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Hieronder kunt u uw verzoek toelichten of een vraag stellen. Bedankt voor uw aanvraag Wij nemen zo spoedig mogelijk contact met u op. Download brochure Vult u alstublieft onderstaande gegevens in om onze brochure in PDF-formaat te downloaden. Het downloaden start direct na het verzenden van deze gegevens. Download brochure. Managementboek Daarom koopt u bij Managementboek Een boek uitgeven, hoe doe je dat? Sluit venster Stel een vraag Van:. It becomes evident that the longitudinal grooved surface used in this experiment should not be merely regarded as a "rough" wall, because it still remains the character of the restricted turbulent vortex, although it cannot reduce drag for water.
It shows a character of "rough" wall due to a larger size of groove and relatively poor smoothness of the grooved surface. This result verifies the conclusion that grooved surfaces could be considered as transitionally rough under certain conditions Tani, ; Saravi and Cheng, Grooves decrease the drag by restricting the spanwise motions of turbulent vortices near the wall. In order to achieve drag reduction, the scale of the turbulent vortex should correspond to the drag-reducing scale range of grooves Bechert et al.
For water, the turbulence is a complicated system with a large number of multi-scale turbulent eddies, the sizes of which still remain undetermined. It can be seen from other literature that the scale of a turbulent vortex near the wall is approximately wall units while vortices of wall units also exist Adrian et al.
The range of the grooved scale in this study is larger than Because the grooved scale is similar to the scale of turbulent vortex near the wall, the grooves cannot restrict effectively the motions of turbulent vortices, and thus the smaller turbulent vortices could intrude into the valley of grooves and scour the sidewall, representing an increase in frictional area and drag. By comparing the grooved scale with the turbulent vortex scale, it is speculated that the former is smaller than the latter when the drag reduction can be achieved, but the accurate drag-reducing scale range of grooves still needs to be determined by further experiments.
Lee et al.
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They found that the longitudinal riblets could restrict the spanwise motions of streamwise turbulent vortices near the wall when riblets reduced drag at a lower Reynolds number, and discovered the phenomenon that turbulent vortices intruded into the valley of grooves and scour the sidewall when the drag-increasing case occurred at a higher Reynolds number.
To some extent, their results could verify the reliability of the experimental results and analysis in the present study. Comparing the curves for CTAC solutions in the smooth channel with that in the grooved channel, we find that the drag reduction effectiveness of surfactant solutions in the smooth channel is better than that in the grooved one for 50 ppm; however, it is just the opposite for ppm CTAC solutions.
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In order to explain the above phenomenon easily, four effects of grooves should be defined in the present study as follows:. The "positive restriction effect"- grooves can decrease the drag by restricting the spanwise motions of turbulent vortices near the wall, when the turbulent vortex scale matches up with the scale of grooves at a lower Reynolds number. The "negative restriction effect"- grooves cannot restrict the spanwise motions of turbulent vortices near the wall and the smaller turbulent vortices could intrude into the valley of grooves and scour the sidewall at a higher Reynolds number, resulting in an increase in drag.
The existence of the above two effects have been verified by Lee et al. The "positive peak effect"- the grooved tip could promote the formation of SIS by providing a larger shear stress at a lower Reynolds number. The "negative peak effect"- the grooved tip destroys the formation of SIS by a larger shear stress, especially at a higher Reynolds number. The influence of shear stress on the SIS in a surfactant solution was reported in the literature by Zhou et al.
To some extent, these previous investigations could provide the basis for the possibility of these two "peak effects" mentioned above. However, it is noted that these two "peak effects" are speculative in the present study, and need further investigation to verify them. These four effects above will be summarized to explain the results obtained in the present experiment and the interaction between grooves and surfactant solutions in a simpler way. For 50 ppm surfactant solution, the number of surfactant molecule is too few due to the lower surfactant concentration, resulting in a weaker SIS and "positive peak effect".
Moreover, the weaker SIS cannot inhibit the formation of small turbulent vortices effectively. Therefore, the turbulent vortex scale is smaller than the grooved scale, leading to the "negative restriction effect" of grooves. Furthermore, grooves exhibit a larger "negative peak effect" at a higher Reynolds number. As a result, the overall drag-reducing effectiveness is weakened.
In contrast, for 70 ppm or higher concentrations, the "positive peak effect" is intensified with increasing numbers of surfactant molecule at a lower Reynolds number. Moreover, the SIS is more effective to inhibit the formation of small turbulent vortex, resulting in an increasing scale of turbulent vortex, so the "positive restriction effect" is obtained. As a result, drag reduction effectiveness of surfactant solution in the grooved channel is enhanced by the interaction of the two effects before the critical Reynolds number Re c.
Figure 5 also shows that the drag-reducing enhancement effect is the best for 70 ppm, and then decreases in the order ppm, ppm and 50 ppm. For the 50 ppm case, there is no enhancement effect. This indicates that the drag-reducing enhancement effect becomes weaker with increasing surfactant concentration.
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In summary, the "restriction effect" and the "peak effect" of grooves change with Reynolds number and concentration of surfactant solution, and the drag reduction effectiveness of surfactant solution in a grooved channel depends on the interaction of the two effects.
This implies that surfactant and grooves reduce drag by separate mechanisms, and they can enhance drag reduction by mutual promotion, that is to say, there is a synergistic effect, which expands the range of applications and their potential applications. The possible synergistic mechanism is that, in the surfactant solution, the scale of turbulent vortex becomes larger due to the inhibition of SIS compared with that in water, and grooves can restrict the penetration of the larger vortices into the grooved valley more effectively at the appropriate surfactant concentration and Reynolds number, and thus fewer turbulent vortices scour the grooved surface and the momentum exchange decreases compared with the smooth surface.
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Moreover, the larger shear stress at the grooved tips can make the formation of the near-wall SIS easier before the Re c. As a result, friction drag can be reduced again by grooves on the basis of the drag-reducing surfactant solution. They are about 1. It can also be found from Figure 5 that, at the same concentration of surfactant solution, the friction factor rises much more rapidly in the grooved channel than in the smooth channel when Re is larger than Re c.
It is understandable that the "negative peak effect" of grooves is too strong to destroy the SIS more quickly, especially at a higher Reynolds number, and thus the friction factor increases faster in the grooved channel. The mutual inhibition between drag-reducing effect and heat transfer effect of surfactant may benefit its application in the field of heat transfer. The surfactant solution can enhance heat transfer performance and reduce drag reduction performance quickly in a groove channel by increasing the Reynolds number slightly over Re c in the heat transfer system.
Furthermore, the drag reduction enhancement performance of grooves in surfactant solution can be used in pipeline transportation. Though the four effects of grooves mentioned above cannot be observed directly in this experiment, they can be verified indirectly by other researchers' discoveries Zhou et al.trawnonpritosor.cf
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It is understandable that these four effects of grooves are used to explain our results. Unfortunately, in the present experiment, because of the rough and poor light transmittance of the grooved surface manufactured directly by a milling machine, it is not appropriate to measure by the particle image velocimetry PIV technique and it is difficult to accurately measure the turbulence structures of the cross section near the grooves due to the small size of the groove. Thus, our speculations cannot be verified directly by the present experimental results due to the absence of corresponding visualization results.
In order to verify directly the validity of the conjecture, additional studies such as a direct numerical simulation DNS method or other effective measurement techniques are necessary to visualize the turbulent structures of drag-reducing surfactant solution over the longitudinal grooved surface. The next step of this study is to make a qualitative research and try to verify the conjecture of this paper by the DNS method in the future.
Drag reduction versus Reynolds numbers for surfactant solutions in the smooth channel or grooved channel at different temperatures and concentrations are respectively presented in Figures 6 - 8. Drag reduction rates DR at different conditions are calculated by Eqs. It can be seen from Figures 6 a , 7 a and 8 a that, for a certain surfactant concentration in the smooth channel, the maximum drag reduction rate DR max grows with increasing temperature until the temperature reaches the point of T c , and the comparison of the three concentrations proves that the range of maximum drag reduction rate increases with surfactant concentration.
Before the temperature rises to T c , the thermal Brownian motions of molecules intensify, and the number of surfactant molecules rises with increasing surfactant concentration. Both of them can make the formation of SIS easier and stronger, and thus the inhibition effect on turbulence is enhanced, resulting in the slight increase in DR. This finding corresponds to the result obtained by Wei et al. However, there exists an interesting phenomenon. However, with the increase of temperature and concentration, the surfactant solution itself has a higher drag reduction rate because the SIS is easier to form.
With further increase of temperature and concentration, these two effects disappear.
European drag-reduction research — recent developments and current status
As a result, the maximum drag reduction rate might only exhibit the maximum drag reduction rate of the surfactant solution itself or even be weakened slightly. In the present study, the complementarity of drag reducing mechanisms between surfactant and grooves was confirmed by experimentally investigating the drag-reducing performance of surfactant solutions in smooth and grooved channels, respectively. The conclusions can be summarized as follows:. The surfactant solution has an excellent drag reduction in both smooth and grooved channels.
Except for 50 ppm solution, the drag-reducing effect of surfactant solution is enhanced by grooves, but the enhancement effect decreases with increasing surfactant concentration, and furthermore, at a higher concentration, even the total drag reduction effect is weakened. This comes from the interaction between the "restriction effect" and the "peak effect" of grooves. It is noted that the "restriction effect" and the "peak effect" may be the positive or negative effect at different Reynolds numbers or surfactant concentrations, and the "peak effect" of grooves has no drag reduction enhancement effect in the Newtonian fluids compared with surfactant solution.
The critical temperature and critical Reynolds number of surfactant solution are smaller in the grooved channel than in the smooth channel.