Augmentation of Heat Transfer in Pipe Flow Using Plain Twisted Tape Inserts for Different Twist Ratios

The heat transfer augmentation of plain twisted tape inserts for different twist ratios has been studied in this study. The data are conducted using the plain twisted tape insert with five different twist ratios respectively. The range of Reynolds number is considered under a uniform heat flux condition. In the case of simulation, the tapes are made from a stainless steel strip with a thickness of 2 mm. A tubular pipe with 850 mm U-loop length and twist length of 800 mm each is considered in our study for simulation. Water is used as working fluids inside the tube for our simulation. The simulation results demonstrate that the important heat transfer parameters including Nusselt number (Nu), friction factor (f) and thermal performance index (η) are gradually increased with the increment of the twist ratio and reached at the saturated level while twist ratio is 3.5, afterward the thermal properties are decreased.


Introduction
Nowadays in the industrial arena, the demands for mechanical devices are increasing gradually. For this purpose, the heat enhancement technology related to heat exchanger has drawn more attention to the development of such devices.
From several studies, it is found that the augmentation of heat varies with different heat transfer parameter including fluid flow rate, the dimension of pipe, different types of inserts, etc. Automobiles, Solar water heaters, Petrochemical Energy and Power Engineering Industries, Power plan, shell, and tube heat exchangers, etc. are the main application of the heat exchanger [1] [2]. Significant research work has been done on heat transfer enhancement technology to improve the system. The Heat Transfer techniques similarly promote secondary flow and twisted tape inserts due to their benefit of fixed performance and effectiveness in case of heat enhancement.
By utilizing the twisted tape inserts, the flow becomes occlude and subsequently produce eddying due to increasing recirculation area between the closest wall surface and the twisted tape insert. So heat transfer in a tube can be increased by fluid mixing with the help of using inserts [3].
It is seen from recent studies that there are some experimental and theoretical methods have been considered on the enhancement of heat transfer coefficient and friction factor for formal fluid flows inside a tube fitted with different types of inserts to influence a swirl in the fluid flow [4] [5] [6] [7]. The study of Zozulya and Seigel [8] [9] observed that for twisted tape insert in a composite flow structure enhances the rate of heat transfer 2.0 to 3.0 times in comparison to a typical plain pipe.
On the other hand, Noothong et al. [2006] and Murugesan et al. [2009] studied experimentally the effect of different types of twisted-tape with twist ratios of 4.0 and 6.0. They found that enhancement of heat transfer and the Nusselt number increases with decreasing the twisted ratio, while friction factor also increases with decreasing the twisted ratio [10] [11]. In the year 2010, Eiamsa et al.
investigated the heat transfer rate, friction factor and thermal enhancement factor of the combined devices of twisted tape and wire coil. It is observed that the heat transfer and friction factor is more efficient in twisted tape than wire coil [12]. In the same year Raju et al. explained the influences of various width twisted tape in the range of 10 -26 mm with the range of Reynolds number 6,000 -13,500, in a circular tube of 27.5 mm inner diameter. They also compared the enhancement of heat transfer for a smooth tube with the twisted tape inserts and found that the rate increased from 36% to 48% [13]. In the same year, Murugesan et al. performed an experiment on heat transfer, friction factor and thermal performance factor characteristics using v-cut twisted tape in a circular tube with twist ratios 2.0, 4.4, and 6.0. Three various combinations of width and depth ratio and also considered in their study. The results have shown that the average Nusselt number and friction factor in the tube with v-cut twisted tape increase with decreasing twisted ratios, width ratios and with increasing depth ratios [14].
In a numerical study done by Guo et al., considering the characteristics of heat transfer and friction factor of a laminar flow in a round tube supplied with center-cleared twisted tape inserts. The thermal performance factor of the tube with typical twisted tape was compared with a tube with center-cleared twisted tape and found the rate of increment from 7.0% to 20.0%. From the results, they proposed that the center-cleared twisted tape was a promised technique for laminar convective heat transfer enhancement [15]

Mathematical Model
The movement of fluid particles and transfer of heat inside the tube, as well as a  [20].
As the domain is a Tubular U-loop pipe, to get a better prediction about the flow around the curve region, we consider the k-ω turbulent model. The parameters k and ω are given by the following equations.
The heat transfer rate through a fluid is governed by the following equation: where, Here in Equation (7), Q contains heat source other than viscous heating (SI unit: W/m 3 ). For obtaining the heat transfer term used Fourier law of heat conduction, the convective heat flux, q is proportional to the temperature gradient.
where K is the thermal conductivity. The convective heat flux is given by The term : S τ in Equation (7) (7) and (8) we find If the velocity is to zero the equation becomes Again we obtain convective heat transfer coefficient where T w and T b are the wall and bulk temperature respectively and 2 The Nusselt number is calculated by Here D is the diameter of the tube. Depended on the numerically measured pressure drop, the Darcy friction factor can be computed as following [21] [22]: where ∆p is pressure drop and head loss is h, From Equation (14) and (15) where, Δp is the pressure drop across the length of the tube l. The performance Evaluation Criterion (PEC) is defined as follows [23]: where Nu 0 and f 0 are the Nusselt number and the friction factor of the plain tube respectively.

Boundary Conditions
In this flow model, the boundary conditions are assumed a different velocity for

Computational Domain and Mesh Design
Design of computational domain with a twist ratio 3.5, and a twisted tape are shown in Figures 1(a)-(c). In our simulation, we have considered a typical U-loop circular tube whose length is 1875.08 mm, inner diameter 26.6 mm, out-  Table 1 and Table 2 respectively.

Numerical Results
The main aim of our numerical simulation is to ensure the enhancement of

Temperature Performance Evaluation
Besides the twist ratio 3.5 we also have investigated for all ratios like 2.9, 3.0, 3.25, 3.5 and 4.0 to check the heat transfer phenomena in different twist ratio.
We found different results are shown in Figure 3. This figure represents the temperature variation with the increment of Reynolds numbers for different twist ratios. For the twist ratio 3.5, we observe a gradual temperature fall with the increase of Reynolds numbers. We observed the same pattern for ratio 2.9 and 3.0 while 3.25 and 4.0. It is shown quite the opposite pattern though both are decreased. It seems 3.5 is the best twist ratio and the saturated level for the maximum heat transfer.

Nusselt Number Performance Evaluation
In

Friction Factor Performance Evaluation
The variation of pressure drop in terms of friction factor (f) with Reynolds   number (Re) is described in Figure 5. From Figure 5 we also observed that the friction factor tends to increase with decreasing twist ratios for all Reynolds number within the range. The twisted tape with inserts with smaller twist ratio process more twist numbers thus induces more consistent with stronger swirl intensity. This creates higher turbulent intensity and consequently better heat transfer. The favorable reduction of friction factor as compared with the ratio 2.9, 3.0, 3.25, 4.0, the twist ratio is 3.5 because of the lower flow scattering caused

Thermal Performance Evaluation Criterion (PEC)
The performance evaluation criterion (PEC) in a tube fitted with different twisted tapes obtained using numerical simulations are shown in Figure 6. It is observed that the PEC value tends to increase with increasing Reynolds number for 5000 to 10,000 but it's shown in different behavior for 15,000 to 25,000. The tubes fitted with twisted tapes inserts of the ratio gives better overall heat transfer performance than the tubes with twisted tapes of the other twist ratios [2.9, 3.0, 3.25 and 4.0].

Conclusion
A computational study of the heat transfer phenomenon of fluid flow through a tubular pipe with five different twist ratios [2.9, 3.0, 3.25, 3.5 and 4.0] for a non-isothermal turbulent flow has been studied. The water consider as working fluid in our study and the initial temperature is assumed at the inlet is 293.15 K.
A no-slip condition on the wall and wall function on the outlet is assumed. For our simulation, we assumed that better heat transfer rate is found while the twist ratio is 3.5 compared with other ratios while the Reynolds number gradually increased from 5000 to 25,000. We found the same scenario for the Nusselts number as well. Also, we have observed that for pressure is reducing when the Reynolds (Re) numbers are increased.