Session R6: Aerodynamics: Wing/Vortex Interaction

High lift generation of low-aspect-ratio wings

The time-averaged flow field in the center-span of low-aspect-ratio rectangular wings is experimentally measured. It is shown that lift stall is preceded by shedding of strong trailing-edge vorticity. The induced downwash of the tip vortices delays the growth of the attached boundary layer as well as leading-edge separation. Reattached flow occurs for sufficiently low aspect ratios and results in a smooth merging of the flow at the trailing edge thus assisting in satisfying a Kutta condition there. As a consequence, the strength of vorticity shed from the trailing edge is decreased and allows for continued lift generation at high angles of attack. When the reattachment point passes beyond the trailing edge, a strong shear layer is generated there and represents negative lift, leading to stall with a slight increase in angle of attack or aspect ratio.   

Identification of separate flow features in the shear layer

Analyzing unsteady flow fields primarily involves the identification of dynamically significant regions of vorticity in the flow. Detection of all the flow features is essential for an accurate description of the physics of the flow, which eventually helps in improving flow modeling and predictions. Eulerian criteria such as $\lambda_2$ and $\Gamma_2$ successfully identify large scale structures based on local velocity gradients and topology but do not detect the coherent vortices with the concentrated vorticity in a shear layer. The identification of these smaller structures within the shear layer is important when predicting the overall circulatory contribution to the aerodynamic forces produced, in applications such as flapping wing design. In order to detect the smaller flow features along with the prominent large scale vortices, an alternative method of vortex identification is proposed in which the flow structures are detected based on the vorticity contours. This method is applied to numerical and experimental data of a pitching panel to highlight its robustness. In addition, the finite time Lyapunov exponent (FTLE) is calculated to show that the boundaries of the material lines and identified vorticity contours coincide.   

Potential flow predictions for a flapping flat plate wing

It is well established that the leading edge vortex is one of the major contributors to the generation of lift on a flapping insect wing. However, the contributions of the trailing edge vortices and the shear layer to unsteady force production mechanisms needs more investigation. The individual contribution of different flow structures is especially important if reliable theoretical predictions of lift and drag are to be made, that eventually assist in the design of micro air vehicles. The current work aims to distinguish different flow features of an unsteady flow field generated by a flapping wing in hover and to quantify the role played by them in the generation of aerodynamic forces. This is achieved by employing a semi-empirical potential flow model that allows for the calculation of lift by theoretically recreating the potential flow field based on the vortex strengths and locations obtained from phase-averaged particle image velocimetry (PIV) data. Individual flow structures are detected in the PIV data based on the vorticity contours. The theoretically predicted lift is compared with direct force measurements to demonstrate the utility and limitations of the model.   

The Structure of a Trailing Vortex from a Perturbed Wing

The unsteady structure of a trailing vortex may be interpreted as a three-dimensional gust. Such a vortex, or gust, potentially impinges upon a follower wing positioned on or near its trajectory, thereby giving rise to unsteady buffeting of its surface and/or disruption of its flight path. Stereoscopic particle image velocimetry and a three-dimensional construction technique are employed to characterize the structure of a trailing vortex from a wing subjected to displacement perturbations in the heaving mode with an amplitude an order of magnitude smaller than the diameter of the vortex and a wavelength two orders of magnitude greater than the diameter of the vortex. This perturbation leads to relatively large undulations of axial velocity deficit within, and circulation of, the vortex. Along the axis of the vortex, these fluctuations are associated with alternating regions of low and high values of swirl ratio. This results in an internal vortex structure comprised of successive regions of instability separated by stabilized regions. These mechanisms are therefore linked to the origin of the large gust-like fluctuations of axial velocity deficit and circulation.   

Characterization of vortical gusts produced by a heaving plate

To experimentally investigate the interaction between a wing and a spanwise vortical gust, a simple gust generator has been built and tested. This consists of a transversely heaving flat plate that changes direction to release a vortex, which then convects downstream to interact with a wing. Previous experiments have shown that, immediately downstream of the plate, the circulation of the generated vortex is proportional to the heaving speed of the plate. The forces that the gusts exert on a downstream wing were shown to be strongly repeatable and consistent with a passing vortex. This presentation will discuss the properties of the vortical gusts as they move downstream, and relate those properties to the important dimensionless parameters of the flow. These properties include the convection speed and circulation of the vortex, as well as the enstrophy due to the wake of the plate.   

Measurement and Modelling of a Heaving Airfoil Flow

An outline of a low order modelling procedure of a heaving airfoil in still fluid using experimental measurements is provided. Due to its relative simplicity, the proposed procedure is applicable for the analysis of flow fields within complex and unsteady geometries and it is ideal for analysing the data obtained by experimentation. Currently, this procedure is used to model and predict the flow field evolution using small number of low profile load sensors and flow field measurements. The time delay neural networks are used in order to estimate the flow field. The neural networks estimate the amplitudes of the most energetic modes using four sensory inputs. The modes are calculated using proper orthogonal decomposition (POD) of the flow field data obtained experimentally by time-resolved, phase-locked particle imaging velocimetry. In order to permit the use of proper orthogonal decomposition, the measured flow field is mapped onto a stationary domain using volume preserving transformation. The analysis performed by the model showed good estimation quality within the parameter range used in the training procedure. However, the performance deteriorates for cases out of this range. This state indicates that, in order to improve the robustness of the model, both the decomposition and the training data sets must be diverse.   

Evaluating low order models for force prediction in high-amplitude gusts

The unsteady forces on a plunging wing were measured for high-amplitude transient motions. The plunging velocity paralleled the canonical sine-squared transverse gust profile, including cases with plunging velocities far greater than the free stream velocity. The ratio of plunging velocity to free stream velocity was varied from one-sixth to 24 which allowed for quantification and demonstration of the increasing error in typical force prediction models. Each velocity ratio was tested at multiple values of free stream velocity. All cases were tested with a free stream to wing incidence angle of zero degrees. Forces and moments were measured on the same rigid flat plate wing for all cases. Measured forces during the gust were compared to forces predicted by various models, and the error between them was quantified. The parameter space defining the sine-squared gust was then partitioned into regions of high accuracy for unsteady force prediction models such as potential flow, quasi-steady based on steady measurements, and indicial functions. This highlights the strengths and weaknesses of each model, and identifies gust conditions that are not adequately modeled by any of these tools.   

A versatile low-dimensional vortex model for investigating unsteady aerodynamics

In previous work, we demonstrated a hybrid vortex sheet/point vortex model that captures the non-linear aerodynamics of a plate translating at a high angle of attack. We used vortex sheets to model the shear layers emerging from the plate, and point vortices to capture the effect of the coherent vortex structures. In this work, we introduce modifications that allow the model to work for a larger range of plate kinematics over longer periods of time. First, following the example of Ramesh et al., we relax the Kutta condition at the leading edge and determine vorticity flux based on a suction parameter instead. To prevent the vortex sheet from becoming unstable near the resulting singular edge, we explicitly filter out short-wave disturbances along the sheet while redistributing the sheet's control points. Second, by looking for intersections between the vortex sheets and any repelling Lagrangian coherent structures, the model can detect the formation of new coherent vortices. Trailing portions of the sheets that become dynamically distinct from the shear layers are rolled up into point vortices. We test these modifications on a variety of problems, including pitch-up, impulsive translation at low angles of attack, as well as flow response to pulse actuation near the leading edge.   

Balance equations for triple-joint vortex-sheet structures

A vortex sheet is the limiting case for a viscous shear layer as the thickness approaches zero. Recently, vortex-sheet based flow models have been demonstrated to provide significant reduction for numerical simulations of viscous and inviscid flows. In such modeling approaches, a prominent phenomenon is the formation of a new vortex sheet from existing vortex sheets, thereby creating a triple-joint vortex-sheet structure. In this study, the formation of the new vortex sheet is analytically determined by applying conservation laws of mass and momentum to flow surrounding the entire triple-joint vortex-sheet structure, together with the boundary conditions specific to any application. As a result, a general condition is obtained to determine the angle, strength, and velocity of the new vortex sheet. This model is validated by simulating airfoils in steady and unsteady background flows and comparing the flow structures and force calculations with experimental data. While the performance of this model is demonstrated in this study for the vortex shedding problem at the trailing edge, its future applications could be extended to flow separation on a smooth surface and triple contact point of multi-phase flows.   

On the leading edge vortex of thin wings

On thin wings, the sharp leading edge triggers laminar separation followed by reattachment, forming a Leading Edge Vortex (LEV). This flow feature is of paramount importance because, if periodically shed, it leads to large amplitude load fluctuations, while if stably attached to the wing, it can provide lift augmentation. We found that on asymmetric-spinnaker-type yacht sails, the LEV can be stable despite the relatively low sweep (30$^{\circ}$). This finding, which was recently predicted numerically by Viola et al. (Ocean Eng., 2014; 90:93-103), has been confirmed through current flume tests on a 1:115th model scale sail. Forces were measured and Particle Image Velocimetry was performed on four horizontal sail sections at a Reynolds number of 1.7x10$^{4}$. Vortex detection revealed that the LEV becomes progressively larger and more stable towards the highest sections, where its axis has a smaller angle with respect to the freestream velocity. Mapping the sail section on a rotating cylinder through a Joukowski transformation, we quantified the lift augmentation provided by the LEV on each sail section. These results open up new sail design strategies based on the manipulation of the LEV and can be applicable to the wings of unmanned aerial vehicles and underwater vehicles.