Numerical and experimental study of the heat transfer process in a double pipe heat exchanger with inner corrugated tubes
Introduction
One of the most commonly used heat exchangers in engineering processes is the double-pipe heat exchanger (). These devices are used in a wide range of industrial applications, such as the food industry [1,2], where they are mainly used for relatively low flow rate applications [3]. In general, are characterised by their simplicity and cost effectiveness, but require the use of techniques to reduce the energy consumption in industrial applications. To enhance heat transfer performance in these devices, several methods [4] can contribute to improving the convective heat transfer coefficient, based on the insertion of elements in the flow or the surface modification of tubes. In this regard, the increase in the convective coefficient can result in an increase in the pressure drop, an aspect that involves a higher requirement of pumping power, increasing the energy costs, depending on the type of pump used. Hence, it is important to carry out research aimed at improving the efficiency of heat transfer with the minimum possible pressure drop.
One method to improve heat transfer performance is the use of passive geometrical devices [5], which promotes mixing of fluid due to swirl flow induction at the secondary flow region. Several studies have focused on experimental analysis of using different passive methods [6,7], based on the use of perforated circular-rings [8], discontinuous helical turbulators [9], vortex generators and helical fins [10], twisted tape inserts [11], coil-wire inserts [12], or helical and coiled circular wires [13,14]. One of the most common tools to analyse heat exchanger performance is the use of computational fluid dynamic techniques (), which can be considered a complementary activity to experimental studies as well as a prior step to the design of heat exchangers. In this regard, numerical studies have also been applied to , using different passive geometrical devices [[15], [16], [17]], based on the use of axial vanes [18], continuous helical baffles [3], a bundle of wing shaped tubes with external fins [19] or analysis in an annulus formed by an inner twisted square duct [20].
One of the most extended passive methods in is the use of corrugated tubes, because the corrugation increases the wet perimeter maintaining a constant cross section area, consequently increasing the convective surface area [21,22]. This method is especially common in the food industry when using high viscosity fluids working in laminar regime, promoting laminar flow or transition flow in a smooth tube into turbulent flow, improving heat transfer performance but also increasing pressure drop. For turbulent flow, corrugation is also used to increase heat transfer [23,24], because it contributes to disturbing the thermal boundary layer [25].
Several studies have experimentally analysed the influence of corrugated tubes in DPHx [26]. [27] studied heat transfer for single phase in the annuli with corrugated inner tubes with parallel flow. [28] analysed the effect of corrugation pitch on the condensation heat transfer and pressure drop of the refrigerant R134a. They reported that the heat transfer coefficient and frictional pressure drop of the corrugated tube were approximately 50%, and 70% higher than the smooth tube. [23] experimentally analysed the effect of pitch and height on the heat transfer enhancement in a concentric tube heat exchanger, reporting that the friction factor and Nusselt number were 2 and 3 times higher than the smooth pipe, respectively. [29] performed an experimental study focused on heat transfer and pressure drop in a . They reported that the use of corrugated tube as the inner tube increased the Nusselt number about to , and the friction factor between to .
Regarding the use of corrugated tubes, many studies have performed numerical simulations for spirally corrugated tubes but only using a single tube as the computational domain [[30], [31], [32], [33], [34], [35], [36], [37]]. However, few numerical studies have analysed the effect of inner corrugated tubes in [38]. [39] studied flow and heat transfer characteristics in outward convex transverse corrugated tubes (20 mm inner diameter and 35 mm external diameter) in turbulent regime (Reynolds number ranging from to ), in three cases with a fixed corrugation height (H) of 2 mm and helical pitch (P) in a range of 20 mm–60 mm, and five cases using a fixed P of 40 mm and H varying in a range of 1 mm–3 mm. In their study, a 2-D axisymmetric model, with a 20-cm-long section cut from the entire heat exchanger, was used to simplify the computational domain, while no experimental setup was used to validate the numerical simulation. They concluded that the use of asymmetric corrugated tubes showed overall heat transfer performance about to higher than with symmetric corrugated tubes. [40] developed a numerical investigation for a with the wall of the inner pipe helically corrugated in a Reynolds number ranging from 420 to 2000 (laminar regime), to analyse heat transfer and pressure drop at parallel flow and counter flow. The authors used a 3-D numerical model, considering a reduced length of the computational domain (40 cm). They only modified the P, using three different twists, and maintaining H and diameter (D) constant. To validate their results, the authors compared the numerical simulations of the helically corrugated tubes with experimental studies of other geometries, such as helical pipes, due to the lack of a suitable experimental setup. They concluded that for the inner tube, the pressure drop for the corrugated wall heat exchanger was approximately two times higher than the smooth pipe. [41] performed a numerical simulation to study the effect of a modified corrugated on heat transfer enhancement. The authors implemented a numerical model using semi-elliptical corrugations on the inner tube of the . The numerical simulation was performed with a 3-D numerical model with a reduced length, the results of which were only validated for a plain tube using theoretical correlations. They concluded that corrugation height increases heat transfer. [42] numerically studied a with five outward helically corrugated tubes in turbulent regime (Reynolds number ranging from to ), only modifying the shell diameter (ranged from 20 mm to 50 mm), and maintaining the remaining parameters, such as inner tube diameter (20 mm), H (2 mm) and P (20 mm), constant. A 3-D numerical model was implemented, using a reduced corrugated tube section of 20 cm, which was validated by comparing the numerical results with experimental data from other studies. They reported that heat transfer was mainly improved by the fluid impact to the wall and pressure drop increased as the shell diameter decreased.
For the numerical studies based on corrugated tubes in , some of the previous works reduced the computational cost using low cost numerical simulations, proposing 2-D models [39] or performing 3-D numerical simulations using a short length of the computational domain [[40], [41], [42]], extrapolating the results for the entire heat exchanger geometry. None of the aforementioned studies validated their numerical models with an experimental setup with the same geometry and dimensions as the numerical model analysed. Moreover, none of these studies analysed the influence on heat transfer performance of different combinations of H and P in a 3-D inward spirally corrugated tube numerical model.
Thus, the aim of the present paper is to analyse the influence of geometrical parameters for eight inner spirally corrugated tubes at turbulent flow in a , using 3-D numerical simulations to better capture the corrugation shape, and to perform a comparison study of the heat transfer performance and flow behaviour for both the inner tube and the annulus for each case study. As a novelty, different combinations of H and P for an inward corrugated tube as the inner tube were analysed, something which had not previously been studied in . In addition, the numerical model included the entire geometry of the , with the dimensions of the computational domain being similar to those used in actual commercial applications, because the results of a simulation using reduced length section may not be extrapolated for a truly 3-D . Another contribution is that the numerical results for a smooth pipe and a corrugated tube were validated using an experimental setup with the same geometry and dimensions as the computational domain. The experimental validation was carried out for different flow rates in one corrugated tube, in a range of turbulent Reynolds numbers between and . Heat transfer rate, friction factor, effectiveness (ε), number of thermal units () and performance evaluation criteria () are presented in this study.
Section snippets
Physical model
Fig. 1 shows a scheme of the geometry of the studied in this work. The heat exchanger was made of stainless steel, with an external diameter of 38 mm and wall thickness of 1.5 mm. The inner tubes had an external diameter of 25 mm and a 1.5 mm thickness of stainless steel with a length (L) of 2.9 m. These dimensions are typically used in commercial applications.
A total of nine cases, with nine different inner tubes (see Table 1) were studied. Case 1 consisted of a smooth tube whereas Cases
Results and discussion
In this section, to analyse the flow pattern and heat transfer behaviour for each of the nine analysed cases, the results in Test 1 are presented. A criterion to determine whether the grid selected was adequate for all the analysed cases is the values obtained along the computational domain. In this regard, the distribution is represented considering the inner tube side and the shell side (Fig. 7) of the . In all the cases, values were below 5 in the entire computational domain,
Conclusions
In this study, we performed a 3-D numerical simulation under turbulent regime of the flow pattern and heat transfer process in a double pipe heat exchanger at counter flow comparing several types of inner spirally corrugated tubes. Using the proposed grid, when comparing the numerical results obtained in Cases 1 (smooth tube) and 2 (corrugated tube) with the experimental results, good agreement was obtained. In both analysed cases, the greatest differences between numerical and experimental
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors wish to express their gratitude to the Provincial Council of Albacete, for providing funding and support for the project on the Analysis of the Behaviour of Food Industry Fluids in Heat Exchangers, and making the implementation of this study possible. In addition, Project SBPLY/17/180501/000412 of the Regional Government of Castilla-La Mancha partially funded this work. This work was also partially funded by the Spanish Ministry of Science, Innovation and Universities - State
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