Spherical-bubble-based four-sensor probe signal processing algorithm for two-phase flow measurement

•A complete four-sensor probe signal processing algorithm is newly developed.•Conventional four-sensor probe algorithm is an example of the new algorithm.•Local instantaneous 3-D bubble velocity vectors are measured and verified.•Local instantaneous bubble diameters are measured and verified.•Local interfacial area concentrations are measured and verified. This paper describes a newly-developed complete four-sensor probe signal processing algorithm for local instantaneous 3-dimensional bubble velocity vector, local instantaneous bubble diameter, local instantaneous interfacial normal unit vector, local interfacial area concentration (IAC) in a multi-dimensional two-phase flow by utilizing the spherical bubbles in the flow. The newly-developed algorithm has opened a way for the measurement of 3-dimensional bubble velocity vector and bubble diameter with a four-sensor probe. The newly-developed algorithm also has overcome the weakness of the conventional four-sensor probe signal processing algorithm, in which the interfaces passing through the tips of the probe sensors are supposed to be planar, even in the small bubble measurement for the local IAC. The newly-developed algorithm can keep a consistency with the conventional algorithm in measuring large bubbles since the newly-developed algorithm is reduced to the conventional algorithm for the local IAC, the local instantaneous interfacial normal unit vector and the local instantaneous 3-dimensional interfacial displacement velocity vector when the bubble size becomes to be much larger than the size of the four-sensor probe and the interface of the bubble can be locally viewed as 2 tangent planes. The bubbles in practical two-phase flows are classified into spherical bubbles and non-spherical bubbles according to a newly-introduced bubble deviation coefficient from spherical shape (namely an aspheric shape factor). Based on the spherical bubbles, the newly-developed signal processing algorithm can perform the measurement for the local parameters in two-phase flows. The newly-developed signal processing algorithm was applied to the measurements in a vertical air–water multi-dimensional two-phase flow in a large-diameter pipe as an example and was checked against the other measurement methods. The comparisons were very satisfactory and showed that the newly-developed four-sensor probe signal processing algorithm can perform the local measurements for the practical multi-dimensional two-phase flow.