Control Of Turbulent Flows Research Articles

On the growth of localised perturbations in isotropic turbulence

Assessing the impact of localised perturbations is staple for the problems of data assimilation and control of turbulent flows. In the present work we exploit the public database of [1] that contains the growth and location of about 105 perturbations of approximately thirty Kolmogorov units in isotropic turbulence at moderate Reynolds numbers. All the terms in the evolution equation for the perturbation kinetic energy are analysed statistically, disregarding in the process the effect of viscosity. Of the relevant terms, only the stretching of the perturbation by the mean flow can result in production of kinetic energy, whereas every other term must only transport the perturbation across the flow field. However, it is shown that if the problem of interest is the coarse-grained propagation of the perturbation, i.e. its radius, the dynamical terms related to incompressibility are of equal importance for the growth. A simplified model based on the balance between these terms is proposed to explain the quasi-linear growth of the radius with time.

Towards optimal [formula omitted]-variational autoencoders combined with transformers for reduced-order modelling of turbulent flows

Variational autoencoders (VAEs) have shown promising potential as artificial neural networks (NN) for developing reduced-order models (ROMs) in the context of turbulent flows. In this study, we propose a method that combines β-VAEs for modal decomposition and transformer neural networks for temporal-dynamics prediction in the latent space to develop ROMs. We apply our method to an existing database of a turbulent flow around a wall-mounted square cylinder obtained by direct numerical simulation (DNS). A parametric study is performed to investigate the effects of the hyperparameters of the proposed β-VAEs and determine the optimal values. For the first time, we incorporate the consideration of the complexity of architecture into our studies, providing new insights into hyperparameter selection for β-VAEs, which remains a challenging problem for optimising model performance. Results regarding the influence of the different hyperparameters and guidelines to design these architectures are reported. Our optimal model achieves a reconstruction accuracy of 97.18% of the entire dataset using only ten modes. Subsequently, we employ the transformer models to identify latent-space temporal dynamics learned by the optimal β-VAE model and build ROMs to predict instantaneous fields. The resulting model achieves promising accuracy in temporal-dynamics predictions and yields energy reconstruction levels of 96.5% and 83% for a field 25 and 50 steps into the future, respectively, showcasing the potential of the transformer in predicting the temporal dynamics. Overall, the proposed method has potential applications in advanced flow control and fundamental studies of complex turbulent flows.

On the comparison between pre- and post-surgery nasal anatomies via computational fluid dynamics

Nasal breathing difficulties (NBD) are widespread and difficult to diagnose; the failure rate of their surgical corrections is high. Computational fluid dynamics (CFD) enables diagnosis of NBD and surgery planning, by comparing a pre-operative (pre-op) situation with the outcome of virtual surgery (post-op). An equivalent comparison is involved when considering distinct anatomies in the search for the functionally normal nose. Currently, this comparison is carried out in more than one way, under the implicit assumption that results are unchanged, which reflects our limited understanding of the driver of the respiratory function. The study describes how to set up a meaningful comparison. A pre-op anatomy, derived via segmentation from a CT scan, is compared with a post-op anatomy obtained via virtual surgery. State-of-the-art numerical simulations for a steady inspiration carry out the comparison under three types of global constraints, derived from the field of turbulent flow control: a constant pressure drop (CPG) between external ambient and throat, a constant flow rate (CFR) through the airways and a constant power input (CPI) from the lungs can be enforced. A significant difference in the quantities of interest is observed depending on the type of comparison. Global quantities (flow rate, pressure drop and nasal resistance) as well as local ones are affected. The type of flow forcing affects the outcome of the comparison between pre-op and post-op anatomies. Among the three available options, we argue that CPG is the least adequate. Arguments favouring either CFR or CPI are presented.

Identifying causally significant features in three-dimensional isotropic turbulence

Flow patterns of causal significance to three-dimensional isotropic turbulence are identified through the recently introduced algorithm of Jiménez (J. Fluid Mech., vol. 854, 2018, R1). Localised perturbations are introduced at arbitrary regions of a triple-periodic decaying flow at ${Re}_\lambda \approx 190$ , and their evolution is used as a marker of the significance of said regions to the flow. Their dimensions are found to be an important parameter, with sizes of the order of the integral scale being controlled by the kinetic energy content, and sizes within the dissipative range, by the enstrophy and dissipation. The three quantities are found to be important at intermediate (inertial) scales. Prominent differences emerge between regions of high and low significance. The former typically contain strong gradients and/or kinetic energy and the latter are weak. An analysis of the structure of significant and insignificant flow patterns reveals that strain is more efficient than vorticity at propagating the contents of the perturbation to other regions of the flow. Moreover, the flow patterns of significant regions are found to be more complex, typically containing vortex clusters, while simpler vortex sheets are found in insignificant regions. The present results suggest that strategies aiming to manipulate the flow should focus on strain-dominated vortex clusters, avoiding enstrophy-dominated vortex sheets. This is confirmed through an assimilation experiment, in which greater synchronisation between two simulations is achieved when simulations share significant regions rather than insignificant ones. These conclusions have implications for both the control of turbulent flows and the making of predictions based on limited or noisy measurements.

Frequency-tuned surfaces for passive control of wall-bounded turbulent flow – a resolvent analysis study

The potential of frequency-tuned surfaces as a passive control strategy for reducing drag in wall-bounded turbulent flows is investigated using resolvent analysis. These surfaces are considered to have geometries with impedances that permit transpiration and/or slip at the wall in response to wall pressure and/or shear and are tuned to target the dynamically important structures of wall turbulence. It is shown that wall impedance can suppress the modes resembling the near-wall cycle and the very-large-scale motions and the Reynolds stress contribution of these modes. Suppression of the near-wall cycle requires a more reactive impedance. In addition to these dynamically important modes, the effect of wall impedance across the spectral space is analysed by considering varying mode speeds and wavelengths. It is shown that the materials designed for suppression of the near-wall modes lead to gain reduction over a wide range across the spectral space. Furthermore, a wall with only shear-driven impedance is found to suppress turbulent structures over a wider range in spectral space, leading to an overall turbulent drag reduction. Most importantly, the present analysis shows that the drag-reducing impedance is non-unique and the control performance is not sensitive to variations of the surface impedance within a favourable range. This implies that specific frequency bandwidths can be targeted with periodic material design.

Cluster-based control for net drag reduction of the fluidic pinball

We propose a Cluster-Based Control (CBC) strategy for model-free feedback drag reduction with multiple actuators and full-state feedback. CBC consists of three steps. First, the input of the feedback law is clustered from unforced flow data. Second, the feedback law is interpolated with actuation commands associated with the cluster centroids. Thus, centroids and these actuation commands facilitate a low-dimensional parameterization of the feedback law. Third, the centroid-based actuation commands are optimized, e.g., with a downhill simplex method. This framework generalizes the feature-based CBC from Nair et al. [“Cluster-based feedback control of turbulent post-stall separated flows,” J. Fluid Mech. 875, 345–375 (2019)] in three aspects. First, the control law input is the velocity field. Second, the control law output commands multiple actuators here. Third, a reformulation of the downhill simplex method allows parallelizing the simulations, thus accelerating the computation threefold. Full-state CBC is demonstrated on a multiple-input configuration, the so-called fluidic pinball in three flow regimes, including symmetric periodic at Re = 30, asymmetric periodic at Re = 100, and chaotic vortex shedding at Re = 150. The net drag reductions for the three cases amount to 33.06%, 24.15%, and 12.23%, respectively. CBC shows distinct advantages for robustness control at different flow conditions. The full-state CBC further reveals the evolution of the control flow associated with the centroids, which contributes to the physical interpretation of the feedback control process.

Numerical Simulation of Turbulent Flow Control at Pipe Inlet to Advance Flow Relaminarization

Various methods of flow relaminarization in a pipe are considered by means of controlling the average and turbulent flow parameters. For numerical simulation of flows with turbulence growth and suppression it is proposed to use a three-parameter RANS turbulence model, which has shown good results in modeling existing experiments on relaminarization. Calculations for three variants of inlet devices with different velocity profiles and the same small-scale turbulence at the inlet show the possibility of achieving flow relaminarization in pipes at Reynolds numbers Re > 10 000. Among three variants of inlet devices considered, the most effective one is the variant with organization of a two-zone flow with slow flow in the central region of the pipe and accelerated flow in the near-wall region. In this version, relaminarization occurs up to the Reynolds number Re* = 16 000. It is shown that decrease in the turbulence intensity and scale leads to an even larger value of the relaminarization Reynolds number Re*.

On the Use of Power-Based Parameters for Blowing Active Flow Control Systems

Boundary-layer control (BLC) of turbulent flows aims to compensate for mean frictional losses on a frozen configuration, while active flow control (AFC) seeks to alter the mean flow by exploiting instabilities. Since AFC performance is judged by the energy required to achieve a prescribed goal, it must be introduced into the aircraft design process at the early conceptual stages. For blowing applications, deciding whether to draw from engine bleed or install smaller compressors adjacent to the actuators is an important system-level consideration that requires the separation of the loss in the air supply system from the input that triggers and amplifies the exterior flow instabilities. The current paper exposes the inadequacy of the momentum coefficient that has primarily been used in the past to assess AFC efficacy and recommends two easily measurable fluid power coefficients to replace it. These enable direct comparisons of actuator efficiencies and system efficiencies, creating a link between the physics of flow control and system integration. This link is demonstrated first on a two-dimensional configuration that uses steady blowing, which is later extended to the use of sweeping jet actuators on a modular swept wing of finite aspect ratio.

Anisotropic property of turbulent flow control through multiple stenosed microtubes

Rapid development in micro-scale systems and devices for drug delivery and biotechnical analysis has been scurrying. Microtube or microchannel roughness is another challenging factor in microfabrication technology. Moreover, the irregular roughness occurs due to the multiple depositions of cholesterol and other substances in the endothelium of the arterial wall. To investigate those issues, the effect of the irregular roughness of the wall on the anisotropy of the turbulent blood flow through an atherosclerotic artery has been analyzed. The flow through a stenosed microtube has been numerically simulated to understand the blood flow phenomenon through arterial stenosis and different turbulent states. The Reynolds stress components are estimated and plotted an invariant map and Eigen map to examine the turbulent states. The comparison results have been studied to show the nature of turbulent flow in low Reynolds numbers due to irregular roughness. The turbulent kinetic energy and turbulent viscous dissipation rate are also examined. Due to wall shear stress, the flow deserves the turbulence flow characteristic downstream of the abnormally narrowed regions of the microtube. The nature of the wall shear rate and the high viscosity of blood impact the disturbance in the flow velocity in microtubes.

Active proportional feedback control of turbulent flow over a circular cylinder with averaged velocity sensor

In the present study, we perform an active proportional (P) feedback control of laminar and turbulent flows over a circular cylinder with an averaged velocity sensor to reduce its drag and lift fluctuations. As a sensor for the feedback control, we adopt an averaged transverse velocity on the centerline of the wake. For the averaging of the transverse sensing velocity, we consider both temporal averaging over a finite period and spatial averaging in the spanwise direction. As a control input, the blowing/suction actuation is provided on the cylinder surface near the flow separation, and its magnitude is linearly proportional to the averaged transverse sensing velocity. With the control, the fluctuations of the transverse sensing velocity are significantly reduced and the vortices right after the cylinder and the Kármán vortex shedding in the wake are weakened, resulting in substantial reductions of the mean drag and lift fluctuations. Furthermore, it is shown that the adoption of the averaged sensing velocity makes the P control successful for a wider range of sensing locations in laminar flow at Re = 100 and is essential for the success of the P control in turbulent flow at Re = 3900. With the optimal control parameters, the reductions of the mean drag and lift fluctuations for turbulent flow at Re = 3900 are about 11% and 61%, respectively. The present P control maintains the magnitude of the blowing/suction actuation less than 1% of the free-stream velocity, and thus, the control input power is very small, leading to an excellent control efficiency.

A surrogate optimization approach for inverse problems: Application to turbulent mixed-convection flows

Optimal control of turbulent mixed-convection flows has attracted considerable attention from researchers. Numerical algorithms such as Genetic Algorithms (GAs) are powerful tools that allow to perform global optimization. These algorithms are particularly of great interest in complex optimization problems where cost functionals may lack smoothness and regularity. In turbulent flow optimization, the hybridization of GA with high fidelity Computational Fluid Dynamics (CFD) is extremely demanding in terms of computational time and memory storage. Thus, alternative approaches aiming to alleviate these requirements are of great interest. Nowadays, surrogate approaches gained attention due to their potential in predicting flow solutions based only on preexisting data. In the present paper, we propose a near-real time surrogate genetic algorithm for inverse parameter identification problems involving turbulent flows. In this optimization framework, the parameterized flow data are used in their reduced form obtained by the POD (Proper Orthogonal Decomposition) and solutions prediction is made by interpolating the temporal and the spatial POD subspaces through a recently developed Riemannian barycentric interpolation. The validation of the proposed optimization approach is carried out in the parameter identification problem of the turbulent mixed-convection flow in a cavity. The objective is to determine the inflow temperature corresponding to a given temperature distribution in a restricted area of the spatial domain. The results show that the proposed surrogate optimization framework is able to deliver good approximations of the optimal solutions within less than two minutes.

Bounded dissipation predicts finite asymptotic state of near-wall turbulence

Enormous efforts have been devoted to the prediction and control of turbulent wall flows. A primary consideration here is the Reynolds number scaling problem in which non-dimensional representations are sought that render the normalized variables of interest unchanged for varying Reynolds number. Relative to this objective and in contrast to the mean velocity, there remains a considerable lack of clarity associated with the apparent failure of inner normalization (i.e. using the friction velocity and kinematic viscosity) when applied to the statistical profiles of fluctuating quantities in the near-wall region. In their present work Chen & Sreenivasan (J. Fluid Mech., vol. 933, 2022, A20) generalize their earlier effort, Chen & Sreenivasan (J. Fluid Mech., vol. 908, 2021, R3), and present a rational framework for characterizing and describing the evolution of turbulence quantities that either attain a near-wall peak or have non-zero wall values. Their analysis enjoys considerable empirical support. Physically, the asymptotic boundedness of the inner-normalized dissipation is used to reason that there is a limiting state of near-wall turbulence at asymptotically large Reynolds numbers. The law of bounded dissipation arguments put forth by Chen and Sreenivasan prescribe the recovery of inner scaling and suggest new possibilities regarding the physics of how wall turbulence matures to its asymptotic state.

Modification of energetic modes for transitional flow control

We introduce a mechanism of using collocated serpentine shaped plasma actuators for controlling the flow via an input electrical signal to either advance or delay transition by amplification or annihilation of energetic modes of turbulent structures. A wall resolved implicit large eddy simulation is conducted to examine the process of turbulent flow control due to this mechanism. Collocation allows for selective superposition of different energetic modes, which can either subtract or add energy to the baseline flow resulting in turbulent streak manipulation. Unlike most flow control methods that use either a localized large amplitude forcing or a low amplitude distributed forcing, this mechanism uses a localized low amplitude forcing to cause reduction in skin friction of more than 53% across the plate. This is achieved by manipulating strength as well as the spacing between the low-speed turbulent streaks, which are ubiquitous in a turbulent flow field. Reduction in skin friction drag can result in decreasing fuel consumption and in turn reducing pollution.

Analysis of Pseudo-spectral Methods Used for Numerical Simulations of Turbulence

Events in turbulent flows computed by direct numerical simulation (DNS) are often calibrated with properties based on homogeneous isotropic turbulence, advanced by Kolmogorov, and given in Turbulence, U. Frisch, Cambridge Univ. Press, UK (1995). However, these computational procedures are not calibrated using numerical analyses in order to assess their strengths and weaknesses for DNS. This is with the exception in "A critical assessment of simulations for transitional and turbulence flows- Sengupta, T.K., In Proc. of IUTAM Symp. on Advances in Computation, Modeling and Control of Transitional and Turbulent Flows, 491-532, (eds. Sengupta, Lele, Sreenivasan, Davidson), WSPC, Singapore (2016)", where such a calibration has been advocated for numerical schemes using global spectral analysis (GSA) for the convection equation. In recent times, due to growing computing power, simulations have been reported using pseudo-spectral methods, with spatial discretization performed in Fourier spectral space and time-integration by multi-stage Runge-Kutta (RK) methods. Here, we perform GSA of Fourier spectral methods for the first time with RK2 and other multistage Runge-Kutta methods using the model linear convection and convection-diffusion equations. With the help of GSA, various sources of numerical errors are quantified. The major limitations of the RK2-Fourier spectral method are demonstrated for DNS and alternate choices are presented. We specify optimal parameters to achieve the best possible accuracy for simulations. There is a one-to-one correspondence of numerical solutions obtained by linear convection-diffusion equation and nonlinear Navier-Stokes equation with respect to numerical parameters. This enables us to investigate the capabilities of the numerical methods for DNS.

Mechanism analysis of magnetohydrodynamic control in hypersonic turbulent flow

Under the assumption of the low magnetic Reynolds number, the coupled model is established for the turbulent flow field and the externally applied magnetic field. The AUSMPW+ scheme and LUSGS method are used to solve turbulent magnetohydrodynamics (MHD) flow equations, in which the Spalart-Allmaras one-equation turbulence model is used. A series of numerical simulations over various geometry configurations, namely, a flat plate and a compression corner, is conducted by using an external electromagnetic field. Results show that the performance of MHD boundary layer flow control is determined mainly by the Lorentz force in the streamwise direction. With an external magnetic field used, the low velocity fluid in the boundary layer can decelerate and increase the static temperature locally. Moreover, the counter-flow Lorentz force always brings a negative effect on the turbulent skin friction coefficient, and the location for the MHD zone has a great influence on the control efficiency of the ramp-induced separation. A reasonable magnetic field layout scheme should be configured in practical engineering application.

Prediction of Drag Reduction Effect by Machine Learning toward Optimization of Pulsating Control in Turbulent Pipe Flow

Machine learning based on experimental data was performed to predict the drag reduction effects of various pulsating pipe flows. In the experiment, the voltages input to the pumps were changed over time to generate 2448 different pulsating flows. Pulsating flows with higher pressure gradients than in previous study was investigated with high responsive pumps. Using machine learning model specialized for time series prediction based on experimental data, time series data of flow velocity and differential pressure from the voltages applied to the pumps to calculate the drag reduction rates. It was confirmed that the model could predict the drag reduction effect of complex pulsating flows with the almost same accuracy as in the previous study. Optimization of the voltage waveforms for pulsating control was also performed using the learned model. As a result, the drag reduction rate of optimal voltage waveform within the conditions equivalent to those of the experiment is predicted to be 42%. This is a larger value than the maximum drag reduction rate of 39% which is measured in the experiment.

Excitation of Airborne Acoustic Surface Modes Driven by a Turbulent Flow

This experiment demonstrates the generation of trapped acoustic surface waves excited by a turbulent flow source through the coupling of pressure fluctuations at the interface between an acoustic metamaterial and a flow environment. The turbulent flow, which behaves as a stochastic pressure source, was interfaced with an acoustic metasurface waveguide stationed in a quiescent environment via a single Kevlar-covered cavity, which ensured no significant disturbance to the flow. The metasurface waveguide produced an acoustic surface mode through evanescent diffractive coupling of the pressure field. This acoustic mode was trapped at the quiescent surface, with its mode dispersion determined by the surface geometry. The results of two different metasurface geometries are discussed: 1) a slotted cavity array, and 2) a meander connected cavity array, with each demonstrating a different trapped surface wave characteristic. Fourier transform and correlation analyses of spatially resolved temporal acoustic signals, measured close to the metamaterial surface, were used to construct the frequency- and wavevector-dependent acoustic mode dispersion. The results demonstrate that the flow can be used to excite acoustic surface modes and that their mode dispersion may be tailored toward realizing novel control of turbulent flow through acoustic-flow interactions.

Unsteady control of supersonic turbulent cavity flow based on resolvent analysis

We use resolvent analysis to develop a physics-based, open-loop, unsteady control strategy to attenuate pressure fluctuations in turbulent flow over a rectangular cavity with a length-to-depth ratio of $6$ at a Mach number of $1.4$ and a Reynolds number based on cavity depth of $10\,000$. Large-eddy simulations (LES) of the baseline uncontrolled flow reveal the dominance of Rossiter modes II and IV that generate high-amplitude unsteadiness via trailing-edge impingement and oblique shock waves that obstruct the free stream. To suppress the oscillations, we introduce three-dimensional unsteady blowing along the cavity leading edge. We leverage resolvent analysis as a linear model with respect to the baseline flow to guide the selections of the optimal spanwise wavenumber and frequency of the unsteady actuation input for a fixed momentum coefficient of 0.02. Instead of choosing the most amplified resolvent forcing modes, we seek a disturbance that yields sustained amplification of the primary response mode-based kinetic energy distribution over the entire cavity length. This necessary but not sufficient guideline for effective mean flow modification is evaluated using LES of the controlled cavity flows. The most effective control case reduces the pressure root mean square level up to $52\,\%$ along cavity walls relative to the baseline and is approximately twice that achievable by comparable steady blowing. Dynamic mode decomposition on the controlled flows confirms that the optimal actuation input indeed suppresses the formation of the large-scale Rossiter modes. It is expected that the present flow control guideline derived from resolvent analysis will also be applicable at higher Reynolds numbers with the aid of physical insights and further validation.

Investigation of Blowing and Suction for Turbulent Flow Control on Airfoils

An extensive parametric study of turbulent boundary-layer control on airfoils via uniform blowing or suction is presented. The control is applied on either the suction or pressure side of several four-digit NACA-series airfoils. The considered parameter variations include angle of attack, Reynolds number, control intensity, airfoil camber, and airfoil thickness. Two comprehensive metrics, designed to account for the additional energy required by the control, are introduced to evaluate the net aerodynamic performance enhancements. The study confirms previous findings for suction-side boundary-layer control and demonstrates the interesting potential of blowing on the pressure side under various conditions, which achieves a maximum total net drag saving of 14% within the considered parameter space. The broad parameter space covered by the presented Reynolds-average Navier–Stokes simulations allows for more general conclusions than previous studies and can thus provide guidelines for the design of future detailed experimental or numerical studies on similar boundary-layer control schemes.

Single-step deep reinforcement learning for open-loop control of laminar and turbulent flows

We introduce single-step proximal policy optimization, a deep reinforcement learning algorithm for situations where neural network optimization does not depend on state. Optimization is examined with open-loop control problems of laminar and turbulent flows (Re up to a few ${10}^{4}$). For turbulent flow past a square cylinder, the approach reduces drag by 30% by finding the best placement of a small control cylinder, in agreement with existing experimental data. For turbulent flow past a fluidic pinball, drag is reduced by 60% by using boat tailing actuation made up of a slowly rotating front cylinder and two oppositely rotating downstream cylinders, matching existing machine learning results.