The lock-in technique applied to heat exchangers: A semi-analytical approach and its application to fouling detection

Abstract

One of the current methods to detect fouling in heat exchangers is based on the analysis of the evolution of the effectiveness over time. The present results show that, using this kind of analysis, a 6% decrease of the overall heat transfer coefficient cannot be detected when measurement noise (±0.5 °C) is taken into account. On the contrary, the present study shows that the analysis of the evolution of the modulus of the variable computed using the lock-in technique is simple and leads to a very sensitive detection when it is well tuned. In this study, the excitation needed for the application of the lock-in technique is a periodical variation of the inlet temperature of one fluid. It is shown that a 4 million sample sliding observation window is necessary to obtain an accurate value of the modulus. This corresponds to a time span from a few hours up to 5 days, depending on the sampling period. The latter can then be adapted to the expected fouling rate. One important finding is that, in order to detect fouling, the excitation has to be done on the side where fouling is expected.

Introduction

The lock-in technique, also called the synchronous detection technique, is a very powerful method for analyzing time series. It is used in various fields such as fluid mechanics [1], [2], bio-mechanics [3], thermography [4]. The main motivation for using this technique is the fact that the synchronous technique provides improved signal-to-noise ratio [5] and high noise rejection characteristics [6]. This is linked to a very high sensitivity [7], [8], [9]. It must be noted that these characteristics are balanced by a trade-off between the signal-to-noise ratio and the corresponding measurement time [10]. It is also used for filtering time series [11], [12]. It has been shown [13] that the lock-in technique performs better than the Local Narrow-Band Signal decomposition although there is a time lag.

Apart from a specific application where two angular frequencies are used to extract two quantities simultaneously [14], the standard application aims at determining the real and imaginary parts of a complex number [15]. The computation of this complex number is not complicated, as mentioned in [6]. But it must be noted that the excitation angular frequency must be adapted to the phenomenon under supervision [3], [7], and must be chosen so that it avoids the “blind frequencies” [16]. This adaptation can be carried out by trial and error, but it is more convenient to use an analytical approach as presented in [17].

Concerning thermal systems, the lock-in technique can be used in the detection of drifts such as fouling. In the increasing complexity order, previous studies have shown the interest of the lock-in technique. Firstly, an analytical approach is presented in [18] for lumped systems; i.e. only time dependent. Secondly, a comparison of theoretical and experimental results is presented in [19] for electrical heaters; i.e. dependent on time and on one spatial function. In the latter, it is shown that there is a zone of interest for the angular frequency used to excite the system. After a first test presented in [21], the present study shows that a simple procedure can be used for heat exchangers (i.e. dependent on time and on two spatial functions) to predict the evolution of what is computed by the lock-in technique versus the angular frequency so that the zone of interest can be easily determined.