A Computational Study of Perforated Helical Tube Inserted in a Double Pipe Heat Exchanger with Fluid Injection

Heat exchangers have a dominated presence in various engineering fields, where the heat plays a significant role. These areas of application include, but are not limited to, power plants, chemical processing systems, food processing systems, automobile radiators, waste heat recovery units, heating and air conditioning systems, and refrigeration systems. For example, double-pipe heat exchangers are crucial when sensible fluid heating or cooling procedures are required and compact heat transfer zones are available. The oil cooler is an example of such a process. Thus, there have been numerous studies conducted to improve their design, performance, and types of working fluid inside them. The researches [1, 2] offer the most in-depth reviews of this topic. Obviously, the purpose of these devices is to transfer heat from one medium to another while no work other than the pumping power for fluids is imposed. Usually, to maximize the rate of heat transfer while maintaining the fluid pressure drop reasonably reduced appears to be a design challenge. Nevertheless, two categories can be found to enhance the thermal performance: active and passive. When a system needs to be supplemented with external power in order to achieve better outcomes, the technique is referred to as active. The passive method, however, such as manipulating with the geometry by inserting twisted tapes, wire coils, swirl flow generators, or mounting ribs, conical rings, wings, and so on, is still preferable.

The evaluation [3] was to the pressure drop and heat transfer rates for a horizontal DPHE incorporating wire coil. The inner pipe was 8.92 (mm) in diameter while the outer diameter was 9.52 (mm). The iron wire of one millimeter was inserted with a diameter of 7.8 (mm) inside the DPHE's shell. The experiments were conducted at mass flow rates that range from 0.01 to 0.07 (kg/s) and from 0.04 to 0.08 (kg/s) for cold and hot waters, respectively. The inlet cold and hot water temperatures were correspondingly between 15 and 20 and between 40 and 45℃. It was found that the coil-wire inserts significantly improve the heat transfer, particularly in the laminar flow regime.

The experimental work [4] studied the consequences of inserting wire coils together with twisted tapes under a uniform heat-flux in circular channel utilizing air as a working fluid. The findings revealed that the use of wire coils and twisted tapes combined results a double increase in heat transfer compared with employing the wire coil or twisted tape separately. Under the same circumstances, twisted tape and wire coils with smaller twist and coil pitch ratios are better than those with bigger ratios.

With respect to the shell-and-tube heat exchangers of porous passages, named helixchangers, helical baffles are more commonly used. They usually lead to reasonable pressure drop, vibration, and fouling effect with a greater heat transfer boost. The paper [5] provides a comprehensive survey of developments and advancements in helixchangers, including the combination of multiple shell-pass helixchangers, continuous or mixed helical baffles, and discontinuous helical baffles. They found that helixchangers outperform traditional segmental baffled heat exchangers in terms of flow and heat transfer, according to several experiments and computer simulations.

In the work [6], the wire coil was attached to the inner pipe interrupting the developed boundary-layer to increase turbulence activity and fluid mixing and thus the heat transfer. The achieved enhancements in the mean Nusselt numbers using the wire coil were found to be 110%, 116%, and 112%, respectively, in comparison to the plain pipe. Accordingly, the friction factor was around 11%, 10%, and 9% measured with respect to the plain case at the same Reynolds number.

The authors [7] provided a full survey on passive heat transfer enhancements. They determined that the twisted tape inserts perform better in the laminar flow than in the turbulent flow. Other techniques such as ribs, conical nozzles, and conical rings are generally more effective in the turbulent flow because the shorter pitch length leads to stronger swirling flow and longer residence time in the tube. Also, the helical screw tape can promote a higher heat exchange rate than the twisted tape. When the pressure drop loss is considered, the wire coil provides superior overall performance.

Experimental tests [8] to the double pipe heat exchanger in terms of heat transfer coefficient for Reynolds numbers between 4,000 and 14,000. The investigation was carried out in turbulent regime for both parallel and counter arrangements, where the cold fluid is inside the annulus. Turbulators were made of 2 (mm) diameter circular cross-section and were turned into coils with various pitches of 5, 6, 12, and 20 (mm). The introduction of coiled circular wire resulted in a significant increase to the heat transfer rate but also an elevation to the pressure drops, which is mostly dependent on spring pitches and wire thickness. The results demonstrated that higher coil pitch values and higher mass flow rates enhance the relative average Nusselt number of counter flow up to 450%, while higher coil pitch values and higher mass flow rates can improve the relative average Nusselt number of parallel flows up to 400%.

In order to improve the performance of heat exchanger, various turbulators were examined by Sheikholeslami et al. [9], including coiled tubes, extended surfaces (fin, louvered strip, winglet), rough surfaces (corrugated tube, rib), and swirl flow devices (twisted tape, conical ring, snail entry turbulator, vortex rings, coiled wire). The wire coil provides the highest overall performance when the pressure drop penalty is taken into consideration. The use of coiled square wire turbulators considerably increases heat transfer and friction loss when compared to smooth wall tubes. The pressure drop across the tube is a result of drag forces, flow obstruction, turbulence amplification, and rotating flow brought on by the helical rib. The thermal performance factor increases when a conical ring has more perforated holes.

It can be seen from the literature, for example, the paper [9], if the Prandtl number is high, the twisted tape will not serve as good as other inserts such as wire coil regarding the thermo-hydraulic performance. This is due to the fact that the wire coil induces more turbulence than the tape does when the Prandtl number is large, indicating that the hydrodynamic boundary layer is thick. The use of swirl flow devices enhances convective heat transfer in two ways: by swirling into the bulk flow and by breaking the boundary layer at the tube's surface. That is to say, such devices produce turbulence and superimpose vortex motion (swirl flow), which induces the boundary layer and, as a result, causes a larger Nusselt number and a better heat transfer coefficient.

Measurements were taken by San et al. [10] to the pressure drop, heat transfer, and water flow rate in a smooth pipe accompanied by coiled-wire inserts. The ratios of coil pitch to tube inner diameter and wire diameter to tube inner diameter, or e/d and d_c/d, respectively, were from 0.0725 to 0.134 and 1.304 to 2.319. The Nusselt number rose directly with the e/d value and inversely with the d_c/d value. It should be emphasized that the optimal settings were e/d = 0.101 and d_c/d = 2.319 for air and e/d = 0.101 and d_c/d = 1.739 for water, where these values were proved to be in favor of better thermal performance.

The researchers [11] carried out an experiment for heat exchanger with internal helical coil at a range of 14400 < Re < 42900, in the turbulent regime. They examined the effect of the Reynolds number, wire diameter, and coil pitch ratio on the Nusselt number and friction factor. Within these analyzed range of various parameters, the biggest achievements in the thermal performance were from 100 to 128%.

The paper [12] provides a detailed review of experimental and numerical studies conducted by various researchers in order to improve heat transfer through the use of roughness elements (vortex generator) of various shapes, sizes, and orientations. An effort was given to select the best roughness shape for maximum heat transfer with minimum pressure drop. Also, it was restated that the high rate of heat transfer with the existing of objects such as twisted tape, wire coils, ribs, and dimples is primarily due to the flow blockage, flow partitioning, and secondary flow.

A shell and coiled-tube heat exchanger were experimentally investigated by Panahi and Zamzamian [13] in which a wire was used inside the helically coiled tube as a turbulator. In the first mode, the fluid of coiled tube was water, and in the second mode, the fluid of coiled tube was air. Findings showed that this type of turbulator can be incorporated in the heat exchanger and significantly increase the overall heat transfer coefficient and obviously pressure drop.

In the study [1], the majority of data pertaining to the performance of heat exchanger with tabulator was compiled from the literature. They concluded that the twisted turbulators are evidently more functioned than others. Also, the devices that have perforated baffles are thermally superior among those without holes.

A passive enhancement approach used by Pérez-García et al. [14] was examined at Reynolds number ranging from 200 to 2000. The transition shape parameter (TSP), a new dimensionless measure, was utilized to classify the wire coils based on their hydraulic performance. This criterion can predict the friction factor alterations with Reynolds number in the transition region with and without inserting the wire coil. When compared to the high TSP group (TSP > 750), the low TSP group (TSP = 10) exhibited an abrupt transition. The intermediate TSP (between 10 and 750) had three wire-coil subgroups distinguished by the hydraulic behavior.

An experimental investigation was carried out by Maithani and Kumar [15] to determine the impact of helical perforated twisted tape on the thermal and hydrodynamic performance of heat exchanger. This study covers diameter ratio (tube per helical diameters), relative pitch ratio (perforated pitch per length of the tape), perforation index (perforated per total areas), and Reynolds number (Re). The best records were noted at diameter ratio of 0.65, relative pitch ratio of 0.086, and perforation index of 10%. For the range of parameters investigated, it was achieved a high thermal-hydrodynamic performance of 2.12.

The researcher [16] used a helical coil of a 19 (mm) pitch with an average helix diameter of 305 (mm). Adjustments were made for the temperature and water flow rate, in the annulus and helical coil side, at different values. The design of the heat exchanger was determined with a full range of data for outlet conditions as functions of inlets. The input parameters include the amount of constant heat flux, flow rate and temperature of primary and secondary fluids. Results showed that there is a rise in the overall heat transfer coefficient and thus heat transfer rate when the mass flow rate of cold water in the coil or hot water in the annulus is increased.

The experiment of Bhattacharyya and Paul [17] was for turbulent forced convection using circular-hole spring tape (CHST) placed in a circular tube. For a wide range of Reynolds numbers (from 10,000 to 50,000), the CHST inserts with varying hole and spring ratios were explored. Results indicated that using CHST can improve heat transfer by 35% and 51% when compared to other inserts and plain tube, respectively. Additionally, a study on entropy generation demonstrated that the irreversibility rises noticeably as the diameter ratio and Reynolds number increase. The thermo-hydraulic performance was roughly more than unity in all situations.

The work [18] was an experimental investigation for the effects of air bubble injection on the efficiency of a horizontal heat exchanger. The differences in the number of thermal units (NTU), energy loss, and efficiency caused by the injection of air bubbles at various air flow rates were assessed. As the air bubbles were injected, the heat exchanger's efficiency and NTU significantly increased. Thus, it is believed that the motion of air bubbles induces disturbances and then the level of turbulence in the shell side flow to rise, increasing the value of NTU and energy loss.

A shell and multi-tube heat exchanger using two air injection methods: parallel (upper and lower nozzles) and transverse (side nozzles) were installed within the experimental apparatus of El-Said and Abou Alsood [19]. In all test settings, the second approach (cross injection) had a greater impact on the heat exchanger efficiency, number of transfer units (NTU), and overall heat transfer coefficient (U) than the first way (parallel injection). In comparison to parallel injection, the cross injection resulted in a larger shell side pressure loss.

Multiple types of injectors were used by Heyhat et al. [20] to blow air into the annulus side of heat exchanger. Experimental data were collected for different annulus side and inner tube flow rates. Exegetic analysis was added to examine the impact of air flow rate and heat exchanger positioning angle on the overall performance. The collected data showed that the overall heat transfer coefficient could be raised by 10.3 to 149.5% by injecting air bubbles.

In the apparatus of the paper [21], a ring tube was located at the bottom of vertical annular pipe, which contains holes to allow air bubbles to flow into the annular space of heat exchanger. Due to the difference in density between the liquid and these tiny bubbles, there was high vibration, turbulence, and heat transfer. It was concluded that the heat exchanger performance can be enhanced by creating perforations on a plastic tube and then choosing the right number and dimension of holes. The Nusselt number and dimensionless exergy destruction were highly changed by roughly 57% and 30%, respectively.

Air was supplied to the coil side of a horizontal shell and coiled tube heat exchanger in the study by Khorasani et al. [22]. The findings showed that air bubbles injection into the heat exchanger enhanced the thermal effectiveness. In a T-junction of the instrument [23], outside the heat exchanger, hot water and air were mixed before moving inside the heat exchanger's inner tube. The flow rate of hot water was maintained at 2 (lit/min). Four potential flow rates: 3, 4, 5, and 6 (lit/min) were taken into consideration for the hot water flow rate. The results showed an increase in the heat transfer coefficient by 33%, and in the number of transfer units by 38%, respectively.

Researchers [24] studied the effect of air bubble injection on the thermal performance of a counter flow heat exchanger with vertical, helical coil tube. The effectiveness was increased due to the air bubbles to hot water, and at a flow rate of 3.5 (lit/min), the maximum effectiveness value reached 0.22. With compressing more air bubbles from 0.1 to 0.31 (lit/min) at a Reynolds number of 9823, the friction factor jumped to high values. The maximum enhancement ratio of Nusselt number was between 2.4 and 3.1 with air flow rate of 3.5 (lit/min) and Reynolds number between 9823 and 48028. With air bubble injection rate of 3.5 (lit/min), the maximum thermal performance factor was 1.33 whereas the exergy loss rose from 74 to 88%.

The study [25] tried the combined impact of twisted tape turbulators and air injection on the enhancement of heat transfer. It was reported that the air injection increases the pressure drop and heat transfer coefficient by up to 62 and 30.3%, respectively. The cost-benefit ratio was estimated to be acceptable at air and water flow rates of 1 and 5 (lit/min) with the best value of approximately 0.93. Other researchers, including [26], investigated the effect of rotating turbulators on forced convection to produce entropy and enhance heat transfer. With the entropy generation being significantly reduced while the thermal performance was noticeably improved, this supports the assumption that the rotating turbulator is more energetic.

The objective of the work [27] was to quantitatively analyze the relation between the use of twisted tape and the heat transfer rate and friction factor for double pipe heat exchanger. It was reported that the Nusselt number and friction factor for a plain-tube flow can be predicted more precisely by the turbulence model SST k-ω than by conventional standard k-ϵ, RNG k-ϵ, and Realizable k-ϵ. The twisted tape caused swirl flows in two areas: one that is adjacent to the twisted tape wall and another one is in the core region. The usage of triangular-cut twisted tape was found to improve fluid mixing because of swirl phenomena. To assess the thermal-hydraulic performance of two improved heat transfer tubes, Santos et al. [28] conducted a computational fluid dynamics analysis. They discovered that for the Nusselt number and friction factor prediction, the SST k-ω provides the best accuracy.

The experimental and numerical results were obtained by Andrzejczyk et al. [29, 30] for DPHE incorporating passive and active enhancement techniques, which were helical turbulator and air-bubble injection. The configurations of turbulator alone performed the highest heat transfer, pressure drop, and overall efficiency. The heat exchangers were made of copper pipes with the following diameters: d = 10, e = 2.4, d_c = 13, D = 18 (mm) and wall thickness of 530 mm. The whole length of the heat exchanger was constant 530 (mm). Moreover, the shell-side Reynolds number (based on water inlet flow rate and shell-side hydraulic diameter) was changed from around 1000 to 4000 during the experiments.

In this paper, the solution data and geometry specifications of the studies [29-31] experiments are relied on for further investigation. The new technique to include perforations in a turbulator is evaluated herein. The use of a helical tube injecting fluid through holes increases swirls and mixes in the main flow, which is the main motivation behind conducting this investigation. Compared to other methods employed, such as twisted tape or rigid turbulator, the new layout thought to be more effective. The flow rates are provided to the turbulator with 10% of the annulus's water on some occasions or 0.0063 (kg/s) on others. Thus, four flow divisions are delivered to the turbulator using either the same cold water from the heat exchanger or air. In comparison to plain turbulators, there has been a 45% increase in thermal effectiveness and a 600% gain in overall heat transfer coefficient. Consequently, the pressure loss has now doubled to 100%. In the part on mathematical analysis, the problem description will be presented, and then the CFD analysis of mesh modeling, boundary conditions, and methodology. The details regarding the heat exchanger's performance will be given in results section.

The geometry model for the current computational analysis was built in Ansys Design Modeler (version 2022 R1). It was imported into ANSYS Workbench and meshed separately for each part. Many attempts were given to the mesh to be optimized such as using tetrahedral elements with inflation near the walls or refinement zones that are subjected to intense flow changes due to the added geometry holes.

The mesh details are listed in Table 2. Figure 2 presents four sections displaying: (a) whole domains, (b) section planes of whole domains (c) cold water domain, and (d) helical tube domain. The difficulty of creating a good quality mesh comes from the helical tube. The mesh was construed with taking into account the most refined meshes for the small holes with small flow passages. The mesh independence tests were started with a mesh covering the description provided by Andrzejczyk et al. [30]. Then, the number of elements was increased 50% three times for each: coarse, fine, and refined mesh. The residuals of the main parameters were set at 10^-5, and the pressure drops and temperatures were monitored at each level of refinement. For steady state computations, and after passing the initial transient period of iterations, these variables were almost fixed for the fine and refined meshes. It has been determined that the fine mesh of 7, 635, 314 elements with other details written in Table 2 is sufficient for the current study. The same mesh was also employed for simulations of oscillatory flow with time step of 10^-3. The time step was also tested to be independent from alternating the results.

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Figure 2. The employed mesh constructed using different treatments especially the partitions near the turbulator: (a) whole geometry, (b) three-quarters section, (c) cold-fluid section, and (d) turbulator section

First, the simulations were performed for experimental validations, where the turbulator was solid coil. Second, the flow was setup to split into two flows in both the annulus and the helical tube in the cases of perforated turbulator, or PT-1, 2, and 3. The PT-1 stands for the first case when the mass flow rate of turbulator is 10% of that of annulus. If the mass flow rate is fixed at one value, say 0.0063 (kg/s), the case is symbolled as PT-2. The last case, PT-3, is when the oscillations are introduced to the flow inside the turbulator only. The SST K-ω turbulence model was used in Fluent setting. The computations were divided into two groups: single-phase flow and two-phase flow. The multiphase mixture model was chosen for the dispersed air bubbles that are distributed into the continuous, cold water. Thus, the primary phase is cold water in the annulus while the dispersed phase is air coming from the helical tube.

In earlier studies, helical turbulators were found to have the ultimate effect on the double pipe heat exchanger's performance. This study focuses on a new flow arrangement that creates holes around the turbulator to further increase the thermal effectiveness. These perforations in the helical tube bring more benefits to the plain turbulator. They can contain both steady and oscillatory flows, which will result in more disturbances, and they can produce vortices in a variety of directions. Despite the fact that it allows for more modifications in place, size, or fluid type, this kind of configuration is not found in the literature.

It is possible to divide the annular fluid into two amounts ensuring supplying the helical tube. The most successful modification is discovered to be the same fluid being injected through the perforations at different flow rate percentages. There has been a 600% increase in the overall heat transfer coefficient and a 45% improvement in the effectiveness with respect to those of the plain turbulator. The pressure loss, however, has also been doubled to 100%. The fluid may be combined with air in an effort to create additional turbulence. To give results that are meaningful, it must be blown at high pressure or pumped as an oscillatory flow. Although the oscillating flow has a big influence on heat transfer, its flow losses are quite expensive. If the turbulator does not exist, the same original flow amounts can be supplied, or additional flow quantities can be added to the perforated turbulator for good outcomes. It may be even better in the future to use different perforations with varying positions or to add more perforations all around the helical tube.