Experimental investigation on heat transfer effect of conical strip inserts in a circular tube under laminar flow

Abstract

The aim of this paper is to observe the Nusselt number and friction factor behavior of the circular tube with conical strip inserts as turbulators in a laminar flow condition, using staggered and non-staggered conical strips with three different twist ratios (Y = 2, 3 and 5). The conical strip is inserted in the forward and backward direction individually compared to the flow of water which is the working fluid. The results indicate that the conical strip inserts increases the Nusselt number when compared to the plain surface tube. It is observed that the strip geometry has a major effect on the thermal performance of the circular tube. On examination of different strips for determining the enhancement of Nusselt number, the staggered conical strip with the twist ratio of Y = 3 has given a better result compared to the other two strips. Finally, correlations have been derived using regression analysis for predicting the Nusselt number and friction factor.

Keywords

Nusselt number / friction factor / conical strip

Introduction

Heat transfer enhancement techniques can be incorporated in the design of new compact heat exchangers used in various industries, especially automotive, refrigeration system, chemical reactor and heat recovery process. The enhancement techniques are used not only to save materials and cost of equipment, but also to decrease energy consumption [ 1]. Additionally, heat transfer enhancement allows heat exchangers to operate at a lower velocity, which means a reduction in pressure drop and hence corresponds to less operating cost [ 2]. Heat transfer enhancement methods are divided into active and passive methods. The former is the one in which external power is required, whereas the latter is the one that does not require external power source [ 3]. The passive technique incorporates the use of treated, extended, rough surfaces and coiled tubes. Among the most common passive heat transfer enhancement techniques, tube insert technique is the most prevalently used [ 4]. Tube inserts can increase the Nusselt number due to the generation of swirls in the tube, which decreases the thermal boundary layers and intensifies fluid mixing [ 5].

Several experiments on twisted tapes with regularly spaced, varying length, with different cut shapes, with baffles and with different surface modifications were reviewed by Liu and Sakr [ 6]. Promvonge [ 7] studied the increase in heat transfer rate using conical ring with three different diameter ratios and placed with three different arrangements. Sivashanmugam and Suresh [ 8] found that the Nusselt number and friction factor increased with the twist in circular tube with full-length helical screw inserts and the heat transfer coefficient enhanced with decreasing twist ratio. They [ 9, 10] also developed a correlation to predict the Nusselt number enhancement in a circular tube with spaced helical screw-tape inserts and with conventional helical screw-tape inserts. Noothong et al. [ 11] found that the twisted tape inserts gave rise to the vortex or swirl motions which decreased the boundary layer thickness and improved the Nusselt number rate in twisted tape insert with varying twist ratios in a double pipe heat exchanger. García et al. [ 12] showed that wire inserts perform better when compared to twisted tapes in the laminar flow. Akhavan-Behabadi et al. [ 13] studied the behavior of lower diameter wire coil inserts at laminar flow in a horizontal tube with performance evaluation factor. Tu et al. [ 14] reported that the maximum Nusselt number of the tube with small pipe inserts is 2.61 to 3.33 times than that of the empty tube. You et al. [ 15] numerically indicated that heat transfer rate increased largely with smaller strip-wall gap and smaller strip pitch. Pal and Saha [ 16] found better performance in a circular duct under laminar flow with the combination of integral spiral rib roughness with twisted-tape with oblique teeth inserts.

From the literature, it is found that twisted tape and wire coil inserts with various geometrical considerations like equilateral triangle cross sectioned coiled wire inserts [ 17], alternate clockwise and counter-clockwise twisted-tapes [ 18] and conical rings [ 19, 20] were only the focus of study, whereas the effect of conical strip insert with a different twist ratio were not discussed.

This paper studies the Nusselt number and friction factor behavior of laminar flow through a circular tube with conical strip inserts of various twist ratio, and different geometrical considerations. The conical strips generate more swirl flow and give larger fluid mixing with increased Nusselt number rate.

Technical details of conical strip inserts

Figure 1 schematically shows the conical strip inserts. The strips are uniformly connected to a central rod of 1000 mm in length and 1 mm in diameter. The staggered and non-staggered conical strip inserts are made of copper sheet of 1 mm in thickness. The staggered conical strips are those which are uniformly connected over the entire length of the rod. On the contrary, the non-staggered conical strips are those which are randomly distributed over the entire length of the rod. The staggered and non-staggered conical strip inserts with different twist ratios of 2, 3 and 5 are used in this paper. The twist ratio ‘Y’ is defined as the ratio of the length of the rod to the diameter of the test section.

The dimensions of the conical strip of the surface of the cone are illustrated in Fig. 2. The conical strip inserts are designated as S, M and L for twist ratios of 2, 3 and 5 respectively and prefixed with 1 and 2 for non-staggered and staggered respectively. The conical strips with the twist ratios of 2, 3 and 5 are designated as S₁, M₁, and L₁ as shown in Fig. 1 and S₂, M₂ and L₂ as shown in Fig. 3 for non-staggered and staggered respectively. A swirl is introduced into the bulk flow for increasing the convective Nusselt number. Further, due to changes in the surface geometry, the boundary layers are disrupted.

Figure 4 demonstrates the schematic diagram of the experimental setup and Fig. 5, the photographic view. The experimental setup consists of the calming section, the test section, the riser section, the cooling unit, the pump, and the fluid reservoir. The calming section is designed to reduce the entrance effect and to provide a smooth flow of the fluid. The dimension of the test section is 1000 mm long, 12 mm in outer diameter and 10 mm in inner diameter. The test section is uniformly heated with an electrical Standard Wire Gauge Ni-chrome heating wire with a resistance 120 Ω wounded around by ceramic beads. Thick glass wool insulation is provided over the electrical winding to minimize heat loss. The riser section is a vertical pipe to provide uniform flow of the working fluid in the test section. The cooling unit is an air cooled heat exchanger where a pump is used to circulate the fluid through the riser and the heated test sections. The fluid reservoir is a stainless steel vessel with a drain valve, having a capacity of four liters. The constant heat flux on the test section can be maintained by an auto transformer. Seven RTDs with an accuracy of 0.1°C is used to measure the fluid and wall temperatures. The pressure drop, if any, is monitored by a differential pressure transducer mounted across the test section. A U-Tube manometer is set up across the test section to validate the pressure transducer. A glass tube rotameter with an accuracy of±2% is mounted on vertically to measure the flow rate of the working fluid. It consists of tapered glass tube and is shielded from all sides with clear front visibility.

A uniform wall heat flux boundary was created with the help of an auto-transformer in the test section which was heated using a Ni-Chrome heater. Water was pumped at a controlled flow rate into the test section by using a by-pass valve. The system stabilized within 1 h for the first run and took 45 min for subsequent runs. The RTD temperature sensors were used to check the fluid outlet and the wall temperatures at seven axial locations. Further, a conventional thermometer was used to measure the fluid inlet temperature. The electrical heat flux was monitored using a calibrated ammeter, voltmeter and watt meter. The heat flux and flow rate were varied and observations were recorded after attaining steady-states for each of the runs at the designated locations. Experiments were done using staggered and non-staggered conical strips with different twist ratios of 2, 3 and 5 as mentioned earlier.

Pressure drop and heat transfer calculation

The friction factor for fully developed flow was determined by

(1) f=\left({\displaystyle \frac{D_i}{L}}\right)\left({\displaystyle \frac{\Delta P}{\mathrm{2}\rho u_m^2}}\right),

where D_i is the inner diameter and u_m is the mean velocity.

The variation in pressure was calculated using a U tube manometer where mercury was used as the manometric fluid. The heat transfer rate was calculated by

(2) Q={\displaystyle \frac{V^{\mathrm{2}}}{R}}=U_o{A}_o(T_w-T_f)=\stackrel{\cdot }{m}Cp(T_{\mathrm{out}}-T_{\mathrm{in}}),

where U_o is the overall heat transfer coefficient, A_o is the outer surface area of the tube (m²), T_f is the fluid temperature (°C), T_w is the wall temperature (°C), T_in is the inlet temperature (°C), T_out is the outlet temperature (°C), and

(3) {\displaystyle \frac{\mathrm{1}}{U_o{A}_o}}={\displaystyle \frac{\mathrm{1}}{h_i{A}_i}}+\ln (D_o-D_i)/(\mathrm{2}\pi k_{w}L)

where h_i is the heat transfer coefficient (W/(m²·K)), A_i is the inner surface area of the tube (m²), D_o is the outer diameter (m), and D_i is the inner diameter (m).

The convective heat transfer coefficient was determined using Eq. (3). The Nusselt number was calculated using Eq. (4).

(4) Nu=hD/k,

where k is the thermal conductivity (W/(m·K)).

Experimental uncertainties were found using the Coleman and Steele method [ 21]. The calculations showed that maximum uncertainties are±6% for the Reynolds number,±5% for the friction factor, and±8% for the Nusselt number.

Results and discussion

Initially, the experiment was conducted on a plain tube for validation. The experimental setup was verified by comparing it with Eq. [ 22] for laminar flow. Figure 6 shows that the experimental data are in good agreement with Eq. (5). Similarly, the friction factor comparison is made with Eq. (6). Figure 7 is a comparison of the experimental friction factor with the theoretical equation. Figure 8 represents the developments of the Nusselt number with respect to the Reynolds number for the staggered and non-staggered conical strips with different twist ratios of 2, 3 and 5 for backward direction. The Nusselt number increases due to the swirl flow developed by the inserts. The above comparisons indicate that all the inserts give a better enhancement in the Nusselt number compared to the plain tube. In this, the staggered conical inserts with the twist ratio of Y = 3, namely M₂, gives a better performance than the other inserts for backward direction. This means M₂ generates more swirl than any other strips.

(5) Nu=\mathrm{1.953}{(\mathrm{Re}\mathrm{Pr}{\displaystyle \frac{d}{L}})}^{\mathrm{1}/\mathrm{2}},

(6) f={\displaystyle \frac{\mathrm{64}}{Re}}.

When compared to M₂, the swirl generation decreases in the order of L₂, S₂, S₁, L₁, and M₁. Figure 9 shows the comparison of friction factor with respect to the Reynolds number. The friction factor increases invariably with all inserts. Figure 10 represents the developments of the Nusselt number with respect to the Reynolds number for staggered and non-staggered conical strips with different twist ratios of 2, 3 and 5 for forward direction. The comparison demonstrates that the Nusselt number decreases in the order of M₂, S₁, S₂, L₂, L₁, and M₁.

In the forward direction, the non-staggered insert with a twist ratio of 2 (S₁) generates more swirl close to M₂. An increase in friction factor is observed in Fig. 11. The performance ratio with respect to the Reynolds number is represented in Figs. 12 and 13 for backward and forward direction of inserts respectively. Correlations were derived using regression analysis.

(7) Nu=\mathrm{0.0757}{\mathrm{Re}}^{\mathrm{0.552}}{\mathrm{Pr}}^{\mathrm{1.308}}{Y}^{\mathrm{0.0032}},

(8) f=\mathrm{22.58}{\mathrm{Re}}^{-\mathrm{0.363}}{\mathrm{Pr}}^{-\mathrm{0.645}}{Y}^{-\mathrm{0.036}}.

The values of the fitted Nusselt number were found using Eq. (7) and the values of fitted friction factor were found using Eq. (8). The results of both Eqs. (7) and (8) were compared to the experimental values. Figures 14 and 15 show that the predicted values are in good agreement with the experimental data.

Conclusions

The Nusselt number and friction factor behavior of a circular tube fitted with staggered and non-staggered conical strips with three different twist ratios of 2, 3 and 5 for both forward and backward direction have been experimentally observed.

1)The experimental setup is in good agreement with the theoretical model for the Nusselt number and friction factor. The swirl flow developed by the inserts leads to an increase in the Nusselt number effectively.

2)The staggered conical inserts with a twist ratio of Y = 3, namely M₂, has a better performance than the other types of inserts for both forward direction and backward direction.

3)The Nusselt number decreases in the order of M_2,L₂, S₂, S₁, L₁ and M₁ in backward direction and M₂, S₁, S₂, L₂, L₁, and M₁ in forward direction. The staggered insert generates more swirl than the non-staggered one in both directions.

4)In the non-staggered inserts, S₁ (Y = 2) generates better swirl close to M₂ when the insert is in the forward direction. The increase in the Nusselt number due to the swirl is generated in the tube by conical strip inserts, which decreases the thermal boundary layer and intensifies the fluid mixing.

5)The enhancement in the Nusselt number overcomes the negative effect of the friction factor. Correlations have been derived using regression analysis to predict the Nusselt number and friction factor.

References

[1] Yakut K, Sahin B. Flow-induced vibration analysis of conical rings used for heat transfer enhancement in heat exchangers. Applied Energy, 2004, 78(3): 273–288

[2] Promvonge P, Eiamsa-ard S. Heat transfer augmentation in a circular tube using V-nozzle turbulator inserts and snail entry. Experimental Thermal and Fluid Science, 2007, 32(1): 332–340

[3] Bergles A E. Recent developments in convective heat transfer augmentation. Applied Mechanics Reviews, 1973, 26: 675–682

[4] Bergles A E. Techniques to augment heat transfer. In: Rohsenow W M, Hartnett J P, Ganie E. eds. Handbook of Heat Transfer Application. New York: McGraw-Hill, 1985

[5] Wang L, Sunden B. Performance comparison of some tube inserts. International Communications in Heat and Mass Transfer, 2002, 29(1): 45–56

[6] Liu S, Sakr M. A comprehensive review on passive heat transfer enhancements in pipe exchangers. Renewable & Sustainable Energy Reviews, 2013, 19: 64–81

[7] Promvonge P. Heat transfer behaviors in round tube with conical ring inserts. Energy Conversion and Management, 2008, 49(1): 8–15

[8] Sivashanmugam P, Suresh S. Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with regularly spaced helical screw-tape inserts. Experimental Thermal and Fluid Science, 2007, 31(4): 301–308

[9] Sivashanmugam P, Suresh S. Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with helical screw-tape inserts. Applied Thermal Engineering, 2006, 26(16): 1990–1997

[10] Sivashanmugam P, Suresh S. Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube fitted with regularly spaced helical screw-tape inserts. Applied Thermal Engineering, 2007, 27(8-9): 1311–1319

[11] Noothong W, Eiamsa-ard S, Promvonge P. Effect of twisted-tape inserts on heat transfer in a tube. In: The 2nd Joint International Conference on Sustainable Energy and Environment. Bangkok, Thailand. 2006, 21–23

[12] García A, Solano J P, Vicente P G, Viedma A. Enhancement of laminar and transitional flow heat transferin tubes by means of wire coil inserts. International Journal of Heat and Mass Transfer, 2007, 50(15-16): 3176–3189 doi:10.1016/j.ijheatmasstransfer.2007.01.015.

[13] Akhavan-Behabadi M A, Kumar R, Salimpour M R, Azimi R. Pressure drop and heat transfer augmentation due to coiled wire inserts during laminar flow of oil inside a horizontal tube. International Journal of Thermal Sciences, 2010, 49(2): 373–379

[14] Tu W, Tang Y, Zhou B, Lu L. Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube with small pipe inserts. International Communications in Heat and Mass Transfer, 2014, 56: 1–7

[15] You Y, Fan A, Liu W, Huang S. Thermo-hydraulic characteristics of laminar flow in an enhanced tube with conical strip inserts. International Journal of Thermal Sciences, 2012, 61: 28–37

[16] Pal S, Saha S K. Laminar fluid flow and heat transfer through a circular tube having spiralribs and twisted tapes. Experimental Thermal and Fluid Science, 2015, 60: 173–181

[17] Gunes S, Ozceyhan V, Buyukalaca O. Heat transfer enhancement in a tube with equilateral triangle cross sectioned coiled wire inserts. Experimental Thermal and Fluid Science, 2010, 34(6): 684–691

[18] Wongcharee K, Eiamsa-ard S. Friction and heat transfer characteristics of laminar swirl flow through the round tubes inserted with alternate clockwise and counter-clockwise twisted-tapes. International Communications in Heat and Mass Transfer, 2011, 38(3): 348–352

[19] Anvari A R, Lotfi R, Rashidi A M, Sattari S. Experimental research on heat transfer of water in tubes with conical ring inserts in transient regime. International Communications in Heat and Mass Transfer, 2011, 38(5): 668–671

[20] Yakut K, Sahin B. Flow-induced vibration analysis of conical rings used for heat transfer enhancement in heat exchangers. Applied Energy, 2004, 78(3): 273–288

[21] Coleman H W, Steele W G. Experimental and uncertainty analysis for engineers. New York: Wiley, 1989

[22] Chandrasekar M, Suresh S, Chandra Bose A. Experimental studies on heat transfer and friction factor characteristics of Al₂O₃/water nanofluid in a circular pipe under laminar flow with wire coil inserts. Experimental Thermal and Fluid Science, 2010, 34(2): 122–130

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