Frequency Of Disturbance Waves Research Articles

Experimental study on the upward annular two-phase flow of nitrogen and ethanol aqueous solutions with different concentrations

Vertical upward annular flow experiments of nitrogen gas and ethanol aqueous solutions with volume fractions of 30 %, 60 %, and 95 % under 0.2 MPa were conducted. The characteristics of the liquid film including base, average, and maximum film thickness and height, velocity, and frequency of disturbance waves were obtained and studied based on the constant electric current method in a 5 mm inner diameter polycarbonate tube. The flow behavior was observed using a high-speed camera simultaneously. It is found that a large number of bubbles in the liquid film is critical to these characteristics. A connection between ethanol concentration and bubbles in the liquid film is found and interpreted by considering bubble stability which arises from the dynamic rise in surface tension. Our experimental investigation suggests that the effect of bubbles in the liquid film on the flow characteristics is not negligible in such annular flows under high liquid flow rates and bubble stability should be considered for annular flows employing solutions consisting of two or more components with large differences in surface tension.

Stability Analysis for High-Speed Boundary-Layer Flow with Cavities

This study uses direct numerical simulation and stability analysis methods to investigate the impact of wall cavity defects on the instability of boundary layers at Ma=5.92 and Ma=1.38. For flow at Ma=5.92, synchronization points with equal phase velocities in both fast and slow modes play a crucial role in controlling disturbance wave growth. When the inlet disturbance wave frequency (ω=0.98) approaches the synchronization point frequency, the impact of cavity size on the growth of the disturbance wave can be divided into three regions in the (L/δ99, D/δ99) plane, namely, region A, region B, and region C. Region A refers to small cavities with L/δ99<2, which have the weakest suppression effect. Region B includes large cavities with L/δ99>2 and D/δ99<1.5 and exhibits the best suppression effect. Finally, region C covers cavities with L/δ99>3 and D/δ99>1.5 and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at Ma=1.38, cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities (L/δ99>5, D/δ99<2) exhibit the most significant enhancement.

Wet gas flow metering by combining a vortex flowmeter with disturbance wave frequency

Based on a conductance-vortex meter dual-modality system, a novel wet gas flow measurement method is proposed, which combines a vortex meter with disturbance wave frequency. A negative relationship between the vortex signal quality and the disturbance wave frequency is found, on which basis a new segmented fast Fourier transform–continuous wavelet transform vortex frequency extraction method is proposed. Uniform exponential equations are derived for meter over-reading, taking into account the liquid-phase Reynolds and gas-phase Weber numbers, the disturbance wave Strouhal number, density ratio, and the liquid-phase Reynolds number. Finally, a Newton–Armijo-based wet gas metering model is developed by combining these two correlation equations. The percentage errors (PEs) of the gas flow in wet gas are within ±1.0% error bands with uncertainty of 0.56%. The full-scale PEs of liquid flow are within ±10% error bands with uncertainty of 4.71%. The disturbance wave frequency is used to correct the meter over-reading. As no liquid film thickness calibration is needed, the proposed method has low requirements on the conductivity of the medium and hence the application scope of media could be expanded.

On the velocity and frequency of disturbance waves in vertical annular flow with different surface tension and gas–liquid density ratio

In this study, the characteristics of disturbance waves, including velocity, longitudinal size, and frequency, are comprehensively investigated by conducting gas–liquid upward annular flow experiments in a 5 mm tube through the constant electric current method (CECM). The film thickness time trace is recorded with respect to time, and the information on disturbance waves is subsequently extracted. The effect of liquid and gas flow rate, density ratio, and surface tension on the disturbance wave is quantitatively analyzed. A predictive model of the wave velocity based on the shear stress balance of the liquid film is proposed. A physical model for wave frequency prediction is derived on the basis of the mass conservation equation. A simple empirical model with good prediction accuracy of wave frequency is also derived. Compared with existing correlations available in the literature, the newly derived models show better performance under a wide range of flow conditions.

The effect of high-frequency oscillations on the disturbance waves in annular flow

In this paper, an analysis of susceptibility of wave structure in annular flow to small high-frequency oscillations is carried out. Downward adiabatic air-water flow at atmospheric pressure is studied in a vertical 11.7 mm pipe. The range of superficial gas velocities is 0 – 70 m/s and the range of wetting densities is 1.6 – 4.6 cm2/s. Spatiotemporal records of liquid film thickness are obtained with the Brightness-Based Laser-Induced Fluorescence technique. The region of interrogation is one longitudinal section of the pipe with a length of 470 mm, starting from the inlet. The oscillations are imposed by a solenoid-driven membrane causing periodic pulsations of liquid flow rate. The oscillation frequency range is 0 – 100 Hz. The amplitude of pulsations decreases with the oscillation frequency. The effect of oscillations is first tested on liquid films falling in absence of gas flow. In this case, the excited waves are of the same frequency as the imposed oscillations, and the stages of wave development are shifted closer to the inlet. In the case of liquid films under strong gas shear, the oscillations induce low-amplitude waves, which interfere with high-frequency initial waves, produced by the shear instability. Without excitation, groups of successive initial waves coalesce to produce the disturbance waves, which vary in speed and coalesce with each other. Within a certain range of excitation frequency, each period of low-amplitude wave produces one disturbance wave, so that coalescence nearly disappears and the waves become regular. Various criteria of susceptibility are proposed; the best ones are based on spectral analysis. The susceptibility range of excitation frequencies encompasses the ‘natural’ passing frequency of disturbance waves far downstream. The width of this range is of the order of 20 Hz but decreases at high frequencies when the amplitude of the pulsations decreases. Under excitation, the disturbance waves accelerate and grow in amplitude very fast, reaching saturated values near the inlet. The saturated values are not very different from the ‘natural’ ones. An increase in the excitation frequency within the range of susceptibility leads to a small decrease in the speed and amplitude of the disturbance waves. The entrained fraction shows only a minor increase due to the excitation.

Development and interaction of disturbance waves in downward annular gas-liquid flow

The behavior of the disturbance waves is studied in downward adiabatic air-water annular flow in a vertical pipe with an inner diameter of 11.7 mm. The range of liquid wetting densities is 2.5–4.6 cm2/s and the range of superficial gas velocities is 22–57 m/s. The paper is focused on the downstream evolution of the main properties of individual disturbance waves at the stage of flow development along with the process of coalescence of disturbance waves. Brightness-based laser-induced fluorescence technique enabled us to obtain spatiotemporal matrices of the local instantaneous thickness of liquid film along one longitudinal section of the pipe with a length of 400 mm. Dependencies of the main characteristics of the flow on the downstream distance are analyzed. Local shear stress, base film thickness, and longitudinal size of the disturbance waves are stabilized at the distance of 150–200 mm below the inlet. Disturbance wave velocity increases strongly up to this point; further downstream, the acceleration is reduced significantly. Disturbance wave amplitude grows approximately as the square root of distance within the whole region of interrogation. Entrained fraction grows linearly within this region. Disturbance wave frequency decreases exponentially due to the coalescence. It is found that an average disturbance wave surviving through the development stage absorbs two other waves. Individual acts of coalescence of disturbance waves are analyzed quantitatively to investigate their contribution to the change of disturbance wave properties. On average, when a disturbance wave absorbs another one, its speed increases by 2%, its amplitude – by 5–6% and its longitudinal size remains the same. Thus, the disturbance wave properties change downstream mainly due to their individual evolution, not due to coalescence.

Liquid-film thickness and disturbance-wave characterization in a vertical, upward, two-phase annular flow of saturated R245fa inside a rectangular channel

The liquid-film flow in a vertical, upward, two-phase annular flow of saturated R245fa is characterized experimentally under adiabatic conditions. The experiments are conducted inside a rectangular channel with a cross section of 11.6 × 36 mm2 for mass velocities ranging from 95 to 130 kg/m2s, vapor qualities from 0.63 to 0.9 and saturation temperature of 23 °C. Liquid-film thickness and disturbance-wave velocity and frequency are measured optically. Liquid-film thickness is recorded at a sampling frequency of 2000 Hz, while disturbance-wave velocity is recorded at a sampling frequency of 20 Hz. A parametric study as a function of quality and mass velocity is performed. Results show that the liquid-film thickness decreases linearly with increasing vapor quality. The liquid films investigated are very thin, and thinner than the critical liquid-film thickness below which momentum and mass transport are no longer driven by disturbance waves. Indeed, at high vapor quality, when the liquid film is very thin, the liquid-vapor interface becomes smoother and disturbance waves slow down and vanish. The frictional pressure gradient increases with quality until it reaches a peak. Results suggest that the subsequent decrease in pressure gradient is closely linked to the disappearance of disturbance waves. For the range of studied operating conditions, the frequency of disturbance waves remains constant within the uncertainty of the measurements. Experimental data is compared with prediction methods from the literature. Although reasonable predictions were obtained for the liquid film thickness, none of the tested methods could predict disturbance-wave velocity and frequency accurately.

Analysis of annular flow disturbance wave frequency in two different installation conditions

The dynamic local liquid film thickness of annular flow was measured with a near infrared (NIR) equipment. Basing on the power spectral density (PSD) to analyze this signal, the frequency of disturbance wave was obtained. The experiment was carried out for both horizontal and vertical annular flow. Considering the effects of flow velocity and gas pressure, the results showed that the wave frequency increases with the increase of flow velocity and gas density in both installation conditions. For the numerical correlation, the frequencies of the vertical is more regular than those of the horizontal.

Analysis of spatial and temporal evolution of disturbance waves and ripples in annular gas–liquid flow

Wavy structure of liquid film in downward annular gas–liquid flow is studied with high-speed laser-induced fluorescence technique. Film thickness measurements are resolved in both longitudinal distance and time with high spatial and temporal resolution. A method is developed to identify the characteristic lines of individual disturbance waves. Change of frequency of disturbance waves with downstream distance is modelled based on the obtained distributions of the disturbance waves by velocity and separation time. Using obtained characteristic lines further investigation of ripples’ properties is performed in reference system moving with the disturbance wave. As a result, velocities, amplitudes and frequencies of ripples are measured with relation to the distance from disturbance waves. Fast ripples travelling over crests of disturbance waves and slow ripples travelling over back slopes of disturbance waves and over the base film are studied separately. Besides, the average length of crest and back slope of disturbance waves were measured.

Properties of disturbance waves in vertical annular two-phase flow

Disturbance waves play an important role in interfacial transfer of mass, momentum and energy in annular two-phase flow. In spite of their importance, majority of the experimental data available in literature on disturbance wave properties such as velocity, frequency, wavelength and amplitude are limited to near atmospheric conditions (Azzopardi, B.J., 1997. Drops in annular two-phase flow. International Journal of Multiphase Flow, 23, 1–53). In view of this, air–water annular flow experiments have been conducted at three pressure conditions (1.2, 4.0 and 5.8 bar) in a tubular test section having an inside diameter 9.4 mm. At each pressure condition liquid and gas phase flow rates are varied over a large range so that the effects of density ratio, liquid flow rate and gas flow rate on disturbance wave properties can be studied systematically. A liquid film thickness is measured by two flush mounted ring shaped conductance probes located 38.1 mm apart. Disturbance wave velocity, frequency, amplitude and wavelength are estimated from the liquid film thickness measurements by following the statistical analysis methods. Parametric trends in variations of disturbance wave properties are analyzed using the non-dimensional numbers; liquid phase Reynolds number ( Re f), gas phase Reynolds number ( Re g), Weber number ( We) and Strouhal number ( Sr). Finally, the existing correlations available for the prediction of disturbance wave velocity and frequency are analyzed and a new, improved correlation is proposed for the prediction of disturbance wave frequency. The new correlation satisfactorily predicted the current data and the data available in literature.

Experimental study on axial development of liquid film in vertical upward annular two-phase flow

Accurate measurements of the interfacial wave structure of upward annular two-phase flow in a vertical pipe were performed using a laser focus displacement meter (LFD). The purpose of this study was to clarify the effectiveness of the LFD for obtaining detailed information on the interfacial displacement of a liquid film in annular two-phase flow and to investigate the effect of axial distance from the air–water inlet on the phenomena. Adiabatic upward annular air–water flow experiments were conducted using a 3 m long, 11 mm ID pipe. Measurements of interfacial waves were conducted at 21 axial locations, spaced 110 mm apart in the pipe. The axial distances from the inlet ( z) normalized by the pipe diameter ( D) varied over z/ D = 50–250. Data were collected for predetermined gas and liquid flow conditions and for Reynolds numbers ranging from Re G = 31,800 to 98,300 for the gas phase and Re L = 1050 to 9430 for the liquid phase. Using the LFD, we obtained such local properties as the minimum thickness, maximum thickness, and passing frequency of the waves. The maximum film thickness and passing frequency of disturbance waves decreased gradually, with some oscillations, as flow developed. The flow development, i.e., decreasing film thickness and passing frequency, persisted until the end of the pipe, which means that the flow might never reach the fully developed state. The minimum film thickness decreased with flow development and with increasing gas flow rate. These results are discussed, taking into account the buffer layer calculated from Karman’s three-layer model. A correlation is proposed between the minimum film thickness obtained in relation to the interfacial shear stress and the Reynolds number of the liquid.

Measurement of Interfacial Structure on Liquid Film in Annular Flow Using Laser Focus Displacement Meter (2nd Report, Disturbance Wave Frequency and Local Minimum Film Thickness)

In this study, a precise database of microscopic interfacil wave-structure was obtained for annular two-phase flow developing in a vertical pipe. Using a laser focus displacement meter (LFD), measurements of such local properties as the minimum film thickness and passing frequency of the waves along the pipe were conducted. The results showed that the passing frequency of disturbance waves decreased gradually with some oscillations in the pipe axial direction, whose phenomena had a similarity with those of maximum film thickness reported in the 1st report. These unique phenomena were also discussed from a view of pressure resonant interactions based on the experimental results of pressure propagation in the pipe. Minimum thickness of the film decreased with flow development and with increasing gas flow rate. These results were discussed taking into account the buffer layer calculated from Karman's three-layer model. Correlation was proposed for obtained minimum film thickness in regarding to interfacial shear stress and the Reynolds number of the liquid. This correlation expressed the minimum film thickness obtained from the experiment withis 5% deviation.

Gas-Liquid Interfacial Characteristics in an Inclined Upward Annular Flow.

This paper presents experimental data of the effects of pipe inclination on the circumferential variation of characteristics of annular liquid film and on the interfacial shear stress. In this experiment, film thickness was measured using the needle contact method and disturbance wave frequency and wave velocity were calculated from the output signals of time varying liquid film thickness by the constant current method. The inclination angles examined were 0°, 15°, 30°, 45°, 60° and 75° from the horizontal. Superficial velocities of air and water ranged from 20 m/s to 40 m/s and from 0.06 m/s and 0.20 m/s, respectively. The following results were obtained : i) The increase in pipe inclination makes the circumferential distribution of disturbance wave height uniform, while the wave velocity, frequency and length are not affected by the inclination. ii) A new correlation for the interfacial friction factor in an inclined upward pipe is obtained by modification of Fukano's correlation. iii) Simple charts were obtained to represent the relationship among interfacial shear stress, film thickness and flow rates of both phases.