Calculation of leakage and dynamic coefficients of stepped labyrinth gas seals

Yücel, Uğur

doi:10.1016/s0096-3003(03)00574-5

Cited by 24 publications

(26 citation statements)

References 6 publications

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“…Unlike the isothermal air flow (m 0 = C 0 C 1 A 0 [5,10,11]), the leakage steam flow m 0 through the seals, when the critical condition is not reached at the last tooth, is taken to be isenthalpic [17] and determined as…”

Section: Calculation Of Leakage Steam Flowmentioning

confidence: 99%

“…This was proposed to correct the nonuniformity of velocity distribution [5,10,11]. The orifice contraction coefficient C 0 adopted in Eq.…”

Section: Calculation Of Leakage Steam Flowmentioning

confidence: 99%

“…Recently, various seal geometries, e.g., stepped labyrinth seal and honeycomb seal, were numerically investigated by Kleynhans [8], Yucel and Kazakia [9] and Dursun [10]. Cross-coupled stiffness coefficients of stepped labyrinth seal predicted by Yucel [11] showed relatively good agreement with the experimental data [12]. Further more, a set of differential equations were employed to allow the clear flow structure of the leakage air flow through a straight-labyrinth seal [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…As for steam flow, few studies of rotor dynamics associated with the periodical non-uniform aerodynamic forcing in labyrinth seals were reported so far. However, assumptions for the case of air flow, e.g., perfect gas law and isothermal flow [5,10,11], cannot be readily adopted for steam flow. Furthermore, laboratory experiments using steam flow are, in most cases, prohibitively hazardous and often impossible.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, a straight-through labyrinth seal [5] was chosen for study. A mathematical model of calculating rotordynamic coefficients that represent quantitative influence of leakage steam flow through the labyrinth seal on rotor dynamics was determined by using perturbation analysis [5,10,11]. Incorporation of the thermal properties of the steam fluid into the mathematical model resulted in a series of rotordynamic coefficients closely related to the fluid properties.…”

Section: Introductionmentioning

confidence: 99%

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Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

et al. 2007

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A mathematical model of calculating rotordynamic coefficients associated with leakage steam flow through labyrinth seals was presented. Particular attention was given to incorporating thermal properties of the steam fluid into prediction of leakage flow and subsequent derivation of rotordynamic coefficients, which quantitatively characterize influence of aerodynamic forcing of the leakage steam flow on the rotordynamics. By using perturbation analysis, we determined periodic and analytic solutions of the continuity and circumferential momentum equations for the time-dependent flow induced by non-axisymmetric rotation of the rotor encompassed by a labyrinth seal. Pressure distributions along labyrinth seal cavities and rotordynamic coefficients were compared at the same condition for air and steam flows. Influence of steam flow through the labyrinth seal cavities on rotordynamic coefficients was analyzed in terms of inlet pressure, inlet swirl velocity and rotor speed. List of symbolA unsteady cross-sectional area of the cavity [m 2 ] A 0 steady annular flow area [m 2 ] B tooth height [m] C 0 orifice contraction coefficient C 1 kinetic energy carry-over coefficient C r steady radial clearance [m] C x x , C yy damping coefficients [N s/m] C xy , C yx cross-couple damping coefficients [N s/m] Dh 0 , Dh steady and unsteady hydraulic diameter of the cross-sectional area of the cavity [m] F total air reaction force [N] F x , F y annular seal reaction force components [N] h 0 stagnant enthalpy [J/Kg] h iseal enthalpy at the ith orifice [J/Kg] H unsteady labyrinth seal radial clearance [m] H 1 (t, θ) perturbation clearance [m] K x x , K yy direct stiffness coefficients [N/m] K xy , K yx cross-couple stiffness coefficients [N/m] L cavity length [m] N tooth number n specific heat ratio P 0i , P i steady and unsteady pressure at the ith cavity [Pa] P 0iseal , P iseal steady and unsteady pressure at the ith orifice [Pa] P 1i (t, θ) 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 (t, θ) perturbation leakage flow rate per unit length [kg/s m] R steam constant [J/kg K] R s rotor radius [m] T i temperature at the ith cavity [K] T iseal temperature at the ith orifice [K] U iseal velocity at the ith orifice [m/s] V 0i , V i steady and unsteady circumferential velocities at the ith cavity [m/s] V 1i (t, θ) perturbation pressure at the ith cavity [m/s] (x, y)x and y coordinates of rotor whirling motionGreek symbols ε eccentricity ratio η imaginary number ρ i , ρ 0i steady and unsteady gas density of the ith cavity [kg/m 3 ] ρ 1 (t, θ) perturbation gas density of the ith cavity [kg/m 3 ] ρ 0iseal , ρ iseal steady and unsteady gas density at the ith clearance [kg/m 3 ] ρ 1iseal (t, θ) perturbation 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 (t, θ) perturbation shear stresses at the rotor wall [N/m 2 ] τ s0i , τ si steady and unsteady shear stresses at the stator wall [N/m 2 ] ...

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Section: Calculation Of Leakage Steam Flowmentioning

confidence: 99%

“…This was proposed to correct the nonuniformity of velocity distribution [5,10,11]. The orifice contraction coefficient C 0 adopted in Eq.…”

Section: Calculation Of Leakage Steam Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

et al. 2007

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Influence of leakage flow through labyrinth seals on rotordynamics: numerical calculations and experimental measurements

et al. 2007

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An extensive investigation of the influence of the leakage flow through a labyrinth seal at supply pressure of 12 bar on the rotordynamics was performed by using numerical calculations and experimental measurements. Toward this end, an experimental rotor setup was established in Shanghai Jiao Tong University. Two labyrinth seals were chosen for comparison, e.g., an interlocking seal and a stepped one. The numerical calculations based on the bulk-flow theory and the perturbation analysis were accomplished. Simultaneous acquisitions of the fluctuating static pressure at the stator wall and the displacement of the whirling rotor were made. The influence of the aerodynamic forcing on the rotor was analyzed in terms of the axial distribution of the mean static pressure, the circumferential distribution of the fluctuating pressure, the fist critical speed and the destabilization rotating speed of the rotor. The experimental results demonstrated that the sinusoidal distribution of the fluctuating static pressure on the stator wall was closely related to the whirling motion of the rotor. The first critical speed of the rotor was reduced by the aerodynamic forcing, resulting in intensified destabilization of the rotor system. Furthermore, the numerical analyses were in good agreement to the experimental measurements. List of symbols AUnsteady cross-sectional area of the cavity (m 2 ) A n Steady annular flow area (m 2 ) [C]Damping matrix C 0Orifice contraction coefficient C 1 Kinetic energy carry-over coefficient C r Steady radial seal clearance (m) C x x , C yy Damping coefficients (N-s/m) C xy , C yx Cross-couple damping coefficients (N-s/m)

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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

et al. 2011

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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...

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Calculation of leakage and dynamic coefficients of stepped labyrinth gas seals

Cited by 24 publications

References 6 publications

Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

Influence of leakage flow through labyrinth seals on rotordynamics: numerical calculations and experimental measurements

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

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