1 Copyright © 2007 by ASME

Proceedings of HT2007

2007 ASME-JSME Thermal Engineering Summer Heat Transfer Conference July 8-12, 2007, Vancouver, British Columbia, CANADA

HT2007-32275

OPTIMIZATION OF LABYRINTH SEAL FOR SCREW COMPRESSOR

Selvaraji M, Dy. Manager, Technology Development, Elgi Equipments Ltd, Coimbatore -641005

India selji@elgi.com www.elgi.com

Sam P. Joseph, Engineer, Technology Development, Elgi Equipments Ltd, Coimbatore -641005

India ���������������samjoseph@elgi.com

www.elgi.com

Nirmal N. Post Graduate of Thermal Engineering, Department of Mechanical Engineering, Government College of Technology, Coimbatore – 641 013.

India

ABSTRACT

Keywords: Screw compressor, Labyrinth seals, Leakage Optimisation Heat-transfer analysis, Thermal analysis, and CFD analysis. There is a growing demand for compressed air in the industry for various applications. Majority of industrial requirements is in line with screw compressor operating range. Design and construction of screw compressors are demanding tasks that require advanced calculations and theoretical knowledge. Clearances play a major role in the performance and reliability aspects of a screw compressor. Seals are provided in compressors to fit around rotor shafts in order to prevent the leakage of lubricating oil and working medium. However there is a small clearance between the seal and rotor shaft, which can cause potential leakage of the working medium. The performance of the compressor is directly related to the leakage rate through the seals. The labyrinth seal is a special type of seal, used in screw compressors and turbo-machinery for sealing purpose.

Labyrinth seal is a non-contacting type seal that uses a tortuous path to minimize the gas leakage. The pressure drop occurs at each labyrinth tooth as the medium is squeezed between the labyrinth tooth and the rotor. The leakage through the seal is directly related to the labyrinth profile and also the clearance between the rotor and the labyrinth tooth. The present work is carried out to reduce the leakage through the labyrinth seal by optimising the tooth profile and operating clearances. Heat transfer analysis is carried out on the housing of the labyrinth seal to find out the boundary temperature of the seal. Also the heat transfer analysis on the labyrinth seal followed by Thermo-structural analysis is carried out to find out the accurate operating clearance of the seal. By using CFD as a tool, the optimisation is carried out on different design configurations of labyrinth seal by comparing the deviation in leakage rates. Effect of rotor speed, width of seal and pressure ratio on air leakage rate is also investigated.

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A set of labyrinth seals has been designed based on the above optimisation and tested in the compressor. The results have been compared with the CFD prediction.

INTRODUCTION

In a screw compressor, a pair of intermeshing helical screw rotors is housed in the housing. The rotor with profile outside the pitch circle is called male or main rotor, the rotor with profile inside the pitch circle is called female or gate rotor. The ball bearing on the rotors takes axial forces of the screw compressor. Similarly, the cylindrical roller bearing on both ends of the rotor receives radial forces from the screw compressor. Screw compressors are same as piston compressors in the principle of the rise of the air pressure, one rotor acts as piston and other forms as cylinder in screw compressor and both belong to positive displacement compressors. Seals are devices provided in all compressors and turbines. Labyrinth (Laby) seals are characterised as controlled clearance seals without rubbing contact with the moving parts and with some tolerable leakage. As is most usually the case, the seal here is stationary and the shaft is rotating. Refer the Fig -1 for geometry and boundary condition of the analysis. One of the earliest mathematical treatments of Laby seals was by Egli [5] in the 1930’s where an idealised flow equation was derived with empirically determined correction factors. This model was the subject of study in this work against which the numerical (CFD) model was built up. The heat transfer coefficients output from the flow analysis were used in the thermo-structural analysis of the housing–seal system along with empirical thermal coefficients for cooling water and high temperature air flows. The combined expansion effect was observed.

NOMENCLATURE

m = Leakage rate in kg/s A = Area in m2 P = Pressure in bar V = Velocity in m/s K = Index of expansion (1.4) ρ0 = Upstram Density α = Flow coefficient ψn = Leakage function γ = Carry over correction factor β = Pressure ratio = Pn / P0 P0 = Upstream pressure Pn = Down stream pressure n = Number of throttling(or) number of fins γ = Kinematic visocity of hot and cold medium, m2/sec

hα ,s - Thermal expansion coefficient of housing, m/mdegC

Rh,s - Housing and seal radius, m Th,s,f - Temperature of housing and reference, degC Vh,c - Velocity of hot and cold fluid, m

D - Hydraulic mean diameter, m hh,c - Heat transfer coefficient of hot, cold fluid, W/m2K

ch,λ – Thermal conductivity of hot, cold fluid, W/mK

Reh,ec - Reynolds number of hot, cold fluid Prh,rc - Prandtl number of hot, cold fluid Nuh,c - Nusselt number of hot, cold fluid δrf,rc – Thermal expansion of housing and seal, mm

THEORETICAL ANALYSIS OF LABYRINTH SEALS In a labyrinth seal; as the fluid flows from high pressure to low pressure; it is forced to change directions and expand in stages. Airflow is assumed to be compressible and each stage is considered as a throttling. As air passes through the orifice, the entropy remains constant, while the pressure decreases owing to the throttling. This will cause the velocity of air to increase. The pressure in the cavity is taken as uniform.

EGLI’S MODEL

Initially, flow is considered as the isentropic expansion of a compressible fluid through a single ideal orifice. Later this is extended to include more than one orifice. Although the effects of rotation are neglected, this model includes an experimentally determined coefficient to account for the effects of kinetic energy carry-over in straight –through seals. Empirical values of the carry-over coefficient as a function of the number of throttles and the clearance to pitch ratio are used. In addition, a flow coefficient to compensate for the effects of friction and for the contraction of the flow through the seal throttles is employed. Graphs yield the variation of flow coefficient as a function of the number of throttles, seal clearance, tooth thickness and overall pressure ratio.

MATHEMATICAL EXPRESSION TO CALCULATE THE

LEAKAGE RATE THROUGH THE LABYRINTH The final equation for flow through ‘n’ throttlings is:

m = 00 ργαψ PA n

…..……. (1)

Where ( )

( )2

log1

ββψe

n n +−=

…..……. (2)

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NUMERICAL ANALYSIS THROUGH CFD

A commercial CFD code, FLUENT 6.1 was used for numerical analysis. After initial trials, the implicit solver and k-epsilon (2-eqn) flow model were chosen to simulate the compressible, viscous flow under steady-state conditions. The Labyrinth seal is subjected to 3 Barg and ambeint conditions between inlet and outlet respectively. Although a 3-D model was attempted, the 2-D axisymmetric case has sufficed for the course of this work.

The mesh dependence of the solution was studied and only the converged results presented. The CFD model was thus credibly created to simulate results of sufficient accuracy, better than the idealised theoretical model.

Thermal expansion of Housing and Seal Using the commercial Finite element code, ANSYS 8.1, thermal expansion of the housing and seal are analysed. The heat transfer coefficients of cooling water and compressed air flow are calculated for the housing as below.

Heat transfer coefficient of hot medium The empirical relations for calculating the heat transfer coefficients are based on the twin shell heat exchanger. Reynolds number

h

hh

DVγ

=Re

Nusselt number 4.08.0 PrRe023.0 hhhNu =

------ (3) Heat transfer coefficient of air

DNu

h hhh

λ=

------ (4)

Heat transfer coefficient of cold medium Reynolds number

c

cc

DVγ

=Re

Nusselt number 4.08.0 PrRe023.0 cccNu =

------ (5) Heat transfer coefficient of cold medium

DNu

h ccc

λ=

------ (6) The boundary condition obtained from the above calculation is applied in the thermal analysis and the temperature distribution of the rotors and the average value at required locations found.

Thermal Analysis of Housings Theoretical calculation of the thermal expansion of the housing at different locations is very complex due to the geometry, loading and boundary conditions and hence the Computer Aided Engineering assistance becomes mandatory. The equivalent 3D model was imported. 3D ELEMENTS were used with the free mesh option to obtain a sufficiently fine Mesh. Convective heat transfer coefficients were calculated using the equations 4 & 6 and input to areas where heat transfer was known to take place. Bulk temperatures and heat transfer coefficients of hot and cold medium were also given, refer Fig6.

The thermal expansion can be calculated from the local temperature of the material as Radial thermal expansion of Housing

( )fhhh TTRrh −= αδ

------ (7) Radial thermal expansion of Seal

( )fsss TTRrs −= αδ

------ (8) The operating clearance of the seal is obtained, which is a function of thermal expansion of seal housing and seal. RESULTS

The CFD results for the pressure, density and velocity are

indicated in the Fig 2 to 4 for the basic profile-1. The effect of the various profile configurations on leakage

are analysed and compared in the table no.1. The Fig-5 indicates the flow of the analysis performed in

Ansys. The temperature distribution plot obtained from the heat

transfer analysis of the housing is shown in Fig 6.

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CONCLUSION

The advantages with CFD are that the effects of

turbulence and friction, which required an empirically determined correction factor in the theoretical analysis, are accounted automatically by the solver. Thus, for any specified labyrinth seal configuration with number of throttling, geometry and clearance, CFD can give a better solution. Also we observed that the effect of rotation on air leakage can be considered as negligible. Investigations for possible profiles and their leakage effects are compared.

The optimized clearance is obtained from the thermo-structural analysis of housing and seal based on the boundary temperatures from heat transfer analysis. The seal is developed (refer Fig-7) with clearance optimized from above procedure and the test results found to correlate with the prediction.

SCOPE FOR FUTURE WORK The combined CFD, heat transfer and thermo-structural

analysis of the entire assembly can be analysed to get better predictions of leakage.

ACKNOWLEDGMENTS We are grateful to Dr. Madhu Ganesh, General Manager

and Mr. Venumadhav, Senior Manager, Technology Development, Elgi Equipments Ltd, Coimbatore, India-641005 for their approval and support during this optimisation, design, development and testing work.

We are also thankful to all reference authors like Martin

[1], Stodola [2], Dollin and Brown [3], Gercke [4], Egli [5], Hodkinson [6], Heffener [7], Benvenuti [8], Rao and Narayanamurthi [9], Meyer and Lowrie [10], Ahmed kovacevic, Nikola Stosic, Ian K. Smith [17], C. Zamfirescu, N. Nannan, M. Marin and C. A. Infante Ferreira [19],, Takao Inoue, Tomokazu Nakagawa, Eiji Fujita, Hisao Hamakawa [20], and Mikio Oi,Mariko Suzuki,Natsuko Matsuura [21].

REFERENCES

[1] Martin,H.M.,(1908), “Labyrinth packings,” Engineering,Vol.85,pp.35-38. [2] Stodola, A.,(1927), “Steam and Gas Turbines,” McGraw-Hill,Vol.1,pp.189-194. [3] Dollin, F. and Brown,W.,(1937),”Flow of fluids through openings in series, ” The Engineer, Vol.164,PP.223-224. [4] Gercke, M.,(1934), “Flow through Labyrinth Packing, ”Mechanical Engineer, Vol.86, pp.678-680. [5] Egli,A. (1935),“Leakage of steam through labyrinth seals,” ASME Transactions, pp.115-122. [6] Hodinson,B. (1939), “Estimation of leakage through a Labyrinth Gland,” proceedings of the Institute of Mechanical Engineers, Vol.141,pp.283-288. [7] Heffener,F.E. (1960), “A General Method for correlating Labyrinth seal Leakrate data, ”ASME Journal of Basic Engineerings,Vol.82,pp.265-275. [8] Rao, K.V., and Narayanamurthi,R.G., (1973), “An Experimental study of the performance characteristics of Labyrinth seal, “ Indian Engineering Journal, Vol.56,pp.176-181. [9] Benvenuti, E., (1980), ”Analytical and Experimental Development of Labyrinth Seals for process Centrifugal Compressor,” ASME Publication, pp.273-285. [10] Meyer, C.A., and Lowrie, J.A., (1975), "The leakage through Straight and Slant Labyrinths and Honey Comb Seals," ASME Journal of Engineering for Power,Vol.97, pp.495-502. [11] Gordo Kirk,R.,(2005), “Applications of Computational Fluid Dynamics Analysis for Rotating Machinery-part II: Labyrinth Seal Analysis,” ASME Transactions, Vol.127,pp.820-826. [12] John, D., and Anderson, J.R. (1995) “Computational Fluid Dynamics the Basic and Applications" McGraw-Hill International Edition. pp. 1-47. [13] Dr Ahmed Kovacevic, Nikola Stosic, Ian K. Smith, Numerical analysis of the fluid-solid interaction in twin-screw positive displacement machines, ICNPAA 2004: Mathematical Problems in Engineering and Aerospace Sciences, June 2-4, 2004, The West University of Timisoara [14] Dr A Kovacevic, CFD and stress analysis in screw compressor design, City University London, UK [15] C. Zamfirescu, N. Nannan, M. Marin and C. A. Infante Ferreira OIL FREE TWO PHASE AMMONIA (WATER) COMPRESSOR, FINAL REPORT, DELFT UNIVERSITY OF TECHNOLOGY Faculty of Design, Construction and Production , Contract BSE-NEO 0268.02.03.03.0002 , Report K-336 [16] Takao Inoue, Tomokazu Nakagawa, Eiji Fujita, Hisao Hamakawa, Thermo-elastic analysis of Oil free screw compressors, Kobe steel Engineering reports, Vol.49, No.1 April 1999. (Translated from Japanese)

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[17] Mikio Oi,Mariko Suzuki,Natsuko Matsuura, Structural Analysis and Shape Optimization in Turbocharger Development, Ishikawajima-Harima Heavy Industries Co., Ltd. [18] Selvaraji M, Finite Element Analysis of Screw Compressor, Proceedings of the Convergence-2006 ANSYS India Conference.

APPENDIX A

Fig-1 Layout of the Compressor with Labyrinth Seal

CFD RESULTS

Fig-2 plot of absolute pressure of profile-1

Fig-3 Density contour of profile-1

Fig-4 Velocity vector contour of profile-1

Effect of different Profiles Leakage rates from CFD Model are arrived at using

Fluent Software. These investigations clearly revealed that flow in a Labyrinth cavity is quite complex exhibiting at least one large re-circulation zone, which fills the inner portion of each cavity.

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Table 1 Comparison of leakage rate between CFD and theoretical models

APPENDIX B

ANALYSIS -FLOW DIAGRAM Fig-5 ANSYS -Flow Diagram

Figure no.6 Boundary Condition of Housing

Thermal Analysis of Housings

Structural Analysis of Housing + seal using

thermal results

Cumulative Effect: expansion results

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Figure no.7 Thermal analysis of Bearing Housing-

Temperature Plots

Figure no.8 Optmized Seal (developed)