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

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

The aerodynamic performance of hovering insects is largely explained by the presence of a stably attached leading edge vortex (LEV) on top of their wings. Although LEVs have been visualized on real, physically modeled, and simulated insects, the physical mechanisms responsible for their stability are poorly understood. To gain fundamental insight into LEV stability on flapping fly wings we expressed the Navier–Stokes equations in a rotating frame of reference attached to the wing's surface. Using these equations we show that LEV dynamics on flapping wings are governed by three terms: angular, centripetal and Coriolis acceleration. Our analysis for hovering conditions shows that angular acceleration is proportional to the inverse of dimensionless stroke amplitude, whereas Coriolis and centripetal acceleration are proportional to the inverse of the Rossby number. Using a dynamically scaled robot model of a flapping fruit fly wing to systematically vary these dimensionless numbers, we determined which of the three accelerations mediate LEV stability. Our force measurements and flow visualizations indicate that the LEV is stabilized by the `quasi-steady' centripetal and Coriolis accelerations that are present at low Rossby number and result from the propeller-like sweep of the wing. In contrast, the unsteady angular acceleration that results from the back and forth motion of a flapping wing does not appear to play a role in the stable attachment of the LEV. Angular acceleration is, however, critical for LEV integrity as we found it can mediate LEV spiral bursting, a high Reynolds number effect. Our analysis and experiments further suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100<Re<14,000). LEVs are stable and continue to augment force even when they burst. These and similar findings for propellers and wind turbines at much higher Reynolds numbers suggest that even large flying animals could potentially exploit LEV-based force augmentation during slow hovering flight, take-offs or landing. We calculated the Rossby number from single-wing aspect ratios of over 300 insects, birds, bats, autorotating seeds, and pectoral fins of fish. We found that, on average, wings and fins have a Rossby number close to that of flies (Ro=3). Theoretically, many of these animals should therefore be able to generate a stable LEV, a prediction that is supported by recent findings for several insects, one bat, one bird and one fish. This suggests that force augmentation through stably attached (leading edge) vortices could represent a convergent solution for the generation of high fluid forces over a quite large range in size.

/pdf/rotational-accelerations-stabilize-leading-edge-vortices-on-2vxyvw418u.pdf

Rotational accelerations stabilize leading edge vortices on revolving fly wings

Particle image velocimetry (PIV) has evolved to be the dominant method for velocimetry in experimental fluid mechanics and has contributed to many advances in our understanding of turbulent and complex flows. In this article we review the achievements of PIV and its latest implementations: time-resolved PIV for the rapid capture of sequences of vector fields; tomographic PIV for the capture of fully resolved volumetric data; and statistical PIV, designed to optimize measurements of mean statistical quantities rather than instantaneous fields. In each implementation, the accuracy and spatial resolution are limited. To advance the method to the next level, we need a completely new approach. We consider the fundamental limitations of two-pulse PIV in terms of its dynamic ranges. We then discuss new paths and developments that hold the promise of achieving a fundamental reduction in uncertainty.

Particle Image Velocimetry for Complex and Turbulent Flows

The topic of this article is a review of the approach to extract pressure fields from flow velocity field data, typically obtained with particle image velocimetry (PIV), by combining the experimental data with the governing equations. Although the basic working principles on which this procedure relies have been known for quite some time, the recent expansion of PIV capabilities has greatly increased its practical potential, up to the extent that nowadays a time-resolved volumetric pressure determination has become feasible. This has led to a novel diagnostic methodology for determining the instantaneous flow field pressure in a non-intrusive way, which is rapidly finding acceptance in an increasing variety of application areas. The current review describes the operating principles, illustrating how the flow-governing equations, in particular the equation of momentum, are employed to compute the pressure from the material acceleration of the flow. Accuracy aspects are discussed in relation to the most dominating experimental influences, notably the accuracy of the velocity source data, the temporal and spatial resolution and the method invoked to estimate the material derivative. In view of its nature of an emerging technique, recently published dedicated validation studies will be given specific attention. Different application areas are addressed, including turbulent flows, aeroacoustics, unsteady wing aerodynamics and other aeronautical applications.

/pdf/piv-based-pressure-measurement-4meoomjt7c.pdf

PIV-based pressure measurement

Gliding birds continually change the shape and size of their wings, presumably to exploit the profound effect of wing morphology on aerodynamic performance. That birds should adjust wing sweep to suit glide speed has been predicted qualitatively by analytical glide models, which extrapolated the wing's performance envelope from aerodynamic theory. Here we describe the aerodynamic and structural performance of actual swift wings, as measured in a wind tunnel, and on this basis build a semi-empirical glide model. By measuring inside and outside swifts' behavioural envelope, we show that choosing the most suitable sweep can halve sink speed or triple turning rate. Extended wings are superior for slow glides and turns; swept wings are superior for fast glides and turns. This superiority is due to better aerodynamic performance-with the exception of fast turns. Swept wings are less effective at generating lift while turning at high speeds, but can bear the extreme loads. Finally, our glide model predicts that cost-effective gliding occurs at speeds of 8-10 m s(-1), whereas agility-related figures of merit peak at 15-25 m s(-1). In fact, swifts spend the night ('roost') in flight at 8-10 m s(-1) (ref. 11), thus our model can explain this choice for a resting behaviour. Morphing not only adjusts birds' wing performance to the task at hand, but could also control the flight of future aircraft.

How swifts control their glide performance with morphing wings

A novel technique is proposed and investigated for the estimation of the body force field resulting from the operation of a dielectric barrier discharge plasma actuator. The technique relies on the measurement of the spatio-temporal evolution of the induced velocity field using high-speed particle image velocimetry (PIV). The technique has the advantage of providing spatial distribution of the body force vector field. A full Navier–Stokes term decomposition is applied on the evolving field along with additional closure norms in order to decouple the pressure gradient and body force terms. Results are compared with load-cell measurements of the direct reaction force and also momentum balance calculations based on the PIV field. Agreement between the different methods is observed. The data can easily be incorporated in computational flow solvers and also be used for validation and calibration of numerical plasma models.

/pdf/measurement-of-the-body-force-field-of-plasma-actuators-14kknzli7p.pdf

Measurement of the body force field of plasma actuators

Propeller Wing Aerodynamic Interference

This paper examines the capability of a commercial RANS solver for the simulation of wingtip-mounted propellers. The applicability of actuator-disk and actuator-line models to reduce the cost of propeller modeling is investigated in its most accurate form, by extracting and applying propeller blade loading from full-blade simulations. The results obtained from all numerical simulations are validated based on measurement data from an in-house wind-tunnel experiment. An extensive grid dependency study is presented for the isolated propeller and the wing to distinguish discretization errors from model errors. It is concluded that RANS CFD with a simple one-equation turbulence model (Spalart–Allmaras) is capable of modeling the aerodynamic interactions for the wingtip-mounted propeller in tractor configuration, provided that numerical diffusion is accounted for by a grid dependency study or prevented by local grid refinement. The actuator-line model is fully able to replace propeller blade modeling in the simulation, and agreement with the full-blade simulations is found in time-accurate and time-average wing loading. The actuator-disk model further reduces the cost of the simulation by removing time dependency, at the cost of a small penalty in the accuracy of the time-averaged flowfield and lift distribution on the wing.

/pdf/validation-and-comparison-of-rans-propeller-modeling-methods-5dcn6wbvhb.pdf

Leo Veldhuis

Papers

How swifts control their glide performance with morphing wings

Measurement of the body force field of plasma actuators

Propeller Wing Aerodynamic Interference

How swifts control their glide performance with morphing wings

Validation and Comparison of RANS Propeller Modeling Methods for Tip-Mounted Applications