Three-dimensional Turbulent Flow Research Articles

Reference map technique for Lagrangian exploration of coherent structures

We explore the application of the reference map technique, originally developed for Eulerian simulation of solid mechanics, in Lagrangian kinematics of turbulent flows. Unlike traditional methods based on explicit particle tracking, the reference map facilitates the calculation of flow maps and gradients without the need for particles. This is achieved through an Eulerian update of the reference map, which records the take-off positions of fluid particles. This approach is found to be mathematically equivalent to the work of Leung (J. Comput. Phys., vol. 230, issue 9, 2011, pp. 3500–3524), who computed the flow map of simple two-dimensional flows using an Eulerian approach. We discuss important modifications necessary for its first application to complex three-dimensional turbulent flows, including the conservative, low-dissipation update of the flow map and the treatment of periodic boundary conditions. We first demonstrate the accuracy of finite-time Lyapunov exponent (FTLE) calculations based on the reference map against the standard particle-based approach in a two-dimensional Taylor–Green vortex. Then we apply it to turbulent channel flow at $Re_\tau =180$ , where Lagrangian coherent structures identified as ridges of the backward-time FTLE are found to bound vortical regions of flow, consistent with Eulerian coherent structures from the $Q$ -criterion. The reference map also proves suitable for material surface tracking despite not explicitly tracking particles. This capability can provide valuable insights into the Lagrangian landscape of turbulent momentum transport, complementing Eulerian velocity field analysis. The evolution of initially wall-normal material surfaces in the viscous sublayer, buffer layer and log layer sheds light on the Reynolds stress-generating events from a Lagrangian perspective.

Neural deflection field for sparse-view tomographic background oriented Schlieren

Three-dimensional (3D) density-varying turbulent flows are widely encountered in high-speed aerodynamics, combustion, and heterogeneous mixing processes. Multicamera-based tomographic background-oriented Schlieren (TBOS) has emerged as a powerful technique for revealing 3D flow density structures. However, dozens of cameras are typically required to obtain high-quality reconstructed density fields. Limited by the number of available optical windows and confined space in the harsh experimental environments, TBOS with only sparse views and limited viewing angles often becomes the necessary choice practically, rendering the inverse problem for TBOS reconstruction severely ill-posed and resulting in degraded tomography quality. In this study, we propose a novel TBOS reconstruction method, neural deflection field, utilizing an extremely light-weight deep neural networks to represent the density gradient fields without using any pretrained neural network models. Particularly, state-of-the-art positional encoding techniques and hierarchical sampling strategies are incorporated to capture the density structures of high spatial frequencies. Required background images for TBOS reconstructions are synthesized based on a high-fidelity nonlinear ray-tracing method with the ground truth flows from conducting large eddy simulations on premixed turbulent flames. Owing to these synthesized BOS images, the superiority of the proposed method is quantitatively verified compared to the classical TBOS reconstruction methods, and the specific contributions from the position encoding and the hierarchical sampling strategy are also elucidated.

Linear stability and spectral modal decomposition of three-dimensional turbulent wake flow of a generic high-speed train

Linear stability and spectral modal decomposition of three-dimensional turbulent wake flow of a generic high-speed train

Streamline coordinates in three-dimensional turbulent flows

Streamline coordinates in three-dimensional turbulent flows

Generative learning for forecasting the dynamics of high-dimensional complex systems

We introduce generative models for accelerating simulations of high-dimensional systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are down sampled to a lower dimensional manifold that is evolved through an auto-regressive attention mechanism. In turn, Bayesian diffusion models, that map this low-dimensional manifold onto its corresponding high-dimensional space, operate on batches of physics correlated, time sequences of data and capture the statistics of the system dynamics. We demonstrate the capabilities and drawbacks of G-LED in simulations of several benchmark systems, including the Kuramoto-Sivashinsky (KS) equation, two-dimensional high Reynolds number flow over a backward-facing step, and simulations of three-dimensional turbulent channel flow. The results demonstrate that generative learning offers new frontiers for the accurate forecasting of the statistical properties of high-dimensional systems at a reduced computational cost.

Impact of emergent vegetation on three-dimensional turbulent flow properties and bed morphology in a partially vegetated channel

The study aimed to explore three-dimensional turbulent flow properties and bed morphology in a partially vegetated channel with sand bed conditions. Presence of flexible vegetation in the river and its interaction with the flow are of great significance in understanding the momentum and mass transport in the flow. Experiments were conducted in a straight, tilting rectangular flume with staggered emergent vegetation covering half of the channel width. The results show that the presence of vegetation diverts streamwise velocity from the vegetated side to the non-vegetated side. The study reveals that the presence of vegetation leads to an increase in turbulent intensity, turbulent kinetic energy, and Reynolds shear stress at the transition area between the vegetated and non-vegetated sides of the channel. This increase is attributed to higher transverse flow and momentum exchange in the transition area between the vegetated and non-vegetated sides. In the vegetated side, the vegetation serves as an obstruction, reducing turbulent intensity, turbulent kinetic energy, and Reynolds shear stress compared to the transition area between the vegetated and non-vegetated sides. This reduction in turbulence supports the stability of bed materials and promotes sediment deposition. The presence of vegetation significantly alters the secondary current in the channel. Scour depth along the non-vegetated side was higher than the vegetated side, mainly because the flow concentrated in the centre and non-vegetated side of the channel. The investigation determines that the existence of vegetation on the vegetated side effectively protects against bed erosion and sediment transport. Understanding the impact of emergent flexible vegetation on flow properties and sediment transport can inform decisions about vegetation layouts in river ecosystems.

Simulation and study of the flow field in a kettle-type reactor for ethylene polymerization

Abstract Addressing the complexities inherent in the polymerization process for solution method polyethylene production, particularly the challenges in describing the turbulent three-dimensional flow field within the reactor and the precise design of reactor structural parameters, this research leverages computational fluid dynamics (CFD) methods integrated with polymerization reaction kinetics equations. We have formulated User-Defined Functions (UDFs) for a quantitative representation of the polymerization process. Employing the Realizable k-epsilon turbulence model and Sliding Grid (SG) technique, we analyzed the flow dynamics and field distribution within the reactor, elucidating the distribution patterns of temperature, pressure, and concentration fields. A comparative assessment of simulation outcomes against experimental data revealed that the average deviation of the simulated temperature field from actual operating conditions falls within the permissible error range, thereby affirming the simulation model’s validity. Utilizing local sensitivity analysis, we investigated the impact of impeller structural parameters on mixing time and stirring power. Our analysis of the most sensitive structural parameters indicated that impeller diameter and the number of impellers are pivotal in reducing mixing time and stirring power, respectively. Notably, the stirring power escalates with an increase in the number of impellers, while the mixing time exhibits a trend of initial decrease followed by an increase with varying impeller diameters. The methodologies and patterns discerned in this study provide insightful design references for the design and optimization of reactors across different tonnages.

Similarity solutions of a class of unsteady laminar boundary layer

The study of laminar unsteady boundary layer flows is essential for understanding the transition from laminar to turbulent flow, as well as the origins of turbulence. However, finding solutions to this phenomenon poses significant challenges. In this study, we introduce a novel method that employs a similarity transformation to convert the two-dimensional unsteady laminar boundary layer equations into a single partial differential equation with constant coefficients. By applying this transformation, we successfully derive similarity solutions for flat plate boundary layer flow, expressed in terms of Kummer functions. For convergent boundary layer flow, we derive an approximate analytical solution that includes both shock wave and soliton wave solutions. The superposition of these solutions provides evidence for the existence of solitons or soliton-like coherent structures (SCS) within boundary layers. Additionally, this paper explores two- and three-dimensional laminar flows, as well as three-dimensional turbulent flow equations, revealing that they all incorporate third-order derivatives with respect to spatial coordinates. This finding suggests that all viscous fluid motions have the potential to exhibit solitons/like coherent structures (SCS).

Numerical simulations of a stochastic dynamics leading to cascades and loss of regularity: Applications to fluid turbulence and generation of fractional Gaussian fields

Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics was recently proposed that can generate high velocity gradients from a smooth-in-space forcing term. It is based on a linear partial differential equation stirred by an additive random forcing term that is δ-correlated in time. The underlying proposed deterministic mechanism corresponds to a transport in Fourier space that aims to transfer energy injected at large scales towards small scales. The key role of the random forcing is to realize these transfers in a statistically homogeneous way. Whereas at finite times and positive viscosity the solutions are smooth, a loss of regularity is observed for the statistically stationary state in the inviscid limit. We present here simulations, based on finite volume methods in the Fourier domain and a splitting method in time, which are more accurate than the pseudospectral simulations. We show that our algorithm is able to reproduce accurately the expected local and statistical structure of the predicted solutions. We conduct numerical simulations in one, two, and three spatial dimensions, and we display the solutions both in physical and Fourier space. We additionally display key statistical quantities such as second-order structure functions and power spectral densities at various viscosities. Published by the American Physical Society 2024

Dynamic feature-based deep reinforcement learning for flow control of circular cylinder with sparse surface pressure sensing

This study proposes a self-learning algorithm for closed-loop cylinder wake control targeting lower drag and lower lift fluctuations with the additional challenge of sparse sensor information, taking deep reinforcement learning (DRL) as the starting point. The DRL performance is significantly improved by lifting the sensor signals to dynamic features (DFs), which predict future flow states. The resulting DF-based DRL (DF-DRL) automatically learns a feedback control in the plant without a dynamic model. Results show that the drag coefficient of the DF-DRL model is 25 % less than the vanilla model based on direct sensor feedback. More importantly, using only one surface pressure sensor, DF-DRL can reduce the drag coefficient to a state-of-the-art performance of approximately 8 % at Reynolds number $(Re) = 100$ and significantly mitigates lift coefficient fluctuations. Hence, DF-DRL allows the deployment of sparse sensing of the flow without degrading the control performance. This method also exhibits strong robustness in flow control under more complex flow scenarios, reducing the drag coefficient by 32.2 % and 46.55 % at $Re =500$ and 1000, respectively. Additionally, the drag coefficient decreases by 28.6 % in a three-dimensional turbulent flow at $Re =10\,000$ . Since surface pressure information is more straightforward to measure in realistic scenarios than flow velocity information, this study provides a valuable reference for experimentally designing the active flow control of a circular cylinder based on wall pressure signals, which is an essential step toward further developing intelligent control in a realistic multi-input multi-output system.

Numerical prediction of mean flow and acoustic field of a supersonic impinging jet

The three-dimensional turbulent mean flow and acoustic field of a supersonic jet impinging on a solid plate is studied computationally using the general purpose CFD code Ansys Fluent. A pressure-based coupled solver formulation with the second order weighted central-upwind spatial discretization is applied to compute transient solutions. Cold and hot jet thermal conditions are considered. Mean flow characteristics are investigated by a steady-state modeling approach. Acoustic radiation of impingement tones is simulated using a transient time-domain formulation. The effects of turbulence in steady-state are modeled by the SST k-ω turbulence model. The Wall-Modeled Large-Eddy Simulation (WMLES) model is applied to compute transient solutions. The near-wall mesh on the impingement plate is fine enough to resolve the viscosity-affected near-wall region all the way to the laminar sublayer. Nozzle-to-plate distance is parameterized in the model for automatic re-generation of the mesh and results. Steady-state predictions of hover lift loss and mean jet velocity distributions are compared with experimental data, and favorable agreement is reported. The transient solution reproduces the mechanism of impingement tone generation by the interaction of large scale vortical structures with the impingement plate. The acoustic near-field is directly resolved by Computational Aeroacoustics (CAA) to accurately propagate impingement tone waves to near-field microphone locations. Calculated impingement tone frequencies and sound pressure levels agree with experimental values.

Analyzing the performance of hull and water jet propeller under mooring conditions: effects of shallow water depths and varying inflow speeds

PurposeWater jet propulsion is widely used in various military and civilian fields due to its advantages of simple structure and high propulsion efficiency. The process of mooring involves utilizing specially designed equipment to secure a ship at a designated berth. During the process of water jet propulsion, the single propeller operates within a complex and turbulent three-dimensional flow. Hence, studying the coupling between the water jet propeller and the hull is critical to comprehending the characteristics of the device and the distribution of the flow field in detail.Design/methodology/approachFirstly, we conducted computational fluid dynamics (CFD)-based self-propulsion calculations to evaluate the interaction between the hull and the propeller. We subsequently analyzed the propeller's performance and the forces acting on the hull to understand how the presence or absence of the hull influenced the water jet propeller. Finally, we performed calculations and analysis of the cavitation characteristics of the coupling between the hull and the water jet propeller, considering different rotational speeds and water depths at the bottom of the pool.FindingsThe study demonstrated that the presence of the hull boundary layer under the hull-propeller coupling condition led to reduced uniformity of propeller inlet flow and lower efficiency of the propulsion pump. However, it also increased the bias toward low-flow conditions. Additionally, increasing the impeller speed led to a gradual increase in the cavitation volume within the water jet propeller, resulting in a gradual decrease in the propeller's performance.Originality/valueThis research provides the technical support required for effective design and operation of water jet propulsion systems. This paper involves studying and analyzing the performance and flow field of the coupling between the hull and propeller under mooring conditions with a specified hull model.

Dual-Orthogonal-Plane Particle Image Velocimetry Measurement of the Turbulent Flow in the Channel Head of a Large-Scale Steam Generator Mockup

Abstract In this work, a large-scale mockup of a compact complex system integrating a steam generator (SG) and a reactor coolant pump (RCP) is considered. The three-dimensional turbulent flow in the steam generator channel head (SGCH) is measured in detail. Dual-orthogonal-plane particle image velocimetry (PIV) is employed to extract high-resolution flow information in two orthogonal planes. Two separate measurements are first made to see the three-dimensional time-mean flow dynamics and the statistical quantities in the two planes. These measurements highlight two distinct flow phenomena: jet arrays and massive turbulent separation bubbles (TSBs). These patterns are attributed to mass flow redistribution in the U-shaped tubes. Proper orthogonal decomposition (POD) identifies the first POD mode as corresponding to the TSB breathing-like motion, which significantly intensifies the side view streamwise velocity fluctuations, leading to them reaching 370% of the local mean velocity. To examine the unsteady behavior of massively separated regions, the dual-orthogonal-plane PIV system is then synchronized to simultaneously measure variations in the flow fields, and the missing data due to illumination interference are reconstructed using gappy POD. The synchronized analysis reveals a direct relationship between the low-frequency fluctuations in the side and front views. These fluctuations are in phase across both views, indicating a synchronized behavior that spans the entire field. This large-scale low-frequency breathing motion has critical implications for numerical simulations and sheds light on the unsteady behavior of the RCP system within the SGCH.

Experimental investigation of three-dimensional flow dynamics in a laboratory-scale meandering channel under subcritical flow condition

This study investigates the three-dimensional turbulence flow properties in a meandering channel under subcritical flow conditions, specifically focusing on a few critical parameters such as three-dimensional velocity behaviour, Turbulent kinetic energy, skewness, and kurtosis. A model study has been attempted by considering the same sinuosity, Froude number, and bed material from an Indian peninsular river to understand the basic hydrodynamics of a meandering channel. Understanding these critical parameters is crucial for comprehending the complex flow behaviour and its implications in meandering channels. Experimental measurements were conducted to collect data on Velocity, Turbulent Kinetic energy, skewness, and kurtosis in all three directions. The objective was to analyse their variations and behaviour along the meandering path, providing insights into the flow dynamics and turbulence characteristics. Advanced measurement techniques, such as Acoustic Doppler Velocimeters (ADV), were utilized to obtain accurate and detailed data. The study revealed distinct patterns and trends in the velocity, Turbulent Kinetic energy, skewness, and kurtosis along the flow path of a sand bed meandering channel. These parameters were found to vary significantly in different sections, highlighting the influence of channel geometry and flow conditions. Graphical representations of the flow profiles were employed to visualize the spatial distribution and understand the variations in these turbulence properties. The findings of this study enhance our understanding of the three-dimensional turbulence flow properties in sand bed meandering channels under subcritical flow conditions. The results offer valuable information for designing hydraulic structures, flood control measures, and river restoration projects.

Effect of confinement on the transition from two- to three-dimensional fast-rotating turbulent flows

Effect of confinement on the transition from two- to three-dimensional fast-rotating turbulent flows

Numerical study of a fish swimming in hydrokinetic turbine wake

The environmental effects of hydrokinetic turbines are still under investigation, reflecting the emerging status of this technology. This study investigates the interaction between hydrokinetic rotor wakes and fish swimming, revealing insights into fish biomechanics in complex flows and assessing the environmental implications of marine energy solutions. We conducted numerical simulations with the URANS approach and k−ω−SST turbulence closure model to predict three-dimensional turbulent flow in the OpenFOAM software. The hydrokinetic rotor wake was simulated employing the actuator line method, providing a computationally efficient alternative to full geometry simulations. For accurate replication of the motion of a fish-like tuna (Thunnus atlanticus), dynamic adaptive mesh discretization was employed. The results offer a comparative analysis of fish swimming performance within the wake rotor, particularly when immersed in the tip blade vortex, contrasted with scenarios where fish swim in undisturbed flow conditions. The analysis encompasses three-dimensional wake structures, force generation, efficiency, and equilibrium states (balancing drag and thrust) across varying Swimming numbers (Sw). Key findings include the enhanced attachment of the leading-edge vortex due to the caudal fin’s interaction with the tip blade vortex, resulting in improved auto-propulsive force production; a reduced tail stride frequency observed in fish swimming downstream of the rotor to achieve longitudinal force balance compared to unperturbed flow; and transverse hydrodynamic forces pushing fish radially away from the wake’s influence zone, potentially mitigating the risk of collision with turbine blades.

Direct numerical simulation of the turbulent flow around a Flettner rotor

The three-dimensional turbulent flow around a Flettner rotor, i.e. an engine-driven rotating cylinder in an atmospheric boundary layer, is studied via direct numerical simulations (DNS) for three different rotation speeds (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}). This technology offers a sustainable alternative mainly for marine propulsion, underscoring the critical importance of comprehending the characteristics of such flow. In this study, we evaluate the aerodynamic loads produced by the rotor of height h, with a specific focus on the changes in lift and drag force along the vertical axis of the cylinder. Correspondingly, we observe that vortex shedding is inhibited at the highest α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} values investigated. However, in the case of intermediate α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}, vortices continue to be shed in the upper section of the cylinder (y/h>0.3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y/h>0.3$$\\end{document}). As the cylinder begins to rotate, a large-scale motion becomes apparent on the high-pressure side, close to the bottom wall. We offer both a qualitative and quantitative description of this motion, outlining its impact on the wake deflection. This finding is significant as it influences the rotor wake to an extent of approximately one hundred diameters downstream. In practical applications, this phenomenon could influence the performance of subsequent boats and have an impact on the cylinder drag, affecting its fuel consumption. This fundamental study, which investigates a limited yet significant (for DNS) Reynolds number and explores various spinning ratios, provides valuable insights into the complex flow around a Flettner rotor. The simulations were performed using a modern GPU-based spectral element method, leveraging the power of modern supercomputers towards fundamental engineering problems.

Theoretical study of the influence of gas phase turbulent disturbances on the kinetics of ultrasonic coagulation of PM2.5

A numerical model of ultrasonic coagulation of PM2.5 aerosol particles in three-dimensional vortex and turbulent acoustic flows is proposed in the article. The model is intended to identify the possibility of increasing the efficiency of the process. A numerical analysis of the model using the example of PM2.5 aerosol made it possible to establish that the presence of three-dimensional turbulent disturbances leads to the fact that the coagulation efficiency of PM2.5 reaches almost 100% at a sound pressure level of no more than 165 dB.

A fast three-dimensional flow field prediction around bluff bodies using deep learning

This study presents a deep learning approach for predicting the flow field in the incompressible turbulent three-dimensional (3D) external flow around right-rhombic prism-shaped bluff bodies. The approach involves treating the nodes of the unstructured grid in the computational fluid dynamics domain as a point cloud, which is used as an input for a neural network. The neural network is trained to map the spatial coordinates of the nodes to the corresponding velocity and pressure values in the domain. The PointNet, a reliable solution in 3D vision tasks, is selected as the neural network architecture. Implementing this architecture makes it feasible to use irregular positions of the nodes of an unstructured grid as an input without needing interpolation. A dataset, comprising 3511 cases, is generated for training and testing the network. This is achieved by changing the geometric parameters of a right rhombic prism and varying its angle to the flow stream. Then, the continuity and momentum equations for turbulent flow are solved using a solver. Given the need for a larger number of points to accurately represent a 3D flow, the architecture of PointNet is modified. This modification involves adding extra layers and adjusting the number of neurons inside the layers to overcome this challenge. Once the training is completed, given the unseen samples from the test dataset to the model, our model can predict the velocity and pressure of the flow field at a speed that exceeds our conventional solver by several orders of magnitude with a maximum relative error of 4.58%.

A cell-based smoothed finite element model for the analysis of turbulent flow using realizable k-ε model and mixed meshes

Smoothed finite element method (S-FEM) has been widely employed in computational mechanics, particularly in computational solid mechanics (CSM) and, to a lesser extent, in computational fluid dynamics (CFD). The present work focuses on the development of S-FEM for solving three-dimensional incompressible turbulent flow problems using the realizable k-ε model. The Streamline Upwind Petrov-Galerkin approach combined with Stabilized Pressure Gradient Projection (SUPG/SPGP) was used to restrain/control the spatial oscillation and instability in conjunction with mixed meshes employed to discretize complex geometries. The presented turbulent cell-based S-FEM (CS-FEM) was validated under several common flow types, including mesh turbulence, turbulent channel flow, turbulent flow past a circular cylinder, flow separation around an obstacle, flow in the dimpled channel, and flow in the upper human airway. In particular, the presented work exhibited the latent capability of the CS-FEM in solving turbulent flows near boundary regions and strong convection regions. Meanwhile, the results of the CS-FEM were compared to those of the lowest equal-order finite element method (i.e. P1–P1 or Q1–Q1 elements) in simulating turbulent flows, and it was found that the CS-FEM had better agreement with other published works.