Experimental and theoretical study of the gas-water two phase flow through a conductance multiphase Venturi meter in vertical annular (wet gas) flow

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1 Experiental and theoretical study of the as-ater to phase flo throuh a conductance ultiphase Venturi eter in vertical annular (et as) flo Abbas a H. A. M. Hasan and G. P. Lucas a University of Huddersfield, School of Coputin and Enineerin Queensate, Huddersfield, HD 3DH, United Kindo Abstract Annular as-liquid to phase flo is idely encountered in the nuclear industry. Various cobinations of techniques have been eployed in annular as-liquid to phase flos to easure the flo paraeters (e.. liquid fil thickness, as volue fraction and the phase flo rates). One of the ost useful techniques hich has proven attractive for any ultiphase flo applications is the electrical conductance technique. This paper presents an advanced Conductance Multiphase Venturi Meter (CMVM) hich is capable of easurin the as volue fractions at the inlet and the throat of the Venturi. A ne odel as investiated to easure the as flo rate. This odel is based on the easureent of the as volue fractions at the inlet and the throat of the Venturi eter usin a conductance technique rather than relyin on the prior knolede of the ass flo quality x. We easure conductance usin to rin electrodes flush ith the inner surface of the Venturi throat and to rin electrodes flush ith the inner surface of the Venturi inlet. The basic operation of the electrical conductance technique in a ultiphase flo is that the conductance of the ixture depends on the as volue fraction in the ater. An electronic circuit as built and calibrated to ive a dc voltae output hich is proportional to the conductance of the ixture hich can then be related to the ater fil thickness in annular flo (and hence to the as volue fraction). It as inferred fro the experiental results that the iniu averae percentae error of the predicted as ass flo rates (i.e %) can be achieved at the optiu as dischare coefficient of Keyords: Venturi eter, electrical conductance technique, annular flo.. Introduction Annular as-liquid to phase flo is idely occurred in flo channels of nuclear processes. In ater continuous ultiphase flo, the electrical conductance technique has proven attractive for any industrial applications. The idea behind this technique is that an electric current is ade to flo throuh the as-ater ixture, beteen to rin electrodes in contact ith the ixture, and the resultant easured voltae drop is proportional to the ixture conductance. The as volue fraction can then be deterined fro this easured ixture conductance. Differential pressure devices can be used in ultiphase flo eterin. The ost coon differential pressure device is the Venturi eter, but orifice plates have also been used idely. The advantae of the Venturi eter over the orifice plate is that the Venturi eter is uch ore predictable and repeatable than the orifice plate for a ide rane of flo conditions. Further, the sooth flo profile in a Venturi eter reduces frictional losses hich (i) increases the reliability of the device and (ii) iproves the pressure recovery. An interestin result, relevant to this paper as obtained by (Malayeri et al. 00) ho studied the behaviour of as liquid upard

2 bubbly flo throuh a vertical Venturi usin a aa densitoeter and found that the void fraction at the throat as alays less than at the inlet of the Venturi at fixed ater flo rate over a rane of as flo rates. Considerable theoretical and experiental studies have been published to describe atheatical odels of Venturis in ultiphase flo applications. The study of ultiphase flo throuh contraction eters is described for exaple by (Murdock 96; R. V. Sith & Lean 975; Chishol 967; Chishol 977; Lin 98; de Leeu 994; Steven 00). All of these correlations depend either on the ass flo quality, x or epirical constants. None of these odels depend on the easureents of the as volue fraction at the inlet and the throat of the Venturi/orifice eter. Hoever, online easureent of ass quality x is difficult and not practical in ultiphase flo applications. This paper develops a ne advanced desin of a conductance ultiphase Venturi eter (CMVM) hich is capable of easurin the as volue fraction at the inlet and the throat of the Venturi in annular as-ater to phase flos. The basic operation of the electrical conductance technique in a ultiphase flo is that the conductance of the ixture depends on the as volue fraction in the ater. An electronic circuit as built and calibrated to ive a dc voltae output hich is proportional to the conductance of the ixture and hich can then be related to the ater fil thickness in annular flo (and hence to the as volue fraction). A ne separated to phase flo odel throuh a vertical Venturi eter hich depends on the easureent of as volue fractions at the inlet and the throat of the Venturi as investiated.. Matheatical odels and correlations. Previous correlations throuh contraction eters in a separated flo Soe of the correlations found in literature pertinent to the present study are listed belo... Murdock correlation Murdock (96) studied the to phase flo throuh an Orifice plate eter and his ork as not restricted only to et as flos. Murdock developed a rational equation odifyin the sinle phase equation by introducin an experiental constant (correction factor). Murdock s correlation considers to phase flo to be separated flo and he coputed the total ass flo rate usin an epirical constant (equal to.6) and by assuin that the quality of the ixture is knon. The correction factor in Murdock s correlation as solely a function of the odified version of Lockhart- Martinelli paraeter X od hich is defined as the ratio of the superficial flos oentu pressure drops (and not the friction pressure drops as in the oriinal definition by Lockhart-Martinelli paraeter). The odified Lockhart-Martinelli paraeter is iven by; P & k x k X od = = P = k x k () & here and P are the differential pressures hen the liquid and as phases P respectively flo alone, & and & are the ater and as flo rates respectively,

3 k and k are the as and ater flo coefficients, and are the as and ater x = & & + & ). The as ass density respectively and x is the ass flo quality ( /( ) flo rate in to phase flo fro Murdock s correlation can be ritten as; here PTP At k PTP At k PTP & = = () x k +.6X od +.6 x k is the to phase pressure drop... Chishol correlation Chishol (967, 977) studied to phase separated flo throuh a sharp ede orifice plate. The Chishol correlation is a function of the to phase pressure drop and the odified Lockhart-Martinelli paraeter. The as ass flo rate in the Chishol correlation can be ritten as; k At PTP & = (3) + CX + X here At is the total flo area durin to phase flo and C is the Chishol paraeter and is iven (in ters of a slip ratio S) by; od od.. Lin correlation C = + S (4) S Lin (98) developed his odel on the basis of a separated flo odel (for eneral stratified to phase flo) and copared his odel aainst the experiental data. This coparison shos that the Lin odel can be used to calculate the flo rate or the quality of as-liquid ixture in the rane to 0.38 of the density ratio, and in the pipe size ranin fro 8 to 75. The Lin correction factor K is iven by; K = The as ass flo rate in Lin correlation can be ritten as; (5) k A x t TP & = = P K( x) + x k A t & K & P TP + (6) 3

.. A ne Separated To Phase Flo Model throuh a Venturi Meter It is clear fro the previous odels that they all depend on prior knolede of the ass flo quality x.

4 .. A ne Separated To Phase Flo Model throuh a Venturi Meter It is clear fro the previous odels that they all depend on prior knolede of the ass flo quality x. Online easureent of x is very difficult and not practical in nearly all ultiphase flo applications. The ne odel depends on easureent of the as volue fractions at the inlet and the throat of the Venturi eter rather than relyin on prior knolede of the ass flo quality. In a separated flo, the assuption that the velocities of the phases are equal is invalid and the slip ratio S is not unity. In other ords, each phase flos separately ith different velocity. A ne separated to phase flo odel throuh a Venturi eter has been investiated. This odel is based on the fact that each phase flos separately as shon in Fi.. Fi. shos ho the as volue fractions are defined throuh a Venturi eter. For the as phase, the Bernoulli equation can be ritten as; P + U = P + U + P (7) here P is static pressure, is density, U is velocity and P H is the anitude of the hydrostatic head loss beteen the inlet and the throat of the Venturi (i.e. beteen pressure tappin separation). The subscripts, and refer to the inlet, throat and the as phase respectively. Any frictional pressure losses ill be accounted for in a dischare coefficient at a later stae. H Throat Converin section P h α h v α Inlet section h α P Fiure : Gas-ater to phase flo throuh a Venturi eter Fiure : Inlet, converin and throat sections of the Venturi eter The as density at the inlet of the Venturi is related to the as density at the throat of the Venturi by the folloin equation; P P = (8) γ γ here γ is the adiabatic index. Includin Eq. (8) in an equation for ass continuity ives; γ α A P U = U (9) αa P here α and α are the as volue fractions at the inlet and the throat of the Venturi. Cobinin equations (7) (8) and (9), and introducin a dischare coefficient C d for the as phase, enables derivation of the folloin expression for the as ass flo rate. 4

5 ( { P P }) TP H A Aαα &, predicted = Cd (0) P γ ( αa ) ( α A ) P The hydrostatic head loss ter P H in Eq. (0) can be calculated by akin an assuption that the ean as volue fraction in the converin section is α here; α + α α = () The hydrostatic head loss ter can no be expresses as follos; (usin the position of the pressure tappins shon in Fi. ) { ( α ) + α } + h { ( α) + α} + h { ( α + α } P = h () H v ) here is the averae as density beteen inlet and the Venturi throat, h, h and h v are the heihts defined in Fi.. The as density at the throat section is iven by; P = (3) P The as density at the inlet can be obtained fro Eq. (4); P = (4) rt here P and T are the absolute pressure and teperature at inlet section respectively and r is the specific as constant and is iven by; 000R r = (5) M here R is the universal as constant and M is the relative olecular ass of the as. The as dischare coefficient C can be expressed as; d C & γ, ref d = (6) &, predicted here &, predicted is the predicted value of the as volue flo rate and &, ref is the reference as ass flo rate obtained fro Variable Area Floeter (VAF). It is clear that, the advantae of the ne odel (Eq. 0) over the previous odels is that it does not require prior knolede of ass flo quality x. In other ords, the ne odel depends only on the easureent of α and α hich akes the easureent technique ore practical than those used previously. 3. Desin of the conductance ultiphase flo eter. To deterine the as flo rate in Eq. (0), the easureent of the as volue fractions at the inlet and the throat ( α and α ) ust be achieved. To do so, a ne conductance ultiphase flo eter as desined and constructed (Fi. 3 and Fi. 4). This eter consists of to sections; the conductance Inlet Void Fraction eter (IVFM) and the Conductance Multiphase Venturi Meter (CMVM) hich is capable of easurin the as volue fractions at the inlet and the throat of the Venturi ( α and α respectively). Four rin electrodes ere used (to at the inlet section and 5

to at the throat section). The rin electrodes ere desined to be flush ounted to the inner surfaces of the inlet and the throat of the Venturi) in order to avoid flo disturbances.

Another advantae of this desin is that it is very straihtforard to chane the throat section (Hasan & Lucas 008).

6 to at the throat section). The rin electrodes ere desined to be flush ounted to the inner surfaces of the inlet and the throat of the Venturi) in order to avoid flo disturbances. One of the ost advanced features of this desin is that, all parts can be assebled/disassebled easily includin the threaded flanes. Another advantae of this desin is that it is very straihtforard to chane the throat section (Hasan & Lucas 008). Fiure 3: The desin of the conductance ultiphase Venturi eter (CMVM) Fiure 4: The desin of the conductance Inlet Void Fraction Meter (IVFM) 4. Bench Tests on the Conductance eter (CMVM and IVFM) Before the CMVM and IVFM ere used dynaically in the flo loop as a ultiphase flo eter, a nuber of experiental bench testin procedures ere carried out. A bench test ri as desined and built in order to calibrate the conductance easureent systes of both the CMVM and IVFM. For the CMVM vertical experients (siulatin annular flo), different diaeters of nylon rods ere inserted throuh the throat of the Venturi and the ap beteen the outer surface of the rod and the inner surface of the Venturi as filled ith ater, representin the ater fil in a real annular flo situation as shon in Fi. 5a. The coplete block diara of the easureent electronics syste is also shon in Fi. 5b. At the beinnin of 6

7 the experient the zero offset stae as adjusted to ive a zero output voltae hen no ater as present at the throat of the Venturi. The aplifier stae as then adjusted to ive a axiu voltae hen the reion beteen the electrodes at the Venturi throat as copletely filled ith ater. A siilar procedure as used to calibrate conductance easureent syste of the IVFM. Water fil D D rod Electrodes Nylon rod δ = (D-D rod )/ A A δ Nylon rod holder (a) (b) Fiure 5: Bench test experiental setup and the block diara of the easureent electronics syste 4.. Results fro Bench Tests As described above, bench tests ere perfored by insertin non-conductive nylon rods ith different diaeters throuh the CMVM and IVFM. The dc output voltaes fro the electronic easureent circuits ere recorded hich ere related to the liquid fil thickness (and hence the as volue fractions) in the IVFM and at the throat of the Venturi. The ixture resistance (and hence the conductance of the ixture) can be practically easured fro the pre-aplifier stae shon in Fi. 5b. It should be noted that the static and dynaic easureents ere taken at the laboratory conditions in hich the teperature of the ater as kept constant at an averae value of.5 o C. Measureent of the ater conductivity taken usin a conventional conductivity eter shoed that the ater conductivity took as value of 43 µsc - for all of the experients described in this paper. Fi. 6 and Fi. 7 sho the calibration curves of the inlet and the throat of the conductance Venturi eter. Vdc α Vdc α Fiure 6: Calibration curve for the CMVM Fiure 7: Calibration curve for the IVFM 7

5. Multiphase flo loop and experiental setup One of the ultiphase flo loops at the University of Huddersfield is capable of providin as-ater annular flos (see Fi. 8).

The test section can be vertical, horizontal or inclined at any interediate anle but it as used in the vertical orientation for the experients described in this paper.

8 5. Multiphase flo loop and experiental setup One of the ultiphase flo loops at the University of Huddersfield is capable of providin as-ater annular flos (see Fi. 8). This flo loop has an 80 inner diaeter and a 3 eter lon test section. The test section can be vertical, horizontal or inclined at any interediate anle but it as used in the vertical orientation for the experients described in this paper. A rane of auxiliary test equipent is available for use ith the flo loop includin differential pressure sensors, teperature sensors, a aue pressure sensor, a turbine flo eter, as flo eters and ultiphase conductance eters. The teperature as kept constant at an averae value of.5 o C. A scheatic diara of the ultiphase test section ith interfacin syste is shon in Fi. 9. Fiure 8: A scheatic diara of the as-ater annular flo loop Fiure 9: A scheatic diara of the ultiphase test section ith interfacin syste 8

9 6. Experiental results Experients ere carried out in vertical upard as-ater flos usin the conductance ultiphase Venturi eter. Eihty five different flo conditions ere tested. The suary of the flo conditions are iven in table. Table : Suary of the flo conditions Data set no. Superficial as velocity Superficial ater velocity U s (s - ) U s (s - ) 6.99 to to to to To deterine the as flo rate in Equation (3.66) the easureent of the as volue fraction at the inlet and the throat of the Venturi in annular (et as) flo ( α and α, ) ust be achieved. To do so, a ne conductance ultiphase Venturi eter as desined and constructed (see section 4.3 ). It is clear fro the odel described in section 3.. that the easureent of the as volue fraction at the inlet and the throat of the Venturi, α, and α, the as ass flo rate throuh a Venturi,, respectively in annular (et as) flo enables &, to be deterined. de Leeu (994) analyzed his data based on the Froude nuber rather than velocities. The as Froude nuber Fr in ters of the superficial as velocity U is defined as; s Fr 0.5 U s ( [ ]) = (7) 0.5 [ D] A ood predication of the as velocity at the throat of the Venturi U can be obtained fro the as Froude nuber as shon in Fi. 0. This ay further siplify the odel investiated in this paper. The as dischare coefficient in a vertical annular (et as) flo throuh a Conductance Multiphase Venturi Meter (CMVM), C is iven by equation (6). It is clear fro Fi. that the as dischare coefficient C d for four sets of data can be treated as independent of the reference as ass flo rate & and can be averaed d, ref at This value of the dischare coefficient represents the optiu value in hich a iniu averae percentae error in the predicted as ass flo rate can be achieved (see also fiures 4 to 6). The predicted as ass flo rate & can be deterined usin Eq. (0). The, predicted coparison beteen the reference as ass flo rate and the predicted as ass flo rate for C d = is shon in Fi.. The reference as ass flo rate &, ref as 9

10 obtained fro a Variable Area Flo eter (VAF) as shon in Fiures 8 and 9. The o solid lines in Fi. represent the reference lines ( 45 lines). Data set Data set Data set 3 Data set 4 U (/s) Cd F r &, ref (khr - ) Fiure 0: The relationship beteen the as velocity at the throat and Froude nuber Fiure : Gas dischare coefficient C d of the Conductance Multiphase Venturi eter (CMVM) (k hr - ) (k hr - ) Predicted ( Data set ) Reference (Data set ) &, ref (khr - ) Prdicted ( Data set 3) Reference (Data set 3) &, ref (khr - ) (k hr - ) (k hr - ) Predicted (Data set ) Reference (Data set ) &, ref (khr - ) Prdicted ( Data set 4) Reference (Data set 4) &, ref (khr - ) Fiure : Coparison beteen reference and predicted as ass flo rates Fi. 3 shos the variations of the as volue fraction at the inlet and the throat of the Venturi in a vertical annular (et as) flo. It can be seen fro Fi.3 that, in eneral, α (at the Venturi inlet) is reater than α (at the Venturi throat). This difference becoes ore visible at loer ater flo rates (data set # ). 0

11 Fiure 3: Variations of the as volue fraction at the inlet and throat of the Venturi The percentae error in the predicted as ass flo rates ε is obtained fro the predicted as ass flo rate & (obtained usin easureents fro the, predicted CMVM and the odel described in Equations () to (6)) and fro the reference as ass flo rate & obtained fro a conventional variable area floeter (VAF) usin;, ref & ε =, predicted &, ref &, ref 00 % (7) In order to easure the & in Eq. (7), the absolute pressure P and the absolute, ref teperature T ust be easured at the upstrea section of the Venturi. Measureents of P and T enables the as density at the inlet of the Venturi to be deterined (see Equations (4) and (5)).The reference as volue flo rate Q, obtained fro the VAF can be then converted into the reference as ass flo ref &, ref rate usin; & (8), ref = Q, ref here Q, ref is the reference as volue fraction obtained fro the variable area floeter (VAF) before the as phase enters the to-phase flo test section.

12 Fiures 4 to 6 sho the percentae error of the theoretical as ass flo rates, ε for C = 0.9, 0.93 and It is clear fro these fiures that the iniu d averae percentae error in the predicted as ass flo rate & (i.e %), predicted can be achieved at C d =0.93. The standard deviations are also shon in Fiures 4 to 6. At C d =0.93, the ε is approxiately varied ithin ±.8% (see Fi. 5). As the Cd increased to the variations of the ε is approxiately ithin ±.9% (see Fi. 6). Fiure 4: The percentae error in the predicted as ass flo rates for all sets of data ( Cd, = 0. 9 and the standard deviation, STD = ) Fiure 5: The percentae error in the predicted as ass flo rates for all sets of data ( Cd, = and the standard deviation, STD = )

13 Fiure 6: The percentae error in the predicted as ass flo rates for all sets of data ( Cd, = and the standard deviation, STD = 0.984) 6. Conclusions The results reported in the present paper indicate that a Conductance Multiphase Venturi Meter (CMVM) can be used for the easureent of the as flo rate in annular as-ater to phase flos (et as flos). An advanced CMVM as desined and tested successfully hich is capable of easurin the as volue fraction at the inlet and the throat of the Venturi. It as found, in eneral, that the as volue fraction α at the inlet of the Venturi is rater than the as volue fraction α at the throat of the Venturi. The optiu value of the as dischare coefficient in hich a iniu percentae error in the predicted as ass flo rate (i.e %) can be achieved as A ne odel as also investiated hich depends on the as volue fraction at the inlet and the throat of the Venturi instead of just relayin on the prior knolede of the ass flo quality x. online easureent of the ass flo quality x is rather difficult and not practical in ultiphase flo applications. 7. References Chishol, D., 967. Flo of Incopressible To-Phase Mixtures Throuh Sharp- Eded Orifices. Journal of Mechanical Enineerin Science, 9(), Chishol, D., 977. Research note: To-Phase Flo Throuh Sharp-Eded Orifices. Journal of Mechanical Enineerin Science, 9(3), Hasan, A.H.A.M. & Lucas, G.P., 008. Siulation and Static Measureent of the Gas Volue Fraction in a Separated Flo Model Usin a Conductance Multiphase Venturi Meter (CMVM). In The proceedins of the Coputin and Enineerin Annual Conference. Huddersfield, UK: University of Huddersfield, pp ISBN:

14 de Leeu, H., 994. Wet Gas Flo Measureent by Means of a Venturi Meter and a Tracer Technique. In North Sea Flo Measureent Workshop, Noray, Shell Expro. Scotland. Lin, Z.H., 98. To-phase flo easureents ith sharp-eded orifices. International Journal of Multiphase Flo, 8(6), Malayeri, M.R., Sith, J.M. & Steinhaen, H., 00. The behaviour of as-liquid and vapour-liquid upard bubbly flos passin throuh a vertical Venturi. Trans. ICheE, 79(Part A), Murdock, J.W., 96. To-phase flo easureents ith orifices. Journal of Basic Enineerin, 84, Sith, R.V. & Lean, J.T., 975. Evaluations of Correction For To-Phase Floeter Three Current-One Ne. Journal of Enineerin for Poer, 97(4), Steven, R.N., 00. Wet as eterin ith a horizontally ounted Venturi eter. Journal of Flo Measureent and Inst., 36-37,

University of Huddersfield Repository

University of Huddersfield Repository Hasan, Abbas Multiphase Flo Rate Measurement Usin a Novel Conductance Venturi Meter: Experimental and Theoretical Study In Different Flo Reimes Oriinal Citation Hasan,