Computational Fluid Dynamics Predictions of Stability Derivatives for Airship

Abstract

In this paper, an approach that can obtain the stability derivatives through the unsteady computational fluid dynamics approach and Fourier analysis is proposed. Hybrid grids composed of boundary-layer viscous structure meshes and unstructured meshes were used. The flowfield was divided into two regions: the inner region and the outer region. The dynamic deformation grid was updated through the grid move with the body in the inner region and spring analogy in the outer region. This method can keep the quality of mesh preferably than one whole region dynamic mesh method during the course of movement of body. The validity of the computational method and dynamic mesh approach was verified by the calculation of the AGARD NACA 0012 airfoil. The calculation method of stability derivatives was verified by 6:1 prolate spheroid. The effects of the presence of the fins on stability derivatives of the airship were analyzed in this paper. The method proposed in this paper can be used to calculate the stability derivatives for other aircraft and submarine vehicles. Nomenclature a = the amplitude of oscillation c = the airfoil chord length F z = the normal force F w z = the stability derivatives of longitudinal force about velocity, F w z @F z =@w F _ w z = the stability derivatives of longitudinal force about velocity acceleration, F _ w z @F z =@ _ w F s x;y;z = the nondimension stability derivatives of force, F s x;y;z F s x;y;z V 1 S ref L ref =4 ft = the function of time k = the reduced frequency L ref = the reference length M y = the pitching moment M y = the stability derivatives of pitching moment about angle of attack, M y @M y =@ M _ y = the stability derivatives of pitch moment about acceleration angle of attack, M _ y @M y =@ _ M q y = the stability derivatives of pitch moment about pitch angle velocity, M q y @M y =@q M _ q z = the stability derivatives of pitch moment about pitch angle acceleration velocity, M _ q y @M y =@ _ q M s x;y;z = the nondimension stability derivatives of moment, M s x;y;z M s x;y;z V 1 S ref L 2 ref =4 q = the pitch angle velocity, q _ # S ref = the reference area T 0 = the period of one cycle of unsteadiness, T 0 2=$ t = the time V 1 = the freestream velocity # = the pitch angle w = the longitudinal oscillation velocity _ w = the longitudinal oscillation acceleration $ = the frequency of oscillation x = the nondimension state variable,x x 2V 1 =L ref z = the longitudinal oscillation displacement m = the mean angle of pitching 0 = the amplitude of pitching = the angle of attack, # _ = the accelerate of angle of attack, _ _ # t = the time step, t T 0 =400 ii = the added mass, ii , (i 1; 2; . . . 6)

Study of Hybrid Air Vehicle Stability Using Computational Fluid Dynamics

“…Figure 5 shows the pitching moment M y over one cycle. As can be observed, both CFD solutions (time-accurate and harmonic balance with 3 modes) agree perfectly with the signal provided by Wang [11].…”

“…II C. The method was validated by reproducing the results obtained by Wang [11] for the Zhiyuan-1 airship. Table 4 shows the values presented in Ref.…”

“…Table 4 shows the values presented in Ref. [11] and those computed with the current implementation of the method. Differences of less than 1.5% were obtained.…”

“…The first part of this study concerned the flow around a 6:1 prolate spheroid and the solutions were compared with the data published by Wang [11]. In the second part, the flow around the MLB is analysed.…”

“…This is possible with potential flow theory, but it requires extensive corrections and geometry simplifications. In the literature, Wang [11] computed the stability derivatives of the ZHIYUAN-1 airship from CFD solutions. Forced heaving motion and pitch oscillations (at reduced frequencies of 0.06 and 0.1) were studied and results on the bare hull and hull with fins were compared.…”