Session G07: Flow Control: Drag Reduction (5:00pm - 5:45pm CST)

Three Regimes of Laminar Drag Modification via Travelling Wave Forcing

Spatially-localized drag modification for a laminar boundary layer is predicted for travelling-wave flow actuation at specific wave speeds. In the past, asymptotically high-speed travelling waves have been used to modify a base laminar flow by Stokes streaming, but the effect of lower-speed disturbances has not been fully explored. We present a numeric solution of the full momentum balance for the streaming flow induced in a laminar boundary layer, based on Lin's Reynolds decomposition analysis, and identify three distinct regimes of drag modification. In addition to the traditional high speed case, we report on a critical-layer dominated regime and a low-speed, limiting regime which induce significant but divergent changes to the skin friction over a range of streamwise locations downstream of the leading edge. We characterize the extent of the drag modification in all three regimes as a function of the disturbance speed and streamwise location, providing a framework for practical implementation of streaming drag-reduction techniques.   

Toward Understanding Underlying Mechanisms of Drag Reduction in Turbulent Flow Control

The ability to control the amount of drag reduction in turbulent flow is important for industries to reduce costs and save energy. In this study, three control methods are investigated to better understand the underlying mechanisms behind drag reduction in a turbulent flow. These methods include imposing an external body force, adding long-chain polymers to a fluid, and utilizing slip surfaces. Direct numerical simulations are performed and analyzed based on the lifetime of turbulent phases represented by the active and hibernating phases of minimal channel turbulence (Xi {\&} Graham PRL 2010). The hibernating phase is referred to as a low-drag state, while others are active phases. Depending on the drag reduction percentages of control methods, the low drag reduction (LDR) and high drag reduction (HDR) regimes are classified for detailed analysis. In terms of temporal dynamics of hibernating phases, such as its frequency and duration, for LDR, the polymer and slip methods are similar, while the body force method is different. For HDR, however, a similar mechanism is observed for all methods. To elucidate drag-reducing mechanisms of three control methods, the vortex structures at LDR and HDR are analyzed to relate it to the temporal dynamics of hibernating phases.   

Identification of Amplified Scales Under Opposition Control Through Modal Analysis

The opposition control scheme is a proportional feedback control law with unit gain (e.g. Kim & Choi, J Fluid Mech, 2017). Recent studies suggest that a constant controller gain applied to all scales, which are described here as Fourier modes, results in a mixed controller performance in spectral space: some modes are attenuated, while others are amplified (e.g. Toedtli et al, IJHFF, 2020) and the observed drag change is the result of a competition between suppressed and amplified scales. Drag reduction can presumably be improved if the amplified scales are either not controlled, or if the gain for those modes is changed so as to result in suppression. In this study, we review a formulation of opposition control in Fourier space and show that the phase of the complex controller gain determines which scales are amplified or attenuated. We further show that for a given controller gain, there is a strong correlation between presence of an amplified eigenvalue in the temporal eigenspectrum of the linearized Navier-Stokes operator and amplification of the corresponding scale in the full nonlinear system. This suggests that modal analyses offer a computationally cheap tool to (at least) identify amplified scales. Implications for active and passive flow control will be discussed.   

The effects of an external body force on drag reduction in turbulent channel flow up to $Re_{\tau} \approx 1000$

Reducing turbulent drag at high speeds is a subject of great interest due to the potential benefits, especially in aircraft. As an alternative to the passive vortex generators that tend to create some amount of cruise penalty, an innovative plasma actuator has been recently proposed. As the plasma actuator imposes a body force-type effect on a surrounding flow, we have developed and performed direct numerical simulations (DNS) of turbulent channel flow up to $Re_{\tau} = 1,014$ with an external body force having four control parameters. Firstly, while drag reduction appears to scale inversely with Reynolds number, an optimal combination of the control parameters at different Reynolds numbers is yet to be concluded. Secondly, we have found an intriguing observation on fluctuations of the skin friction coefficient, where the fluctuation of the controlled cases is larger than the uncontrolled cases for $Re_{\tau} < 550$, while still displaying drag reduction. For $Re_{\tau} > 550$, the trend becomes flipped. The relationship between an external body force and the fluctuation of skin friction will be further discussed and investigated. This observation could be crucial in that it may lead to a further fundamental understanding of the drag reduction process at high Reynolds numbers.   

Drag reduction and stability of superhydrophobic surface with flexible re-entrant structure

Air plastron in microstructures of a superhydrophobic (SHPo) surface induces a liquid to flow with slip over the surface and it increase drag reduction efficiency. However, unstability of the air inhibit utilization of the SHPo surface. Here, a pressurization and a pressure gradient are considered as physical conditions of the application including ships. SHPo surfaces with differently sized ridges with partition structures and re-entrant structures are fabricated. Partition structures are introduced in the ridges to control length of the ridges Air depletion in transparent ridge structures is visualized in various pressure condition. Increased pressure and pressure gradient condition deform air-water meniscus and disrupt the air in the ridge. Critical conditions for air depletion and drag reduction efficiency are compared between different sizes and flexibility of the micro-structures. Ridges with smaller width, length and high flexibility could sustain the air plastron in higher pressure and pressure gradient condition. Theoretical models are derived to anticipate the stability condition.   

Drag reduction on a circular cylinder by uniform and discrete blowing

Vortex shedding occurs in the wake behind a bluff body when the Reynolds number exceeds a critical value, resulting in a significant drag increase. In this study, we apply uniform and discrete blowing, respectively, to flow over a circular cylinder at the Reynolds number of 20,000 for drag reduction. Two slits and two rows of nozzles are installed near the separation points (on the upper and lower surfaces) to realize uniform and discrete blowing, respectively. These uniform and discrete blowing are performed in steady and time-periodic modes, and their actuation amplitude and frequency are optimized systematically. Steady discrete blowing is much more effective and efficient in drag reduction than steady uniform blowing, providing maximum drag reduction of 52{\%}. On the other hand, time-periodic, uniform and discrete blowing result in maximum drag reductions of 52{\%} and 62{\%}, respectively. With smoke-wire flow visualizations and PIV measurements, we show that counter-rotating vortices induced by optimal discrete blowing change the K\'{a}rm\'{a}n vortex cores into three-dimensional vortices and weaken their strength. Additionally, high-frequency blowing works better for sup-pressing the formation of the K\'{a}rm\'{a}n vortices than steady or low-frequency blowing.   

Physics of a dynamic free-slip boundary

Recently we demonstrate that a dynamically modulated air-water interface can reduce the wall shear stress of a turbulent boundary layer (TBL) for more than 40{\%} (Wang {\&} Gharib 2020). In addition, a pumping effect which increases the momentum flux of TBL was observed. Here we present the physics of modulated air-water interface. With modulation frequencies above certain cut-off criterion, the air-water interface exhibits instability features of an elastic film. The periodically oscillating air-water interface produces a mean streaming jet in the water phase. Results of DPIV measurement indicate that the streaming jet is connected to the vorticity production and transportation at the air-water interface. The current findings support our claim of significant wall skin friction reduction effect in Wang {\&} Gharib 2020, as the streaming jet could push the near-wall vortical structures away from the wall.   

Only certain riblets experience the Kelvin-Helmholtz instability

The Kelvin-Helmholtz instability develops in turbulent flow above blade riblets and degrades their drag-reduction performance (Garcia-Mayoral \& Jimenez 2011). Based on our direct numerical simulations of 21 cases comprising six riblet cross-sections and various viscous-scale sizes, the instability also develops over sharp triangular riblets, but not over blunt triangular or trapezoidal riblets. Specifically, two out of six riblet shapes in the present data set experience strong Kelvin-Helmholtz rollers. In this presentation, we offer an explanation for the occurrence of the instability over only certain riblets: we observe that only riblet shapes with high momentum absorption in the tip region seem to create a pronounced mixing-layer profile that drives the instability. Additionally, as previously known for blade riblets, only riblet grooves with a large viscous-scaled cross-sectional area provide the necessary effective wall-normal permeability at the riblet tips.   

Drag reduction of sustainable slippery surface of marine algae Miyeok (Undaria pinnatifida)

The development of a sustainable drag reduction surface is important in various engineering applications. Miyeok has mucilage gland cells to secrete mucus which works as a lubricant. In this work, the effects of surface structure of Miyeok on drag reduction and sustainability were experimentally investigated. A negative mold of Miyeok replica was fabricated to mimic the morphological structures and the replica surface was dipped into silicone oil solution. The structural similarity between the replica and Miyeok was confirmed by their scanning electron microscopy images. Pressure drop and slip length were measured to estimate their drag reduction effects. The slip lengths were estimated by using both particle image velocimetry and particle tracking velocimetry velocity field measurement techniques. The structural effects of the fabricated replica on sustainability under external flow in a circulating water channel were examined by measuring contact angle hysteresis. The replica exhibits higher drag reduction effect and better sustainability, compared to an oil-infused flat PDMS. The present results would be utilized for better understanding on the drag reduction mechanism of natural seaweeds and developing a biomimetic sustainable drag reduction surface.   

Active Drag Reduction for Flows over Swept Wings

The friction drag and hence the energy consumption of slender bodies in turbulent flows, e.g., large passenger aircraft, are strongly determined by turbulent boundary layers. Therefore, there is considerable scientific interest in influencing the turbulent flow field to decrease the viscous drag. Research nowadays focuses on active methods, i.e., the introduction of energy into the system to reduce skin friction. In most investigations, the direction of propagation is either perfectly perpendicular to the mean flow direction or along the mean flow direction. However, the flow, for instance, over a swept wing of an aircraft is subject to a spanwise pressure gradient, therefore incident angles of the flow towards the proposed surface waves are to be expected. As a consequence, in this work we consider a turbulent boundary layer flow subject to spanwise traveling transversal surface waves with sweep angles of up to 30 degrees. The results show that a general drag reduction effect persists, however, additional effects, e.g., increased pressure drag, have to be accounted for. A detailed analysis of the results will be presented at the conference.   

Turbulent skin friction drag reduction with rigid or flexible surface micro-textures

Turbulent skin-friction drag reduction with rigid or flexible surface micro-textures has been investigated by direct numerical simulation (DNS) using an immersed-boundary, lattice Boltzmann method. In this method, the dynamics of the flow field is tracked on a fixed Cartesian grid using standard D3Q19, single relaxation time, Bhatnagar-Gross-Krook lattice models, while the motion of the surface micro-texture is tracked by Lagrangian markers which are embedded in the immersed boundary. In contrast to traditional immersed boundary methods, here the interaction forces are determined by reciprocal interpolation-spreading operators, thus obviating the need for empirical parameters and resulting in consistent and more accurate numerical simulations. Grid embedding, of grid ratio 2:1, was employed in all the simulations to improve the accuracy of the computations in the near wall regions. The numerical methods were applied to DNS of skin friction drag reduction with blade riblets and flexible surface micro-textures in turbulent channel flows at $Re_{\tau 0} \approx 222$. DNS results with blade riblets show good agreement with available experimental data. The results with flexible surface micro-textures will be discussed.   

Microfiber coating for drag reduction in a cylinder flow

A microfiber coating with a hair-like structure is studied as a passive drag reduction device for flow over a cylinder. The hair-like structure provides flexibility and permeability much like dense vegetation or a canopy. The microfiber coating controls the flow around the cylinder, which features both attached and separated flow. The impact of the microfiber coating on drag is experimentally investigated at a Reynolds number of 61000 based on the cylinder diameter. The configuration of the microfiber coatings is changed, including microfiber length and coating location. It is found that the microfiber length and location both play essential roles in drag reduction. The drag is reduced significantly if the microfiber coating is applied to areas of attached flow. There is moderate drag reduction if the microfiber coating is applied after the point of flow separation. The former requires relatively short fibers, where the length of the microfiber is less than 1.8{\%} of the cylinder diameter. The latter is achieved using relatively long fibers, where the length of the microfiber is greater than 3.3{\%} of the cylinder diameter.   

Hydrodynamic interferences of two rigid foils in a flowing soap film

We investigated two separated rigid foils by altering their relative locations in soap film. The arrangements of the foils can be divided as tandem configuration, side-by-side configuration and staggered configuration. The flow patterns are classified and the drag forces are measured to investigate the hydrodynamical interference under these conditions. Based on shear layer behaviors and wake structures, the flow interference regimes are classified as three types: wake interference, proximity interference and distance interference. We then mapped out the variation of the drag forces with 1045 different locations. Compared to the drag of the single foil in the soap film, the drag on a foil reduces significantly when it is located at a trailing position under tandem configuration. However, it will suffer a heavier burden under side-by-side configuration. The drag is minimally affected in the staggered configuration. The relationship between flow interference and drag force variation is also discussed.   

Polymer Drag Reduction: Impact on Near-Wall Structure.

Even though it had been thought to be well understood for decades, recent work has shown that the classical view of how drag-reducing polymer solutions modify the mean turbulent velocity profile is incorrect. The classical view is that the log-region is unmodified from the traditional law-of-the-wall for Newtonian fluids, though shifted outward in proportion to the level of drag reduction. However, improvements to both experimental methods and DNS modelling has demonstrated that polymeric properties also play a critical role, especially at higher drag reduction levels. Over the past few years, there have been great strides with improving our understanding of the impact of polymer properties on the near-wall modifications. This presentation will give an overview of our recent advancements including details of the modifications to both the mean structure as well as coherent structures.