arXiv subjects

Jennifer A. Franck

Publications and source records attributed to Jennifer A. Franck.

17 recordsLinked to original sources

arXiv2026

Vortex gust interactions with a freely-flying rigid airfoil

This study numerically investigates the interaction between an isolated vortex gust and a freely-flying airfoil, introducing a theoretical framework for interpreting the coupled lift and heave response. This complex and coupled dynamics is important for modern light-weight aircraft where gusts may easily perturb the wing, generating transient changes in trajectory and attitude. Here, the freely-flying airfoil is modeled with a single degree-of-freedom in heave, and is impacted by an isolated vortex gust generated upstream. Computational results demonstrate that the freely-flying airfoil reaches a maximum heave displacement after vortex impingement and subsequently rebounds with a comparable magnitude. The lift coefficient is then modeled by augmenting the lift from a corresponding stationary airfoil interaction with motion induced contributions associated with the induced angle of attack and added-mass. A comparison of the modeled lift with the simulation data confirms that the dynamics of the airfoil before impingement is dominated by these two terms, however the rebound after impingement is only partially explained by the model since it is also influenced by the gust-induced vortex shedding. Comparisons across various parameters show that the pre-impingement motion depends primarily on vortex rotation direction, whereas the post-impingement and induced shedding patterns vary with respect to angle of attack and vortex transverse position. With the lift coefficient of the corresponding stationary airfoil interaction as an input, the model can successfully predict the heave trajectory, thus providing a mechanism to assess the dynamic motion of an airfoil from experimental/computational data of gusts interacting with fixed airfoils.

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arXiv2026

Sweep Angle Effects of Flow Over a Seal Whisker-Inspired Undulated Cylinder

Flow over a seal whisker-inspired undulated cylinder at swept back angles is computationally investigated, comparing the vortex shedding, forces, and wake characteristics to those of an equivalent smooth geometry. Numerous prior studies have demonstrated that undulated cylinders can reduce mean drag and unsteady lift oscillations; however, none have isolated the effects of the sweep angle resulting from whisker positioning in flow. Inspired by the active control seals exert over their whiskers while navigating and sensing in unsteady aquatic environments, this study investigates how such orientation influences the hydrodynamic performance of the geometry. Simulations are performed of flow across a rigid, infinite-span, undulated cylinder at sweep angles from 0 to 60° and at Reynolds numbers of 250 and 500. At zero sweep, the undulated cylinder breaks up coherent two-dimensional vortices, having the effect of reducing drag by 11.4% and root mean square lift by 90.8% compared to a smooth elliptical cylinder. With sweep added, the prominence of spanwise vortex breakup and force suppression is reduced, approximating flow over smooth ellipse geometry as sweep increases. At low sweep angles of 15 and 30 degrees, lift is still suppressed by 72.4% and 47.6% while drag results in a smaller difference of 5.7 and 1.6% reduction from a smooth ellipse. These results reinforce that sweep angle is a significant parameter both mechanically and biologically in the flow physics of whisker-inspired undulated geometries

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arXiv2026

Generation of an isolated vortex gust through a heaving and pitching foil

This study introduces a vortex gust generation method for isolated vortices impacting a downstream airfoil that is applicable to both numerical simulations and experiments. The vortex gust is generated by a symmetric airfoil undergoing a rapid pitching maneuver during a prescribed heaving motion. The resulting vortices propagate along trajectories nearly parallel to the incoming flow, while the associated wake extends obliquely from the vortex core. Despite differences in Reynolds number, rapid pitching duration and detailed vortex structure between simulations and experiments, consistent trends are observed in how the vortex rotation orientation, strength, and position vary with the prescribed motion parameters. Analysis of the lift response of the downstream airfoil shows that the aerodynamic influence associated with the wake does not persist over extended time scales. These results demonstrate that the proposed method enables the controlled generation of vortex gusts with prescribed characteristics, providing a flexible approach for systematic studies of vortex-airfoil interaction.

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arXiv2025

Impacts of Blade Camber on Cross-Flow Turbine Performance and Loading

Cross-flow turbines show promise for renewable energy generation from wind and tidal sources. The rotating reference frame of cross-flow turbine blades results in virtual camber and incidence due to streamline curvature, altering the lift, drag and pitching moment of the blades. Adding geometric camber is therefore likely to alter performance and loading, however there is little consensus regarding the direction of camber that might be most favorable. This study compares 2% concave-in and concave-out cambered blades (NACA 2418) with symmetrical NACA 0018 foils for a turbine with a 0.49 chord-to-radius ratio. Experimental performance measurements are compared across a range of tip-speeds, and particle image velocimetry is used to explore the in-rotor flow evolution through the cycle. Concave-out blades, which enhance virtual camber and lift in the power stroke are found to exhibit sub-optimal performance. In contrast, concave-in cambered blades slightly improved symmetrical blade performance by enhancing downstream flow reattachment, more than compensating for reduced peak power generation. The difference between each cambered foil is seen to grow with increasing tip-speed ratio. Moreover, these concave-in blades reduce peak loading by 13%, which may prove critical in future designs, especially at high tip-speed ratios. Exploration of the near-blade flow fields suggest that the influence of geometric camber is non-linear, and that use of a simplistic summation of both geometric and virtual camber to account for camber effects may be overly simplistic. Despite this, corresponding validated simulations suggest that a small but positive total camber (geometric plus virtual) is optimal for this turbine.

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arXiv2025

Experimental identification of blade-level forces, torque, and pitching moment for cross-flow turbines

Cross-flow turbine power is a net sum of power generation from rotating blades and power loss from rotating support structures. While the aggregate forces and torques at the turbine level are important for end use, these can inhibit a deeper understanding of fluid-structure interactions. Identification of blade-level forces and torques allows for specific investigations into how the fluid forcing on the blade drives rotation and can aid blade structural design. Here, we present a physics-based methodology for extracting blade-level forces and torques from experimental measurements at the axis of rotation of a cross-flow turbine, and demonstrate strong agreement with equivalent blade-only simulations. In doing so, we highlight the often-overlooked pitching moment, which offsets continuous increases in power generation from the tangential force and leads to net-zero power generation at freewheel.

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arXiv2025

Dynamics of intracycle angular velocity control applied to cross-flow turbines

Understanding the intricate dynamics of cross-flow turbines (CFT) is critical to the improvement of performance and optimal control strategies. The current study numerically investigates intracycle control by modulating the angular velocity as a function of blade position for a 2-bladed NACA0018 turbine at a lab-scale chord-based Reynolds number of 45,000. Previous work has implemented intracycle control in attempts to improve turbine efficiency at the best performing tip-speed ratio (TSR). However, intracycle modulation of angular velocity simultaneously changes the time-averaged TSR, making it difficult to understand if the effects on performance are due to changes in mean TSR or imposed by the intracycle dynamics. Thus, this work explores a wider region of TSR across which intracycle control is applied, and assesses turbine performance with respect to time-averaged TSR. The effect of intracycle amplitude and phase shift of the velocity modulation is reported in terms of power generation and blade-level forces, and time-resolved flow fields reveal mechanisms behind changes in efficiency. For the 2-bladed turbine explored, the peak performance at constant angular velocity occurs at approximately TSR = 2. Intracycle control is found to be most beneficial at TSR < 2 where power is increased up to 71% over its constant speed baseline and 12% over the peak performance without control. This is accomplished through boundary layer reattachment through the acceleration portion of the stroke. In contrast, applying control when TSR $\ge 2$ is not beneficial due to degraded performance in the downstream portion of the stroke.

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arXiv2023

Analysis of dynamic stall development on a cross-flow turbine blade

This research computationally investigates the complex dynamic stall phenomena of a cross-flow turbine blade utilizing modal analysis to identify pertinent events within the cycle. The blade rotation perpendicular to the freestream generates a curved relative flow, a non-sinusoidal variation of relative flow speed and angle of attack, and the necessity of travelling through its own wake. These complexities have challenged traditional predictors of dynamic stall such as pitch rate, pitching moment, or relative angle of attack. To investigate these phenomena, aerodynamic loads and flow fields on the blade from large-eddy simulations are examined across two tip speed ratios. Proper orthogonal decomposition of the velocity fields is employed to analyze the spatio-temporal evolution of the dominant flow features. The modes' time development coefficients reveal a stronger representation of the flow at the higher rotation rate, capturing the trend of relative flow velocity magnitude and lift generation on the blade, along with critical events such as vortex formation and detachment. Additionally, mean power generation is enhanced by 40\% by applying a non-constant rotation rate (intracycle control or angular velocity control). The flow fields, supported by corresponding changes in the modal analysis, demonstrate that a delayed stall behavior is responsible for the additional power extraction. Finally, flow curvature, history effects, and induced flow are identified as significant factors that modify the dynamic stall onset and resulting force and moment curves as compared to non-rotating pitching or plunging foils.

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arXiv2023

Effects of wavelength on vortex structure and turbulence kinetic energy transfer of flow over undulated cylinders

Passive flow control research is commonly utilized to provide desirable drag and oscillating lift reduction across a range of engineering applications. This research explores the spanwise undulated cylinder inspired by seal whiskers, shown to reduce lift and drag forces when compared to smooth cylinders. Although the fluid flow over this unique complex geometry has been documented experimentally and computationally, investigations surrounding geometric modifications to the undulation topography have been limited, and fluid mechanisms by which force reduction is induced have not been fully examined. Five undulation wavelength variations of the undulated cylinder model are simulated at Reynolds number $\Rey=250$ and compared with results from a smooth elliptical cylinder. Vortex structures and turbulence kinetic energy (TKE) transfer in the wake are analyzed to explain how undulation wavelength affects force reduction. Modifications to the undulation wavelength generate a variety of flow patterns including alternating vortex rollers and hairpin vortices. Maximum force reduction is observed at wavelengths that are large enough to allow hairpin vortices to develop without intersecting each other and small enough to prevent the generation of additional alternating flow structures. The differences in flow structures modify the magnitude and location of TKE production and dissipation due to changes in mean and fluctuating strain. Decreased TKE production and increased dissipation in the near wake result in overall lower TKE and reduced body forces. Understanding the flow physics linking geometry to force reduction will guide appropriate parameter selection in bio-inspired design applications.

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arXiv2022

A Machine Learning Approach to Classify Vortex Wakes of Energy Harvesting Oscillating Foils

A machine learning model is developed to establish wake patterns behind oscillating foils whose kinematics are within the energy harvesting regime. The role of wake structure is particularly important for array deployments of oscillating foils, since the unsteady wake highly influences performance of downstream foils. This work explores 46 oscillating foil kinematics, with the goal of parameterizing the wake based on the input kinematic variables and grouping vortex wakes through image analysis of vorticity fields. A combination of a convolutional neural network (CNN) with long short-term memory (LSTM) units is developed to classify the wakes into three groups. To fully verify the physical wake differences among foil kinematics, a convolutional autoencoder combined with k-means++ clustering is utilized and four different wake patterns are found. With the classification model, these patterns are associated with a range of foil kinematics. Future work can use these correlations to predict the performance of foils placed in the wake and build optimal foil arrangements for tidal energy harvesting.

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arXiv2022

Leading edge vortex formation and wake trajectory: Synthesizing measurements, analysis, and machine learning

The strength and trajectory of a leading edge vortex (LEV) formed by a pitching-heaving hydrofoil (chord $c$) is studied. The LEV is identified using the $Q$-criterion method, which is calculated from the 2D velocity field obtained from PIV measurements. The relative angle of attack at mid-stroke, ${α_{T/4}} $, proves to be an effective method of combining heave amplitude ($h_0/c$), pitch amplitude ($θ_0$), and reduced frequency ($f^*$) into a single variable that predicts the maximum value of $Q$ over a wide range of operating conditions. Once the LEV separates from the foil, it travels downstream and rapidly weakens and diffuses. The downstream trajectory of the LEV has two characteristic shapes. At low values of ${α_{T/4}}$, it travels straight downstream after separating from the foil, while at higher values of ${α_{T/4}} $, an accompanying Trailing Edge Vortex (TEV) forms and the induced velocity generates a cross-stream component to the vortex trajectories. This behavior is accurately predicted using a potential flow model for the LEV and TEV. Supervised machine learning algorithms, namely Support Vector Regression and Gaussian Process Regression, are used to create regression models that predicts the vortex strength, shape and trajectory during growth and after separation. The regression model successfully captures the features of two vortex regimes observed at different values of ${α_{T/4}} $. However, the predicted LEV trajectories are somewhat smoother than observed in the experiments. The strengths of the vortex is often under-predicted. Both of these shortcomings may be attributed to the relatively small size of the training data set.

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arXiv2021

A Machine Learning Approach to Classify Kinematics and Vortex Wake Modes of Oscillating Foils

Machine learning techniques have received attention in fluid dynamics in terms of predicting, clustering and classifying complex flow physics. One application has been the classification or clustering of various wake structures that emanate from bluff bodies such as cylinders or flapping foils, creating a rich diversity of vortex formations specific to flow conditions, geometry, and/or kinematics of the body. When utilizing oscillating foils to harvest energy from tidal or river flows, it is critical to understand the intricate and nonlinear relationship between flapping kinematics and the downstream vortex wake structure for optimal siting and operation of arrays. This paper develops a classification model to obtain groups of kinematics that contain similar wake patterns within the energy harvesting regime. Data is obtained through simulations of 27 unique oscillating foil kinematics for a total of 13,650 samples of the wake vorticity field. Within these samples three groups are visually labeled based on the relative angle of attack. A machine learning approach combining a convolutional neural network (CNN) with long short-term memory (LSTM) units is utilized to automatically classify the wakes into the three groups. The average accuracy on five test data subsets is 80% when the three visually labeled groups are used for classification. After analyzing the test subset with lowest accuracy, an update on the group division boundaries is proposed. With this update, the algorithm achieves an average accuracy of 90%, demonstrating that the three groups are able to discern distinct wake structures within a range of energy harvesting kinematics.

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arXiv2021

Wake-foil interactions and energy harvesting efficiency in tandem oscillating foils

Oscillating foils in synchronized pitch/heave motions can be used to harvest hydrokinetic energy. By understanding the wake structure and its correlation with the foil kinematics, predictive models for how foils can operate in array configurations can be developed. To establish a relationship between foil kinematics and wake characteristics, a wide range of kinematics is explored in a two-foil tandem configuration with interfoil spacing from four to nine chord lengths separation and multiple interfoil phases. Using data from experiments and simulations, an in-depth wake analysis is performed and the mean velocity and the turbulent kinetic energy are quantified in the wake. With this energy quantification, the trailing foil efficiency is modified to account for the mean flow in addition to the energy transported by the coherent leading edge vortices (LEVs) shed from the leading foil. With the mean wake velocity, a predictive wake model is able to distinguish three regimes through analyzing trailing foil efficiency profiles and the strength of the primary LEV shed from the leading foil. Dividing the wake into regimes is an insightful way to narrow the range of foil kinematics and configurations and improve the energy harvesting in a two-tandem foil array.

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arXiv2021

Unsupervised Clustering and Performance Prediction of Vortex Wakes from Bio-inspired Propulsors

An unsupervised machine learning strategy is developed to automatically cluster the vortex wakes of bio-inspired propulsors into groups of similar propulsive thrust and efficiency metrics. A pitching and heaving foil is simulated via computational fluid dynamics with $121$ unique kinematics by varying the frequency, heaving amplitude, and pitching amplitude. A Reynolds averaged Navier-Stokes (RANS) model is employed to simulate the flow over the oscillating foils at $Re=10^6$, computing the propulsive efficiency, thrust coefficient and the unsteady vorticity wake signature. Using a pairwise Pearson correlation it is found that the Strouhal number most strongly influences the thrust coefficient, whereas the relative angle of attack, defined by both the mid-stroke and maximum have the most significant impact on propulsive efficiency. Next, the various kinematics are automatically clustered into distinct groups exclusively using the vorticity footprint in the wake. A convolutional autoencoder is developed to reduce vortex wake images to their most significant features, and a k-means++ algorithm performs the clustering. The results are assessed by comparing clusters to a thrust versus propulsive efficiency map, which confirms that wakes of similar performance metrics are successfully clustered together. This automated clustering has the potential to identify complex vorticity patterns in the wake and modes of propulsion not easily discerned from traditional classification methods.

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arXiv2020

Variable thrust and high efficiency propulsion with oscillating foils at high Reynolds numbers

Bio-inspired oscillatory foil propulsion has the ability to traverse various propulsive modes by dynamically changing the foil's heave and pitch kinematics. This research characterizes the propulsion properties and wake dynamics of a symmetric oscillating foil, specifically targeting the high Reynolds number operation of small to medium surface vessels whose propulsive specifications have a broad range of loads and speeds. An unsteady Reynolds-averaged Navier-Stokes (URANS) solver with a k-$ω$ SST turbulence model is used to sweep through pitch amplitude and frequency at two heave amplitudes of $h_0/c=1$ and $h_0/c=2$ at $Re=10^6$. At $h_0/c=2$, the maximum thrust coefficient is $C_T=8.2$ due to the large intercepted flow area of the foil, whereas at a decreased Strouhal number the thrust coefficient decreases and the maximum propulsive efficiency reaches 75%. Results illustrate the kinematics required to transition between the high-efficiency and high-thrust regimes at high Reynolds number and the resulting changes to the vortex wake structure. The unsteady vortex dynamics throughout the heave-pitch cycle strongly influence the characterization of thrust and propulsive efficiency, and are classified into flow regimes based on performance and vortex structure.

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arXiv2020

Simulations of Intracycle Angular Velocity Control for a Cross-Flow Turbine

Straight-bladed cross-flow turbines are computationally explored for harvesting energy in wind and water currents. One challenge for cross-flow turbines is the transient occurrence of high apparent angles of attack on the blades that reduces efficiency due to flow separation. This paper explores kinematic manipulation of the apparent angle of attack through intracycle control of the angular velocity. Using an unsteady Reynolds-averaged Navier-Stokes (URANS) model at moderate Reynolds numbers, the kinematics and associated flow physics are explored for confined and unconfined configurations. The computations demonstrate an increase in turbine efficiency up to 54%, very closely matching the benefits shown by previous intracycle control experiments. Simulations display the time-evolution of angle of attack and flow velocity relative to the blade, which are modified with sinusoidal angular velocity such that the peak torque generation aligns with the peak angular velocity. With optimal kinematics in a confined flow there is minimal flow separation during peak power generation, however there is a large trailing edge vortex (TEV) shed as the torque decreases. The unconfined configuration has more prominent flow separation and is more susceptible to Reynolds number, resulting in a 41% increase in power generation under the same kinematic conditions as the confined flow.

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arXiv2020

Vortex dynamics and Reynolds number effects of an oscillating hydrofoil in energy harvesting mode

The energy extraction and vortex dynamics from the sinusoidal heaving and pitching motion of an elliptical hydrofoil is explored through large-eddy simulations (LES) at a Reynolds number of $50,000$. The LES is able to capture the time-dependent vortex shedding and dynamic stall properties of the foil as it undergoes high relative angles of attack. Results of the computations are validated against experimental flume data in terms of power extraction and leading edge vortex (LEV) position and trajectory. The kinematics for optimal efficiency are found in the range of heave amplitude $h_o/c=0.5-1$ and pitch amplitude $θ_o=60^{\circ}-65^{\circ}$ for $fc/U_{\infty}=0.1$ and of $h_o/c=1-1.5$ and $θ_o=75^{\circ}-85^{\circ}$ for $fc/U_{\infty}=0.15$. Direct comparison with low Reynolds number simulations and experiments demonstrate strong agreement in energy harvesting performance between Reynolds numbers of $1000$ to $50,000$, with the high Reynolds number flows demonstrating a moderate $0.8-6.7\%$ increase in power compared to the low Reynolds number flow. In the high Reynolds number flows, the coherent LEV, which is critical for high-efficiency energy conversion, forms earlier and is slightly stronger, resulting in more power extraction. After the LEV is shed from the foil, the LEV trajectory is demonstrated to be relatively independent of Reynolds number, but has a very strong nonlinear dependence with kinematics. It is shown that the LEV trajectories are highly influenced by the heave and pitch amplitudes as well as the oscillation frequency. This has strong implications for arrays of oscillating foils since the coherent LEVs can influence the energy extraction efficiency and performance of downstream foils.

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arXiv2017

Unsteady High-Lift Mechanisms from Heaving Flat Plate Simulations

Flapping animal flight is often modeled as a combined pitching and heaving motion in order to investigate the unsteady flow structures and resulting forces that could augment the animal's lift and propulsive capabilities. This work isolates the heaving motion of flapping flight in order to numerically investigate the flow physics at a Reynolds number of 40,000, a regime typical for large birds and bats and challenging to simulate due to the added complexity of laminar to turbulent transition in which boundary layer separation and reattachment are traditionally more difficult to predict. Periodic heaving of a thin flat plate at fixed angles of attacks of 1, 5, 9, 13, and 18 degrees are simulated using a large-eddy simulation (LES). The heaving motion significantly increases the average lift compared with the steady flow, and also surpasses the quasi-steady predictions due to the formation of a leading edge vortex (LEV) that persists well into the static stall region. The progression of the high-lift mechanisms throughout the heaving cycle is presented over the range of angles of attack. Lift enhancement compared with the equivalent steady state flow was found to be up to 17% greater, and up to 24% greater than that predicted by a quasi-steady analysis. For the range of kinematics explored it is found that maximum lift enhancement occurs at an angle of attack of 13 degrees, with a maximum lift coefficient of 2.1, a mean lift coefficient of 1.04.

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