Sheryl M. Grace

Modeling the dynamics of spring-driven oscillating-foil propulsion

In this paper we present a model for oscillating-foil propulsion in which springs are used to transmit forces from the actuators to the foil. The expressions for hydrodynamic force and moment on the foil come from classical, linear, unsteady aerodynamics, and these are coupled to linearized rigid-body mechanics to obtain the complete model for swimming. The model is presented as a low-order set of ordinary differential equations, which makes it suitable for the application of techniques from systems and control theory. The springs serve to reduce energy costs, and we derive explicit expressions for spring constants which are optimal in this sense. However, the use of springs can potentially lead to unstable dynamics. Therefore, we also derive a set of necessary and sufficient conditions for stability. A detailed example is presented in which energy costs for one actuator are reduced by 33%.

Decreasing the energy costs of swimming robots through passive elastic elements

This paper investigates the potential benefit of elastic energy storage in the propulsion of a swimming robot. A discussion of the hydrodynamic models of von Karman and Sears (1938) and Lighthill (1969, 1970) is presented and is followed by an analysis of the input power required for cases with and without elastic energy storage. It is concluded that the addition of linear springs to the system provides a means to reduce the energy required of the power supply. A transfer function for the system is also derived for purposes of controlling a swimming robot.

Experimental Study of Quadcopter Acoustics and Performance at Static Thrust Conditions

A quadcopter, DJI Phantom II, was tested in the Virginia Tech Anechoic Chamber to study its aeroacoustics performance. Noise and thrust measured by a single microphone and a load cell were acquired for 4 different rotor configurations, two plastic and two carbon fiber rotors. To study the effects of multi-rotor interaction, the quadcopter was also set to operate with 1, 2 and 4 rotors. Results of 4-rotor operation show that tones at the blade passing frequency, shaft rate and their harmonics dominate the quadcopter acoustic spectrum up to 6000 Hz without much deterioration. Also significant is a broadband hump present in the mid frequency range which increases over 10 dB above the broadband level at low frequencies. Motor noise is also noticeable in the mid frequency range. For a smallscaled rotor, thrust performance is greatly influenced by rotor configuration whereas its acoustic signature is only altered near mid and high frequencies resulting in 1-2 dB change in the OASPL for the same thrust setting. Having 1, 2 or 4 rotors operating does not affect the acoustic signature but a significant increase was found in broadband noise when switching from 2 non-adjacent rotors to 4 rotors.

Effect of Rotor Wake Structure on Fan Interaction Tone Noise

The prediction of noise produced by fan-wake interaction with the fan exit guide vane (FEGV) is studied. The acoustic response of the FEGV is computed using LINFLUX, a three-dimensional, frequency-domain, linearized Euler solver for turbomachinery. The research focuses on tonal noise predictions for the advanced ducted propulsor (ADP) and the source diagnostic test (SDT) scaled turbofan rigs. The sensitivity of the 2BPF noise prediction to the inow specication is quantied. Inow models are generated based on both experimental and computational fan-wake data. The computational data are provided by four dierent Reynolds-Averaged Navier Stokes (RANS) computational uid dynamic (CFD) solutions. When compared to experimental results, the computations provide comparable mean ow solutions but overpredict the wake decit. The CFD solutions dier more for higher wheel speed cases, especially in the tip region. It is shown that inputs generated from the various experimental and CFD data also dier, but that these dierences weakly impact the prediction of the sound power level (PWL) at the lower wheel speed. At the higher wheel speeds, where the dierences in the inputs near the tip are greatest, the PWL reects this dierence. For a given wheel speed, the predictions using input values based on the dierent CFD data and the experimental wake data agree to within 5 dB. However, they vary from the experimentally measured acoustic PWLs by up to 14 dB.

Simulation of the Binaural Environmental Transfer Function for Gerbils Using a Boundary Element Method

The auditory system relies on spectral notches in the binaural environmental transfer function (BETF) as cues for localization of sources in the median plane. Experiments have shown that the BETF for gerbils in free space, regularly termed the head related transfer function (HRTF), contains a single notch in the ultrasonic range, while the BETF for a gerbil standing on a solid surface contains several notches at much lower frequency due to comb-filtering effects. In this research, the BETF for a model gerbil geometry is computed using a boundary element method (BEM). A parallel implementation of the BEM that includes the CHIEF regularization scheme is applied. The gerbils BETFs for various source elevations and distances in the free-field and in the presence of a solid surface are computed. Comparisons with gerbil HRTF measurements show good agreement. The reflection due to the solid surface is shown to provide an acoustic cue for source elevation as well as source distance. It is demonstrated that the full variation of the BETF with source location can only be captured through a simulation that can account for both the solid surface and the gerbil and their combined influence on the sound field.

Fan Broadband Interaction Noise Modeling

Results from a detailed investigation into the eect of modeling assumptions used with the RSI method to compute broadband interaction noise downstream of a turbofan engine’s fan stage are presented. The modeling assumptions that are considered include the use of a Green’s function to obtain the exhaust noise from the unsteady vane surface pressure, the implementation of a 2D vs. 3D vane model, and the form of the turbulence velocity correlation function. Calculation of the duct acoustics via the Green’s function is shown to be robust when one selects the frequencies used for the calculation such that they do not coincide with a duct cut-on/cut-o edge frequency. The unsteady vane response calculated by strip theory is found to be dierent than that predicted with a three-dimensional vane model. However, it is not clear yet how these dierences specically impact the predicted exhaust noise. Inclusion of the inhomogeneity of the turbulence across the passage is not so important because the average passage value provides good results. The form of the correlation function used to model the inow turbulence is shown to have a strong impact on the overall sound power level. Within the RSI framework, it is shown that using a common 3D spectrum (e. g. Liepmann and Gaussian spectra) but disregarding the k3 contribution gives results 20 dB lower than when the nontraditional RSI spectrum is used. The inclusion of the k3 eect with the common 3D spectrum within RSI leads to a dierence of 10 dB

Effect of CFD Wake Prediction in a Hybrid Simulation of Fan Broadband Interaction Noise

A fully computational hybrid method for simulating broadband interaction noise downstream of the fan stage in a turbofan engine is explored in this paper. The particular noise source of interest is due to the interaction of the fan rotor wake with the fan exit guide vanes (FEGVs). The broadband noise is predicted with the RSI code coupled to a Reynolds Averaged Navier Stokes (RANS) ow simulation. Input ow quantities for the RSI calculation of the FEGV response are derived from the rotor wake ow predicted by four dierent RANS simulations. The RANS solutions are shown to be in reasonable agreement with each other and with the hot-wire data available at the approach condition. The RANS solutions dier from each other more at higher rotor speeds but are self consistent in their wake ow predictions across the 3 rotor speeds: approach, cutback, and takeo.

Inverse Aeroacoustic Problem for a Rectangular Wing

An investigation is made of the feasibility of aeroacoustic inversion, where the pressure on a thin, flat, rigid rectangular wing undergoing rigid oscillations or interacting with unsteady, subsonic flow is to be predicted from the far-field acoustic signal. This problem is ill-posed because small pressure fluctuations in the far field are larger in the near field by a factor equal to the reciprocal of the distance from the wing. In the inverse model, this ill-posedness manifests itself in the kernel of a two-dimensional Fredholm integral equation of the first kind. Discretization of this integral equation using a physically meaningful collocation series results in an ill-conditioned system of equations which is solved using the singular value decomposition (SVD). The SVD generally requires regularization techniques to discard redundant or unphysical information. An algorithm is developed for optimally determining the near-field pressure without relying on a user-specified regularization parameter. Tests using numerically generated input data show the inversion is feasible and accurate for accurate input data. The inversion remains feasible when errors are introduced in the far-field measurements and the measurable parameters of the flow.

Influence of model parameters and the vane response method on a low-order prediction of fan broadband noise

The influence of modeling choices on a low-order method for predicting broadband interaction noise downstream of a fan stage in a turbofan engine is explored. The general method relies on experimentally or computationally obtained rotor-wake turbulence parameters as input. These parameters are used together with the Liepmann spectrum to define the inflow into the exit guide vane. Strip-theory allows the full 3D vane response to be constructed using a gust response model for a 2D vane. The sound power in the duct downstream of the exit guide vanes is calculated using the Green’s method for an annular duct. Comparison is made between the predictions obtained with a 2D flat-plate cascade gust response and a 2D flat-plate airfoil gust response. In addition, the effect of the inclusion of real vane geometry via an asymptotic gust response method is investigated. It is shown that for the current modeling method, a cascade response must be used and that the asymptotic method does not extend to high enough camber and angle of attack to be representative of modern vane geometries. It is concluded that the simpler flat-plate-based model is sufficient.

Hybrid Prediction of Fan Tonal Noise

A hybrid method is used to simulate the downstream rotor-vane interaction tonal noise associated with the NASA Source Diagnostic Test (SDT) 22-in fan rig. A 3-D, unsteady, Reynolds-averaged Navier-Stokes (URANS) CFD simulation is used to predict the unsteady surface pressure on the exit guide vanes (EGVs). The resulting downstream duct acoustics are then computed using two methods. The first is an analytical Green’s function method approximation for an infinite, fixed duct geometry. The second is a finite element model for a realistic duct geometry. One case from the SDT matrix is the main focus of this paper: approach condition for 22 rotor blades and 54 vanes. The configuration was designed for cut-o at the first blade-passing frequency. Comparison of the exhaust power level results for the 22x54 case reveal that the nonuniformity of the duct does not significantly influence the overall power level but it does cut-o the fifth radial mode and redistributes the energy between the other modes. The current acoustic simulation which models only the vane-wake interaction predicts an exhaust power approximately 13 dB lower than the experimental exhaust power.