Radioactive Particle
Tracking technique for velocity measurements in coiled geometries: Design of
experiments and experimental flow patterns

Loveleen Sharma, K.
D. P. Nigamand Shantanu Roy^*

Department of
Chemical Engineering, Indian Institute of Technology-Delhi, New Delhi 110016,
India

(*roys@chemical.iitd.ac.in)

Keywords:
Dean vortices; Radioactive Particle Tracking; RPT; Resolution;
Sensitivity

Introduction

Flow
of incompressible fluids in coiled pipes are known to develop secondary flow
patterns, owing to centrifugal forces experienced by the fluid. This kind of
flow behavior progresses in a double vortex circulating pattern in the cross
section (as shown schematically in Figure 1). This pattern was first reported
through theoretical considerations by Dean [1-2]. Such patterns are of great
importance from hydrodynamics point of view, as they cause significant
modification of the boundary layer structure and turbulent transition and hence
affect the use of coiled tubes as laminar mixers or mixer-reactor. Therefore,
the examination of the vortex formation and its structural change with increasing
mean flow velocity or Reynolds numbers (N_Re) is in order.

In
the coiled geometries, there have been very few experimental observations for
the vortex flow pattern reported so far [3-5]. Further, these studies have been
done only for a limited range of flow conditions and in single phase. The
motivation for this contribution is to map the flow field produced by a double
vortex circulating pattern using the non-invasive Radioactive Particle Tracking
(RPT) technique. The principle of the RPT involves tracking the motion of
single tracer particle (a highly penetrative γ-ray source), which mimics
the fluid under interrogation. The unbiased motion of tracer particle in the
system is assessed by the strategically arranged array of NaI(Tl) scintillation
detectors. By inverse image processing from the photon counts time series, the Lagrangian
motion time series is obtained. This results in ensemble averaged flow fields [6].

Figure
1. Formation of Dean vortices for coiled flow (schematic).

RPT technique is now a
time-tested technique for non-invasive flow monitoring. However, thus far all
implementations of RPT have been in either rectangular or cylindrical process
vessels (such as bubble columns and fluidized beds) but never in coiled
geometries (such as that shown in Figure 1). It is noteworthy that RPT is not
an ?off-the-shelf? technique, and every implementation in a new geometry
requires careful planning and implementation, which in many cases presents
issues which are specific to that system. Thus, there are considerable
challenges to implementation of this technique in such complex geometries, and
we believe that its successful implementation in coiled geometries would open
up pathways for further work in even more complex domains.

This contribution consists of two
parts. In the first part, the issues related to implementation of the RPT
technique in coiled geometries is discussed. Since all past implementations of
RPT have been in simple cylindrical or rectangular geometries, this
contribution is unique since it discusses, based on theoretical considerations,
various experimental issues related to the judicious use of hardware and the
theoretical limits of resolution and sensitivity that one can obtain from the
experimentation.

The second part of this
contribution relates to the actual implementation of RPT in coils, and the
results of velocity field and other flow variables obtained as a result of that
implementation. Further, comparative studies of single and multiphase
(gas-liquid) flow are presented. While some past work is there in literature on
the circulation patterns in coiled tubes in single phase flow, absolutely no
information is available on multiphase flow. In that respect as well, this
contribution in unique.

Design
of RPT Experiments in Coiled Geometries

To design the optimal detector
configuration this step is performed a priori to the actual experimental
implementation. Model based on Monte-Carlo algorithms is used to estimate the
photon counts emitted from γ-ray source by NaI(Tl) scintillation
detector [7-8]. The photon counts (C) emitted by γ-ray source are
recorded by a detector using the following functional relationship [6, 8]:

By using the Monte-Carlo
algorithm and Equation (1), counts are generated as would be recorded in each
detector location for various source locations inside the geometry. From the
counts received by the detector a position count matrix is generated, on the
basis of which estimation of the two performance parameters namely resolution
and sensitivity are calculated. Due to dimensional complexities involved in
coiled geometries, the performance parameters for each plane are expressed in
2-D or 3-D. The mathematical formulation of the resolution and sensitivity for
2-D (y, z) and 3-D (x, y, z) motion are expressed by using Equations
(2a, 2b) and (3a, 3b) respectively [9]. The detector configuration is
finalised by means of the best obtained results for the resolution and
sensitivity.   

Through theoretical modelling and
simulation, different detector arrangements are tested on the coiled geometry.
The two performance
indicators namely resolution and sensitivity are evaluated for the planes at different angular
positions as shown in Figure 2. Typical results of the detectors configuration
used in the present study are shown in Figures 3(a) and 3(b).

Figure
2. Planes under evaluation at different angular locations.

Figure 3. (a) Sensitivity for
planes at different angular locations
and (b) Resolution for
planes at different angular locations.

Implementation
of RPT Experiments in Coiled Geometries

The RPT experiments are conducted
in two steps: namely calibration and experiment. In calibration step tracer
particle (hydrodynamically similar to the phase under interrogation) is placed
at various known locations in the geometry and the photon counts generated by this
tracer particle are recorded by array of NaI(Tl) scintillation detectors
strategically placed all around the geometry. In this manner, a distance?photon
count map is generated for each detector. During the experiment, the tracer
particle moves freely inside the geometry to fetch-up the required information
and using the calibration data (obtained in first step), the particle position
as a function of time is obtained.

The schematic of the RPT
experimental configuration is shown in Figure 4(a), where eight NaI(Tl) scintillation
detectors are used. In this arrangement, two detectors are placed at central
axis (facing each other) and other six distributed into two different staggered
planes (three on each plane). Using this detector arrangement, calibration is
performed by placing the tracer on the cylindrical disc, which is then managed
to move throughout the coiled geometry made from Teflon^® (tube inside diameter (d_t)
= 65 mm, coil diameter (d_c) = 494 mm and curvature ratios (λ
= d_c / d_t = 7.6)) as shown in Figure 4(b). For
each set of flow conditions, experiments
for the non-invasive measurements will be conducted.  

Figure 4. (a) Schematic of CARPT experimental configuration and
(b) Schematic of the calibration disc.

The final submission will discuss
the experimental findings for the flow field produced by Dean vortices and
describes the structural changes of vortices with Dean number (N_De= N_Re/ (λ)^1/2) to
present the effective operational zone of coiled geometries with stabilized
flow (laminar flow). In
addition, the residence time distribution and overall trajectory length
distribution for the fluid will be presented. 

References

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8.       
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9.       
Roy S,
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