Enhancement in heat transfer characteristics by using truncated conical turbulators in a double pipe heat exchanger under turbulent conditions

Abstract

The rising use of fossil fuels has had major environmental impacts, including global warming, pollution, and higher heating system costs. This emphasizes the need of increasing the efficiency of equipments such as heat exchangers used in heating and air conditioning systems. In the present study, heat transfer augmentation in a double pipe heat exchanger is numerically studied by the use of truncated conical turbulators. Truncated conical structures with a base diameter of 12 mm height, 7 mm, and pitch values ranging from 25 mm to 100 mm with an increment of 25 mm, have been considered in the study. The air flow rate varied from a Reynolds number of 3000 to 15,000 in increments of 3000. Results have been compared with the bare pipe without any turbulators. The heat exchanger with the turbulator showed better performance than the bare heat exchanger in terms of higher Nu, but at the cost of higher pressure drop. Increased Nu was observed up to pitch 50 mm and reduced afterward. Results indicated a highest Nu of 77.7 for Pitch 50 mm at Re 15,000. Maximum Thermohydraulic efficiency of 1.13 was observed for pitch 50 mm at a Re of 11,000. Hence, it is concluded that truncated conical structures can be used as a heat augmentation device in a double pipe heat exchanger to increase the heat transfer rate and thermohydraulic efficiency.

Keywords:

• conical turbulator
• turbulent intensity
• contour plot
• thermohydraulic performance parameter
• turbulent

1. Introduction

Air heaters find wide applications in domestic and industrial purposes. They are used for heating the room air, drying food items, clothes, and other hydrated items in a drier, oven, and so on. They are also used in various industries, such as chemical, textile, and automobile sectors for various applications. Air heating can be done by using various kinds of primary energy of which solar is the most promising one. Electrical and waste heat are other forms of energy generally utilized for air heating (Lanjewar et al., 2011). Solar energy is renewable and is widely used for air heating. The major advantages include being renewable, and it is available free of cost. However, there are a few disadvantages, such as, (a) they can be used only when there is ample sunshine, (b) thermal storage devices will make the system bulky and also costly, and (c) the requirement for a higher surface area and poor conversion efficiency (Karwa & Chitoshiya, 2013). Several novel techniques have been implemented by researchers over the years to improve efficiency (Mousavi Ajarostaghi et al., 2022)– (Saedodin et al., 2021). It includes different types of heat transfer augmentation devices placed on the absorber plates termed turbulators. They help to break the laminar sublayer, thus increasing the air turbulence. This modified flow helps to increase the fluid outlet temperature mere to the exit. Table 1 shows the various kinds of flow modification devices implemented and their influence on the thermal performance of a solar air heater. They include rectangular ribs, v-shaped ribs, multiple V-shaped, arc, w-shaped, and spherical-shaped turbulators.

Table 1. Influence of turbulators on the solar air heater performance

Authors	Geometry modification	Outcomes	Remarks
Gill et al., (2017)	Broken arc rib type of turbulator	The maximum increase in Nu and f were 3.06 and 2.5 times that of a plain absorber plate	A relative staggered rib ratio of 4 gave maximum thermo hydraulic efficiency.4
Prasad & Saini, (1988).	Small diameter wire type protrusions on the absorber plate	They observed a higher Stanton number and friction factor for the modified absorber plate compared to that of normal.	They concluded that both pitch and height of the roughness turbulators significantly influence the thermal performance
Gilani et al., (2017).	Conical-shaped fin protrusions on the absorber plate	Thermal efficiency was increased by 26% for the fin pitch of 16 mm compared to that of a smooth one.	Fin height of 4 mm pitch 16 mm with staggered arrangement gave optimum results
Promthaisong & Eiamsa-Ard, (2019).	Wavy triangular ribs	Nu and friction factor increased in the range of 5.8–304% and 13.8–171% respectively	Increase in Re, blockage ratio and decreasing the longitudinal pitch enhanced the thermal performance
Manjunath et al., (2017).	Spherical shaped turbulators	A spherical diameter of 3mm with P/d ratio 3, at Re 23,600 showed the highest thermal performance about 23.4% higher than the base model	Thermal efficiency increased by increasing the spherical turbulator diameter and decreasing the relative roughness pitch
Ravi & Saini, (2018).	Multi V-shaped staggered ribs	A maximum increase in Nu by 4.52 times and friction factor of 3.13 times that of a smooth duct was noticed for the modified absorber duct	Optimum performance was witnessed for rib size of 3.5, roughness width ratio of 7, and pitch ratio of 0.6
Zaboli et al., (2021).	Inner helical axial fins	For pitch =2500 and 1000 mm 14% and 21.5% improvement in performance respectively	Overall 21% improvement of thermal performance obeserved
Nouri Kadijani et al., (2022)	Rectangular channel solar air heater with v-shaped ribs	Increasing RH from 0 to 50% led to an increase in heat transfer by 50%	For a Re of 4000 and 12,000 performance increased by 7.3% and 31.4 %
Olfian et al., (2020)	Rectangular and V-shaped baffles	For 90 angled baffle, Nu increased by 148% and ΔP increased by 316% as compared to without baffle case	For 90 ° and 30 ° V-shaped baffles, thermal performance is 27% and 13% higher than no baffled case.

Experimental and numerical investigations concluded that adding different shaped obstructions will help to increase air turbulence. They help to increase the heat transfer rate and also the temperature of the absorber plate. Enhancement of the heat transfer rate also depends on the geometry and size of the turbulator, their positioning, number and their pitch values. To reduce the floor area requirements and also when a continuous supply of processed air is required, a double-pipe air heater is the most common structure used in industries. As compared to the other categories, such as plate type and shell and tube type of heat exchangers, the efficiency of double pipe heat exchangers is lower. Various techniques have been implemented over the years to increase the efficiency of such heat exchangers. These techniques can be classified as an active and passive types based on whether external energy is used for heat augmentation or not (Ge et al., 2022; Ghachem et al., 2021; Hussein et al., 2015; Kumar et al., 2018; Li et al., 2023; Salem et al., 2018; Zhang et al., 2020). They can also be categorized based on the position of flow modification inserts. In the direct type, a flow modifying insert is placed in the inner pipe itself. Inserts placed inside the inner pipe will help to break the normal flow field by the swirling motion. It helps to increase the mixing of the fluid and decrease the thermal boundary, thereby improving the heat transfer characteristics. Twisted tapes, wired inserts, and helically coiled tubes are commonly used as inserts for heat augmentation. Table 2 shows the experimental and numerical studies conducted by various researchers using inserts placed in the inner pipe which helps to increase the thermal performance.

Table 2. Details of the inserts used in a tubular heat exchanger

Authors	Geometry modification	Outcomes	remarks
Kumar & Prasad, (2000).	A twisted tape insert	Increase of Nu by 18–70% whereas ΔP increased by 87–132% as compared to the plain tube.	In water heater applications twisted tape collectors performed better in the lower Re ie up to 12,000 beyond which the performance deteriorated.
Eiamsa-Ard & Promvonge, (2010).	Alternate clock-wise and anticlockwise twisted tape	Alternate clockwise-anticlockwise twisted tapes showed an increased Nu in the range of 12.8–41.8 and 27.3–90.5 compared to that of a single twisted tape insert and a plain tube.	Twist angle of 90°, twist ratio 3 gave a maximum increase in thermal performance.
Bhuiya et al., (2013).	Perforated twisted tape	Twisted tape with porosities 1.6,4.5, 8.9, and 14.7 was used. They revealed Nu, f, and thermal performance was enhanced by 110–340, 110–360, and 28–59% as compared to that of a normal plain tube.	Empirical correlations were developed and found that Nu, f, and thermal performance were within the deviation of 4%,4%, and 2% respectively for predicted and experimental results.
Murugesan et al., (2011).	V-cut twisted tape insert	V-cut twisted tape with a depth-to-width ratio of 0.34,0.43 is used. Enhancement in the thermal performance was noticed in decreasing twist ratio, width ratio, and increasing depth ratio.	Developed Correlations showed a good agreement between empirical and experimental results with an average deviation of 6% for Nu and 10% for friction factor.
Akyürek et al., (2018).	Wire coiled insert	Coiled wire type inserts with different pitch values were used for heat transfer augmentation in a concentric heat exchanger with Al2O3 nanofluid. For pitch 25 mm wire coil, Nu increased by 51.6% and heat transfer coefficient by 12.6%	An increase in volume concentration of nanoparticles enhanced the thermal performance, pitch 25 mm, volume concentration of 1.6% at Re of 20,000 showed maximum thermal performance.
Kumar et al., (2019).	Helical tape insert	Helically coiled tape inserts with varying width ratios and twist ratios are used. A combination of width ratio 3 and twist ratio 1.25 maximum thermos hydraulic performance was noticed.	Both tape width and tape pitch significantly contribute to the heat transfer enhancement in a double pipe heat exchanger.
Wongcharee & Eiamsa-Ard, (2011).	Twisted tape with triangular, rectangular, and trapezoidal wings.	Experiments were conducted using triangular, rectangular, and trapezoidal winglets with chord length ratios of 0.1,02, and 0.3 in each type. Trapezoidal wings outperformed the other types with better thermal performance	A maximum performance factor of 1.42 was noticed for trapezoidal wings with a chord ratio of 0.3. Nu and f increased by 2.84 and 8.02 times that of a bare pipe.
Kazemi Moghadam et al., (2020)	Corrugated tube with a coiled wire as a tubulator	Maximum increase in performance noted for Re =5000 with Nu =11.16% for p/d =3 and 17.4% for p/d =5	Roughness height of 3 exhibited best performance
Zaboli et al., (2022)	Corrugate tube with different lobe shaped c/s with spiral twisted tape	Five lobe c/c showed 9.1% and 3.7% higher Nu and ΔP than 3 lobed c/s	Providing corrugated shape with swirl generator effectively increased the thermal performance.
Mousavi Ajarostaghi et al., (2022)	Curved conical turbulator	Re varied from 10,000–35000 As the angle of curvature is increased Nu also increased.	Curved swirl generator showed higher than the uncurved structure.
Noorbakhsh et al., (2020).	Twisted tapes on both sides of the double pipe heat exchanger	Increasing the number of twisted tape from one-fin to four-fin increased Nu by 3.1%, ΔP by 64%, and coefficient of performance by 63.9%.	Creating hollows with aspect ratio =1 on the twisted tape yielded higher coefficient of performance.

Turbulators placed in the inner pipe will abruptly increase the pressure drop which increases the energy consumption for pushing the fluid. The complexity of the geometry will also lead to difficulties in the manufacturing and fabrication of the heat exchanger. Overall efficiency will be reduced. When air heating is to be done using an indirect heat exchanger, the double pipe heat exchanger is widely used in industries. To overcome the drawbacks of these types such as increased length for a particular heat duty, lower heat transfer coefficient of air, various flow modifying projections placed in the annulus body will induce turbulence and enhance the heat transfer rate. Some researchers have conducted studies using flow-modifying devices in the annulus of a double pipe heat exchanger. The effect of hemispherical turbulators placed in the annulus of a double pipe heat exchanger has been numerically studied by Kumar et al. (Kumar et al., 2020). Different diameter ratios of 0.29, 0.44, and 0.58 and pitch ratios of 1.47, 4.41, and 7.35 have been used for the turbulator modelling. Predicted results indicated that a diameter ratio of 0.58 with a pitch ratio of 1.47 gave a higher rise in Nu (Nusselt number) and THPI (Thermo-hydraulic Performance Index) which are 2.7 and 1.44 times that of a bare pipe. Mathanraj et al. (Mathanraj et al., 2018) observed a higher heat transfer rate by using triangular fins in the outer body of the inner pipe of a double pipe heat exchanger. Heat transfer enhancement in a double pipe heat exchanger with a combination of helical fins and vortex generators in the annulus has been studied by Zhang et al. (Zhang et al., 2012). They concluded that compound heat transfer due to the combination of helical fins and a vortex generator is higher than using only fins on the annulus side. Shekholeslami et al. (Sheikholeslami & Ganji, 2016) carried experimental investigation in a concentric tube heat exchanger with perforated turbulators placed on the annulus side. Pitch ratio, open area ratio, and Re (Reynold’s number) were varied and an optimum value of THPI of 1.59 was noticed for a combination of Re = 6000, pitch ratio 1.06, and the open ratio of 0.07.

From the above literature survey, it is seen that the efficacy of the flow modifying device depends on the type, shape, and position of the turbulator. It is observed that the use of heat augmentation devices on the annulus side has not been focused on, over the years in a double pipe heat exchanger. In particular, the use of conical-shaped turbulators placed in the annulus body is not studied extensively by researchers. As the performance enhancement depends on the shape, geometry, and also dimensions of the turbulator, numerical studies to compare their performance are essential and CFD studies in this context are also inadequate. The use of truncated conical turbulators for heat transfer enhancement in a tubular pipe has not been explored in the published literature. Hence, to fulfil the above research gaps, a numerical simulation of the double pipe heat exchanger with annulus turbulators has been undertaken. Truncated conical turbulators with a constant base diameter and height are considered and their influence on the heat transfer augmentation has been studied numerically. Turbulator dimensions and the pitch values have been optimized to obtain the maximum performance on heat transfer performance.

2. Background theory

Considering the double pipe heat exchanger with inside diameter d_i and outside d_o. The Nusselt number, Nu_i is calculated by knowing the Re of the fluid flowing in the inner pipe as shown in equation 1 and 2 (Manjunath et al., 2017).

(1) $\mathit{Re}=\frac{{\rho }_i{V}_i{d}_i}{{\mathit{\mu }}_i}$(1)

(2) $\mathit{N}{u}_i=0.023\mathit{R}{e}^{0.8}\mathit{P}{r}^{0.3}$(2)

Where d_i is the hydraulic diameter of the inner pipe and v_i is the velocity of the fluid in the inner pipe.

Hydraulic diameter of the inner pipe is given by

$\mathrm{di}=\frac{4A_i}{P_i}$ with A_i is the area of the inner pipe and P_i is its perimeter. (2a)

Further (Manjunath et al., 2017),

(3) $\mathrm{Nui}=\frac{h_i{d}_i}{k_i}$(3)

The inside fluid flow rate is held constant and hence Nusselt number Nu_i is constant whereas the outer fluid mass flow rate is varied. Knowing the average heat transfer rate, Nu_o is calculated using the equation (4(4) $Q_h=m_h{c}_{\mathit{ph}}\left(T_{\mathit{hi}}-T_{\mathit{ho}}\right)$(4) -9(9) $\mathrm{Nu}0\mathit{\hspace{0.17em}}=\frac{h_0{D}_{\mathit{air}}}{k_0}$(9) ) (Eiamsa-Ard & Promvonge, 2010).

(4) $Q_h=m_h{c}_{\mathit{ph}}\left(T_{\mathit{hi}}-T_{\mathit{ho}}\right)$(4)

(5) $Q_c=m_c{c}_{\mathit{pc}}\left(T_{\mathit{co}}-T_{\mathit{ci}}\right)$(5)

$Q_{\mathit{avg}}=\mathit{Q}=\frac{Q_h+Q_c}{2}$

(6) $\mathit{LMTD}\mathit{\hspace{0.17em}}=\frac{\left({\mathit{T}}_{\mathit{hi}}-T_{\mathit{co}}\right)-\left(T_{\mathit{ho}}-T_{\mathit{ci}}\right)}{ln\left[\frac{{\mathit{T}}_{\mathit{hi}}-T_{\mathit{co}}}{T_{\mathit{ho}}-T_{\mathit{ci}}}\right]}$(6)

(7) $Q_{\mathit{avg}}=U_o{A}_o\mathit{LMTD}$(7)

(8) $U_0=\frac{1}{\frac{r_0}{h_i{r}_i}+\frac{1}{h_0}+\mathit{ln}\frac{r_o}{r_i}\frac{r_0}{\mathit{k}}}$(8)

Where U₀ is the overall heat transfer coefficient, h_o is the outside heat transfer coefficient, and LMTD is the log mean temperature difference.

By knowing the value of U₀, the outside heat transfer coefficient h_o and Nu_o can be calculated.

For the annulus body, the hydraulic diameter is given by

$\mathrm{Dair}=\frac{4\mathit{A}}{P}$ where A is the area of the annulus and P is the wetted perimeter of the annulus body together with conical turbulators.

By substituting the value of h_o, Nu_o values can be obtained (Kumar et al., 2020).

(9) $\mathrm{Nu}0\mathit{\hspace{0.17em}}=\frac{h_0{D}_{\mathit{air}}}{k_0}$(9)

Further, the annulus pressure drop along the flow length is used to calculate the friction factor values (Eiamsa-Ard & Promvonge, 2010).

(10) $\mathrm{f}=\frac{2\mathrm{\Delta }\mathit{P}{\mathit{D}}_{\mathit{air}}}{\mathit{\nu L}{V}^2}$(10)

where ΔP is the pressure drop (Pa) of the fluid in the annulus, L is the heat exchanger length and v is the air velocity(m/s)

3. Numerical scheme and validation

3.1. Bare heat exchanger

Initially, a plain tubular simple double pipe heat exchanger is modelled in the Ansys work bench environment. Tetrahedral elements are used for meshing the geometry with an inflation of 15 layers in both the water and air domain to capture the boundary layer effects. Inner fluid cell zone conditions are set as water whereas the fluid in the annulus is air. Ansys Fluent (Ansys® Fluent, 2021) is used to solve the fluid dynamic equations as mentioned in Equations (11(11) $\frac{\mathrm{\partial }\bar{u}}{\mathrm{\partial x}}+\frac{\mathrm{\partial }\bar{v}}{\mathrm{\partial y}}+\frac{\mathrm{\partial }\bar{w}}{\mathrm{\partial z}}=0$(11) - 13(13) $\frac{\mathrm{\partial }{u}_i{u}_j}{\mathrm{\partial }{x}_i}=-\frac{1}{\rho }\frac{\mathrm{\partial }\mathit{p}}{\mathrm{\partial }{x}_i}+\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_j}\left\{\left(\mathit{v}+v_t\right)\left(\frac{\mathrm{\partial }{u}_i}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }{u}_j}{\mathrm{\partial }{x}_i}\right)\right\}$(13) ) (Manjunath et al., 2017).

Continuity Equation

(11) $\frac{\mathrm{\partial }\bar{u}}{\mathrm{\partial x}}+\frac{\mathrm{\partial }\bar{v}}{\mathrm{\partial y}}+\frac{\mathrm{\partial }\bar{w}}{\mathrm{\partial z}}=0$(11)

Energy equation

(12) $\frac{\mathrm{\partial }{u}_i\mathit{T}}{\mathrm{\partial }{x}_i}=\mathit{\rho }\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_i}\left\{\left(\frac{v}{\mathit{Pr}}+\frac{v_t}{\mathit{P}{r}_t}\right)\frac{\mathrm{\partial T}}{\mathrm{\partial }{x}_i}\right\}$(12)

Momentum Equation

(13) $\frac{\mathrm{\partial }{u}_i{u}_j}{\mathrm{\partial }{x}_i}=-\frac{1}{\rho }\frac{\mathrm{\partial }\mathit{p}}{\mathrm{\partial }{x}_i}+\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_j}\left\{\left(\mathit{v}+v_t\right)\left(\frac{\mathrm{\partial }{u}_i}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }{u}_j}{\mathrm{\partial }{x}_i}\right)\right\}$(13)

Boundary conditions have been imposed for the fluids in both the inner pipe and annulus at the inlet and outlet. Inner fluid is subjected to a mass flow rate of 0.028 kg/s corresponding to a Re of 3000. The temperature of the hot water in the inner pipe is fixed at 353 K. The temperature of the cold fluid air in the annulus is fixed at 293 K with its Re ranging from 3000 to 15,000 in the turbulent domain. At the outlet, the pressure outlet condition is defined. The convergence limit of 10⁻³ is fixed for the velocity and 10⁻⁶ for the energy. The Shear Stress Transport (SST) k-ω has been used for the simulation. This combines the k-ω model (for the inner boundary layer region) and the k-ε model (for the outer boundary layer region). It is a two equilibrium model that includes the turbulence kinetic energy (k) and specific dissipation rate (ω) (Menter, 1994).

After convergence, CFD predicted Nu for the bare pipe has been compared with analytically predicted values under similar operating conditions. Figure 1 shows the comparison between the numerical and analytical Nu from the (Dittus—Boelter) equation given by $\mathit{Nu}=0.023\mathit{R}{e}^{0.8}\mathit{P}{r}^{0.4}$ (Manjunath et al., 2017) where Nu is the average Nu and Pr is the Prandtl number. These values are very close to each other with a maximum difference of 2.3%.

Figure 1. Comparison between the CFD predicted and analytical values for Nu.

3.2. Heat exchanger with truncated conical turbulators

A tubular heat exchanger with an inner pipe diameter of 15 mm, a thickness of 1 mm, and an outer annulus diameter of 40 mm is considered for the study. The length of the heat exchanger is taken as 500 mm. Hot water flows in the inner pipe, whereas air is chosen as the fluid flowing in the annulus. The temperature of hot water is maintained constant, whereas the air flow rate varied from a Re of 3000 to 15,000 in increments of 3000. Conical-shaped turbulators with a base diameter of 12 mm and height of 12 mm with a draft angle of 15° are placed with a circumferential angular separation of 90 degrees. Inside dimeter of the pipe is taken as 15 mm. The height of the conical turbulators has been fixed as 12 mm so as to leave some gap for the air to pass freely. After some initial trials, it was found that 15 included angle for the turbulator gave good meaningful results. Hence, the angle was fixed as 15°. Circumferentially 4 numbers have been chosen to avoid any overlapping of the turbulators. A schematic representation of the heat exchanger with the conical truncated turbulator is shown in Figure 2. Specifications of the heat exchanger and also the turbulators are mentioned in Table 3. The geometry of the conical turbulators is maintained constant with the pitch value varied from 25 mm to 100 mm and the numerical studies are conducted. Meshing is done by using tetrahedral elements. Figure 3(a) shows the meshed model of the heat exchanger with the turbulators.

Figure 2. Schematic representation of the heat exchanger with the conical turbulator.

Figure 3a. Meshed model of the truncated conical turbulated heat exchanger.

Figure 3b. Grid independence study for the truncated conical turbulated heat exchanger.

Table 3. Dimensions and Specifications of the heat exchanger

Specifications	Dimensions
Inner tube Diameter	15mm
Outer tube Diameter	40mm
Tube Thickness	1mm
Length of the heat exchanger	500 mm
Base diameter of the truncated conical turbulator	12 mm
Height of the turbulator	12 mm
Pitch values in mm	25, 50,75 and 100
Material of heat exchanger and turbulator	Copper
Inner pipe fluid	Water
outer pipe fluid	Air
Water Reynolds number	3000
Reynolds number of air	3000, 6000, 9000,12000 and 15,000

Initially, grid independence study has been performed to optimize the number of elements required. Air outlet temperature value has been plotted with the number of elements. Initially on increasing the number of elements from 85 Lakh to higher values, there was a steep rise in outlet temperature and the curve almost flattened at 97.7 Lakh elements and further increase in the number of elements resulted in not much improvement in the out temperature values as shown in figure 3(b). Hence, 97.7 Lakh elements have been chosen as the optimum number of elements for the study. Cell zone conditions, Boundary conditions, and the convergence criteria are maintained the same as discussed in the earlier section. Outlet temperature predicted by the numerical simulation are used and performance parameters, such as Nu, heat transfer coefficient, and THPI are calculated by using Equations (1(1) $\mathit{Re}=\frac{{\rho }_i{V}_i{d}_i}{{\mathit{\mu }}_i}$(1) -10(10) $\mathrm{f}=\frac{2\mathrm{\Delta }\mathit{P}{\mathit{D}}_{\mathit{air}}}{\mathit{\nu L}{V}^2}$(10) ).

4. Results and discussions

4.1. Flow modification

Mass flow rate if the inner fluid is maintained constant whereas Re of air is varied from 3000 to 15,000. Outlet temperatures of both water and air are noted. Performance parameters such as Nu, h, and THPI are calculated. Various contour plots related to the temperature, velocity, and turbulence effects are taken to understand the influence of turbulators on the heat transfer performance of the heat exchanger.

Figure 4 shows the velocity contour plots for Re 3000 and 15,000. It is seen that the local velocity values near the conical surface will experience turbulence. Air stream strikes the surface encircles it and moves across the turbulator and giving rise to a vortex motion as seen in the contour plot. Due to this recirculation occurs and hence velocity values will increase at the surface and will be very low at the point of recirculation. As the Re is increased, these effects will be enhanced and hence higher turbulence will be induced which also increases the recirculation. These effects can be observed in Figure 4.

Figure 4. Contour plot showing the velocity variation (a) along the length (b) exit velocity for Re 3000 and 15,000.

Figure 5. Contour plot showing the temperature variation along the length for Re 3000 and 15,000.

Figure 5 shows the influence of turbulators on the outlet temperature along the length of the heat exchanger for Re 3000 and 15,000. When a conical structure is adopted, due to the formation of eddies, higher fluid mixing takes place as compared to that of bare pipe. This increases the effective fluid mixing and hence local fluid temperature increases. The induced vortex flows will disrupt the thermal boundary layer leading to an increase in the local fluid temperature. Similar effects will be experienced near the subsequent conical turbulators and hence the effective outlet temperature at the exit increases. As Re is increased, the turbulator effects will be increased, but the retention time of the fluid reduces as the fluid moves faster along the length of the pipe. This will reduce the contact time of the fluid and hence the outlet temperature reduces as compared to that lower Re. These effects can be seen in Figure 5.

Figure 6. Contour plot showing the turbulent intensity variation along the length for Re 3000 and 15,000.

Figure 7. Contour plot showing the turbulent kinetic energy variation along the length for Re 3000 and 15,000.

The turbulent intensity and turbulent kinetic energy are the two factors depicting the turbulence level of the fluid during its flow through the pipe. Turbulent intensity is defined as the ratio of the root mean square of the velocity fluctuations to the mean fluctuations.

Mathematically, it is written as

$\mathit{Turbulentintensity}=\frac{U_{\mathit{RMS}}}{\mathit{t}},$

where $U_{\mathit{RMS}}$ is the root mean square of the turbulent velocity fluctuations at a particular point over a specified interval of time t.

The higher the value, the higher will be the turbulence level. As seen in Figure 6, the maximum value of turbulent intensity is around 0.44 for Re of 3000, whereas for Re 15,000 it is around 2.1. This indicates as the fluid Re is increased, turbulent intensity increases. When the fluid enters the heat exchanger under turbulent conditions, conical-shaped turbulators placed along the axial length further increase the turbulence due to effective mixing. When the fluid encircles the conical-shaped structures and meets at the back of this, vortex motion will be generated, or in other words, turbulence will be increased.

Turbulent kinetic energy is the mean kinetic energy per unit mass associated with eddies (Manjunath et al., 2017). As the fluid turbulence increases, turbulence kinetic energy also increases as seen in Figure 7. A higher value of turbulent kinetic energy increases boundary layer disturbance near the turbulator bodies. This augments the heat transfer characteristics resulting in a higher heat transfer rate. The maximum value of Turbulent kinetic energy for the flow with Re 3000 is 0.29 m²s⁻² whereas when the Re is 15,000 it is near 7.0 m²s⁻². These contour plots will depict the advantage of providing the conical projections in the annulus side of a double

4.1.1. Parametric variation

To understand the influence of pitch variation on the performance of the heat exchanger, four different pitch values have been considered. Dimensions of the turbulators have been maintained constant and the pitch values are increased from 25 mm to 100 mm in increments of 25 mm. Figure 8(a) shows the velocity contours for the heat exchanger with pitch 25 mm and 100 mm at Re 6000. When the pitch value reduces, the turbulators are closely arranged and the flow disturbance will be higher. This enhances the vortex flow and recirculation. Hence, flow modification will be enhanced which leads to better heat transfer characteristics. The turbulent intensity values as shown in Figure 8(b), wherein, the advantage of smaller pitch values are clearly visible. When the pitch is reduced, instances of flow modification will be higher resulting in superior turbulent intensity. It results in effective fluid mixing and maximum disordered thermal boundary layer. These favour the heat transfer characteristics near each turbulator and as the number of turbulators are higher, effectively increases the heat transfer rate. Higher heat transfer results in higher energy transfer to the fluid in the annulus, in other words, exit temperature of the fluid will be higher as shown in Figure 8(c). when the pitch values are higher, flow modification that happens near each turbulator will not be able to reach till the next turbulator. Thermal boundary layer disruption will be minimized as the fins are placed considerably apart. The effects are clearly seen in Figures 8(a-b).

Figure 8. (A) variation of velocity contours (b) variation of turbulent intensity (c) exit temperature variation for different pitch values.

4.1.2. Temperature

Figure 9. Variation of temperature along the length of the heat exchanger for different pitch values.

Figure 9. shows the comparison of the temperature rise along the length for the pitch values 25 mm, 50 mm, and 100 mm measured for Re 6000. It is evident that at each of the conical turbulator augmentation in heat transfer takes place by which higher energy will be imparted to the fluid than the bare pipe. Hence, the local increase in the temperature occurs along the flow length. It is seen that for an initial length of 100 mm there is not much temperature variation for any pitch values. It is seen that when the pitch is very large, temperature rise starts at a larger length from the entrance. Till that point, it is seen as a horizontal line. As the pitch is reduced, augmentation starts earlier or at smaller distance from the fluid entry which is clearly visible. As the flow progresses, due to the increased number of instances of flow modification for 25 mm pitch, the temperature rise is higher as compared to the pitch of 100 mm and less than 50 mm. When the number of turbulators is significantly higher, the distance between them drastically reduces. Due to the abrupt boundary layer disruption, energy conversion and energy transfer may not be effective resulting in a slightly reduced temperature rise as seen for 25 mm pitch. Similarly, when the pitch values are too higher as in case of 100 mm, thermal boundary layer disruption will be ineffective. Hence, when the pitch values are too smaller or too higher, performance in terms of temperature rise will be reduced. Optimum pitch values are necessary to induce efficient turbulence as well as a better heat transfer rate.

4.1.3. Nusselt number (Nu) and Annulus heat transfer coefficient

Figure 10. Variation of Nu and annulus HTC with pitch values for different Re.

Figure 10 shows the Nu variation for various pitch values plotted for different Re. It is seen that as Re increases, Nu also increases. Increased turbulence effects enhance the heat transfer rate as the Re is increased. This results in a higher heat transfer coefficient and Nu. The comparison of Nu for varied pitch values reveals that initially as the pitch values increase, Nu increases. It reaches an optimum for a pitch value corresponding to 50 mm and a further increase in pitch reduces Nu. Therefore, both too higher and too lower pitch values are detrimental to Nu. When it is too low, even though flow circulation is increased, it is ineffective in transferring the entire energy to the fluid in the annulus causing reduced Nu values. When the pitch values are too high, due to the reduction in the retention time, flow recirculation and vortex motion decreases which directly affects the flow turbulence. At 50 mm pitch, flow modification is most efficient, thus transferring maximum energy to the fluid in the annulus as seen by the maximum Nu. Similar trends are also seen for the convective heat transfer coefficient for the annulus fluid. As the turbulator pitch increases, h_o also increases and attains a peak value corresponding to 50 mm pitch and again drops for higher values of the longitudinal pitch. It is seen that for 50 mm pitch values, Nu values are 10.8% higher than 100 mm pitch and 28.2% higher than the bare tube measured at Re 6000.

4.1.4. Pressure drop and friction factor

Figure 11. Variation of ΔP and friction factor with pitch values for different Re.

Simulated pressure drop values for different Re and various pitch values are shown in Figure 11. It is generally seen that as Re is increased, ΔP increases for all pitch values. An increase in velocity creates more frictional resistance which increases ΔP. For the bare pipe, it is lower and steeply increases as the Re is increased for conical turbulated pipes as seen in Figure 11. When the pitch is larger, it offers less resistance to the motion due to the fewer number of turbulators placed along the axial length. A lower pitch value increases the instances of recirculation and mixing. Due to this, a considerable pressure drop occurs. In the current study, a pitch of 25 mm shows the highest, and a pitch of 100 mm shows the lowest pressure drop values. When the pitch value reduces from 100 mm to 25 mm pressure drop values rose by 144%. These values are 1.9 times and 7.1 times that of bare pipe at Re 6000. The friction factor is a dimensionless quantity as calculated by using equation 10(10) $\mathrm{f}=\frac{2\mathrm{\Delta }\mathit{P}{\mathit{D}}_{\mathit{air}}}{\mathit{\nu L}{V}^2}$(10) for the turbulent flow. It is seen that as Re increases f values decrease for all pitch values. Pitch 25 mm shows the highest value, whereas bare and higher pitch values show a decreasing trend for f.

4.1.5. Thermo Hydraulic Performance Index (THPI)

Figure 12. Variation of THPI with pitch values for different Re.

When the truncated conical turbulators are arranged in the annulus region, both Nu and heat transfer rate will be increased. Similarly, pressure drop and the f value also increases. A rise in ΔP value requires additional pumping power to push the fluid from the inlet to the outlet. Hence, a performance parameter called thermo hydraulic performance index THPI is used to compare the thermal performance of heat augmentation devices considering the same pumping power. It is defined by the relation $\mathrm{THPI}=\mathit{\hspace{0.17em}}\frac{\frac{N{u}_T}{\mathit{N}{u}_b}}{{\left[\frac{f_T}{f_b}\right]}^{\frac{1}{3}}}$ (Zaboli et al., 2021). Where Nu_T and Nu_b are the Nu for the conical turbulator and bare pipe, respectively. f_T and f_b are the friction factors for the turbulator and bare pipe, respectively. It is seen in Figure 12 that the highest THPI is observed for the 50 mm pitch and at a Re of 9000. For Lower pitch values even though the heat transfer rate increases, ΔP also increases. As the pitch values are increased, the heat transfer rate decreases. It is seen that for the same Re of 9000, for pitch 100 mm and 25 mm, THPI is reduced by 10.7% and 2.7%, respectively. Further, as the Re increases, the increase in Nu will be lower as ΔP values increase. Hence, there lies an optimum range of Re (9000–11000) and pitch values for which the THPI is maximum. Hence, if the heat exchanger is operated under the above-mentioned conditions maximum increase in the performance could be achieved. With conical turbulators for pitch values of 50 mm and when the Re is maintained in the range 9000–11000, maximum performance can be attained.

In order to predict the values for any combination of the design variables and operating variables Correlations have been framed from the simulated results for NU and friction factor and are as shown below.

(14) $\mathit{Nu}=0.0678\mathit{R}{e}^{0.74}\mathit{P}{r}^{0.33}{\left(\frac{P}{d}\right)}^{0.017}$(14)

(15) $\mathit{f}=2.445\mathit{R}{e}^{-0.207}{\left(\frac{P}{d}\right)}^{-0.586}$(15)

Where (P/d) represents the ratio of pitch to the inner diameter of the heat exchanger.

Further, the present study results have been compared with the literature values. Even though the exact and similar arrangements, configurations and operating conditions are not available, similar types of work conducted by different authors have been compared with the present study and shown in Table 4. It can be seen that the present work results are at par with the literature values.

Table 4. Comparison of the present results with Published literature

Authors	Geometry	Operating conditions	Results obtained
Eiamsa-Ard & Promvonge, (2010).	Alternate clockwise and anticlockwise twisted tape inserts	Re varied from 3000–27000	Nu is 41.9% higher than the plain tube Heat transfer rate increased by 90% than the plain tube
Kumar et al., (2020).	Hemispherical Turbulators in the annulus body	Re varied from 2500 – 10000	Maximum Nu and THPI occurred for pitch ratio of 0.58. Nu is 2.71 times the base value and the corresponding THPI value 1.41
Kazemi Moghadam et al., (2020).	Corrugated tube with coiled wire	Re varied from 5000–20000	For P/d = 5 max increase in Nu observed for Re =5000
Zhang et al., (2012).	Helical fins with vortex generators	Re varied from 6000–14000	Nu for rectangular winglet pair was 46% higher than with only helical fins. For the same pitch
Present study	Truncated conical turbulators	Re varied from 3000–15000	Highest Nu and THPI of 78 and 1.13 obtained for pitch 50 mm.

5. Conclusions

In the current study, the application of truncated conical turbulators in the annulus body of the double pipe heat exchanger has been numerically studied. Conical turbulators of uniform geometry are placed at different pitch values and the simulation has been conducted. The following observations are noticed.

1. The thermal performance of the modified heat exchanger is superior to that of the bare pipe in terms of higher outlet temperature for the same Re.

2. Conical turbulators are found to be very effective in increasing the flow turbulence as seen by the higher turbulent intensity and turbulent kinetic energy values.

3. Nu and h₀ have been significantly improved for the turbulated heat exchanger. The maximum increase was observed for the pitch 50 mm and Re 15,000 which is 63% higher than the bare pipe.

4. Pressure drop values increased with Re and lower pitch values. The highest ΔP is obtained for the operating conditions of Re 15,000 and a pitch of 25 mm which is 153% higher than the 100 mm pitch for the same Re.

5. Maximum THPI is noticed for the combination of 50 mm pitch and Re of 9000. These values are 4.76% and 10% higher than Re of 3000 and 15,000. Similarly, it is 2.7% and 10.7% higher as compared to 25 mm and 100 pitch values.

6. For the tested conditions with conical turbulators for pitch values of 50 mm and when the Re is maintained in the range 9000–11,000, maximum performance can be attained.

Conical turbulators can be conveniently used as passive heat augmentation devices in air heaters to increase heat transfer characteristics. This helps to increase the thermal performance of the double pipe heat exchanger without requiring extra energy and also space requirements.

Nomenclature

Nu	=	Nusselt Number
Re	=	Reynolds Number
p	=	Pitch (m)
d	=	Diameter (m)
$\mathrm{\Delta }$P	=	Pressure Difference (Pa)
THPI	=	Thermo Hydraulic Performance Index
Pr	=	Prandtl Number
mhi	=	hot fluid inlet mass flow (kg/s)
mco	=	cold fluid outlet mass flow (kg/s)
Thi	=	inlet temperature of hot fluid (ﾰC)
Tho	=	outlet temperature of hot fluid (ﾰC)
Tci	=	inlet temperature of cold fluid (ﾰC)
Tco	=	outlet temperature of cold fluid (ﾰC)
LMTD	=	Log Mean Temperature Difference
f	=	friction factor

Future scope

Numerical studies can be extended for varying the number of turbulators circumferentially. Further, the basic geometry of each turbulator can be changed by varying the included angle. In addition, optimization of the thermohydraulic efficiency could be done by using the various optimization techniques.

Disclosure statement

No potential conflict of interest was reported by the author(s).