Profile of huge wave in gas-liquid churn flow

- We proposed a normal-distribution function to describe the huge wave shape.
- We analyzed the relationship between the wave amplitude and wavelength.
- The normal-distribution function reproduces the evolution of the huge wave quite well.
- The sinusoidal function comparatively has the lowest precision in prediction.
- The hemispherical function is recommended to simplify the calculation.

The knowledge of wave profile of the huge waves is crucial for the thorough study on the pressure drop in churn flow, which is of great interest in many industries where such chaotic flow occurs. The literature lacks information on the profile of a huge wave under churn flow condition. Usually, hemispherical and sinusoidal shapes are employed to feature the general characteristic of the huge wave. No doubt, errors will be inevitably result. To explore this issue, we used a high-speed camera to capture a more detailed description of the huge wave in a 19 mm i.d. tube under churn flow condition. The experimental results indicate that the ratio between wave length and wave amplitude is found to be about 5 irrespective of gas and liquid velocities. By analyzing the silhouette of the huge wave at its critical condition (stationary), we proposed a Gaussian function to describe such wave shape more accurately. Compared with the existing wave shapes, the Gaussian function qualitatively and quantitatively reproduces the evolution of the huge wave quite well whereas the sinusoidal function comparatively has the lowest precision in prediction. Though a far cry from the real wave shape, the hemispherical function is recommended to simplify the calculation on the basis of a simpler form but a sufficient accuracy.