Session T17: Flow Control: Drag Reduction I

Active gas replenishment for super-hydrophobic surface by porous material and gas injection

Super-Hydrophobic Surface (SHS) has a wide range of engineering applications, from reducing drag, to enhancing heat and mass transfer, protecting solid surface against icing, corrosion, and bio-fouling. However, most of these benefits can be destroyed when the gas (or plastron) trapped on the SHS is replaced by the liquid, a process known as wetting transition. Here, we developed and tested an active gas replenishment technology based on creating SHS on a porous base and injecting gas through the porous material. A series of SHSs were fabricated by spraying Ultra-Ever-Dry coating (a commercial superhydrophobic coating) on porous stainless steel. The porous bases have a pore size ranging from 2 to 20 μm. For comparison, non-porous SHSs were also fabricated by the same procedure. The fabricated SHSs was experimentally tests in both stationary liquid and turbulent channel flows. The pressure difference across the porous SHS was precisely controlled by pressure regulators. The gas layer on SHS was evaluated by total- internal-reflection. We found that the porous SHSs sustained dry when subjected to high pressure, gas dissolution, and turbulent flows, while the non-porous SHSs underwent a wetting transition at same experimental conditions.   

Direct Numerical Simulation of Microbubble Drag Reduction on Superhydrophobic Surface based on Nek5000

The microbubble generation technology in the underwater vehicle is considered one of the promising techniques to reduce skin friction resistance. In the present work, the behavior of microbubbles over the superhydrophobic surface was simulated using the Nek5000 code based on the spectral element method. The 2-way coupling Euler-Lagrange approach was adopted to predict the microbubble dynamics with the assumption of a non-deformable and spherical one. The fully elastic collision model was implemented to consider the effect of wall-bubble interaction. The simulation domain was horizontal channel flow and one of the channel surfaces was set as a superhydrophobic surface. Two types of superhydrophobic surfaces, ridge type and post one, were adopted in the present work. The drag reduction effect by the void fraction of microbubble and superhydrophobic surface type were investigated in detail.   

On the effective slip length of superhydrophobic surfaces in turbulent flows

Superhydrophobic surfaces have been widely used for drag reduction in laminar and turbulent flows. These surfaces are capable of entrapping air pockets within surface textures to sustain a slip boundary condition in a certain range of Reynolds numbers. These heterogeneous surfaces can be effectively modeled as homogenous surfaces with a single effective slip length. Although several studies have investigated the relation between the heterogeneous surface features and effective slip length, it has yet to be fully explored. In this talk, we will present our two recent efforts in this regard. Firstly, using the phenomenological model developed by Seo and Mani, PoF (2016), the realistically-achievable effective slip length is calculated in terms of surface features such as texture size and solid fraction up to a friction Reynolds number of 600. Given the texture size and effective slip length, the physically-possible solid fraction is also calculated. Secondly, direct numerical simulations are performed to develop a new phenomenological model for the relation between superhydrophobic surface features and effective slip length. Drag reduction of superhydrophobic surfaces with various surface textures and homogenous surfaces with various slip lengths will be considered for the model.   

Laminar drag reduction in surfactant-contaminated superhydrophobic channels

Although superhydrophobic surfaces (SHSs) show promise for drag reduction (DR) applications, their performance can be compromised by traces of surfactant that accumulate at liquid-gas interfaces, generating Marangoni stresses that increase drag. This question is addressed for a three-dimensional laminar flow in a plane periodic channel with SHSs along both walls, in the presence of soluble surfactant. We consider the regime in which bulk diffusion is sufficiently strong for concentration gradients normal to the SHSs to be small. Seeking solutions that are periodic in the streamwise and spanwise directions, and exploiting a long-wave theory that accounts for rapid transverse Marangoni-driven flow and shear-dispersion effects, we thereby reduce this high-dimensional problem to a one-dimensional model for the surfactant distribution. The system exhibits multiple regimes where asymptotic solutions can be constructed, which compare favourably with numerics. Some are characterised by advection and diffusion-dominated processes, where the liquid-gas interface exhibits shear-free behaviour and the DR is at its maximum. In contrast, others are dominated by Marangoni effects, where the liquid-gas interface exhibits no-slip behaviour and the DR vanishes. This analysis provides a guide for designing surfactant-contaminated SHSs to maximise the DR for applications.   

Water-lubricated channel flow.

We use direct numerical simulation (DNS) to study the problem of drag reduction in a lubricated channel, a flow instance in which two thin layers of a lubricating fluid (density ρ1, viscosity η1, thickness h1) are injected in the near-wall region of a plane channel, so to favor the transportation of a primary fluid (density ρ2, viscosity η2, thickness h2). All DNS are run within the constant power input (CPI) approach, which prescribes that the flow rate is adjusted according to the actual pressure gradient so to keep constant the power injected into the flow. The CPI approach has been purposely extended here for the first time to the case of multiphase flows. A phase-field method (PFM) is used to describe the dynamics of the liquid-liquid interface. We unambiguously show that a significant drag reduction (DR) can be achieved for all four configurations considered. Upon a detailed analysis of the turbulence activity in the two lubricating layers and of the interfacial wave dynamics, we are able to characterize the effects of surface tension forces, surfactant concentration, and viscosity contrast on the drag reduction performance.   

Active Drag Reduction in Turbulent Open Channel Flow using Deep Reinforcement Learning

Deep reinforcement learning (DRL) is an optimization framework to discover control laws. It has been successfully applied to fluid dynamics, for turbulence modelling and drag reduction.

While most works in literature considered two-dimensional, simplified environments, in this work we focus on a fully-turbulent, 3D open channel flow, with uncontrolled friction Reynolds number Re_τ=180. A turbulent flow introduces additional challenges because of the stochasticity of the system, and its higher dimensionality. Also, a higher number of control parameters is considered.

In DRL algorithms we refer to the controller as agent. Its control policy is modified in order to maximize a reward. In our case, we aim to reduce the overall drag in the flow, so we consider the reduction of shear stress at the wall as reward.

The control is performed by introducing blowing/suction at the wall. The agent controls the amplitude of the wall-normal velocity component imposed at the wall.

The resulting DRL policies are compared with opposition control by Choi et al. (1994), which represent the best-performing control strategy available in the literature.   

Reduced-Order Models for Reinforcement Learning Control of Turbulent Plane Couette Flow

A few challenges in active control of turbulent flows include dealing with high-dimensional states, implementing control strategies in real time, and discovering complex control strategies. Reinforcement learning (RL) is a promising machine learning method which overcomes these challenges in fluids problems like flow around a cylinder. In RL there is an offline training phase in which the RL agent iteratively interacts with an environment to learn a control policy, which can be quickly applied in an online fashion. Unfortunately, for computationally demanding simulations, like direct numerical simulations (DNS), this training process becomes prohibitively expensive. We overcome this challenge by building a data-driven reduced-order model (ROM) of the system that we train an RL policy to control. The ROM is trained in two phases, first the dimension is reduced via an autoencoder, then the dynamics are learned using a neural ordinary differential equation. This ROM dramatically reduces dimension while maintaining high fidelity. We demonstrate this method on turbulent Couette flow controlled by two slot jets with the aim of minimizing drag and penalizing control actuation. The RL agent, trained on the model, learns a strategy to effectively relaminarize trajectories of the full DNS.   

Robust, data-efficient active flow control using embedded deep learning

A neural-network flow control model is developed by optimizing over the Navier--Stokes equations. The model's weights are optimized using an embedded deep learning (DL) method, which solves adjoints of the governing equations to provide the end-to-end sensitivities of model parameters needed for optimization. This algorithm is more robust and data-efficient compared to purely data-driven algorithms such as reinforcement learning. 

First, a 1D Burgers equation is controlled to exhibit purely convective behavior. The performance of the embedded DL control is more accurate compared to a supervised learning model trained using an analytical control function, the error of which accumulates during the evolution process. Out-of-sample tests for different objective behaviors are similarly accurate, which illustrates the robustness of the learned control model.

Second, the drag and laminar vortex shedding in incompressible flow over a cylinder are reduced  via controlled body forces near the cylinder boundary.  A significant drag reduction demonstrates the effectiveness of the embedded controller.   Sparse input data near the cylinder boundary and the downstream area makes the training of the controller more efficient compared to a dense flow field dataset. The learned control performs better over a range of testing Reynolds numbers than comparable reinforcement learning-trained models despite the fact that it uses orders of magnitude fewer model parameters. Therefore, the embedded DL method is a robust and data-efficient algorithm with promise for complicated applications such as turbulence control.   

Input-output analysis of turbulent channel flow subject to the imperfect transverse wall oscillations

Transverse wall oscillations have shown to suppress kinetic energy and skin-friction drag in turbulent channel flows. The performance of this flow control strategy in providing optimal drag reduction has been shown to crucially depend on the frequency and amplitude of oscillations. We analyze the robust performance of this control strategy in the presence of parametric uncertainties in the amplitude and phase of oscillations that can be caused by imperfect implementation. Such parametric uncertainties enter the linearized dynamics in a multiplicative manner and can dramatically affect the mean-square properties of flow fluctuations. We adopt an input-output approach to show that certain levels of parametric uncertainty can indeed violate stability conditions. For those that preserve stability, we observe a series of adverse effects that range from the promotion of turbulence to the increase in drag and changes to the optimal drag-reducing frequency of wall oscillations.   

Decomposition of drag-reducing turbulent events into scale and quadrant contributions using Fukagata-Iwamoto-Kasagi (FIK) identity for a pipe flow with spanwise-oscillated walls

Increased turbulent drag in wall bounded shear flows is associated with an increased velocity gradient in the near wall region resulting from the turbulent momentum transfer. The Fukagata-Iwamoto-Kasagi (FIK) identity allows one to relate the surface drag, or the bulk mean velocity, depending on the problem formulation, with the statistics of the fluid stresses in the interior of the fluid domain. The FIK identity illustrates that, as a function of the distance from the wall, the turbulent Reynolds shear stress contributes to the reduction of the bulk mean velocity or increase in the skin friction from the equivalent laminar flow for a given Reynolds number. The streamwise-wall normal Reynolds shear stress is the product of streamwise and wall normal velocity fluctuations, which can be decomposed into four quadrants based on the sign of the fluctuating pair: outward interactions (Q1), turbulent ejections (Q2), wall-ward interactions (Q3), and turbulent sweeps (Q4). Turbulent ejections and sweeps increase the Reynolds shear stress and thus the near wall velocity gradient. However, where these events occur and what length scales affects the contribution to the mean velocity has not been previously identified. We present the FIK identity recast using the conditionally averaged and filtered streamwise momentum equation to isolate the wall location and length scale at which spanwise wall oscillations in turbulent pipe flow reduce turbulence to affect drag reduction.