1 Schematic of longitudinal control (white) and uncontrolled (black) surfaces repeatedly distributed in the spanwise direction in turbulent channel flow. The eddies are shown using isosurfaces of 25% of the maximum eddy strength (λci) of the initial eddy: (a) unregulated flow and (b-e) regulating flows:. i) and (ii) indicate control surfaces and non-control surfaces. Vortices are shown using isosurfaces of 30% of the maximum vorticity intensity (λci) of the initial vortex. a) unregulated current and (b-d) regulated currents:. i) and (ii) indicate control surfaces and non-control surfaces.
Vortices are shown using uniform surfaces of 30% of the maximum vorticity (λci) of the initial vortex. a) flows without control and (b-d) flows of control:. i) and (ii) show the control and non-control surfaces.
Introduction
Two different models have been widely adopted in DNS studies to describe wall SHSs. However, it is noted that the no-cut condition at the interface may not be valid in real application. Despite some difficulties in constructing an idealized solid-liquid interface in reality, the numerical scheme (e.g. no wall shear condition) in DNS studies for modeling SHSs is very attractive due to the induction of significant DR .
Many DNSs of turbulent channel flows with symmetric walls are performed to investigate flow physics related to the shear-free control at the wall.
Numerical method
Although not shown here, the drag reduction is confirmed to be highly effective in the longitudinal array, consistent with previous study of Rastegari & Akhavan [20] in turbulent channel flow with SHSs. Many simulations are performed varying the pitch P/h and the area ratio AR between no control and control surfaces for the purpose of high DR using the same initial velocity field. Because the SSFC is applied through a limited area on the entire wall, it is natural to statistically expect spatial variation of flow properties, which requires phase-averaging in space.
For phase averaging in the spatial direction, is a spatial phase relative to the periodic surface on the wall.
Shear-free control
The slight increase in skin friction drag due to no-shear regulation through the horizontal plane is due to the negative effect of no-shear regulation in the span on DR as reported in turbulent channel flow [ 17 , 33 ]. 19] for fully developed channel flows over SHS shows excellent agreement, indicating the accuracy and reliability of the present numerical simulations. In Figure 3.2(a), with increasing P/h for a fixed AR=0.5, the skin friction resistance of the v- and w-control channel flows (triangles) has a maximum decrease of 15% at small P/h and rapidly approaches higher stable values (~10%).
The SSFC of turbulent channel flows results in slightly larger DR (3~6%) than the no-shear control (square) along all P/h, and a similar trend is shown in the variation of normalized drag with variable AR at a fixed P/h in Figure 3.2(b), regardless of AR. In contrast to the behavior in Figure 3.2(a), the v- and w-controls with variable AR show an almost linear decrease in drag. For small AR, a negligible difference in drag between the v- and w-controls is shown, but the w-control results in higher DR (~5%) than that of the v-control for large AR (>0.7), similar to the previous observation of Choi et al.
Although the SSFC results in the significant DR, compared to the opposition control and shear-free control, the maximum turbulent DR possible is about 55%, when the turbulent channel flow is controlled over half of the entire wall (AR=0.5 and P/ h =3). 3.1) where (dU/dy)w is the wall-normal gradient of the mean streamwise velocity at the wall and uw. These observations in figures 3.4 and 3.5 indicate that although the use of the forcing amplitude rapidly increases the reduction of the skin frictional drag, it.
However, it should be noted that for small A (<1.004), increasing the amplitude leads to a slight increase (or almost constant) in the net energy saving rates with significant DR, especially at large P/h and AR. 3 Time history of skin friction drag coefficients in turbulent channel flows under SSFC with different force amplitude A.
APnet(%)
Turbulent statistics
The distribution of the Reynolds stresses scaled by uτo is present in Figure 4.2 as SSFC is induced when P/h increases for fixed AR=0.5 and A=1. For shear-free control, because the flow and span velocity shear at the wall are controlled simultaneously, the flow and span components of the near-wall Reynolds stresses are amplified. In Figure 4.2(c), it indicates that the spanwise normal stress with the w control has a larger value than that of the shear-free control near the wall.
The profile of root mean square fluctuations of vorticity compared to u2o / is shown in Figure 4.4 when P/h increases for a fixed AR=0.5 and A=1 (left column) and with changing A for a fixed P/h =0.375 and AR=0.5 (right column). The change of vorticity fluctuations far from the wall is similar to that of For the spanwise vorticity fluctuations as P/h increases in Fig. 4.4(e), all the data are scattered with no clear dependence on P/h near the wall.
Comparison of the vorticity fluctuations with the v and w controls and shear-free control for fixed AR=0.5, P/h=0.375 and A=1 (left column) indicates that the w control significantly increases the streamwise vorticity. fluctuation near the wall. However, the v-control and displacement-free control weaken them than the unmanipulated flow. Because the shear-free control leads to ∂w/∂y=0 at the wall, which is a dominant contributor to the streamwise component of the vorticity, the direct streamwise vorticity fluctuation is reduced.
The tighter control of the wall flow from the no-shear condition than that of SSFC creates a larger near-wall velocity shear, leading to larger normal and broad wall vorticity fluctuations under the no-shear control . The insets are logarithmic plots of the Reynolds stresses normalized by uτo to clarify near-wall behavior.
Turbulent structure
- Quadrant analysis
- Vortical structures
- Autogeneration
For small P/h (≤1.5), the vorticity structures above the non-controlled surface are directly affected by the control surface, leading to weakening of the vorticity structures throughout the domain. However, since P/h exceeds 1.5, the influence of the control surface is not important to affect the vortex structures above the non-controlled surface. So quasi-streamwise vortices in the near-wall region and hairpin vortices above the buffer layer above the uncontrolled surface are still dominant, inducing the increase of the wall-normal and spanwise turbulent stresses and the Reynolds shear stress for P/h= 3 (Figure 4.2).
These two eddy flow terms are related to the gradient of the Reynolds shear stress. For the no-control flow in figure 5.5(a), a clear swing motion with the clockwise rotation is evident due to the induction of hairpin head. A is attributed to the generation of the counterclockwise rotating vortices in the near-wall region.
The increase of the angle for P/h=3 (~40°) shows that the pitch angle of the initial vortex legs is greater than that of no control flow. The appearance of the PHVs in terms of size and shape is similar across the no control and control surfaces. On the other hand, for the no control flow, there is a maximum of the normalized Reynolds shear stress at t+=50 due to the organization of the PHV.
On the other hand, with increasing P/h, the gap of the sizes across the no control and control surfaces is significant. The largest gap difference of the Reynolds shear stress between no-control and control surfaces is indicated for P/h=3 due to active auto-excitation process over the no-control surface (figure 5.8c). The increase of the normalized Reynolds shear stress is induced by the continuous growth of the PHV in the outer layer.
Vortexes are shown using the isosurfaces of 30% of the maximum eddy strength (λci) of the initial vorticity. i) and (ii) indicate control and no-control surfaces.
Summary and conclusions
The increase in Reynolds shear stress by a large P/h in the near-wall region was caused by active turbulent structures located above the uncontrolled surface, although the vortex structures above the control surface were significantly weakened. The self-generation process for the new vortex was found to play an important role in activating coherent near-wall structures above the uncontrolled surface for large P/h, causing active motions of Q2 and Q4 events with an intense shear layer. However, it has been confirmed that the increased negative Reynolds shear stress for large A produces an enhanced eddy transport term that is closely related to the formation of ob-wall eddies from the advection of the mean shear by the streamwise vorticity.
Conditional mean flow fields with a spanwise vorticity event showed that the newly created wall vortices above the control surface for large A rotate counterclockwise, which is the opposite of the spatial signature of the hairpin vortex head for non-control flow in a statistical sense. . In the outer layer, the autogeneration process of new eddies was significantly weakened regardless of P/h and A due to less significant streamwise stretching and reduced vorticity, although the dynamic interaction of the eddy structure was constant for small P/h. thus for uncontrolled flow. It is worth noting that the basic DR mechanism proposed above is applicable to turbulent channel flows with SHS using a no-shear condition at the wall.
When the shear-free state in the streamwise and spanwise directions at the wall is imposed on an initial vortex structure, the additional shear-free state in the spanwise direction reinforces the vortical structure over time, while a new vertical structure in the upstream directions is not spawned by the autogeneration process (Figure 6.1). The greater stretching of the vortices during the no-shear control in (b) and (d) indicates the induction of more drag than during SSFC, consistent with the larger magnitude of the Reynolds stresses during no-shear control compared to those during SSFC. SSFC. Finally, it is extremely difficult to install many small sensors and actuators over a wide range of wall areas in real experiments.
Nevertheless, an active flow control concept for DR provides useful information on how wall turbulence responds to the input state with structural changes to devise an effective active flow control strategy in the future.
2013 A numerical study of the effects of superhydrophobic surface on skin friction drag in turbulent channel flow. 2016 Effects of the air layer on an idealized superhydrophobic surface on the slip length and skin friction drag.
