1 Introduction

Heat exchangers are used in heating, cooling and air conditioning systems, in chemical processes, thermal power plants and in many industrial applications implementing waste heat recovery. The purpose in heat exchangers is to provide the maximum possible heat transfer from a hot fluid to a coolant or a cooler fluid. By ensuring the maximum heat transfer in heat exchangers, both energy saving as well as efficient and effective use of energy is attained. Considering the increasing energy demand and depletion of energy resources, the importance of improved heat transfer in heat exchangers where huge amount of energy is employed is better recognized. Numerous experimental and numerical studies have been conducted on this matter.

Heat transfer enhancement techniques developed for heat exchangers in the process industry offer an opportunity to reduce the heat transfer area. With the use of these techniques, the performance of the heat exchanger is increased with reduced cost, material and energy savings depending on the process (Dehankar et al. 2016). Convective heat transfer improvement methods are generally divided into active, passive and a combination of both. In order to improve heat transfer in passive techniques, since no external power input to the system is required, changes are usually made on heat transfer, flow geometry and thermal properties of the heat transfer fluid. In a study by Kurniaa et al., the contribution of using twisted tape in a helical tube at constant wall temperature to the flow behavior and heat transfer was numerically investigated. It was seen that there is good agreement between the numerical estimation and the empirical correlation calculation, in the Reynolds range of 100–2000. The effects of twist rate, inlet Reynolds number and wall temperature were investigated in the light of numerical results. While the methods used to improve heat transfer in thermal systems are generally studied in straight pipe, in this study in which helical coil pipe is examined, it has been proven that higher heat transfer is provided than straight pipe. It has been found that applying twisted tape to a helical heat exchanger can improve heat transfer performance by up to four times compared to a conventional straight tube heat exchanger, with the cost of higher friction pressure drop. It has been found that a higher Reynolds and lower twist rate heat transfer will give the best results in coiled tubing with twisted tape applied for water (Kurnia et al. 2020).

In order to maximize the heat transfer in a concentric straight pipe arrangement, maximum heat transfer from, maximum the hot fluid to the cold fluid can be achieved only with area and high pumping power, while in one study heat transfer was tried to be achieved by using the passive method, with the help of twisted strip with a twist rate of y1 = 4.3 and y2 = 7.7. With a mass flow rate of 0.02–0.07 kg/s, when twisted strip is used, the temperature deviation increases by an average of 6 °C for y1 = 4.3, and by 4 °C for y2 = 7.7, compared to a straight pipe, due to the turbulence that occurs inside the pipe (Dehankar et al. 2016). Dehankar stated that by placing twisted tape with two different twist values (y1 = 4.3 and y2 = 7.7) on the flow line, the heat transfer increased and the pressure drop led to a higher level of turbulence (Dehankar 2022).

In their study, Lim et al. studied the performance of the concentric heat exchanger and the basic criteria of constant and variable pumping power. Convection with eddy flow and free convection were realized with the balance between centrifugal and buoyancy force. They interpreted the heat transfer characteristics for different Reynolds numbers. Their analysis showed that the counterflow laminar forced flow created using twisted wire makes an important contribution to the performance analysis (Lim et al. 2017).

In the study of Durmuş et al., in order to increase the heat transfer passively, a secondary flow or rotational flow was created in the cold air passing through the inner pipe with the help of a snail placed at the entrance of the inner pipe in a concentric heat exchanger where hot water is sent from the interspace. It has been observed that the rotary flow increases the heat transfer due to the decreasing boundary layer and increasing velocity. Up to 120% increase in Nusselt number was obtained in the case of swirl flow, counter flow and 45 rotation angle (Durmuş and Esen 2002).

A numerical study is conducted for different positions in laminar natural convection within the differentially heated space, in the case of a single horizontal fin attached to the hot wall of a square enclosure. It has been observed that the fin efficiency increases with the fin length and conductivity ratio, and the fin length negatively affects the fin efficiency, and the fin thickness affects the heat transfer rate negligibly (Elatar, Teamah and Hassab 2016).

The studies of Mozley (1956), Cohen and Johanson (1956) on heat exchangers are considered as the main studies in this field. In their theoretical and experimental studies on double-pipe heat exchangers (DPHE), they saw that the dynamic characteristics they obtained from the simple setups they set up were close to the experimental data.

In the literature, many researchers studied, theoretically and experimentally, the flow in concentric pipe heat exchangers (Ghobadi and Muzychka 2016; Akpınar 2004; Yildiz et al. 1997; Bilen et al. 2009; Pachegaonkar et al. 2014). Akpınar et al. (2004), passed hot fluid (air) through the inner pipe and cool liquid (water) through the outer pipe in a concentric pipe heat exchanger. They placed helically wound wires having certain pitches inside the inner pipe. Thus, they investigated the effects of helically wound wires on dimensionless exergy loss in different pitch and number of turns. For both opposite and parallel flows, dimensionless exergy loss was observed to increase with increased efficiency. At the same time, the exergy loss increases with the increase of pitch and with the decrease of the number of turns, whereas in the contrary case the Nusselt number increased, hence the heat transfer improved. It was concluded in this study that the heat transfer can be improved up to 240% with the use of helically wound wires. Also, it was seen that the increase in heat transfer was achieved through the renewal of boundary layer by getting the fluid near the pipe wall mixed by means of helical windings. Despite they reported the friction factor be slightly higher compared to the pipe without winding, they also reported that this loss can be minimized with proper arrangement of the position of the helix wire in the pipe, the helix angle, the number of turns, and the pitch.

In a number studies, extended or processed surfaces, passive methods that do not require additional power such as rotary flow devices, and active methods such as surface vibration, fluid vibration, suction or pumping have been used as means of improving heat transfer (Bergles and AE 1973). Prata and Sparrow (1984) placed another pipe with variable cross-section spaced into a straight pipe and solved the problem by using SIMPLER (SIMPLE-Revised) algorithm. Agrawal and Subrata investigated the flow and heat transfer in an annular pipe where the flow is blocked by special obstacles (Agrawal and Sengupta 1989). Sparrow et al. (1977) and Nguyen et al. (1989) have also reported in their respective numerical studies some results regarding flow and heat transfer in heat exchangers and protruding channels with specific geometry.

Yıldız et al. (1996) investigated the effect of blades that can rotate freely with the force applied by the fluid flowing inside the inner pipe of a double-pipe heat exchanger on heat transfer and pressure.

The experiments were conducted at 2500–15,000 Reynolds numbers with a number of different turbulators. The heat transfer rates in the system with turbulator were observed to be approximately 250% more effective than the case without turbulator. It was observed that the type of turbulator and the number thereof were effective on the heat transfer and that, besides, the increase in the pressure drop changed by 500% to 1000% depending on the Reynolds number and the number of turbulators compared to the empty pipe.

Fu and Tseng (1994) have proposed a numerical solution for a geometry that expands, and Straight pipe are inserted into a straight pipe. In the study, finite difference equations, obtained using a staggered grid system, were solved by SOR (Successive Over Relaxation) method. Fu et al. (1995), in the experimental study using the same physical model, calculated local and average Nusselt numbers for 07 Prandtl number and 1058, 1360 and 1965 Reynolds numbers relying on the analogy between mass and heat transfer and compared their findings with the numerical results. They reported that experimental and numerical results were in agreement.

Roys et al. (1921; Durmuş and Akbulut 2003) investigated the effect of rotational flow generation on the heat transfer by using different types of inserts in the forms of radial blades, short twisted strips and angular grooves. Zaharzadeh et al. (Durmuş, and akbulut 2003; Zaherzadeh and Jagadish 1975), with their custom-built rotational flow generator, achieved an increase of up to 80% in heat transfer rates at Reynolds numbers 20000–100,000. Durmuş et al. (2003) reported that heat transfer increased depending on the blade angle and shape after having tested bar-blade inserts with different blade angles and shapes in a coaxial, double pipe heat exchanger having constant surface temperature.

Eimsa-Ard et al. (2009) experimentally and theoretically examined the heat transfer, pressure loss and efficiency by using propeller type turbulators manufactured with different blade numbers and angles. In a numerical study, Uğurlubilek et al. (Bilen et al. 2009; Uğurlubilek and Uralcan 2011) reported that the heat transfer in laminar flow in a pipe with helical turbulator was only a little higher than that in the empty pipe, whereas it is very close to each other in the turbulent flow case, therefore concluded as thermodynamically inefficient. Guardo et al. (2005) modeled the wall-to-fluid heat transfer in packed beds with pipes in different diameters. In the study employing air as the fluid, they investigated the effects of turbulence models on pressure drop, velocity and thermal areas in the bed. Prata and Sparrow (1984; Dağtekin and Öztop 2000) also examined the heat transfer with SIMPLER (SIMPLE-Revised) algorithm in case the inner one of the two concentric pipes has a spacingly variable cross-section. They reported that rings placed in the inner pipe increased the heat transfer without causing a significant pressure drop. Dağdekin and Öztop (2000), numerically investigated the heat transfer in laminar flow in concentric pipes by using SIMPLER algorithm. Heat transfer was reported to have increased at low peclet number when the diameter of the inner one of the concentric pipes was small, i.e., the pipe wall was close to the symmetry axis, whereas at high peclet numbers it increased when the wall of inner pipe was close to the wall of outer pipe.

In another study, Sheikholeslami (2015) investigated the friction correlations and the variation of Nusselt number according to experimental data in his study in a turbulent flow with hot water from the inner tube and cold air from the axial cavity in a double-pipe heat exchanger. While the opposite situation was observed in the Nusselt number on the air side, it was observed that the Nusselt number on the water side increased with the water tank inlet temperature and water flow rate. In another study, Sheikholeslami (2016) investigated the effect of placing a typical circular ring (TCR) and perforated circular ring (PCR) in the axial cavity in the same setup on thermal performance. The thermal performance increased with the increase of the number of perforated hole (N), but decreased with the decrease of the Reynolds number and pitch ratio reported. Nusselt number increased with the increase of Reynolds number and perforated hole (N) number. The results were found to be compatible with this study.

Lee and Abdel Moneim (2001) numerically investigated the heat transfer and flow behavior in a channel in which two-dimensional elements are mounted on a horizontal surface using the CFD model. Constant heat flux has been applied in the study. The elements used were found to improve heat transfer significantly (Lee and Abdel-Moneim 2001). The effect of angled turbulator placed at the pipe inlet in concentric double-pipe heat exchangers on heat transfer was numerically investigated by Yakut et al. (Khalaji et al. 2018). In many studies, turbulators were installed in the inner pipe in order to increase the passive heat transfer in the tube heat exchanger (Lee and Abdel-Moneim 2001; Çakmak and Yıldız 2003; Kayataş. and Ilbaş 2005; Lozza and Merlo 2001).

The experimental setup was designed by reviewing the studies conducted on the pipe design and on heat transfer enhancement techniques in concentric pipes. In which the passive technique method is used by changing the shape of the flow with the current power of the system without the effect of external power, swirl (wire wrapping) is applied to the outside of the inner tube in order to improve the heat transfer rate and economically of the heat exchanger process. In double-pipe heat exchangers, there are various studies, mostly in turbulent flow, for heating the cold fluid passing through the axial space with the hot fluid passing through the inner tube by creating a rotational flow with turbulators in the axial clearance. This study is unlike the literature, aimed at improving heat transfer from the hot fluid running in the axial clearance between the two concentric pipes, where aluminum wire was wound round the inner pipe in order to create rotational flow, to the cool water flow passing through the inner pipe. In the experimental studies in the literature, the heat transfer of the hot fluid to the cold fluid flowing from the axial space is increased with the help of swirls placed in the inner pipe where the hot water flows. Thus, it is aimed to provide a more effective heat transfer by reducing the hydraulic diameter, creating a secondary flow with the eddy formed by rotating flow in axial clearance (via wire and increasing the turbulence density. There is a limited number of studies in the literature investigating the effect of rotational flow generation in axial clearance of a concentric double-pipe heat exchanger on the overall heat transfer coefficient of the fluid passing through the inner pipe. Therefore, a simple concentric double-pipe heat exchanger was set up to investigate this effect. For this purpose, the Navier–Stokes equations of continuity and energy were solved using the laminar model and finite volume method in ANSYS Fluent, and analysis was performed for all experimental conditions and the results were simulated.

2 Material and Method

2.1 Experimental Setup and Conduction of Experiments

A simple 1-m long heat exchanger consisting of two concentric pipes, experimental setup of which is shown in Fig. 1, was used. The hot fluid flows through the axial clearance, between the outer and inner pipes, while the cool fluid flows through the inner pipe. The inner pipe of the heat exchanger is of copper and is 1000 mm long with an internal diameter of 5.8 mm and a wall thickness of 1.1 mm. The outer pipe, on the other hand, is of plastic and has 17 mm internal diameter and 4 mm wall thickness. The heat loss that might occur from the system to the environment was prevented by insulating the outer pipe by using 20 mm thick polyethylene foam. Distilled water was used as the fluid in the system. Rotational flow was obtained in the axial clearance by means of 2-m long aluminum wire 4-mm in diameter wound 40 turns round the inner pipe.

Fig. 1
figure 1

Experimental setup of concentric double pipe heat exchanger

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While the heat is being transferred from the hot fluid to the cool fluid during the flow, it is certain that there a temperature difference of ΔT between the average temperatures of the fluids was maintained. Fluid passing through the axial clearance was studied for three volume flow rates ranging between 1 and 3 LPM, whereas the volume flow rates of the fluid passing through the inner, copper, pipe had five different values ranged between 0.2 and 1 LPM. A water bath with a capacity of 20 L was used to supply hot fluid to the system at 50 °C and 60 °C. The flow rates of the fluid were measured using flowmeters, equipped with regulating valves and floats, that can measure in the range of 1–7 LPM for hot fluid and 100–1000 ml/min for cold fluid. Figure 2a, b shows the locations of flowmeters (q1(1–3 LPM) and q2 (0.2–1 LPM)), thermocouple connections (T1, T2, T3 and T4) and the pump, as well as the helical aluminum wire wound round the inner pipe as used in the system. Figure 2c shows schematic view of the experimental setup.

Fig. 2
figure 2

a Aluminum wire wound round the inner pipe b Schematic view of the test section c Schematic view of the experimental setup

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In addition, temperature measurements were taken for each test by means of four K-type nickel chromium-nickel mineral insulated thermocouples placed in the inlet and outlet of hot fluid and cool fluid lines, shown on the experimental setup. The temperature measurements taken at 1-s intervals were transferred to a computer through 5-channel ORDEL data logger of UDL-100-5 type. The pipes that circulates the fluid across the system were of special heat resistant silicone material, with 5.8 mm inner diameter and 6.2 mm outer diameter.

At the beginning of the experiments, it was ensured that the hot fluid and cool fluid were supplied to the heat exchanger at the same time, and the measurements were taken only after the system and the temperature values became stable. The temperature measurements in all three flow rates for hot fluid and five flow rates for cool fluid were recorded in the computer environment and the test parameters were calculated. The inlet temperature of the hot fluid was 50 °C and 60 °C, and of the cool fluid was 17 °C. While performing the experiments, the average of four temperature values measured in a frame of 30 s after the system became stable was taken. Then the pumps were stopped and thermocouples were let cool for 30 s. This process was repeated for each flow rate of the cool fluid rate versus all three flow rates of hot fluid. Reynolds numbers were in the range of 700–3700 for five flow rates of inner fluid (cool fluid), and in the range of 1600–5000 for three flow rates of the hot fluid, in the case the flow in the axial clearance was irrotational.

In this study, the effect of flow rate and temperature of the outer fluid and of the formation of rotational flow in the axial clearance on the overall convective heat transfer coefficient of inner fluid (cool fluid) in a concentric pipe heat exchanger was examined experimentally and numerically for different volume flow rates of the inner fluid (cool fluid). Experimental and numerical results were consistent. In the experimental study, increasing the temperature and flow rate of the outer fluid was observed to have increased the convective heat transfer coefficient of inner fluid (cool fluid), however, compared to other effective parameters, the increase provided by the formation of rotational flow in the axial clearance was higher.

2.2 Numerical and Simulation Methods

One of the most important steps in numerical solution applications is to divide the model to be solved into a finite number of surfaces (volumes) on which numerical equation solutions will be made. Depending on the network structure created, the general solution for the total solution area is obtained by solving the conservation equations for each element sequentially. In two-dimensional geometries, the smallest element is surfaces, while in three-dimensional geometries, volumes. Joint points of surfaces or volumes are nodes. Solution meshes are formed in two ways, called structured and unstructured, depending on their geometry properties.

Finite element method is a method that can be used for discretization of linear and nonlinear differential equations. In this method, the solution is started by making algebraic estimations for the solution area divided into small areas, then the error is reduced by making iterations. The finite volume method divides the solution area into a finite number of control volumes, and the control points from which the variable values are calculated are located in the center of the control cells. The method used by the Fluent program is the finite volume method. In this method, the conservation equations are integrated for each control volume, creating a discretized equation that satisfies the conservation law for each volume. Values in the control volume border regions are calculated by the interpolation method.

As a result of the created network model, 1,320,867 nodes, 1,963,068 elements were created. The highest skewness ratio is 0.82. In the graph, it is seen that the skewness distribution ratio is mostly in the range of 0.09–0.28. Figure 3a, b shows generated mesh of double-pipe heat exchanger.

Fig. 3
figure 3

Generated mesh of double-pipe heat exchanger a Three-dimensional view b Cross-section

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3 Results and Discussion

Experimental data were used to calculate the forced convective heat transfer coefficient and Nusselt number of the inner fluid (cool fluid). The cool water running through the inner pipe was heated with the hot water running in the axial clearance. In other words, the water running inside the inner pipe of the liquid/liquid heat exchanger functioned as coolant. The general equations used in processing of experimental data are as follows.

If the thermal balance of the hot and cold fluid (water) is written,

$$Q = \dot{m}_{{\text{c}}} Cp_{{\text{c}}} \left( {T_{3} - T_{4} } \right) = \dot{m}_{{\text{h}}} Cp_{{\text{h}}} \left( {T_{1} - T_{2} } \right)$$
(1)

where Q is the amount of heat absorbed by the cool fluid or the amount of heat transferred by the hot fluid; \({m}_{\mathrm{c}}\) and \({m}_{\mathrm{h}}\) are, respectively, the mass flow rate of the cool and hot water; \({Cp}_{\mathrm{c}}\) and \({Cp}_{\mathrm{h}}\) effective specific heat of the cool and hot water; T3 and T4 are, respectively, the temperatures of water at the inlet and outlet of the inner pipe. T1 and T2 are, respectively, the temperatures of water at the inlet and outlet of the outer pipe.

$${{\dot{m}}_{c}Cp}_{\mathrm{c}}\left({{T}_{3}-T}_{4}\right)={U}_{i}{A}_{i}\Delta {T}_{\mathrm{lm}}$$
(2)

where Ui is the overall heat transfer coefficient through the area of inner pipe, Ai = πDiL, is the heat transfer surface area of the inner fluid (cool fluid), ΔTlm is the logarithmic temperature difference between the wall and fluid in contact with the wall.

$${\Delta T}_{{{\text{lm}}}} = \frac{{{\Delta T}1 - {\Delta T}2}}{{\ln \left( {\frac{{{\Delta T}1}}{{{\Delta T}2}}} \right)}}$$
(3)
$$\Delta T1 = T_{1} - T_{4} \quad {\text{and}}\quad \Delta T2 = T_{2} - T_{3}$$
(4)
$$\dot{m}_{{\text{c}}} Cp_{{\text{c}}} \left( {T_{3} - T_{4} } \right) = \frac{{UA\left\{ {\left( {T_{1} - T_{4} } \right) - \left( {T_{2} - T_{3} } \right)} \right\}}}{{{\text{ln}}\frac{{\left( {T_{1} - T_{4} } \right)}}{{\left( {T_{2} - T_{3} } \right)}}}}$$
(5)
$$\mathrm{Nu}={\mathrm{h}}_{\mathrm{i}}{\mathrm{D}}_{\mathrm{hi}}/k$$
(6)

In Eq. (6), k is the effective thermal conductivity of the cool fluid, hi is the convective heat transfer coefficient and Dhi is the hydrolic diameter of the inner pipe.

In Fig. 4a, increases achieved in the convective heat transfer coefficient of inner fluid (cool fluid) (for all flow rates thereof), in rotational flow condition in comparison to the same flow rate in irrotational flow at 50 °C, was about 182% at 1 LPM, 115% at 2 LPM and 63% at 3 LPM. It was observed that the effect on convective heat transfer coefficient of the inner fluid (cool fluid) in rotational flow decreased as the flow rate of the outer fluid increased.

Fig. 4
figure 4

The change in overall convective heat transfer coefficient of the cool fluid in the range of 0.2–1 LPM flow rates a 50 °C hot fluid temperature b 60° C hot fluid temperature

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In the Naphon (2006) study, which uses a coiled wire in the horizontal heat exchanger where hot fluid is passed through the inner tube and cold fluid is passed through the axial tube, the effect of the inlet conditions and winding spacing of the study fluids on the heat transfer was investigated. As obtained from the experimental results in this study, it was observed that the heat transfer coefficient increased depending on the flow rates of cold and hot fluids, and the use of helical wire was effective in increasing the heat transfer in the laminar flow region.

As can be seen Fig. 4b, the experimental results obtained at 60 °C hot fluid temperature under same other conditions, were consistent in terms of the increase rates of the convective heat transfer coefficient U incurred by the changes in the same parameters as in Fig. 4a. In Fig. 4b, increases achieved in the convective heat transfer coefficient of inner fluid (for all flow rates thereof), in rotational flow condition in comparison to the same flow rate in irrotational flow at 60 °C, was about 130% at 1 LPM, 75.3% at 2 LPM and 62% at 3 LPM. In this case, the effect of rotational flow on convective heat transfer coefficient of inner fluid (cool fluid) decreased as the flow rate of the outer fluid increased. Consequently, increasing the temperature of outer fluid from 50 to 60 °C yielded almost the same effect on convective heat transfer coefficient of inner fluid (cool fluid) at 3 LPM hot fluid flow rate.

Figures 5 and 6, in general, are obtained by changing the flow rates of hot and cool fluids in cases of irrotational and rotational flows in the axial clearance. As seen in Figure, in case the flow in the axial clearance was irrotational, increasing the flow rate of the hot fluid at 50 °C from 1 to 2 LPM and from 1 to 3 LPM, (against all five flow rates of cool fluids ranged between 0.2 and 1 LPM), induced 57% and 138% improvements, respectively, in the convective heat transfer coefficient (U) of the cool fluid.

Fig. 5
figure 5

Change of Nusselt numbers for different Reynolds numbers (that correspond to the flow rates in the range of 0.2–1 LPM) of cool fluid a 50 °C hot fluid temperature b 60 °C hot fluid temperature

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Fig. 6
figure 6

Overall heat transfer coefficient of the cool fluid at flow rates in the range of 0.2–1 LPM at 50 °C and 60 °C hot fluid temperatures a 1 LPM b 2 LPM c 3 LPM

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Figure 5a and b shows Nusselt numbers determined for Reynolds numbers that correspond to the flow rates of the inner fluid in the range of 0.2–1 LPM at 50 °C and 60 °C. Increased Reynolds numbers in the rotational flow also increased the Nusselt numbers in the irrotational flow. Thus, an increase in the convective heat transfer was observed due to that the increased Reynolds numbers had thinned the boundary layer on the pipe surface.

In Fig. 6a, b, and c, the changes incurred in the convective heat transfer coefficient of the inner fluid (cool fluid) by the irrotatational and rotational flows at 50 °C and 60 °C in the axial clearance of the concentric double-pipe heat exchanger for same respective flow rates of the hot and cool fluid are given.

Increasing the temperature of the fluid in axial clearance from 50 to 60 °C under same flow rate conditions, an increase in the convective heat transfer coefficient of the inner fluid (cool fluid) was observed in both rotational and irrotational flow conditions. Experimental results were consistent with the theoretical predictions on the convective heat transfer.

The results obtained in Figs. 5a, b and 6a–c are consistent with the study by Zhang et al. (2012). In the aforementioned study, helical fins and vortex generators are used together on the outer surface of the inner tube. It has been observed that the hydraulic diameter is reduced by the helical vanes and vortex generators in the axial cavity, the fluid flow becomes destabilization with the formation of secondary flow, and the turbulence density is increased.

Therefore, the highest increase in the convective heat transfer coefficient U of the inner fluid (cool fluid) (compared to that at 50 °C and 1 LPM flow rate) obtained in the experiments conducted in the absence of turbulator in axial clearance was at 3 LPM flow rate and with rotational flow in axial clearance. The highest increase rate was observed as approximately 291% as mentioned above. Akpınar et al. reported that the heat transfer could be improved by up to 240% with the insertion of helical wound wire into the inner pipe (Akpınar 2004).

In Figs. 7 and 8, the change in the amount of heat absorbed by the cool fluid due to the increase of the flow rate of cool fluid in irrotational and rotational flow conditions in the axial clearance at 50 °C and 60 °C was expressed graphically (for the flow rates of hot fluid in the range of 1–3 LPM and of cool fluid in the range of 0.2–1 LPM). Under same conditions in all flow rates, the amount of heat absorbed by the cool fluid was greater at 60 °C than it was at 50 °C.

Fig. 7
figure 7

Change in the amount of heat absorbed by the cool fluid at all flow rates in rotational and irrotational flow conditions at 50 °C

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Fig. 8
figure 8

Change in the amount of heat absorbed by the cool fluid at all flow rates in rotational and irrotational flow conditions at 60 °C

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As seen in Fig. 12, in all experiments at 50 °C outer fluid temperature, the maximum increase in the amount of heat absorbed by the cool fluid was with rotational outer flow at 3 LPM. The ratio of increase was about 34% compared to the same flow rate of 3 LPM with irrotational flow. As seen in Fig. 13, under same conditions, the maximum increase in the amount of heat absorbed by the cool fluid at 60 °C outer fluid temperature was again at 3 LPM flow rate. The ratio of increase was about 42% compared to the same flow rate of 3 LPM with irrotational flow. For all flow rates of the inner fluid (cool fluid), the amount of heat absorbed by the inner fluid (cool fluid) increased, in both rotational and irrotational flow conditions, as the flow rate of the outer fluid increased.

In Figs. 9 and 10, velocity analysis with CFD for rotary flow in the axial cavity shows the external flow in the axial cavity for 1, 2 and 3 LPM flow rates in regions A, B, C, each approximately 10 cm. CFD analysis has been made for each flow rate separately in Fig. 9, and as a result, the secondary flow rate and velocity counters at 3 LPM are higher than other flow rates.

Fig. 9
figure 9

Velocity Contor change at all flow rates in rotational flow condition at 60 °C (While the internal flow is 0.2)

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Fig. 10
figure 10

Velocity Contor change at all flow rates in irrotational flow condition at 60 °C (While the internal flow is 0.2)

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The velocity distribution counter at 1, 2 and 3 LPM flow rates is shown in Figs. 9 and 10. In the case of rotary flow at all flow rates, there was no secondary flow in the empty pipe where turbulence occurred in the axial cavity. In Fig. 11, turbulent flow lines and vectors are shown for 3 LPM in axial clearance.

Fig. 11
figure 11

Velocity vector and secondary flow for 3LPM a pipe inlet b middle of pipe c pipe outlet d secondary flow around the spring

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In Fig. 12, temperature distribution contour analysis with CFD for rotary flow in axial cavity was performed at 60 degrees Celsius for 1,2 and 3 LPM. According to the CFD analysis, as we have shown before, the flow at 3 LPM gave better results than the other flow rates due to the secondary flow, therefore, as the flow rate increased, the temperature and heat transfer coefficient increased.

Fig. 12
figure 12

Temperature Contor change at all flow rates in rotational flow condition at 60 °C (While the internal flow is 0.2)

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In Figs. 12 and 13, temperature distribution contour analysis with CFD for rotational and non-rotational flow in axial cavity, respectively, was performed at 60 degrees Celsius for 1, 2 and 3 LPM. According to these analyses, better temperature results were observed compared to non-rotational flow due to secondary flow formation with rotational flow in the axial cavity, and it was observed that the outlet temperature difference for 3 LPM was at minimum 3 °C, which is approximately equal to our experimental results.

Fig. 13
figure 13

Temperature Contor change at all flow rates in irrotational flow condition at 60 °C (While the internal flow is 0.2)

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4 Conclusions

As a result of the experimental study and the numerical analysis, rotational flow generation in the axial clearance in a concentric double pipe heat exchanger was observed to have a significant increase in the overall convective heat transfer coefficient of cool liquid passing through the inner pipe and in the amount of heat absorbed thereby compared to the irrotational flow.

When the temperature of water running through the axial clearance was increased from 50 to 60 °C and tests were repeated with same flow rates, the amount of heat transferred to the cool fluid and the convective heat transfer coefficient of inner fluid (cool fluid) also increased.

The effect of rotational flow on convective heat transfer coefficient of the inner fluid decreased as the flow rate of the outer fluid increased. The effect of increasing the temperature of the outer fluid from 50 to 60 °C at 3 LPM outer flow rate on the convective heat transfer coefficient of the inner fluid was almost the same as that of rotational flow.

Increasing the flow rate of the inner fluid in concentric heat exchanger also increased the amount of heat absorbed. Comparing the amount of heat absorbed by the cool fluid in irrotational and rotational flow conditions at 3 LPM flow rate at 50 °C, the ratio of increase was about 34%, whereas it was approximately 42% at 60 °C. The highest increase, in comparison to 1 LPM irrotational outer flow condition, was obtained at 3 LPM rotational flow.

Under same conditions, the improvement in the convective heat transfer coefficient (U) of the inner fluid (cool fluid) in rotational external flow condition was observed to increase to approximately 182% at 1 LPM, to 242% at 2 LPM and to 291% at 3 LPM, compared to the irrotational flow against the hot fluid flow rate of 1 LPM. Thus, at 3 LPM flow rate, generation of rotational flow was found to be approximately 153% more beneficial than increasing the flow rate.

Therefore, the highest increase in the convective heat transfer coefficient U of the inner fluid (cool fluid) (compared to that at 50 °C and 1 LPM flow rate) obtained in the experiments conducted in the absence of turbulator in axial clearance was at 3 LPM flow rate and with rotational flow in axial clearance. The highest increase rate was observed as approximately 291% as mentioned above.

In addition, a study can be conducted to investigate the effect of changing the winding frequency of the wire winding used in this study on the amount of heat transfer from the hot water flowing in the annular space to the cold water flowing through the inner pipe.

It was concluded, as a result, that investigation of energy loss that might arise from the pressure drop and increased pumping power induced by rotational flow in the axial clearance would be beneficial in determining the efficiency of heat exchanger.