Model of film coating with weakly curved surface

We use the perturbation method to construct a solution of the plane problem of elasticity for a film-foundation composite where the film surface is weakly curved. In the case where the film surface has a periodic shape, the problem solution in each approximation is represented in terms of Fourier series with coefficients expressed in terms of quadrature. In the first approximation, we obtain the stresses on the film surface and on the interphase surface in terms of the surface curvature, the film average thickness, and the film-to-foundation Young’s modulus ratio.     

Entry flow in weakly curved ducts

Summary The properties of steady incompressible flow in the entry region of curved ducts are studied theoretically for large Reynolds numbers. Under the assumption that the inviscid core flow may be approximated sufficiently well by a potential vortex the boundary layer equations are solved by means of integral methods. In order to improve the accuracy momentum as well as energy relationships are used.

---

Einlaufströmung in schwach gekrümmten Rohren

Übersicht Die Eigenschaften einer stationären, inkompressiblen Strömung im Einlaufbereich gekrümmter Rohre werden für große Reynoldszahlen theoretisch untersucht. Unter der Voraussetzung, daß die reibungsfreie Kernströmung hinreichend genau durch einen Potentialwirbel angenähert werden kann, werden die Grenzschichtgleichungen mit Integralmethoden gelöst. Um die Genauigkeit zu erhöhen, werden sowohl Impuls- als auch Energiebeziehungen verwendet.

     

Passive flow control by membrane wings for aerodynamic benefit

The coupling of passive structural response of flexible membranes with the flow over them can significantly alter the aerodynamic characteristic of simple flat-plate wings. The use of flexible wings is common throughout biological flying systems inspiring many engineers to incorporate them into small engineering flying systems. In many of these systems, the motion of the membrane serves to passively alter the flow over the wing potentially resulting in an aerodynamic benefit. In this study, the aerodynamic loads and the flow field for a rigid flat-plate wing are compared to free trailing-edge membrane wings with two different pre-tensions at a chord-based Reynolds number of approximately 50,000. The membrane was silicon rubber with a scalloped free trailing edge. The analysis presented includes load measurements from a sting balance along with velocity fields and membrane deflections from synchronized, time-resolved particle image velocimetry and digital image correlation. The load measurements demonstrate increased aerodynamic efficiency and lift, while the synchronized flow and membrane measurements show how the membrane motion serves to force the flow. This passive flow control introduced by the membranes motion alters the flows development over the wing and into the wake region demonstrating how, at least for lower angles of attack, the membranes motion drives the flow as opposed to the flow driving the membrane motion.     

On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings

Insect wings are subjected to fluid, inertia and gravitational forces during flapping flight. Owing to their limited rigidity, they bent under the influence of these forces. Numerical study by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007) showed that a flexible wing is able to generate almost as much lift as a rigid wing during flapping. In this paper, we take a closer look at the relationship between wing flexibility (or stiffness) and aerodynamic force generation in flapping hovering flight. The experimental study was conducted in two stages. The first stage consisted of detailed force measurement and flow visualization of a rigid hawkmoth-like wing undergoing hovering hawkmoth flapping motion and simple harmonic flapping motion, with the aim of establishing a benchmark database for the second stage, which involved hawkmoth-like wing of different flexibility performing the same flapping motions. Hawkmoth motion was conducted at Re = 7,254 and reduced frequency of 0.26, while simple harmonic flapping motion at Re = 7,800 and 11,700, and reduced frequency of 0.25. Results show that aerodynamic force generation on the rigid wing is governed primarily by the combined effect of wing acceleration and leading edge vortex generated on the upper surface of the wing, while the remnants of the wake vortices generated from the previous stroke play only a minor role. Our results from the flexible wing study, while generally supportive of the finding by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007), also reveal the existence of a critical stiffness constant, below which lift coefficient deteriorates significantly. This finding suggests that although using flexible wing in micro air vehicle application may be beneficial in term of lightweight, too much flexibility can lead to deterioration in flapping performance in terms of aerodynamic force generation. The results further show that wings with stiffness constant above the critical value can deliver mean lift coefficient almost the same as a rigid wing when executing hawkmoth motion, but lower than the rigid wing when performing a simple harmonic motion. In all cases studied (7,800 ≤ Re ≤ 11,700), the Reynolds number does not alter the force generation significantly.     

A case of analogy between the unsteady aerodynamic characteristics of wings

The problems of harmonic oscillations and aperiodic wing motions are considered in the linear formulation. On the basis of the representation of the aerodynamic characteristics in terms of the rotary derivative coefficients it is shown that these coefficients are the same for the case of very low oscillation frequencies and the case of a linear variation of the parameters for aperiodic motion.     

Computation of field structure and aerodynamic characteristics of delta wings at high angles of attack

A numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics that are dominated by the effect of the breakdown of the leading-edge vortices. The methods that analyze the flowfield structure quantitatively were given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and farther away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, that is, A is negativee, so the vortex is unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small perturbation occurs at high angles of attack. However, after a critical angle of attack is reached the vortices breakdown completely at the wing apex, and the instability resulting from the vortex breakdown disappears.     

Iteration schemes for rapid post‐stall aerodynamic prediction of wings using a decambering approach

Nonlinear aerodynamics of wings may be evaluated using an iterative decambering approach. In this approach, the effect of flow separation due to stall at any wing section is modeled as an effective reduction in section camber. The approach uses a wing analysis method for potential‐flow calculations and viscous airfoil lift curves for the sections as input. The calculation procedure is implemented using a Newton–Raphson iteration to simultaneously satisfy the boundary condition, which comes from potential‐flow wing theory, and drive the sectional operating points toward their respective viscous lift curves, as required for convergence. Of particular interest in this research is the calculation of the residuals during the Newton iteration. Unlike a typical implementation of the Newton iteration, the residual calculation is not performed via a straightforward function evaluation, but rather by estimating the target operating points on the input viscous lift curves. Estimation of these target operating points depends on the assumptions made in the cross‐coupling of the decambering at the different sections. This paper presents four residual calculation schemes for the decambering approach. The residual calculation schemes are compared against each other to assess computational speed and robustness. Decambering results are also compared with higher‐order computational fluid dynamics (CFD) solutions for rectangular and swept wings. Results from the best scheme compare well with the CFD solutions for the rectangular wing, motivating further development of the method. Poor predictions for the swept wings are traced to spanwise propagation of separated flow at stall, highlighting the limitations of the current approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Thin wings in the presence of a moving pressure wave of finite thickness

A study is made of the velocity field induced by the motion of a thin wing and an incident pressure wave of finite extent with variable gas parameters behind the wave front.     

Effect of skin flexibility on aerodynamic performance of flexible skin flapping wings for micro air vehicles

Experimental Techniques - As part of the ongoing research on micro air vehicles, the present work focuses on the effect of membrane flexibility on the aerodynamic performance of flexible latex...     

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform (shape and aspect ratio) on the aerodynamic force production of model insect wings in sweeping (rotating after an initial start) motion at Reynolds number 200 and 3500 at angle of attack 40° are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio (AR) of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing (forewing), hawkmoth and dragonfly (forewing), respectively (AR of these wings varies greatly, from 2.84 to 5.45). The following facts are shown. (1) The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex (LEV). (2) The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r ₂ (the radius of the second moment of wing area) is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. (3) The effects of AR are remarkably small: when AR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.     

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform (shape and aspect ratio) on the aerodynamic force production of model insect wings in sweeping (rotating after an initial start) motion at Reynolds number 200 and 3500 at angle of attack 40° are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio (AR) of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing (forewing), hawkmoth and dragonfly (forewing), respectively (AR of these wings varies greatly, from 2.84 to 5.45). The following facts are shown. (1) The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex (LEV). (2) The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r ₂ (the radius of the second moment of wing area) is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. (3) The effects of AR are remarkably small: when AR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients. The project supported by the National Natural Science Foundation of China (10232010 and 10472008) and Ph. D. Student Foundation of Chinese Ministry of Education (20030006022) The English text was polished by Keren Wang.     

Slip coefficients and macroparameter jumps of a diatomic gas with rotational degrees of freedom on a weakly curved spherical surface

Using the half-space moment method, the problem of the slip of a diatomic gas along a rigid spherical surface is solved within the framework of a model kinetic equation previously proposed which takes into account the rotational degrees of freedom of the gas. Second-order slip coefficients (correctionsC _m ^′ , β _R ^′ , and β _R to the isothermal and thermal slip which are linear with respect to the Knudsen number Kn) are obtained. The gas macroparameter jump coefficientsC _v andC _q, which are of the second order in the Knudsen number and characterize the discontinuity of the normal mass and heat fluxes on the gas-rigid phase interface, are calculated. These coefficients are given as functions of the tangential momentum accommodation coefficient, the translational and rotational energy accommodation coefficients, and the Prandtl number. The coefficients are calculated for certain diatomic gases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–173, January–February, 2000.