Influence of steam leakage through vane, gland, and shaft seals on rotordynamics of high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine

Abstract

A comparative analysis of the influence of steam leakage through vane, gland, and shaft seals on the rotordynamics of the high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine was performed using numerical calculations. The rotordynamic coefficients associated with steam leakage through the three labyrinth seals were calculated using the control-volume method and perturbation analysis. A stability analysis of the rotor system subject to the steam forcing induced by the leakage flow was performed using the finite element method. An analysis of the influence of the labyrinth seal forcing on the rotordynamics was carried out by varying the geometrical parameters pertaining to the tooth number, seal clearance, and inner diameter of the labyrinth seals, along with the thermal parameters with respect to pressures and temperatures. The results demonstrated that the steam forcing with an increase in the length of the blade for the vane seal significantly influences the rotordynamic coefficients. Furthermore, the contribution of steam forcing to the instability of the rotor is decreased and increased with increases in the seal clearance and tooth number, respectively. The comparison of the rotordynamic coefficients associated with steam leakage through the vane seal, gland seal, and shaft seal convincingly disclosed that, although the steam forcing attenuates the stability of the rotor system, the steam turbine is still operating under safe conditions. List of symbolsA unsteady cross-sectional area of the cavity (m 2 ) A 0 steady annular flow area (m 2 ) C 0 orifice contraction coefficient C 1 kinetic energy carry-over coefficient C r steady radial clearance (m) [C] matrix of damping coefficients for the rotor system with seals h 0 stagnant enthalpy (J/kg) h 0iseal enthalpy at the ith orifice (J/kg) H unsteady labyrinth seal radial clearance (m) H 1 (θ, t) perturbation clearance (m) [K ] matrix of stiffness coefficients for the rotor system with seals L cavity length (m) m i steady-state leakage flow rate at the ith orifice (kg/s) [M] matrix of mass for the rotor system with seals N tooth number P 0i , P i steady and unsteady pressure at the ith cavity (Pa) P 1i (θ, t) perturbation pressure in the ith cavity (Pa) q 0i ,q i steady and unsteady leakage flow rate per unit length (kg/s-m) q 1i (θ, t) perturbation leakage flow rate per unit length (kg/s-m) R s rotor radius (m) U 0iseal velocity at the ith orifice (m/s) V 0i , V i steady and unsteady circumferential velocities in the ith cavity (m/s) V 1i (θ, t) perturbation circumferential velocities in the ith cavity (m/s)Greek symbols δ i the ith order logarithmic decrement ρ 0i , ρ i steady and unsteady gas density in the ith cavity (kg/m 3 ) ρ 1i (θ, t) perturbation gas density in the ith cavity (kg/m 3 ) ρ 0iseal steady gas density at the ith clearance (kg/m 3 ) τ r 0i , τ ri steady and unsteady shear stresses at the rotor wall (N/m 2 ) τ r 1i (θ, t) perturbation shear stress at the rotor wall (N/m 2 ) τ s0i , τ si steady and unsteady shear stresses at...

Numerical modeling of supercritical carbon dioxide flow in see-through labyrinth seals

“…Suryanarayanan [15], also used ideal gas, on the other hand presented a new model to calculate the carry-over coefficient in Hodkinson's model [9]. A recent study by Jiang [16] presents a numerical study on vane, gland, and shaft seals for supercritical water. They used finite element method to solve fluid dynamic equations to find the value of rotordynamic coefficients for these seals.…”