Investigation of the residence time distribution in a plate heat exchanger with series and parallel arrangements using a non-ideal tracer detection technique
Graphical abstract
Highlights
► Active volume of exchanger was determined and correlated with pass arrangement. ► Combined PFR + CSTR model provided the best fit to RTD data. ► Numerical convolution used to correct signal distortion from tracer detection unit. ► Results useful to flow distribution diagnostics and hydrodynamics modeling.
Introduction
Plate heat exchangers (PHEs) are used in a wide range of industrial applications. This type of heat exchanger consists of a pack of corrugated metal plates. Hot and cold fluids flow in alternate flow channels while heat is exchanged through the thin plates. The corrugated (wavy) surface of the plates is designed to improve turbulence, thus increasing the heat exchange rate. The alignment of the plate orifices forms continuous ducts (manifolds) inside the plate pack that distributes the fluids among the narrow channels. Closed plate orifices can be used to create multipass arrangements, in which passes with a certain number of channels are connected in series. Usually the numbers of passes and channels per pass are the same for hot and for cold fluids (symmetrical flow configuration). A lower number of channels per pass increase the fluid velocity and, consequently, the heat transfer coefficient and the friction factor.
For the design and analysis of PHEs, it is often assumed that the flow is uniformly distributed throughout the channels of a pass and that the plug flow velocity profile develops inside each channel. However, these assumptions are unrealistic in practice. Recent studies investigate the flow distribution inside PHEs experimentally [1], [2] or using computational fluid dynamics (CFD) tools [3], [4], [5], [6]. The study of the PHE hydrodynamics is of interest to improve the plate design and to support the development of better sizing or evaluation methods that takes into account flow distribution issues.
When the fluid undergoes heat-induced changes inside the heat exchanger, the hydrodynamics of the exchanger is also important for process evaluation. For example, in the continuous thermal processing of foods using heat exchangers, the high temperature promotes enzyme inactivation, microorganism destruction and deterioration of quality attributes [7]. The coupling between hydrodynamics, heat transfer and heat-induced kinetics provides a comprehensive model that can be used for design, analysis and optimization purposes [8], [9], [10], [11], [12].
Characterization of the hydrodynamics of a vessel can be conducted by interpretation of its residence time distribution (RTD). The RTD of a vessel (single fluid, constant density, steady state) can be determined by a stimulus response technique by which a tracer is introduced into the inlet stream and its concentration C(t) is recorded at the outlet stream. This technique is widely used for the evaluation of chemical reactors and packed beds. For an instantaneous pulse input signal, the age distribution function (E-curve) is obtained from Equation (1), where C0 is the tracer background concentration, if existent.
The analysis of RTD data is very useful to study the flow pattern inside the vessel, to determine the degree of mixing and to diagnose flow problems such as recirculation, channeling, short-circuiting or stagnation. The departure from the idealized flow patterns of the plug flow and the perfectly mixed flow should be accounted for proper process analysis and design. Mathematical models of RTD such as “axial dispersion”, “tanks-in-series” or “convection model”, can be used to characterize non-ideal flow patterns [13], [14].
In the study of thermal processing of liquid or particulate foods, the determination of the RTD in heat exchangers is quite usual, especially for non-Newtonian and viscous products. For instance, Ditchfield et al. [15] determined the RTD of banana puree in a double-pipe heat exchanger, Mabit et al. [16] studied the RTD of viscous fluids in a scraped-surface heat exchanger and Landfeld et al. [17] determined the RTD of egg yolk in a plate heat exchanger. Moreover, Roetzel and Balzereit [18] determined the axial dispersion coefficient in a PHE through RTD experiments [18]. The results showed a considerable deviation from plug flow and confirmed the need of a dispersion model to better describe the transient behavior of PHEs.
The purpose of this work was to determine the RTD of a PHE in order to evaluate its flow pattern and to study the influence of the pass arrangement on the RTD. The PHE used was part of a laboratory scale pasteurization unit. Due to the small scale of the equipment and the short residence times, a technique was proposed to take into account the influence of the tracer detection unit on the RTD data. The results obtained can be useful for the evaluation of heat-induced changes of a liquid food product after thermal processing.
Section snippets
Residence time distribution models
Ideal flow models such as plug flow and perfectly mixed flow rarely reflect a real system accurately enough. Non-ideal models are usually derived from ideal models for accounting deviations implicit in real systems [19]. When the flow pattern largely deviates from the plug flow, a combined model can be used to characterize the flow in the vessel. A combined model consists of interconnected ideal flow regions. One of its most usual forms comprises three regions: plug flow, mixed flow and dead
Correction for non-ideal tracer detection
The RTD data from a pulse response experiment is affected by the way the tracer is injected and by how it is detected [26]. When measuring short residence times, the efficiency of the injection and detection units is of considerable importance [29]. If it is not possible to produce an instantaneous pulse input signal, a supplementary detection unit has to be placed at the entrance of the process to record the real input signal [30], [31], [32]. Nevertheless, the detection unit can distort the
Plate heat exchanger
The PHE used was that of an FT-43 laboratory plate pasteurizer (Armfield, Hampshire, UK). This equipment was designed for milk pasteurization with a nominal capacity of 20 L/h, into which the product is fed by a 7017-20 peristaltic pump (Masterflex, Vernon Hills, USA). The FT-43 PHE has 12 × 8 cm stainless steel flat plates with silicon gaskets (see Fig. 3) and the plate main dimensions are presented in Table 1. The equivalent channel diameter is De = 2 b/Φ, where Φ is the plate area
Analysis of results and discussion
Fig. 4 presents an example of RTD curve fitting for a given experimental run. Each E × t plot provides the model curve, the convoluted curve and the experimental points. The clear difference between the model curve and the convoluted curve shows that the signal distortion promoted by the detection unit is significant. The model curves of the combined and convection models are similar except for the curvature of the decay part. The first one has an exp(–γt) shape while the last one has a t−γ
Conclusions
The RTD of a small scale PHE with flat plates was studied for series and parallel arrangements with a variable number of channels. This study was useful for diagnosing the equipment flow since it was possible to determine the contribution of the plug flow, mixed flow and dead space regions in the equipment hydrodynamics. This type of study could be applied to compare the performance of different plate corrugation patterns.
The combined model and the generalized convection model better
Acknowledgements
The authors would like to acknowledge the financial support from FAPESP (The State of São Paulo Research Foundation), CAPES (Coordination for the Improvement of Higher Education Personnel) and AEP (Association of Polytechnic Engineers).
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