Super-critical compressible flow through a square-edged orifice

172 Pages·06.258 MB·English

by  Cunningham, Richard Greenlaw

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NAME AND ADDRESS DATE

NORTHWESTERN UNIVERSITY
SUPER-CRITICAL COMPRESSIBLE FLOW
THROUGH A SQUARE-EDGED ORIFICE
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree
DOCTOR OF PHILOSOPHY
DEPARTMENT OF MECHANICAL ENGINEERING
By
Richard Greenlaw Cunningham
Evanston, Illinois
April 1950
ProQuest Number: 10101309
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ACKNOWLEDGMENTS
This work was made possible by a graduate
fellowship granted by the Pure Oil Company, and
aided by a research grant from the Technological
Institute of Northwestern University«
The author wishes to thank Professor Edward
F* Obert for his valuable help and encouragement
during the course of this investigation.
TABLE OF CONTENTS
Fage
LIST OF..............TABLES...................... iv
LIST OF........... ILLUSTRATIONS.................... v
NOMENCLATURE viii
Chapter
INTRODUCTION ............................ 1
STATEMENT OF THE PROBLEM.................. 2
I THE METERING OF COMPRESSIBLE FLUIDS ......... 3
II A STUDY OF THE ORIFICE JET
Survey of the, Literature ......... 19
Experimental Inve s 11gat ions......... 26
III A THEORETICAL SOLUTION FOR SUPER-CRITICAL
COMPRESSIBLE FLOW THROUGH AN ORIFICE....... H
IV LABORATORY INVESTIGATION OF ORIFICE FLOW
Introduction .................... 63
Extension of Expansion Factors
To the Super-Critical Region
1. Air Flow Through an Orifice in a
Two Inch Pipe . ........ 67
2. Steam Flow Through an Orifice in
a Three Inch Pipe............ 85
Super-Critical Flow With High Velocity
of Approach ..................... 95
V COMPARISON OF THE EXPERIMENTAL RESULTS
WITH THE THEORETICAL SOLUTION.............. 122
VI SUMMARY AND DISCUSSION .................. 125
APPENDIX i .......................... 133
APPENDIX ii .......................... HI
APPENDIX iii ............ 151
BIBLIOGRAPHY ........................... 153
VITA 159
LIST OF TABLES
Table Page
1. Air Flow Through an Orifice in a Two Inch Pipe . . . 78
2* Steam Flow Through an Orifice in a Three Inch
Pipe........................................... 89
3. Dimensions of Orifice Plates for a Meter with
High Velocities of Approach......................101
4* Air Flow Through an Orifice Meter with High
Velocities of Approach............ 103
5* Experimental Discharge Coefficients for an
Orifice Meter with High Velocities of Approach . . . 113
6* Comparison of Expansion Factors at a Pressure
Ratio of 0.63 ................. •* 117
LIST OF ILLUSTRATIONS
Figure Page
1. Apparatus Used by Stanton .................... 22
2a. Radial Distributions of Pressures Over the Minimum
Jet Section as Determined by Stanton 23
2b. Shape of the Orifice Jet Plotted from the Data of
Stanton ....................................... 23
3. Orifice and Probe Arrangement for Free Discharge
Into the Atmosphere • 28
4* Axial Pressures in an Orifice Jet.............. 30
5* Axial Pressure Traverses with Condensation Shocks ... 32
6. Effect of Orifice Pressure Ratio on the Axial
Pressures in the Free Jet...................... 34
7. Orifice Discharge Chamber with Probe Guide • • • • • • 36
8. Axial Pressure Traverses of Air Jets Discharging
from an Orifice with Constant Initial Conditions ... 38
9o Effect of Pressure Ratio on the Axial Pressures
Near the Orifice Plate....................... 39
10. Orifice and Pressure Probe for Steam Jet Measurements . 4*1
11. Static Pressure Traverses of Steam Jets Showing
Shock Phenomena.............. 4*2
12. Approximate Pressure and Velocity Profiles of the
Orifice Jet .......... 4*8
13. Square-Edged Orifice ....................... 4*9
14a, Super-Critical Flow Impulse Forces ............... 49
14b. Constant Density Flow Impulse Forces.............. 49
15a. Orifice Discharge Coefficients from Bachmann*s Air
Tests Compared with the Theoretical Solutions . . . . . 58
Figure Page
15b, Values of computed from Schiller^ Data for
Steam Flow Compared with the Theoretical Solutions • • 58
16a, Borda Nozzle in a Plane Wall • • • • • ............. 62
16b, Super-Critical Jet Issuing from a Borda Nozzle • , 62
17, Contraction Coefficient for the Borda Nozzle Versus
the Pressure Ratio 62
18. Apparatus for Metering Air Flow................ . 68
19* Test Orifice Meter in Two Inch Pipe • 70
20. Experimental Expansion Factors Versus the Orifice
Pressure Ratio for Air Flow in a Two Inch Pipe
Measured with Corner and Flange Taps ............ 81
21. Experimental Expansion Factors Versus the Orifice
Pressure Ratio for Air Flow in a Two Inch Pipe
Measured with Pipe Taps ........................ 81
22. Apparatus for Measuring the Flow of Steam Through
an Orifice Meter in a Three Inch Pipe ...... 85
23. Expansion Factors Measured for the Flow of Super­
heated Steam Plotted Versus the Pressure Ratio .. . . 92
24-* Orifice Meter for High Velocity of Approach Tests . . 97
25. Temperature Relations for High Velocity Flow Meter . . 99
26. Orifice Plates Used for High Velocity of Approach
Tests ....................... 101
27. Discharge Coefficients KY Versus the Pressure Ratio
Determined from Tests on Seven Orifice Plates in a
Smooth Copper Pipe ................. Ill
28. Incompressible Flow Coefficient K as a Function of
the Orifice Diameter Ratio........ 114
29* Expansion Factors Versus Orifice Pressure Ratios for
Air Flow at High Approach Velocities . • • • . . . • • 116
30, Experimentally Determined Expansion Factors for Air
Flow in a Two Inch Pipe Meter Compared with the
Theoretical Solutions ....................... 124