Gust Model Research Articles

Prediction of loaded airfoil unsteady aerodynamic gust response by a locally analytical method

A complete first-order model is formulated to analyze the effects of steady loading on the incompressible unsteady aerodynamics generated by a two-dimensional gust convected with the steady mean flow past an arbitrary airfoil at finite nonzero angle of attack. A locally analytical solution is then developed in which the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements. The unsteady flow field is rotational and is linearized about the full potential steady flow past the airfoil. Thus, the effects of airfoil geometry and angle of attack are completely accounted for through the mean potential flow field. The steady flow is independent of the unsteady flow. However, the strong dependence of the unsteady flow on the steady effects of airfoil geometry and finite angle of attack are manifested in the unsteady boundary conditions which are coupled to the steady flow. A body-fitted computational grid is utilized. Analytical solutions to the transformed flow equations in individual grid elements are then developed, with the complete solution obtained by assembling these locally analytical solutions. This model and locally analytical solution are then applied to a series of airfoil and flow configurations. The results demonstrate that accurate predictions for the unsteady aerodynamic gust response are obtained only by including the coupled steady flow effects on the unsteady aerodynamics. Thus for cambered, or cambered and thick airfoils at zero or finite angle of attack, or a thin flat plate airfoil at a nonzero angle of attack, the model and solution developed herein accurately predict the gust response. It was also demonstrated that the classical small perturbation combined transverse and chordwise gust models yield accurate predictions only for the special case of a thin flat plate airfoil at zero angle of attack, i.e. only when the chordwise gust is zero.

On-line aircraft state and stability derivative estimation using themodified-gain extended Kalman filter

A new on-line state and parameter identification algorithm called the modified-gain extended Kalman filter (MGEKF) is applied to the problem of on-line state estimation and identification of the stability derivatives of a F-111 type of vehicle. The conceptual basis for the MGEKF is the existence of a class of nonlinear functions that allow a universal linearization with respect to the measurement function. This class includes the problem of identification of linear systems. The previous single-output formulation is extended to a multioutput formulation where the only available measurements are acceleration and pitch rate, but not elevator deflection. The filter formulation includes a simplified Dryden wind gust model. The inclusion of the wind gust model results mainly in a slowed response in the estimation of the stability derivatives associated with the acceleration state; estimates of the stability derivatives associated with the pitch rate still respond very quickly. The accuracy of the acceleration stability derivatives depends upon the amplitude and frequency components of the persistently exciting dither signal.

A statistical analysis of gust characteristics

Measurements of the turbulent atmospheric wind field have been analysed using different types of gust model concepts. The data represent a large variety of surface roughnesses and also a wide range of thermal stratifications. Measuring heights were between 7 and 135 m. The resulting gust amplitudes and times have been analysed statistically. Suitable normalizations have made it possible to obtain generally valid probability distributions.

Unsteady blade row interactions in a multistage compressor

A three-stage research compressor has been utilized to investigate the multistage blade row interaction gust aerodynamics for the first time. The aerodynamic forcing functions as well as the chordwise distributions of the steady surface pressures and the first harmonic unsteady pressure differences on the first and second stage stator vane rows were experimentally determined over a range of operating and geometric conditions. This series of experiments determined that the complex unsteady aerodynamic loading on downstream blade rows is directly related to the forcing function to the blade row, with this forcing function significantly affected by multistage blade row interactions. These results have an implication towards the modeling of unsteady aerodynamic blade row interaction phenomena. Namely, the variations of the second stage unsteady data with forcing function waveform cannot be predicted by harmonic gust models.

An assessment of the sensitivity of lattice towers to fatigue induced by wind gusts

The dynamic properties of lattice towers are closely constrained by practical economic design. It is thus possible to generalize the prediction of dynamic response, using the stochastic wind gust model, with details as outlined in the seminar ‘Wind engineering in the eighties’ (CIRIA, London, 1980). An approximation to the combined effect of resonant and non-resonant components of the response is presented, as a factor to be applied to the effective stress range based on the dynamic response alone, computed at a single ‘reference wind speed’. Results are presented for a range of practical structures, which indicate that good detailing can generally ensure that fatigue damage caused by wind gusts does not seriously limit design. The sensitivity of the normalized results to changes of location and of tower function and geometry is shown to be relatively small.

A Discrete Gust Model for Use in the Design of Wind Energy Conversion Systems

A discrete gust model has been designed which includes an expression for the number of times per unit time thy wind exceeds a specific value. This expression, based on Rice's (1944, 1945) number-of-crossings model, assumes that the yearly mean wind speed is averaged over a period of 10 minutes to 1 (one) hour. Vertical and lateral coherence functions are the basis for a mathematical filter which isolates atmospheric disturbances of a characteristic size (e. g., those which would completely engulf a rotor). Predictions are calculated usising the given definition of cut-off frequency, then they are compared with actual data, showing that the model is reliable. The expression is provided in a format such that it may be used for engineering design calculations.

Gust Model Based on the Bivariate Gamma Probability Distribution

The conventional approach to gust modeling for vertically rising vehicles involves the application of a digital filter to a sample of Jimsphere wind profiles, defining the resulting residual amplitudes as gusts, and developing statistical summaries or power spectra of the gusts. In this paper a new approach models the largest gust amplitude and gust length using the properties of the bivariate gamma distribution. The gust amplitude and gust length are strongly dependent on the filter function. Gust amplitude increases with altitude and is larger in winter than in summer.

A Non-Gaussian Gust Model for Aircraft Response Analysis

N UMEROUS investigations have been performed on the dynamic response of aircraft to continuous atmospheric turbulence (gust) by assuming that the turbulence field can be modeled as one, or a number of individually Gaussian and stationary patches. However, the observed statistical properties of atmospheric turbulence encountered by aircraft, especially those with the highest severity and potentially most destructive, are in many cases non-Gaussian. For instance, Ref. 1 deals with the aeronautical effects of surface winds and gusts. Tke investigation revealed that turbulence can rarely be realistically represented by a Gaussian process. This paper describes a non-Gaussian model for continuous atmospheric turbulence based on zero-memory transformation of a Gaussian model. Single or multiple transformation parameters are used to control the severity and other statistical characteristics of the non-Gaussian process. The composite nature of gust patches of various intensity is accounted for through the accumulative statistics. Methods to predict the aircraft response statistics to the non-Gaussian gust model are developed by approximating the response integral as its Riemann sum. Application of the probabilistic theory indicates that the statistical properties of response can be expressed in multifold integral forms and its moments can be expressed in explicit forms.

The plunging-mode response of an idealized airplane to atmospheric turbulent gusts

For the plunging-mode motion of an idealized airplane with pitch neglected, the response statistics have been formulated subject to atmospheric turbulence prescribed by the so-called Dryden's energy spectrum. The stationary input-response relation yields the following conclusions. (1) Atmospheric turbulent gusts should be modeled by incorporating not only the intensity modulation but also the time-varying energy spectrum. (2) The response exceedance curve can display convexity depending on the combination of gust intensity and spectrum parameter. (3) The integral length scale may be estimated alternately from the accelerometer data at the center of gravity and the gust intensity. As a consequence of conclusion (1), a discrete non-stationary gust model is proposed, consisting of a series of stationary processes, having different gust intensities and spectrum parameters. For such a modified Press' gust model, the response covariances of the plunging velocity and acceleration have been computed. Based on the elementary two-stationary-process gust model, sample calculations indeed produce convexity in the response exceedance curves, thereby substantiating (2). Finally, the implication of (3) is that one now has a means of checking consistency of the integral-length-scale measurements.

Helicopter Noise due to Blade-Vortex Interaction

The generation of impulsive sound, commonly called blade slap, due to blade-vortex interaction for helicopter rotors is discussed. The unsteady lift on the blades is calculated using linear unsteady aerodynamic theory for an oblique gust model of the blade-vortex interaction. A theoretical model for the radiated sound due to the transient lift fluctuations is presented. Expressions for the directivity, frequency spectrum, transient signal, and total power of the acoustic signal are derived. Typical results are presented and discussed. Calculations of the transient signal are presented in comparison with recent experimental results. The agreement is very good.

Evaluations of a spectral gust model using VGH and V-G flight data.

Evaluations of a spectral gust model using VGH and V-G flight data.