The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

2006 ◽  
Vol 129 (4) ◽  
pp. 1028-1034 ◽  
Author(s):  
Mihai Arghir ◽  
Cyril Defaye ◽  
Jean Frêne
Keyword(s):  
Static Stability ◽  
Radial Force ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Friction Forces ◽  
Choked Flow ◽  
Annular Seal ◽  
Quantitative Results ◽  
Gas Seals

The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal, choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons to the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section, the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section, the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint, this behavior is explained by the modification of the Lomakin effect, which changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

2006 ◽  
Author(s):  
Mihai Arghir ◽  
Cyril Defaye ◽  
Jean Freˆne
Keyword(s):  
Static Stability ◽  
Radial Force ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Friction Forces ◽  
Choked Flow ◽  
Annular Seal ◽  
Quantitative Results ◽  
Gas Seals

The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons with the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint this behaviour is explained by the modification of the Lomakin effect that changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

Numerical Investigation on the Leakage and Static Stability Characteristics of Pocket Damper Seals at High Eccentricity Ratios

2017 ◽  
Vol 140 (4) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Static Stability ◽  
Operating Conditions ◽  
Eccentricity Ratio ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Experiment Data ◽  
High Eccentricity ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Gas Seals

Annular gas seals for compressors and turbines are designed to operate in a nominally centered position in which the rotor and stator are at concentric condition, but due to the rotor–stator misalignment or flexible rotor deflection, many seals usually are suffering from high eccentricity. The centering force (represented by static stiffness) of an annular gas seal at eccentricity plays a pronounced effect on the rotordynamic and static stability behavior of rotating machines. The paper deals with the leakage and static stability behavior of a fully partitioned pocket damper seal (FPDS) at high eccentricity ratios. The present work introduces a novel mesh generation method for the full 360 deg mesh of annular gas seals with eccentric rotor, based on the mesh deformation technique. The leakage flow rates, static fluid-induced response forces, and static stiffness coefficients were solved for the FPDS at high eccentricity ratios, using the steady Reynolds-averaged Navier–Stokes solution approach. The calculations were performed at typical operating conditions including seven rotor eccentricity ratios up to 0.9 for four rotational speeds (0 rpm, 7000 rpm, 11,000 rpm, and 15,000 rpm) including the nonrotating condition, three pressure ratios (0.17, 0.35, and 0.50) including the choked exit flow condition, two inlet preswirl velocities (0 m/s, 60 m/s). The numerical method was validated by comparisons to the experiment data of static stiffness coefficients at choked exit flow conditions. The static direct and cross-coupling stiffness coefficients are in reasonable agreement with the experiment data. An interesting observation stemming from these numerical results is that the FPDS has a positive direct stiffness as long as it operates at subsonic exit flow conditions; no matter the eccentricity ratio and rotational speed are high or low. For the choked exit condition, the FPDS shows negative direct stiffness at low eccentricity ratio and then crosses over to positive value at the crossover eccentricity ratio (0.5–0.7) following a trend indicative of a parabola. Therefore, the negative static direct stiffness is limited to the specific operating conditions: choked exit flow condition and low eccentricity ratio less than the crossover eccentricity ratio, where the pocket damper seal (PDS) would be statically unstable.

Numerical Investigation on the Leakage and Static Stability Characteristics of Pocket Damper Seals at High Eccentricity Ratios

2017 ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Static Stability ◽  
Operating Conditions ◽  
Eccentricity Ratio ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Experiment Data ◽  
High Eccentricity ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Gas Seals

Annular gas seals for compressors and turbines are designed to operate in a nominally centered position in which the rotor and stator are at concentric condition, but due to the rotor-stator misalignment or flexible rotor deflection, many seals usually are suffering from high eccentricity. The centering force (represented by static stiffness) of an annular gas seal at eccentricity plays a pronounced effect on the rotordynamic and static stability behavior of rotating machines. The paper deals with the leakage and static stability behavior of a fully-partitioned pocket damper seal (FPDS) at high eccentricity ratios. The present work introduces a novel mesh generation method for the full 360° mesh of annular gas seals with eccentric rotor, based on the mesh deformation technique. The leakage flow rates, static fluid-induced response forces and static stiffness coefficients were solved for the FPDS at high eccentricity ratios, using the steady Reynolds-Averaged Navier-Stokes (RANS) solution approach. The calculations were performed at typical operating conditions including seven rotor eccentricity ratios up to 0.9 for four rotational speeds (0 rpm, 7 000 rpm, 11 000 rpm and 15 000 rpm) including the non-rotating condition, three pressure ratios (0.17, 0.35 and 0.50) including the choked exit flow condition, two inlet preswirl velocities (0 m/s, 60 m/s). The numerical method was validated by comparisons to the experiment data of static stiffness coefficients at choked exit flow conditions. The static direct and cross-coupling stiffness coefficients are in reasonable agreement with the experiment data. An interesting observation stemming from these numerical results is that the FPDS has a positive direct stiffness as long as it operates at subsonic exit flow conditions, no matter the eccentricity ratio and rotational speed are high or low. For the choked exit condition, the FPDS shows negative direct stiffness at low eccentricity ratio and then crosses over to positive value at the crossover eccentricity ratio (0.5–0.7) following a trend indicative of a parabola. Therefore, the negative static direct stiffness is limited to the specific operating conditions: choked exit flow condition and low eccentricity ratio less than the crossover eccentricity ratio, where the pocket damper seal would be statically unstable.

About the Negative Direct Static Stiffness of Highly Eccentric Straight Annular Seals

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Mihai Arghir ◽  
Antoine Mariot
Keyword(s):  
Working Conditions ◽  
Rotation Speed ◽  
Theoretical Explanation ◽  
Exit Section ◽  
Static Stiffness ◽  
High Eccentricity ◽  
Flow Equations ◽  
Annular Seal ◽  
Asme Paper ◽  
Annular Seals

Experimental results indicating negative direct static stiffness of highly eccentric straight gas annular seals were very recently presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). This instability occurred at zero rotation speed and at high eccentricities. Up to then only gas annular seals with zero rotation speed, operating in centered position and with choked exit section were known as being susceptible of developing negative direct static stiffness. The seals and the working conditions presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201) had clearly no choked exit section. The present work advances a theoretical explanation of results reported by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). The analysis is based on the numerical solution of the bulk flow equations of the flow in the annular seal. Theoretical results show a negative static stiffness at high eccentricities and zero rotation speeds. Other seal geometries and working conditions were tested and showed that the decrease of the direct static stiffness at high eccentricities and zero rotation speeds is a characteristic of all straight annular seals whether the fluid is compressible or not. Nevertheless with increasing rotation speed, the static stiffness becomes again positive and may increase with increasing eccentricity. The negative static stiffness is then limited to very specific working conditions: high eccentricities and zero rotation speed.

About the Negative Direct Static Stiffness of Highly Eccentric Straight Annular Seals

2014 ◽  
Author(s):  
Mihai Arghir ◽  
Antoine Mariot
Keyword(s):  
Working Conditions ◽  
Rotation Speed ◽  
Theoretical Explanation ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Equations ◽  
Annular Seal ◽  
Theoretical Results ◽  
Specific Working ◽  
Annular Seals

Experimental results indicating negative direct static stiffness of highly eccentric straight gas annular seals were very recently presented in [1] by Childs and Arthur. This instability occurred at zero rotation speed and at high eccentricities. Up to then only gas annular seals with zero rotation speed, operating in centered position and with choked exit section were known as being susceptible of developing negative direct static stiffness. The seals and the working conditions presented in [1] had clearly no choked exit section. The present work advances a theoretical explanation of results reported in [1]. The analysis is based on the numerical solution of the bulk flow equations of the flow in the annular seal. Theoretical results show a negative static stiffness at high eccentricities and zero rotation speeds. Other seal geometries and working conditions were tested and showed that the decrease of the direct static stiffness at high eccentricities and zero rotation speeds is a characteristic of all straight annular seals whether the fluid is compressible or not. Nevertheless with increasing rotation speed, the static stiffness becomes again positive and may increase with increasing eccentricity. The negative static stiffness is then limited to very specific working conditions: high eccentricities and zero rotation speed.

Numerical Study on Choked Flow of CO2 Refrigerant in Helical Capillary Tube

2018 ◽  
Vol 26 (03) ◽  
pp. 1850027 ◽  
Author(s):  
Pravin Jadhav ◽  
Neeraj Agrawal
Keyword(s):  
Fluid Dynamics ◽  
Present Model ◽  
Capillary Tube ◽  
Numerical Study ◽  
Fundamental Principle ◽  
Tube Diameter ◽  
Published Data ◽  
Flow Conditions ◽  
Pressure Drops ◽  
Choked Flow

This paper presents a numerical study on an adiabatic helical capillary tube employing homogenous and choked flow conditions of a CO2 transcritical system. The theoretical model is based on the fundamental principle of fluid dynamics and thermodynamics. The result of the present model validates with the previously published data. The influence of operating and geometric parameters on the performance of the capillary tube has been evaluated. Flow characterizations of choked and unchoked flow conditions are determined. As the evaporator pressure drops, from unchoked condition to choked state, the percentage change in mass flow rate is minimal. A simulation graph is developed which has been helpful for the design of the helical capillary tube. The choked flow condition in a capillary tube is avoided by either increasing tube diameter of the fixed length tube or decreasing the length of the fixed tube diameter.

A Design to Improve the Effective Damping Characteristics of Hole-Pattern-Stator Annular Gas Seals

2006 ◽  
Author(s):  
Dara W. Childs ◽  
Yoon-Shik Shin ◽  
Brent Seifert
Keyword(s):  
Friction Factor ◽  
Flow Path ◽  
Test Results ◽  
Static Stiffness ◽  
Hole Depth ◽  
Negative Test ◽  
Damping Characteristics ◽  
Jump Phenomena ◽  
The Cross ◽  
Gas Seals

Predictions are presented for hole pattern seals for which the hole depth is varied axially, showing that various depth patterns can significantly improve damping performance in terms of both increasing the seal’s effective damping and reducing its cross-over frequency — the frequency at which effective damping changes from positive to negative. Test results are presented for the seal with the best variable hole depth (VHD) pattern showing an increase in peak damping by a factor of 1.6 over a constant hole depth (CHD) design, versus predictions of 2.7. The cross over frequency is reduced by approximately 40%. The VHD seal has a significant negative static stiffness that probably arises from a friction-factor jump phenomena, not flow path divergence. The VHD seal leaks less than a comparable CHD design.

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