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A novel reduced-order model for the simulation of bluff bodies in unsteady, arbitrary motion has been developed. The model is physics-based, meaning that it is derived from known fundamental aerodynamic phenomena of bluff bodies instead of response fitting of experimental data. This physics-based approach is essential to ensure that the model is applicable to new, untested configurations. We describe the development of a physics-based model, including detailed explanations of the fundamental aerodynamic phenomena and how they are modeled in simulation. The reduced-order model is evaluated by application to rotorcraft-tethered loads and validated against much more expensive high-fidelity computational fluid dynamics simulations and flight tests. Excellent correlation in the predictions of aerodynamic forces and moments, as well as the dynamic response, is observed, while the computational cost has been reduced by several orders of magnitude relative to high-fidelity computational-fluid-dynamics-based simulations. Additionally, the important role that unsteady aerodynamics play in bluff body dynamics and instability is demonstrated.

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... For the analysis, a reduced-order, physics-based solver, the Georgia Tech Aerodynamics of Bluff Bodies (GTABB) (Ref. 15,17,26,27), a Lattice-Boltzmann Method (LBM), and uRANS CFD were compared with one another and correlated with experimental results from wind tunnel measurements. These measurements included integrated vehicle forces and moments, and flow field measurements using time-resolved particle image velocimetry (PIV). ...

... The approach, the Georgia Tech Aerodynamics of Bluff Bodies (GTABB), was originally developed for the assessment of dynamic sling loads (Ref. 26), but has been successfully applied to UAVs (Ref. 15,30) and independently validated (Ref. ...

... FUN3D has been validated for a variety of incompressible applications for rotorcraft, bluff bodies, and many other structures (Ref. 26,36). This high-fidelity solver provides many turbulence diffusion models, and for the purposes of this paper, a Spalart-Allmaras Delayed Detached Eddy Simulation (SA-DDES) turbulence closure is applied to resolve the bluff body wake aerodynamics. ...

Rotary-wing vehicle development and application have expanded in the past two decades to include a multitude of configurations and operational environments. More efficient approaches to obtain vehicle flight characteristics during design, as well as for modeling and simulation, are needed to augment traditional approaches such as wind tunnel testing and high-fidelity unsteady Reynolds-Averaged Navier-Stokes (uRANS) computational fluid dynamics (CFD). This effort details the evaluation of the ability of two approaches, solutions to the Lattice-Boltzmann equations and a physics-based reduced-order model, to predict the airloads on an uncrewed aerial vehicle (UAV), correlated with CFD and wind tunnel tests. The sensitivity of differences observed in these predictions is quantified through a flight simulation code designed for vehicle design and simulation.

... [4][5][6], and model-based simulation environments (MBSE) (Refs. 7,8). Dynamic wind tunnel tests have demonstrated some viability when care is taken with the testing (Ref. ...

... 11,12), has led to a new MBSE approach (Refs. 8,13) that, after validation with flight tests, appears to be a leading contender to meet the Army's goals not only for load certification, but also enhanced safety via pilot simulation training, and engineering design of new stabilization devices or load delivery systems. ...

... The correlations continue to hold true as new data are examined, and the concept was successfully demonstrated in 2014 and published in 2015 for a truck using CONEX data (Refs. 8,13). More recently in 2016 the approach was also applied to an unmanned aerial vehicle (UAV) control law design to control unconstrained free fall (Ref. ...

A model-based simulation technique has recently been developed and is being transitioned for use in two-body aerodynamic-dynamic problems of interest (slung loads, airdrops) to the vertical lift community. This model, the Georgia Tech Aerodynamics for Bluff Bodies (GTABB), has been shown to accurately predict the behavior of rectangular loads, validated with both computational fluid dynamics and flight test. This paper presents additional validation of the GTABB solver and its six degree of freedom dynamic modeling tool (6DOF) with flight test on new slung load configurations that are connected via either a hook or a gimbal. A new tether algorithm capable of modeling wind-up is demonstrated. In addition, the introduction of a long tether model in 6DOF and a graphical user interface to rapidly build and analyze, visually and quantitatively, tethered load simulations are described. In this paper, a new pre-processor that develops the quasi-steady data tables for arbitrary configurations, COMPlex Aerodynamic Shape Simulator (COMPASS), is introduced with initial verification and validation, demonstrating a concept first introduced in 2011-2012. COMPASS demonstrates the ability to reconstruct the dynamic mechanisms responsible for driving the motion of two-body aerodynamic-dynamic problems.

... A reduced-order aerodynamics model to capture the unsteady forces and moments of bluff and aerodynamically-conforming geometries, such as those found in fuselage and UAV bodies has been developed at Georgia Tech [16,17,[19][20][21][22]. This reduced-order model, entitled Georgia Tech Aerodynamics for Bluff Bodies (GTABB) is based on the principles of classic unsteady aerodynamics theory [13] with additional theoretical considerations related to wake shedding associated with finite bluff bodies. ...

... 16, 17, 19-22. The model and its underlying unsteady components (see Fig. 5) have been validated against high fidelity computational fluid dynamics (CFD), wind tunnel tests, and flight tests [16,17,[19][20][21][22]. Figure 6 illustrates the model's ability to capture the nonlinear behavior of a bluff body such as a UAV fuselage. For dynamically varying orientations of the approximately 1:1:1.25 rectangular body, the forces and yaw moments predicted by the GTABB ROM model correlate very well with large eddy simulation-based CFD analyses, even for highly nonlinear behavior [16]. ...

... Many examples of the GTABB validation with wind tunnel and numerical experiments, as well as flight tests can be found in prior publications [16,17,[19][20][21][22]. This model is currently under evaluation and further development towards certification by the U.S. Army for use in slung loads operations, including design and simulation. ...

Unmanned aerial vehicles (UAVs) are capable of rapid, agile maneuvers that were not previously possible in piloted vehicles. Nap-of-the-earth flight in natural and urban terrain, as well as swarm or manned-unmanned teaming flight, requires both accurate quasi-steady aerodynamics and the inclusion of relevant unsteady physics in order to accurately extend current methods for these applications. In this effort, the impact of these aerodynamic assumptions are assessed on vehicle performance and control law design during agile maneuvers. A previously validated reduced-order unsteady aerodynamics model provides an appraisal of the importance of the unsteady terms for UAV flight control, which are shown to result in different trajecto-ries and performance over a maneuver. The sensitivity of the performance and stability of the UAV when simplified canonical configurations are employed is also demonstrated.

... The aerodynamic model in GTABB has been described in detail in previous papers (Refs. 30,31), so only a basic overview, along with recent improvements, is given here. Figure 1 illustrates the relationships between the different aerodynamic phenomena in the model. ...

... The random function draws a number from a normal distribution with mean and standard deviation determined from turbulence characteristics in hybrid RANS-LES simulations (Ref. 31). The magnitudes of the fluctuations are stored in tables, much like the quasi-steady data, and the quasi-linear assumption is applied. ...

... In dynamic scenarios, vortex shedding serves to excite the various degrees of freedom and to influence dynamic stability characteristics for box-type tethered loads in single-point suspension (Ref. 31). ...

The ability to accurately and rapidly predict tethered load instabilities and behavior is required if expensive flight test qualification flights are to be minimized. Tethered or slung loads are complex systems of systems, wherein the system and each constituent must be carefully classified, quantified, and modeled. A physics-based six degree-of-freedom simulation model, the Georgia Tech Aerodynamic Model for Bluff Bodies (GTABB), is under development, and has been adopted by the U.S. Army AMRDEC to support Army slung load simulations (FlightLab). An innovative feature of the GTABB model is that it can be informed using quasi-steady experimental test data, high-fidelity computations, or aerodynamic theory. This model is coupled with empirically-determined unsteady aerodynamic characteristics to provide a flexible, accurate, and extensible modeling and simulation framework. In this effort, unsteady aerodynamic refinements and computational cost reductions are demonstrated. A rigorous uncertainty quantification framework at both the system and component level, necessary for model certification, is established, along with examples. Model validation is extended to include correlations of full-scale flight test with a CONEX container, and comparisons with a complex configuration (truck) evaluated in a wind tunnel. The ramifications of predicting slung load behavior with and without helicopter degrees of freedom and wind are presented.

... Georgia Tech Aerodynamics for Bluff Bodies (GTABB) is a reduced-order aerodynamics model developed to predict the unsteady forces and moments of bluff and aerodynamicallyconforming geometries undergoing dynamic motion (Refs. 7,8,[14][15][16][17]. The solver and its components have been validated against high fidelity computational fluid dynamics (CFD), wind tunnel tests, and flight tests. ...

Reduced-order aerodynamic models developed to rapidly estimate the quasi-steady behavior of aerodynamic and bluff bodies were applied to the fuselage of a small quad-copter. A new model to generate the quasi-steady aerodynamic data on a complex body using data derived from canonical shapes is demonstrated and compared to high-fidelity Computational Fluid Dynamics (CFD) simulations. The resulting aerodynamic influences on controls and performance during maneuvers were assessed in a flight simulation framework. The dynamic behavior of the reduced-order model was found to be comparable to that obtained with CFD-generated quasi-steady data and better than flat plate models. This reduced-order approach provides a viable alternative to expensive CFD simulations or wind tunnel testing necessary to obtain quasi-steady aerodynamic predictions for complex vehicle fuselages. These unsteady aerodynamic models with relatively accurate quasi-steady aerodynamics are recommended over steady aerodynamic assumptions to more accurately estimate the performance, as well as dynamic behavior during aggressive maneuvers.

... This work and related efforts have resulted in some significant advancements in numerical efforts related to improvements of the fluid/structure interactions (Quon et al. 2012;Jacobson and Smith 2018) and reducing computational costs with physics-based reduced order modeling (Prosser and Smith 2015;Koukpaizan et al. 2018a, b). In addition, this collaboration has influenced additional lower Reynolds number water tunnel experiments (Reich et al. 2015) using a 1:17 scaled model similar to that of Reich et al. (2014a). ...

The current study investigates the long-age wake behind rotating helicopter hub models composed of geometrically simple, canonical bluff-body shapes. The models consisted of a 4-arm rotor mounted on a shaft above a 2-arm (scissor) rotor with all the rotor arms having a rectangular cross section. The relative phase between the 2- and 4-arm rotors was either 0° (in-phase) or 45° (out-of-phase). The rotors were oriented at zero angle-of-attack and rotated at 30 Hz. Their wakes were measured with particle-image-velocimetry within a water tunnel at a hub diameter based Reynolds number of 820,000 and an advance ratio of 0.2. Mean profiles, fluctuating profiles, and spectral analysis using time-series analysis as well as dynamic mode decomposition were used to characterize the wake and identify coherent structures associated with specific frequency content. The canonical geometry produced coherent structures that were consistent with previous results using more complex geometries. It was shown that the dominant structures (2 and 4 times per hub revolution) decay slowly and were not sensitive to the relative phase between the rotors. Conversely, the next strongest structure (6 times per hub revolution) was sensitive to the relative phase with almost no coherence observed for the in-phase model. This is strong evidence that the 6 per revolution content is a nonlinear interaction between the 2 and 4 revolution structures. This study demonstrates that the far wake region is dominated by the main rotor arms wake, the scissor rotor wake, and interactions between these two features.
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... Similarly, the unsteady wake velocity fluctuations have peaks at the proper frequencies but accurate prediction of the amplitudes still fail to match experimental data (Raghav et al., 2013). In addition, current modeling efforts include improved modeling of the fluid/structure interactions (Quon et al., 2012;Jacobson & Smith, 2018) and reducing computational costs with physics-based reduced order modeling (Prosser & Smith, 2015). Consequently, computational models require improvements to resolve both the unsteady drag and spectral content of the wake while minimizing computational cost for practical use. ...

The current study investigates the far wake region behind helicopter hub models composed of geometrically simple, canonical bluff body shapes. The models consisted of a 4-arm rotor mounted on a shaft above a 2-arm (scissor) rotor with all the arms having a rectangular cross section. The relative phase between the 2- and 4-arm rotors was either $0\deg$ (in-phase) or $45\deg$ (out- of-phase). The rotors were oriented at a zero angle-of-attack and rotated at $30$ Hz. Their wakes were measured with particle-image-velocimetry within a water tunnel operating at a freestream speed of 10 m/s, which produced a hub diameter based Reynolds number of $760,000$ and a $0.2$ advance ratio. Mean profiles, fluctuating profiles and spectral analysis using time-series analysis as well as dynamic mode decomposition were used to characterize the wake and identify coherent structures associated with specific frequency content. The canonical geometry produced coherent structures that were consistent with previous results using more complex geometries. It was shown that the dominant structures ($2$ and $4$ times per hub revolution) decay slowly and were not sensitive to the relative phase between the rotors. Conversely, the next strongest structure ($6$ times per hub revolution) was sensitive to the relative phase with almost no coherence observed for the in-phase model. This study demonstrates that the far wake region is dominated by the main rotor arms wake, the scissor rotor wake and interactions between these two features.

... To assess this impact, the GTABB reduced-order HSL model was used to evaluate each of these three configurations under the same flight conditions where the baseline CONEX was validated. 7,11,24 ...

... In particular, the role of turbulence modeling, grid density and local refinement, and time-step are addressed in this current study, as they are integral parts of the CREATE TM -AV program software tools, and as such are particularly well suited to addressing tethered sling loads. The overall objectives of this research e↵ort are to use CREATE TM -AV software to enlarge the database for validation of dynamic and reduced-order models, such as the Georgia Tech Aerodynamic Model for Blu↵ Bodies (GTABB), 7,10,11 with complex extensions of previous canonical geometries, supplement current flight certification tests to enhance the definition of the flight envelope safety boundaries, and provide a process for future development of HSL drag reduction devices. The reported results and analysis, while applicable, by design, across all objectives, will focus on the initial objective, and accordingly will follow three major themes: 1) correlation of flow solver results for blu↵ bodies, 2) documentation of large scale versus small scale geometry changes associated with the CONEX cargo container, and 3) initial quantification of di↵erences between canonical and "complex" blu↵ bodies, where complex is defined as a relevant combination of geometric primitives, such as rectangular prisms and circular cylinders. ...

... Using a numerical approach, Prosser & Smith (2016) explored the 3D aerodynamics of prismatic bodies and circular cylinders, and pointed out that shear layer reattachment dominates the mean forces and moments of the bluff bodies. Prosser & Smith (2015) proposed a physical-based, reduced-order aerodynamics model for predicting the motions of bluff bodies. ...

The distinctive pendulum-like oscillation and pitching patterns of cubic and rectangular slung prisms were inspected for two aspect ratios at various Reynolds numbers $Re$ under two free-stream turbulence levels. Systematic experiments were performed using high-resolution telemetry and hotwire anemometry to quantitatively characterize the dynamics of the prisms and the wake fluctuation. The results show that the dynamics of the prisms can be characterized by two distinctive regions depending on the prism shape. Specifically, in the case of cubic prisms the regions are defined by the growth rate of the pitching amplitude; whereas the dynamics of the rectangular prisms is more sensitive to the angle of attack. In particular, when the large side initially faces the flow, the regions are defined by the synchronization between the vortex shedding and pure oscillations under very low turbulence. When the smaller side initially faces the flow, the regions are defined by the equilibrium pitching position. Regardless of the geometry of the prism and flow condition the dominant oscillation frequency resulted as being close to the natural frequency of the small-amplitude pendulum-like oscillation.

... In aviation operations, a wide variety of bluff bodies may be transported underneath a helicopter attached by a system of cables. These configurations result in complex aerodynamic-dynamic interactions of the tethered load, which are also coupled with the dynamics of the tether system and helicopter (Greenwell 2011;Prosser & Smith 2015a). Typical tethered loads include cargo containers such as the CONEX, which is a short rectangular bluff body (or rectangular prism), and oil drums and engine 2 D. T. Prosser and M. J. Smith canisters, which may be approximately represented as short finite cylinders. ...

Three-dimensional bluff body aerodynamics are pertinent across a broad range of engineering disciplines. In three-dimensional bluff body flows, shear layer behaviour has a primary influence on the surface pressure distributions and, therefore, the integrated forces and moments. There currently exists a significant gap in understanding of the flow around canonical three-dimensional bluff bodies such as rectangular prisms and short circular cylinders. High-fidelity numerical experiments using a hybrid turbulence closure that resolves large eddies in separated wakes close this gap and provide new insights into the unsteady behaviour of these bodies. A time-averaging technique that captures the mean shear layer behaviours in these unsteady turbulent flows is developed, and empirical characterizations are developed for important quantities, including the shear layer reattachment distance, the separation bubble pressure, the maximum reattachment pressure, and the stagnation point location. Many of these quantities are found to exhibit a universal behaviour that varies only with the incidence angle and face shape (flat or curved) when an appropriate normalization is applied.

... A new physics-based modeling and simulation approach, the Georgia Tech Aerodynamics of Bluff Bodies (GTABB), has been validated with wind tunnel (Refs. [5][6][7] and flight test (Ref. 8) slung loads, illustrating its potential to address the Army's needs for a variety of configurations. ...

Details of certification process of a slung loads instability and modeling and simulation approach using well-known certification and uncertainty quantification techniques. First documented paper on the subject.

Fundamental three-dimensional aerodynamic phenomena have been investigated for small-aspect-ratio rectangular prisms and circular cylinders, canonical bluff body geometries representative of typical helicopter sling loads. A detailed identification and quantification of the unsteady aerodynamic phenomena at differing orientation angles associated with instabilities has been undertaken. The numerical experiments indicate that shear layer reattachment is the primary factor in determining the mean forces and moments of the bluff bodies. Many characteristics of the shear layer behavior are similar for the three-dimensional bluff bodies and, in some cases, similar to two-dimensional behavior extant in the literature. Differences in the canonical shape and aspect ratios occur and are quantified with varying reattachment distances as the orientation changes. Strouhal numbers vary in the range from 0.15-0.3 and exhibited a highly three- dimensional, multimodal nature at the Reynolds numbers investigated. These findings are significant for the development of reduced-order aerodynamic modeling of sling loads. Copyright © (2014) by the Royal Aeronautical Society. All rights reserved.

The aerodynamics of rotorcraft in forward flight, particularly at high advance ratios, are highly complex. Of particular interest is the impact of crossflow on forward flight performance that occurs over large portions of the rotor disk. Results from high fidelity numerical experiments on an infinite yawed wing, previously validated with experimental data for a wide range of Mach numbers, angles of attack and yaw angles, are analyzed for use in airfoil tables (C81 tables) for rotorcraft comprehensive codes. Investigation of the errors introduced by interpolation of airfoil tables and application of the Betz crossflow and independence principles in various flight regimes has been completed, including further understanding of the physics driving the behavior of the integrated airfoil performance. The analysis has also been extended to reverse flow conditions, which become significant at high advance ratios. Empirical corrections have been developed that improve the lift, drag and pitching moment predictions of the crossflow model. Copyright © (2014) by the Royal Aeronautical Society. All rights reserved.

Unsteady aerodynamic models are necessary to accurately simulate forces and
develop feedback controllers for wings in agile motion; however, these models
are often high dimensional or incompatible with modern control techniques.
Recently, reduced-order unsteady aerodynamic models have been developed for a
pitching and plunging airfoil by linearizing the discretized Navier-Stokes
equation with lift-force output. In this work, we extend these reduced-order
models to include multiple inputs (pitch, plunge, and surge) and explicit
parameterization by the pitch-axis location, inspired by Theodorsen's model.
Next, we investigate the na\"{\i}ve application of system identification
techniques to input--output data and the resulting pitfalls, such as unstable
or inaccurate models. Finally, robust feedback controllers are constructed
based on these low-dimensional state-space models for simulations of a rigid
flat plate at Reynolds number 100. Various controllers are implemented for
models linearized at base angles of attack $\alpha_0=0^\circ,
\alpha_0=10^\circ$, and $\alpha_0=20^\circ$. The resulting control laws are
able to track an aggressive reference lift trajectory while attenuating sensor
noise and compensating for strong nonlinearities.

In this work, we cast Theodorsen's unsteady aerodynamic model into a
general form that allows for the introduction of empirically determined
quasi-steady and added-mass coefficients as well as an empirical
Theodorsen function. An empirically determined Theodorsen model is
constructed using data from direct numerical simulations of a flat plate
pitching at low Reynolds number, Re=100. Next, we develop
low-dimensional, state-space realizations that are useful for either the
classical Theodorsen lift model or the empirical model. The resulting
model is parameterized by pitch-axis location and has physically
meaningful states that isolate the effect of added-mass and quasi-steady
forces, as well as the effect of the wake. A low-order approximation of
Theodorsen's function is developed based on balanced truncation of a
model fit to the analytical frequency response, and it is shown that
this approximation outperforms other models from the literature. We
demonstrate the utility of these state-space lift models by constructing
a robust controller that tracks a reference lift coefficient by varying
pitch angle while rejecting gust disturbances.

The extension of the surrogate-based recurrence framework approach to account for time-varying swept flow effects under dynamic stall conditions is described. Using full-order solutions generated by the OVERFLOW computational fluid dynamics code, the surrogate-based recurrence framework reduced-order modeling approach is shown to effectively mimic full-order solutions of unsteady lift, moment, and drag under dynamic stall conditions while maintaining the computational efficiency associated with semiempirical dynamic stall models. This level of functionality represents a new capability for rotary-wing aeroelasticity applications. Furthermore, a generalized kriging formulation based on nonstationary Gaussian process modeling is implemented in a tractable manner by locally optimizing the high-dimensional likelihood function in the vicinity of the stationary solution. The resulting nonstationary covariance structures are shown to significantly improve the accuracy of the surrogate-based recurrence framework predicted moment stall characteristics compared to a stationary model. It is shown that the nonstationary surrogate-based recurrence framework approach is better able to adapt to abrupt changes in airload behavior caused by the underlying dynamic stall vortex dynamics. The results indicate that the surrogate-based recurrence framework approach based on nonstationary Gaussian process models is a promising alternative to widely used semiempirical rotorcraft dynamic stall models that cannot account for the effects of time-varying velocity components associated with forward flight.

The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread use of kriging models appears to be hampered by 1) computationally efficient algorithms for accurately estimating the model's parameters, 2) an effective method to assess the resulting model's quality, and 3) the lack of guidance in selecting the appropriate form of the kriging model. We attempt to address these issues by comparing 1) maximum likelihood estimation and cross validation parameter estimation methods for selecting a kriging model's parameters given its form and 2) an R2 of prediction and the corrected Akaike information criterion assessment methods for quantifying the quality of the created kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

This paper presents the result of modelling and verification of a generic slung load system using a small-scale helicopter. The model is intended for use in simulation, pilot training, estimation, and control. The model is derived using a redundant coordinate formulation based on Gauss' Principle of Least Constraint using the Udwadia-Kalaba equation and can be used to model all body to body slung load suspension types. The model gives an intuitive and easy-to-use way of modelling and simulating dierent slung load suspension types and it includes detection and response of wire slacking and tightening, and aerodynamical coupling between the helicopter and the load. Furthermore, it is shown how the model can be easily used for multi-lift systems either with multiple helicopers or multiple loads. A numerical stabilisation algorithm as well as a trim algorithm is presented for the complete helicopter/load system and finally the use of the model is illustrated through simulations.

In forward flight helicopters carrying slung-loads frequently encounter load instability problems that reduce their speed envelope to well below the power limit of the helicopter/slung-load system. The paper presents a procedure for the development and flight test verification of passive stabilizers designed to increase the maximum flight speed of the system. Most of the development is carried out during wind tunnel tests. A scale model is suspended from the tunnel ceiling by a gimbaled set-up that simulates the hook-sling attachment. The model is free to perform lateral and longitudinal pendulum motions, as well as yaw rotation. All three motions are recorded as functions of time. The model dynamics are studied as a function of the wind tunnel speed. Various techniques for stabilizing the load can be investigated by wind tunnel tests, which are much cheaper, faster, and less risky than equivalent flight tests. The present study investigates the use of passive vertical fins to stabilize the 8×6×6ft CONEX cargo container. The optimal geometry and location of the fins were determined in wind tunnel tests. Later on this optimal configuration was built and tested in full scale flight tests. The dynamic behavior during these flight tests is compared with the wind tunnel results. Good agreement between both can result in a significant reduction in the number and duration of the flight tests that are required in order to certify the stabilization method. By using the above described technique, the maximum flight speed of a UH-60/CONEX system was increased from 60 kts (the operational limit for the unstabilized CONEX) to 110 kts (the power limit of the system). Copyright © 2008 by the American Helicopter Society International, Inc. All rights reserved.

The problem of simulation models capable of predicting the aerodynamic instability of helicopter slung-load cargo containers and bluff bodies is addressed. Instability for these loads is known to depend on unsteady frequency-dependent aerodynamics, but simulation models that include the unsteady aerodynamics do not currently exist. This paper presents a method for generating such models using computational fluid dynamics (CFD) to generate forced-oscillation aerodynamic data and frequency domain system identification techniques to generate a frequency response from the CFD data and to identify a transfer function fit to the frequency response. The method is independent of the responsible flow phenomenon and is expected to apply to bluff-bodies generally. Preliminary results are presented for the case of the 6- by 6- by 8-ft CONEX (container express) cargo container. The present work is based on two-dimensional (2D) aerodynamic data for the CONEX side force and yaw moment generated by a forced oscillation in which frequency is varied smoothly over the range of interest. A first-order rational polynomial transfer function is found adequate to fit the aerodynamics, and this is shown to provide a good match with flight test data for the yawing motion of the CONEX.

The complex aerodynamics of rectangular underslung helicopter loads can lead to severe stability problems, but are difficult to represent in flight dynamics models. Current models for box aerodynamics are highly unsatisfactory, being entirely empirical and requiring large amounts of experimental data to generate. This paper presents a new modelling approach, which takes account of the bluff-body nature of the flow, where loads are dominated by normal pressure forces. Existing experimental data is recast in body-axes form, with α and β replaced by velocity components perpendicular and parallel to the box faces. Force and moment data for a wide range of boxes then collapse onto a set of simple generic characteristics, with features that can be related directly to the underlying flow physics. Modelling of container aerodynamics is greatly simplified, and allowance for effects of turbulence, Reynolds Number, wind tunnel interference and geometry modifications becomes possible.

In this paper we present a differential dynamic programming based guidance framework for slung load operations and demonstrate it through simulation studies and a preliminary flight test. Specifically, an optimal control problem is solved with the Differential Dynamic Programming (DDP) algorithm. The resulting optimal vehicle trajectory is used in the vehicle's existing guidance, navigation and control architecture. Furthermore, the state of the slung load is estimated via an augmentation to the existing navigation system that utilizes only vision-based measurements of the load. Therefore, minimal hardware and software changes are needed to an existing system in order to implement the proposed framework. The simulation studies and the preliminary flight test prove that the DDP algorithm can be solved iteratively on-line and is a feasible approach for the control of slung load systems. Copyright © 2014 by the American Helicopter Society International, Inc. All rights reserved.

An approach is presented, to the long-term problem of certifying the safe limits for helicopter operations with slung loads of arbitrary geometry. Recent work showed that at least two combinations of roll and yaw oscillations would amplify in free flight without rotor wake swirl. The acquisition of detailed airload maps for arbitrary shapes, with sufficient resolution in attitude, became the primary aeromechanical obstacle to predicting divergence speed. The conventional approach is to use wind tunnel testing at a few sample conditions and computational predictions to fill in the detailed parameter space. However, the technique of swing tests and continuous-rotation (STCR) presented in this paper, opens the way to direct calculation of the divergence speeds for known configurations, and a large enough empirical knowledge base to predict divergence speeds for entirely new configurations. The STCR and example test cases are described. A low-inertia cylinder, a loaded flat plate, and a porous box are used as test cases. Assumptions of symmetry are removed, and uniformly high resolution is available through regions of high gradients, to generate closed-form periodic representations of air loads for simulation. Wind tunnel video and encoder information improve efficiency in finding likely modes of amplification, and to validate simulations. Copyright© 2013 by the American Helicopter Society International, Inc. All rights reserved.

This paper summarizes work on the aerodynamics of the box-shaped Container Express (CONEX), used as a slung load cargo container. Two different computational fluid dynamics codes, OVERFLOW and STAR-CD, were used to study the three-dimensional flow over the stationary CONEX. Two-dimensional simulation of the stationary and oscillating CONEX were reported elsewhere (Ref. 1). The present computations demonstrate a capability to accurately predict the static aerodynamics using these two different CFD methods, and using both steady-state and unsteady flow simulations of the Navier-Stokes equations for both OVERFLOW and steady-state STAR-CD.

This paper presents two previously unreported aspects of the autorotation dynamics of low aspect ratio rectangular prisms, observed during an experimental study of the dynamics of helicopter underslung loads. Low-speed wind tunnel tests of a simplified container model free to rotate on a fixed axis demonstrated (a) that autorotation rate can lock-in to a structural mode and (b) that static hysteresis in autorotation rate can occur at low speeds. Autorotation lock-in behaves in a similar manner to vortex-shedding lock-in, suggesting that a similar feedback flow process between vortex wake dynamics and body motion is operating, and may provide a partial explanation for the complex changes in behaviour of rotating slung loads at high airspeeds. Static hysteresis at low speeds results in a bifurcation diagram for autorotation which is similar to that for cross-wind galloping of a square prism, including the effects of friction and inertia. The similarity in bifurcation behaviour seems likely to indicate similar dynamics rather than flow physics, suggesting that it may be possible to apply techniques developed to model the effect of non-linear damping characteristics in galloping to the modelling of autorotation.

Schemes for anisotropic grid adaptation for dynamic overset simulations are presented. These approaches permit adaptation over a periodic time window in a dynamic flowfield so that an accurate evolution of the unsteady wake may be obtained, as demonstrated on an unstructured flow solver. Unlike prior adaptive schemes, this approach permits grid adaptation to occur seamlessly across any number of grids that are overset, excluding only the boundary layer to avoid surface manipulations. A demonstration on a rotor/fuselage-interaction configuration includes correlations with time-averaged and instantaneous fuselage pressures, and wake trajectories. Additionally, the effects of modeling the flow as inviscid and turbulent are reported. The ability of the methodology to improve these predictions is confirmed, including a vortex/fuselage-impingement phenomenon that has before now not been captured by computational simulations. The adapted solutions exhibit dependency based on the choice of the feature to form the adaptation indicator, indicating that there is no single best practice for feature-based adaptation across the spectrum of rotorcraft applications.

Computational uid dynamics (CFD) is used to resolve the unsteady Navier Stokes equations for prediction of aerodynamic forces and moments acting on dynamic helicopter sling loads. The six-degree-of-freedom (6-DOF) rigid-body equations are tightly coupled with CFD to simulate body motion, and a model of the cables is developed to provide constraint forces and moments. This work presents the methodology and results of the coupled simulations with validation against experimental data. In addition, integration schemes for the 6-DOF equations are evaluated, and the effect of feature-based grid adapta- tion is investigated. Results of the simulations demonstrate good correlation with available experimental data and also show that the cable model assumptions are important in the dynamic behavior of the sling load.

The unsteady aerodynamic-dynamic interaction of a tethered bluff body is of vital importance to military and life-saving operations. Bluff bodies are encountered as airdrop, low altitude parachute extraction systems, and slung load packages, as well as comprising static and dynamic structures around which rotorcraft maneuver. Interactions between flow-induced forces/moments, inertial and elastic characteristics of the loads, and the handling qualities of the vehicle itself, can lead to large and divergent oscillations of the loads and pose threats to safety. Fundamental issues include the causal physics of unsteady, turbulent wakes of static and dynamic bluff bodies. As a first step, wind tunnel experiments have been performed using two generic shapes, a rectangular box and a cylinder of small aspect ratio. Dynamic behavior has been studied with various levels of inertia and various types of tethers, correlated with some full-scale flight test results and prior research on these generic shapes. Measured divergence speed is seen to reasonably scale to full-scale flight test results on tethered rectangular box shapes. Quasi-steady loads exhibit a sharp sensitivity of side force and yawing moment over some ranges of yaw angles, associated with the separation location. Computed frequencies appear to scale with Strouhal number over a wide range of Reynolds number. Copyright © 2011 by the American Helicopter Society International, Inc. All rights reserved.

Turbulent flows are characterized by a very wide range of scales in both time and space. Most of the kinetic energy of a turbulent flow is stored in the large-scale structures of the flow. In contrast, kinetic energy is dissipated as heat at the smallest scales. Although the much more computationally intensive large eddy simulations (LES) and direct numerical simulations (DNS) are performed in research environments, simulations that resolve the Reynolds-averaged Navier-Stokes (RANS) equations are still required for rapid engineering results. The hybrid RANS-LES method (HR-LES) was evaluated with a circular cylinder at a Mach number of 0.2 and a diameter-based Reynolds number of 3900 at standard sea-level conditions on three different grid systems. Strouhal number is calculated from the frequency spectrum of the fluctuating lift. Separation location is given in degrees over the circumference of the cylinder from the leading-edge stagnation point to the point where skin friction along the cylinder centerline drops to zero.

Current rotorcraft research to increase flight speed or to alleviate adverse physical phenomena expand the Mach/angle-of-attack envelope in which the rotor blades operate. For example, rotor blades will experience large areas over the rotor disk where reverse-flow effects cannot be neglected during the design and analysis of an efficient rotor at high advance ratios. A cost-effective alternative to extensive experimental analyses is the use of computational fluid dynamics codes to quantify the behavior of airfoils at high and reverse angles of attack, as well as to add to the knowledge of the behavior of airfoils when they are immersed in these flows. Numerical experiments have been performed with correlation to experimental databases that examine the ability of computational fluid dynamics to accurately model airfoil characteristics at these angles of attack. It is observed that the use of recently developed hybrid Reynolds-averaged Navier-Stokes and large-eddy simulation turbulence methods result in a significant improvement in the ability of computational fluid dynamics to predict the characteristics of airfoils in these angle-of-attack regimes. Modeling of the airfoil trailing edge is more sensitive when reverse-flow angles of attack are considered.

Airfoils and wings undergoing static and dynamic stall still elude accurate simulation by computational methods. While significant emphasis has been placed on the quantification of grid dependence, as well as influence of the turbulence method, many elements defining temporal convergence remain ad hoc. To address this, convergence and accuracy for two different turbulence methods were examined for both static and dynamic stall. New approaches to define numerical convergence that include an assessment of the physical accuracy have been developed and evaluated via a blind analysis at other stall conditions. A key finding is the need to ensure that the combination of time step and subiterations achieves a true second order accurate solution. It was also observed that accurate prediction of separation was controlled primarily by the turbulent transport terms, while the mean flow equations influenced reattachment. Temporal convergence of dynamic stall can be quantitatively assessed by an approach developed in this effort.

The most widely used shape in engineering, the circular cylinder, provides great challenges to researchers as well as mathematical and computer modellers. This book offers an authoritative compilation of experimental data, theoretical models, and computer simulations which will provide the reader with a comprehensive survey of research work on the phenomenon of flow around circular cylinders. Researchers and professionals in the field will find it an invaluable source for ideas and solutions to design and theoretical problems encountered in their work.

This paper presents recent results from a cooperative effort by the U.S. Army Aeroflightdynamics Directorate, the Technion Israel Institute of Technology, and Northern Arizona University to study and simulate the behavior of the 6 x 6 x 8 ft CONEX cargo container in forward flight suspended beneath a UH-60 Black Hawk helicopter. This load, like other cargo containers, is subject to massively separated unsteady flow and is limited by stability to operational airspeeds well below the power-limited speed of the configuration. The study makes use of aerodynamic data from wind tunnel, flight test, and computational fluid dynamics. The objective is a simulation of the helicopter slung load system validated over the complete flight envelope. The principal remaining technical challenge is a model of the unsteady load aerodynamics capable of predicting the critical unstable speed. Some progress has been made in meeting this challenge.

In forward flight helicopters carrying slung loads frequently encounter load instability problems that reduce their speed envelope to well below the power limit of the helicopter/slung-load system. The paper presents a procedure for the development and flight test verification of passive stabilizers designed to increase the maximum flight speed of the system. Most of the development is carried out during wind tunnel tests. A scale model is suspended from the tunnel ceiling by a gimbaled setup that simulates the hook-sling attachment. The model is free to perform lateral and longitudinal pendulum motions, as well as yaw rotation. All three motions are recorded as functions of time. The model dynamics are studied as a function of the wind tunnel speed. Various techniques for stabilizing the load can be investigated by wind tunnel tests, which are much cheaper, faster, and less risky than equivalent flight tests. The present study investigates the use of passive vertical fins to stabilize the 6 x 6 x 8 ft CONEX cargo container. The optimal geometry and location of the fins are determined in wind tunnel tests. Later on this optimal configuration is built and tested in full-scale flight tests. The dynamic behavior during these flight tests is compared with the wind tunnel results. Good agreement between both can result in a significant reduction in the number and duration of the flight tests that are required to certify the stabilization method. By using the above-described technique, the maximum flight speed of a UH-60/CONEX system is increased from 60 kt (the operational limit for the unstabilized CONEX) to 110 kt (the power limit of the system).

A single-degree-of-freedom mathematical model for describing vortex-induced response of a structure at "lock-in" includes certain aeroelastic parameters that need to be extracted from wind tunnel tests. The methods available in the literature for extraction of these parameters have certain limitations that inhibit accuracy in the extracted parameters of certain bluff-body sections. In the work reported herein, a new approach, which can be universally applied for the identification of vortex-shedding parameters even in turbulent-flow situations, has been proposed based on the concepts of invariant imbedding and nonlinear filtering theory. The new approach has been verified through experiments in the wind tunnel for both smooth and turbulent flow situations. The classical case of a circular cylinder has been employed to verify the accuracy of the approach. Experiments were also conducted with a circular-cylindrical section (rough surface) and two bridge-deck configurations to test the new approach on different types of cross sections.

A model is presented for predicting the across-wind response of constant-diameter circular cylinders vibrating in a mode of uniform amplitude and subject to uniform flow. A key feature of the model is the representation of all motion-dependent phenomena by a nonlinear aerodynamic damping force. This force coexists with the fluctuating force which arises from vortex shedding on a stationary cylinder, and the two forces are assumed to be uncorrelated.The ability of the device used in representing the motion-induced force to model certain aeroelastic characteristics associated with vibrating cylinders is demonstrated. The device is shown to be capable of successfully reproducing two effects; namely, the increase of the spanwise correlation of forces with increasing amplitude, and the phenomenon of “lock in” where the shedding frequency is apparently dictated by the vibration frequency.The model is developed within the framework of random-vibration theory, and a number of simplifying assumptions are necessary to incorporate the nonlinear aerodynamic damping force and also to account for the influence of turbulence. Numerical experiments, undertaken to examine the nature of the approximations involved in the assumptions adopted, are described. The results of the numerical experiments are very encouraging and justify the simplifications made in the modelling process.

Wake-body interactions for a two-dimensional structural angle member during stationary and vortex induced oscillatory conditions are studied using a conventional low turbulence wind tunnel. The response of an angle section with combined plunging and torsion indicates that the oscillations occur essentially in one of the two degrees of freedom. The measurements of frequency and phase substantiated this observation. The plunging resonance exhibits the familiar vortex capture phenomenon where the shedding frequency is controlled by the cylinder motion over a finite wind speed range. On the other hand, the torsional vibration shows a vortex control phenomenon where the vortex shedding governs the frequency of oscillation. The vortex induced torsional resonance was found to be severe even at moderate damping levels. The results should prove useful in structural designs such as high voltage transmission towers, antenna masts, bridges, etc. where angle sections are often used as secondary members.

Previous experiments by other workers have shown that when a cylinder vibrates in a steady flow the frequency of the vortex shedding from the cylinder can synchronize with the frequency of the cylinder's vibration. As a result the shedding frequency remains constant over a range of flow velocities, and the oscillatory forces acting on the cylinder increase. It has been suggested that synchronization should also occur for a stationary cylinder in a flow which has a superimposed oscillatory perturbation. An experimental investigation was made, therefore, of the vortex shedding from rectangular and circular cylinders in such a flow. Synchronization of the frequency of the vortex shedding from a circular cylinder with the perturbation frequency was found when the vortex shedding frequency was half the perturbation frequency. This result confirms the prediction by Clements (1975). The flow is similar to that which occurs in water when waves are superimposed on a steady current. That synchronization can occur for this type of flow could be important in the design of certain offshore structures.

The effects of the afterbody shape on the structure of the flow past a prismatic cylinder were investigated numerically. The shape of the cross-section of the cylinder varies from the square to trapezoids and finally to the triangle. Flow characteristics of vortex formation and shedding after the cylinder as well as its interaction with the separating shear layer from the leading edges were revealed by studying the patterns of instantaneous streamlines and the time-dependent pressure distribution on the surface of the cylinder. The present results show that when the ratio of rear and front width, λ0.5, the frequency decreases with the increase of λ. The mean value of the drag coefficients decreases monotonously with the increase of λ. Comparisons with experimental data and visualized flow field are included. Findings from this research are very useful for prismatic tower structures.

The Australian Armed Forces have class 16 airportable bridges in service, and there is a requirement to transport them beneath Chinook helicopters. Before the bridges can be carried as routine, it is necessary to determine the effects they have on the stability and flying qualities of the helicopter. In this report, information available concerning the operation of helicopters carrying airportable bridges is reviewed. In addition, a series of wind tunnel tests have been made with 1/15 scale models to determine the maximum safe speed for a helicopter carrying two different class 16 bridges, a 16 m (52 ft) clear span, and a 22 m (72 ft) raft, separately on a single hook. The tests indicated that the 16 m (52 ft) bridge could be carried safely at speeds up to 65 knot on a 16 m (53 ft) cable, provided it was slung 5 deg nose up in the static condition, and two small flat fins were attached to the aft end. The raft had to be carried in two loads, A and B, because of weight limitations. Load A, which consisted mainly of deck boxes and accessories, could be safely carried without fins at speeds up to 60 knot on a 16 m (53 ft) cable provided it was rigged 1 deg to 2 deg nose up. Load B, which consisted of four ramps and four articulators, could also be carried at 60 knot, but small flat fins were required and it had to be slung 5 deg nose up and carried on a 10 m (33 ft) cable.

Preliminary tests have been carried out on short circular cylinders with both ends free. Drag force is measured across the range 6 × 104 < Re < 2.6 × 105 for cylinders of length to diameter ratio L/D between 1 and 10. The effect of hemispherical ends is also investigated. A kind of periodic vortex shedding is found in the range 2 < L/D < 8. The oil-film surface flow visualization shows that the ‘eyes’ near the free ends (regions of low pressure) gradually disappear as L/D is reduced to 3. An asymmetric flow pattern is established for very short cylinders (L/D < 3). The detailed measurements of pressure distribution along and across models shows asymmetries of minimum and base pressures along the span. The asymmetric flow produces yawing and rolling moments which are also measured.

The present paper proposes a one degree of freedom (1DOF) non-linear model of self limiting cyclic wind loads for application in finite element method analyses of light structures subjected to vortex shedding excitation under lock-in conditions. Being empirical by nature, the model includes three independent parameters to be determined from response tests with representative aero-elastic wind tunnel models or prototypes. The paper discusses methods for parameter identification from response data. The paper also evaluates the proposed load model versus other 1DOF empirical vortex shedding models which have found some acceptance in wind engineering.

In this paper the various types of vortex generation and the related response characteristics of bluff bodies are described. The vortices are, in general, generated by a certain stimulation, leading to one- or two-shear layer instability; the related unsteady forces could excite flexible structures such as tall towers, tall buildings and long-span bridges. Karman vortex shedding is well known as the alternate shedding vortex behind bluff bodies, but the one-shear layer instability related vortices and symmetrical vortex shedding should also be taken into account as additional mechanisms for the evaluation of structural safety, because they result in structural response at comparatively low wind speeds. In this paper, the symmetrical vortex shedding, which is enhanced by the longitudinally fluctuating flow for 2-D rectangular cylinders with a 0.5 side ratio, and one-shear layer related vortices, which are generated on the side surfaces of flat 2-D rectangular cylinders and many bridge girder box sections by the stimulation of body motion or applied sound, are introduced. Furthermore, as a peculiar 3-D vortex, the “axial vortex”, which is formed in near wake of inclined cables and then over restricted velocity ranges, is also discussed.

This work deals with the response of a square cylinder free to rotate in a uniform flow. The two-dimensional, incompressible, time-dependent Navier-Stokes equation for flow around a fixed-cylinder are numerically solved for Reynolds numbers up to 250. The static rotational stability of the cylinder is analysed by considering moments around the fixed cylinder at different angles to the flow. The separation pattern and resulting wake are also investigated. Experiments are conducted on fixed and freely rotatable cylinders in the range of Reynolds number from 1,000 to 10,000. Variation of shedding frequency with cylinder orientation is determined for the fixed cylinder. The rotatable cylinder shows four distinct regimes of motion: a stable position where the cylinder side surfaces are parallel to the flow, periodic oscillations about this position, rotation with reversal of direction, and autorotation. Some of the dynamics of the freely rotatable cylinder can be modelled by a nonlinear, second-order differential equation. Numerical solutions of this simplified equation are compared qualitatively with experimental results.

This paper illustrates and discusses the progress and the prospects of analytical methods for estimating the wind-induced response of structures, with special regard to cantilever vertical structures. Also in this era of large facilities and super-computers, closed form solutions, eventually assisted by user-friendly numerical programs, electronic sheets and symbolic calculus tools, imply relevant significance and great potentialities. Their use may be divided into two operative lines, referred to as direct applications and integrated procedures. Direct applications concern those analyses that pursue their aims by applying analytical methods autonomously; they comprehend two broad classes of procedures addressed, respectively, to solve specific engineering problems and to assess general tendencies. Integrated procedures concern those analyses that pursue their aims through articulated flow-charts whose logical blocks imply analytical methods, numerical algorithms and experimental measurements; embedded in such a context, analytical methods are powerful tools to establish reliable procedures for the aerodynamic identification of structures and to solve complex wind engineering problems, among which the propagation of uncertainties, structural reliability and wind-induced fatigue, otherwise almost prohibitive.

This paper provides the exciting factors and mechanism of rain-wind induced vibration of polyethylene-lapped cable of cable-stayed bridges and the aerodynamic countermeasure to suppress the vibration.

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming.

A semiempirical model to predict the unsteady loads on an airfoil that is experiencing dynamic stall, is investigated. The mathematical model is described from an engineering point of view, demonstrates the procedure for obtaining various empirical parameters, and compares the loads predicted by the model with those obtained in the experiment. It is found that the procedure is straightforward, and the final calculations are in qualitative agreement with the experimental results. Comparisons between calculations and measurements also indicate that a decrease in accuracy results when the values of both the reduced frequency and the amplitude of oscillation are large. Potential quantitative improvements in the accuracy of the calculations are discussed for accounting of both the hysteresis in the static data and the effects of stall delay in the governing equations.

Equations of Motion of Slung Load Systems with Results for Dual Lift NASA TM-102246, National Aeronautics and Space Administration Modeling of a Generic Slung Load System Unsteady Aerodynamic Model of a Cargo Container for Slung-Load Navier–Stokes-Based Dynamic Simulations of Sling Loads

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Wind Tunnel and Flight Evaluation of Stability and Passive Stabilization of Cargo Container Slung Load Simulation of a Cargo Container Slung Load at Speeds with Significant Aerodynamic Effects Testing-Based Approach to Determining the Divergence Speed of Slung Loads

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