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EN
The central theme of this work was to analyze high aspect ratio structure having structural nonlinearity in low subsonic flow and to model nonlinear stiffness by finite element-modal approach. Total stiffness of high aspect ratio wing can be decomposed to linear and nonlinear stiffnesses. Linear stiffness is modeled by its eigenvalues and eigenvectors, while nonlinear stiffness is calculated by the method of combined Finite Element-Modal approach. The nonlinear modal stiffness is calculated by defining nonlinear static load cases first. The nonlinear stiffness in the present work is modeled in two ways, i.e., based on bending modes only and based on bending and torsion modes both. Doublet lattice method (DLM) is used for dynamic analysis which accounts for the dependency of aerodynamic forces and moments on the frequency content of dynamic motion. Minimum state rational fraction approximation (RFA) of the aerodynamic influence coefficient (AIC) matrix is used to formulate full aeroelastic state-space time domain equation. Time domain dynamics analyses show that structure behavior becomes exponentially growing at speed above the flutter speed when linear stiffness is considered, however, Limit Cycle Oscillations (LCO) is observed when linear stiffness along with nonlinear stiffness, modeled by FE-Modal approach is considered. The amplitude of LCO increases with the increase in the speed. This method is based on cantilevered configuration. Nonlinear static tests are generated while wing root chord is fixed in all degrees of freedom and it needs modification if one requires considering full aircraft. It uses dedicated commercial finite element package in conjunction with commercial aeroelastic package making the method very attractive for quick nonlinear aeroelastic analysis. It is the extension of M.Y. Harmin and J.E. Cooper method in which they used the same equations of motion and modeled geometrical nonlinearity in bending modes only. In the current work, geometrical nonlinearities in bending and in torsion modes have been considered.
2
Content available Unsteady loads evaluation for a wind turbine rotor
EN
This paper presents a method for calculating the flow around a wind turbine rotor. The real flow is replaced by a free stream past a vortex model of the rotor. This model consists of lifting vortex lines which replace the blades and a trailing free vorticity. The vorticity shed from the blade is concentrated in two vortices issued from tip and root. To compute the unsteady forces exerted on the rotor, a free wake method is used. The evolution of the wake is obtained by tracking the markers representing the vortices issued from the blade tips and roots. To solve the wake governing equation and to obtain the marker positions, a time-marching method is applied and the solution is obtained by a second order predictor-corrector scheme. To validate the proposed method a comparison is made with experimental data obtained in the case of a model of wind turbine where the flow field immediately behind the rotor is measured by means of PIV. It is shown that the numerical simulation captures correctly the near wake development. The comparison shows satisfactory accuracy for the velocity field downstream of the rotor.
EN
The problem of interference between an aircraft and a strong vortex field, generated by another larger aircraft is addressed in this paper. A combined aerodynamics-flight dynamics model is used in the present study. For the solution of the aerodynamic problem, a potential three-dimensional, unsteady vortex lattice method (UVLM) with closed vortex ring as a singularity is utilised to get a numerical approximation for the governing equation of motion. Time history solution of the longitudinal motion of a small hypothetical, general aviation, aircraft is presented. The vortex generating, large aircraft, is represented by a large wing (swept and tapered), and the small aircraft is represented by a small straight wing and control surface (horizontal stabiliser), with all aerodynamic surfaces assumed to be of zero thickness. The effect of the vortex fiels generated by the large wing, on the initially trimmed approaching small aircraft is investigated through the variation of several parameters, such as, the relative position, and direction of motion. Large changes in the small aircraft aerodynamics are recorded when flight mechanics is included in the solution.
PL
W pracy przedstawiono zagadnienia interferencji małego samolotu z silną strukturą wirową pozostawioną przez inny większy samolot. W tym celu opracowano model matematyczny, uwzględniający wzajemne sprzężenia pomiędzy wartościami sił aerodynamicznych a ruchem małego samolotu z uwzględnieniem jego bezwładności. Do obliczeń zastosowano nieustaloną wersję metody siatki wirowej (UVLM). W charakterze osobliwości wykorzystano pierścienie wirowe. Rozwiązania dynamicznych równań ruchu ruchu symetrycznego dla małego (hipotetycznego) samolotu przedsatwiono w funkcji czasu. Model dużego samolotu, generującego struktury wirowe wykonano jako izolowany, cienki, zbieżny i skośny płat. Model małego samolotu wykonano jako dwa cienkie, prostokątne płaty: płat główny oraz usterzenie poziome, zaklinowane tak, aby była spełniona równowaga momentów pochylających. Przeanalizowano wpływ pola wirowego (pozostawionego przez duży samolot) na mały samolot w funkji wzajemnej odległości oraz kierunku ruchu. Stwierdzono, że obciążenia aerodynamiczne i przemieszczenia małego samolotu zależą istotnie od uwzględnienia jego bezwładności w wyniku sprzeżeń pomiędzy aerodynamiką a dynamiką.
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