1 Introduction - WIT Press · 2014. 5. 12. · The spreading of the tracer was monitored using a...

Measurement and simulation of the turbulent

dispersion of a radioactive tracer in a two-

phase flow system

F. Hensel and U. Rohde

Forschungszentrum Rossendorfe. V.

f!O. #ox J707 79, D-70J74Dr&MbM, Germany

Email: [email protected]

Abstract

Studies on the measurement of turbulent dispersion of a radiotracer in an experi-mental setup with natural convection liquid-gaseous flow were carried out at theForschungszentrum Rossendorf. Liquid-gaseous bubbly flow was generated in anarrow tank by injection of pressurized air into water or by catalytic disintegrationof HiO?. A small amount of a positron emitting radiotracer liquid (^F in an aque-ous NaF solution) was injected instantaneously at a certain point of the tank. ThePositron Emission Tomography (PET) technique was used to observe the spread-ing of the tracer liquid in the bubbly flow. A double head gamma detector arraywas used for measuring the positron annihilation rate which is proportional to thetracer concentration. The dispersion coefficient D for the tracer liquid was calcu-lated from the experimental data assuming an isotropic spreading of the concentra-tion profile after separation of the linear displacement of the maximumconcentration point. Calculations of the two-phase flow with spreading tracerwere carried out for selected experiments using the computational fluid dynamicscode CFX-4. The Euler-Euler continuum approach including a homogeneous lowReynolds number K,e -model was applied for the two-phase flow. TurbulentPrandtl numbers for gas and tracer dispersion were varied. In case of higher gasinjection rates into water (superficial gas velocities jg^ of 5 - 15 mm/s), a reason-able agreement was achieved between calculated and measured values of the tracertransport velocity and the dispersion coefficient. A nearly linear correlation be-tween jgas and D was found in agreement with other authors. However, it was nec-essary to take into account the significant deviation of the tracer distribution fromthe ideal diffusion equation solution in some cases, in particular if the tracer hasbeen spread over upwards and downwards regions of the natural circulation veloc-ity field. Further investigations are necessary to improve the agreement betweenmeasured and calculated values of the dispersion coefficient and tracer transportvelocity in the case of F̂ O? disintegration and low gas superficial velocities.

Transactions on Engineering Sciences vol 18, © 1998 WIT Press, www.witpress.com, ISSN 1743-3533

284 Advances in Fluid Mechanics II

1 Introduction

The imaging technique Positron Emission Tomography PET originates from nu-clear medicine. It is mainly applied as an in vivo non invasive tool by which met-abolic activities can be investigated. Typical PET positron emitters like **C, ^N,^O and *% can substitute naturally occurring isotopes in a wide range of organiccompounds. Besides medical imaging, industrial and engineering applications areknown, including the investigation of chemical processes like catalysis* and flowmonitoring in an oil reservoir rock̂ . Using this technique, the spreading of a tracerin a bubbly flow in a tank was monitored. The objective of these investigations wasto study the turbulent mixing in chlorine electrolysis cells, particularly the estima-tion of turbulent dispersion coefficients.

Besides of the experimental investigations, an attempt was made to simulate thetwo-phase natural circulation flow in the tank by using a computational fluid dy-namics code. The results contribute to better understanding of the phenomena andinterpretation of the measurement results as well as to the validation of the CFDcode for turbulent two-phase flow applications by a direct comparison betweenmeasured and calculated characteristic parameters.

2 Description of the Measurements

In a series of experiments the transport of a tracer in a turbulent bubbly flow oc-curring in a narrow tank (Fig. 2.1) was studied. At the bottom of the tank gas bub-bles are generated. This can be done by injection of pressurized air or by adecomposition reaction. In the first case the bubbles are created at nozzles on topof the gas injection rod. If a decomposition reaction is used, the gas and the bubblesare generated at the whole surface of the injection rod covered with the catalyst. In

Fig. 2.1: Experimental setup for the PET measurements. The tank iscentred between the heads of the PET scanner. The spreading of thetracer distribution can be monitored in an area of about 20x40 cm.


Advances in Fluid Mechanics II 285

some experiments, the tank was subdivided in a riser part and a downcomer partfor enhancement of the fluid circulation rate.

The tracer injector allows a low momentum injection of about 0.8 ml of the tracerliquid. Using this transparent tank, preliminary tests with ink injection tests werecarried out.

In the experiments with air bubbles distilled water was used as liquid phase withadditives of isopropanol and NaCl. NaF (̂ F) was selected as tracer because of itshalf-life of 1.83h and a low maximum positron energy (0.63 MeV) causing a smallpositron range. The positron ranges provoke resolution limitations particularly inlow density media, i.e. at a high gas fraction of the flow. Then a point source ofpositrons causes annihilations in a certain area around the source. Therefore, a nu-clide causing low ranges was chosen. Further, NaF behaves very similar to NaCland is therefore suited to study the spreading of the NaCl in this bubbly flow, i.e.the spreading of fresh NaCl brine in the tank. In the case of I^C^-decomposition,the liquid phase in the tank consists of a HiĈ solution with a Ĥ Ĉ content of35Vol%, The reaction speed was modified by the variation of the temperature ofthe catalyst rod. The same tracer was applied.

The spreading of the tracer was monitored using a double head PET scanner . Thescanner was operated in the list mode, where each registered annihilation event isstored separately, together with so-called time events. From these data, intensitydistributions for any time slices can be calculated by a midplane backprojection.Due to the narrow tank geometry, the reduced resolution of the limited angle PETscanner perpendicular to the midplane and a limited applicable tracer activity, thebackprojection was considered to be the best fitting method for the evaluation ofthe experimental data. Applying corrections for the geometry of the scanner, thetwo-dimensional midplane intensity values are proportional to the tracer concen-tration in the tank. The concentration profile in the 3rd dimension (x-axis, Fig. 2.1)can not be resolved.Fig. 2.2 shows typical normalized tracer concentration distributions. In each of the500 ms time intervals about 50.000 events have been processed. The resulting dis-tributions prove that even activities of only about 5 MBq can supply quantitativeinsight into the spreading process.

Fig. 2.2: Midplane concentrations of the tracer in the bubbly medium(0.5s and 2s after injection)

The dispersion coefficient D for the tracer liquid in the bubbly flow was calculatedfrom the experimental data assuming an isotropic spreading of the concentrationprofile within a diffusion approximation



= D- Vu (2.1)

Thus, D was estimated by fitting the backprojected activity distributions to the so-lution of the two-dimensional diffusion equation in polar coordinates, after a sep-aration of the convective displacement of the tracer distribution from theexperimental data, which is given by

C -

= ' "*( Wt J '


high. In contrast to the experiments of Ohki and Inoue here the gas was injectedthrough 23 holes of 0.3mm diameter in a metal rod or along a platinum coveredrod, respectively. Equation (2.6) is valid for the injection of air into water. The biginfluence of d[ in (2.6) is possibly overestimated. It expresses the influence of thebubble diameters on the dispersion This influence has to be corrected for low gassuperficial velocities below the range investigated in', For the decomposition ex-periments, this parameter has no physical meaning at all, (2.6) can not be applied.

oQ1'o

A pressurized airB decomposition with subdivisionC decomposition without subdivision

' J

superficial velocity ĵ ,̂ cm/s

Fig. 2.3: Dispersion coefficients for several experiments (Table 4.1)

3 Models and Assumptions for CFD Simulation

Calculations of the two-phase flow with a spreading tracer were carried out for se-lected experiments using the computational fluid dynamics code CFX-4̂ . To limitcomputer time requirements, most of the calculations are carried out in 2D geom-etry assuming an infinite length of the measurement cell in z-direction and usingabout 7500 mesh cells. Some calculations are performed in 3D geometry to studyreal geometry effects, where at least about 40.000 cells are required. The Euler-Euler continuum model was applied for the two-phase flow. The flow is assumedto be a dispersed bubbly flow with bubbles of constant diameter. The gas is inject-ed using a volume source near the gas injection tube. The separation of the gas atthe fluid surface is performed modelling a wall with free slip conditions for the liq-uid and arbitrary velocity conditions for the gas phase.

While the mass and momentum balance equations are considered for both phasesseparately, a homogeneous low Reynolds number homogeneous K,e - model wasused considering balance equations for the turbulent energy and its dissipation rateonly for a homogeneous phase mixture. This assumption was made due to the lackof generalized models for source terms and phase exchange rates of K and e of thephases. The 3D calculations were performed using the standard K,£ - model, be-cause the low Reynolds number model needs a finer nodalisation for better resolu-tion of boundary layer effects.

The turbulent dispersion of a scalar quantity O of one of the phases is modelledwithin the frame of the K.e - model using the eddy diffusivity hypothesis

(3.1)



where a is the volumetric phase fraction, p is the density of the correspondingphase, U the phase velocity and S is a source term, while F = û ,./,/ô ^ is theturbulent diffussivity. The relation between turbulent viscosity (î y and F is givenby the turbulent Prandtl number (T̂,,̂. The value Ĝ,,.̂ = 0.1 was used for the de-scription of turbulent dispersion of the gas phase (scalar O in equation 3.1 is unity).

Because the radioactive tracer was assumed not to affect the velocity field, it ispossible to describe it as a scalar connected with the liquid phase. First, two-phaseflow was calculated without tracer until achieving convergence of the steady-statesolution. Then tracer was injected into the flow by switching on a source in a smallvolume at the injection position for a short time (0.1 s). After that, the dispersionof the tracer was observed during an instationary calculation over the measurementtime interval. The value of the turbulent Prandtl number for the tracer diffusionwas varied in the calculations. The best results were achieved using a value of ô ,,y= 0.45 what means an increase of the turbulent diffusivity coefficient in compari-son with the recommendations within the K,e - model by a factor two.

The effective turbulent dispersion coefficient D of the tracer was obtained from thecalculated tracer concentration distribution backprojected to the midplane of thetank after separation of the convective tracer movement in the analogous mannerlike from the measured tracer distributions, i.e. from equation (2.5) with three dif-ferent threshold values.

4 Results of CFD Simulation

Experiments were carried out with injection of pressurized air into water throughsmall holes in a tube or catalytic disintegration of Î Ĉ at the surface of a tubeplaced at the same location. In some experiments, the tank was subdivided in a ris-er part and a downcomer part for enhancement of fluid circulation rate. The fol-lowing selected experiments have been simulated by means of the code CFX-4:

• injection of pressurized air into water, tank without subdivision(experiments Al - A4),

• catalytic disintegration of FÎ Ĉ , tank with subdivision (Bl - B3),

• catalytic disintegration of IĤ Oi, tank without subdivision (Cl - 3).

In Table 4.1 the values of the effective linear tracer movement velocity and the dis-persion coefficient D obtained from the calculations are compared with measuredvalues.

It can be seen from the table, that for some experiments, particularly of group A,the error of the calculated dispersion coefficient value is rather high. This is due tothe physical effect, that in these experiments with relatively high superficial gasvelocities and without subdivision of the tank a part of the tracer is spread to thedowncoming stream. This part moves downwards, while the other part of the tracermoves upwards. In the calculation we can observe the development of two maximain the backprojected tracer concentration distribution (see Fig. 4.1). This causes afictional broadening of the tracer distribution which was used for the determinationof the dispersion coefficient leading to an overestimation of the coefficient. Usingdifferent threshold values, equation (2.5) gives very different values for the disper-sion coefficient, because the backprojected tracer distribution deviates significant-



ly from the homogeneous diffusion curve.

Table 4.1: Comparison between measured and calculated parameters

Experi-ment

Al

A2

A3

A4

Bl

B2

B3

Cl

C2

C3

Measurement values

Jgasincm/s

0.40

0.767

1.192

1.543

0.290

0.423

0.605

0.022

0.151

0.330

Vtracin cm/s

1.82

3.47

4.49

2.99

5.37

3.67

2.92

0.62

-0.67

0.76

D

in cnf/s

6.73±0.85

10.3±0.96

13.4±1.23

7.41±0.90

8.80±1.37

4.49±0.49

3.35±0.43

3.37±0.16

4.45±0.71

4.16±0.66

Calculated values

^tracin cm/s

2.32

2.42

1.98

2.83

8.75

8.71

8.64

0.86

3.63

3.31

D

in crn̂ /s

5.24±3.23

7.46±2.48

14.8±5.66

17.6±6.8

2.66±0.28

3.52±0.33

4.2±2.9

0.24±0.06

1.33±0.34

9.50±5.83

CFX-4 calculation Risingflow

Down-comingflow

Tracerinjection

Gasinjection

0.40

Fig. 4.1: Tracer distribution in the x-y-plane of the tank (right) and axialdistribution projected to the tank midplane (left) for experiment A1



This effect could not be de-tected in the measurements,because the lower part of thetank could not be seen by thedetector array (Fig. 2.1).

A similar effect was found inthe calculated results of ex-periment B3. Here the traceris not able to penetrate intothe downcomer zone becauseof the subdivision of thetank, but it swaps over thetop of the subdividing shield.

Within the range of uncer-tainties caused by the effectdiscussed above, the calcu-lated values of the dispersioncoefficient for the experi-ments of group A are in goodagreement with our experi-mental results and the resultsobtained by Ohki and Inoue^for bubble columns.

In general, the effective val-ues of the turbulent disper-sion coefficient and thetracer movement velocity de-termined in the experimentsdepend rather sensitively onthe local fluid velocity andthe turbulent viscosity distri-bution. Fig. 4.2 shows thesedistributions in the lower partof the tank (around the gasinjection tube up to the tracerinjection location) for the ex-periment Al.

From the comparison be-tween measured and calcu-lated turbulent flowparameters compiled in Ta-ble 4.1 the following conclu-sions can be drawn: Fig. 4.2: Local distribution of effectiveFor the experiments of group viscosity and fluid velocity in the tankA (air injection into water),the relation between measured and calculated values can be interpreted taking into



account the effect of tracer penetration into the area of the downcoming flow. Thiseffect can also explain the stagnation or even reduction of the linear tracer move-ment velocity with increasing gas volumetric flow in the experiments of groups Aand C. It even leads to a negative tracer rising velocity measured in experiment C2.

For low gas flow rates (jĝ < 0.4 cm/s), the measured values of the dispersion co-efficient D are underestimated by the calculations, while the calculated tracer ve-locity values are higher than the measured ones. This is probably caused by theunderestimation of the turbulent dispersion due to the limited applicability of theturbulence model in this region of low Reynolds numbers.

For the experiments of group B (with subdivision between riser and downcomer inthe circulation tank) tracer penetration into the downcomer part is not possible.Furthermore, the natural circulation rate is enhanced by the effect of the tank sub-division. Because of these reasons, the measured and calculated tracer movementvelocities are higher than in the experiments without subdivision of the tank forequal gas superficial velocities. However, the calculated values overestimate themeasured ones. This can possibly be explained by the fact, that in the experimentssignificant oscillating components of the fluid velocity in z-direction were ob-served. This turbulent oscillations increase the effective measured dispersion co-efficient and decrease the transport velocity. Since this velocity component couldnot be modelled in the 2D calculations principally, some 3D calculations were car-ried out. However, the experimentally observed oscillations could not be repro-duced in these calculations.

CFX-4 calculation

0.02Horizontal position x (in m)

Fig. 4.3: Gas volumetric fraction distribution for experiment Al

In general, the agreement between calculated and measured results is much worsefor H2Oi disintegration than for air injection into water. A possible reason for thisfact is the different bubble size spectrum. While the uniform bubble diameter



seems to be a good approximation for the air-water flow, we observe very smallbubble sizes during FT̂ Ĉ generation at the surface of the tube and generation oflarger bubbles by coalescence during the fluid movement. This effect is not takeninto account in the calculation model, but will be a subject of further investiga-tions.

Fig. 4.3 shows the void fraction distribution over the tank width for the same ex-periment at different heights and a global view of the void distribution. It can beseen, that it is rather uniform in the upper part of the tank in spite of the fact, thatwe have a rising fluid flow on the one side of the tank and a downcoming flow atthe other side. The bubbles are spread in the fluid due to turbulent dispersion. Asthe bubble drift velocity in the liquid is higher than the velocity of downcomingfluid, bubbles can rise also in the downcoming stream. This result is in agreementwith observations in the experiment. It was not obtained, if the turbulent Prandtlnumber for turbulent diffusion of the gas phase is not properly chosen. Of course,the velocity of the gas phase is much lower in the downcoming stream than in therising stream.

5 Conclusions

The feasibility of the estimation of turbulent dispersion coefficients in a naturalcirculation two-phase flow using a Positron Emission Tomography (PET) tech-nique has been shown. Selected experiments were simulated by means of the Com-putational Fluid Dynamics code CFX-4. The measured average turbulentdispersion coefficient values are significantly affected by local fluid velocity andturbulent viscosity distributions. However, measured and calculated values of theturbulent dispersion coefficient are in good agreement with literature results forbubble columns in the case of air injection into water. In the case of catalytic de-composition of H2O2, discrepancies occur which are probably caused by the spe-cific bubble size spectrum, what has to be clarified in further investigations.

References

[ 1 ] Jonkers G. et al: Surface catalysis studied by in situ positron emission, Nature63(1992), 355

[2] Bergen E.A. van den et al: Industrial Applications of positron emission com-puted tomography, Nucl.Geophys. Vol. 3 No. 4 (1989), 407-418

[3] Pawelke J., Byars L., Enghardt W. et al: The investigation of different cam-eras for in-beam PET imaging. Phys. Med. Biol. 41 (1996), 279-296

[4] Ohki Y., Inoue H.: Longitudinal mixing of the liquid phase in bubble col-umns. Chem. Eng. Sci. 25 (1970), 1-16

[5] Millies M.: Fluiddynamik, Vermischung und Stoffubergang in Zirkulation-szellen in Blasensaulen. Fortschr.-Ber. VDI Reihe 3 Nr. 307 (1993), 100-108

[6] Hensel, F.: Studies of Liquid-Gaseous Two-Phase Systems by Positron Emit-ting Radiotracers. to be published in Appl. Radiat. Isot. O228 (1998)

[7] CFX-4.1 Users Guide, AEA Technology, Computational Fluid Dynamics Di-vision, Oxfordshire, 1996


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