Rectangular Winglet Vortex Generators Research Articles

Analysis of the thermal improvement of plate fin-tube heat exchanger with straight and curved rectangular winglet vortex generators

A novel combination of curved and straight rectangular winglet vortex generator (RWVG) pairs was arranged in a common-flow-up (CFU) configuration on plate fins for enhancing the comprehensive performance of the fin-tube heat exchanger. The effects of RWVGs were compared with those of non-RWVGs for flow streamline, temperature distribution, and pressure field. Then the thermohydraulic performance and the comprehensive performance were numerically investigated among the cases with varied locations and sizes of RWVGs. The results revealed that j for all cases with RWVGs was higher than non-RWVGs and the values of JF were greater than 1.0 for all cases except for case 4. Especially, apparent improvements in heat transfer characteristics and comprehensive performance were observed with the novel combination. Furthermore, it was found that the appropriate location and size of RWVGs were able to influence the thermohydraulic characteristic positively. The curved RWVGs with a smaller offset showed better comprehensive performance, and the larger attack angle of the straight RWVGs was accompanied by a higher heat transfer intensity and a greater flowing drag force. Moreover, the curved RWVGs with a larger arc angle performed better in the comprehensive performance, and the length of the straight RWVGs was larger and JF smaller.

A Comparative study on thermo-hydraulic performance in a tube with different punched winglets

In this work, heat removal and flow behaviors of rectangular winglet vortex generators (VGs) in a heated tube are analyzed experimentally and numerically. The object of present work is to quantify the heat removal performance of VGs with five different holes (circular, regular triangle, square, rectangular, and rhombus). The winglet parameters include three different pitch ratios (PR=1.63,3.27,4.89) at a fixed attack angle (α=45°). Comparisons of thermal performances between planar VGs and drilled VGs are made. It is found that jet flow from holes boosts local heat removal but weakens heat removal of the entire tube. Visualization of the temperature fields and local turbulent kinetic energy fields show that the holes with circular shapes are beneficial for fluid to pass through the hole with rotation. This kind of flow pattern results in a relatively intense flow mixing in the recirculation region, which boosts local heat removal. However, the holes with sharp corners are not helpful to heat removal enrichment. Thermal enhancement factor (TEF), the ratio of the boosted heat removal and cost in energy, is used to scale the comprehensive performance. The maximum TEF is 1.14 for Case A (circular hole) at Re=9090.

Flow and thermal characteristics produced by a curved rectangular winglet vortex generator in a channel

Three-dimensional numerical computations are performed to investigate the performance of curved winglets mounted on a rectangular channel. The concave and convex shapes of curved rectangular winglet vortex generators (RWVGs) are named according to flow facing surface. Curvature of winglet mainly depends on arc angle, radius of curvature, arc length and chord length. Present study investigates the influence of arc angle variation of curved RWVG on flow and thermal characteristics for fixed chord length. Arc length and radius of curvature of curved RWVG vary according to arc angle. With the help of streaklines plots and iso-Q surfaces, flow behavior around the curved RWVG has been investigated. Heat transfer enhancement of curved RWVGs has been examined by using the dimensionless parameters surface-averaged Nusselt number, while pressure loss is estimated by friction factor. The overall thermohydraulic performance of curved RWVGs is inspected by thermal performance factor. Investigations of secondary flow intensity are carried out to understand its impact on heat transfer mechanism. From the investigation of secondary flow, it is observed that secondary flow provides a supplement to the traditional method of analyzing heat transfer performance.

Experimental investigation and numerical investigations of heat transfer enhancement in a tube with punched winglets

As an effective technology to reduce flow resistance, drilling holes on the surface of vortex generators had been studied extensively. In this paper, thermal performance of punched rectangular winglet vortex generators (PRWVGs) in turbulent regime (Reynolds number was in the range of 9,090∼21,210) was studied experimentally and numerically. Air was applied as the working fluid. The PRWVGs were inserted into the tube with three attack angles (α=30°,45°,60°). The punched holes were set in three different positions (g=3mm,5mm,7mm) in the vertical direction and at three different hole heights (d=1mm,3mm,6mm). The performance of PRWVGs was quantified by the heat transfer coefficient ratio (h/h0), the friction factor ratio (f/f0), and a combined thermal enhancement factor (TEF) of the two. The results revealed that h/h0 as well as f/f0 values of PRWVGs compared with those of planar VGs (without holes) were reduced. The flow and temperature fields of different cases were obtained by numerical simulations, and the experimental results were verified by analyzing the fluid flow behaviors. The results showed that the jet flow (defined as a jet emanating from the punched hole of a VG), would enhance the heat transfer efficiency in the recirculation area. And the TEF value of VGs was improved by punching holes on the surface of VGs. However, the shape of the jet flow depended on the position of the hole. When the position of the hole was lower in the vertical direction, the jet flow was effective in increasing its TEF value. Additionally, the size of the hole had a large effect on the TEF value. Besides, entropy generation analysis showed that PRWVGs were thermodynamically advantageous. Whend=1mm,w=5mm, the Bejan number reached the minimum. Under this condition, the proposed PRWVGs performed best in practice. When the height of the hole was d=1mm, TEF was the maximum, which was 1.25 at α=45° and Re=9,090.

Experimental investigation of heat transfer enhancement and pressure drop of fin-and-circular tube heat exchangers with modified rectangular winglet vortex generator

The presence of vortices in a flow field significantly impacts heat transmission. The effect of a modified rectangular winglet vortex generator on heat transfer and pressure drop performance for a fin-tube heat exchanger (FTHE) is experimentally explored in this work. Design and fabrication of full-scale prototype of an FTHE are carried out. Two types of rectangular winglet vortex generators (RWVGs), i.e., Flat RWVG and RWVG with a circular punched hole are installed into the FTHE for experimentation purposes. The experimental studies are conducted with Reynolds numbers ranging from 8000 to 25,000. The experimental results show that the use of RWVG in FTHE provided a much greater heat transfer coefficient than FTHE without RWVGs with an increase in pressure loss penalty. For better wake management, the RWVG are installed behind the circular tubes in a common flow down (CFD) arrangement. The comparative study is carried out to explore thermo-fluid performance of fin-and-tube heat exchanger with two inline circular tube arrangements for all considered cases of RWVGs. By varying the tube wall temperature (i.e., 65, 75, and 85 °C), thermo-hydraulic performance criteria such as Nusselt number (Nu), friction factor (f), and thermal performance factor (η) are compared. Lower tube surface temperature gave the highest enhancement in heat transfer performance with a lower friction factor. However, the thermal performance factor (η) for the RWVG with a circular punched hole is about 1.04–3.2%, 1.3–5.4% and 2.3–10.52% higher than RWVG-Flat for the tube wall temperature 65 °C, 75 °C, and 85 °C, respectively.

Numerical Analysis on Thermohydraulic Performance of the Tube Inserted with Rectangular Winglet Vortex Generators

The aim of this design was to improve the heat transfer performance significantly due to larger turbulent region and much vortices formed by tube inserted. In this article, the BSL k-ω model was chosen as turbulence model to simulate the thermohydraulic performance of the proposed tubes inserted with rectangular winglet vortex generators (RWVGs) when the Re was set as 5000 to 15,000. The reliability of the simulation results was obtained by comparing with the empirical formulas and experimental results. By means of numerical simulation, the influence mechanism of geometric parameters of RWVGs on thermal-hydraulic performance in tubes was analyzed. And the impact of three configurational parameters on the thermal performance was studied, namely the angle α, the height H and the number N of the RWVGs, respectively. The results revealed that the capacity of heat transfer in tubes with RWVG inserts was obviously larger than that in ordinary circular tube. In addition, it could be seen from the results that both Nu and f increased with the increase of H and N. At the same time, the case of α = 135° showed the greatest enhancement of thermal performance than the case of α = 45° and α = 90°.The PEC achieved the highest value of 1.23 when the height H of RWVG was 0.7 mm, the number N was 20, and angle α was 135°.

Thermal-Hydraulic Performance Analysis by Means of Rectangular Winglet Vortex Generators in a Channel: An Experimental Study

Vortex generators (VGs) are one of the effective passive models used to increase the heat transfer rate in heat exchangers. In this experiment, heat transfer from six cylinders heated to the airflow was improved by attaching rectangular winglet vortex generators (RWVGs) to a plate in a rectangular channel. The installation aimed to increase the value of the thermal-hydraulic performance evaluation criteria in the line. This experimental study was carried out by varying the fluid flow velocity from 0.4 m/s to 2 m/s with an interval of 0.2 m/s in the channel. Three pairs of VGs were arranged in both in-line and staggered configurations. The experimental results show that the thermal-hydraulic performance evaluation criteria for three pairs of vortex generators in the staggered configuration was 15.17% higher than the baseline, while the thermal-hydraulic performance of the in-line arrangement was 1.54% higher than the staggered one.

Thermal-Hydraulic Performance Analysis by Means of Rectangular Winglet Vortex Generators in a Channel: An Experimental Study

Vortex generators (VGs) are one of the effective passive models used to increase the heat transfer rate in heat exchangers. In this experiment, heat transfer from six cylinders heated to the airflow was improved by attaching rectangular winglet vortex generators (RWVGs) to a plate in a rectangular channel. The installation aimed to increase the value of the thermal-hydraulic performance evaluation criteria in the line. This experimental study was carried out by varying the fluid flow velocity from 0.4 m/s to 2 m/s with an interval of 0.2 m/s in the channel. Three pairs of VGs were arranged in both in-line and staggered configurations. The experimental results show that the thermal-hydraulic performance evaluation criteria for three pairs of vortex generators in the staggered configuration was 15.17% higher than the baseline, while the thermal-hydraulic performance of the in-line arrangement was 1.54% higher than the staggered one.

Performa Termal dan Hidrolik Aliran Udara Melalui Vortex Generator Berlubang Tipe Concave Rectangular Winglet di dalam Saluran Persegiempat: Studi Eksperimen

Fin and tube heat exchangers use gas as a cooling/heating medium on the fin side. The low thermal conductivity of gases results in high thermal resistance, which results in a low rate of heat transfer. Therefore, the researchers sought to reduce thermal resistance on the fin side. This study aims to increase heat transfer by reducing thermal resistance using a longitudinal vortex generator. However, the use of vortex generators will increase the pressure drop. Perforated vortex generators were investigated in this study to overcome this problem. Concave rectangular winglet vortex generator at an angle of attack of 30° with variations of without hole, one, two, and three holes were studied. In this experiment, the number of pairs of vortex generators was varied from one to three pairs. A plate on which the vortex generator is mounted is heated at a heat rate of 35 W. Air enters the channel through the straightener at variations in the velocity of 0.4 m/s to 2 m/s at intervals of 0.2 m/s. The results showed that the value of the convection heat transfer coefficient for the use of perforated concave rectangular winglet vortex generators was 85.4% higher than the baseline. This value is 13.7% higher than the use of perforated rectangular winglet vortex generators. Whereas the value of pressure drop for the use of perforated concave rectangular winglet vortex generators is five times higher than that of the baseline. This value is 104.9% higher than the use of perforated rectangular winglet vortex generators.

Thermal performance augmentation of fin-and-tube heat exchanger using rectangular winglet vortex generators having circular punched holes

In fin-and-tube heat exchangers (FTHEs), vortex generation is found as one of the promising emerging passive technique for augmenting the rate of heat transfer on air-side. In the present study, three dimensional numerical study is performed to evaluate thermo-hydraulic performance of FTHEs equipped with rectangular winglet vortex generators (RWVGs) with circular punched holes for Reynolds number varying from 400 to 2000. Various cases of RWVGs without and with circular punched holes (1, 2, 4, and 6 holes) are considered. The pairs of RWVG are placed in common flow down (CFD) orientation behind the circular tubes to improve wake management. The effect of number of punched holes is compared with non-VG baseline case and RWVG without hole for flow structure and thermo-hydraulic performance of FTHE with four inline circular tube arrangement. Comparison is also carried out with thermo-hydraulic performance criterions which include Nusselt number (Nu), Pressure drop (ΔP), friction factor (f), colburn factor (j), London area goodness factor (j/f). Effects of number of punched hole on the performance of RWVGs is also evaluated using dimensionless number (j/j0)/(f/f0) as performance evaluation criteria (PEC) . It is observed that RWVGs with circular punched holes remarkably improve the thermo-hydraulic performance of FTHE. The punched holes exhibit reduction in the flow resistance for all cases with slight reduction in Nusselt number. RWVG with 6 holes shows better performance as compared to other cases. Nusselt number for RWVG with 6 holes increases about 45.95% and 57.37% at Reynolds number 400 and 2000, respectively. However, friction factor is decreased by about 13.81%. Thus, from the point of view of London area goodness factor, RWVG with 6 holes found better than other considered cases of RWVG.

Effects of the configuration of winglet vortex generators on turbulent heat transfer enhancement in circular tubes

Rectangular winglet vortex generators (RWVGs) are put forward to intensify turbulent heat transfer in circular tubes. Two configurations of RWVGs, including parallel type (P-RWVGs) and V-shaped type (V-RWVGs), are considered. Numerical results demonstrate that P-RWVGs generate a single longitudinal vortex, while V-RWVGs induce multiple longitudinal vortices. Both the flow patterns above increase the turbulent kinetic energy of the fluid and thus enhance fluid mixing in the tube. The influences of the attack angle (α) and length ratio (LR) of RWVGs on the thermal-hydraulic performance are examined experimentally. The results indicate that an increase in the length ratio of RWVGs contributes to the augmented pressure drop and heat transfer for both P-RWVGs and V-RWVGs. The heat transfer rate and flow resistance for the tube with P-RWVGs are increased respectively by 54–118% and 152–568 % over those for the smooth tube, and the corresponding values for V-RWVGs are 60–118% and 141–644%, respectively. The overall thermal performance of the tubes with P-RWVGs and V-RWVGs rises with the pressure drop. Overall, P-RWVGs with the combination of LR0.2-α75° and V-RWVGs with the combination of LR0.2-α45° show the higher thermal performance under the same pressure drop than the other cases.

Investigations of the turbulent thermal-hydraulic performance in circular heat exchanger tubes with multiple rectangular winglet vortex generators

This work explores the turbulent thermal-hydraulic performance in circular heat exchanger tubes with multiple rectangular winglet vortex generators. Numerical simulations demonstrate that multi-longitudinal vortices are induced, which enhances fluid mixing in the tubes. The effects of geometric parameters including the circumferential number of rectangular winglets (N = 4, 6, 8), height ratio (HR = 0.05, 0.1, 0.2), and pitch ratio (PR = 1.57, 3.14, 4.71), are examined experimentally. The results demonstrate that both the friction factor and Nusselt number increase with the height ratio and the number of rectangular winglets due to the better fluid mixing performance caused by multi-longitudinal vortices with higher turbulent kinetic energy. For the considered Reynolds numbers, the friction factor and Nusselt number ratios are in the range of 1.46–11.63 and 1.15–2.32, respectively. An increase in the number of rectangular winglets improves the thermal enhancement factor (TEF) for HR = 0.05, while the opposite trend is found for the other cases. The maximum TEF is up to 1.27. Moreover, correlations for the friction factor and Nusselt number are derived based on the experimental results for practical applications.

Numerical study of an impinging jet in cross-flow within and without influence of vortex generator structures on heat transfer

An impinging jet heat transfer in cross-flow within and without influence of a vortex generator pair (VGP) is studied using the unsteady Reynolds averaged Navier-Stokes (URANS) and the large-eddy simulation (LES). The jet Reynolds number is 15,000 and the cross-flow Reynolds number is 30,000. The elliptic-blending Reynolds stress model (EBRSM) is implemented and adapted to capture the effect of the jet close to the wall. A v2 − f model is also implemented to study the ability in predicting such a benchmark. Both models benefit from the elliptic relaxation equation in the entire computational domain. The URANS results are compared with the accurate results of the LES method and also the experimental data. The URANS method successfully presents the flow features of the impinging jet while underpredicts the enhancing heat transfer over the channel bottom wall. The URANS method fails to correctly predict the flow structures forming around the impinging region, because the method is more diffusive than the LES method. When manipulating VGP, a rectangular winglet vortex generator pair is placed in the cross-flow channel and upstream of the jet nozzle to enhance the impinging heat transfer. The VGP increases the Nusselt number at the impingement region. The structures generated by the VGP alter the effects of the cross-flow on the impinging heat transfer. There are Kelvin-Helmholtz instabilities at the shear layer of the jet and the cross-flow in the base flow (the flow without VGP). These instabilities are altered in the flow with VGP. A swirl component is added in the jet to study the effects on the heat transfer. The result shows that for a high or moderate level of swirl, the jet is diffused before the impinging.

Effect of winglet vortex generators configuration on thermal performance of a heated rectangular channel

In present paper, a three dimensional turbulent flow; and heat transfer inside a rectangular channel equipped with array of winglet vortex generators has been investigated experimentally and numerically. Three pairs array of winglet vortex generators of different geometrical configuration as rectangular, triangular, semi circle and parabolic are considered. The array of winglet vortex generators is formed and distributed on the bottom hot surface with a facility for changing the angle of attack from (0° to 60°). ANSYS Fluent Code (15.0) based on a finite volume method is used to get the numerical results while a k-w turbulence model is used to model the turbulent . The Reynolds number range is from 10000 to 50,000 under a constant heat flux boundary condition. The spin wise between the vortex generators are set to 1 cm and 1.5 cm while the stream wise between the vortex are 9cm,12cm and 18 cm respectively. The results indicated that the rectangular winglet vortex generators array indicated the optimum thermal performance with considerable penalty of the pressure drop while the parabolic vortex generator stated the minimum performance among the considered vortex generators shapes. The overall efficiency for rectangular, triangular, semi circle and parabolic winglet vortex generators is enhanced by (166%), (130%), (165%) and (121%) respectively as compared with plane channel.

A new method of enhancing heat transfer in sudden expansion channel using vortex generators with toe-out and toe-in configurations by acquiring perquisites of recirculation and secondary vortex flow

The relative positions of leading edges and trailing edges of rectangular vortex generators (VG) in the winglet form play a crucial role in modifying thermal and hydraulic boundary layers thereby affecting the heat transfer augmentation and pressure drop in a sudden expansion channel having expansion ratio (ER) 2:1. A numerical simulation was carried out for solving the momentum and energy equations of a three dimensional vortex- laminar flow (Reynolds number < 190) with a finite volume method based commercial code FLUENT 16.2. Reynolds number, angle of attack and VG configuration have been considered as influential parameters affecting the thermo-hydraulic performance of the sudden expansion channel due to the combined effect of primary recirculation and secondary vortex flow. The heat transfer enhancement along with corresponding pressure drop penalty was compared for the toe-out and toe-in configurations at various Reynolds (Re) numbers and angle of attacks (β). Eventually irrespective of configurations, rectangular winglet VGs are found to have better overall performance at β = 30° and β = 45° in both toe-out and toe-in configurations due to strong secondary vortex flow.

Comparative study of heat transfer enhancement and pressure drop for fin-and-circular tube compact heat exchangers with sinusoidal wavy and elliptical curved rectangular winglet vortex generator

Vortex generation has emerged as a promising passive method for enhancing air-side heat transfer. In the present work, two-dimensional numerical analysis is carried out to examine the thermo-fluid analysis of fin-and-tube compact heat exchangers with sinusoidal wavy and elliptical curved type rectangular winglet vortex generator (RWVG) having varying Reynolds number ranges from 400 to 1000. The wavy and curved VGs are also placed as up and down configurations with respect to flow direction. Thus the effect of the different common flow down (CFD) configurations of wavy-up, wavy-down, curved-up, curved-down and flat rectangular winglet is compared with baseline configuration (non-winglet case) for flow structure, temperature distribution and pressure distribution for fin-and-tube compact heat exchanger with seven inline circular tube arrangement. They are also compared with thermo-hydraulic performance criterions which include Nusselt number (Nu), Pressure drop (ΔP), friction factor (f), London area goodness factor (j/f). Appreciable improvement in heat transfer characteristics is observed with wavy and curved rectangular winglet with a moderate loss in pressure. Compared with the non-winglet baseline and flat RWVG case, the heat transfer performance of the fin-and-tube heat exchanger is significantly improved with wavy-up and down and curved-up and down configurations. Further, it is also noted that up-wavy RWVG showed the best heat transfer improvement compared to any other RWVG configuration considered. However, Wavy-up configuration has the lowest values of j/f than others and curved-down has higher values of j/f than others. Thus, curved-down RWVG found suitable than other cases of RWVG as far as London goodness factor strategy.

Longitudinal vortex generator applied to heat transfer enhancement of a flat plate solar water heater

The population growth and industrial development increase the demand for energy and the solar energy conversion is an important alternative to complement the world energy matrix. Flat plate solar collectors are devices that convert the solar energy into thermal energy and store the thermal energy in a working fluid, which could reduce the required electricity to heat water. However, an increase in the heat transfer in this type of equipment remains a great challenge. In the current research, two types of longitudinal vortex generators are placed into circular tube of a solar collector in order to enhance the heat transfer between tube walls and working fluid. The numerical modeling is performed by ANSYS 18.0 software and the flow pattern and heat transfer characteristics are analyzed in details for two types of vortex generators (delta-winglet and rectangular-winglet), Reynolds number of 300, 600 and 900, and angle of attack of 15°, 30° and 45°. Ten vortex generators were uniformly arranged on a flat-plate inside the tube. The results show that the delta-winglet and rectangular-winglet longitudinal vortex generators are in fact a passive technique capable to enhance the heat transfer in a solar water heater. The highest heat transfer is obtained for attack of the angle of 45° for both vortex generators, which is more pronounced for the rectangular-winglet vortex generator. However, the best ratio between the heat transfer and the pressure drop penalty is achieved for the delta-winglet vortex generator for angle of attack of 30°. The secondary flow is successfully generated by the inserts, although the corner vortex is observed only by rectangular-winglet vortex generator. Finally, the first vortex generator only impacts on the friction factor and can be removed with no significant losses on the heat transfer.

Heat Transfer Enhancement with Considering Pressure Loss Penalty of Airflow through Heated Plate Mounted by Perforated Concave Rectangular Winglet Vortex Generators

The use of longitudinal vortex generator results in decreased hydrodynamic flow performance by increasing pressure drop values. The purpose of this research is to obtain the improvement of heat transfer with pressure drop as low as possible. In order to achieve this purpose, experiment was performed on perforated concave rectangular winglet pair vortex generators (CRWP VGs). The test results show that the CRWP VGs without hole increase thermal performance by 24.02% up to 129.75% against baseline (without using any vortex generators) and by 12,21% up to 19,41% against rectangular winglet pair vortex generator (RWP VG). The pressure drop value for the CRWP VGs case increased by more than 10 times against the baseline case and increased by almost 100% against RWP VGs case. By using the perforated CRWP VGs, pressure drop value can be reduced by 15.07% to 72.73% followed by a slight decrease in thermal performance of 5.50% to 5.73% against the CRWP VGs without hole. Based on the evaluation using London goodness factor criteria, perforated CRWP VGs is better than the CRWP VGs without hole.

Investigation of Vortex Generator Enhanced Double-Fin and Tube Heat Exchanger

In the present work, a numerical analysis of conjugate heat transfer and fluid flow in vortex generator (VG) enhanced double-fin and tube heat exchanger is carried out. The enhanced design aims to improve the heat transfer performance of a conventional double-fin and tube heat exchanger for waste heat recovery applications. A three-dimensional (3D) numerical model is developed using ANSYS cfx to simulate fluid flow and conjugate heat transfer process. Numerical simulations with rectangular winglet vortex generators (RWVGs) at five different angles of attack (−20deg≤α≤20deg) are performed for the Reynolds number range of 5000≤Re≤11,000. Salient performance characteristics are analyzed in addition to the temperature distribution and flow fields. Based on the numerical results, it is concluded that the overall performance of the double-fin and tube heat exchanger can be improved by 27–91% by employing RWVGs at α=−20deg for the range of Reynolds number investigated. The study provides useful design information and necessary performance data that can be adopted for the design development of the heat exchanger at a lower manufacturing cost.

Parametric investigation of heat transfer enhancement and pressure loss in louvered fins with longitudinal vortex generators

The present work aims to perform a parametric study of heat transfer enhancement and the associated pressure loss applied to louvered fins with rectangular winglet vortex generators (RWL). The contributions of a set of design variables on heat transfer and pressure drop are evaluated for two geometry types, L1 and L2. The procedure to investigate the relative importance of the geometrical design variables on thermal-hydraulic performance is enabled by a Design of Simulations (DOS) method called Latin Hypercube Sampling (LHS) in association with a modern non-parametric statistical method (Smoothing Spline ANOVA method) and Computational Fluid Dynamics. Outcomes from the screening analyses turned out that the louver angle is the unique contributor to friction factor for both geometry types and this behaviour is independent of Reynolds number. With respect to heat transfer, the contributions of the input variables are different for both geometry types and Reynolds numbers. For ReDh=120, no important two-factor interaction effects were observed for both L1 and L2, in the same way as occurred in terms of friction factor. Conversely, for ReDh=240 one relevant interaction effect was observed.