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Title: The development of the relationships governing the flow of two-phase mixtures and their particular application to inculation in water-tube boilers
Author: Chisholm, Duncan
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 1953
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The normal theory for the prediction of circulation in water-tube boilers assumes that the steam-water mixtures in the heated tubes behave as a homogeneous fluid. A theory is here developed which allows for the different vapour and liquid velocities; there is ample evidence to indicate that during two-phase flow even with horizontal tubes the gas, or vapour, flows faster than the liquid. The flow pattern is assumed to consist of an annulus of liquid in contact with the tube wall, and a core of gas, or vapour, with entrained liquid. While this flow pattern may not occur at all flow rates the application of the theory gives good agreement over a wide range of experimental data. The "Prandtl mixing lengths" throughout the two phases are assumed to have the same values as during homogeneous flow. Prom these assumptions the application of Prandtl's Equation relating density, shearing stress, mixing length, and velocity profile gradient enables the velocity profile to be obtained for a particular shear distribution, and the respective phase velocities determined. This led to an expression for the ratio of the gas, or vapour, velocity to the liquid velocity. The application of the expression is complicated by the presence of an unknown quantity of entrained liquid in the gas, or vapour. Where conditions are such that the liquid content, of the gas may be assumed negligible, the equations may be directly applied. Good agreement was obtained with experimental/experimental data for the downward flow of air-water mixtures under such conditions. On the other hand where liquid is contained in the core, the quantity of liquid must he known before a solution is possible. So far no direct information is available regarding the probable liquid content of the core. The nearest possible approach to this information is to be obtained from Armand's work on air-water mixtures. Examination of the problem led to the conclusion that the terms involving the water concentration in the core could be taken as common to both air-water and steam-water flow. This enabled the equations to be applied to steam-water flow. Confirmation of the theory is obtained from the data of previous investigators both for air-water flow and steam-water flow. Test results which are obtained from a full-scale two-tube boiler operating up to a pressure of 1500 lb/in and heat transfer rates up to 120,000 B.Th.U./hr.ft2 of heated riser surface are also analysed. The proposed theory enabled the prediction of pressure changes during steam-water flow within 22%, in contrast to the homogeneous theory which gave errors as large as 60%. The appendices include, in addition to detailed calculations and developments of a number of the theoretical equations, the details of test equipment designed to permit the study of steam-water mixtures flowing adiabatically at pressures close to atmospheric. Also included is the development of the theoretical equations to permit their application to rough tubes.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available