Research On Dynamic Characteristics Of Smooth Annular Seals

The smooth annular seal is the key component of turbomachines such as steam turbines,pumps and centrifugal compressors,to restrain the leakage of working fluid.Its performance has significant influences on the working efficiency,as well as the safe and stable operation of turbogenerator units.With the development of turbomachines towards high parameters,the problem of fluid-induced vibration caused by seals becomes increasingly serious.Therefore,it is of great theoretical significance and engineering value to carry out the research on the dynamic characteristics and mechanism of fluid-induced vibration for the smooth annular seal.Study on the critical pressure ratio of annular seals was carried out.An improved method for the critical pressure ratio calculation of the annular seal based on the thermodynamic theory shows higher accuracy comparing with the traditional Stodola method,and results agree well with the experimental results.The method avoids a series of assumptions about the flow field of the seal in the traditional Stodola method,and can effectively determine the critical state at the seal outlet.This paper investigated the critical pressure ratio of the seal with non-uniform clearance using the current improved method.The results show that as the tooth ratioφincreases,the critical pressure ratio decreases,and the seal is less likely to work in the choked state.This method provides a theoretical basis for judging the choked and subsonic states of the smooth annular seal.In this paper,a computational fluid dynamics（CFD）method was used to establish a full three-dimensional numerical model of the smooth annular seal.Based on the Childs’s experimental seal（L=100mm）,the paper investigated the static characteristics for the annular seal with 3 kinds of seal lengths（L=50mm,100mm,150mm）and 5 types of taper coefficients（f=-0.097,-0.054,0,0.054,0.097）.The influence factors（length-diameter ratios,taper coefficients and eccentricities）and formation mechanism of static instability of the smooth annular seal under choked or subsonic flow were analyzed.Results show that the magnitude and direction of the fluid-induced force in the experimental seal（f=0,L=100mm）are related to the choked or subsonic flow.The fluid-induced force is negative in the choked flow,but positive in the subsonic flow.With the increasing ratio of the length-diameter,the static stiffness coefficient becomes to be negative,which results in the static instability of the smooth annular seal.The taper coefficient affects the static stability of the seal.A larger the taper coefficient tends to result in greater the fluid-induced forces and static stiffness coefficients,and improve the seal stability.The negative circumferential velocity gradient in the minimum clearance of the annular seal is large.The resulting viscous effect reduces the pressure in the minimum clearance and creates a negative direct static stiffness coefficient,resulting in static instability of the tapered annular seal.Based on multiple frequencies elliptical whirling orbit model,the paper analyzed the dynamic coefficients of a smooth annular seal under choked or subsonic flow.The influences of length-diameter ratios,taper coefficients and eccentricities on the dynamic characteristics were investigated.The results show that the direct stiffness coefficient K_xx、K_yy of the experimental seal（L=100mm）decreases as the eccentricity increases.The absolute value of the cross stiffness coefficient|K_xy|、|K_yx|increases as the eccentricity increases,and the direct damping coefficient C_xx、C_yy increases as the eccentricity increases.As the eccentricity increases,|K_yy|,|K_xy|,|C_yy|,|C_xy|become to be greater than|K_xx|,|K_yx|,|C_xx|,|C_yx|,respectively.The variation trend of the effective damping coefficient C_eff is closely related to the change of the whirling frequency and eccentricity.For a low whirling frequency,the high eccentric rotor is more likely to be unstable.As the length-diameter ratio increases,the average direct stiffness coefficient decreases,then the system stiffness decreases.The average cross stiffness coefficient increases,and the average direct damping coefficient increases with the increasing length-diameter ratio.For high whirling frequency,the effective damping coefficient increases with increasing the length-diameter ratio,and the stability of the sealing system increases.At low whirling frequency,the effective damping coefficient decreases with increasing length-diameter ratio,and the stability of the sealing system decreases.The greater length-diameter ratio tends to bring about the system instability more easily.As the taper coefficient increases,the average direct stiffness coefficient increases.The constant-clearance seal have the largest average cross stiffness coefficients,followed by the convergent annular seal and the divergent annular seal.The trends of average direct damping coefficient and effective damping coefficient are closely related to whirling frequency,eccentricity and taper coefficient.Under high whirling frequency,the effective damping coefficient decreases with the increase of the absolute value of the taper coefficient.For low whirling frequency,the effective damping coefficient decreases with the increasing taper coefficient.