Numerical
investigation of phase fraction measurements with wire-mesh sensors

Y.M. Lau &
M. Schubert

Helmholtz-Zentrum
Dresden-Rossendorf e.V., Institut für Fluiddynamik

Bautzner
Landstraße 400 | 01328 Dresden

Tel: +49 (0) 351
260 3766, Email: y.m.lau@hzdr.de

115%;font-family:"Times New Roman","serif"'>Introduction

Wire-mesh
sensor (WMS) is an electrical experimental technique to determine the gas phase
distribution in two-phase gas-liquid flows within the cross-section of pipes or
bubble columns. An image is given in Figure 1 showing a possible wire mesh-sensor
configuration. The sensor consists of two layers of parallel wires, which span
over the measuring cross-section. The two layers are perpendicular to each
other, separated by a distance. In operational mode, each layer functions differently.
During the signal acquisition, one layer acts as transmitter, while the other
acts as receiver. The transmitter electrodes are consecutively activated and
the resulting signals are measured in parallel at each receiver wire. Thereby,
a specific electrical property, respectively the electrical conductivity or
capacitance (permittivity) of the fluid mixture at each crossing point, is
measured in a multiplex manner (Da Silva et al. (2007)). The resulting matrix
represents a two-dimensional visualization of the phase distribution within the
wire-mesh sensors' plane.

The
main drawback in the use of wire-mesh sensors is its intrusiveness. By inserting
the electrode wires in the two-phase flow, the flow conditions are altered
compared to no wire insertion and thereby, may affect the accuracy of the
measurements. The wires' effect has already been experimentally studied to some
degree using high-speed camera observations showing bubbles? fragmentation and
deceleration of the bubbles? rise during sensor passage (Prasser et al. (2001)).
The aim of this study is to quantify the degree of disturbance of the wires on
the fluid dynamics of the gas phase (bubbles) passing through the WMS via
direct numerical simulations (DNS) and the accuracy of the wire-mesh sensors.
The DNS results can be used to optimize the designs of future generations of
WMS.

Figure
1: Illustration of a wire-mesh sensor: (a) overview and (b) zoomed-in view
showing the two layers of parallel electrode wires perpendicular to each other
but not touching each other.

Numerical
model

In
this work, the Volume of Fluid (VOF) model from the open source code OpenFOAM,
respectively interFoam, is used for the simulations coupled with an electrical field
simulation. In VOF the transport equation of the VOF function, γ, of each
phase is solved simultaneously with a single set of continuity and Navier-Stokes
equations for the whole flow field:

where
"Times New Roman","serif"'>ρ line-height:115%;font-family:"Times New Roman","serif"'> is the density, µ
is the viscosity, u is the fluid velocity, p is the pressure and g
is the gravitational acceleration. The surface tension force F_σ
is included as an additional source term in the Navier-Stokes equations.

For
the electrical field simulation, in the case of capacitance measurements, the
potential V(r) caused by the active transmitter wire has to be
calculated from the Poisson?s equation. The potential field depends on the
charge density 115%;font-family:"Times New Roman","serif"'>ρ₀
and the permittivity distribution ε₀ε(r). The electric field
is given by E=V(r). The simulation of the electric field demands a very
fine mesh grid of the transmitter wire and its adjacent wires since the shape
of the field lines are greatly influenced by the surface angle of the wires
they hit.

normal"> 

text-align:center;line-height:normal"> "Times New Roman","serif"'>

Figure
2: Snapshot of a 3D simulation of a bubble (2 mm diameter) crossing the
junction of the wire-mesh sensor in quiescent liquid. The interface of the
bubble is visualized along with a number of streamlines.

115%;font-family:"Times New Roman","serif"'>Results

3D
simulations are performed for a bubble crossing a) a single wire and b) a
junction of the wire-mesh sensor within quiescent liquid. Figure 2 illustrates
the case of a bubble with a diameter of 2 mm crossing the junction of the
wire-mesh. Prior to 3D simulations, exploratory 2D-DNS simulations were
performed for a simplified case, where a single bubble crosses a single wire.
These simulations are used to study the dynamics of the bubble by eliminating
the added complexity of the second wire of the wire-mesh sensor. An example of
a 2D-DNS simulation is shown in Figure 3, where the oscillation of the aspect
ratio is tracked throughout the crossing of the wire. This configuration of the
illustrated case is where the bubble is located in line with the wire. The
timeline shows that after the bubble makes contact with the wire at t = 0.12 s,
the aspect ratio drops initially and increases from t = 0.125 s. The amplitude
of the bubble due to the initial contact with the wire is reached at
approximately t = 0.13 s and starts to decrease. However due to the constant
presence of the wire holding the liquid down, the aspect ratio rises up till a
point at t = 0.1355 s where the bubble pinches off from the wire and the
oscillations starts to dampen to reach a steady state. Further analysis of the
2D and 3D simulations will provide more insights of the bubble crossing wires
and the relation to the phase fraction measurements using capacitance wire-mesh
sensors.

Figure
3: 2D-DNS simulation illustrating the rise of a single bubble (2 mm diameter)
crossing a single wire in quiescent liquid (air-water system). The wire (0.012
mm diameter) is a very small dot shown in the above illustrated slices of the
clipped liquid domain. The slices correspond to the time given in the timeline
with the calculated aspect ratio.

font-family:"Times New Roman","serif"'>References

12.0pt;line-height:115%;font-family:"Times New Roman","serif"'>Da Silva, M.J.,
Schleicher, E., Hampel, U., 2007. 12.0pt;line-height:115%;font-family:"Times New Roman","serif"'>Capacitance
wire-mesh sensor for fast measurement of phase fraction distributions.
Meas.
Sci. Technol. 18, 22452251.

12.0pt;line-height:115%;font-family:"Times New Roman","serif"'>Prasser, H.-M.,
Scholz, D., Zippe, C., 2001. line-height:115%;font-family:"Times New Roman","serif"'>Bubble size measurement
using wire-mesh sensors. line-height:115%;font-family:"Times New Roman","serif"'> Flow Measurement and
Instrumentation 12 (4) 299312.