A program of study of the transient operation of natural-circulation loops has been underway at the University of Minnesota (1) and this paper is concerned with the oscillatory behavior of a twophase natural-circulation loop. These studies are of interest for the emergency cooling of nuclear reactors and in the design of boiling-water reactors. The lib erature survey pertaining to the transient operation of a natural-circulation loop is given by Alstad, Isbin, Amundson, and Silvers ( l ) , and a survey of two-phase flow literature is given by Isbin, Moen, and Mosher (2). Normally the surge tank, El, was not used for two-phase natural-circulation runs. For those runs in which the pressure a t one point in the loop was held constant, the gate valve between the surge tank E, and the loop was opened; for the constant-volume run, the gate valve waa closed. A heater and pump were installed to maintain the cooling-watcr supply a t 5 gal./min. and a t 130°F. EXPERIMENTAL LOOP THEORETICAL ANALYSIS General EquationsThe continuity equation, the equation of motion, and the energy equation for a viscous fluid flowing in a region of general geometry were formulated for a phase having continuous properties. A similar set of equations was derived for flow across a surface of discontinuity. The combination of these two sets of equations gave the equations for the two-phase flow. If these equations are applied to flow through a pipe of uniform cross section in which the steam and water phases are assumed to be in equilibrium (that is, p
Two-phase critical flow of steam-water mixtures has been investigated over a pressure range from 4 to 43 lb./sq. in. abs. and a quality range from saturated vapor to 1% (weight) vapor. Discharges were measured from 1/4-, 1/2-, 3/4-, and I-in. pipes and from annuli of intermediate cross-sectional areas. The experimental mass flow rates are always greater than the values calculated on the basis of a homogeneous flow model. Several empirical methods for correlating the data were determined, and comparisons are presented of the predictions of several analytical flow models. The flow of flashing-water mixtures has received considerable attention (1 to 6, 8, 10, 12, 1'7, 18, 19) Vol. 3, No. 3 section) served to change only the axial pressure distribution in the test section and not the discharge rates. The pressure drops along the length of the test section were measured to about 1 diam. of the discharge end. Figure 2 illustrates the pressure profiles for the test section for changes in downstream pressure. Nearly all runs were made with a downstream pressure of 1 lb./sq. in. abs., and the critical pressure in the test section at the discharge was determined by extrapolating the pressure profiles to the end of the pipe; however, it is to be noted that even a t this low downstream pressure the effects on the pressure profile. did not entirely disappear. The propagation of pressure disturbances through a thin liquid annulus is not unexpected.
The pressure-drop characteristics associated with one liquid and one gaseous phase flowing concurrently in a pipe or tube have yet to be understood. The operation of evaporators, boilers, and condensers has long stimulated interest in the pressure drop of steamwater mixtures, and more recently this specialized case of one-component, two-phase flow has received even greater attention from the applications in cooling nuclear reactors. The two-phase-flow problems have not been amenable to thorough theoretical analyses, and therefore empirical and semiempirical correlations have attained unusual prominence in practical applications. The present investigation employs a new research tool for the study of two-phase-flow structure.A variety of geometric flow patterns is possible. Bergelin, Alves, and others have classified these patterns according to visual appearance ; whereas the Martinelli classifications were based upon whether the flow in each phase was termed viscous or furbu2ent. The distinction between viscous and turbulent flow in either phase is rather arbitrary, and if the Reynolds number for one phase, calculated on the basis of the total tube diameter, is greater than 2,000, the flow in the phase is called furbu2ent. This investigation is confined to the study of annular flow, in which most of the liquid is found in an annular ring surrounding the central vapor core and the flow in each phase is turbulent.Boiling or flashing occurs when superheated water rises in an insulated vertical tube at atmospheric pressure. For a separated two-phase flow geometry, the mean linear steam velocity may exceed that of the water. The fraction of the tube occupied by the steam (void fraction) at a given cross section cannot be obtained directly from a determination of the thermodynamic quality. Void fractions, however, must be known for the estimation of the pressure drops due to head and momentum changes.Void fractions and pressure drops for steam-water flows were measured in an 0.872-in. I.D. vertical tube at atmospheric pressure over a quality range of 0 to 4%. The test section was the hot leg of a natural-circulation loop, and the inlet liquid flow rate ranged from 1 to 3 ft./sec. A new technique for measuring void fractions was used, and the method utilizes the difference between the gamma-ray absorption coefficients of water and steam.
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