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DESIGN AND ANALYSIS OF AEROSTATIC

BEARINGS OF CRYOGENIC TURBINES FOR

HELIUM REFRIGERATOR/LIQUEFIER

Thesis submitted in partial fulfillment of the requirements for the degree of

Master of Technology

In

Mechanical Engineering

(Cryogenic and Vacuum Technology) By

Dhiren Mohapatra

Roll No. 213ME5450

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA

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DESIGN AND ANALYSIS OF AEROSTATIC

BEARINGS OF CRYOGENIC TURBINES FOR

HELIUM REFRIGERATOR/LIQUEFIER

Thesis submitted in partial fulfillment of the requirements for the degree of

Master of Technology

In

Mechanical Engineering

By

Dhiren Mohapatra

Roll No. 213ME5450

Under the guidance of

Mr. A. K. Sahu

Scientist / Engineer SF

Division Head,

Large Cryogenic Plant and Cryosystem,

Institute for Plasma Research,

Bhat, Gandhinagar-382428

Gujarat

Prof. R. K. Sahoo

Department of Mechanical Engineering,

National Institute of Technology,

Rourkela-769008

Odisha

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National Institute of Technology

Rourkela

CERTIFICATE

Design And Analysis Of Aerostatic Bearings Of

Cryogenic Turbines For Helium Refrigerator/Liquefier National Institute of Technology, Rourkela by Dhiren Mohapatra, Roll No. 213ME5450 for the award of the Degree of Master of Technology in Mechanical Engineering with specialization in is a record of bonafide research work carried out by him under my supervision and guidance. The results presented in this thesis have not been, to the best of my knowledge, submitted to any other University/ Institute for the award of any degree or diploma. The thesis, in my opinion, has reached the standards fulfilling the requirement for the award of degree of Master of Technology in accordance with regulations of the Institute.

Prof. R.K Sahoo

Department of Mechanical Engineering,

National Institute of Technology

Rourkela-769008

Odisha

Mr. A. K. Sahu

Scientist / Engineer SF

Division Head,

Large Cryogenic Plant and Cryosystem,

Institute for Plasma Research,

Bhat, Gandhinagar-382428

Gujarat

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CERTIFICATE

This is to certify that the dissertation, entitled Design and Analysis of Aerostatic Bearings of Cryogenic

Turbines for Helium Refrigerator/Liquefier

Is a bonafide work done by

Dhiren Mohapatra

Under my close guidance and supervision in the Large Cryogenic Plant and Cryosystem Group of Institute for Plasma Research, Gandhinagar, Gujarat for the partial fulfillment of the award of the Degree of Master of Technology in Mechanical Engineering with specialization in Cryogenic and Vacuum Technology at

National Institute of Technology, Rourkela

The work presented here, to the best of my knowledge, has not been submitted to any university for the award of similar degree.

Mr. A. K. Sahu

Scientist / Engineer SF

Division Head,

Large Cryogenic Plant and Cryosystem,

Institute for Plasma Research,

Bhat, Gandhinagar-382428

Gujarat

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ACKNOWLEDGEMENT

I am extremely thankful to Mr. A.K. SAHU Scientist / Engineer SF, Division Head, Large Cryogenic Plant and Cryosystem, Institute for Plasma Research, for his erudite suggestions, perceptive remarks, wondrous guidance and affection. I remain ever grateful to him for his valuable suggestions for the accomplishment of this project work. I take this opportunity to express my profound sense of gratitude and indebtedness to my supervisor Prof. R. K. SAHOO, Professor, Department of Mechanical Engineering, NIT Rourkela, for his encouragement, guidance and great support during the project work. He was always motivated and shares his expertise during the whole course of project work. I owe a deep debt of gratitude to him and remain grateful to him. I would like to thank my colleagues, working with me at the Institute for Plasma Research for their great support and advices at hard times.

NIT ROURKELA for

providing me the financial help in the form of stipend and also encouragement to complete the study successfully. Last but not the least, I want to convey my heartiest gratitude to my parents and friends for their immeasurable love, support and encouragement.

Dhiren Mohapatra

Roll no. 213ME5450

Cryogenic and Vacuum Technology

Mechanical Engineering Department

National Institute of Technology

Rourkela

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ABSTRACT

Aerostatic bearings are generally used in the field of high speed applications. The Helium Refrigerator/Liquefier (HRL) needs turbines as expansion machines to produce cooling effect which is further used for production of liquid helium. Cryogenic turbines are significantly smaller in size compared to those for room temperature applications but rotational speed is very high, about few hundred thousands of rpm and hence these have contactless gas bearings or magnetic bearings. This project involves the design and analysis of the aerostatic bearings

with horizontal shaft configuration. In the aerostatic bearings, pressurized helium gas is

passed through the bearings. Based on this pressure and temperature and the rotational speed of the turbines, the shaft of the turbine rotates without contact with bearing wall and the leakage between process gas and bearing gas is minimum. For different normal and off- normal operations, speeds will be different and hence the flow parameters for bearing gas flow will be controlled via control valves and the bearing should be designed to provide such contactless rotation. In this study, a theoretical analysis is presented for the load capacity, stiffness, flow rate of aerostatic journal bearing and thrust bearing with pocketed orifice.

Effects of orifice diameter, radial clearance, inlet pressure and outlet pressure on load

capacity, mass flow rate and stiffness have been analyzed. Dynamic unbalances like whirling of the shaft have also been covered in this study. Design considerations for limiting dispersion effect, and to avoid pneumatic hammer has also been taken into account. Validation of the analysis has been done by using ANSYS CFX with the numerical results. Keywords: Aerostatic journal bearing, aerostatic thrust bearing, pneumatic hammer, dispersion effect, dynamic unbalance, whirling, load capacity, stiffness, mass flow rate,

ANSYS CFX.

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Table of Contents

List of figures ........................................................................................................................ 3

List of Tables ........................................................................................................................ 4

Nomenclature ........................................................................................................................ 5

1 INTRODUCTION ......................................................................................................... 8

1.1 Helium Liquefaction Process at IPR ........................................................................ 9

1.2 Role of Gas Bearing in Cryogenic Application ........................................................ 9

1.3 Types of gas bearing ............................................................................................. 10

1.3.1 Aerodynamic bearing ..................................................................................... 10

1.3.2 Aerostatic bearing: ......................................................................................... 10

1.4 Advantages of Aerostatic bearing: ......................................................................... 12

1.5 Disadvantages of Aerostatic bearing:..................................................................... 12

1.6 Aim of the present study: ...................................................................................... 12

2 LITERATURE REVIEW ............................................................................................. 13

2.1 History and Application ........................................................................................ 14

2.2 Different approaches made for the analysis of journal bearing ............................... 14

2.2.1 Radial load Capacity ...................................................................................... 15

2.2.2 Aerodynamic Performance of hybrid journal bearing ..................................... 16

2.3 Thrust Bearing ...................................................................................................... 17

2.4 Different modern bearings ..................................................................................... 19

3 DESIGN PROCEDURE............................................................................................... 20

3.1 Elements of Turbo-expander: ................................................................................ 21

3.2 Design Considerations........................................................................................... 22

3.3 Design Procedure of Feed hole .............................................................................. 23

3.4 Design Procedure of Hybrid journal Bearing ......................................................... 24

3.4.1 Mass flow rate Calculation ............................................................................. 24

3.4.2 Static load Capacity Calculation ..................................................................... 25

3.4.3 Radial Stiffness Calculation of Hybrid Journal Bearing .................................. 25

3.4.4 Aerodynamic load Calculation ....................................................................... 25

3.4.5 Overall load capacity and Stiffness Calculation .............................................. 25

3.5 Design Procedure of Thrust Bearing ...................................................................... 26

3.5.1 Mass Flow rate Calculation ............................................................................ 26

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3.5.2 Load Capacity and Stiffness Calculation ........................................................ 26

3.6 Dynamic Analysis of the Shaft .............................................................................. 26

4 RESULT AND ANALYSIS ......................................................................................... 29

4.1 Journal Bearing ..................................................................................................... 30

4.2 Thrust Bearing ...................................................................................................... 36

4.3 Dynamic Analysis of the shaft ............................................................................... 38

5 VALIDATION OF ANALYSIS USING ANSYS CFX ................................................ 40

5.1 Journal Bearing ..................................................................................................... 41

5.2 Thrust Bearing ...................................................................................................... 46

6 MATERIAL SELECTION ........................................................................................... 48

7 CONCLUSION ............................................................................................................ 50

8 REFERENCES ............................................................................................................ 52

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List of figures

Figure 1.1: Schematic diagram of indigenous HRL plant ....................................................... 9

Figure 2.1: Pressure Distribution of Journal bearing [1] ....................................................... 15

Figure 2.2: Flow of gas inside journal bearing clearance and pressure distribution [1] ......... 16

Figure 2.3: Force and Displacement Diagram of shaft [1] .................................................... 17

Figure 2.4: Sectional View of Annular thrust Bearing and shaft collar ................................. 18

Figure 3.1: Schematic diagram of Turbo-expander [12] ....................................................... 21

Figure 3.2: Gas flow path of Turbo-expander and Bearing system ....................................... 22

Figure 3.3: Sectional view of feedhole ................................................................................. 23

Figure 4.1: Effect of orifice Radius and radial clearance on Mass flow rate ......................... 30

Figure 4.2: Effect of Pressure ratio Po/Pa on Mass flow rate ................................................. 30

Figure 4.3: Effect of radial clearance on Radial Load Capacity ............................................ 31

Figure 4.4: Effect of pressure ratio on Radial Load Capacity ............................................... 31

Figure 4.5: Effect of radial clearance on Radial Stiffness ..................................................... 32

Figure 4.6: Effect of pressure ratio on Radial Stiffness ........................................................ 32

Figure 4.7: Values of Pd/Po at different feedhole positions .................................................. 33

Figure 4.8: Values of Pd/Po at different feedhole positions ................................................... 33

Figure 4.9: Effect of outlet pressure on Mass flow rate ........................................................ 34

Figure 4.10: Effect of outlet pressure on Radial Load Capacity ........................................... 34

Figure 4.11: Effect of rotational speed on Overall Radial Load capacity .............................. 35

Figure 4.12: Effect of Rotational speed on Radial Load capacity Increased ......................... 35

Figure 4.13: Effect of Orifice diameter and clearance on Load Capacity .............................. 36

Figure 4.14: Effect of Orifice diameter and clearance on Axial Stiffness ............................. 36

Figure 4.15: Load Capacity Vs Clearance for different R2/R1 values.................................... 37

Figure 4.16: Stiffness Vs Clearance for different R2/R1 values ............................................. 37

Figure 4.17: Load Capacity Vs Stiffness for different outlet pressures ................................. 38

Figure 4.18: Amplitude of whirling without damping Vs frequency..................................... 38

Figure 4.19: Magnification of figure 4.18 ............................................................................ 39

Figure 4.20: Amplitude of whirling with damping Vs frequency ......................................... 39

Figure 5.1: Inlet and Outlet of the flow model of journal bearing ......................................... 41

Figure 5.2: Absolute pressure contour of the fluid flow region............................................. 42

Figure 5.3: Sliced plane view .............................................................................................. 42

Figure 5.4: Absolute pressure contour of the feedhole region............................................... 43

Figure 5.5: Absolute pressure contour of the feedhole region............................................... 43

Figure 5.6: Absolute pressure contour of the feedhole region............................................... 44

Figure 5.7: velocity contour of the feedhole region .............................................................. 44

Figure 5.8: velocity contour at 1000 Hz ............................................................................... 45

Figure 5.9: velocity contour at 5000 Hz ............................................................................... 45

Figure 5.10: Inlet and Outlet of the flow model of thrust bearing ......................................... 46

Figure 5.11: Absolute pressure contour of thrust bearing ..................................................... 47

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List of Tables

Table 5.1: Theoretical data considered for the analysis of journal bearing ........................... 41

Table 5.2: Change in pressure at throat of the orifice with change in rotational speed .......... 46

Table 5.3: Theoretical data considered for the analysis of thrust bearing.............................. 46

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Nomenclature

a radius of journal bearing b pocket depth

C damping constant

Cd coefficient of discharge

CL load coefficient

CLo load coefficient of axial flow model of journal bearing do diameter of orifice dR pocket diameter

D diameter of bearing

G slot factor

h radial clearance ho radial clearance at no load

I transverse moment of inertia of the rotor

Io polar moment of inertia of the rotor

2J distance between the bearings

K stiffness of bearing

Kg optimum gauge pressure ratio

l distance of orifice form end of bearing

L length of journal bearing

LS length of shaft

m mass flow rate through orifice mR mass of rotor

M bearing mass flow rate

n no of feed holes per rowquotesdbs_dbs12.pdfusesText_18

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