The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, thes...

A Review of Morphing Aircraft

Shape morphing of aircraft wing: Status and challenges

Variable stiffness material and structural concepts for morphing applications

Low Speed Aerodynamics

A new concept for actively controlling wing twist is described. The concept relied on introducing warping deformation of the wing skin, which was split at the trailing edge to create an open-section airfoil. An internal screw mechanism was introduced near the trailing edge, so that the load-carrying capability of the wing was maintained while allowing the introduction of warping displacement between the lower and upper wing skins at the trailing edge. Simple structural modeling of the warping wing based on generalized thin-walled beam theory was performed. A demonstration wing was built based on a NACA 23012 airfoil section with a span of 0.68 m and a chord length of 0.235 m. A maximum peak-to-peak twist of 27 deg was demonstrated, with excellent correlation between theory and experiment. Wind-tunnel tests showed that warping could change the lift coefficient by as much as 0.7 at maximum peak-to-peak twist. Analytical and vortex-lattice models were demonstrated to give accurate predictions of the lift coefficient at smaller absolute twist angles. Furthermore, analytic modeling of the wing drag was shown to be in close correspondence with the drag measurements and showed that wing warping could be used to influence the lift induced drag. In general, it was demonstrated that at lower angles of attack, a more positive twist resulted in a higher lift-to-drag ratio. This study proved that a twist-active wing can have sufficient gain to control the rolling motion of an aircraft and to ensure that the lift-to-drag ratio is maximized at various flight conditions.

Mechanism for Warp-Controlled Twist of a Morphing Wing

The design, modeling, and testing of a morphing wing for flight control of an uninhabited aerial vehicle is detailed. The design employed a new type of piezoelectric flight control mechanism which relied on axial precompression to magnify control deflections and forces simultaneously. This postbuckled precompressed bending actuator was oriented in the plane of the 12% thick wing and mounted between the end of a tapered D-spar at the 40% chord and a trailing-edge stiffener at the 98% chord. Axial precompression was generated in the piezoelectric elements by an elastic skin which covered the outside of the wing and served as the aerodynamic surface over the aft 70 % of the wing chord. A two-dimensional semi-analytical model based on the Rayleigh-Ritz method of assumed modes was used to predict the static and dynamic trailing-edge deflections as a function of the applied voltage and aerodynamic loading. It was shown that static trailing-edge deflections of ±3.1 deg could be attained statically and dynamically through 34 Hz, with excellent correlation between theory and experiment. Wind tunnel and flight tests showed that the postbuckled precompressed morphing wing increased roll control authority on a 1.4 meter span uninhabited aerial vehicle while reducing weight, slop, part-count, and power consumption.

Morphing wing flight control via postbuckled precompressed piezoelectric actuators

This paper describes how post-buckled precompressed (PBP) piezoelectric bender actuators are employed in a deformable wing structure to manipulate its camber distribution and thereby induce roll control on a subscale UAV. By applying axial compression to piezoelectric bimorph bender actuators, significantly higher deflections can be achieved than for conventional piezoelectric bender actuators. Classical laminated plate theory is shown to capture the behavior of the unloaded elements. A Newtonian deflection model employing nonlinear structural relations is demonstrated to predict the behavior of the PBP elements accurately. A proof of concept 100 mm (3.94 �� ) span wing employing two outboard PBP actuator sets and a highly compliant latex skin was fabricated. Bench tests showed that, with a wing chord of 145 mm (5.8 �� ) and an axial compression of 70.7 gmf mm −1 , deflection levels increased by more than a factor of 2 to 15.25 ◦ peak-to-peak, with a corner frequency of 34 Hz (an order of magnitude higher than conventional subscale servoactuators). A 1.4 m span subscale UAV was equipped with two PBP morphing panels at the outboard stations, each measuring 230 mm

/pdf/post-buckled-precompressed-elements-a-new-class-of-control-1cwlsab9sh.pdf

Post-buckled precompressed elements: a new class of control actuators for morphing wing UAVs

The use of hybrid-electric propulsion (HEP) entails several potential benefits such as the distribution of power along the airframe, which enables synergistic configurations with improved aerodynamic and propulsive efficiency. This paper presents a comprehensive preliminary sizing method suitable for the conceptual design process of hybridelectric aircraft, taking into account the powertrain architecture and associated propulsion–airframe integration effects. To this end, the flight-performance equations are modified to account for aeropropulsive interaction. A series of component-oriented constraint diagrams are used to provide a visual representation of the design space. A HEPcompatible mission analysis and weight estimation are then carried out to compute the wing area, powerplant size, and takeoff weight. The resulting method is applicable to a wide range of electric and hybrid-electric aircraft configurations and can be used to estimate the optimal power-control profiles. For demonstration purposes, the method is applied to a regional HEP aircraft featuring leading-edge distributed propulsion (DP). Three powertrain architectures are compared, showing how the aeropropulsive effects are included in the model. Results indicate that DP significantly increases wing loading and improves the cruise lift-to-drag ratio by 6%, although the growth in aircraft weight leads to an energy consumption increase of 3% for the considered mission.

/pdf/preliminary-sizing-method-for-hybrid-electric-distributed-5306xfvago.pdf

Preliminary Sizing Method for Hybrid-Electric Distributed-Propulsion Aircraft

Current, highly active classes of adaptive materials have been considered for use in many different aerospace applications. From adaptive flight control surfaces to wing surfaces, shape-memory alloy (SMA), piezoelectric and electrorheological fluids are making their way into wings, stabilizers and rotor blades. Despite the benefits which can be seen in many classes of aircraft, some profound challenges are ever present, including low power and energy density, high power consumption, high development and installation costs and outright programmatic blockages due to a lack of a materials certification database on FAR 23/25 and 27/29 certified aircraft. Three years ago, a class of adaptive structure was developed to skirt these daunting challenges. This pressure-adaptive honeycomb (PAH) is capable of extremely high performance and is FAA/EASA certifiable because it employs well characterized materials arranged in ways that lend a high level of adaptivity to the structure. This study is centered on laying out the mechanics, analytical models and experimental test data describing this new form of adaptive material. A directionally biased PAH system using an external (spring) force acting on the PAH bending structure was examined. The paper discusses the mechanics of pressure adaptive honeycomb and describes a simple reduced order model that can be used to simplify the geometric model in a finite element environment. The model assumes that a variable stiffness honeycomb results in an overall deformation of the honeycomb. Strains in excess of 50% can be generated through this mechanism without encountering local material (yield) limits. It was also shown that the energy density of pressure-adaptive honeycomb is akin to that of shape-memory alloy, while exhibiting strains that are an order of magnitude greater with an energy efficiency close to 100%. Excellent correlation between theory and experiment is demonstrated in a number of tests. A proof-of-concept wing section test was conducted on a 12% thick wing section representative of a modern commercial aircraft winglet or flight control surface with a 35% PAH trailing edge. It was shown that camber variations in excess of 5% can be generated by a pressure differential of 40 kPa. Results of subsequent wind tunnel test show an increase in lift coefficient of 0.3 at 23 m s − 1 through an angle of attack from − 6° to + 20°.

http://iopscience.iop.org/article/10.1088/0964-1726/20/9/094010/pdf

Roelof Vos

Papers

Mechanism for Warp-Controlled Twist of a Morphing Wing

Morphing wing flight control via postbuckled precompressed piezoelectric actuators

Post-buckled precompressed elements: a new class of control actuators for morphing wing UAVs

Preliminary Sizing Method for Hybrid-Electric Distributed-Propulsion Aircraft

Mechanics of pressure-adaptive honeycomb and its application to wing morphing*