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To predict the performance of centrifugal pumps under air-water two-phase flow conditions, a consistent one-dimensional two-fluid model with fluid viscosity and air-phase compressibility in a rotating impeller is proposed by considering energy changes in the transitional flow from the rotating impeller to the stationary volute casing. The two-fluid model is numerically solved for the case of a radial-flow pump after various constitutive equations are applied. The head and shaft power predicted are found to agree well with the measured values within ±20 percent of the rated flow capacity.

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To predict the behavior of gas-liquid two-phase flows in a centrifugal pump impeller, a three-dimensional numerical method is proposed on the basis of a bubbly flow model. Under the assumption of homogeneous bubbly flow entraining fine bubbles, the equation of motion of the mixture is represented by that of liquid-phase and the liquid velocity is expressed as a potential for a quasi-harmonic equation. This equation is solved with a finite element method to obtain the velocities, and the equation of motion of an air bubble is integrated numerically in the flow field to obtain the void fraction. These calculations are iterated to obtain a converged solution. The method has been applied to a radial-flow pump, and the results obtained have been confirmed by experiments within the range of bubbly flow regime.

A turbine flowmeter is employed in this study in connection with offshore oil field development, in order to measure simultaneously both the volumetric flow rates of air-water two-phase mixture. Though a conventional turbine flowmeter is generally used to measure the single-phase volumetric flow rate by obtaining the rotational rotor speed, the method proposed additionally reads the pressure drop across the meter. After the pressure drop and rotor speed measured are correlated as functions of the volumetric flow ratio of the air to the whole fluid and the total volumetric flow rate, both the flow rates are iteratively evaluated with the functions on the premise that the liquid density is known. The evaluated flow rates are confirmed to have adequate accuracy, and thus the applicability of the method to oil fields.

The performance of an axial-flow pump was investigated under air-admitting conditions and the results were compared with those obtained for radial-flow pumps investigated in our previous studies. For the axial-flow pump we measured head as a function of impeller speed, liquid flow rate, and air void fraction. Flow visualization was performed and we correlated air bubble size as a function of Weber number based on mean impeller velocity. Overall flow patterns and the locations of air coalesence within the impeller were observed and diagrammed. These data contribute to earlier data obtained by ourselves and others to develop analytical models to predict pump performance degradation due to air admittance.