An integral approach to lifting wing theory at Mach one

A novel method of calculating static derivatives and acceleration derivatives using Computational Fluid Dynamics is presented. This method uses field velocity approach to simulate the unsteady forced-plunging flow field over the aircraft without updating the field grids during each time step. This provides an improvement in computational efficiency over similar precision without loss of generality. Finally, to verify the present method, the Basic Finner missile as the benchmark example was taken to calculate its acceleration derivatives at various Mach number. Results are in fairly good agreement with traditionally method and the tunnel experimental results. Comparisons with the results of time-dependent simulations are also included.

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack. >

The desire to match the bow shock of a hypersonic vehicle to the lip of the engine cowl provides for a design constraint on the hypersonic forebody. For in viscid flow, it is shown that there is one particular wedge angle which provides for shock matching which is insensitive to steady-state changes in vehicle angle of attack, though it is not possible to match against changes in flight Mach number. The angle-of-attack sensitivity of a hypersonic boundary layer makes this matching process more difficult. Design rules for cowl matching with secondary shocks are presented, though it is shown that it is never possible to fix them against changes in angle of attack.

The downstroke-to-upstroke transition of many insects is characterized by rapid wing rotation. The aerodynamic consequences of these rapid changes in angle of attack have been investigated using a mechanical model dynamically scaled to the Reynolds number appropriate for the flight of small insects such as Drosophila. Several kinematic parameters of the wing flip were examined, including the speed and axis of rotation, as well as the duration and angle of attack during the wing stroke preceding rotation. Alteration of these kinematic parameters altered force generation during the subsequent stroke in a variety of ways. 1. When the rotational axis was close to the trailing edge, the model wing could capture vorticity generated during rotation and greatly increase aerodynamic performance. This vortex capture was most clearly manifested by the generation of lift at an angle of attack of 0°. Lift at a 0° angle of attack was also generated following rotation about the leading edge, but only if the downstroke angle was large enough to generate a von Karman street. The lift may be due to an alteration in the effective angle of attack caused by the inter-vortex stream in the downstroke wake. 2. The maximum lift attained (over all angles of attack) was substantially elevated if the wing translated backwards through a wake generated by the previous stroke. Transient lift coefficient values of nearly 4 were obtained when the wing translated back through a von Karman street generated at a 76.5° angle of attack. This effect might also be explained by the influence of the inter-vortex stream, which contributes a small component to fluid velocity in the direction of translation. 3. The growth of lift with angle of attack was significantly elevated following a 7.5 chord stroke with a 76.5° angle of attack, although it was relatively constant under all other kinematic conditions. 4. The results also indicate the discrepancies between transient and time-averaged measures of performance that arise when unsteady mechanisms are responsible for force generation. Although the influence of wing rotation was strong during the first few chords of translation, averaging the performance over as little as 6.5 chords of motion greatly attenuated the effects of rotation. 5. Together, these modeling results suggest that the unsteady mechanisms generated by simple wing flips could provide an important source for the production of aerodynamic forces in insect flight. Furthermore, the extreme sensitivity to small variations in almost all kinematic parameters could provide a foundation for understanding the aerodynamic mechanisms underlying active flight control.

In the present paper, the controlled flight of fruitflies after voluntary takeoff is studied. Wing and body kinematics of the insects after takeoff are measured using high-speed video techniques, and the aerodynamic force and moment are calculated by the computational fluid dynamics method based on the measured data. How the control moments are generated is analyzed by correlating the computed moments with the wing kinematics. A fruit-fly has a large pitch-up angular velocity owing to the takeoff jump and the fly controls its body attitude by producing pitching moments. It is found that the pitching moment is produced by changes in both the aerodynamic force and the moment arm. The change in the aerodynamic force is mainly due to the change in angle of attack. The change in the moment arm is mainly due to the change in the mean stroke angle and deviation angle, and the deviation angle plays a more important role than the mean stroke angle in changing the moment arm (note that change in deviation angle implies variation in the position of the aerodynamic stroke plane with respect to the anatomical stroke plane). This is unlike the case of fruitflies correcting pitch perturbations in steady free flight, where they produce pitching moment mainly by changes in mean stroke angle.

The hypersonic flight vehicle is powered by ram jet engine whose work has high requirements for its attitude and flight conditions. For example, the control of its angle of attack and sideslip angle must be precise to a certain degree; its flight Mach number and dynamic pressure must be big enough. This paper explores the aerodynamic characteristics such as the variations of drag coefficient, lift coefficient and pitch-moment coefficient with that of angle of attack at different Mach numbers. It contrasts two flight control methods in terms of their merits and drawbacks and then analyzes the feasibility of using the normal overload control pilot. It concludes preliminarily that: 1) the lift coefficient of the hypersonic flight vehicle and its drag coefficient increase with increasing angle of attack, whereas its longitudinal moment coefficient decreases with increasing angle of attack; when Mach numbers are quite big, its aerodynamic force and moment are very linear with the changes in angle of attack; 2) the normal overload control pilot can achieve the control of the angle of attack of a flight vehicle and is sensitive to wind field changes, and its accelerometer is quite accurate. Therefore, the control method enjoys a better engineering feasibility.

This paper considers the application of two types of performance accounting systems to a boundary layer ingesting (BLI) propulsion configuration to identify features that arise due to propulsion-airframe integration. To do this, a canonical, two-dimensional BLI configuration consisting of a fuselage element propelled by an integrated ducted propulsor has been developed, and aerodynamic forces and power for a range of angle of attack and propulsor mass flow has been calculated using MSES, a viscous-inviscid flow solver for multi-element airfoils. In a traditional thrust-drag accounting, BLI manifests as a negative “interference drag,” equal to 46% of the isolated fuselage element drag at zero angle of attack and design mass flow. The results also show that accounting for changes in vehicle angle of attack before changes in throttle setting reduces variation in the throttle-dependent force and power increments with respect to the angle of attack, suggesting that such an approach may be appropriate for BLI configurations. The second type of accounting system was the Power Balance Method, which has been suggested to be more suitable for the analysis of integrated geometries with BLI. The results show that the boundary layer, wake, and jet dissipation of the BLI configuration vary with configuration angle of attack and mass flow, a behavior that must be considered when using power-based accounting. The analysis also highlights the difficulty in defining separate contributions to viscous dissipation from adjacent surface wake and jet flows that are inherent to BLI configurations.

The aerodynamic properties of a bird’s tail, and the forces produced by it, can be predicted by using slender lifting surface theory. The results of the model show that unlike conventional wings, which generate lift proportional to their area, the lift generated by the tail is proportional to the square of its maximum continuous span. Lift is unaffected by substantial variations in tail shape provided that the tail initially expands in width along the direction of flow. Behind the point of maximum width of the tail the flow is dominated by the wake of the forward section. Any area behind this point therefore causes only drag, not lift. The centre of lift is at the centre of area of the part of the tail in front of the point of maximum width. The moment arm of the tail, about its apex, is therefore more than twice the moment arm of a conventional wing about its leading edge. The drag of the tail is a combination of induced drag proportional to lift, and profile drag proportional to surface area. Induced drag can be halved by drooping the outer tail feathers to generate leading edge suction. This may be used for control, particularly in slow flight when both wings and tail are generating maximum lift. The slender lifting surface model is very accurate at angles of attack below about 15°. At higher angles of attack vortex formation at the leading edge can stabilize the flow over the tail and thereby generate increased lift by a detached vortex mechanism. Asymmetry in the orientation of the leading edges with relation to the freestream (either in roll, yaw or caused by asymmetry in the planform) is amplified in the flow field and leads to large rolling and yawing forces that could be used for control in turning manoeuvres. The slender lifting surface model can be used to examine the effect of variations in tail shape and tail spread on the aerodynamic performance of the tail. A forked tail that has a triangular planform when spread to just over 120° gives the best aerodynamic performance and this may be close to a universal optimum, in terms of aerodynamic efficiency, for a means to control pitch and yaw. However, natural selection may act to optimise the performance of the tail when it is not widely spread. The tail is normally only widely spread during manoeuvres, or at low speeds, selection may act to improve the efficiency of the tail when it is spread to only a relatively narrow angle - for example to maximize the bird’s overall lift to drag ratio - the optimum shape at any angle of spread is that which gives a straight trailing edge to the tail. This will always give a slightly forked planform, but fork depth will depend on how widely the tail is spread when selection acts, and this depends on the criteria for optimization under natural selection. A forked tail is more sensitive to changes in angle of attack and angle of spread, than other tail types. Forked tails are more susceptible to damage than other tail morphologies, and suffer a greater loss of performance following damage. Forked tails also confer less inherent stability than any other type of tail. Aerodynamic performance may not be an im portant optimization criterion for birds that fly in a cluttered environment, or do not fly very much. Natural selection, under these conditions, may favour tails of other shapes. The aerodynamic costs of sexually selected elongated tails can be predicted from the model. These predictions can be used to distinguish between the various models for the evolution of elongated tails. Elongated graduated tails and pintails could have evolved either through a Fisherian or H andicap mechanism. The evolution of long forked tails can be initially favoured by natural selection, the pattern of feather elongation seen in sexually selected forked tails is predicted by the Fisher hypothesis (Fisher 1930) but not by any of the other theories of sexual selection.

The length of wind turbine rotor blades has been increasing over the last few decades. Higher stresses arise, particularly at the blade root because of the longer lever arm. One way to reduce unsteady blade-root stresses caused by turbulence, gusts, or wind shear is to actively control the lift in the blade tip region. Airfoils with morphing trailing edges represent one promising method to control the lift, and consequently the loads acting on the blade. In the present study, the unsteady behavior and load reduction potential of an airfoil with a morphing trailing edge is investigated. Time-resolved, two-dimensional Reynolds-Averaged Navier-Stokes (RANS) simulations are performed for a typical thin wind turbine airfoil with a morphing trailing edge. A deformable grid is used to simulate the trailing edge movement. First, simulations are carried out focusing on the phase shift between the trailing edge deflection and the dynamic lift coefficient. Based on the results, a dynamic change in angle of attack and a simultaneously variably deflected trailing edge is simulated. It is shown that the unsteady lift coefficient resulting from the dynamic angle of attack can be reduced to a near-zero value, if the trailing edge is phased such as to counter the pitch motion. In contrast, the dynamic lift can be increased by the trailing edge deflection if the angle of attack and the deformable trailing edge oscillate in phase.

A viable active rotor blade flap system for vibration control needs to address the actuator authority, the sensitivity of flap pitch deflections to changes in angle of attack, aerodynamic moments generated by flap deflections themselves and inertial moments due to blade plunge motions. This paper presents the experimental wind tunnel results of a new active rotor blade flap system that has the potential to overcome these problems. This active rotor blade flap system is insensitive to airspeed, angle of attack changes and plunge motions because of a novel high authority actuation system, C-blocks, and the utilization of a mass and aerodynamically balanced flap. C-block actuators are curved piezoelectric benders which can provide over twice the force of comparable straight benders without requiring the use of external leveraging systems necessary with piezoelectric stacks. The initial wind tunnel results proved that the use of C-block actuators and a mass and aerodynamically balanced flap can generate flap deflections in excess of 17” pealc-topeak that are independent of airspeed. Additionally, it was proven that the C-block driven flap is capable of creating pitch changes of the entire rotor blade section demonstrating potential for full flight control.

We compare computational, experimental and quasi-steady forces in a generic hovering wing undergoing sinusoidal motion along a horizontal stroke plane. In particular, we investigate unsteady effects and compare two-dimensional (2D) computations and three-dimensional (3D) experiments in several qualitatively different kinematic patterns. In all cases, the computed drag compares well with the experiments. The computed lift agrees in the cases in which the sinusoidal changes in angle of attack are symmetrical or advanced with respect to stroke positions, but lags behind the measured 3D lift in the delayed case. In the range of amplitudes studied here, 3-5 chords, the force coefficients have a weak dependence on stroke amplitude. As expected, the forces are sensitive to the phase between stroke angle and angle of attack, a result that can be explained by the orientation of the wing at reversal. This dependence on amplitude and phase suggests a simple maneuver strategy that could be used by a flapping wing device. In all cases the unsteady forces quickly reach an almost periodic state with continuous flapping. The fluid forces are dominated by the pressure contribution. The force component directly proportional to the linear acceleration is smaller by a factor proportional to the ratio of wing thickness and stroke amplitude; its net contribution is zero in hovering. The ratio of wing inertia and fluid force is proportional to the product of the ratio of wing and fluid density and the ratio of wing thickness and stroke amplitude; it is negligible in the robotic wing experiment, but need not be in insect flight. To identify unsteady effects associated with wing acceleration, and coupling between rotation and translation, as well as wake capture, we examine the difference between the unsteady forces and the estimates based on translational velocities, and compare them against the estimate of the coupling between rotation and translation, which have simple analytic forms for sinusoidal motions. The agreement and disagreement between the computed forces and experiments offer further insight into when the 3D effects are important. A main difference between a 3D revolving wing and a 2D translating wing is the absence of vortex shedding by a revolving wing over a distance much longer than the typical stroke length of insects. No doubt such a difference in shedding dynamics is responsible in part for the differences in steady state force coefficients measured in 2D and 3D. On the other hand, it is unclear whether such differences would have a significant effect on transient force coefficients before the onset of shedding. While the 2D steady state force coefficients underpredict 3D forces, the transient 2D forces measured prior to shedding are much closer to the 3D forces. In the cases studied here, the chord is moving between 3 to 5 chords, typical of hovering insect stroke length, and the flow does not appear to separate during each stroke in the cases of advanced and symmetrical rotation. In these cases, the wing reverses before the leading edge vortex would have time to separate even in 2D. This suggests that the time scale for flow separation in these strokes is dictated by the flapping frequency, which is dimensionally independent. In such cases, the 2D unsteady forces turn out to be good approximations of 3D experiments.

The penguin is the fastest underwater swimmer among the wing-propelled diving birds. To figure out the mechanism for its excellent swimming, the hydrodynamic performance of a penguin wing is numerically investigated using an immersed boundary method with the incompressible flow solver. This study examines the effects of feathering, flapping, and Strouhal number (St) under preset motion. Results indicate that feathering is the primary contributor to thrust generation. The change in angle of attack (AoA) can qualitatively reflect the change in lift but not thrust. Therefore, a new variable, angle of thrust (AoT, αT), is introduced to effectively reflect the change of thrust across different kinematic parameters. Optimal feathering amplitude balances the decrease in AoA and the increase in feathering angle to achieve the highest AoT and thrust. Excessive feathering amplitude degrades the leading-edge vortex to shear layers, transforms the pressure side to the suction side, and ultimately causes negative thrust (drag). Spatial analysis of the thrust shows that the outer three-fifths of the wing are the primary source of thrust, contributing 85.4% of thrust generation at optimal feathering amplitude. Flapping amplitude has little impact on the optimal feathering amplitude. The optimal feathering amplitude increases linearly with the St number in the scope of examination, leading to larger thrust but lower swimming efficiency. Thus, a dimensionless number, Stm, is introduced to describe the optimal wing motion. This work provides new insights into the propulsion mechanism of aquatic swimmers with flapping–feathering wings and helps design novel bio-inspired aquatic vehicles.

Intracycle control for cross-flow turbines employs sinusoidal perturbations in rotational speed to affect turbine power output and loads. This technique is explored for one- and two-bladed turbines with experiments that combine performance measurements with in-rotor flow-field measurements using non-intrusive particle image velocimetry. Performance enhancement is demonstrated for a wide range of control parameters but is found to be more sensitive to the sinusoidal phase offset than amplitude. Optimal performance is observed under conditions which maintain constant nominal blade angle of attack and consistently high blade-relative velocities once the static stall angle is exceeded during the power stroke. This maintains high lift and delays vortex separation. Perhaps most significantly, kinematics are also identified which decrease peak turbine loading by 12% while still producing marginally higher power output, highlighting the utility of intracycle control for load mitigation. The range of control parameters that produce these beneficial loading properties is relatively narrow and flow-fields are similar to operation at a constant rotation rate. We hypothesize that reductions in maximum loading are achieved by smoothing the changes in angle of attack and blade relative velocity profiles throughout the cycle.

Fixed-wing miniature aerial vehicles usually fly at low altitudes that are often exposed to turbulent environments. Gust soaring is a flight technique of energy harvesting in such a complex and stochastic domain. The presented work shows the feasibility and benefits of exploiting a nonstationary environment for a small unmanned aerial vehicle. A longitudinal dynamics trajectory is derived, showing significant benefits in extended flight with a sinusoidal wind profile. An optimization strategy for active control is performed, with the aim of obtaining the most effective set of gains for energy retrieval. Moreover, a three-dimensional multipoint model confirms the feasibility of energy harvesting in a more complex spatial wind field. The influence of unsteady aerodynamics is determined on the overall energy gain along the flight path with active proportional control. The aerodynamic derivatives describing the contribution to lift by a change in angle of attack and elevator deflection are identified as the most contributing aerodynamic parameters for energy harvesting in a gusty environment, and are therefore suggested as a basic objective function of an unmanned aerial vehicle design for such a flight strategy.

In the realm of marine science and engineering, hydrofoils play a pivotal role in the efficiency and performance of marine turbines and water-jet pumps. In this investigation, the boundary layer characteristics of an NACA0009 hydrofoil with a blunt trailing edge are focused on. The effectiveness of both the two-equation gamma theta (γ-Reθt) transition model and the one-equation intermittency (γ) transition model in forecasting boundary layer behavior is evaluated. When considering natural transition, these two models outperform the shear stress transport two-equation (SST k-ω) turbulence model, notably enhancing the accuracy of predicting boundary layer flow distribution for chord-length Reynolds numbers (ReL) below 1.6 × 106. However, as ReL increases, both transition models deviate from experimental values, particularly when ReL is greater than 2 × 106. The results indicate that the laminar separation bubble (LSB) is sensitive to changes in angles of attack (AOA) and ReL, with its formation observed at AOA greater than 2°. The dimensions of the LSB, including the initiation and reattachment points, are found to contract as ReL increases while maintaining a constant AOA. Conversely, an increase in AOA at similar ReL values leads to a reduced size of the LSB. The findings are essential for the design and performance optimization of water-jet pumps, particularly in predicting and flow separation and transition phenomena.