DOI: 10.3303/CET25120072 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 15 May 2025; Revised: 02 October 2025; Accepted: 24 September 2025 
Please cite this article as: García-Castillo J.L., Picón-Núñez M., Crespo-Quintanilla J.A., 2025, Retrofit of Tubular Heat Exchangers Using 
Twisted Tubes for a Target Thermal Effectiveness, Chemical Engineering Transactions, 120, 427-432  DOI:10.3303/CET25120072 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 120, 2025 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Bing Shen How, Viknesh Andiappan, Denny K.S. Ng, Hon Loong Lam, Petar S. Varbanov 

Copyright © 2025, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-21-2; ISSN 2283-9216 

Retrofit of Tubular Heat Exchangers Using Twisted Tubes for 

a Target Thermal Effectiveness 

Jorge Luis García-Castilloa,*, Martín Picón-Núñezb, Jesús Alberto Crespo-

Quintanillaa  

aDepartment of Environmental Sciences, Division of Life Sciences, University of Guanajuato 
bDepartment of Chemical Engineering, Division of Natural and Exact Sciences, University of Guanajuato, Mexico 

 garcia.jl@ugto.mx 

This study introduces a systematic approach for retrofitting tubular heat exchangers with twisted tubes, 

considering the tube twist pitch as a design variable. Twisted tubes enhance the thermal operation of shell and 

tube heat exchangers, which increases the overall heat transfer coefficient without significant pressure drop 

penalties. The methodology is based on expressions for the friction factor and Nusselt number, in the range of 

twist pitch from 0.05 m to 0.2 m. These expressions are developed using CFD and validated with experimental 

data, with an average absolute error of 10.40 % and 6.47 % for the Nusselt number and friction factor. Using a 

twist pitch P=0.05 m, an increase of 130 % in convective heat transfer coefficient is achieved; this represents 

an increase of 30.44 % in thermal load. The results show that under the assumption that twist pitch is a 

continuous variable, the specific twist pitch can be determined to achieve a fixed increment in heat load. A 15 % 

target in thermal load increment can be achieved with a twisted tube with P=0.11 m without any changes in total 

operating cost. A case study is presented to demonstrate the application of the design approach. 

1. Introduction 

Shell and Tube Heat Exchangers (STHE) are one of the most widely used equipment in the chemical industry 

due to their versatility and relative ease of construction. One of the most widely used strategies to improve the 

performance of these devices and increase the thermal load is to improve the overall heat transfer coefficient at 

the expense of pressure drop. This can be achieved by modifying the convective coefficient by installing 

turbulence promoters or by modifying the surface to increase local turbulence. An alternative that achieves these 

objectives is the use of twisted tubes, which have a corrugated surface due to the twisting of the tube and 

generate turbulence inside and outside the tubes. These types of tubes can also work with twisted tape type 

turbulence promoters, as demonstrated by Samruaisin et al. (2019), who experimentally studied a combined 

twisted tube and twisted tape. These works reported that with a twist ratio of 2, a greater increase in the Thermal 

Performance Factor is obtained, achieving an increase of 5.4 % compared to a twisted tube with a twist ratio of 

5. Work in this direction has included the use of new configurations, such as the work done by Yu et al. (2022), 

where they found that with a twisted tube and a center-clear twisted tape, a 35.58 % increase in Nusselt can be 

achieved compared to a smooth tube. The combination of these technologies has extended to the 

implementation of retrofit projects to reduce the use of external services. Crespo et al. (2024) evaluated the use 

of different configurations of twisted tubes with twisted tapes with different numbers of channels, finding that the 

best performance for these applications is obtained by combining a twisted tube with a triple-channel twisted 

tape. While the combination of technologies allows for increased thermal load, its use has been observed to 

generate increased pressure drop levels, leading to higher pumping costs. The importance of its geometry and 

the impact on thermal and hydraulic performance have been highlighted in the literature. Some works have 

shown that the variation in the aspect ratio is an important parameter, and for a larger aspect ratio and a smaller 

twist pitch, a greater increase in the convective coefficient is achieved without significant increases in the 

pressure drop (Yang et al., 2011). For this reason, research has focused on finding the best combination of 

geometric variables to utilize only twisted tubes and improve their thermohydraulic performance. For example, 

427



Li et al. (2021) numerically studied twisted oval tubes by varying geometric aspects such as twist direction, 

aspect ratio, twist pitch, and inner radius of the tube; the best performance was obtained for the lowest twist 

pitch with the largest inner radius. Twisted tubes also offer improvements in tube exterior due to their external 

shape, which allows for increases in the Nusselt number without substantial changes in pressure drop. The use 

of a twisted tube bundle at STHE has revealed that temperatures inside the equipment are more uniform due to 

the turbulence and vortex generation processes. The results indicate that the use of small twist pitch and aspect 

ratios close to 1 generates increases of 12.8 % in the Nusselt number and 15.2 % in the friction factor (Gu et 

al., 2020). While the thermohydraulic study of different systems to increase heat transfer is essential, its use in 

design or retrofit situations is of utmost importance. When comparing the designs in terms of surface area and 

pressure drop with respect to conventional exchangers, the advantages of using these systems become evident 

(Barraza-Colón and Picón-Núñez, 2022), where the required surface area can be reduced by 45 % and even 

with pressure drop reductions of 15 %. The state of the art shows that the design of twisted tube geometry for 

specific applications in shell-and-tube exchangers has not been addressed, so this work seeks to fill this gap. 

An approach to the design of twisted tubes is introduced by setting a desired thermal load as a target through 

the determination of the degree of twist of the tube using the twist pitch P as the design variable. The 

methodology uses correlations for the friction factor and the Nusselt number, obtained using CFD, in a P range 

of 0.05 m to 0.2 m. It is applied to a practical case. 

2. Thermohydraulic data of twisted tubes 

The thermohydraulic data of the tube interior were generated using CFD. These were validated with 

experimental data provided by Yang et al. (2011), who studied twisted tubes with different twist pitches (P). The 

main geometric characteristics of a twisted tube are shown in Figure 1. 

 

Figure 1: Main geometrical parameters of twisted tube 

For validation purposes, a twisted tube with a length L=1.75 m, aspect ratio A/B=1.6, and P=0.104 m is studied, 

using water as the working fluid. The model was solved using the k − ω turbulence model in Ansys Fluent, while 

mesh sensitivity analysis showed mesh independence with 897,373 elements. Figure 2 shows the comparison 

of the Nusselt number and friction factor obtained by CFD against the experimental data obtained by Yang et 

al. (2011). 

  

Figure 2: Validation of CFD data with experimental data (Yang et al., 2020). a) Nusselt number b) Friction factor 

Nusselt number predictions show small errors at Reynolds values below 5,000; beyond this point, the values 

remain within the average, with the error increasing again at Reynolds values above 40,000. The minimum and 

maximum errors for the entire Reynolds range are 5 % and 14 %, with an average absolute error of 10.40 %. 

The same trend is observed in the case of the friction factor; starting at a Reynolds number of 10,000, there is 

a) b) 

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an improvement, with values very similar to the experimental ones. The minimum error is 1.8 % and the 

maximum is 18.65 %, with an average absolute error of 6.48 % for the entire Reynolds range. A more detailed 

analysis of the prediction errors for Nu and f is presented in Table 1. 

Table 1: Absolute error for CFD data versus experimental data 

Reynolds Nusselt  

(Yang et al., 2011) 

Nusselt  

CFD 

Error Nu 

(%) 

Friction factor  

(Yang et al., 2011) 

Friction factor 

CFD 

Error f  

(%) 

3,694 34.10 29.81 12.56 0.094 0.080 14.24 

5,060 37.85 35.94 5.06 0.082 0.067 18.65 

9,959 55.09 60.72 10.22 0.065 0.063 3.67 

15,903 76.08 85.62 12.54 0.056 0.054 3.96 

18,232 82.84 94.40 13.96 0.054 0.052 2.53 

24,337 104.58 118.31 13.13 0.051 0.050 2.00 

32,610 140.91 151.86 7.77 0.046 0.046 1.80 

40,642 165.29 180.55 9.23 0.044 0.045 3.48 

49,317 190.05 211.89 11.49 0.041 0.044 8.19 

55,261 213.65 230.88 8.06 0.040 0.043 6.24 

 

According to the deviations shown in Figure 2 and Table 1, the average absolute errors for Nu and f are 10.40 % 

and 6.50 %. Using the numerical model, data are generated for Nu and f for P values of 0.05, 0.1, 0.15, and 

0.2 m. The generated data are shown in Figure 3. 

  

Figure 3: Data generated for twist pitch values from 0.05 to 0.2 m, a) Nusselt number and b) Friction factor 

In Figure 3a, it can be observed that for values of P=0.05 m, the Nusselt number presents higher values. This 

is because the greater the degree of twist, the greater the local turbulence generated, which increases the 

Nusselt number and the convective heat transfer coefficient. The trend shows that decreasing the twist pitch 

results in a higher Nusselt number. The friction analysis shows a similar behaviour, for values of P=0.05 m the 

friction factor increases up to 66 % with respect to P=0.1 m, while the increase of the latter with respect to P=0.2 

m is 53 %. From this numerical information, the correlations of Eq(1) and Eq(2) are generated using the 

methodology proposed by Picón et al. (2023). 

𝑁𝑢𝑡 = (−0.0716𝑃 + 0.0587)𝑅𝑒(0.0016𝑃+0.771) (1) 

𝑓𝑡 = (0.0834𝑃 + 0.5431)𝑅𝑒(−1.138𝑃−0.097) (2) 

Eq(1) and Eq(2) were generated for discrete values; however, for the purposes of this study, they are considered 

continuous in the range of P between 0.05 and 0.2 m, a Reynolds range of 3,678 to 55,261, and a Prandtl 

number between 2 and 20. When comparing CFD data with predictions using correlations, these have an 

average error of 2.5 % for Nu and 21 % for f over the entire range of P. For the shell-side analysis, the 

correlations proposed by Gu et al. (2020) are used for a coupled vortex configuration in the Froude number 

range of 9.3 to 312.9. 

𝑁𝑢𝑠ℎ = 0.155𝑅𝑒0.64𝑃𝑟0.4 (
𝐴

𝐵
)

0.4

(𝑃/𝑑ℎ)−0.1 (3) 

a) b) 

429



𝑓𝑠ℎ = 3.831𝑅𝑒−0.33𝑃𝑟−0.25 (
𝐴

𝐵
)

0.62

(𝑃/𝑑ℎ)−0.4 
(4) 

3. Twisted tube Design Approach 

The approach to designing a twisted tube to achieve a thermal performance uses the thermal effectiveness- 

Number of Transfer Units model. The methodology consists of the following steps: 1. Set an initial twist pitch P, 

2. Calculate the convective coefficients inside the tubes and for the shell side using Eqs(1) to (4), 3. Obtain the 

new overall heat transfer coefficient (U) and the number of transfer units (Ntu), 4. Determine the new thermal 

effectiveness for the shell and tube heat exchangers, and finally 5. Obtain the new outlet temperatures and the 

thermal load increase Δ𝑄 . The procedure is iterative until the target thermal load is reached. Figure 4a 

graphically shows the design approach, and Figure 4b shows the block diagram of the methodology. 

  

Figure 4: Design approach for designing twisted tubes a) Pictorial diagram, b) Flowchart 

4. Case study 

The case study consists of a tubular exchanger with a surface area of 410 m2 and a length of 6.63 m, with a 

shell diameter of 0.889 m and 1,031 tubes of 0.019 m external diameter and a thickness of 0.002 m. The 

operating data and physical properties are shown in Table 2. The smooth tube bundle will be replaced by twisted 

tubes with A=0.024 m, B=0.019 m, and a thickness of 0.002 m. The cost of the shell and tube heat exchanger 

is determined using the expression proposed by Wang et al. (2020) and the operating cost analysis according 

to the methodology proposed by Picón et al. (2024). By using the same shell and tube count, the available area 

for heat transfer is increased due to the torsion effect of the tube. 

Table 3 shows the main design results for the twist pitch range between 0.05 m and 0.2 m. From a thermal 

perspective, it is observed that for small values of P, there are higher convective heat transfer coefficients. This 

allows for increases in the overall U coefficient in the range of 14 % to 34.1 %. Compared with the original 

design, by using P=0.05 m, the convective coefficient on the tube side increases by 130 %, resulting in an 

increase in thermal load Δ𝑄  of 30.44 %, while the thermal effectiveness increases from 0.58 to 0.84, 

representing an increase of 43.8 %. 

Table 1: Operating data for case study 

Parameter Shell side Tube Side 

Inlet temperature [°C] 28 250 

Outlet temperature [°C] 96 120 

Thermal effectiveness [-] 0.58 

Mass flow rate [kg/s] 16.17 10 

Pressure drop [Pa] 45,030 120 

Heat capacity mass flow rate [kW/°C] 67.91 35.00 

Convective heat transfer coefficient [W/m2 °C] 234.56 193.12 

Overall heat transfer coefficient [W/m2 °C] 91.84 

Viscosity [kg/m s] 0.00080 0.00040 

Heat capacity [J/kg °C] 4,200 3,500 

Conductivity [W/m °C] 0.140 0.130 

Density [kg/m3] 999 560 

a) b) 

430



Table 3: Design results for case study for the entire range of twist pitch 

𝑃[𝑚] 
ℎ𝑡 

[𝑊/𝑚2 °𝐶] 

ℎ𝑠ℎ 

[𝑊/𝑚2°𝐶] 

𝑈 

[𝑊/𝑚2°𝐶] 

Δ𝑄 

[%] 

𝐴𝑠 

[𝑚2] 

𝑇𝑜𝑡𝑎𝑙 𝛥𝑃 

[𝑃𝑎] 

𝑃𝑢𝑚𝑝𝑖𝑛𝑔𝐶𝑜𝑠𝑡 

[$/𝑦] 

𝑇𝑜𝑡𝑎𝑙𝐶𝑜𝑠𝑡 

[$/𝑦] 

0.05 444 174.4 123.2 30.44 747.6 13,114.7 482.70 14,967.73 

0.06 438.3 171.3 121 26.62 638.2 11,059.6 407.06 13,131.34 

0.08 426.9 166.4 117.5 20.69 529.5 8,390.4 308.82 11,245.65 

0.1 415.4 162.8 114.7 16.57 479.2 6,648.3 244.70 10,339.26 

0.12 404 159.8 112.3 13.61 451.8 5,377.2 197.91 9,829.06 

0.14 392.6 157.4 110.2 11.35 435.4 4,396.1 161.80 9,513.90 

0.16 381.1 155.3 108.2 9.551 424.7 3,616.0 133.09 9,302.42 

0.18 369.7 153.5 106.4 8.036 417.3 2,986.0 109.90 9,152.50 

0.2 358.2 151.9 104.7 6.71 412.1 2,470.9 90.94 9,044.31 

 

Pressure drop analysis shows that the increase is primarily due to the effect within the tubes. However, the 

levels are not as high, remaining within normal operating ranges. This is mainly due to the self-supporting twisted 

tube technology and the absence of baffles. The overall effect is a reduction in velocity but an increase in internal 

turbulence due to the geometry of the tube. 

  
 

Figure 5: Design results. a) 𝛥𝑄 and total cost for the entire range of P, b) Twisted tube for a target 𝛥𝑄 = 15 % 

Figure 5a shows the increase in thermal load due to the use of twisted tubes for different values of P. The current 

equipment operating cost is 10,427.80 $/y. Designs with P greater than 0.09 m are below current operating 

costs. For this reason, replacing smooth tubes with twisted tubes is an attractive and economically viable 

alternative to increasing thermal load. To illustrate this approach, if a 15 % increase in heat load is desired, it 

can be achieved by using a twisted tube with a twist pitch of P=0.11 m (Figure 5b). This option would have an 

operating cost of 10,052.50 $/y. 

5. Conclusions 

The use of twisted tubes as a tool for the retrofit of tubular heat exchangers is presented. A design approach is 

introduced that allows a twisted tube to be designed by modifying its twist pitch to achieve an increase in thermal 

load. The approach is based on Nusselt and friction factor correlations generated by CFD and validated with 

experimental data. The main conclusions of this work are: 

• The methodology allows for evaluating the increase in thermal load as a function of the twist pitch in the 

operating range of the correlations and for a Prandtl range between 2 and 20. 

• The twist pitch has a direct effect on the thermal effectiveness, twisted tubes with a P=0.05 m increase the 

convective coefficient on the tube side by 130 %, achieving a Δ𝑄 of 30.44 % and an increase in thermal 

effectiveness from 0.58 to 0.84.  

• The increase in thermal load is accompanied by an increase in pressure drop on the tube side, but a 

reduction on the shell side. The combined effect translates into competitive operating costs. A 15 % 

increase in thermal load can be achieved with a twisted tube with a P of 0.11 m, while maintaining nearly 

constant operating costs. 

Nomenclature

A – Twisted tube long axis, m 

𝐴𝑠 – Heat transfer area, m2 

B – Twisted tube short axis, m 

D – Twisted tape diameter, m 

𝑑ℎ – Hydraulic diameter, m 

ΔP – Pressure drop, Pa 

a) b) 

431



ΔQ – Thermal load increment, % 

f – Friction factor, -  

h – Heat transfer coefficient, W/m2 °C 

L – Tube Length, m 

Nu – Nusselt number, - 

Ntu – Number of heat transfer units, - 

P – Twist pitch, m 

Pr – Prandtl number, - 

Re – Reynold number, -  

U – Overall heat transfer coefficient, W/m2 °C 

Abbreviations 

CFD – Computational Fluid Dynamics 

STHE – Shell and tube heat exchanger 

Subscripts 

t – tube side 

Sh - Shell side

 

References 

Barraza-Colón J., Picón-Núñez M., 2022, Improved Heat Recovery Using Twisted Tube Exchanger Technology. 

Cleaner Engineering and Technology, 10, 100557. 

Crespo-Quintanilla J.A., García-Castillo J.L., Minchaca-Mojica J.I., Picón-Núñez M., 2024, Enhancing Heat 

Exchanger Performance with Combined Twisted Tubes and Twisted Tapes. Design and Retrofit Strategies. 

Thermal Science and Engineering Progress, 54, 102817. 

García-Castillo J.L., Crespo-Quintanilla J.A., Picón-Núñez M., 2024, A novel design approach of plate heat 

exchangers considering the economic impact of chevron angles. Chemical Engineering & Processing: 

Process Intensification, 199, 109759. 

Gu H., Chen Y., Wu J., Sunden B., 2020, Performance investigation on twisted elliptical tube heat exchangers 

with coupling-vortex square tube layout. International Journal of Heat and Mass Transfer, 151, 119473. 

Li X., Wang L., Feng R., Wang Z., Liu S., Zhu D., 2021, Study on Shell Side Heat Transport Enhancement of 

Double Tube Heat Exchangers by Twisted Oval Tubes. International Communications in Heat and Mass 

Transfer, 124, 105273. 

Picón-Núñez M., García-Castillo J.L., Crespo-Quintanilla J.A., Minchaca-Mojica J.I., 2023, Increasing Heat 

Recovery in Heat Exchanger Design Using a Combined Twisted Tape and Twisted Tube Technology. 

Chemical Engineering Transactions, 103, 403–408. 

Samruaisin P., Kunlabud S., Kunnarak K., Chuwattanakul V., Eiamsa-ard S., 2019, Intensification of Convective 

Heat Transfer and Heat Exchanger Performance by the Combined Influence of a Twisted Tube and Twisted 

Tape. Case Studies in Thermal Engineering, 14, 100489. 

Wang B., Arsenyeva O., Zeng M., Klemes J.J., Varbanov P.S., 2022, An advanced Grid Diagram for heat 

exchanger network retrofit with detailed plate heat exchanger design. Energy, 248, 123485. 

Yang S., Zhang L., Xu H., 2011, Experimental Study on Convective Heat Transfer and Flow Resistance 

Characteristics of Water Flow in Twisted Elliptical Tubes. Applied Thermal Engineering, 31(14–15), 2981–

2991. 

Yu C., Cui Y., Zhang H., Gao B., Zeng M., Han L., 2022, Comparative Study on Turbulent Flow Characteristics 

and Heat Transfer Mechanism of a Twisted Oval Tube with Different Twisted Tapes. International Journal 

of Thermal Sciences, 174, 107455. 

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	Retrofit of Tubular Heat Exchangers Using Twisted Tubes for a Target Thermal Effectiveness