12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

HEAT TRANSFER ENHANCEMENT OF SWIRLING FLOW IN A CIRCULAR PIPE
IN THE TRANSITION REGIME
Hajime Nakamura
Department of Mechanical Engineering
National Defense Academy of Japan
1-10-20 Hashirimizu, Yokosuka, Kanagawa, Japannhajime@nda.ac.jp

Yoshinori Sugawara
Graduate School of Science and Engineering
National Defense Academy of Japan
1-10-20 Hashirimizu, Yokosuka, Kanagawa, Japan

Shunsuke Yamada
Department of Mechanical Engineering
National Defense Academy of Japan
1-10-20 Hashirimizu, Yokosuka, Kanagawa, Japan
yamadas@nda.ac.jp

Yuki Funami
Department of Mechanical Engineering
National Defense Academy of Japan
1-10-20 Hashirimizu, Yokosuka, Kanagawa, Japan
funami@nda.ac.jp

ABSTRACT
Experiments were conducted focusing on the heat transfer
enhancement of a swirling pipe flow in the bulk Reynolds
number Re = 1000 ~ 12000, including the transition regime.
Measurements were performed downstream of the swirl
generator composed of a twisted tape to eliminate the turbulencecaused by the insert and focus only on the effect of flow swirling.
The spatiotemporal variation of the heat transfer, which wasreflected by the flow field near the wall, was measured by highspeed infrared imaging technique. In addition, change in the flow
field was measured by laser Doppler velocimetry. By applying
the swirl to the flow, the heat transfer coefficient increased
against the wall shear stress. In particular, it increased up to 30%
at Re ≈ 1500 ~ 2000. In the turbulent regime, the turbulent
streaky structure in the spatiotemporal heat transfer inclined in
the swirling direction. The mean streak spacing became
narrower due to the increase in the shear velocity, while the nondimensional spacing by the wall parameters did not change
significantly with the flow swirling. In the laminar regime, theinclined streaky structure, which fluctuated with time, appearedin the spatiotemporal heat transfer by swirling the flow. This isconsidered to be caused by the flow instability due to the flow
swirling, which leads to a large heat transfer enhancement in thisregime.

conducted from the laminar and turbulent regimes including thetransition regime.
Measurements were performed downstream of the swirl
generator (a twisted tape was used in this experiment) toeliminate the turbulence caused by the insert and focus only on
the effect of flow swirling. The spatiotemporal variation of theheat transfer, which was reflected by the flow field near the wall,
was measured by high-speed infrared imaging technique(Nakamura, 2007), and investigated the change in the thermal
streaks when the flow was swirled. In addition, change in theflow field in the pipe was measured by laser Doppler

INTRODUCTION
It is well known that flow swirling in a pipe improves heattransfer compared to the pressure drop penalty. (Lopina andBergles, 1969, Sheikholeslami, et at., 2015, among others).
Therefore, swirl generators such as twisted tapes or spiralgrooves are often installed in pipelines to enhance the heattransfer in such as heat exchangers. However, the mechanism of
the heat transfer enhancement has not been well understoodsince the swirling flow becomes a very complicated nature inwhich centrifugal instability acts on the wall turbulence.
In this study, experiments were conducted focusing on theheat transfer enhancement of a swirling pipe flow. Previous
studies have suggested that the flow swirling enhances the heattransfer with increasing Reynolds number in the laminar regime(Date, 1974; Manglik and Bergles, 1993a), whereas it isenhanced with decreasing Reynolds number in the turbulent
regime (Koch, 1968; Manglik and Bergles, 1993b; Eiamsa-ard
et al. 2010). Therefore, in this study, experiments were

Figure 1. Experimental setup and swirl generator.

(a) Photograph(b) Top-down cross-sectional view (c) Measurement process
Figure 2. Test section for heat transfer measurements.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
velocimetry (LDV) to consider the mechanism that causes theheat transfer enhancement.

and quartz are different, the traverse coordinates were adjusted
to prevent distortion of the measured coordinates.

EXPERIMENTS
Figure 1 shows the experimental setup that drives the waterflow in a horizontal circular pipe by the head difference. The innerdiameter of the circular pipe was D = 20 mm and the mean flow
velocity ranged from Um = 0.05 to 0.5 m/s, resulting in the bulk
Reynolds number ranged Re = 1000 ~ 12000. The flow in the pipe
was swirled by a twisted tape with a length of 200 mm and awidth of 20 mm, which was installed behind the inlet section of
about 2 m. The twist pitch (length of 180° twist) was P/D = 2.5,
3.3 or 5, whose velocity ratio Uθ/Um calculated from (π/2)/(P/D)
were respectively 0.63, 0.47, or 0.31, where Uθ is mean
azimuthal velocity.
Figure 2 shows the test section for the heat transfer
measurements. The circular duct was fabricated from an acrylic
pipe of 280 mm in length (located from z/D = 1.3 to 15.3, z is thestreamwise coordinate starting from the twisted tape exit).
Titanium foil with a thickness of 30 μm was glued around theentire circumference of the inner surface of the pipe, including
the excised section of the pipe. The temperature fluctuation
corresponding to the flow turbulence that appeared when thetitanium foil was heated electrically was measured by highspeed infrared thermography, as shown in Fig. 2 (c).
Simultaneously, the pressure loss Δp between the inlet and outletof the test section was measured by a high-sensitivity differential
manometer.
Time series data of instantaneous temperature distribution
measured here, Tw, were used to calculate the spatiotemporal
heat transfer coefficient h, considering convection and radiation
losses to outside the pipe, thermal diffusion in the heated surface,
and thermal inertia of the heated surface (Nakamura et al., 2017).
The mean heat transfer coefficient hm was evaluated from thespatiotemporal averaged values of convective heat flux qcv andtemperature difference Tw – Tm (Tm is mixed-mean temperature).
For the velocity measurement, a quartz glass test pipe with awater jacket was used instead of the test model shown in Fig. 2.
A biaxial LDV was used to measure the distributions of mean
and fluctuating velocities in the pipe. The streamwise velocity uz
and the radial (wall-normal) velocity ur were measured by thevertical traverse, and the azimuthal velocity uθ was measured by
the horizontal traverse of the pipe cross section. Here, thevelocity u is expressed as the sum of the mean velocity U andthe fluctuation velocity u'. Since the refractive indexes of water

RESULTSHeat Transfer Enhancement
The pipe friction coefficient λ = (Δp/Δz)D/(0.5ρUm2) and themean heat transfer coefficient hm measured in the absence of thetwisted tape reasonably agreed with the well-known empiricalformulas in both the turbulent (Re ≥ 5000) and laminar (Re ≤2200) regimes. Figure 3 shows the mean heat transfer coefficientagainst the wall shear stress τw = (Δp/Δz)D/4. When the flow isswirled, the heat transfer coefficient increases at the same wall
shear stress. In particular, it shows that the heat transfer is largely
enhanced at around Re ≈ 2000 (up to 30% at the same wall shear
stress τw).
Spatiotemporal Heat Transfer
Figures 4, 5, 6 and 7 show contours of instantaneous heattransfer coefficient at Re = 12000, 5800, 2200 and 1700,
respectively. The upper contours of each figure show the casewithout the twisted tape, and the lower show the case with P/D= 2.5 twisted tape installed.
In the turbulent regime (Figs. 4 and 5), the structure
corresponds to the well-known turbulent streaks appears without
the twisted tape. In contrast, the streaky structure inclines in the
swirling direction when the flow is swirled. The spacing between
adjacent streaks becomes narrower by giving the swirl, which
increases the heat transfer coefficient. This is mainly because thevelocity distribution changes due to the centrifugal force, which
increases the shear velocity uτ (see Fig. 9 (a): velocity gradientat the wall increases due to the swirling). Figure 8 shows themean spacing of thermal streaks lc+ evaluated from the premultiplied spectrum of h distribution vertical to the streaks. The
superscript ‘+’ indicates the non-dimensional value with the wallparameters (uτ and kinematic viscosity ν). The non-dimensional
streak spacing does not change significantly with the flow
swirling to maintain the spacing of about lc+ ≈ 100. This meansthat the characteristics of wall turbulence are maintained evenwhen the flow is swirled, although the boundary layer becomesthinner and the shear velocity increases. Incidentally, the nondimensional streak spacing seems to be reduced at Re ≈ 5000
when the flow is swirled. This is likely to be related to theformation of clearer thermal streaks due to swirling at Re ≈ 5000
(see Fig. 5).
It is interesting to note that the inclination angle of thestreaks at z/D ≈ 4 (about 30° on average, see Fig. 5 (b) at Re =5800) is larger than the flow inclination angle estimated by Uθ/Uz≈ 0.33 as shown in Fig. 10 (a) (tan-1(0.33) = 18° at z/D = 4.3 at
Re = 5000). The reason for this is not clear, but it is possible toassume that the Taylor vortices which may be formed by thecentrifugal instability affects the turbulent streaky structure.
In the laminar regime (Figs. 6 and 7), the heat transfer
coefficient is almost uniform when the flow is not swirled. And
it does not fluctuate over time. In contrast, when the flow isswirled, a streaky structure that inclines in the swirl direction
appears. This structure fluctuates over time, which increases theheat transfer. The similar streaky structure was observed at thelower Reynolds number of Re ≈ 1000 at P/D = 2.5, only in the
upstream region.
It is known that when a laminar pipe flow is rotated in theaxial direction to swirl the flow, the flow becomes unstable andforms a helical vortex structure (Toplosky and Akylas, 1988;

Figure 3. Heat transfer enhancement against wall shear stress.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 4. Contours of instantaneous heat transfer coefficient at Re = 12000: (a) no swirl (top); (b) P/D = 2.5 (bottom).

Figure 5. Contours of instantaneous heat transfer coefficient at Re = 5800: (a) no swirl (top); (b) P/D = 2.5 (bottom).

Figure 6. Contour of instantaneous heat transfer coefficient at Re = 2200: (a) no swirl (top); (b) P/D = 2.5 (bottom).

Figure 7. Contour of instantaneous heat transfer coefficient at Re =1700: (a) no swirl (top); (b) P/D = 2.5 (bottom).

Imao et al. 1992). Similarly, stability analysis of a laminar flow
in a pipe shows that the helical wave does not decay and it issustained when a swirl is applied to the inlet (Landman, 1990).
Based on these facts, it is considered that the inclined streaky
structure appearing in Figs. 6 (b) and 7 (b) is related to the flow
instability due to swirling the laminar pipe flow.
Mean Velocity Field
Figures 9 and 10 show mean streamwise and azimuthal
velocities Uz and Uθ, respectively, at Re = 5000 (turbulent
regime) and Re = 1500 (laminar regime). Here, the velocity andlength are non-dimensionalized by 2Um and pipe radius R.

Figure 8. Mean spacing of thermal streaks.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(a) uz '+ ur '+(b) ur '+ θ'+ (rough estimate)
Figure 14. Comparison between turbulent shear stress andturbulent heat flux near the wall at z/D = 8.3 at Re = 5000.

(a) Re = 5000(b) Re = 1500
Figure 9. Mean streamwise velocity profiles at z/D = 8.3.

(a) Re = 5000(b) Re = 2000
Figure 10. Mean azimuthal velocity and angular momentum
profiles of P/D = 2.5 at z/D = 4.3.

(a) uz '+ ur '+(b) ur '+ θ'+ (rough estimate)
Figure 15. Comparison between turbulent shear stress andturbulent heat flux near the wall at z/D = 8.3 at Re = 1500.

1991; Pashtrapanska et al., 2006; among others). For thereference, it is known that the turbulent flow in a rotating pipe
shows the opposite trend to approach the Hagen-Poiseuille flow
(Kikuyama et al., 1983; Reich and Beer, 1989; Orlandi andFatica, 1997; among others). This difference can be explained by
the following Richardson number, which was derived from theanalogy between the buoyancy and centrifugal forces (Bradshaw,
1969; Kikuyama et al., 1983).

(a) Re = 5000(b) Re = 1500
Figure 11. Streamwise turbulence intensities uz'+rms at z/D = 8.3.

Ri =

(1)

Based on Eq.(1), in the case of Ri > 0, that is, when the angularmomentum rUθ increases in the radial direction, the flow is
stabilized and the turbulence is suppressed. However, when Ri <0, the flow is destabilized and the turbulence is enhanced. As
shown in Fig. 10, for the swirling flow of this experiment, rUθ
increases in the radial direction in the central part (r < 0.8), but
decreases near the wall (r > 0.85). This suggests that the flow is
stabilized in the central part but becomes unstable near the wall.
This may be related to the smaller streak spacing of lc+ at Re ≈5000. In contrast, in the case of a rotating pipe, Ri number
becomes positive in the entire region, resulting in thelaminarization of the flow.
In the laminar regime (Fig. 9 (b)), a parabolic velocity
distribution of Hagen-Poiseuille flow changes to that similar to
the turbulent flow by swirling the flow. This is related to theappearance of the unsteady streaky structure which is considered
to be caused by the flow instability due to swirling (Figs. 6 (b)and 7 (b)).

(a) Re = 5000(b) Re = 1500
Figure 12. Radial turbulence intensities ur'+rms at z/D = 8.3.

(a) Re = 5000

2Uθ ∂(rUθ )
r2 ∂r2∂Uz∂ Uθ 2+ r∂z r∂z(b) Re = 1500

Figure 13. Turbulent shear stress uz '+ ur '+ at z/D = 8.3.

In the turbulent regime at Re = 5000, the streamwise velocity
in the central part decreases and that near the wall increases
when the flow is swirled. This is a general trend by giving theswirl to the turbulent pipe flow (Kreith and Sonju, 1965; Kitoh,

Turbulence distributions
Figures 11 and 12 show turbulent intensities in thestreamwise and radial directions uz'+rms and ur'+rms, respectively.
At Re = 5000, both distributions of no swirl are in good4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
agreement with the results of direct numerical simulation (Wuand Moin, 2008, at Re = 5300). By giving the swirl, uz'+rms
decreases between the wall and central regions (r = 0.5 ⁓ 0.8),
whereas ur'+rms hardly changes. The similar trends have been
observed in the previous studies (Pashtrapanska et al. 2006;
among others). This is likely that there is an energy transfer fromthe streamwise to other components turbulence between the nearwall and the wake region (Chin and Phillip, 2019).
Figure 13 (a) shows turbulent shear stress uz '+ ur '+ at Re =5000. It is remarkable that the turbulent shear stress is
significantly reduced in the central part (r < 0.8) by swirling theflow. This corresponds to the flow stabilization due to Ri > 0
where the flow is characterized by a forced vortex (Kitoh, 1991).
In the near wall region, the turbulent shear stress keeps arelatively large value in the region where Ri < 0. As a whole, theturbulent shear stress is reduced by the flow swirling at Re =5000, as shown in Fig. 13 (a). Note that uz '+ ur '+ decreases
significantly in the central part (r < 0.5), whereas uz'+rms andur'+rms are relatively high. This means that the turbulences in thecentral region are less correlated each other, and does notcontribute much to the turbulent shear stress.
Figure 14 compares the turbulent shear stress uz '+ ur '+ and theestimated turbulent heat flux ur '+ θ'+ near the wall at Re = 5000.
Here, the non-dimensional fluid temperature is defined by θ+ =(Tm – T)/Tτ, where T is fluid temperature and Tτ = qw/(ρcpuτ) is
friction temperature. The turbulent heat flux ur '+ θ'+ =Rur'θ'ꞏur+'rmsꞏθ+'rms was estimated using the measured wall
temperature fluctuation Tw'rms and the correlation coefficient
Rur'θ' of DNS (Tiselj et al. 2001: turbulent channel flow at Reτ =171, constant heat flux, Pr = 5.4). The temperature fluctuation
θ+'rms was substituted by the measured wall temperaturefluctuation based on the fact that the value θ+'rms near the wall(y+ < 13 at Pr ≈ 5) does not change significantly under a constantheat flux condition. Since there appeared some asymmetry in theflow field when the flow was swirled, the distribution of both theupper and the lower walls were plotted here. As shown in Fig.
14, both the turbulent shear stress and the turbulent heat flux
have a similar trend, the value decreases slightly as the flow
swirls.
As shown in Fig. 3, the heat transfer increases to the wall
shear stress at Re ≈ 5000. The reason for this is not clear atpresent, but one of the factors is considered to be the larger
decrease in the turbulent shear stress than the turbulent heat flux,
as suggested in Fig. 14. This is likely to be due to the significant
decrease in the streamwise turbulence uz'+ compared to the wallnormal turbulence ur'+. From another point of view, it can be said
that the change in the mean streamwise velocity distribution(velocity increase near the wall) due to the swirling (see Fig. 9(a)) is likely to be a factor of the heat transfer enhancement to
the wall shear stress, which can be explained by FIK identity(Kasagi et al. 2012). In any case, the heat transfer enhancementin this regime is considered to be closely related to the change inthe vortical structure observed in Figs. 4 and 5, which dominates
the momentum and heat transports near the wall.
In the laminar regime at Re = 1500, the turbulence is small
in the absence of the twisted tape (no swirl), as shown in Figures
11 (b) and 12 (b) (the turbulence observed here is considered tobe mainly due to measurement noise). In addition, measurements
were performed with a flat tape without twist (noted as P/D = ∞in the Figures) to investigate the effect of turbulence by the tapeinsert itself. In this case, the turbulence hardly increases
especially near the wall. That is, the disturbance caused by thetape insert itself was small. In contrast, when the swirl is given

with the twisted tape, the turbulence intensity approaches the
distribution of the turbulent flow. Also, as shown in Fig. 15, theturbulent shear stress and the turbulent heat flux near the wall
increase to the similar values as the turbulent flow. Based onthese results, it is reasonable to say that the turbulent transition
occurs by swirling the flow in the laminar regime. This
corresponds to the occurrence of the inclined unsteady streaky
structure, as shown in Figs. 6 (b) and 7 (b). According toexperiments by Garcίa et al. (2012), when the wire coil was
installed inside the pipe to swirl the flow, the transition Reynolds
number was lower than when other turbulence promoters were
installed. This also support the fact that the swirling the laminarflow promotes the turbulent transition.
The heat transfer enhancement against the wall shear stressis often discussed by the ratio of Stanton number to the friction
coefficient, St/Cf, derived from the Reynolds analogy. The value
St/Cf of the laminar pipe flow for a constant heat flux is 0.27/Pr,
which is derived from Cf = 16/Re and St = Nu/Re‧Pr = 4.36/Re‧Pr.
For the turbulent pipe flow, the value St/Cf can be estimated to
0.5/Pr2/3 from the Chilton and Colburn j-factor analogy ofSt‧Pr2/3 = Cf/2 in the range Pr = 0.7 ~ 1000 (Chilton and Colburn,1934). Namely, the parameter St/Cf is generally higher in the
turbulent flow than in the laminar flow, especially for the higher
Prandtl number. (In the case of Pr = 5, the value St/Cf in thelaminar and turbulent regimes are 0.054 and 0.171,
respectively.) From this fact, it is fairly certain that the large
increase in the heat transfer against the wall shear stress in thelaminar regime is caused by the turbulent transition.
Accordingly, it can be said that the decrease in the transition
Reynolds number due to the flow swirling leads to a large heattransfer enhancement in this regime.

SUMMARY
In this paper, the mechanism of heat transfer enhancement
by applying the swirl to an in-pipe flow was considered basedon the measurements of spatiotemporal heat transfer andvelocity field.
In the turbulent regime, the turbulent shear stress decreased
significantly in the central part due to the stabilization by
swirling the flow. In contrast, the turbulent shear stress kept a
relatively large value in the near wall region, while the nondimensional streak spacing did not change significantly with theflow swirling. The reason for the heat transfer enhancement inthis regime was not clear at present, but one of the factors wasconsidered to be the larger decrease in the turbulent shear stressthan the turbulent heat flux near the wall.
In the laminar regime, the decrease in the transition
Reynolds number due to the instability by the flow swirling is
considered to be the reason for a large heat transfer enhancement.
This can be explained by the fact that the parameter St/Cf isgenerally higher in the turbulent flow than in the laminar flow.

REFERENCES
Bradshaw, P., 1969, “The Analogy Between Streamline
Curvature and Buoyancy in Turbulent Shear Flow”, Journal of
Fluid Mechanics, Vol. 36, pp. 177-191.
Chilton, T. H., and Colburn, A. P., 1934, “Mass Transfer(Absorption) Coefficients”, Industrial and Engineering
Chemistry, Vol. 26, pp. 1183-1187.
Chin, R. C., and Philip, J., 2019, “Direct Numerical
Simulation of Low Reynolds Number Turbulent Swirling Pipe
Flows”, Physical Review Fluids, Vol. 4, 114607.

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
Date, A. W., 1974, “Prediction of Fully-Developed Flow ina Tube Containing a Twisted-Tape”, Int. J. Heat Mass Transf.,
Vol. 17, pp. 845-859.
Eiamsa-ard et al., 2010, “Thermohydraulic Investigation of
Turbulent Flow Through a Round Tube Equipped with Twisted
Tapes Consisting of Centre Wings and Alternate-Axes”,
Experimental Thermal and Fluid Science, Vol. 34, pp. 1151–
1161.
Garcίa, A., Solano, J. P., Vicente, P. G., and Viedma, A.,
2012, “The Influence of Artificial Roughness Shape on Heat
Transfer Enhancement: Corrugated Tubes, Dimpled Tubes andWire Coils”, Applied Thermal Engineering, Vol. 35, pp. 196201.
Imao, S., Itoh, M., Yamada, Y., and Zhang, Q., 1992, “TheCharacteristics of Spiral Waves in an Axially Rotating Pipe”,
Experiments in Fluids, Vol. 12. pp. 277-285.
Kasagi, N., Hasagawa, Y., Fukagata, K., and Iwamoto, K.,
Contral of Turbulent Transport: Less Friction and More Heat
Transfer”, ASME J. Heat Transfer, Vol. 134, 031009.
Kikuyama, K., Murakami, M., and Nishibori, K., 1983,“Development of Three-Dimensional Turbulent Boundary
Layer in an Axially Rotating Pipe”, ASME Journal of Heat
Transfer, Vol. 105, pp. 154-160.
Kitoh, O., 1991, “Experimental Study of Turbulent Swirling
Flow in a Straight Pipe”, Journal of Fluid Mechanics, Vol. 225,
pp. 445-479.
Koch, R., 1960, “Pressure Loss and Heat Transfer for
Turbulent Flow”, United States Atomic Energy Commission,
Office of Technical Information, AEC-tr-3857, Translated from
VDI-Forschungsheft, Ser. B. 24, No. 469, 1-44 (1958).
Kreith, F., and Sonju, O. K., 1965, “The decay of a Turbulent
Swirl in a Pipe”, Journal of Fluid Mechanics, Vol. 22, pp. 257271.
Landman, M. J., 1990, “On the Generation of Helical Waves
in Circular Pipe Flow”, Physics in Fluids A, Vol. 2, pp. 738-747.
Lopina, R. F., and Bergles, A. E., 1969, "Heat Transfer andPressure Drop in Tape-Generated Swirl Flow of Single-Phase
Water", ASME J. Heat Transfer, Vol. 91, pp. 434-442.
Manglik, R. M., and Bergles, A. E., 1993a, “Heat Transfer
and Pressure Drop Correlations for Twisted-Tape Inserts in
Isothermal Tubes: Part I – Laminar Flows”, ASME Journal of
Heat Transfer, Vol. 115, pp. 881-889.
Manglik, R. M., and Bergles, A. E., 1993b, “Heat Transfer
and Pressure Drop Correlations for Twisted-Tape Inserts in
Isothermal Tubes: Part II – Transition and Turbulent Flows”,
ASME Journal of Heat Transfer, Vol. 115, pp. 890-896.
Nakamura, H., 2007, “Measurements of Time-Space
Distribution of Convective Heat Transfer to Air Using a Thin
Conductive-Film”, 5th Int. Symp. on Turbulence and Shear Flow
Phenomena, München, pp. 773-778.
Nakamura, H., Shiibara, N., and Yamada, S., 2017,“Quantitative Measurement of Spatio-Temporal Heat Transfer
to a Turbulent Water Pipe Flow”, Int. J. Heat Fluid Flow, Vol.
63, pp. 46-55.
Orlandi, P., and Fatica, M., 1997, “Direct Simulations of
Turbulent Flow in a Pipe Rotating about Its Axis”, Journal of
Fluid Mechanics, Vol. 343, pp. 43-72.
Pashtrapanska, M., Jovanovic, J., Lienhart, H, and Durst, F.,
2006, “Turbulence Measurements in a Swirling Pipe Flow”,
Experiments in Fluids, Vol. 41, pp. 813-827.
Reich, G., and Beer, H., 1989, “Fluid Flow and Heat
Transfer in an Axially Rotating Pipe – I. Effect of Rotation on
Turbulent Pipe Flow”, Int. J. Heat and Mass Transf., Vol. 32, pp.
551-562.

Sheikholeslami, M., Gorji-Bandpy, M., and Ganji, D. D.,
2015, “Review of Heat Transfer Enhancement Methods: Focus
on Passive Methods Using Swirl Flow Devices”, Renewable andSustainable Energy Reviews, Vol. 49, pp. 444-469.
Tiselj, I., et al., 2001, “Effect of Wall Boundary Condition
on Scalar Transfer in a Fully Developed Turbulent Flume”,
Physics of Fluids, Vol. 13, pp. 1028-1039.
Toplosky, N., and Akylas, T. R., 1988, “Nonlinear Spiral
Waves in Rotating Pipe Flow”, Journal of Fluid Mechanics, Vol.
190, pp. 39-54.
Wu, X., and Mion, P., 2008, “A Direct Numerical
Simulation Study on the Mean Velocity Characteristics in
Turbulent Pipe Flow”, Journal of Fluid Mechanics, Vol. 606, pp.
81-112.

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