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Analytical developments relative to gust response are discussed. Turbulence length scale, spectral functions, zero crossing values, gust loads analysis, power spectral techniques for analyzing the response of aircraft in turbulence, the spectrum of the rolling moment coefficient, and the spectrum correction factor are among the issues considered.
Atmospheric turbulence cueing produced by flight simulator motion systems has been less than satisfactory because the turbulence profiles have been attenuated by the motion cueing algorithms. Cardullo and Ellor initially addressed this problem by directly porting the turbulence model output to the motion system. Reid and Robinson addressed the problem by employing a parallel aircraft model, which is only stimulated by the turbulence inputs and adding a filter specially designed to pass the higher turbulence frequencies. There have been advances in motion cueing algorithm development at the Man-Machine Systems Laboratory, at SUNY Binghamton. In particular, the system used to generate turbulence cues has been studied. The Reid approach, implemented by Telban and Cardullo, was employed to augment the optimal motion cueing algorithm installed at the NASA LaRC Simulation Laboratory, driving the Visual Motion Simulator. In this implementation, the output of the primary flight channel was added to the output of the turbulence channel and then sent through a non-linear cueing filter. The cueing filter is an adaptive filter; therefore, it is not desirable for the output of the turbulence channel to be augmented by this type of filter. The likelihood of the signal becoming divergent was also an issue in this design. After testing on-site it became apparent that the architecture of the turbulence algorithm was generating unacceptable cues. As mentioned above, this cueing algorithm comprised a filter that was designed to operate at low bandwidth. Therefore, the turbulence was also filtered, augmenting the cues generated by the model. If any filtering is to be done to the turbulence, it will utilize a filter with a much higher bandwidth, above the frequencies produced by the aircraft response to turbulence. The authors have developed an implementation wherein only the signal from the primary flight channel passes through the nonlinear cueing filter. This paper discusses three new algorithms. Testing shows that the new methods provide the pilot with a more realistic sensation of turbulence; the cues are not attenuated by algorithm. Results of offline testing show the credibility of the models. Offline test verification was based primarily on the evaluation of the power spectral density of the outputs and the time response.
The paper describes turbulence simulation experiments based on the principles of control system theory, that is, the construction of a system characterized by a system function such that upon exciting the system with prescribed noise processes the output of the system is a realization of a random processing the desired statistical attributes of turbulence. An experimental autocorrelation of Jimsphere measurements of wind velocity was approximated to simulate turbulent wind. From the approximate autocorrelation function, the required system function is obtained, and a discrete time system is designed. Another method of simulation is to solve the convolution integral by filter techniques. Other methods include discrete Fourier simulation and self-similar simulation.
Turbulence simulation is computationally much simpler using rational spectra, but turbulence falls off as f exp -5/3 in frequency ranges of interest to aircraft response and as predicted by von Karman's model. Rational approximations to von Karman spectra should satisfy three requirements: (1) the rational spectra should provide a good approximation to the von Karman spectra in the frequency range of interest; (2) for stability, the resulting rational transfer function should have all its poles in the left half-plane; and (3) at high frequencies, the rational spectra must fall off as an integer power of frequency, and since the -2 power is closest to the -5/3 power, the rational approximation should roll off as the -2 power at high frequencies. Rational approximations to von Karman spectra that satisfy these three criteria are presented, along with spectra from simulated turbulence. Agreement between the spectra of the simulated turbulence and von Karman spectra is excellent.
An atmospheric turbulence model which accommodates variability of turbulence properties along an aerospace vehicle trajectory was developed. The technique involves the use of Dryden spectral forms in which the defining parameters are the standard deviations (sigma) and integral scales (L) of turbulence. These spectra are expressed as nondimensional functions of the nondimensional frequency Omega = omega L/V where omega is dimensional radian frequency and V is the true air speed of the aerospace vehicle. The nondimensional spectra are factored by standard techniques to obtain nondimensional linear recursive filters in the time domain whereby band-limited white-like noise can be operated upon to obtain nondimensional longitudinal, lateral, and vertical turbulence velocities, as functions of nondimensional time, tV/L, where t is time. Application of the technique to the simulation of the space shuttle orbiter entry flight phase is discussed.
An exact turbulent flow field was calculated on a three-dimensional grid with 64 points on a side. The flow simulates grid-generated turbulence from wind tunnel experiments. In this simulation, the grid spacing is small enough to include essentially all of the viscous energy dissipation, and the box is large enough to contain the largest eddy in the flow. The method is limited to low-turbulence Reynolds numbers, in our case R sub lambda = 36.6. To complete the calculation using a reasonable amount of computer time with reasonable accuracy, a third-order time-integration scheme was developed which runs at about the same speed as a simple first-order scheme. It obtains this accuracy by saving the velocity field and its first-time derivative at each time step. Fourth-order accurate space-differencing is used.
The optimal finite difference discretization used in simulations of turbulent flows is influenced by both, the type of the scale resolving simulation (DNS or LES), as well as the flow-physics (hydrodynamic instabilities, shocks, acoustics, etc.) one expects to resolve. Insight into dispersion and dissipation error requirements for some common scale-resolving simulation scenarios help to highlight the issues faced in selecting a scheme.
Statistical modeling of atmospheric turbulence is discussed. The statistical properties of atmospheric turbulence, in particular the probability distribution, the spectra, and the coherence are reviewed. Different atmospheric turbulence simulation models are investigated, and appropriate statistical analyses are carried out to verify their validity. The models for simulation are incorporated into a computer model of aircraft flight dynamics. Statistical results of computer simulated landings for an aircraft having characteristics of a DC-8 are reported for the different turbulence simulation techniques. The significance of various degrees of sophistication in the turbulence simulation techniques on the landing performance of the aircraft is discussed.
The influence of simulated turbulence on aircraft handling qualities is presented. Pilot opinions of the handling qualities of a light general aviation aircraft were evaluated in a motion-base simulator using a simulated turbulence environment. A realistic representation of turbulence disturbances is described in terms of rms intensity and scale length and their random variations with time. The time histories generated by the proposed turbulence models showed characteristics which are more similar to real turbulence than the frequently-used Gaussian turbulence model. The proposed turbulence models flexibly accommodate changes in atmospheric conditions and are easily implemented in flight simulator studies.
A simulation study of a recently developed hover/low speed Mixer Equivalent Turbulence Simulation (METS) model for the UH-60 Black Hawk helicopter was conducted in the NASA Ames Research Center Vertical Motion Simulator (VMS). The experiment was a continuation of previous work to develop a simple, but validated, turbulence model for hovering rotorcraft. To validate the METS model, two experienced test pilots replicated precision hover tasks that had been conducted in an instrumented UH-60 helicopter in turbulence. Objective simulation data were collected for comparison with flight test data, and subjective data were collected that included handling qualities ratings and pilot comments for increasing levels of turbulence. Analyses of the simulation results show good analytic agreement between the METS model and flight test data, with favorable pilot perception of the simulated turbulence. Precision hover tasks were also repeated using the more complex rotating-frame SORBET (Simulation Of Rotor Blade Element Turbulence) model to generate turbulence. Comparisons of the empirically derived METS model with the theoretical SORBET model show good agreement providing validation of the more complex blade element method of simulating turbulence.
A previous paper (1977) has presented results from flight simulator experiments on instrument-flight-rule handling-quality studies of a STOL-type aircraft in the presence of various models of simulated turbulence (Gaussian, modified Gaussian, Rayleigh, and variable length and intensity, VLI). In this paper, additional results are presented for flight simulator experiments on visual-flight-rule approach landings of a STOL-type aircraft. Pilot opinion ratings of the landing approach with visual display are analyzed to determine the most realistic turbulence model and to identify the variables that critically affect the handling quality of aircraft in turbulence. It is shown that turbulence simulated by a VLI model adequately match the desired statistical properties of real atmospheric turbulence, and that aircraft handling quality and pilot task performance are critically affected by turbulence. Realistic turbulence models present greater difficulty in controlling the aircraft than a simple Gaussian model.
Frequently in aerospace vehicle flight simulation, random turbulence is generated using the assumption that the craft is small compared to the length scales of turbulence. The turbulence is presumed to vary only along the flight path of the vehicle but not across the vehicle span. The addition of the realism of three-dimensionality is a worthy goal, but any such attempt will not gain acceptance in the simulator community unless it is computationally efficient. A concept for adding three-dimensional realism with a minimum of computational complexity is presented. The concept involves the use of close rational approximations to irrational spectra and cross-spectra so that systems of stable, explicit difference equations can be used to generate the turbulence.
A guide for potential users of Shuttle Simulation Turbulence Tapes is presented. It provides an appropriate description of the characteristics of the simulated turbulence stored on the tapes as well as instructions regarding their proper use. The characteristics of the turbulence series, including the spectral shape, cutoff frequencies, and variation of turbulence parameters with altitude, are discussed.
The purpose of Monte Carlo turbulence simulation is to add statistically accurate 'bumps' to aerospace vehicle flight simulation. Several recent improvements in the state of the art are reviewed and classified according to various characteristics affecting the realism of the simulation. Areas for future research are made clear by the classification scheme.
Turbulent flow simulations were completed of the THX-III single hole film cooling experiment performed at NASA Glenn Research Center (GRC). Two different Large-Eddy Simulation (LES) approaches were completed along with a RANS based study. The first LES approach utilizes the Flux Reconstruction (FR) based finite element code GFR, while the second approach makes use of the compact difference solver FDL3DI. Both LES codes were run on grids larger than 1.5 Billion degrees of freedom (DoF). The RANS simulations used FUN3D and included a grid convergence as a turbulence closure study. A summary of the computational approaches and key findings are presented along with the experimental measurements. Significant progress has been made towards the completion of this work, as all but one simulation have been completed. The preliminary findings have shown the LES approaches have excellent agreement with each other, and closely follow the trends of the experiment. The Reynolds stress RANS closure, while the best of the RANS results, had difficulty matching the results of the LES and experimental measurements.
A nonrecursive model (based on von Karman spectra) for atmospheric turbulence along the flight path of the shuttle orbiter was developed which provides for simulation of instantaneous vertical and horizontal gusts at the vehicle center-of-gravity and also for simulation of instantaneous gust gradients. Based on this model, the time series for both gusts and gust gradients was generated and stored on a series of magnetic tapes which are entitled shuttle simulation turbulence tapes (SSTT). The time series are designed to represent atmospheric turbulence from ground level to an altitude of 120,000 meters. An appropriate description of the characteristics of the simulated turbulence stored on the tapes, as well as instructions regarding their proper use are provided. The characteristics of the turbulence series, including the spectral shape, cutoff frequencies, and variation of turbulence parameters with altitude, are discussed. Information regarding the tapes and their use is presented. Appendices provide results of spectral and statistical analyses of the SSTT and examples of how the SSTT should be used.
Report on a new and general technique for simulating atmospheric turbulence-like random processes which are statistically homogeneous along the horizontal and nonhomogeneous along the vertical. This technique is general in the sense that it can be used for a broad class of similar problems. Like the other presently available schemes, the techniques presented are based on the Dryden hypothesis and Taylor's frozen eddy hypothesis; however, they go a step further by utilizing certain self-similarity properties of the Dryden spectral density function which permits the development of height invariant filters. These filters are in turn used to generate vertically homogeneous (statistically) random processes from which turbulence at any specified level in the boundary layer can be simulated, thus facilitating the simulation of a nonstationary turbulence process along the flight path of an aircraft during take-off or landing.
A turbulence model for Space Shuttle reentry simulation is presented, which may be used to improve redline selection. It is suggested that the turbulence model in current use is overly conservative because it assumes severe turbulence from reentry altitude to the earth's surface. Two improved versions of the turbulence simulation equations are presented. These are third and fifth order approximations to the von Karman spectrum. The equations are in a form suitable for digital simulation. Both sets of equations can be used to generate a probability distribution of fuel remaining at landing.