Statistical characterization of interfacial waves in turbulent stratified gas-liquid pipe flows

Abstract

This study presents a statistical analysis of interfacial waves in a turbulent stratified air-water flow inside a 10 cm diameter pipe. Wave elevation measurements were acquired using conductance probes with high sampling rate, Sr = 500Hz. Local wave parameters (elevation, crest height, trough height, etc.) were extracted using a zero-crossing technique. The evolution of their corresponding statistical distributions and statistical moments was investigated for varying flow conditions.The main goal of this study is to offer an alternative method for distinguishing between various wavy flow patterns. The proposed approach is based on the Gaussian model, which is widely used in the characterization of ocean waves. Instead of the traditional sub-regime categorization which is based on a combination of visual observations and qualitative spectral description, this method categorizes a wave field depending on its degree of non-linearity and statistics of elevation parameters. This approach also allows parametrization of the interfacial structure. As a first step, this approach was carried out only for a selected set of flow rate combinations, in which the liquid superficial velocity was kept constant at U sl = 0.10 m/s whilst the superficial velocity was increased from 1.0 m/s to 4.0 m/s with increments of 0.25 m/s. Subsequently, statistical moments of the interface elevation were computed and compared to literature data, for varying U sl and U sg . Based on the detailed statistical description of wave data, two flow regimes are categorized: wave amplitude growth and saturation. These regimes were also identified as quasi-Gaussian and non-Gaussian, respec-Email addresses: awalaa@math.uio.no (A.A. Ayati),

Experimental investigation of airflow above waves in a horizontal pipe

“…This indicates that in case B1, the waves have some degree of non-linearity. This is in line with the characterization of the wave field by Ayati & Carneiro (2018), where it is found that the U sg = 1.50 m/s case behaves according to Gaussian statistics, while the U sg = 2.1 m/s case deviates significantly from linear theory. Furthermore, the second quadrant of case B1 is considerably shorter and steeper than the other quadrants.…”

“…Meanwhile, case B belongs to a regime in which wave amplitudes remain more or less constant within a wide range of gas velocities above U sg = 1.75 m/s. In this regime, the waves are steeper and their statistical distributions deviate strongly from Gaussian statistics, implying the presence of nonlinear processes (Ayati & Carneiro, 2018). Similar results have been reported by Toffoli et al (2017) for a circular, fetch-unlimited wind-wave tank.…”

“…As the interface friction is estimated based on a pressure drop evaluated over a 12.3 meter section of the pipe, this represents a characteristic interface friction for the system, rather than for the centerplane of the PIV section. Detailed analysis of the evolution of the wave field with different U sl /U sg -combinations has previously been performed by Ayati et al (2015) and Ayati & Carneiro (2018). Here it has been demonstrated that case A is in a region of the flow map where η rms increases with increasing gas flow rates, while case B is in a region of "amplitude saturation", where η rms is independent of the gas flow rate.…”

“…In order to keep the paper concise, we conduct a detailed comparison of two different flow cases in which the liquid superficial velocity is kept constant at U sl = 0.1 m/s, whilst the gas velocity increases from U sg = 1.5 in case A, to 2.1 m/s in case B. These cases were selected as they feature in two different sub-regimes, as shown by Ayati & Carneiro (2018). Case A belongs to a region of flow conditions in which waves grow as a consequence of increasing gas flow rates.…”

Microscale wave breaking in stratified air-water pipe flow

“…The severity of breaking was however not reported, nor was the point of breaking onset in the flow map specified. Ayati and Carneiro 33 analyzed the statistics from interfacial wave probes in two-phase stratified flow, considering the same experimental setup and flow rate combinations closely matching the cases under investigation in the present work. By comparing the wave statistics with Gaussian statistics (linear wave theory), they observed a clear transition from a quasi-linear regime to a non-linear regime where linear wave theory considerably over predicts the maximum observed surface elevation η.…”