Application of spectral analysis in radiometric measurements of two-phase liquid-gas flow

This article presents use of the classical spectral analysis to identify a type of flow in investigation of gas transportation by liquid with a measurement of gamma radiation absorption. During numerous experiments it was found that a magnitude of the cross-spectral density distribution of recording signals reveals type of air-water mixture flow in a horizontal pipeline. As an example, some results of laboratory measurements equipped in Am radiation source and scintillation probes with of NaI(Tl) crystals are presented. Moreover attached figures facilitate interpretation of observed results and in details illustrating the


Introduction
The flow when gas is transporting by liquid occurs in many industries, especially in heat transfer installations.Depending of the liquid velocity, viscosity, and presence of micro turbulences, the same volume of gas may be transported in a different way, evolving from slug, up to homogenous or annular flow.Hence there is a need for development of methods of continuous observation and mathematical description of such type of flow.
In our case the nuclear method base on application of radiotracers and (or) using a gamma radiation for the flow analysis.The last of those methods is especially convenient for continuous observation of unstable twophase flows, providing velocity of gas phase and manner of its transportation.That goal is achieved by advanced analysis of signals delivered by scintillation probes in time and frequency domains.
Flow regime identification inspires many studies of two-phase flows.Recent works shows use for this purpose the power spectral density, wavelet transform, Hilbert-Huang transform, artificial neural networks and expert systems, electrical capacitance tomography and fuzzy-logic classification [11][12][13][14][15].
The article provided use of the cross-spectral density function (CSDF) to identify the type of flow, illustrated by the attached examples.

Laboratory stand
The paper, based on results collected in the pilot installation built at the Laboratory of Industrial Radiometry, Faculty of Physics and Applied Computer Science, AGH in Krakow [16].The simplistic schema of the stand is shown in Figure 1. to which water is pumped by a rotary pump (4) and air from the compressor ( 5) by an injector nozzle (7).Due to that the controlled mixture of water and air supply the measuring pipe and flowing up to the air-removing tank (6).The measurement of air bubbles velocity and flow regime recognition was arrange by the measuring system consisting of two linear γ-radioactive sources, 241 Am ( 1) with an activity of 100 mCi and two probes with NaI(Tl) (2) scintillation detector.The measuring set is mounted on a special trolley (8), which allows moving the set along the pipeline.Water flowrate was continuously measured by Uniflow 990 ultrasonic flowmeter (3).The rotary pump (4) controlled by a waver allows adjustment of the revolution in range between 1000 and 2800 rpm, which allows selection of water velocity in the measuring pipe between 0.5 -2.5 m/s.The data acquisition system was connected with a PC by the dedicated counters card and USB port.The general view of the stand during nuclear measurement is shown in Figure 2.

Application of Gamma absorption in two-phase flow measurement
The idea and geometry of the measurement are shown in figure 3. Two 241 Am sealed radioactive sources (2) emit γ radiation beams (6, 7), shaped by the collimator (1).Photons pass through the pipeline with analyzed mixture (5) and collimator (3) before achieved the detector (4).In investigations the linear radiation sources 241 Am, QSA Global were used, which structure and dimensions are shown in figure 4.
The data acquisition equipment allows recording of I x (t) and I y (t) intensity representing the composition of the flowing mixture.Results recorded in the BUB006 experiment are shown in Figure 5.In the paper the autospectral density function (ASDF) and cross-spectral density function CSDF, determined unilateral in practice (for the frequency range 0 < f <) ASDF: G xx (f), G yy (f) and CSDF: G xy (f) can be expressed by the following formulas [17]: (3) where: R xx (Ĳ), R yy (Ĳ) and R xy (Ĳ) are the autocorrelation and cross-correlation function properly, f -frequency, Ĳ -time delay.
During data processing the Fast Fourier Transform (FFT) was used directly to the discrete x(n) and y(n) signals.In consequence the phase distribution of CSDF were used to measure the average velocity of air bubbles, as the minority phase of the mixture [8,18].The same results were obtained by the cross-correlation analysis facilitated by the band pass filtering of the recorded signals [16,19].
Additionally the spectral analysis can be used to recognize the type of the gas bubbles transportation in the flow.The literature shows a use for this purpose ASDF [10], however, according to the authors, better results can be accomplished using a magnitude of cross-spectral density |CSDF|.For illustration the figure 6 shows ASDF and |CSDF| designated for data recorded in the experiment BUB006 (slug flow of water -air mixture).

Conclusion
Competed investigations justified advantages of the gamma absorption techniques application to examination of two phase flow and simultaneous determination both the velocity of gas bubbles and pattern recognition of its forms.Moreover collected results prove advantages of cross-spectral density in compare to autospectral density function to processing recorded signals.
Due to that the proposed method is worthwhile to consider application in other laboratories or even to control of selected heating installations.

Figure 2 .
Figure 2. General view of the measuring stand during tracer and absorption experiment Transparent measuring section of the pipeline allows additionally a photographic documentation of the observed phenomena.

Figure 5 .
Figure 5. Intensity of γ-ray beam recorded by the first probe in the run BUB006

Figure 6 .Figure 7 .
Figure 6.Comparison of the ASDF (a) and |CSDF| (b) calculated in the run BUB006.The comparison of figure6aand 6b shows that the frequency range associated with the used signal is more apparent in the course of |CSDF| than ASDF.