Ferreira, Vilson Carlos da Silva

Gutkoski, Lucas Luis

Laan, Flavio Tadeu van der

Pires, M.

English

Lume 5.8

TWO-PHASE FLOW  (WATER-AIR) ANALYSIS IN A DISPERSED BUBBLESREGIMESPires, M. – manolo@mecanica.ufrgsFerreira, V. C.S. – vferreira@pro.via-rs.com.brGutkoski, L.L. – hukax@ct.ufrgs.brUniversidade Federal do Rio Grande do Sul – Laboratório de Turbo-Máquinas e Medições deFluxo – LTMF – UFRGSCEP 900560-170 – Porto Alegre – RS, BrasilVan der Laan, F.T. – ftdlc@vortex.ufrgs.brUniversidade Federal do Rio Grande do Sul – Departamento de Engenharia Nuclear –DENUC – UFRGSAbstract. The present work investigates experimentally the pressure fluctuations due todiscontinuities and internal instabilities in both phases of a two-phase flow. Specifically,  isanalysed the effects of the dynamic response of a cloud of bubbles in the transient regime. Theinteractive effects due to the variation of the bubbles volume upon the pressure distributionand on the flow field are very significant. Also, the flow velocity is strongly affected as theconcentration of the bubbles increases turning larger the possibility of a global movement ofthe mixture. The results of this investigation reveal how the presence of the air bubbles affectsthe nature of the medium throughout  the pressure wave, changing the specific gravity of themixture and the bulk compressibility, therefore, changing the speed of the sound. It isapparent that an increment of the void fraction causes substantial reduction of amplituderesponse of the bubble.Key words: Group of Bubbles, Two-phase Flow, Discontinuities, Attenuation1. INTRODUCTION Two-phase flow became important since the 40’s. The great interest started with thenuclear power plant and its application, but soon afterwards, the aerospace industry, as wellas, the chemical and petroleum industries presented their own complex problems. There are,also, many natural situations where the two-phase flow occurs with great importance, such asthe case of geothermal sources for energy generation.Among the great variety of problems, to measure flowrate in a two-phase situationshows an appreciable difficulty in any industrial plant because the random effects of the flow,which are present intentionally or not, change all the hydrodynamic parameters of the flow.Gas bubbles fluctuating in a liquid flow suffer several interactions too much complex for acomplete and appropriate mathematical formulation. The existing physical-mathematicmodels including a complete hydrodynamic interactions of the two-phase flow, as far as theauthor’s knowledge, are not  yet available. In general, all these models totally neglect theinternal transient processes, such as the case of the homogeneous or the average time models.Many theoretical models describe the evolution of the two-phase flow structure while neglectimportant parameters of the two-phase mixture, such as, the amount of gas injected in theflow in terms of quality (0<x<1). Only mass, momentum and energy conservation equationsare not enough to describe the spatial structure and strong interactions of the two-phase flow.It is necessary to supply a model with supplementary constituent equations, expressing theinterfacial laws of transference in terms of  dependent variables.In the two-phase flow, with a dispersed bubbles, complicated interactions appear suchas collisions, coalescence among adjacent bubbles, interactions between bubbles and the wall,instantaneous variations of the geometry of the bubbles, affecting the potential hydrodynamicof the flow and causing static pressure and velocity fluctuations as well as increasing theturbulent intensity of the liquid. As a result, variation in the flow field induces changes of thebubbles movement and a more violent buoyancy and heterogeneity inside the flow. Manyanalytical and experimental studies have been made to discover the mechanism of the two-phase flow, such as the work of Hsieh and Plesset (1961), Wijngaarden (1976,1968,1966),Biesheuvel (1984), Scott (1981), D’Ágostino and Brennen(1989), Nakoryakov et al. (1994),Takahira et al. (1994), Ferreira (1997). All such models, though, cannot represent the actualflow, can only be applied to a restrict flow in very limited conditions. On the other hand,comparisons among results from different researches are also very difficult due to the absenceof a similarity parameter, like a non dimensional number, which may embodied the wholephenomenon. So, although a great amount of experimental work, for the flow with bubbles indifferent systems liquid-gas, little basic information are supplied to give the actual view of thephysical phenomenon. Thus, the basic knowledge of the mechanism of this complex flow isstill very limited, although bubbles of gas in liquid are a very familiar and have been studiedsince long time.The present work investigates experimentally the fluctuations of local pressure of thetwo-phase flow in a dispersed bubble regime seeking new clues to solve this puzzle flow. Thepurpose of this study is to get an overall information looking the flow as a whole. A mixtureof water and air flows through a horizontal pipe of 50 mm internal diameter at low totalpressures of 250 kPa. The study gives emphases  to the following topics:1) pressure fluctuations frequencies and2) pressure fluctuations intensity produced by the dynamic of the bubbles;2. EQUIPMENT AND PROCEDUREThe experimental data were obtained from the test circuit shown in Figure 1. The testcircuit is part of the calibration gravimetric rig of the Turbomachine and Flow MeasurementLaboratory - LTMF used to calibrate liquid flowmeters from 0.1kg/s up to 5.0 kg/s with anextended (k95% = 2) uncertainty of ± 1.0 % full scale (FS). The rig comprises by threedifferent sections: the inlet section; the developing section and the test section. The inletsection has a enlarged cross section tube of 150mm diameter with a flow straightener tocondition the flow and prevent large eddies, swirls as well as possible secondary flows andfluctuations produced by the pump or coming from previous bends and several hydrauliccomponents. A vent installed on the top of the inlet section eliminate air from other sourcesdifferent from the measured one. The developing section consists of a long straight pipe of 50diameter mm with an equivalent length of 60 diameter (3000 mm) before the test section. Theobjective is promote a fully development of the flow profile.Figure 1  Test SectionThe test section consists of a horizontal acrylic tube of 50 mm of diameter internal,with two piezoelectric sensors vertically opposite installed. The transmitter sensor is the oneon the top and the receiver the one on bottom of the tube. The piezoelectric sensors have aresonance frequency of 140 kHz and response signal from 4 to 20 mA.The measured air is injected by a small tube in a "L" shape through many small holes of10mm diameter. This solution allows the air being mixed in water with vertical movement.A function generator drives a 140 kHz sinusoidal wave signal to the transmitter sensoron the top of the pipe. The ultrasonics signals reach the piezoelectric receiver sensor,diametrically installed, suffering variations due to the presence of bubbles altering theintensity and phase related to the incoming signal. The amount of bubbles varies randomlywith the time and with the flow established. The signals from the piezoelectric receiver wereamplified and demodulated to remove noise and the high frequency carrier signal. The treatedsignal reveals the random characteristic of the flow.In order to acquire the experimental  results a fast acquisition system, was used. Thedata system may run from a frequency of 100 up to 300 kHz acquiring up to 100.000 pointsfor each test. At the same time, in a synchronised images of the flow is recorded onto a DVvideo tape by a digital VCR through a CCD digital monochrome video camera. This videocamera allows shutting at a variable speed ranging from 1/30 to 1/10000 seconds in a discreteway of eight options. All the images were digitalized and stored into a microcomputer bymeans of a interface board.3. EXPERIMENTAL RESULTS AND ANALYSISThe measurements were made for different flow rate of the mixture water and air. Thissection presents some obtained results. The Figure 2 shows the pressure fluctuations in thedomain of the time for the flow single - phase with flow rate of water of (1,03±0,01) kg/s andfor two-phase flow with a flow rate of (1,03 ±0,01) kg/ s of water and( 1,0775± 0,001)x10-5kg / s of air, so much in the domain of the time and the spectrum of corresponding frequency.Figure  2   Pressure Fluctuations : a) Monophase Flow m = (1,03 ±0,01) kg/s (water)                     b) Two-phase Flow m = (1,03 ±0,01) kg/s (water) and m = ( 1,0775± 0,001)x10-5kg/s (air)  c) Frequency Spectrum of Two-Phase FlowThe Figure 3 exhibition the pressure fluctuations in the domain of the time for the flowsingle phase with flow rate of water of (1,37 ±0,01) kg/s and for the two-phase flow with flowrate of (1,37±0,01) kg / s of water and  (2,155±0,001 )x10-5  kg / s of air in the domain of thetime and the spectrum of corresponding frequency.      Figure  3   Pressure Fluctuations : a) Monophase Flow m = (1,37 ±0,01) kg/s (water)b) Two-phase Flow m = (1,37 ±0,01) kg/s (water) and m = ( 2,155± 0,001)x10-5kg/s (air) c) Frequency Spectrum of Two-Phase FlowDifferent correlation among flow single phase and two-phase they were applied. Theywere made several analysis, so much in the domain of the time, as in the one of the frequency,for different tested fractions of emptiness. Although the Figures 2 and 3 are private cases, theyare representative and very similar to the other made tests. Of the graphs of the Figures 2 and3, it was observed that with the introduction of the dispersed phase (air bubbles) in the flowwith water:  ·  the intensity of the fluctuations in the two-phase flow is larger an order of greatnessor more than the one of the flow single phase for the same water flow rate;·  the spectrum of frequency of the two-phase flow there are some well defined picks offrequencies in both flows, which probably represent some supported of flow measurementseffects of the own;· In contrast with the flow single phase, the spectrum of fluctuations of eachhydrodynamic parameter is characterised by a maximum fall in low frequency of the order of1-10 Hz.Analysis of several pressure diagrams in the two-phase flow situations reveals thepresence of a so called progressive waves which alters the time and space structure of theflow.By using  of analytic expressions proposed by Fokin, (1995), for the transient  two-phase flow, the intensity of the fluctuations of pressures was calculated in form of  root meansquare values. The correspondent values used was for test established in Figure 2 and 3 andthe mean value achieved was  0,81213 Pa. Comparison between experimental and analyticalresults showed agreement. The actual pressure fluctuations represent a superimposition aharmonic process with an random noise. The Figure 4 shows the pressure fluctuations produced by the addition of the dispersedphase (bubbles) in the flows corresponding to the Figures 2.Figure 4 Pressure Fluctuations produced by Dispersed Phase ( Bubbles): Signal of theDifference Two-Phase Flow and Monophase of Figure 2.The results show non linear effects caused by  radial fluctuations of the bubbles in theliquid. Oscillations produced by group of bubbles affect the basic flow turning impossible ananalytic treatment of the flow single phase.According to Scott, (1981), oscillations produced by bubbles are describe by certaineigenvalue problems, which give the normal manners and corresponding frequencies ofoscillations. These manners represent collective oscillations of the system of bubbles, and itcannot in general, to be attributed to private bubbles.4. CONCLUSIONSAlthough to present analysis it doesn't allow an accuracy of the quantitative results,not having given enough to be conclusive, the results of this investigation reveal a number ofimportant effects in flows confined with bubbles. A pressure fluctuation signal in a bubblyflow is complex, due the fact the continuos phase conducts pressure fluctuations very well.Attenuation extremely high are produced in water contends suspended bubbles of air.The presence of the air bubbles affects the nature of the middle through the ones which thewave this progressing.The power spectrum, also, showed some selected frequencies that may be referred toinstallation effects and some to the flow behaviour.  It was observed that an increment of the void fraction causes a substantial reductionin the bandwidth response of the dynamic of the  bubble.The work is still underway and in the near future some of theses questions will certainlybe answered.5. REFERENCES Biesheuvel, Wijngaarden L. van 1984, Two Flow Equations for a Dilute Dispersion ofGas Bubble in Liquid J. Fluid Mech., Vol.148 – pp. 301-318 D’ágostino L., Brennen C.E. , 1989,  Linearized Dynamics of  Spherical Bubble Clouds – J.Fluid  Mech. Vol. l. 199, pp.155-176Ferreira V.C.S. 1997, Differential Pressure Spectral Analysis for Two-Phase Flow through anOrifice Plate - Int. J.Press.& Piping Vol.73, pp.19-23 Fokin, B.S.,1995, Calculation of Pulsation and Averaged Hydrodynamic Characteristics of                 Two-Phase Flow, Russ. J.Eng. Thermophys.,Vol.5, n 3,pp. 265-292.Hsieh D.Y., Plesset M.S., 1961, On Propagation of Sound in a Liquid Containing Gas Bubble– Phys. Fluid Vol.4, N. 8-pp. 970-975Nakoryakov V., Dontsov V.E. , Pouasaev B.G. 1994, Propagation of Pressure Waves inLiquid with Gas Bubbles and Solid Particles – Russian Journal of EngineeringThermophyysics, , Vol. 4, pp 173Scott J.F. , 1981, Singular Perturbation Theory Applied to the Colletive Oscillation of GasBubbles in a Liquid – J. Fluid MechVol.113 , pp.  487 –511Takahira H, Akamatsua T, Fujikawa S . 1994,  Dynamics of a Cluster of Bubble in a Liquid –JSME- International Journal serie B, V.37, N. 2 pp.Wijngaarden , L. van . 1976a , Hydrodynamics Interation between Gas Bubbles in Liquid- J.Fluid MechVol.77 , pp.  27- 44Wijngaarden , L. van,1968, On the Equations for motion of Mixtures of Liquid and GasBubbles – J. Fluid Mech, vol.33,part 3, pp.465-474Wijngaarden , L. van 1966, Linear na Non Lineart Dispersion of Pressure Pulses in Liquid –Bubble Mixtures – Technische Hogeschool Twente Afdelnig der Werktuigbounddunde-Postbus 217, Enschede, Netherlands, pp. 115-135

Two-phase flow (water-air) analysis in a dispersed bubbles regimes

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Two-phase flow (water-air) analysis in a dispersed bubbles regimes

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