A Generalized Prediction Method for Rotordynamic Coefficients of Annular Gas Seals

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Xin Yan ◽  
Kun He ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Reaction Force ◽  
Excitation Frequency ◽  
Prediction Method ◽  
Experimental Tests ◽  
Computational Time ◽  
Transform Method ◽  
Rotordynamic Coefficients ◽  
The Laplace Transform ◽  
Computational Fluid Dynamics Cfd ◽  
Gas Seals

The improvement in rotordynamic performance of the annular gas seal requires efficient and accurate prediction methods of rotordynamic coefficients. Although the existed transient computational fluid dynamics (CFD) methods in published literature have excellent numerical accuracy, most of them face the challenge due to rotordynamic coefficients at every excitation frequency to be solved by a separate transient CFD prediction thus much time-consuming. In this paper, a generalized prediction method is proposed to address this difficulty. Based on the Laplace transform method, the solution procedures for the reaction force/motion equation of the annular gas seal are deduced. With the specified excitations (rotor motion), the rotordynamic coefficients at all excitation frequencies can be solved by only one or two transient CFD solutions. To verify the present generalized method, the rotordynamic coefficients of two typical hole-pattern seals are computed and compared to the available experimental data. The results show that the predicted rotordynamic coefficients are in good agreement with the experimental tests. Compared to the previous transient CFD methods, the computational time of the present generalized method is reduced significantly while the accuracy is still maintained.

Two-Dimensional Transient Solutions for Crossflow Heat Exchangers With Neither Gas Mixed

1987 ◽  
Vol 109 (2) ◽  
pp. 281-286 ◽  
Author(s):  
G. Spiga ◽  
M. Spiga
Keyword(s):  
Heat Exchangers ◽  
Initial Conditions ◽  
Transient Behavior ◽  
Computational Time ◽  
Two Dimensional ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Inlet Conditions ◽  
Conductance Ratio

The two-dimensional transient behavior of gas-to-gas crossflow heat exchangers is investigated, solving by analytical methods the thermal balance equations in order to determine the transient distribution of temperatures in the core wall and in both the unmixed gases. Assuming large wall capacitance, the general solutions are deduced by the Laplace transform method and are presented as integrals of modified Bessel functions on space and time, for a transient response with any arbitrary initial and inlet conditions, in terms of the number of transfer units, capacity rate and conductance ratio. Specializing the entrance temperature and assuming constant initial conditions, the most meaningful transient conditions (such as step, ramp, and exponential responses) have been simulated and the relevant solutions, expressed by means of either integrals or series, have been accurately computed with extremely low computational time. The temperature responses are then presented in graphic form for a wide range of the number of transfer units.

Application of a Novel Rotordynamic Identification Method for Annular Seals With Arbitrary Elliptical Orbits and Eccentricities

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Wanfu Zhang ◽  
Qianlei Gu ◽  
Jiangang Yang ◽  
Chun Li
Keyword(s):  
Fluid Velocity ◽  
Reaction Force ◽  
Grid Method ◽  
Labyrinth Seal ◽  
Damping Coefficient ◽  
Eccentricity Ratio ◽  
Rotordynamic Coefficients ◽  
Identification Method ◽  
Gas Seals ◽  
Annular Seals

The identification method using infinitesimal theory is proposed to predict rotordynamic coefficients of annular gas seals. The transient solution combined with moving grid method was unitized to obtain the fluid reaction force at a specific position under different whirling frequencies. The infinitesimal method is then applied to obtain the rotordynamic coefficients, which agrees well with published experimental results for both labyrinth seals and eccentric smooth annular seals. Particularly, the stability parameter of the effective damping coefficient can be solved precisely. Results show that the whirling frequency has little influence on direct damping coefficient, effective damping coefficient, and cross-coupled stiffness coefficient for the labyrinth seal. And the effective damping coefficients decrease as the eccentricity ratio increases. A higher eccentricity ratio tends to destabilize the seal system, especially at a low whirling frequency. Results also show that the fluid velocity in the maximum clearance in the seal leakage path is less than that in the minimum clearance. The inertial effect dominates the flow field. Then it results in higher pressure appearing in maximum clearances. The pressure difference aggravates the eccentricity of rotor and results in static instabilities of the seal system.

Measurement Versus Predictions of Rotordynamic Coefficients of a Hole-Pattern Gas Seal With Negative Preswirl

2012 ◽  
Author(s):  
Philip D. Brown ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
Ideal Gas ◽  
Rotor Speed ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
The Cross ◽  
Gas Seals ◽  
Stiffness And Damping

Test results are presented for rotordynamic coefficients of a hole-pattern annular gas seals at supply pressures to 84 bar and running speeds to 20,200 RPM. The principal test variable of interest was negative preswirl. Preswirl signifies the circumferential fluid flow entering a seal, and negative preswirl indicates a fluid swirl in a direction opposite to rotor rotation. The influences of pressure ratio and rotor speed were also investigated. Measured results produce direct and cross-coupled stiffness and damping coefficients that are a function of excitation frequency Ω. Changes in pressure ratio had only small effects on most rotordynamic coefficients. Cross-coupled stiffness showed slightly different profiles through the mid-range of Ω values. Increasing rotor speed significantly increased cross-coupled stiffness and cross-coupled damping. At 10,200 RPM, high negative inlet preswirl produced negative cross-coupled stiffness over an excitation frequency range of 200–250 Hz. Negative preswirl did not affect direct stiffness and damping coefficients. Effective damping combines the stabilizing effect of direct damping and the destabilizing effect of cross-coupled stiffness. The cross-over frequency is the precession frequency where effective damping transitions from a negative value to a positive value with increasing frequency. At 20,200 RPM with a pressure ratio of 50%, peak effective damping was increased by 50%, and the cross-over frequency was reduced by 50% for high-negative preswirl versus zero preswirl. Hence, reverse swirl can greatly enhance the stabilizing capacity of hole-pattern balance-piston or division-wall seals for compressors. A two-control-volume model that uses the ideal gas law at constant temperature was used to predict rotordynamic coefficients. The model predicted direct rotordynamic coefficients well, but substantially under predicted cross-coupled rotordynamic coefficients especially at high negative preswirls.

scholarly journals Theory Versus Experiment for the Rotordynamic Coefficients of Annular Gas Seals: Part 1—Test Facility and Apparatus

1986 ◽  
Vol 108 (3) ◽  
pp. 426-431 ◽  
Author(s):  
D. W. Childs ◽  
C. E. Nelson ◽  
C. Nicks ◽  
J. Scharrer ◽  
D. Elrod ◽  
...  
Keyword(s):  
Pressure Ratio ◽  
Excitation Frequency ◽  
Tangential Velocity ◽  
Test Facility ◽  
Rotordynamic Coefficients ◽  
Air Supply ◽  
Theory Versus ◽  
Leakage Characteristics ◽  
Gas Seals ◽  
A Current

A facility and apparatus are described for determining the rotordynamic coefficients and leakage characteristics of annular gas seals. The apparatus has a current top speed of 8000 cpm with a nominal seal diameter of 15.24 cm (6 in.). The air-supply unit yields a seal pressure ratio of approximately 7. The inlet tangential velocity can also be controlled. An external shaker is used to excite the test rotor. The apparatus has the capability to independently calculate all rotordynamic coefficients at a given operating condition with one excitation frequency.

scholarly journals Rotordynamic Coefficients for Stepped Labyrinth Gas Seals

1989 ◽  
Vol 111 (1) ◽  
pp. 101-107 ◽  
Author(s):  
J. K. Scharrer
Keyword(s):  
Pressure Distribution ◽  
Parametric Study ◽  
Separation Of Variables ◽  
Reaction Force ◽  
Zeroth Order ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Gas Seals ◽  
Basic Equations

The basic equations are derived for compressible flow in a stepped labyrinth gas seal. The flow is assumed to be completely turbulent in the circumferential direction where the friction factor is determined by the Blasius relation. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variables solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are presented in the form of a parametric study, since there are no known experimental data for the rotordynamic coefficients of stepped labyrinth gas seals. The parametric study investigates the relative rotordynamic stability of convergent, straight and divergent stepped labyrinth gas seals. The results show that, generally, the divergent seal is more stable, rotordynamically, than the straight or convergent seals. The results also show that the teeth-on-stator seals are not always more stable, rotordynamically, then the teeth-on-rotor seals as was shown by experiment by Childs and Scharrer (1986b) for a 15 tooth seal.

Theory Versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals: Part I—A Two Control Volume Model

1988 ◽  
Vol 110 (3) ◽  
pp. 270-280 ◽  
Author(s):  
Joseph K. Scharrer
Keyword(s):  
Pressure Distribution ◽  
Control Volume ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Wall Friction ◽  
Small Motion ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Volume Model ◽  
Gas Seals

The basic equations are derived for a two-control-volume model for compressible flow in a labyrinth seal. The recirculation velocity in the cavity is incorporated into the model for the first time. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equations. The first-order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients.

Yaw Galloping of a TLWP Platform Under High Speed Currents by Analytical Methods and its Comparison With Experimental Results

2017 ◽  
Author(s):  
Francisco Lamas ◽  
Miguel A. M. Ramirez ◽  
Antonio Carlos Fernandes
Keyword(s):  
High Speed ◽  
Production Systems ◽  
Experimental Tests ◽  
Experimental Results ◽  
Analytical Methodology ◽  
New Approach ◽  
Laboratory Facilities ◽  
Polynomial Curve ◽  
Computational Fluid Dynamics Cfd ◽  
Cfd Analyses

Flow Induced Motions are always an important subject during both design and operational phases of an offshore platform life. These motions could significantly affect the performance of the platform, including its mooring and oil production systems. These kind of analyses are performed using basically two different approaches: experimental tests with reduced models and, more recently, with Computational Fluid Dynamics (CFD) dynamic analysis. The main objective of this work is to present a new approach, based on an analytical methodology using static CFD analyses to estimate the response on yaw motions of a Tension Leg Wellhead Platform on one of the several types of motions that can be classified as flow-induced motions, known as galloping. The first step is to review the equations that govern the yaw motions of an ocean platform when subjected to currents from different angles of attack. The yaw moment coefficients will be obtained using CFD steady-state analysis, on which the yaw moments will be calculated for several angles of attack, placed around the central angle where the analysis is being carried out. Having the force coefficients plotted against the angle values, we can adjust a polynomial curve around each analysis point in order to evaluate the amplitude of the yaw motion using a limit cycle approach. Other properties of the system which are flow-dependent, such as damping and added mass, will also be estimated using CFD. The last part of this work consists in comparing the analytical results with experimental results obtained at the LOC/COPPE-UFRJ laboratory facilities.

scholarly journals Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals

2021 ◽  
Vol 11 (9) ◽  
pp. 4237
Author(s):  
Mingjie Zhang ◽  
Jiangang Yang ◽  
Wanfu Zhang ◽  
Qianlei Gu
Keyword(s):  
Circular Orbit ◽  
Present Method ◽  
Decomposition Method ◽  
Parameter Analysis ◽  
Elliptical Orbit ◽  
Computational Time ◽  
Solution Technique ◽  
Rotordynamic Coefficients ◽  
Cfd Method ◽  
Annular Seals

The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

A System Identification Method for Excitation-Frequency Dependent Rotordynamic Coefficients

2012 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul Allaire
Keyword(s):  
System Identification ◽  
Measurement Uncertainty ◽  
Excitation Frequency ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Adjoint Systems ◽  
Dynamic Coefficients ◽  
Backward Whirl ◽  
Identification Technique ◽  
Damped Systems

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.

Sign in / Sign up

Export Citation Format

Share Document