Dynamic Coefficients of Labyrinth Gas Seals: A Comparison of Experimental Results and Numerical Calculations

2000 ◽  
Author(s):  
K. Kwanka ◽  
J. Sobotzik ◽  
R. Nordmann
Keyword(s):  
Stokes Equations ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Rotating Speed ◽  
Dynamic Coefficients ◽  
Flow Through ◽  
Gas Seals ◽  
Good Agreement

Non-contacting labyrinth seals are still the most common constructive elements used to minimize leakage losses in turbomachinery between areas with high pressure and areas with low pressure. Unfortunately, the leakage flow through the labyrinth seal generates forces which can have a great impact on the dynamics of the turborotor. Particularly in cases of instability, the turbomachinery is restricted in its power or rotating speed because of violent self-excited vibrations of the rotor. The occurrence of self-excited rotor vibrations due to lateral forces must definitely be excluded. To consider the labyrinth forces in Finite-Element prediction, a set of preferably exact dynamic coefficients is required. Numerical approaches used to calculate the coefficients are based on Navier-Stokes equations. A comparison with experimental data is essential for a validation of the calculation. The experimental identification is difficult, because of the littleness of the forces to be measured in gas seals. Especially the non-conservative coefficients, cross-coupled stiffness and direct damping, show a good agreement in both magnitude and trend depending on the entry swirl of the seal.

Improving the Stability of Labyrinth Gas Seals

1997 ◽  
Vol 123 (2) ◽  
pp. 383-387 ◽  
Author(s):  
K. Kwanka
Keyword(s):  
Stability Limit ◽  
Labyrinth Seal ◽  
Flexible Rotor ◽  
Labyrinth Seals ◽  
Continuous Growth ◽  
Rotating Speed ◽  
Dynamic Coefficients ◽  
Flow Through ◽  
Gas Seals ◽  
The Stability

The flow through labyrinth seals of turbomachinery generates forces which can cause self-excited vibrations of the rotor above the stability limit. The stability limit is reached at a specific rotating speed or power. The continuous growth of power density and rotating speed necessitates an exact prediction of the stability limit of turbomachinery. Usually the seal forces are described with dynamic coefficients. A new, easy-to-handle identification procedure uses the stability behavior of a flexible rotor to determine the dynamic coefficients. Systematic measurements with a great number of labyrinth seal geometries lead to reasonable results and demonstrate the accuracy and sensitivity of the procedure. A comparison of the various methods used to minimize the excitation indicates which seal is more stable and will thus improve the dynamic behavior of the rotor.

Rotordynamic Coefficients of Labseals for Turbines: Comparing CFD Results With Experimental Data on a Comb-Grooved Labyrinth

2005 ◽  
Author(s):  
Joachim Schettel ◽  
Martin Deckner ◽  
Klaus Kwanka ◽  
Bernd Lu¨neburg ◽  
Rainer Nordmann
Keyword(s):  
Stokes Equations ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Test Rig ◽  
Navier Stokes Equations ◽  
Detailed Model ◽  
Identification Methods ◽  
Rotating Speed ◽  
Flow Models ◽  
Rotordynamic Coefficients

The main goal of this paper is to improve identification methods for rotordynamic coefficients of labseals for turbines. This aim was achieved in joint effort of the Technische Universita¨t Mu¨nchen, working on experimental identification methods for rotordynamic coefficients, the University of Technology, Darmstadt, working on prediction methods, and Siemens AG, realizing the results. The paper focuses on a short comb-grooved labyrinth seal. Short labseals, amongst others the above mentioned comb-grooved labyrinth, were examined. by means of a very accurately measuring test rig. The rotor was brought into statically eccentric positions relative to the stator, in order to measure the circumferential pressure distribution as a function of pressure, rotating speed and entrance swirl. The data collected were used to validate results obtained with a numerical method. The theoretical approach is based on a commercial CFD tool, which solves the Navier Stokes equations using numerical methods. As a result, a detailed model of the flow within the test rig is produced. The efforts of computation here are greater than when compared with the likewise wide-spread Bulk flow models, however improved accuracy and flexibility is expected. As the validation of the model is successful, it could then be used to gain further insight in the flow within the seal, and to understand the results better. This showed that rotordynamic coefficients of labseals gained from different test rigs are not necessarily comparable.

Numerical Solutions of the Navier-Stokes Equations for Axisymmetric Flows

1968 ◽  
Vol 10 (5) ◽  
pp. 389-401 ◽  
Author(s):  
D. R. Strawbridge ◽  
G. T. J. Hooper
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Labyrinth Seal ◽  
Taylor Vortex ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
Flow Through

A numerical method is presented for the solution of the time dependent Navier-Stokes equations for the axisymmetric flow of an incompressible viscous fluid. The method is applied to the problems of Taylor-vortex flow about an enclosed rotating cylinder and between infinite concentric cylinders, and to the analysis of the flow through a labyrinth seal. The torque calculations, which show favourable agreement with experiment, and the resulting flow patterns are presented graphically.

Rotordynamic Impact of Swirl Brakes on Labyrinth Seals With Smooth or Honeycomb Stators

1997 ◽  
Author(s):  
K. Kwanka
Keyword(s):  
Stability Limit ◽  
Labyrinth Seal ◽  
Flexible Rotor ◽  
Labyrinth Seals ◽  
Identification Procedure ◽  
Continuous Growth ◽  
Rotating Speed ◽  
Dynamic Coefficients ◽  
Flow Through ◽  
The Stability

The flow through labyrinth seals of turbomachinery generates forces which can cause self-excited vibrations of the rotor above the stability limit. The stability limit is reached at a specific rotating speed or power. The continuous growth in of power density and rotating speed necessitates an exact prediction of the stability limit of turbomachinery. Usually the seal forces are described with dynamic coefficients. A new, easy-to-handle identification procedure uses the stability behavior of a flexible rotor to determine the dynamic coefficients. Systematic measurements with a great number of labyrinth seal geometries lead to reasonable results and demonstrate the accuracy and sensitivity of the procedure. A comparison of the various methods used to minimize the excitation indicates which seal is more stable and will thus improve the dynamic behavior of the rotor.

Steady two-dimensional flow through a row of normal flat plates

1990 ◽  
Vol 210 ◽  
pp. 281-302 ◽  
Author(s):  
D. B. Ingham ◽  
T. Tang ◽  
B. R. Morton
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Corner Singularities ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Good Agreement

A numerical and experimental study is described for the two-dimensional steady flow through a uniform cascade of normal flat plates. The Navier–Stokes equations are written in terms of the stream function and vorticity and are solved using a second-order-accurate finite-difference scheme which is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers. The upstream and downstream boundary conditions are discussed and an asymptotic solution is employed both upstream and downstream. A frequently used method for dealing with corner singularities is shown to be inaccurate and a method for overcoming this problem is described. Numerical solutions have been obtained for blockage ratio of 50 % and Reynolds numbers in the range 0 [les ]R[les ] 500 and results for both the lengths of attached eddies and the drag coefficients are presented. The calculations indicate that the eddy length increases linearly withR, at least up toR= 500, and that the multiplicative constant is in very good agreement with the theoretical prediction of Smith (1985a), who considered a related problem. In the case ofR= 0 the Navier–Stokes equations are solved using the finite-difference scheme and a modification of the boundary-element method which treats the corner singularities. The solutions obtained by the two methods are compared and the results are shown to be in good agreement. An experimental investigation has been performed at small and moderate values of the Reynolds numbers and there is excellent agreement with the numerical results both for flow streamlines and eddy lengths.

Comparison of Different Shroud Configurations in High-Pressure Turbines Using Unsteady CFD

2006 ◽  
Author(s):  
P. Adami ◽  
A. Milli ◽  
F. Martelli ◽  
S. Cecchi
Keyword(s):  
High Pressure ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Jet Interaction ◽  
Potential Source ◽  
Flow Through ◽  
Numerical Solver ◽  
End Wall

The objective of this work is to analyze the end wall leakage interaction in shrouded high pressure turbines to provide useful indications about the flow pattern and its impact on performances. The prediction of flow through the seal and the understanding of the leakage jet interaction with the main flow in turbine end wall regions is nowadays possible using 3D CFD approaches. Modern solvers allow the coupling of the labyrinth and the main vane flows accounting for most of the geometric and aerodynamic features characterizing this phenomenon. Two similar shroud configurations are here analysed for two high pressure turbine configurations. Each configuration refers to a different blade technology commonly used by ANSALDO ENERGIA. The computational algorithm is based on a numerical solver developed and applied for the simulation of compressible Navier-Stokes equations in a multi rows unsteady environment. In order to reproduce the basic physic of the leakages, the problem has been investigated modelling the unsteady 1 1/2 stage interaction together with the complete geometry of the labyrinth seals. The CFD results are commented addressing the potential source of losses to help the development of solutions for reducing the leakage losses.

Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals

2001 ◽  
Author(s):  
J. Jeffrey Moore
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Internal Flow ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Labyrinth Seals ◽  
Navier Stokes Equations ◽  
Rotordynamic Forces

Abstract Labyrinth seals are utilized inside turbomachinery to provide non-contacting control of internal leakage. These seals can also play an important role in determining the rotordynamic stability of the machine. Traditional labyrinth seal models are based on bulk-flow assumptions where the fluid is assumed to behave as a rigid body affected by shear stress at the interfaces. To model the labyrinth seal cavity, a single, driven vortex is assumed and relationships for the shear stress and divergence angle of the through flow jet are developed. These models, while efficient to compute, typically show poor prediction for seals with small clearances, high running speed, and high pressure (Childs, 1993). In an effort to improve the prediction of these components, this work utilizes three-dimensional computational fluid dynamics (CFD) to model the labyrinth seal flow path by solving the Reynolds Averaged Navier Stokes equations. Unlike bulk-flow techniques, CFD makes no fundamental assumptions on geometry, shear stress at the walls, as well as internal flow structure. The method allows modeling of any arbitrarily shaped domain including stepped and interlocking labyrinths with straight or angled teeth. When only leakage prediction is required, an axisymmetric model is created. To calculate rotordynamic forces, a full 3D, eccentric model is solved. The results demonstrate improved leakage and rotordynamic prediction over bulk-flow approaches compared to experimental measurements.

Numerical Solutions of Viscous Flow through a Pipe Orifice at Low Reynolds Numbers

1968 ◽  
Vol 10 (2) ◽  
pp. 133-140 ◽  
Author(s):  
R. D. Mills
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations have been obtained in the low range of Reynolds numbers for steady, axially symmetric, viscous, incompressible fluid flow through an orifice in a circular pipe with a fixed orifice/pipe diameter ratio. Streamline patterns and vorticity contours are presented as functions of Reynolds number. The theoretically determined discharge coefficients are in good agreement with experimental results of Johansen (2).

A new mathematical model for studying fully ionized plasma flows in MPD thrusters

2016 ◽  
Vol 07 (03) ◽  
pp. 1650014
Author(s):  
S Vijai Kumar ◽  
S Thanigaiarasu
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Integration Scheme ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
New Equation ◽  
Work Done ◽  
Mpd Thrusters ◽  
Good Agreement

The paper describes a novel mathematical model to study the physics of fully ionized plasma flow through MPD thrusters otherwise known as magnetoplasmadynamic thrusters. The developed model consists of a set of differential equations obtained by coupling the Navier–Stokes equations with Maxwell’s equations. The model developed was tested for various 1D and 1.5D cases. These simulations have been carried out for a special case of geometries called Tikhonov fitted geometries for alleviating the instability phenomenon commonly known as onset phenomenon in self-field MPD thrusters. The work was also extended to applied field MPD thrusters. A new equation for magnetic field was introduced to incorporate a virtual cathode. All the computations were carried out using a higher order integration scheme. The results obtained were found to be in good agreement with the previous work done on similar models.

Steady flow through a channel with a symmetrical constriction in the form of a step

1980 ◽  
Vol 372 (1750) ◽  
pp. 393-414 ◽  
Keyword(s):  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Uniform Grids ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations are given for the steady, two-dimensional, laminar flow of an incompressible fluid through a channel with a symmetric constriction in the form of a semi-infinite step change in width. The flow proceeds from a steady Poiseuille velocity distribution far enough upstream of the step in the wider part of the channel to a corresponding distribution downstream in the narrower part and is assumed to remain symmetrical about the centre line of the channel. The numerical scheme involves an accurate and efficient centred difference treatment developed by Dennis & Hudson (1978) and results are obtained for Reynolds numbers, based on half the volumetric flow rate, up to 2000. For a step that halves the width of the channel it is found that very fine uniform grids, with 80 intervals spaced across half of the wider channel upstream, are necessary for resolution of the solution for the flow downstream of the onset of the step. Slightly less refined grids are adequate to resolve the flow upstream. The calculated flow ahead of the step exhibits very good agreement with the asymptotic theory of Smith (1979 b)for Reynolds numbers greater than about 100; indeed, comparisons of the upstream separation position and of the wall vorticity nearby are believed to yield the best agreement between numerical and asymptotic solutions yet found. Downstream there is also qualitative agreement regarding separation and reattachment as the grid size is refined in the numerical results.

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