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UBC Theses and Dissertations

Predicting the effect of vertical pipe orientation by the method of characteristics during sudden discharge of a two-phase fluid Mazaffari-Nejad, Hooshang


Present research was undertaken to study the effect of pipe orientation during discharge of saturated water through a sudden opening. Analytical investigations have been made for various ranges of initial pressure, including high pressures previously studied by others. A 4 m long 32 mm in diameter pipe has been used entirely for this investigation to facilitate comparison with available experiments. When the initial pressure in the pipe was just slightly above atmospheric, body forces were obviously expected to play an important role. The effect became especially pronounced when directly comparing upflow versus downflow. Even at higher pressures, it has been seen in flow visualization experiments that the flow becomes stratified in a horizontal pipe. When the pipe is oriented vertically (up or down), this will no longer be true since turbulent mixing occurs. The research was undertaken because of its direct relevance to the loss-of-coolant accident (LOCA). In order to obtain licenses for operating reactors, certain safety standards oust be met. The reactor must be shown to be safe in normal operation as well as in the case of a hypothetical accident. Different models have been used to analyze the LOCA, simplest of which is the equal velocity-equal temperature (EVET) model, which considers both phases in equilibrium at all times. the EVET model (used entirely in this work) was thought to be a good model for vertical flow. Several, computations were made using the method of characteristics to study the effect of gravity on pressure and void fraction histories at the closed end. Void fraction, the ratio of vapor area to pipe area at any cross section, was investigated because of its direct relevance to mixture density and speed of sound. Also, total discharge or mass flow rate, a combined measure of density and velocity, was calculated at the open end. Runs were made for water at initial pressures of 1.2, 1.8, and 35 atm (at the top of the pipe). All cases started just at saturation with a small void fraction of .001 in a 4 m long .032 m diameter pipe (Figure 1). The hydrostatic head of water column exerting an approximate pressure of 40000 Pa was comparable to the former pressures, but quite different from the latter of 35 atm. For 1.2 atm., or .12 MPa, the ratio of gravity force to pressure force (reciprocal of Froude number times Euler number) defined as "3P" was about 33%; it was 25% for the .18 MPa case, and only 1.1 % for the case when initial pressure was 3.5 MPa. The "3P" ratio was shown to be an important measure of the gravity effect. When GP=1.1%, there was negligible difference between the pressures along the pipe for the upflow and downflow case- In both lower initial pressure cases, however, there seemed to be a clear difference between the pressures for upflow and downflow at the closed end.

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