Wave spectrum characterization in turbulent stratified air-water flows in a large diameter pipe

Abstract

This study presents an analysis of interfacial waves in turbulent stratified air-water pipe flow in a 10 cm diameter pipe at atmospheric conditions. Interface elevation measurements are performed by means of conductance probes at a high sampling rate. In particular, the frequency spectra are characterized and the wave structure is assessed through the analysis of the power spectral density (PSD) and its important features, such as dominant frequencies, peak densities and dissipation region. The influence of both gas and liquid superficial velocities is assessed. For the range of superficial velocities investigated (USL = 0.08-0.15 m/s, USG = 1.0-4.5 m/s), dominant frequencies of approximately 7-8 and 3-4 Hz are observed in the wave growth and saturation regimes, respectively, defined by Ayati & Carneiro (2018). A transition from wave growth to wave saturation regime was observed to occur in the range of USG = 1.0-2.0 m/s, for the current conditions studied. In the saturation regime, a secondary peak is observed in the frequency spectra at approximately 7-8 Hz. A scaling analysis is performed to support the interpretation of results and parameterization of spectral parameters, as an indication of the wave structures. In the saturation regime, the high frequency region of the frequency spectra (spectral tail) displays a nearly monotonic decay, and the data supports in general a power law of the form F−n, n ∼ 4-4.5, as evidenced by the non-dimensional analysis covering the full range of conditions tested in this work. This is in accordance with the power law expression derived by Phillips (1985) and supports recent interpretation of air-flow separation and micro-breaking as wave dissipation mechanisms (Ayati, 2018). Power-laws of the form S(F0) ∼(F0) -5 for the peak densities in the PSDs are also found to represent well the current data set for the envelope curve of the spectral peaks, particularly for the wave saturation regime. For the waves analyzed in the current work, a direct relation between the dominant frequencies and the mean liquid depth is shown to hold.