Multiphase Flow Measurement Modeling of an Oil-Water Flow Through an Innovative Orifice Plate - Part II
Authors: Noui-Mehidi Mohamed Nabil , Ahmedi Abdelhadi , Black Michael J. 
Published: March 2015

Abstract
The present work is concerned with a numerical investigation of a hybrid flow metering system that relies on a combination of bluff bodies and orifice plates to minimize process noise effects and have better accuracy measurements. The system is designed for liquid flows comprising different water and oil compositions in a flowline. In the flow simulations, the mesoscopic approach used based on lattice Boltzmann formulations has revealed the existence of a flow instabilities that generate a fluctuation mechanism with a characteristic frequency proportional to the flow rate and that has high amplitude and lower band value compared to conventional vortex shedding meters.

Introduction
Vortex shedding behind circular cylinders is a well-known phenomenon that generates a succession of vortices known as the Von Karman street. In a commercial vortex shedding meter, different bluff body configurations and flow settings are used. The Von Karman street is a description of alternating vortices that form under certain dynamic conditions behind shaped obstacles and has been studied in both fundamental and applied aspects. The shedding frequency of the vortices is directly proportional to the flow rate, and by measuring the shedding frequency, accurate determination of the flow rate with proper calibration can be achieved. The Von Karman flow instability is defined over a certain range of Reynolds number and has been studied for structure reliability to remove any mechanical stress on specific designs (Venugopal et al. 2011; Mittal and Raghuvanshi 2001; Pier 2002). In flow measurements, there are several industrial vortex meters based on vortex shedding in gas, steam, or liquid flows. In theory, the frequency is non-sensitive to the physical properties of the fluid such as density, viscosity, temperature, pressure, and conductivity within a range of Reynolds numbers. A vortex-shedding meter is usually calibrated once for measuring steam, gas, or liquids, which applies over the specified volumetric flow velocity ranges. One of major problems faced by vortex shedding meters in process lines is the noise generated from pumps, compressors, steam traps, valves, etc., that may affect the meter to readings resulting in an over estimate of the frequency values. This will result in wrong readings in the flow rates especially when measuring gas streams. To mitigate process noise effect, filtering circuitries are usually used and, as a result, the dynamic range of the meter decreases. In the study of the vortex shedding mechanism, computational flow modeling was used extensively. In the last decade, Lattice Boltzmann mesoscopic formulations have shown considerable advantages compared to the Navier-Stokes formulations for their simplicity and being able to model fluid flows over a large flow application. The present paper discusses a flow measurement simulation of an oil-water mixture through an orifice plate using a mesoscopic flow formulation. In the simulations, the two-phase mixture is considered homogenous. The results show the effect of the orifice plate geometry on the flow profiles and the flow parameters such as pressure and measurement efficiency.

Flow system
The simulated flow system comprises a circular pipe in which a cylindrical bluff body is inserted in the middle. Behind the bluff body an orifice plate is placed at a distance equivalent to the diameter of the cylindrical body as shown in Fig. 1.
The flow system is assumed to be axisymmetric and 2D representation of the system is investigated numerically to study the flow structure behind the combination cylinder/orifice.