Simulation of a radiotracer experiment by flow and detection-chain modelling: a first step towards better interpretation

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Abstract

The injection of a γ-emitting tracer in backward-facing step flow was modelled. Flow and concentration fields were calculated by CFD and detector responses by a Monte-Carlo code. The objective was to show the influence of the radiotracer energy on the detector response, so as to interpret better data from radiotracer experiments. The radiotracer selection is important in obtaining reliable results, each specific case requiring careful analysis of the experimental data. However, more work is still required to achieve the prescribed goal aimed at.

Introduction

The concept of residence time distribution (RTD) is a useful and well-established one for the characterisation of flow systems (Levenspiel, 1999; Villermaux, 1985; Schweich, 2001). Among the various available tracers, γ-emitting radioisotopes offer several advantages (specificity, low detection limit, “see-through” capability) and the necessary tools for RTD measurement and analysis by radiotracers are now available (IAEA, 1990, Thyn et al., 2000; Thyn and Zitny, 2002). Standard practice requires one detector at the inlet of the system and one at the outlet (Fig. 1, upper part). For a simple flow in the inlet and outlet channels of the system, usually one-dimensional pipe flow, the signals from the detectors are quite unambiguous. However, the system appears truly like a “black box”, with the unhappy consequence that several different flow patterns may account for the same resulting RTD curve.

The radiotracer practitioner is therefore often tempted to locate a few more detectors on the system itself, in the hope of collecting useful information on the local behaviour of the fluids (Thyn et al., 2000). And at this point he is apt to run into another sort of trouble: one feels that the signal from these detectors bears some relation with flow pattern and fluid velocity, but this relationship is often not a simple one, especially in the case of non-one-dimensional flow. This is all the more true since γ measurement is not local, but rather volume-averaged with a complicated distance-dependent weighting function. For example, how should the signal be interpreted if there is steep flow gradient, or even flow reversal, within the detection volume (Fig. 1, lower part)? Obviously, the answer also depends on the properties of the radiotracer: a low-energy tracer will mainly “see” the reverse flow, while at higher energy it may be possible to probe also into the main flow, as illustrated in Thyn et al. (2000).

The objective of this study is to explore the relationship between the characteristics of flow and measurements with radiotracers, using jointly computational fluid dynamics (CFD) and detection-chain modelling. The basic idea is to choose a reasonably complex flow configuration, simulate both flow field and development of the tracer plume with CFD, and couple the results with a model for the detector so as to predict the count rate as a function of time and detector position. The idea is not a novel one and has been expounded for instance by Linden et al. (1998) for the interpretation of flow-rate measurements in pipes by pulsed-neutron activation. In this manner, we hope to obtain information on the link between local flow conditions and signals from the radiotracer, and also on the influence of the parameters of the radiotracer experiment (tracer energy, detector collimation, etc.) on the measured radiotracer response. This is considered as a first step towards the more ambitious goal of solving the “inverse problem”, meaning the determination of the flow field from the detector responses (Fig. 2) as attempted in Linden et al. (1998) in their particular case.

Section snippets

Methods

The basic relationship that allows the calculation of count rate from a detector can be established in the following way: suppose a point source of unit activity is set at some point M(x,y,z) within a system (Fig. 3). Let T(x,y,z) be the count rate generated in the detector by the source (in cps/Bq) when it is located at M(x,y,z). The T(x,y,z) function is known as the “Point Source Response” (PSR—see for example Thyn and Zitny, 2004). A given radioactive tracer with the same characteristics as

Flow field

The flow domain is shown in Fig. 5. Uniform unit velocity is imposed at the inlet, uniform zero pressure at the outlet. The length of the domain is large enough to allow development and reattachment of the recirculation. Once convergence of the flow calculation is attained, a uniform unit concentration is imposed at the inlet, for a duration of one time unit. The injected tracer is supposed to be passive, meaning that it does not affect the velocity field in the fluid.

The mesh comprises 1000×50

Conclusions and perspectives

Our results lead to the following conclusions:

  • From a general point of view, we have verified that the signal created by a γ-emitting radiotracer in a non-one-dimensional flow depends on the energy emitted by the radiotracer. Observed trends correspond to expectations: a detector will “see” deeper into the flow in the case of a higher-energy radiotracer.

  • A consequence of this observation is that much caution should be exerted when interpreting such a signal with the usual tools of RTD analysis.

References (12)

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