Quasi-steady Model Research Articles

Analytical model for the simulation of Trombe wall operation with heat storage

Passive solar systems, such as the Trombe wall, are cost-effective ways to reduce the energy consumption of buildings for heating, cooling, and ventilation. The operation of these systems can be simulated either with Building Energy Simulation Tools—BES like TRNSYS, EnergyPlus, etc either with Computational Fluid Dynamics—CFD. In both cases, the purchase of special software and/or special programming skills are required. In parallel analytical calculating tools are being developed, which also require some programming to solve an implicit system of non-linear equations but with fewer software requirements. The majority of analytical models concerns energy balance models for steady-state conditions with the result that heat storage is not taken into account, which in the case of a Trombe wall has a significant effect on the developed transport phenomena. In the present work, an analytical energy balance implicit model was developed for the simulation of the transient operation of a Trombe wall taking into account the heat storage. Using this model, the operation of a Trombe wall for 7 typical days of the year was simulated. The results are presented in terms of the daily evolution of the temperature with which the air enters the room served by the passive system, of the temperature of the Trombe wall surface adjacent to the served room, and of the airflow rate inside the air gap. These results are compared with the results that a system without heat storage would give. Both systems are assessed based on annual performance as calculated by a quasi-steady explicit model. The developed model can be used to calculate the operation of a Trombe wall as well as to supply explicit quasi-steady models with values for airflow rate inside the air gap for Trombe wall operation without mechanical ventilation. Feeding these values to a quasi-steady model developed by authors it was found that the increase of storage wall heat capacity, either changing the storage wall material, either using phase change materials, can offer better utilization of Trombe wall heat gains up to 35% yearly. Background: The present work aims to develop an analytical model for simulating the operation of a Trombe wall in a transient state taking into account the heat storage in the wall. Methods: A closed system of equations is developed, based on 5 energy balances and a series of assumptions and auxiliary relations, to calculate the operation of a wall Trombe with heat storage with an hourly time step. Results: Characteristics Trombe wall temperatures and mass flow rate through the air gap are calculated for typical days of 7 winter months. These are used for the calculation of utilizable heat gains from Trombe wall. Conclusions: The model that does not take into account heat storage predicts higher temperatures and air mass flow rate in the gap than the present model by 10%. However heat storage increase the utilizable heat gains by 35% compared with a system without heat storage.

Analysis of nonlinear aerodynamic performance and passive deformation of a flexible flapping wing in hover flight

The flexibility of insect wings and model wings in flapping-wing micro air vehicles (FWMAVs) is crucial to guarantee an economic flight. Since the wing deformation is bilaterally coupled with the aerodynamic force, conventional simulations on this fluid–structure interaction (FSI) problem mostly build up their models using computational fluid dynamics (CFD) and computational solid dynamics (CSD) methods, which requires high computational costs. Alternatively, an analytical model is proposed here for a quick estimate of the aerodynamic performance and passive deformation on flexible flapping wings. The deformation is simplified into a rigid-body rotation at the wing root, a spanwise twist, and a shortening along the span. The aerodynamic force is approximated by a predictive quasi-steady model and the spanwise twist is modeled using a quadratic polynomial. Results show that the introduction of wing flexibility can attenuate the lift generation due to the negative rotational lift and adverse translation–rotation coupling effect after each stroke reversal. The wing with moderate stiffness is recommended to achieve a high lift. An increase of aspect ratio and root cutoff can also enhance the dimensional lift generation, while the most economic wing design has an aspect ratio around 5 and no root cut-off. More importantly, the increase of flapping frequency can only result in a lift enhancement within certain limits. However, the power consumption keeps increasing as the frequency goes up, indicating a significant breakdown of performance. Our findings can uncover the role of wing flexibility in both insects and FWMAVs and therefore contribute to the design of FWMAVs.

Approximate approach for improving pressure attenuation accuracy during hydraulic transients

Abstract The quasi-steady friction model is generally adopted in water hammer simulation in pipe network systems, which cannot accurately reflect the attenuation of pressure, while the existing unsteady friction model is challenging to use in complex pipe network systems. In this study, a convenient method for treating the friction term is proposed based on the Moody diagram. The attenuation process of water hammer pressure can be accurately reflected by reading the relationship curve between Reynolds number and the Darcy friction factor in the pipeline transient process. Combined with the classical water hammer experiment and the long pipe valve closing experiment in our laboratory, the accuracy of this model is verified, and the influence of absolute roughness (e) and Reynolds number (Re) on the model was analyzed as well. The results show that the pressure attenuation using the Method of Characteristics (MOC) and the proposed friction model has a good agreement with the experimental data. The absolute roughness has little influence on the results in hydraulically smooth pipe, while the minimum Reynolds number has a significant influence. When selecting the minimum Reynolds number, 2% ∼ 5% of the initial flow rate is recommended for calculation.

The evolution of two distinct strategies of moth flight.

Across insects, wing shape and size have undergone dramatic divergence even in closely related sister groups. However, we do not know how morphology changes in tandem with kinematics to support body weight within available power and how the specific force production patterns are linked to differences in behaviour. Hawkmoths and wild silkmoths are diverse sister families with divergent wing morphology. Using three-dimensional kinematics and quasi-steady aerodynamic modelling, we compare the aerodynamics and the contributions of wing shape, size and kinematics in 10 moth species. We find that wing movement also diverges between the clades and underlies two distinct strategies for flight. Hawkmoths use wing kinematics, especially high frequencies, to enhance force and wing morphologies that reduce power. Silkmoths use wing morphology to enhance force, and slow, high-amplitude wingstrokes to reduce power. Both strategies converge on similar aerodynamic power and can support similar body weight ranges. However, inter-clade within-wingstroke force profiles are quite different and linked to the hovering flight of hawkmoths and the bobbing flight of silkmoths. These two moth groups fly more like other, distantly related insects than they do each other, demonstrating the diversity of flapping flight evolution and a rich bioinspired design space for robotic flappers.

Dynamic Stability and Flight Control of Biomimetic Flapping-Wing Micro Air Vehicle

This paper proposes an approach to analyze the dynamic stability and develop trajectory-tracking controllers for flapping-wing micro air vehicle (FWMAV). A multibody dynamics simulation framework coupled with a modified quasi-steady aerodynamic model was implemented for stability analysis, which was appended with flight control block for accomplishing various flight objectives. A gradient-based trim search algorithm was employed to obtain the trim conditions by solving the fully coupled nonlinear equations of motion at various flight speeds. Eigenmode analysis showed instability that grew with the flight speed in longitudinal dynamics. Using the trim conditions, we linearized dynamic equations of FWMAV to obtain the optimal gain matrices for various flight speeds using the linear-quadratic regulator (LQR) technique. The gain matrices from each of the linearized equations were used for gain scheduling with respect to forward flight speed. The reference tracking augmented LQR control was implemented to achieve transition flight tracking that involves hovering, acceleration, and deceleration phases. The control parameters were updated once in a wingbeat cycle and were changed smoothly to avoid any discontinuities during simulations. Moreover, trajectories tracking control was achieved successfully using a dual loop control approach. Control simulations showed that the proposed controllers worked effectively for this fairly nonlinear multibody system.

Numerical Simulation and Modeling Convention of Unsteady Fluidelastic Forces of Tube Arrays

Abstract This paper presents a numerical investigation on the unsteady fluidelastic forces of tube arrays. The key focus is on the consistency between the unsteady fluidelastic force model and the quasi-steady model for tube arrays at large reduced flow velocities, as well as comparing two well-known conventions for the unsteady model. Two-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) simulations are used to prove that the viscous damping coefficients of Tanaka's convention approach their quasi-steady values as the reduced flow velocity approaches infinity, whereas the hysteretic damping coefficients of Chen's modified convention always approach zero and hence result in low-resolution data plots as the reduced flow velocity becomes large. The nonconstant viscous damping coefficients of Tanaka's experimental data at high reduced flow velocities (which motivated the introduction of Chen's modified convention) might be induced by a systematic identification error in the phase of the fluidelastic force. A row of three flexible cylinders is used as a numerical example to analyze the effect of systematic phase error on the predicted stability boundary of the fluidelastic instability. Although identical fluidelastic forces are simulated by using the two conventions, Tanaka's convention is recommended due to its compatibility with the quasi-steady theory and optimal resolutions of data plots over any range of reduced flow velocities.

Numerical study of synthetic spherically expanding flames for optimization of laminar flame speed experiments

This study presents the performances of four commonly-used extrapolation models, including the linear stretch and linear curvature models, the nonlinear model in expansion form, and the nonlinear quasi-steady model, using synthetic data sets generated over a wide range of conditions. The effects of a number of experimental limitations, such as the facility size, the finite camera framing rate, and the noise in the image detected flame radius, were investigated. Two types of error, model and noise error, which constitute the overall extrapolation uncertainty were investigated. Relative model error is primarily driven by Markstein length (Lb) and the flame radius range; however, it is weakly sensitive to laminar flame speed (Sb0). Noise error is controlled by the size of flame radius data set which depends on framing rate and the selected flame radius range. For small values of |Lb|, the model error is negligible. For large values of |Lb|, the two error types are equally prevalent in the overall uncertainty and they cannot be simultaneously minimized. Experimentally, large experimental facilities and high camera framing rates should be favored to reduce the noise error. For extrapolation to zero-stretch, the model that best reproduces the flame propagation evolution should be favored. The Markstein length demonstrates a high sensitivity to the choice of model and noise addition when compared to the laminar flame speed. The procedures developed in this study can be used to predict extrapolation-induced error under various experimental conditions and can be used to optimize laminar flame speed experiments.

Tuned mass damper for self-excited vibration control: Optimization involving nonlinear aeroelastic effect

The conventional target for self-excited galloping/flutter control of a civil structure often focuses on the critical wind speed. In the present work, a nonlinear control target is introduced, i.e., to ensure that the vibration amplitude is lower than a threshold value (pre-specified according to the expected structural performance) before a target wind speed. Unlike the conventional control target, the nonlinear one can take into account the underlying large-amplitude vibrations before the critical state and/or the structural safety redundancy after the critical state. To obtain the most economical TMD parameters that enable the nonlinear target, an optimization procedure involving nonlinear aeroelastic effect is developed for galloping control based on the quasi-steady aeroelastic force model, and for flutter control based on a nonlinear unsteady model. Three numerical examples involving the galloping/flutter control of different cross-sections are analyzed to demonstrate the different results designed by the conventional and nonlinear targets. It is demonstrated that the nonlinear target and optimization procedure can lead to more economical design results than the conventional ones in the galloping/flutter control for a structure with relatively large post-critical safety redundancy, and they are more reliable than the conventional ones for a structure that may experience large-amplitude vibrations before the critical wind speed. These superiorities of the nonlinear control target and new optimization procedure suggest that they may be utilized in the TMD parameter optimization for galloping/flutter control of structures in a wide domain of engineering fields.

Comparison and adaptability evaluation of formation pressure calculation methods and computer simulation in Jingbian gas field

In the process of oilfield development, formation pressure is an essential parameter for evaluating oilfield development effect, calculating dynamic geological reserves, conducting daily dynamic analysis of oil and water Wells and predicting oilfield performance. The pressure recovery time of conventional gas well after shut-in is very long, and it is difficult to effectively carry out targeted implementation due to the influence of gas field external supply task. In this paper, based on the actual data of Jingbian gas field, through the comparison of several calculation methods of formation pressure, the best method to calculate formation pressure is comprehensively screened out. The results show that: ①For a single method, the accuracy of the method from high to low is the well head casing pressure conversion method, the pressure drop curve method, the binomial productivity equation method, and the quasi-steady state mathematical model method.②The absolute error of multi-method comprehensive calculation method is 0.9MPa, which is far less than the average absolute error directly calculated by one method. The multi-method comprehensive calculation method is reliable when applied to the formation pressure evaluation of typical gas Wells in Jingbian gas field, which lacks data.

Aerodynamic investigation on shifted-back vertical stroke plane of flapping wing in forward flight

In order to properly understand aerodynamic characteristics in a flapping wing in forward flight, additional aerodynamic parameters apart from those in hover—an inclined stroke plane, a shifted-back stroke plane, and an advance ratio—must be comprehended in advance. This paper deals with the aerodynamic characteristics of a flapping wing in a shifted-back vertical stroke plane in freestream. A scaled-up robotic arm in a water towing tank was used to collect time-varying forces of a model flapping wing, and a semi-empirical quasi-steady aerodynamic model, which can decompose the forces into steady, quasi-steady, and unsteady components, was used to estimate the forces of the model flapping wing. It was found that the shifted-back stroke plane left a part of freestream as a non-perpendicular component, giving rise to a time-course change in the aerodynamic forces during the stroke. This also brought out two quasi-steady components (rotational and added-mass forces) apart from the steady one, even the wing moved with a constant stroke velocity. The aerodynamic model underestimated the actual forces of the model flapping wing even it can cover the increasingly distributed angle of attack of the vertical stroke plane with a blade element theory. The locations of the centers of pressure suggested a greater pressure gradient and an elongated leading-edge vortex along a wingspan than that of the estimation, which may explain the higher actual force in forward flight.

At what ambient temperature can thermal runaway of a burning metal particle occur?

A simplified heat and mass transfer model is considered to predict at what ambient temperature can thermal runaway occur for a burning metal particle exposed to an oxidizing gas. The model accounts for transition transport phenomena important for particles with sizes comparable to the mean free path of the gas molecules. The quasi-steady model can be reduced to a set of algebraic equations that can be readily solved numerically if both the reaction kinetics law and the value of thermal accommodation coefficient (TAC) are assumed. Such assumptions are made and the solutions are produced and discussed for particles of different sizes for aluminum, magnesium, and boron burning in air. Different reaction kinetics expressions reported in the literature and different values for the TAC are considered for all three fuels. For aluminum, different reaction kinetics lead to a widely different range of air temperatures, at which the particle thermal runaway is predicted. However, the runaway is expected for particles of all sizes, including nano-particles if the air temperature is sufficiently high. Similarly, thermal runaway is also predicted to occur for boron particles of different sizes, although respective air temperatures must be substantially higher than for aluminum. The effect of TAC on the predicted result is strong; smaller values of TAC lead to a reduced effect of particle size on the gas temperature required for the thermal runaway to occur. It is found that neglecting transition heat and mass transport regimes can be always justified for very large, 200 µm particles. For smaller particles, both higher reaction rates and smaller values of TAC may require considering transition transport when modeling behavior of burning particles.

Mass transfer from small spheroids suspended in a turbulent fluid

By coupling direct numerical simulation of homogeneous isotropic turbulence with a localised solution of the convection–diffusion equation, we model the rate of transfer of a solute (mass transfer) from the surface of small, neutrally buoyant, axisymmetric, ellipsoidal particles (spheroids) in dilute suspension within a turbulent fluid at large Péclet number, $\textit {Pe}$ . We observe that, at $\textit {Pe} = O(10)$ , the average transfer rate for prolate spheroids is larger than that of spheres with equivalent surface area, whereas oblate spheroids experience a lower average transfer rate. However, as the Péclet number is increased, oblate spheroids can experience an enhancement in mass transfer relative to spheres near an optimal aspect ratio $\lambda \approx 1/4$ . Furthermore, we observe that, for spherical particles, the Sherwood number $\textit {Sh}$ scales approximately as $\textit {Pe}^{0.26}$ over $\textit {Pe} = 1.4\times 10^{1}$ to $1.4\times 10^{4}$ , which is below the $\textit {Pe}^{1/3}$ scaling observed for inertial particles but consistent with available experimental data for tracer-like particles. The discrepancy is attributed to the diffusion-limited temporal response of the concentration boundary layer to turbulent strain fluctuations. A simple model, the quasi-steady flux model, captures both of these phenomena and shows good quantitative agreement with our numerical simulations.

A method to estimate peak pressures on low-rise building models based on quasi-steady theory and partial turbulence analysis

A new method for estimating peak area-averaged pressure coefficients on the roof of a low-rise building model is developed. The method relies on the well-known quasi-steady vector model to account for the large-scale, low-frequency fluctuations of the upstream wind. The novel approach is to account for small-scale and body-generated turbulence effects using a stochastic model. Wind tunnel data for a 1/50-scale low-rise building model for six different upstream turbulence conditions are used for the analysis. The fluctuating pressure component induced by the small-scale and body-generated turbulence is obtained by subtracting the quasi-static pressure component from the original pressure signal. It is observed that the small-scale pressure component is highly dependent on turbulence level of the upstream flow, such that normalization by the small-scale components of the upstream turbulence kinetic energy leads to a self-similar distribution. A Monte Carlo simulation was used to combine the small-scale and quasi-steady pressure components. The new model provides good predictions of peak area-averaged pressure coefficients that cannot be captured by the quasi-steady approach.

Aerodynamic Model Updating Using Wind-Tunnel Setup for Hummingbirdlike Flapping Wing Nanorobot

The complex wing motion of insects and small birds leads to high lift production in nature. Specific lift-enhancing mechanisms arise from the combination of a horizontal stroke motion and a secondary wing pitching motion. Research around flapping wing nano air vehicles (FWNAVs) copies this wing motion to fly small drones, in an effort to benefit from the same mechanisms. A flapping wing aerodynamic model can predict the force production of the FWNAV and helps to understand the influence of the wing kinematics thereon. This work starts from a quasi-steady model expression for the aerodynamics and proposes a wind-tunnel procedure to identify the force coefficients in the model empirically. The procedure is based on a test case performed by the AVT-202 research team that combines wing translation and wing rotation, imitating the aerodynamic condition of the flapping wing in a simplified setup. Comparison of measurements and model simulations demonstrates that the procedure can be used to update the model parameters for our specific FWNAV configuration, leading to an empirical relation for the force coefficients. Simulations with the updated model using the empirical relations show good agreement with measured force production for a wide range of input variables.

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

We report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

Wireless sensor networks for pharmaceutical lyophilization: Quantification of local gas pressure and temperature in primary drying

Wireless sensor networks have become prolific in a wide range of industrial processes and offer several key advantages over their wired counterparts in terms of positioning flexibility, modularity, interconnectivity, and data routing. We demonstrate their utility in pharmaceutical lyophilization by developing a series of wireless devices to measure spatial variations in gas pressure and temperature during primary drying. The influence of shelf temperature, chamber pressure, excipient concentration, and dryer configuration are explored for various representative cycles using a laboratory-scale pharmaceutical lyophilizer. Pressure and temperature variations across the shelf for these cases are shown to vary up to 1.2 Pa and 10 °C, respectively. Experimental measurements are supported by computational fluid dynamics simulations to reveal the mechanisms driving the vapor flow. The measurements and simulation data are then combined to estimate the shelf-wise sublimation rate in the inverse sense to within a deviation of 3% based on comparison with gravimetric data. We then apply the sublimation rate profile to obtain the vial heat transfer coefficient and product mass transfer resistance for a 5% w/v mannitol formulation. Finally, these parameters are applied to a one-dimensional quasi-steady heat transfer model to predict the evolution of the product temperature over the course of primary drying. Thermocouple measurements of product temperature are compared directly to the simulated data and demonstrate accuracy comparable to existing published one-dimensional models.

High-fidelity prediction of flight trajectories of plate-type debris in boundary layer winds

From reconnaissance surveys, plate-type objects, such as roof shingles and tiles, are known to be among the most common types of debris objects. Therefore, a reliable prediction of their flight trajectories is instrumental for evaluating the vulnerability of building envelopes, especially in the regions with severe windstorms. Despite the development of several quasi-steady models for this purpose, the current literature lacks high-fidelity models to predict the flight pattern and impact velocity of the windborne debris objects separated from the ground and/or buildings. To address this gap, a coupled computational fluid dynamics and rigid body dynamics simulation framework was developed in the current study to capture the flight trajectories of plate-type debris objects in atmospheric boundary layer winds. Upon establishing a fundamental understanding of main flight characteristics, this study was extended to investigate the effects of initial pitch and yaw angles, plate characteristics, mean wind velocity, and release height on the flight of plate-type debris. In addition, a set of models were developed to predict debris travel distance, as well as linear and angular velocities associated with it. This can be directly employed to assess the impact-induced loading demand that building envelopes are expected to resist due to windborne plate-type debris.

Generalization of the Menegozzi and Lamb maser algorithm to the transient superradiance regime

ABSTRACT We investigate the application of the conventional quasi-steady state maser modelling algorithm of Menegozzi & Lamb (ML) to the high field transient regime of the one-dimensional Maxwell-Bloch (MB) equations for a velocity distribution of atoms or molecules. We quantify the performance of a first order perturbation approximation available within the ML framework when modelling regions of increasing electric field strength, and we show that the ML algorithm is unable to accurately describe the key transient features of R. H. Dicke’s superradiance (SR). We extend the existing approximation to one of variable fidelity, and we derive a generalization of the ML algorithm convergent in the transient SR regime by performing an integration on the MB equations prior to their Fourier representation. We obtain a manifestly unique integral Fourier representation of the MB equations which is $\mathcal {O}\left(N\right)$ complex in the number of velocity channels N and which is capable of simulating transient SR processes at varying degrees of fidelity. As a proof of operation, we demonstrate our algorithm’s accuracy against reference time domain simulations of the MB equations for transient SR responses to the sudden inversion of a sample possessing a velocity distribution of moderate width. We investigate the performance of our algorithm at varying degrees of approximation fidelity, and we prescribe fidelity requirements for future work simulating SR processes across wider velocity distributions.

The relationship between body size and flight power output in the mango stem borer (Batocera rufomaculata)

Adult body size in insects can be influenced by environmental conditions during larval growth. The effect of such intraspecific variation in body mass on flight performance is poorly understood. In Batocera rufomaculata, a large tree boring beetle, adults emerging from larvae that developed in a dying host tree, and therefore, under nutrient-deprived diet conditions, are smaller but have an elevated long-distance flight capability compared to larger conspecifics that developed in viable host trees. The improved endurance for long-distance flight in the smaller individuals appears to contradict the interspecific trend in flying animals of a decrease in Cost of Transport (CoT) with increased body mass. To explore the relationship between intraspecific variation in body size and power expended during steady forward flight, we flew these beetles tethered in a wind tunnel and compared the flapping kinematics and power output of individuals varying in body mass (1–7 gr). Concurrently, we measured the forces the insects applied on the tether allowing us to evaluate the tethering effects and correct for them. From the flapping kinematics we estimated the mechanical power expended using a quasi-steady blade-element model. We found that muscle mass-specific power did not differ between small and large individuals flying at the same wind (flight) speed in the tunnel. Consequently, the CoT of B. rufomaculata does not vary with body mass. Such invariance of mass-specific power with body mass may aid the dispersal of smaller individuals from deteriorating host trees to new ones.

State-space aerodynamic model reveals high force control authority and predictability in flapping flight.

Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterized by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. Here, we developed a computationally efficient and data-driven state-space model to dynamically map wing kinematics to aerodynamic forces/moments. This model was trained and tested with a total of 548 different flapping-wing motions and surpassed the accuracy and generality of the existing quasi-steady models. This model used 12 states to capture the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. We also provided a comprehensive assessment of the control authority of key wing kinematic variables and found that instantaneous aerodynamic forces/moments were largely predictable by the wing motion history within a half-stroke cycle. Furthermore, the angle of attack, normal acceleration and pitching motion had the strongest effects on the aerodynamic force/moment generation. Our results show that flapping flight inherently offers high force control authority and predictability, which can be key to developing agile and stable aerial fliers.