Radiotracer applications for the analysis of complex flow structure in industrial apparatuses

Nuclear Instruments and Methods in Physics Research B 213 (2004) 339–347

www.elsevier.com/locate/nimb

Radiotracer applications for the analysis of complexflow structure in industrial apparatuses

Ji�rr�ıı Th�yyn *, Rudolf �ZZitn�yyCzech Technical University of Prague, Technicka 4, 166 07 Prague, Czech Republic

Abstract

Complex flow analysis by gamma-radiotracer utilizes signals of detectors situated around the apparatus. In this case

the problem of the relation between detected values and radiotracer concentration has to be solved. Analytical relation

was already published for collimated scintillation detector (with several simplifying assumptions) which was used for

analysis of parallel flows assuming uniform concentration in both streams. The suggested algorithms were used in

parametrical analysis of residence time distribution (RTD) model by non-linear regression. For a general distribution of

the tracer concentration another algorithms were suggested and tested by using MC code as well by experiments with

point radioactive source. These algorithms are successfully used in verification of complex flow visualisation by

computer fluid dynamic method. While the verification on the basis of measurement RTD is sufficient for simple flow

structure, the verification on the basis of local responses should be used in the more complex flow structure. Application

of suggested algorithms in the verification procedure is demonstrated on results of analysis of ‘‘parallel’’ flow realized

on a test rig of the ohmic heater.

� 2003 Elsevier B.V. All rights reserved.

Keywords: Computer fluid dynamic (CFD); Residence time distribution (RTD); Radiotracer

1. Introduction

Stimulus response techniques with gamma rad-

iotracer is commonly used for evaluation of flow

characteristic as is the residence time distribution(RTD) function. This method gives information on

the measured system by evaluating concentration

of a tracer compound, which is added as a stimulus

at the system inlet. A stimulus as well as a response

is measured by collimated scintillation detectors

that are situated at the inlet and at the outlet tubes

* Corresponding author.

E-mail addresses: [email protected] (J. Th�yyn), zitny@fsid.

cvut.cz (R. �ZZitn�yy).

0168-583X/$ - see front matter � 2003 Elsevier B.V. All rights reser

doi:10.1016/S0168-583X(03)01648-3

of material flow. While the mean residence or ho-

mogenisation time, determination of so called dead

volume, stagnancy or bypassing and mixing char-

acteristic can be evaluated from the RTD moments

(first central or variance), description of the flowstructure is based upon modelling. Properly de-

signed net of ideally mixed and ideally displace-

ment model (i.e. the plug flow) units leads up to a

set of differential or algebraic equations which are

solved by special software on PC (see [1] for ex-

ample). The applications of differential ordinary

equations as the flow structure models have a great

advantage in their flexibility. The parameters asbackground, different volumes of basic units, or

detector total efficiency can be evaluated. Unfor-

tunately the results obtained from the detector

ved.

mail to: [email protected]

340 J. Th�yyn, R. �ZZitn�yy / Nucl. Instr. and Meth. in Phys. Res. B 213 (2004) 339–347

which measure the response (tracer concentration

at the outlet) cannot offer unambiguous model of

RTD for complex flow. In this case the response

measured by other detector which is situated at thewall or inside of apparatus has to be used in the

procedure of evaluation. Simple and useful multi-

ple detectors technique can be used only in the case,

when a tracer concentration non-uniformity in the

cross-section of the main flow can be neglected.

This assumption is fulfilled when e.g. the model as

series of ideally mixed regions can be applied.

However the existence of parallel streams withdifferent concentration and velocities of a tracer,

complicates interpretation of data from detector

located at the wall which can ‘‘see’’ only part of a

cross-section and special attention has to be paid to

the relation between detector signal and tracer

concentration. The same situation is also in the case

when stimulus response method with radiotracers

are used for the verification of numerical methodsof computer fluid dynamic (CFD). The shape, po-

sition of radioactive cloud and distribution of tra-

cer inside of cloud which is seen by collimated

‘‘wall’’ detector is changing during the experiment

and this fact has to be taken into account in sug-

gestion of the algorithm of detection system and in

its application during data processing.

While the RTD lumped parameter models arebased on the mass balance, the basis of CFD

methods is also balance of momentum and energy.

As CFD describes processes in terms of spatially

localized flow units (control volumes) intercon-

nected by mass, momentum and heat streams, the

results are more precise and have greater infor-

mation content. However this approach needs no

additional information only in the case of laminarone phase flow. Semi-empirical model of momen-

tum, heat and mass transfer have to be used in

most of applications concerning turbulent or

multiphase flows.

Several models are offered by commercial CFD

software and their choice can influence the results.

For example the different ratio of maximal and

mean velocities of flow in tube for different Renumber calculated by different models of turbulent

flows offered by FLUENT are presented in

monograph [2] p. 119. In this case the theoretical

dependence is known and so it is easy to decide

which model is the best. Generally the proper

choice of the model have to be done on the basis of

experience or on the basis of experimental verifi-

cation of results. Application of radioactive tracersin measuring RTD functions offers the informa-

tion about flow structure, which can be used in the

verification procedure.

There are practically two possibilities how to

receive RTD from the velocity field evaluated by

CFD: (1) using particle tracking method or (2)

transient analysis of concentration (or tempera-

ture) spreading.The first standard procedure cannot be gener-

ally recommended because it is difficult to avoid

particle trapping in recycle regions or in turbulent

whirls; the resulting integral distribution function

of RTD is distorted considerably especially for

long times t.The second one is probably better, though more

time consuming procedure, which is based uponmodelling of transient temperature/concentration

field, setting a short pulse at the inlet. The verifi-

cation procedure requires beside numerical evalu-

ation of RTD also additional special CFD data

treatment, which enable to evaluate the ‘‘local’’

responses.

When the proper CFD model is known the

CFD evaluation can be use for prediction ofchange of flow structure for different values of

flowrate, viscosity, etc., presented by dimension-

less number Re. This important advantage of CFD

was used in analysis of flow of gas in chamber with

two baffles [3,2].

2. Multiple detector technique

Multiple detector technique concentrates upon

utilisation signals from the detectors situated in

different positions around an apparatus. Special

models are suggested for simultaneous evaluation

of these local responses together with the input/

output response for the model parameter identi-

fication by non-linear regression. A basic core-annulus flow model suitable for multiple detector

response evaluation have been already presented

[2]. The model is characterized by two parallel

streams with backmixing in the core region and

Fig. 1. (a) Core-annulus model and (b) input/output response (R) and local response (A).

J. Th�yyn, R. �ZZitn�yy / Nucl. Instr. and Meth. in Phys. Res. B 213 (2004) 339–347 341

crossmixing between the core and wall regions

(Fig. 1(a)). The model can be optionally used for

description of flow in a riser, which is important

part of fluidized catalytic cracking unit. Numerical

experiments confirm that model responses of wall

detectors are more sensitive to cross mixing pa-rameter and less sensitive to backmixing.

It should be emphasized, that the different

sensitivity of different responses upon specific pa-

rameter is desirable, because it improves reliability

of identification. Another important conclusion is

that if only one detector is used, it is difficult to

distinguish between the model with two parallel

streams or the model with recycle (the both modelusually predict similar total responses) and at least

two detectors are required for reliable selection of

suitable model. This situation is demonstrated in

Fig. 1(b). The ‘‘wrong’’ parallel flow model can be

excluded only when the response of the wall de-

tector A is taken into consideration.

3. Models of detection system

A simple model of detection system was im-

plemented on the core annulus model mentioned

above. The model assumes that collimated detec-

tor is oriented perpendicular to the flow axis at a

symmetry plane. A very simple collimation and

other simplifications about constant effective linear

absorption coefficient and negligible effect of ra-

diation scattering enable to received the relationbetween detected values and tracer concentrations

even in an analytical form [2,4].

Similar model and similar analysis of collimator

was applied to data, obtained by multiple detector

system on a fluidized catalytic cracking unit [5].

The flow model of annulus-core flow was in this

case even simpler. Two parallel series of mixed

cells without backmixing, however algorithm ofdetectors depends upon a system parameter (dia-

meter of the core region) and therefore the detec-

tor algorithm must be integrated into the flow

model definition (for more details see [2]).

Simplifications applied in the parallel flow

cannot be used in processing CFD data that are

characterized by quite general spatial distribution

of tracer concentration and spatial distribution ofattenuation. It is difficult to solve the problem in

general way taking into account all phenomena

associated with radiation properties. Again several

assumptions (which can be accepted as they can be


fulfilled with some limits in practical experiments)

simplify the solution. Two algorithms of colli-

mated detector are suggested for the verification of

results by numerical analysis of flow by CFDmethods. They should be as much as possible re-

alistic but also simple as they will be used several

Table 1

times in great quantity of nodal points which are

used for description of flow by numerical methods

(by finite elements or by control volume).

The algorithm of view factor and algorithm ofsingle beam absorption are suitable for evaluation

of actual or numerical experiments (see Table 1).


Perfect absorption of radiation in detector is sup-

posed in the both. While the first one is more

suitable for narrow beam and tracer with ‘‘soft’’

gamma radiation, the second one is for ‘‘greater’’beam or ‘‘hard’’ gamma radiation.

The algorithms were tested on the basis of the

point radioactive source responses (PSR) of de-

tector in the water. Experimental responses to the

‘‘point’’ source (99mTc (140 keV or 137Cs (662 keV))

which was situated in the water, were evaluated for

different distance from the frontal area of a lead

block with the collimation hole having diameter of

Fig. 2. (a) The testing of algorithms with 99mTc a

1.4 cm and depth 3 cm, with scintillation crystal

(NaI(Tl)) with diameter 5 cm and height of 3 cm.

Monte Carlo code (which was implemented in

program INSPECT, based upon accelerated al-gorithm suggested by Tola [6]) were also used for

evaluation PSR under the same conditions. The

example of testing – the diagram of decreased

detected values in % are shown in Fig. 2(a) for

experiments with 99mTc and in Fig. 2(b) for ex-

periment with 137Cs. From these diagram it follows

that the both algorithms are acceptable and more

accurate – view factor is better for application of

nd (b) the testing of algorithms with 137Cs.


tracer with energy about 100 keV while the single

ray absorption algorithms can be used for energy

about 600 keV. Testing with another tracers is on

schedule.

Fig. 3. PSR experiment.

Fig. 4. Dðx; y; zÞ interpolation.

4. Verification of CFD results by stimulus response

The verification of CFD by stimulus response

supposes simulation of tracer injection and calcu-

lations of detector response (at outlet and from the

detector situated around an apparatus). While theevaluation of RTD is possible to receive directly

from commercial software (Fluent e.g.) as a mass

average of tracer at the cross-section of outlet

tube, the local response must be evaluated by

Jðt; x; y; zÞ ¼Z Z Z

VDðx; y; zÞcðt; x; y; zÞdxdy dz;

ð1aÞ

where cðt; x; y; zÞ is the distribution of tracer con-

centration obtained from CFD calculations and

Dðx; y; zÞ is transfer function which can be calcu-

lated e.g. by presented algorithms of collimated

detectors. Application of algorithms mentionedabove suppose measurement in ‘‘energetic win-

dows’’ and also geometrically simple configuration

of volume followed by scintillation detectors is

assumed. When the system is geometrically com-

plicated, (with inner baffles e.g.) Dðx; y; zÞ can be

received as a response of collimated detector to the

‘‘point’’ radioactive source (PSR) which is situated

inside the apparatus. PSR can be realized directlyby experiment (if possible), or by numerical sim-

ulation by more complicated software MCNP4C

again by using MC code.

Let us suppose that a volume of apparatus is

divided into finite elements Xe of tetra or hexahe-

dron whose vertexes are nodes xi, yi, zi. The resultsof CFD are concentrations in nodes ci in time

t1; t2 . . . The tracer concentration monitored bycollimated detectors is

JðtÞ ¼ZXcðt; x; y; zÞDðx; y; zÞdX

¼Xe

ZXe

cðt; x; y; zÞDðx; y; zÞdX; ð1bÞ

where Dðx; y; zÞ is the response of collimated de-

tector to tracer with unit concentration in unit

volume, which is situated in x; y; z (PSR with unitactivity).

Results calculated by a CFD program (FLU-

ENT, CFX, COSMOS) have the form of ASCII

files from which the relevant information must be

extracted e.g. in the following format of neutral

file:

(1) Coordinates of nodal points in Cartesian coor-dinate system ðx; y; zÞ. Result is a file, where

each row corresponds to one nodal point:

i; x; y; z.(2) Connectivity matrix. Group of points forming

element or control volume. It is assumed that

the element is a ‘‘brick’’ fully determined by

eight vertices. Result is a file containing nine

integer numbers in each row: ie, i1, i2, i3, i4,i5, i6, i7, i8, where ie is index of element and ijare indices of nodal points (vertices).

Fig. 5. Heater with collimation of detectors.

Table 2

CFD models Q (ml/s) TMean (s)

Laminar (HD) 80 49.91

Turbulent-RNG (HD) 80 49.8

Experiment 79.3 49.87

Where Q is volume flowrate, Tmean – mean and r2 variance of RTD.

Fig. 6. RTD calculated by CFD model for turbulent flow (RNG)


(3) Calculated vector of concentrations at a se-

lected time step. Results are files (each file for

one time step) containing pairs ij, cj.

These data are used for calculation of detector

responses and different techniques can be used in

evaluation of integral (1b). One of them is ‘‘Car-

tesian boxing’’ suggested by �ZZitny [7] and pre-

sented as well in [2] or by integration in finite

elements of CFD model based upon application of

classical isoparametric functions [8].The experiments using PSR inside the appara-

tus in still (without flow) (see Fig. 3) yields infor-

mation about the actual collimated detector

characteristic and information about absorption

and reflection characteristic of the media and in-

ternals inside the vessel.

By monitoring count rate of the collimated de-

tector at different positions of radiation source, theresponse function Dðx; y; zÞ, corresponding to unit

activity at a general point x; y; z can be obtained.

For interpolation of n measured points in three

dimensional space (m ¼ 3) can be used relation

(see Fig. 4):

r2 [1] RjYi � Yexpj=n (l/s)

0.04 0.0021

0.07 0.0008

0.09

and RTD from tracer experiment by conductivity method.


Dðx; y; zÞ ¼

Pnk¼1

Dðxk; yk; zkÞlmkPn

k¼1

1

lmk

; ð2Þ

where lk is distance of the point x; y; z from kthmeasured position.

PSR method is used in the still conditions of the

system, with the same detector and with the same

gamma beam collimation as in tracer experiment.

This approach is suggested for the case whenconditions for application of presented view factor

or single ray algorithms cannot be fulfilled (when

Fig. 7. (a) Local responses calculated with RNG k–e model with vie

perimental response by radiotracer followed by focused detector D4 an

radiotracer experiment followed by focused detectors in position D2.

observed volume contains complicated arrange-

ment of baffles e.g. or when the shielding of the

detector is not sufficient).

5. Tracer experiments with Tc and with KCl

Numerical modelling and experiments were

tested on the model of continuous direct ohmic

heater(volume¼ 4 · 10�3 m3) which is shown in

Fig. 5. Liquid flows towards the bottom in lateral

channels (¼ preheaters) where the flow is reversedand liquid flows upwards through rectangular

w factor (vf) and single ray (sr) as detector algorithms and ex-

d (b) local response evaluated by RNG k–emodel with PSR and


heating channel between planar electrodes. Con-

ductivity method (KCl) and radiotracer method

(99mTc) were used simultaneously in the experi-

ments without heating. The stimulus as well theresponse of the system was followed by conduc-

tivity probes, while the local responses were fol-

lowed by collimated scintillation detectors.

Positions of scintillation detectors are shown in

Fig. 5.

The comparison of the results of numerical so-

lution by commercial software Fluent was done

for experiment with water flow about 80 ml/s. Renumber in the output – outlet tube was about Re¼3 · 103, while the Re calculated for lateral and

central channels were Rel ¼ 1.6· 103 and Rec ¼ 1.3·103. The results received by laminar and turbulent

RNG model as mean and variance of residence

time distribution are presented in Table 2 together

with experimental values. Mesh size in the both

cases was about 8.3 · 105 of nodes with 7.9 · 105hexagonal elements. Closed to reality seems to be

turbulent model, the differences are presented in

Fig. 6.

As an example of the local responses are pre-

sented the results done with 99mTc as a radioac-

tive tracer. The responses were obtained e.g. by

focused collimated scintillation detectors D2 and

D4 (with 8 and 4 wholes with diameter about5 · 10�3 m located on the periphery of two circles

with diameter 15 · 10�3 m and 5 · 10�3 m). The

distance of the focus was 85 · 10�3 m. As RNG

k–e turbulent model for turbulent flow shows

better results at outlet, experimental local re-

sponses were than compared only with this

model. The examples of the results of applica-

tions of algorithms of view factor and single ray

for D4 are presented in Fig. 7(a). The results

evaluated by RNG k–e turbulent model with using

results by PSR are very closed to the results re-

ceived by the algorithm of view factor. An ex-ample of the PSR result for D2 is shown on the

next Fig. 7(b). Presented results demonstrate that

suggested way of verification results of CFD by

experimental stimulus response methods with us-

ing radiotracer is acceptable.

Acknowledgements

The research was realized in the frame of Co-

ordinated Research Project supported by Inter-

national Atomic Energy Agency.

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Documents

Radiotracer applications for the analysis of complex flow structure in industrial apparatuses