Experimental Study of the Flow Conditions and Pressure Drop of Steam-Water Mixtures at High Pressures in Heated and Unheated Tubes

Abstract

The work described in the three parts of this paper was sponsored by the Water-Tube Boilermakers' Association and carried out in the Engineering Department of Cambridge University. In Part I are described the high-pressure experimental plant and its associated instrumentation. A description of the test circuit is followed by a detailed description of the construction and performance of the electrical low-frequency induction heaters specially developed to supply the power input to the test section. Auxiliary electrical resistance heaters are also described. The work required the development of special differential manometers and differential thermocouples suitable for the accurate measurement of small differences in pressure and temperature at high fluid pressures. Gamma-ray absorption equipment was used to make measurements of the apparent density of the two-phase mixture within a cross-section of the tube at the test-section outlet, from which estimates could be obtained of the relative or ‘slip’ velocity between the two phases. Part I of the paper ends with a description of the mode of operation of the plant and the range of variables covered during the tests.

Part II deals with the analysis of the experimental results obtained from measurements of the absorption of gamma-rays in their passage through the two-phase mixture at outlet from the test section. The results of tests on the -in. bore pipe are examined first, although they were the last to be carried out. In these tests the tube cross-section was scanned by a narrow pencil of rays from a collimated beam, and scintillation-counter equipment was used to measure the intensity of the emergent radiation. Preliminary tests involving scans along a number of chords of the tube cross-section gave information on the density distribution of the fluid within the cross-section; this was different for the vertical and horizontal pipes. Data from these readings enabled the main series of tests, during which pressure-drop readings were also taken, to be carried out with a single scan along the tube centre-line only. From the readings taken during the latter tests the area dryness-fraction (void fraction) and slip velocity ratio were calculated and correlated as functions of the mass dryness-fraction. The paper then gives a brief presentation of the less satisfactory results obtained on the 1-in. bore pipe with full-area scanning by an uncollimated beam using an ionization chamber as detector. The foregoing correlations are finally used to calculate slip correction factors by means of which the acceleration and gravitational pressure-drops calculated according to homogeneous theory may be corrected for the effects of slip. The application of these factors to the analysis of the experimental pressure-drops is studied in Part III.

Part III presents an analysis of the pressure-drop measurements made on the . bore pipes in both the horizontal and vertical positions, giving particular attention to comparisons between the experimental results and values predicted by homogeneous theory. These comparisons are made in terms of dimensionless pressure-drop coefficients which enable the respective contributions of friction, acceleration and gravitation to the total pressure drop to be readily displayed. Use is made of the correction curves derived in Part II to apply a correction for the effects of slip to the acceleration and gravitational pressure-drops predicted by homogeneous theory, and thence to compare the corrected predictions of pressure drop with the experimental values.

In an analysis of the results for the horizontal pipes, the frictional pressure-drop under two-phase conditions is evaluated, for the heated pipes, by subtracting from the measured total pressure-drop an estimated acceleration pressure-drop allowing for the effects of slip. Correlation of the frictional pressure-drops in both the heated and unheated pipes enables these to be related to the corresponding homogeneous values through a suitable correction factor. The pipes were fortuitously of different roughness, and the relation of the effective two-phase friction factors to the respective single-phase factors is studied. In the vertical pipes, the gravitational contribution to the total pressure-drop being dominant, the experimental results are compared favourably with predictions in which the gravitational term is computed by correcting the homogeneous value for the effects of slip, while the frictional and acceleration terms are taken to be the same as the homogeneous values. Additional correction of the frictional term in the unheated pipes is seen to give a small improvement in accuracy of prediction. In a concluding section, values of the slip ratio are deduced from pressure-drop measurements on the vertical, unheated pipes, so carrying through the reverse procedure of Part II, and these values are compared with the values deduced from the gamma-ray measurements in Part II.

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References

Haywood

R. W.

1951 Proc. General Discussion on Heat Transfer, p. 63, ‘Research into the Fundamentals of Boiler Circulation Theory’ (Instn Mech. Engrs, London).

Thornton

C. A. M.

1952 Proc. Instn elec. Engrs, Part II, vol. 99, p. 85, ‘Resistance Heating of Mild Steel Containers at Power Frequencies’.

Buckland

B. O.

Stack

S. S.

1941 ‘Temperature, Its Measurement and Control in Science and Industry’, p. 884, ‘Thermocouples for Testing Steam Turbines’ (Rheinhold Publishing Corporation, New York).

Schwarz

1954 V.D.I. Forschungs., B.20, No. 445, p. 1, ‘Investigations of the Distribution of Specific Gravity, the Water and Steam Velocities and the Frictional Pressure Drop in Vertical and Horizontal Boiler Tubes’.

Bailey

R. V.

Zmola

P. C.

Taylor

F. M.

Planchet

R. J.

1957 Tulane University and Oak Ridge National Laboratory, ORNL-LR-DWG-11092, ‘Transport of Gases through Liquid-Gas Mixtures’.

Lottes

P. A.

Marchaterre

J. F.

, and others 1958 Proc. 2nd United Nations Int. Conf. on Peaceful Uses of Atomic Energy, Geneva, vol. 7, p. 784, P/1983, ‘Experimental Studies of Natural Circulation Boiling and their Application to Boiling Reactor Performance’.

Lottes

P. A.

Flinn

W. S.

1956 Nucl. Sci. Engng, vol. 1, No. 6, p. 461, ‘A Method of Analysis of Natural Circulation Boiling Systems’.

Marchaterre

J. F.

1956 Argonne National Laboratory, ANL-5522, ‘The Effect of Pressure on Boiling Density in Multiple Rectangular Channels’.

Egen

R. A.

Dingee

D. A.

Chastain

J. W.

1957 Amer. Soc. mech. Engrs, Paper 57-A-74 and Batelle Memorial Institute Report BMI-1163, ‘Vapor Formation and Behaviour in Boiling Heat Transfer’.

10.

Thom

J. R. S.

1959 Cambridge University Engineering Laboratory, ‘A Study of Pressure Drop and Allied Phenomena during the Flow of a Fluid in the Presence and Absence of Vaporization’.

11.

Knights

G. A.

1960 Cambridge University Engineering Laboratory, ‘A Study of Two-phase Pressure Drop and Density Determination in a High-Pressure Steam-Water Circuit’.

12.

Moody

L. F.

1944 Trans. Amer. Soc. mech. Engrs, vol. 66, p. 671, ‘Friction Factors for Pipe Flow’.

13.

Martinelli

R. C.

Nelson

D. B.

1948 Trans. Amer. Soc. mech. Engrs, vol. 70, p. 695, ‘Prediction of Pressure Drop During Forced-Circulation Boiling of Water’.

14.

Novaković

1959 Queen Mary College, University of London, ‘Pressure Drop and Heat Transfer for Water-Steam Mixtures Flowing in a Tube’.

15.

Hooker

H. H.

Popper

G. F.

1958 Argonne National Laboratory, ANL-5766, ‘A Gamma-Ray Attenuation Method for Void Fraction Determinations in Experimental Boiling Heat Transfer Test Facilities’.

16.

Cameron

J. F.

1958 Proc 1st (UNESCO) Int. Conf. on Radio-isotopes in Scientific Research, vol. 1, p. 426, ‘Fluid Density Measurements in Enclosed Systems’ (Pergamon Press, London and New York).