No abstract

Numerical analysis of turbomachinery based on energy method is used to predict the aeroelastic stability of the straight-through labyrinth seal by solving aerodynamic work and damping. The aeroelastic stability of the labyrinth seal under different working conditions and vibration modes has been compared. It's found that the increase of pressure ratio leads to the greater possibility of aeroelastic instability. The periodic distribution of the aerodynamic work in the circumferential direction of the labyrinth seal corresponds to the number of vibrating nodal diameters. In order to investigate the influence of structure parameters, the effect of relative thickness of the tooth tip, the width of the seal cavity and the eccentricity of the rotor on the aeroelastic stability of the labyrinth seal has been studied. The result of numerical calculation shows that the change of the structural parameters can affect the aeroelastic stability of the labyrinth seal to a certain extent, and can be applied in the structural optimization.

Abstract. An efficient mathematical model to describe the friction of short cylindrical shell structures with a dry friction damping sleeve is proposed. The frictional force in the circumference and axial direction is caused by the opposing bending strains at the interface. Slipping will occur at part region of the interface and the mathematic model of the slipping region is established. Ignoring the effect of contact stiffness on the vibration analysis, the friction energy dissipation capability of damping sleeve would be calculated. Structural vibration mode, positive pressure at the interface and vibration stress of the short cylindrical shell structures is analyzed as influence factors to the critical damping ratio. The results show that the circumferential friction energy dissipation is more sensitive to the number of nodal diameter, and the circumferential friction damping ratio increases rapidly with the number of nodal diameter. The slipping frictional force would increase along with the positive pressure, but the slipping region would decrease with it. The peak damping ratio keeps nearly constant. But the vibration stress corresponding to peak damping ratio would increases with the positive pressure. The dry friction damping ratio of damping sleeve contains the effect of frictional force in the circumference and axial direction, and the axial friction plays a major role.

Four different turbulence models have been employed to investigate the aeroelastic stability of NASA Rotor 67 and a transonic fan by use of the energy method. Firstly, the amplitude and phase of the first harmonic pressure on blade surface have been analyzed. Then the characteristics of flutter at different working points and nodal diameters have been investigated. Finally, the flutter boundary of the fan has been predicted and compared to the measured one. The simulation results for the steady characteristics by use of k-ε model and k-ω model agree better with the test data than those of the SST model and RNG k-ε model. The aerodynamic damping predicted by use of these models are approximately the same at the peak efficiency point. However, compared to the test data, the aerodynamic damping calculated by use of SST model are more conservative than k-ε model at the near-stall point. Therefore, the k-ε model is more suitable to flutter prediction of transonic fans. Nomenclature1B = first bending 1T = first torsion C = damping matrix c = blade chord length, m d k = the k-th vibration displacement vector E = Young's modulus, GPa F a = aerodynamic load matrix K = stiffness matrix M = mass matrix N = number of blade n  = surface unit normal vector p = pressure, Pa PS = pressure surface q cfd = modal amplitude q k = generalized displacement of the k-th modal S = area of blade surface, m 2 Span = height of the blade SS = suction surface T = vibrating period of the blade, s t = time, s v  = vibrating velocity of the blade 2 W aero = aerowork, J x= structural displacement vector y + = dimensionless normal distance from the wall φ k = the k-th modal shape vector λ k = the k-th eigenvalue of system μ = Poisson's ratio ρ = density, kg/m 3 σ = interblade phase angle ω k = the k-th natural angular frequency of the blade, rad/s ζ aero = aerodynamic modal damping ratio