of fluctuations of CL values were observed in the numerical analysis while the CFD analysis over-predicted throughout the time frame considered. [0119] Fig. 31 illustrates graphs representing unsteady C_L of the base wing and the physically morphed wing, in accordance with an embodiment of the present invention. The time history of experimental CL values is presented in Figs.31(a), 31(b) and 31(c) to take a closer look at the aerodynamic behaviour of the base and morphed wings. Time-averaged data was produced from 10000 instantaneous samples with a duration of 10s for any single α using a 95% confidence interval and is tabulated in Table 6, provided below.

Table 6: Comparison of Aerodynamic Coefficients at different α: [% changes are calculated w.r.t the Base Wing] ¯ [0120] It was observed that the time averaged CL denoted as ^^ _^^ for the morphed wing is higher than the base wing at all high angles of attack including post-stall α = 18°. In other words, it was observed that these morphed surface configurations can also be used to enhance aerodynamic characteristics of the base wing at high angles of attack. The percentage increment of aerodynamic characteristics of the morphed wings was observed to be increased with an increase in angles of attack. It was also observed that the time-averaged transient state characteristics were higher than the steady-state values for the base wing as well as a morphed wing, especially the C_D values. [0121] Figs. 32A to 32C show transitional behaviour of the morphed wing surface generated numerically at specific α for Re = 0.1 × 202. Three different patches/strips along the wing-span, i.e. at different y/b locations were chosen to study the distribution of morphing along the wing-span. To study the development of the morphed surface with time, the unsteady section CL distribution along the wing-span was obtained numerically and investigated at α = 11°, α = 14°and α = 18° as shown in Figs.33(a), 33(b) and 33(c). It was observed that, for α = 11°, flow was significantly attached along the wing-span up to t = 4s, which is expected for pre-stall regimes. [0122] Fig. 34 illustrates graphs representing transient aerodynamic characteristics to implement different design C_L conditions, in accordance with an embodiment of the present invention. The transient behaviour of morphed configurations was analyzed to implement the design local 2D CL in two ways, i.e. locally at a particular α, and for a range of α including post-stall. A 20% increment of input 2D CL was implemented, which was found to be reasonable for physical implementation and operations at high angles of attack. It is important to note that the design CL considered here were both at post-stall, i.e. α = 14° and 18°where the wing undergoes a change in angle of attack as 0° < α < 20°. [0123] For the base wing, the implementation of local design C_L at α = 14° is shown in Fig.34(a) and the corresponding transient wing C_L behaviour at α = 14° and 18° is shown in Figures 34(b) and 34(c) respectively. For both α = 14°and 18°, a higher average coefficient of lift (C_Lavg) was observed for overall hike in the design C_L up to t = 1s, indicating dominance of the effect of change in angle of attack. Higher degree of fluctuating wing CL was observed at α = 18°, which indicates deep-stall condition. In initial flow time frames on the other hand, a nearly steady wing CL was observed for overall hike in the design C_L and reduced fluctuations were observed for local hike in the design C_L. [0124] Fig. 35 illustrates graphs representing section C_L characteristics to implement different design C_L conditions, in accordance with an embodiment of the present invention. The section CL distribution along the wing-span was analyzed at α = 14° and 18° shown in Figs. 35(a) and 35(b). At α = 14°, overall hike in design CL results in significantly higher C_L across the wing-span without flow separation. At α = 18°, asymmetric saw-tooth was observed in the section C_L distribution for all cases. The saw-tooth however was smaller and more periodic for a local hike in the design CL. The corresponding morphed surfaces near the tip section and the root section of the wing are shown in Figs. 36A to 36D. A significant increment of effective morphing was observed for all the approaches from the tip section to the root section, which was expected since thickness of the 3D boundary layer is maximum at the root section as the wing is of rectangular planform. Overall, to achieve a given design C_L, the overall hike case required lesser morphing making it more efficient, indicating that morphing when aided by change in angle of attack is more efficient. [0125] Unsteady flow separation behaviour at the root section of the rectangular wing 100 of the cambered section NACA4415 using the CFD analysis for both the base wing and the morphed wing are shown in Fig.37 at α = 11° and 14°. As shown, x-wall shear stresses, τx were plotted as insets for each case, where x is non-dimensional chord length of the wing 100. On the base wing at α = 11°, a dominant trailing edge vortex is located at x ≈ 1c at t = 0.2s, which enlarges itself and another smaller, counter rotating vortex is also seen at t = 0.4s, which extends up to x ≤ 0.8c, i.e. further towards the leading edge 102-1. It was observed that more flow continues to be reversed or turned inwards creating two distinct counter rotating vortices and this continues to spread further towards the leading edge 102- 1. [0126] At t = 1s, the original attached streamline was away from the surface at a trailing edge and attached at x ≤ 0.6c. The distinct vortices also disappeared and free-stream seemed to be pulling the flow with itself, indicating that the boundary layer was beginning to separate. Also, the wall shear stress, τx = 0 at x ≈ 0.8c. For the morphed wing, on the other hand, two counter rotating vortices were are observed at t = 0.2s at x ≥ 1.0, which continue to remain in this location and do not enter into the flow stream of the wing section and the boundary layer remains continuously attached. The wall shear stress also continues to be positive throughout the wing section. [0127] At α = 14° on the base wing, it was observed a trailing edge vortex is located at x ≈ 1c at t = 0.2s, which becomes stronger quickly as the boundary layer keeps turning inwards. It reaches further into the flow field of the wing section till it separates at t = 1s where it is attached at x ≤ 0.5c. The wall shear stress, τ_x = 0 at x ≈ 0.35c and continues to be negative till the trailing edge. For the morphed wing, on the other hand, there is no change in the flow field as two counter rotating vortices was observed at t = 0.2s at x ≥ 1.0c do not enter into the flow stream of the wing section. It was also observed that the boundary layer remains continuously attached and the wall shear stress continues to be positive throughout the wing section. [0128] The flow at α = 14° was analyzed further with experiments and numerical analysis. Numerically, the morphed surface was expected to replicate shape of the boundary layer and result in the same aerodynamic coefficients as the base wing. Therefore, at the root section of the wing 100 at α = 14°, the morphed surface was compared with a separation line using the numerical approach and the CFD analysis shown in Fig. 38(c). The experimental flow separation line shown in green follows the boundary layer from smoke flow visualization on the base wing shown in Fig.38(a). [0129] The morphed surface is implemented using an Aluminium airfoil skin 104 to prevent flow separation at α = 14°, and the experimental flow visualization on this surface is shown in Fig.38(b). It is observed that flow is almost separated at the root section starting from the leading edge 102-1 of the base wing at α = 14° whereas typical vortex-like flow structures were observed on the morphed wing 102, indicating only partial loss of momentum, which further help to reduce the flow separation zone. Hence, CL achieved is not enhanced from the base wing but flow is prevented from separation using the morphed wing 100. [0130] The terms “or” and “and/or” as used herein are to be interpreted as inclusive or meaning any one or any combination. Therefore, “A, B or C” or “A, B and/or C” mean “any of the following: A; B; C; A and B; A and C; B and C; A, B and C.” An exception to this definition will occur only when a combination of elements, functions, steps or acts are in some way inherently mutually exclusive. [0131] Any combination of the above features and functionalities may be used in accordance with one or more embodiments. In the foregoing specification, embodiments have been described with reference to numerous specific details that may vary from implementation to implementation. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. The sole and exclusive indicator of the scope of the invention, and what is intended by the applicants to be the scope of the invention, is the literal and equivalent scope of the set as claimed in claims that issue from this application, in the specific form in which such claims issue, including any subsequent correction.

Claims

CLAIMS: 1. A wing (100) comprising: an external skin (104) attached to a leading edge (102-1) of at least one airfoil (102) of the wing (100) for morphing the at least one airfoil (102); and a plurality of micro fiber composite (MFC) strips (202) attached at pre-defined locations of the external skin (104), wherein electrical actuation of one or more of the plurality of MFC strips (202) changes at least one of a curvature of the external skin (104) and a lift of the wing (100) with respect to the leading edge (102-1), thereby changing an aerodynamic shape of the at least one airfoil (102) for controlling flow separation at pre-defined angles of attack (α) of the wing (100). 2. The wing (100) as claimed in claim 1, wherein the plurality of MFC strips (202) are connected to a power amplifier configured to regulate electrical power supplied to the plurality of MFC strips (202), for changing at least one of the curvature and the lift of the external skin (104) with respect to the leading edge (102-1). 3. The wing (100) as claimed in claim 1, wherein the plurality of MFC strips (202) are calibrated to change at least one of the lift and the curvature of the external skin (104) with respect to the leading edge (102-1) of the at least one airfoil (102), during flight of the wing (100). 4. The wing (100) as claimed in claim 1, wherein the change of the curvature of the external skin (104) is determined by a de-cambering method for known 2D/airfoil aerodynamic characteristics to prevent span-wise flow separation and improve stalling characteristics of the wing (100). 5. The wing (100) as claimed in claim 1, wherein the change of the curvature of the external skin (104) is determined by a de-cambering method for known 2D/airfoil aerodynamic characteristics to operate at an enhanced coefficient of lift (CL) of the wing (100) for the angle of attack (α) in the range of 0 ≤ α ≤ 17 °. 6. The wing (100) as claimed in claim 1, wherein the external skin (104) is attached to a symmetric section or a cambered section of the at least one airfoil (102). 7. The wing (100) as claimed in claim 1, wherein the external skin (104) is made of a ductile material. 8. The wing (100) as claimed in claim 1, wherein a gap between the external skin (104) and an upper surface of the wing (100) is filled with plasticine to prevent flow leakage. 9. The wing (100) as claimed in claim 1, wherein the wing (100) is selected from the group consisting of an aircraft wing, a rudder, a rocket fin, a turbine blade, and a fan blade.