5.1. Effect of Twisted Tape Pitch
In the first step, the effect of twisted tape pitch on the hydrothermal characteristics of the tube is examined and analyzed. Figure 4
represents the local Nusselt number (
) throughout the tube length for the plain tube (PT) and four twisted tape pitch values at
while the twisted tape is fully fitted in the tube (no truncation). Using the twisted tape and decreasing its pitch magnitude noticeably augments the local
along the tube length. The reason is that the twisted tape inserts create secondary flow as a result of flow swirling, which consequently improves the flow mixing, disturbs the thermal boundary layer and increases the heat transfer rate [51
]. In other words, the twisted tape redirects the colder core fluid with a better cooling capacity to the heated walls of the tube where cooling is required.
The cause of the heat transfer enhancement in Figure 4
can be seen in Figure 5
, in which the streamlines colored by velocity magnitude are illustrated for PT and four twisted tape pitch values. It is visible that as the twisted tape pitch value decreases, the flow path undergoes more changes. This is because more swirl flow fronts can be seen in lower pitch values with higher radial velocity, implying stronger secondary and mixing flow. As a result, it leads to a more effective redirection of core colder fluid towards the heated wall and, consequently, more heat is transferred between the fluid and heated wall.
shows how decreasing the twisted tape pitch magnitude affects the cooling of the heated wall at
. The temperature distribution on the heated wall implies that the secondary and mixing flow intensity affect the heated wall. In PT, the uniform enhancement of temperature along the tube length is visible, showing the thermal boundary layer development without any disturbance. On the contrary, as the twisted tape is inserted in the tube, the change in temperature distribution on the heated wall is visible. The temperature value on the heated wall decreases along the tube length and strengthens as the pitch value reduces. In higher pitch values, some hotspot regions are visible on the heated wall temperature contour; however, these regions decline at lower pitch values, resulting in better cooling performance of the system.
To better understand the temperature distribution, four different cross-sections are defined along the tube length and are displayed in Figure 7
. In the following, different parameters, such as temperature and velocity, are illustrated in them.
demonstrates the cross-sectional temperature contours on the surfaces shown in Figure 7
for PT and four twisted tape pitch values at
. The PT temperature contours show the normal development of the thermal boundary layer throughout the tube, leading to a great drop in heat transfer along the tube. On the other hand, the thermal boundary layer disturbance is intensified and gets thinner as the twisted tape is inserted in the tube, which is more effective for a lower pitch in heat transfer between the fluid and heated wall. Besides, fewer hotspot regions causing a reduction in heat transfer enhancement is visible at lower pitch values of the twisted tape, proving the cooling process improvement. Another point that can be noticed in this figure is that the presence of twisted tape and lowering its pitch value redirects the core colder fluid to the vicinity of the hot wall. The twisted tape causes more efficient heat dissipation from the wall and, consequently, more heat is transferred from the wall to the fluid. It should be noted that the contours are almost symmetrical, related to the center of the tube in all cases.
displays the cross-sectional velocity contours on the surfaces shown in Figure 7
for PT and four twisted tape pitch values at
. The velocity contours imply the intensity of secondary and mixing flow in the presence of twisted tape inserts. In other words, the higher velocity of the fluid near the heated wall shows a stronger secondary flow, and, as a result, a higher fluid momentum near the wall and a better cooling process could be achieved. It is visible in this figure that inserting twisted tape with a pitch value of L results in a high-velocity region of the fluid, which is strengthened as the twisted tape pitch value decreases, resulting in the stronger secondary flow observed in Figure 5
. It should be noted that the contours are almost symmetrical, related to the center of the tube in all cases; however, for the case with P = L, it is almost symmetrical related to the twisted tape plane.
To better quantify the heat transfer modification in the presence of twisted tape inserts with different pitch values, Figure 10
is provided for various
changes due to the more effective advection phenomenon and fluid momentum in higher fluid velocities. As seen in this figure, as an example, using twisted tape with pitch values of L, L/2, L/3 and L/4 increases the average
by about 26.87, 55.03, 86.59 and 151.42% at
compared with the PT, respectively.
shows the variations of the friction coefficient ratio with respect to PT for different pitch values and
. This figure shows that applying twisted tape enhances the friction coefficient ratio due to the added surface area and flow blockage [52
]. Furthermore, higher values for the friction coefficient ratio are observed in lower pitch values due to the creation of the more intense secondary flow shown in Figure 5
; however, when the twisted tape pitch is equal to L, its enhancement is insignificant due to the creation of very weak secondary flow in the tube. Moreover, this figure reveals that the friction coefficient ratio increases as
changes because more intense swirling flow.
5.2. Effect of Truncated Twisted Tape Position and Percentage
So far, it has been shown that the twisted tape with a pitch of L/4 results in the best thermal performance of the system. Therefore, the following simulations are performed for this pitch value. To show the effect of twisted tape truncation percentage on local
throughout the tube length for different twisted tape positions, Figure 12
is provided at
. In Figure 12
a, the twisted tape is embedded at the entrance of the tube with different values for λ. It is visible that as the flow enters the twisted tape at the tube inlet, the thermal boundary layer is disturbed and, due to the creation of secondary flow, the local
increases; however, as the flow passes the twisted tape, the thermal boundary layer starts to develop normally, and as a result, it tends to develop towards the local
curve of PT. Consequently, lower values of λ cause a higher heat transfer rate when the twisted tape is inserted at the tube entrance.
In Figure 12
b, the twisted tape is embedded at the center of the tube with different values for λ. In this figure, the local
curve starts to grow as the fluid reaches the twisted tape due to the thermal boundary layer disturbance. It is visible that the local
at the truncated cases surpasses the fully fitted twisted tape, and a higher maximum value for
is visible for higher values of λ. As the flow passes the twisted tape, the thermal boundary layer starts to grow and becomes fully developed.
In Figure 12
c, the twisted tape is embedded at the exit of the tube with different values for λ. This figure also shows the local
enhancement as the fluid enters the twisted tape as a result of thermal boundary layer disturbance and stronger mixing flow. In this case, after a sudden increase in
at the twisted tape entrance, the local
decreases, and its curve tends to reach the value of the fully fitted twisted tape.
displays the streamlines colored by velocity magnitude in different twisted tape truncation percentage values inserted at the tube entrance for
. In the truncated cases, the flow path swirls to the end of tube length, but the secondary flow intensity is reduced as the fluid passes the twisted tape. As a result, truncating the twisted tape results in a reduction in heat transfer rate but less material is used, causing fewer production expenses, and also the pressure loss penalty reduces due to less flow lockage and contact area between the fluid and solid.
To show the effect of truncated twisted tape inserts and changes in the flow patch shown in Figure 13
on the temperature distribution of the heated wall, Figure 14
illustrates the temperature contours at the wall. It is visible that although there are some hotspots after the truncated twisted tape, the number of hotspots is still lower than for the PT, showing the effective cooling process even after the fluid passes the twisted tape. This figure proves the presence of secondary flow (not as intense as it is in the fully twisted tape insert) after the fluid passes the truncated twisted tape.
To clearly show the effect of twisted tape position on the local
throughout the tube length at different twisted tape truncation percentage values, Figure 15
illustrates the local
for three different twisted tape truncation percentage values of 25, 50 and 75% at
for different positions, as shown in Figure 1
b. This figure shows that when the twisted tape is at the tube entrance, no sudden increase in
is visible; in contrast, there is a maximum value for
along the tube length when the twisted tape is inserted at the center and exit of the tube. For all values of λ, the highest maximum
throughout the tube length corresponds to the layouts where twisted tape is inserted at the tube exit, which is higher as λ changes.
illustrates the streamlines colored by velocity magnitude at different positions of the twisted tape in the tube at a twisted tape truncation percentage of 75% and
. This figure shows that when the twisted tape is embedded at the tube entrance, the whole flow patch is affected. When the twisted tape is at the tube center, half of the tube length is affected, and for the case in which twisted tape is at the tube exit, the flow path before reaching the twisted tape is similar to that of PT.
The effect of the position of the truncated twisted tape inserts on the temperature distribution of the heated wall is depicted in Figure 17
. The same temperature distribution before the flow reaches the twisted tape as that of PT for the heated wall temperature distribution is also visible in this figure. Moreover, flow mixing as the fluid passes the twisted tape and the strong secondary flow in the twisted tape regions are observable in this figure.
To quantify the heat transfer rate for different truncation values and positions of the twisted tape, Figure 18
is provided to show the variations of the
ratio compared with PT at various λ and Re values, different twisted tape positions and a pitch of L/4. For all twisted tape positions and
, higher values of λ result in lower
and heat transfer due to the fact that the secondary and mixing flows in a tube fully fitted with twisted tape are much stronger than for a tube equipped with a truncated twisted tape, as shown in Figure 14
. As seen in this figure, using twisted tape with a pitch value of L/4 at the entrance of the tube and λ values of 0, 25, 50 and 75% increase the average
by about 71.26, 68.50, 57.59 and 37.34% at
and 151.42, 133.99, 109.52 and 71.43% at
in comparison with the PT, respectively.
Considering the position of the twisted tape, for all values of λ at Re of 1000, when the truncated twisted tape is placed at the tube entrance, a higher
is obtained, followed by the cases with twisted tape at the tube center, and the lowest
correspond to the cases with twisted tape at the tube exit. This is due to the fact that as the fluid passes the twisted tape, the flow is still affected by the twisted tape and swirl flow is visible to the end of the tube, as shown in Figure 16
. Thus, for the case of twisted tape inserts in the tube entrance, more of the tube length experiences swirl flow, and as a result, the cooling process improves.
represents the variations of friction coefficient ratio with respect to PT at various λ for Re
of 1000, different twisted tape positions and a pitch of L/4. It is visible that for all twisted tape positions, as λ increases, the friction coefficient ratio is reduced due to the lower level of solid material and, as a result, less flow blockage and smaller contact area between the fluid flow and solid. Furthermore, for all values of λ, there are almost similar values for the friction coefficient ratio for the cases where twisted tape is placed at the tube entrance and center; however, lower values for the friction coefficient ratio are observable when the twisted tape is embedded at the tube exit. The cause of this scenario can be attributed to the fact that when the twisted tape is at the tube exit, no swirl flow is generated before the fluid reaches the twisted tape.
As discussed above, the application of twisted tape inserts in the captured cases increases both the heat transfer rate as a desirable outcome and the friction coefficient as an undesirable result. Therefore, there is an interplay between the benefits of using twisted tape in heat transfer enhancement and their side effects in forcing more pumping power into the system. To analyze this issue, the dimensionless PEC number introduced in Equation (9) is discussed here. In fact, this number is used to evaluate the practical use of any modified heat transfer technique from the viewpoint of energy-saving potential. Generally, higher values of PEC imply superior energy saving. Figure 20
illustrates the PEC parameter for all cases investigated in this study for Re of 1000. It is visible that decreasing the twisted tape pitch value from Figure 20
a–d enhances the PEC number, showing the fact that applying twisted tape with a lower pitch value is efficient from the viewpoint of both heat transfer enhancement and energy saving. It is also visible that as the twisted tape pitch increases, the sensitivity of PEC to the λ value is reduced.
Furthermore, for all λ values, placing the twisted tape at the tube entrance leads to higher PEC magnitudes. Therefore, for P = L, L/2, L/3 and L/4, the optimum cases from the viewpoint of energy saving are twisted tapes with λ = 75, 50, 50 and 0%, for which the related PEC numbers at
are almost equal to 1.08, 1.24, 1.4 and 1.76, respectively. In addition, PEC numbers in all cases are tabulated in Appendix A
of this paper.