Research Article  Open Access
Numerical Study on Turbulent Forced Convection and Heat Transfer Characteristic in a Circular Tube with VOrifice
Abstract
Performance assessments on heat transfer, pressure loss, and thermal enhancement factor in the circular tube heat exchanger inserted with the Vorifices are investigated numerically. The influences of the blockage ratio, gap spacing ratio, and orifice arrangement are reported for turbulent regime, . The finite volume method and SIMPLE algorithm are selected to solve the present problem. The mechanisms on flow and heat transfer characteristics are described. The periodic concepts on flow and heat transfer are also studied. The numerical results show that the gap spacing ratio is main reason for the changes of the flow and heat transfer topologies. The gap distance helps to adjust the optimum point of the thermal performance, especially at high flow blockage ratio. In addition, the optimum thermal performance of the present system is around 2.25 at the lowest Reynolds number, .
1. Introduction
The passive technique had been used to improve various types of the heat exchangers. The passive method does not require the additional power to enhance the heat transfer rate and thermal performance. The purpose for the passive technique is to disturb the thermal boundary layer on the heat transfer surface and improve the fluid mixing by the vortex generators or turbulators: winglet, wing, rib, baffle, and so forth. The selection of the vortex generator depends on the application of the heat exchanger.
The circular ring (like orifice) is widely used in the tube heating system to augment the heat transfer rate and performance. The configuration of the circular ring is presented as Figure 1. Kongkaitpaiboon et al. [1] experimentally investigated convective heat transfer and friction loss in a circular tube with circularring vortex generators. The influences of the diameter ratios (diameter of the orifice to the diameter of the tube) and pitch ratios () were examined for turbulent regime, . They reported that the heat transfer augmentation is around 57–195% when compared with the smooth circular tube without vortex generator. The selection of the conicalring to improve the heat exchanger was also reported by many researchers [1–15]. They found that the conicalring in the heat exchanger enhances heat transfer rate and thermal efficiency but also increases very large pressure loss, especially at low diameter ratio (low flow area).
The circularring was applied with the twisted tape called “twistedring turbulators,” which used to enhance thermohydraulic performance in the tube heat exchanger [16]. The parameters, width and pitch ratios, were studied at by the experimental method. The twistedring was compared with the typical conicalring on heat transfer and pressure loss. They concluded that the twistedring provides higher heat transfer rate, pressure loss, and thermal performance than the typical conicalring. They also stated that the maximum thermal enhancement is around 1.24 at .
The Vshaped vortex generators [17–28] had been designed to enhance heat transfer rate in the heating and cooling sections. The Vshaped vortex generators give high effectiveness to increase heat transfer when compared with the other types of the vortex generators such as inclined shape, curve shape, wing, and winglet. The height, flow attack angle, pitch spacing, thickness, and so forth of the vortex generators are important factors, which effect for the heat transfer augmentation.
In the present work, the typical turbulator is modified by combining the configuration of circular ring with that of Vshaped baffle and presented as “Vorifice.” The aim of this research is to generate strong vortex flow, which disturbs the thermal boundary layer near the tube wall. The boundary layer disturbance is a reason for the enhancements of heat transfer and thermal efficiency. The influences of the baffle height (or diameter ratio) and flow directions are investigated numerically. To reduce the pressure loss, the gap spacing between the Vorifice and tube wall is also varied. The forced convection heat transfer with turbulent regime at is considered for the present work.
2. Physical Domain
Figure 2 presents the configuration of the circular tube heat exchanger inserted with the Vorifices. The diameter of the circular tube, , is equal to 0.05 m. The distance between the Vorifices, , is fixed at 0.05 m or (). The flow attack angle around 45° of the Vorifice is applied for all cases. The height of the Vorifice, , and gap between Vorifice and tube wall, , are varied. The or BR is called the blockage ratio, while the is known as the gap spacing ratio. The Vtip of the Vorifice points to both downstream and upstream arrangements called “VDownstream (VD)” and “VUpstream (VU),” respectively. The code of the case investigations is reported as Table 1.

The structures of the tube heat exchanger inserted with the Vorifices at various gaps are depicted as Figure 3. The geometries of the computational domain in plane are displayed as Figures 4 and 5.
3. Mathematical Foundation, Assumption, and Boundary Condition
The flow and heat transfer are steady in three dimensions. The flow is turbulent and incompressible. The radiation heat transfer, body force, natural convection, and viscous dissipation are regarded. The fluid properties are assumed as constant at average bulk mean temperature. The periodic condition is used for the inlet and outlet of the computational domain. The uniform heat flux around 600 W/m^{2} is applied for the tube wall. The Vorifices are set with adiabatic wall condition (insulator). Noslip wall condition is used for all surfaces of the domain.
The circular tube flow is solved by the continuity equation, NavierStokes equation, and energy equation. The mathematical foundation and numerical method are referred to by [29]. The realizable model [30] is selected for the current numerical solution. whereThe constant values are as follows:The QUICK numerical scheme is discretized for all governing equations, decoupling with the SIMPLE algorithm and solved using a finite volume approach [31]. The solutions are set to be converged when the normalized residuals are less than 10^{−9} and 10^{−5} for the energy equation and the other variables.
The important parameters are Reynolds number, friction factor, local Nusselt number, average Nusselt number, and thermal enhancement factor printed as (4)–(8), respectively.The Nusselt number and friction factor of the smooth tube are presented as and , respectively.
4. Numerical Result and Discussion
The comparisons between the numerical results with the experimental results and the values from the correlations are reported in the first part, while the periodic concepts on flow and heat transfer are illustrated in the next part. The mechanisms on flow and heat transfer in the tube heat exchanger are depicted in the third part, while the performance assessments on heat transfer, pressure loss, and thermal enhancement factor are described in the last part.
4.1. Numerical Validation
The validation of the computational domain is the most important procedure for the numerical investigation. The computational validations of the smooth circular tube are performed by comparison between the present results with the values from the correlations [32] on the Nusselt number and friction loss. The results are reported as Table 2.

As the results, the maximum deviations of the Nusselt number and friction factor are around 5.48 and 8.28%, respectively.
The computational model is also validated with the experimental results. The case of and with is selected to verify the accuracy of the domain. The realizable kε model is used to examine the present problem. The numerical results reveal that the deviations of the Nusselt number and friction factor are around 6% and 15%, respectively. The evaluation between the numerical and experimental results is reported as Figure 6.
The hexahedral mesh is selected for all numerical domains. The grid independence test is done by compared four sets of grid cell. The 120000, 180000, 240000, and 360000 mesh are generated for the case of A1D. The augmentation of grid cell from 180000 to 240000 has no effect for the heat transfer rate and pressure loss. Therefore, the computational domain is produced with grid cell around 180000 in all cases.
As the preliminary results, it can be concluded that computational domain has reliability to predict flow and heat transfer behaviors in the tube heat exchanger installed with the Vorifices.
4.2. Periodic Flow and Heat Transfer Profile
The periodic concepts on flow and heat transfer of the computational domain are tested. Figure 7 shows full domain of the tube heat exchanger inserted with Vorifices. The boundary conditions for the full domain are also presented in the figure. The flow and heat transfer profiles are described as Figures 8 and 9, respectively. The flow configuration is separated into two zones: periodic flow and fully developed periodic flow. The periodic flow means that the pattern of flow for each module is similar, but the value of is not equal. The fully developed periodic flow means that the value and profile of the flow are identical. The periodic flow profile is found around (the 3rd module), while the fully developed periodic flow profile is detected around (the 6th module). The periodic concept of heat transfer profile is found to be similar to the flow profile. In conclusion, the periodic condition can apply for the computational domain to save investigated time and numbers of grid cell.
(a)
(b)
(c)
4.3. Flow and Heat Transfer Behaviors
The flow configurations in the test tube inserted with the Vorifices are illustrated by isosurface and streamlines in plane. Figures 10(a), 10(b), 10(c), and 10(d) show the isosurface with for B1D, B3D, B5D, and B7D, respectively, at . The isosurface is an indicator of the vortex core, produced by the Vorifices. As the figures, the vortex flows are found behind the Vorifice in all cases. The reduction of the vortex core is found when the gap between the Vorifice and tube wall decreased. B1D performs the largest vortex core, while B7D provides the opposite trend. The similar results are found in cases B1U, B3U, B5U, and B7U as depicted in Figures 11(a), 11(b), 11(c), and 11(d), respectively.
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
The streamlines in planes at various values for B1D, B3D, B5D, and B7D with are shown in Figure 12. For all cases, the vortex flows are detected through the test section. Except for B3D, the four main vortex flows are found in all planes of the tube heat exchanger. The eight small vortices are created at the second and third planes ( and 3.5) for B3D. B1D provides the counterrotating flow with commonflowup, while B3D, B5D, and B7D produce the reverse rotational flow when considered at the lower pair of the vortex flow. Figure 13 presents the streamlines in planes for B1U, B3U, B5U, and B7U at , 2.25, 3.5, 4.75, and 6 of . The general flow structure of the Vupstream case is similar to the VDownstream case. The four core vortex flows are created in all cases, except for B3U. The eight vortices are found at , 2.25, 4.75, and 6 of B3U. B1U generates the counterrotating flow with commonflowdown, while B7U creates the opposite flow rotation. In addition, the presence of the gap between the Vorifices and tube wall is a reason for the change of the flow structure and vortex strength.
The heat transfer behaviors in the test section are described by the temperature distributions in planes and local Nusselt number distributions on the tube wall. Figure 14 shows the temperature contours in yz planes for B1D, B3D, B5D, and B7D at . The disturbance of the thermal boundary layer is found at the upperlower points of B3D, B5D, and B7D, except for B1D. The red layer of the temperature contours performs higher when the gap spacing ratio increased. The disruption of the thermal boundary layer is detected in the leftright parts of the planes for B1D. The difference location of the thermal disturbance is due to the different flow structure.
Figure 15 reports the temperature distributions in planes of B1U, B3U, B5U, and B7U at . The best thermal disturbance is found in the leftright curves of the tube planes, except for B1U. The enhancement of the gap value provides lower strength of the vortex flow. The upperlower points are disturbed by the vortex flow of B1U. Additionally, the reduction of the gap spacing results in the increasing vortex strength.
The local Nusselt number distributions on the tube wall of the tube heat exchanger inserted with Vorifices for Vtip pointing downstream are displayed in Figure 16. The increasing BR and reducing gap spacing result in the enhancing heat transfer rate. The peak of heat transfer regime is found in the leftright parts for but is found in the upperlower parts for . Figure 17 presents contours for the tube heat exchanger inserted with Vorifices of upstream arrangement. The highest heat transfer regions are detected at the side parts of the tube wall, except for . The augmentation of the gap ratio leads to decrease in the Nusselt number.
In conclusion, the space between Vorifices and tube wall is important factor for flow structure. The spacing can convert the rotational vortex flow that is reason for the difference of the heat transfer regime.
4.4. Performance Analysis
The plots of with Re are reported in Figures 18–20 for , 0.15, and 0.2, respectively. In general, tends to slightly decrease with increasing the Reynolds number. The insertion of the Vorifices in the tube heat exchanger gives higher heat transfer rate than the smooth tube ().
(a)
(b)
(a)
(b)
(a)
(b)
As Figure 18(a), the maximum Nusselt number is found at A1D, while the lowest value is detected at A8D. The nonlinearization decrease of the Nusselt number is found due to the reduction of the gap ratio. It is interesting to note that A2D gives lower heat transfer rate than A1D around 25%, while A3D, A4D, A5D, A6D, A7D, and A8D provide lower values than A1D around 1.18%, 1.18%, 4.72%, 10.38%, 18.56%, and 34.20%, respectively. The maximum Nusselt number is about 4.24, 3.15, 4.19, 4.19, 4.04, 3.80, 3.41, and 2.79 times above the smooth tube at . Figure 18(b), the highest heat transfer rate around 6.32, is clearly obtained at A1U for . A2U, A3U, A4U, A5U, A6U, A7U, and A8U give lower Nusselt number than A1U around 53%, 47.63%, 43.99%, 46.52%, 50.63%, 55.22%, and 62.5%, respectively. The similar trends of the Nusselt number ratio are found in cases B and C. In the range studies, the heat transfer rate is found to be around 2.25–4.50, 1.84–6.32, 3.00–5.03, 2.25–6.00, 3.65–6.70, and 2.75–8.25 times higher than that in the smooth tube for AD, AU, BD, BU, CD, and CU, respectively.
Figures 21–23 report the relations of with the Reynolds number at various cases. Generally, the use of the Vorifice in the heating system yields higher pressure loss than the smooth circular tube in all cases (). The enhancement of the pressure loss is found when increasing the Reynolds number. The rise of the gap spacing helps to reduce the friction loss, except for A1D to A4D (see Figure 21(a)). The reduction of the flow area results in the higher friction loss, especially at CD and CU cases. is around 5.9–22, 4.2–34, 12–61, 7.5–77.5, 20–170, and 15–270 for AD, AU, BD, BU, CD, and CU, respectively.
(a)
(b)
(a)
(b)
(a)
(b)
Figures 24–26 present the variations of the thermal enhancement factor, TEF, with the Reynolds number. In general, the TEF tends to decrease with the rise of the Reynolds number. The optimum TEF at various BRs and arrangements is concluded as Table 3. It is interesting to note that the gap spacing helps to optimize the thermal enhancement factor at high , and 0.20.

(a)
(b)
(a)
(b)
(a)
(b)
Figures 27(a), 27(b), and 27(c) depict the relations between and for , 0.15, and 0.2, respectively. The decrement of is found when and in the range for downstream arrangement. For upstream arrangement, , extremely decreases. Figures 28(a), 28(b), and 28(c) present the variations of with for , 0.15, and 0.2, respectively. The gap ratio around 5% extremely helps to reduce the pressure loss, especially upstream arrangement.
(a)
(b)
(c)
(a)
(b)
(c)
5. Conclusion
The numerical investigations on turbulent forced convection and heat transfer behavior in the circular tube heat exchanger inserted with the Vorifices are reported. The influences of the blockage ratio and gap ratio are examined for . The major outcomes are concluded as follows:(i)The better heat transfer rate and thermal performance are found due to the vortex flows in the heating tube, created by the Vorifices. The disturbance of the thermal boundary layer by the vortex flow is important reason for the heat transfer augmentation.(ii)The gap spacing between Vorifices and tube wall is a cause for the change of the flow topology that leads to a variation of the heat transfer behavior. The optimum gap spacing may lead to the optimum thermal enhancement factor.(iii)In range investigations, the enhancements of the Nusselt number and friction factor are found to be highest around 8.26 and 270 times above the smooth tube, respectively. The maximum thermal enhancement factor is about 2.25.
Nomenclature
BR:  Flow blockage ratio () 
:  Orifice height, m 
:  Diameter of tube 
:  Friction factor 
:  Gap spacing 
:  Convective heat transfer coefficient, W m^{−2} K^{−1} 
:  Thermal conductivity, W m^{−1} K^{−1} 
Nu:  Nusselt number () 
:  Distance between ribs 
:  Static pressure, Pa 
Pr:  Prandtl number () 
PR:  Pitch or spacing ratio () 
Re:  Reynolds number 
:  Temperature, K 
:  Velocity in direction, m s^{−1} 
:  Mean velocity in channel, m s^{−1}. 
:  Dynamic viscosity, kg s^{−1} m^{−1} 
:  Thermal diffusivity, () 
:  Angle of attack, degree 
TEF:  Thermal enhancement factor () 
ρ:  Density, kg m^{−3}. 
in:  Inlet 
0:  Smooth tube 
pp:  Pumping power. 
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this article.
Acknowledgments
This research was funded by College of Industrial Technology, King Mongkut’s University of Technology North Bangkok (Grant no. ResCIT0208/2017). The authors would like to thank Associate Professor Dr. Pongjet Promvonge, KMITL, for suggestions.
References
 V. Kongkaitpaiboon, K. Nanan, and S. EiamsaARD, “Experimental investigation of convective heat transfer and pressure loss in a round tube fitted with circularring turbulators,” International Communications in Heat and Mass Transfer, vol. 37, pp. 568–574, 2010. View at: Publisher Site  Google Scholar
 K. Yakut and B. Sahin, “Flowinduced vibration analysis of conicalrings used of heat transfer enhancement in heat exchanger,” Applied Energy, vol. 78, pp. 273–288, 2004. View at: Publisher Site  Google Scholar
 K. Yakut, B. Sahin, and S. Canbazoglu, “Performance and flowinduced vibration characteristics for conicalring turbulators,” Applied Energy, vol. 79, pp. 65–76, 2004. View at: Publisher Site  Google Scholar
 A. Durmuş, “Heat transfer and exergy loss in cut out conical turbulators,” Energy Conversion and Management, vol. 45, pp. 785–796, 2004. View at: Publisher Site  Google Scholar
 S. EiamsaARD and P. Promvonge, “Experimental investigation of heat transfer and friction characteristics in a circular tube fitted with Vnozzle turbulators,” International Communications in Heat and Mass Transfer, vol. 33, pp. 591–600, 2006. View at: Publisher Site  Google Scholar
 S. EiamsaARD and P. Promvonge, “Effect of Vnozzle inserts and snail with free spacing entry on heat transfer in a heat exchanger,” Journal of Energy Heat and Mass Transfer, vol. 28, pp. 225–239, 2006. View at: Google Scholar
 P. Promvonge and S. EiamsaARD, “Heat transfer augmentation in a circular tube using Vnozzle turbulator inserts and snail entry,” Experimental Thermal and Fluid Science, vol. 32, pp. 332–340, 2007. View at: Publisher Site  Google Scholar
 P. Promvonge and S. EiamsaARD, “Heat transfer and turbulent flow friction in a circular tube fitted with conicalnozzle turbulators,” International Communications in Heat and Mass Transfer, vol. 34, no. 1, pp. 72–82, 2007. View at: Publisher Site  Google Scholar
 P. Promvonge and S. Eiamsaard, “Heat transfer in a circular tube fitted with freespacing snail entry and conicalnozzle turbulators,” International Communications in Heat and Mass Transfer, vol. 34, no. 7, pp. 838–848, 2007. View at: Publisher Site  Google Scholar
 P. Promvonge and S. EiamsaARD, “Heat transfer behaviors in a tube with combined conicalring and twistedtape insert,” International Communications in Heat and Mass Transfer, vol. 34, no. 7, pp. 849–859, 2007. View at: Publisher Site  Google Scholar
 V. Kongkaitpaiboon, K. Nanan, and S. EiamsaARD, “Experimental investigation of heat transfer and turbulent flow friction in a tube fitted with perforated conicalrings,” International Communications in Heat and Mass Transfer, vol. 37, no. 5, pp. 560–567, 2010. View at: Publisher Site  Google Scholar
 V. Ozceyhan, S. Gunes, O. Buyukalaca, and N. Altuntop, “Heat transfer enhancement in a tube using circular cross sectional rings separated from wall,” Applied Energy, vol. 85, no. 10, pp. 988–1001, 2008. View at: Publisher Site  Google Scholar
 S. O. Akansu, “Heat transfers and pressure drops for porousring turbulators in a circular pipe,” Applied Energy, vol. 83, no. 3, pp. 280–298, 2006. View at: Publisher Site  Google Scholar
 R. Kiml, S. Mochizuki, A. Murata, and V. Stoica, “Effects of ribinduced secondary flow on heat transfer augmentation inside a circular tube,” Journal of Enhanced Heat Transfer, vol. 10, no. 1, pp. 9–20, 2003. View at: Publisher Site  Google Scholar
 R. Kiml, A. Magda, S. Mochizuki, and A. Murata, “Ribinduced secondary flow effects on local circumferential heat transfer distribution inside a circular ribroughened tube,” International Journal of Heat and Mass Transfer, vol. 47, no. 67, pp. 1403–1412, 2004. View at: Publisher Site  Google Scholar
 C. Thianpong, K. Yongsiri, K. Nanan, and S. EiamsaARD, “Thermal performance evaluation of heat exchangers fitted with twistedring turbulators,” International Communications in Heat and Mass Transfer, vol. 39, no. 6, pp. 861–868, 2012. View at: Publisher Site  Google Scholar
 W. Jedsadaratanachai and A. Boonloi, “Effects of blockage ratio and pitch ratio on thermal performance in a square channel with 30° double Vbaffles,” Case Studies in Thermal Engineering, vol. 4, pp. 118–128, 2014. View at: Publisher Site  Google Scholar
 S. Tamna, S. Skullong, C. Thianpong, and P. Promvonge, “Heat transfer behaviors in a solar air heater channel with multiple Vbaffle vortex generators,” Solar Energy, vol. 110, pp. 720–735, 2014. View at: Publisher Site  Google Scholar
 S. Singh, S. Chander, and J. S. Saini, “Thermohydraulic performance due to relative roughness pitch in Vdown rib with gap in solar air heater duct—comparison with similar rib roughness geometries,” Renewable and Sustainable Energy Reviews, vol. 43, pp. 1159–1166, 2015. View at: Publisher Site  Google Scholar
 R. Karwa and G. Chitoshiya, “Performance study of solar air heater having vdown discrete ribs onabsorber plate,” Energy, vol. 55, pp. 939–955, 2013. View at: Publisher Site  Google Scholar
 P. Promvonge, W. Changcharoen, S. Kwankaomeng, and C. Thianpong, “Numerical heat transfer study of turbulent squareduct flow through inline Vshaped discrete ribs,” International Communications in Heat and Mass Transfer, vol. 38, no. 10, pp. 1392–1399, 2011. View at: Publisher Site  Google Scholar
 S. Singh, S. Chander, and J. S. Saini, “Investigations on thermohydraulic performance due to flowattackangle in Vdown rib with gap in a rectangular duct of solar air heater,” Applied Energy, vol. 97, pp. 907–912, 2012. View at: Publisher Site  Google Scholar
 V. S. Hans, R. P. Saini, and J. S. Saini, “Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with multiple vribs,” Solar Energy, vol. 84, no. 6, pp. 898–911, 2010. View at: Publisher Site  Google Scholar
 S. Singh, S. Chander, and J. S. Saini, “Heat transfer and friction factor correlations of solar air heater ducts artificially roughened with discrete Vdown ribs,” Energy, vol. 36, no. 8, pp. 5053–5064, 2011. View at: Publisher Site  Google Scholar
 V. SriHarsha, S. V. Prabhu, and R. P. Vedula, “Influence of rib height on the local heat transfer distribution and pressure drop in a square channel with 90° continuous and 60° Vbroken ribs,” Applied Thermal Engineering, vol. 29, no. 1112, pp. 2444–2459, 2009. View at: Publisher Site  Google Scholar
 R. Karwa and K. Chauhan, “Performance evaluation of solar air heaters having vdown discrete rib roughness on the absorber plate,” Energy, vol. 35, no. 1, pp. 398–409, 2010. View at: Publisher Site  Google Scholar
 X.Y. Tang and D.S. Zhu, “Flow structure and heat transfer in a narrow rectangular channel with different discrete rib arrays,” Chemical Engineering and Processing: Process Intensification, vol. 69, pp. 1–14, 2013. View at: Publisher Site  Google Scholar
 W. Peng, P.X. Jiang, Y.P. Wang, and B.Y. Wei, “Experimental and numerical investigation of convection heat transfer in channels with different types of ribs,” Applied Thermal Engineering, vol. 31, no. 1415, pp. 2702–2708, 2011. View at: Publisher Site  Google Scholar
 P. Promthaisong, W. Jedsadaratanachai, and S. EiamsaArd, “3D Numerical study on the flow topology and heat transfer characteristics of turbulent forced convection in spirally corrugated tube,” Numerical Heat Transfer; Part A: Applications, vol. 69, no. 6, pp. 607–629, 2016. View at: Publisher Site  Google Scholar
 B. E. Launder and D. B. Spalding, “The numerical computation of turbulent flows,” Computer Methods in Applied Mechanics and Engineering, vol. 3, no. 2, pp. 269–289, 1974. View at: Publisher Site  Google Scholar
 S. V. Patankar, “Numerical Heat Transfer and Fluid Flow, Hemisphere,” Wash, USA, 1980. View at: Google Scholar
 F. Incropera and P. D. Dewitt, Fundamentals of Heat and Mass Transfer, Wiley, NY, USA, 5th edition, 2002.
Copyright
Copyright © 2017 Withada Jedsadaratanachai and Amnart Boonloi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.