THREE-DIMENSIONAL NUMERICAL SIMULATION OF THERMALHYDRAULIC PERFORMANCE OF A CIRCULAR TUBE WITH EDGEFOLD-TWISTED-TAPE INSERTS*

CUI Yong-zhang

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

School of Thermal Engineering, Shandong Jianzhu University, Jinan 250101, China, E-mail: cyz@sdjzu.edu.cn

TIAN Mao-cheng

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

THREE-DIMENSIONAL NUMERICAL SIMULATION OF THERMALHYDRAULIC PERFORMANCE OF A CIRCULAR TUBE WITH EDGEFOLD-TWISTED-TAPE INSERTS*

CUI Yong-zhang

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

School of Thermal Engineering, Shandong Jianzhu University, Jinan 250101, China, E-mail: cyz@sdjzu.edu.cn

TIAN Mao-cheng

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

(Received November 30, 2009, Revised July 7, 2010)

Three-dimensional numerical simulations and experiments were carried out to study the heat transfer characteristics and the pressure drop of air flow in a circular tube with Edgefold-Twisted Tape (ETT) inserts and with classic Spiral-Twisted-Tape (STT) inserts of the same twist ratio. The RNG turbulence model for mildly swirling flows, the enhanced wall treatment for low Reynolds numbers, and the SIMPLE pressure-velocity method were adopted to simulate the flow and heat transfer characteristics. Within the range of Reynolds number from 2 500 to 9 500 and the twist ratio y from 5.4 to 11.4, the Nusselt number of the tube with ETT inserts is found to be 3.9% - 9.2% higher than that with STT inserts, and the friction factor of the tube with ETT inserts is 8.7% -74% higher than that of STT inserts. The heat enhancement is due to higher tangential velocity and asymmetrical velocity profile with the increase and decrease of the periodic velocity within an edgefold length. It is found that main factors affecting the heat transfer of ETT inserts are the twist angle and the gap width between the tube and inserts. A larger twist angle leads to a higher tangential velocity, and larger Nusselt number and friction factor. The thermal-hydraulic performance slowly decreases as the twist angle increases. The gap width between tube and inserts has a significant influence on the heat transfer, while little influence on pressure drops. The thermal-hydraulic performance increases in average by 124% and 140% when the gap width reduces from 1.5 mm to 1.0 mm and 0.5 mm. The larger the gap width, the higher velocity through the gap will be, which would reduce the main flow velocity and tangential velocity. So a small gap is desirable. Comparing experimental and numerical results at variable air flow and tube wall temperature, the numerical results are found to be in a reasonable agreement with the experiment results, with difference of the Nusselt number in a range of 1.6% - 3.6%, and that of the friction factor in a range of 8.2% - 13.6%.

heat transfer enhancement, Edgefold-Twisted-Tape (ETT), Spiral-Twisted-Tape (STT), thermal-hydraulic performance

1. Introduction

The heat transfer enhancement technology has been developed rapidly and employed in a wide variety of engineering problems, such as condensing gas boiler and water heater. Tape inserts are frequently used to reduce exhaust flue temperature and to make heat exchangers compact. There are mainly five effects of twisted tape inserts in the heat transfer enhancement: (1) increase in flow velocity, (2) decrease in hydraulic diameter, (3) increase in flow path, (4) secondary motion, (5) fin contribution, if tape inserts are in good thermal contact with the tube wall.

The swirl flow in a tube was suggested by Kreit and Margolis (1959), and most of the swirl flows were created by long and short classic Spiral Twisted-Tape (STT) inserts[1-22]with and without holes[1-5], regularly spaced tape inserts[6-7], louvered strip[8]and wire coil inserts[9]. Studies were carried out[1,4,10-12]the heat transfer characteristics and pressure drops in circular tubes with twisted-tape inserts under fully turbulent flow conditions. Fahed[10]studied the effect of the tube-tape clearance on the heat transfer in fully developed turbulent flow in a horizontal isothermal tube, and it is shown that the heat transfer enhancement increases as the tube-tape clearance decreases. Recently, three-dimensional numerical analyses were carried out to study the thermal-hydraulic characteristics of the flow inside a circular tube with different twisted-tape inserts[12-21,23]. The RNG k?ε turbulent model[24,25]was used to simulate self-rotating STT inserts by Zhang[21], and to model STT inserts and perforated and jagged twisted tapes by Rahimi et al.[2]. Results show that the higher turbulence intensity of the fluid close to the wall and the tangential velocities were mainly attributed for the heat transfer enhancement. Eiamsa-Ard[12]adopted the SIMPLE technique, together with four turbulence models to simulate the flow in a circular tube induced by means of loose-fit twisted tapes, and the numerical results show that the shear stress transport k?ω turbulence models give the most consistent results with those of Manglik and Bergles.

Table 1 Geometrical parameters and the twist ratio of inserts

The transition flow regimes in a tube with twisted-tape inserts, specially Edgefold-Twisted-Tape (ETT) inserts, were not well studied. The arrangement enhances the structural stability and makes it possible to adopt thinner stainless inserts. This article presents three-dimensional numerical analyses and experiments on heat transfer characteristics and pressure drops of the air flow in a circular tube fitted with ETT inserts and STT inserts under constant wall temperature.

2. Physical model and mathematical analysis

2.1 Circular tube with inserts

A circular tube with ETT inserts is shown in Fig.1. The tube’s inner diameter is D. The main geometrical parameters of ETT inserts include edgefold length ( L ), twist angle (A), tape width ( B), and tape thickness (δ). The twist angle is a rotation within an edgefold length, with H beingothe twist pitch and n the edgefold number within 360, the gap between tubes and inserts (b ) and the twist ratio ( y) can be expressed as:

Fig.1 Circular tube with edgefold-twisted-tape inserts

The STT inserts have the same twist ratio and the twist width as the ETT inserts in order to compare the thermal and hydraulic performance. Geometrical parameters and the twist ratio of the investigated inserts are listed in Table 1.

2.2 Mathematical analysis

The studied area includes the air between twist tape inserts and inside the tube. The following assumptions are adopted to simplify the physical model: (1) the radiation and natural convection heat transfer can be ignored, (2) the viscosity heating can be ignored, (3) the change of the air composition can be ignored, (4) the twisted-tape surface can be considered as adiabatic, and the conduction along tape inserts can be ignored, (5) no slip motion on tube walland inserts surface, (6) constant wall temperature. For transition turbulent flows, the three-dimensional equations of continuity, momentum, energy, turbulent kinetic energy (k), and the dissipation rate (ε) in the fluid region are as follows:

Continuity equation:

The numerical simulation is carried out using Fluent, with RNG k?ε, SIMPLE pressure-velocity coupling algorithm, and the second upwind discretization scheme for momentum, energy, turbulent kinetic energy and dissipation energy. The convergence criterion is satisfied when the residuals of variables are less than 1×10-4except for the energy where a value of 1×10-7is used. Under-relaxation factors of turbulent kinetic energy, turbulent dissipation rate and turbulent viscosity are changed within the range between 0.2 and 0.4, others take the default values. For accounting for the low Reynolds number and the near wall flow, an enhanced wall treatment is also adopted.

The air inlet is specified with the mass flow rate inlet boundary condition, the air outlet with the pressure outlet boundary condition, the tube wall is a wall with constant temperature and the surface of the inserts is an adiabatic wall.

2.3 Grid-independence

The region near the inner tube wall is meshed with refined hexahedron cells, the other regions are meshed with tetrahedron cells, and the grid number is varied with the tube’s inner diameter. The accuracy and the validity of the numerical results are ensured by a careful check of the grid-independence. Table 2 shows the grid numbers and numerical results for inner diameters of 21 mm and 1 m of No.2 ETT inserts, so the internal count of 80 is used to grid all inserts. By using the boundary adaptation on the tube wall and the insert wall and the gradient adaptation on the whole region, the convergence rate is high. The computations are performed on the workstation with Intel Xeon E4505 CPU and the time is in the range of 2 h to 4 h for each case.

Table2 grid number and numerical results

3. Numerical results and discussions

The steps involved in calculating the tubesideheat transfer coefficient and the friction factor from the simulation temperature, flow rate, and pressure drop are outlined below. All intube flow parameters are based on the inner diameter of the empty tube, all fluid properties are evaluated at the length average bulk temperature, unless otherwise indicated.

The log-mean temperature difference, ΔTm, is defined as

where Tinis the inlet temperature of air, Toutis the outlet temperature of air, Twis the inner wall temperature.

The Nusselt number, Nu, is defined as

where α is the convective heat transfer coefficient, λ is the thermal conductivity, Q is the heat transfer rate and F is the heat transfer area.

The friction factor, f, is calculated from the following equation

where ΔP is the pressure drop in the entire length ( Ltotal), u is the bulk averaged velocity.

The thermal-hydraulic performance with different inserts, φ, is defined as

3.1 STT and ETT insert performance

Figures 2 and 3 show the Nusselt number and the friction factor of a tube with No.5 and No.7 STT inserts and No.2 and No.4 ETT inserts at the same inlet and tube wall temperature, with gap width b of 0.5 mm. It can be seen that the Nusselt number and the friction factor of the tube with ETT inserts are larger than those with STT inserts with the same twist ratio. The Nusselt number of No.2 ETT inserts is 3.9% greater than that of No.5 STT inserts, the Nusselt number of No.4 ETT inserts is 9.2% greater than that of No.7 STT inserts in average. The friction factor of No.2 ETT inserts is 8.7% larger than that of No.5 STT inserts, the friction factor of No.4 ETT inserts is 74% larger than that of No.7 STT inserts in average. The thermal-hydraulic performance φ of No.2 ETT inserts is 1.01 on the base of No.5 STT inserts, that of No.4 ETT inserts is 0.91 on the base of No.7 STT inserts.

Fig.2 Nusselt number of tube with S TT and ETT inserts

Fig.3 Friction factor of tube with STT and ETT inserts

The enhancement is mainly due to a higher tangential velocity and the main flow velocity profile. The tube with STT inserts has a symmetrical profile with the same main velocity and tangential velocity, but the tube with ETT inserts has asymmetrical velocity magnitude and tangential velocity profiles, as shown in Figs.4 and 5. It can be seen that the velocity of ETT assumes a periodic variation within an edgefold length, the velocity first increases and later decreases on one side, but it first decreases and later increases on the other side The tangential velocity has the same variation trend. Such velocity variations help gas mixing.than that for twist angle 20o, and the Nusselt number for twist angle 20ois 1.9% larger than that for twist angle 15oin average. The friction factor for twist angle 30ois 45% greater than that for twist angle 20o, and the friction factor for twist angle 20ois 0.4% greater than that for twist angle 15o. Therefore, under the transition flow, the flow disturbance increases with the increase of the twisted ratio, and the low twisted ratio tape has a strong effect. On the base of 15otape, the thermal-hydraulic performance φ of 20oand 30otapes is 0.996 and 0.988, respectively, and it decreases with the increase of the twist angle.

Fig.4 Velocity magnitude profile of No.3 inserts

Fig.5 Tangential velocity profile of No.3 inserts

Fig.6 Effect of twist angle (A) on Nusselt number

Fig.7 Effect of twist angle (A) on friction factor

Fig.8 Tangential velocity profile at z =0.180 m for twist angles of 20oand 30o

The enhancement by the twist angle is due to different tangential velocities. Figure 8 is the

Fig.9 Effect of gap width (b) on Nusselt number

Fig.10 Effect of gap width (b) on friction factor

3.2.2 Gap between tube and inserts b

Figures 9 and 10 show the Nusselt number and the friction factor for different gap widths at the same inlet temperature and wall temperature. In general, the gap width has a significant influence on the Nusselt number, but little influence on the pressure drop. The Nusselt number and the friction factor decrease as the gap width increases. The Nusselt number for b=1mm and b=0.5 mm is 7.1% and 23.7% larger than that for b=1.5 mm. The friction factor for b=1mm and b=0.5 mm is 3.2% and 12.1% greater than that for b=1.5 mm. On the base of the case b=1.5 mm, the thermal-hydraulic performances for the cases b=1mm and b=0.5 mm are shown in Fig.11, which increase in average by 124% and 140%, respectively. So a small gap width is desirable. The gap width effect comes from the different velocity through the gap. Figures 12 and 13 show the velocity magnitude and the tangential velocity for the cases b=1mm and b=1.5 mm at section z =0.100 m. The traveling velocity through the gap increases with the gap width, which leads to significantly lower main velocity and tangential velocity.

Fig.11 Effect of gap width ( b) on thermal-hydraulic performance

Fig.12 Velocity profile of different gap widths at the same inlet velocity of 3 m/s

3.2.3 Edgefold length L

Figures 14 and 15 show that the edgefold length has little effect on the Nusselt number and the friction factor, which in the case, L=20 mmtakes value 2.4% and 1.4% smaller those in the case L=15 mm. A large edgefold length can be used for easy fabrication.

Fig.13 Tangential velocity profile of different gap widths at the same inlet velocity of 3 m/s

Fig.14 Effect of edgefold length on Nusselt number

Fig.15 Effect of edgefold length on friction factor

Fig.16 Schematic diagram of the test facility

4. Validity test

4.1 Test facility

The experiment setup is shown in Fig.16, where a copper tube with inner diameter d=21mm and wall thickness 2 mm is used as the test section. Length of the test section is 1 000 mm. The tube with ETT inserts is placed in a box and cooled by water, and the working medium inside the tube is air. Cooling water is provided by a thermostatic gas water heater. Air temperature is adjusted by adjustable electric heater, and is measured by eight RTDs. The volume flow rate of air is measured with Swema Flow 125, with a measuring range from 2 l/s to 125 l/s and the accuracy of ±3%. The pressure drop of air is measured with Swema 3 000 , with pressure range from –150 Pa to 1 500 Pa. The average temperature of the tube wall is determined by means of 10 thermocouples located along the tube. All the data signals are collected by a data acquisition system and stored in computer for further analysis.

4.2 Test results and discussions

For a high cooling water rate and a low heat transfer rate, the water temperature rise is within 0.4 k - 0.8 k, so the tube wall temperature is represented by the average temperature at ten locations on the test tube wall

where N is the thermocouple number, TNis the temperature measured at a location on the tube wall.

The total heat transfer capacity

where G is the air flow rate, Tinand Toutare the air inlet and outlet temperature.

The test and numerical results are shown in Figs.17 and 18. The test air inlet temperature is 393 K, the tube wall temperature is 313 K, the air flow rate is adjusted by the fan speed. The Nusselt number in the test is 1.6% - 3.6% smaller than that obtained by the simulation, and the friction factor is 8.2% - 13.6% greater than that of the simulation. So experiment results are in a reasonable agreement with simulation results.

Fig.17 Nusslet number vs. air inlet velocity

Fig.18 Friction factor vs. air inlet velocity

5. Conclusions

Three-dimensional numerical simulations and experiments were carried out to study the heat transfer, friction factor and thermal-hydraulic performance of tubes with STT inserts and ETT inserts. Experiment results are in a reasonable agreement with numerical results. The following conclusions are reached.

(1) The heat transfer of a tube with ETT inserts is enhanced as compared with a tube with STT inserts.Within the range of Reynolds number from 2 500 to 9 500 and the twist ratio y from 5.4 to 11.4, the Nusselt number and the friction factor of the tube with ETT inserts are 3.9% - 9.2% and 8.7% - 74% larger than those with STT inserts, and the thermal-hydraulic performance is within 0.91 to 1.01. The major enhancement of the heat transfer is found due to higher tangential velocity and asymmetrical velocity profile with the increase and decrease of the periodic velocity within an edgefold length

(2) The twist angle is the most important structural factor. A larger twist angle leads to larger Nusselt number and friction factor. The larger the twist angle, the higher tangential velocity will be. As the twist angle increases, the thermal-hydraulic performance decreases slowly.

(3) The gap width has a significant influence on the heat transfer, but little influence on the pressure drop. When the gap width is reduced from 1.5 mm to 1.0 mm and 0.5 mm, the Nusselt number increases by 7.1% and 23.7%, the friction factor increases by 3.2% and 12.1%. The thermal-hydraulic performance increases in average by 124% and 140%. The traveling velocity increases as the gap width increases, which leads to significantly lower main velocity and tangential velocity, therefore, a small gap width is desirable.

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10.1016/S1001-6058(09)60101-3

* Project supported by the National Basic Research Program of China (973 Program, Grant No. 2007CB206903).

Biography: CUI Yong-zhang (1970- ), Male, Ph. D. Candidate, Associate Professor

TIAN Mao-cheng, E-mail: tianmc65@sdu.edu.cn