Atmospheric turbulences are fractional order, and because of that, it is difficult to simulate these disturbances. Past models fall short in providing sufficiently accurate simulation of atmospheric turbulence, especially at high altitudes, for control designs of high-speed atmospheric vehicles. In this innovation, fractional order approximations representative of actual atmospheric turbulence have been formulated that fit measured atmospheric turbulence. This is accomplished by scaling the Kolmogorov spectral factorizations to convert them into finite energy von Karman forms, and then by deriving an explicit fractional circuit-filter analog for this model.

The circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with products of first order transfer functions, which enables accurate frequency and time domain simulations. Given the parameters describing atmospheric disturbances (such as eddy dissipation rate, integral length scale, type of disturbance) and utilizing the derived formulations, the transfer functions describing these disturbances for acoustic velocity, temperature, pressure, and density can be directly computed. Time domain simulations and frequency domain analyses can then be performed to evaluate performance and control robustness of high-speed vehicles in the presence of atmospheric disturbance.

This work was motivated by the high-speed project, whereby dynamic propulsion system simulations are needed to design controls and obtain thrust dynamics to be coupled to the vehicle aero-servoelastic modes in the presence of atmospheric and other vehicle disturbances, in order to perform integrated vehicle controls, vehicle stability, and ride quality studies. However, besides propulsion, this technology is also applicable to flight dynamics and controls/flight loads, as well as rocket loads and controls. Simulation of atmospheric turbulence is very important for the design of propulsion and flight controls to enable efficient and safe operation of atmospheric vehicles for aircraft and rockets.

This innovation is described in the form of a formulation that computes the transfer functions of different types of atmospheric turbulence. The unique features of this innovation are that it provides for an accurate way to model atmospheric turbulence, which is important for the design of atmospheric vehicles to operate efficiently and safely. Also, it overcomes the deficiency of not being able to model the fractional order nature of atmospheric turbulence due to limitations in the technology to solve fractional order problems.

This work was done by George Kopasakis of Glenn Research Center.

Inquiries concerning rights for the commercial use of this invention should be addressed to

NASA Glenn Research Center
Innovative Partnerships Office
Attn: Steven Fedor
Mail Stop 4–8
21000 Brookpark Road
Cleveland
Ohio 44135.

Refer to LEW-18738-1.


NASA Tech Briefs Magazine

This article first appeared in the April, 2014 issue of NASA Tech Briefs Magazine.

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