High Reynolds Number Research Articles

The Basic k-ϵ Model and a New Model Based on General Statistical Descriptions of Anisotropic Inhomogeneous Turbulence Compared with DNS of Channel Flow at High Reynolds Number

Predictions are presented of mean values of statistical variables of large-scale turbulent flow of the widely used basic k-ϵ model, and of a new model, which is based on general statistical descriptions of turbulence. The predictions are verified against published results of direct numerical simulations (DNSs) of Navier–Stokes equations. The verification concerns turbulent channel flow at shear Reynolds numbers of 950, 2000, and 104. The basic k-ϵ model is largely based on empirical formulations accompanied by calibration constants. This contrasts with the new model, where descriptions of leading statistical quantities are based on the general principles of statistical turbulence at a large Reynolds number and stochastic theory. Predicted values of major output variables such as turbulent viscosity, diffusivity of passive admixture, temperature, and fluid velocities compare well with DNS for the new model. Significant differences are seen for the basic k-ϵ model.

Numerical Analysis of Flow-Induced Transverse Vibration of a Cylinder with Cubic Non-Linear Stiffness at High Reynolds Numbers

Numerical calculations were performed to study the vortex-induced vibration (VIV) of a circular cylinder, which was elastically supported by springs of linear and cubic terms. These simulations were conducted at high Reynolds numbers ranging from 4200 to 42,000. To simulate the cylinder’s motion and the associated aerodynamic forces, Computational Fluid Dynamics were employed in conjunction with dynamic mesh capabilities. The numerical method was initially verified by testing it with various grid resolutions and time steps, and subsequently, it was validated using experimental data. The response of cubic nonlinearities was investigated using insights gained from a conventional linear vortex-induced vibration (VIV) system. This 2D study revealed that both the amplitude and frequency of vibrations are contingent on the flow velocity. The highest output was achieved within the frequency lock-in region, where internal resonance occurs. In the case of a hardening spring, the beating response was observed from the lower end of the initial branch to the upper end of the initial branch. The response displacement amplitude obtained for the linear spring case was 27 mm, whereas in the cubic nonlinear case, the value was 31.8 mm. More importantly, the results indicate that the inclusion of nonlinear springs can substantially extend the range of wind velocities in which significant energy extraction through vortex-induced vibration (VIV) is achievable.

Entrainment and mixing of unsteady gravity currents in compound channels

Compound channels are a common hydraulic section of many alluvial and fluvial systems, serving as conduits for the flow of water and sediment. The proper design of these structures requires an understanding of the entrainment and mixing mechanisms in them. This paper presents a three-dimensional numerical study of lock-exchange flow in a compound channel covering the Reynolds numbers (Re) range of 17[Formula: see text]000–39[Formula: see text]000. This study investigates flow structures and mixing patterns for various geometries and flow characteristics. The results show that the entrainment coefficient decreases as the dense flow progresses, and the amplitude of instantaneous mixing fluctuations decreases with an increase in the width of the floodplain and reduced gravity. The averaged flux entrainment profiles show a minimum at [Formula: see text] at different times in the front area. In the head area also, a downward concavity can be seen in the profiles around [Formula: see text]. This study also reveals that changes in floodplain height do not affect the establishment of lobe-and-cleft instability. The wider the floodplain channel, the larger the lobe-and-cleft instability created. Small-scale mixing dominates at high Reynolds numbers, leading to higher fluid mixing.

A Data-Driven Approach for Generalizing the Laminar Kinetic Energy Model for Separation and Bypass Transition in Low- and High-Pressure Turbines

Abstract No common laminar kinetic energy (LKE) transition model has to date been able to predict both separation-induced and bypass transition, both phenomena commonly found in low-pressure turbines and high-pressure turbines. Here, a data-driven approach is adopted to develop a more general LKE transition model suitable for both transition modes. To achieve this, two strategies are adopted. The first is to extend the computational fluid dynamics (CFD)-driven model training framework for simultaneously training models on multiple turbine cases, subject to multiple objectives. By increasing the training data set, different transition modes can be considered. The second strategy employed is the use of a newly derived set of local non-dimensionalized variables as training inputs to reduce the search space. Because one of the training turbine cases is characterized by strong unsteady effects, for the first time an unsteady solver is utilized during the CFD-driven training, and the time-averaged results are used to calculate the cost function as part of the model development process. The results show that the data-driven models do perform better, in terms of their predictions of pressure coefficient, wall shear stress, and wake losses, than the baseline model. The models were then tested on two previously unseen testing cases, one at a higher Reynolds number and one with a different geometry. For both testing cases, stable solutions were obtained with results improved over the predictions using the baseline models.

Numerical study of a synergistic hybrid energy harvesting system for bladeless wind turbines

Using energy of the fluid flow over an oscillating vertically-mounted flexible cylinder, as a representative configuration of bladeless wind turbines (BWTs), has recently attracted wide attention in the fluid mechanics community. In this paper, the fluid–structure interactions of a novel BWT-based hybrid piezo-electromagnetic energy harvesting system have been numerically studied in the vortex-induced-vibration (VIV) lock-in region by using the Reynolds Averaged Navier-Stokes (RANS) equations with the SST k-ω turbulence model. It is found that by implementing the electromagnetic (EMT) and/or piezoelectric (PVDF) transducers, the lock-in region becomes wider (up to 33% for the hybrid system) while being shifted to the higher Reynolds number (Re) range. Also, the dimensionless BWT cross-flow tip displacement amplitude (Yamp∗) is seen to reduce about 20%, 70%, and 70% by using the single-alone EMT-based, single-along piezo-based, and the hybrid harvester, respectively, which can potentially lead to substantial improvements in the fatigue life of the system Furthermore, the synergetic action of the hybrid system is observed to cause an overall increase in the harvested energy levels besides broadening of the associated range, as each of energy harvesting components appears to produce higher output power as compared to the respective single-alone system. In other words, up to 260% increase (100% increase) in the overall harvested energy level and up to 300% increase (60% increase) in the harvestable Re range with respect to the single-alone piezo-based (EMT-based) system are obtained, in which about 50% (about 10%) synergetic effects can be associated with the EMT- and piezo-based transducers, respectively.

An Analytical Study of Fluid Flow Through a Porous Filled Channel with Permeable Wall: Suction/Injection Wall Conditions

To depict fluid movement in a channel with a rectangle-shaped cross-section and porous walls, the twodimensional Darcy Brinkman equation of motion with uniform suction and injection is analytically solved using the perturbation method. The analytical expressions for non-dimensional axial velocity, normal velocity, skin friction coefficient and pressure drop are obtained using the perturbation method at a low Reynolds number. Graphical analysis has been done for the derived quantities for different Darcy and Reynolds numbers. At higher Reynolds numbers, the emergence of the velocity overshoots and the presence of an unfavourable pressure gradient zone are significantly less noticeable. The streamlines follow the same pattern since the flow is steady. When the Darcy number is large, the non-dimensional stream function expression reduces to the stream function expression available in the literature. Non-dimensional pressure drop increases up to a specific entry length. The skin friction coefficient decreases as the Reynolds number increases. Acceleration of the fluid in the porous region leads to lesser skin friction; hence, pressure drop rises.

On the laminar wake of curved plates

Numerical simulations are performed to investigate the effect of the Reynolds number (Re) on flow over curved plates. Concave and convex plates, obtained by introducing curvature on a flat plate, are analyzed in the Reynolds number range 0.1 ≤Re≤ 120. It is observed that for a concave plate, the separation point is dependent on Re, while for a convex plate, the flow separates from the outermost tips for all Reynolds numbers. The analysis of time-averaged quantities reveals that concave and convex plates behave differently for the same Reynolds number. In the steady flow regime, visualization of streamlines reveals the presence of a recirculation bubble on the front side of the concave plate, even for the lowest Reynolds number (Re = 0.1). However, at higher Reynolds numbers (Re = 110, 120), the near wake of concave plate witnesses secondary and tertiary recirculating entities. The present simulations also report the unique phenomenon of vortex realignment and divergence of vortex street in the wake of a concave plate. For a convex plate, the vortex realignment is followed by the movement of upper and lower vortices as two parallel vortex streets. The existence of multiple instabilities is another highlight in the near and far wakes of the concave plate, some of which arise due to the secondary vortex interactions. A comprehensive analysis further reveals a handful of novel phenomenal occurrences in the wake of concave surfaces.

Transition Threshold for the 3D Couette Flow in a Finite Channel

In this paper, we study nonlinear stability of the 3D plane Couette flow ( y , 0 , 0 ) (y,0,0) at high Reynolds number R e {Re} in a finite channel T × [ − 1 , 1 ] × T \mathbb {T}\times [-1,1]\times \mathbb {T} . It is well known that the plane Couette flow is linearly stable for any Reynolds number. However, it could become nonlinearly unstable and transition to turbulence for small but finite perturbations at high Reynolds number. This is so-called Sommerfeld paradox. One resolution of this paradox is to study the transition threshold problem, which is concerned with how much disturbance will lead to the instability of the flow and the dependence of disturbance on the Reynolds number. This work shows that if the initial velocity v 0 v_0 satisfies ‖ v 0 − ( y , 0 , 0 ) ‖ H 2 ≤ c 0 R e − 1 \|v_0-(y,0,0)\|_{H^2}\le c_0{Re}^{-1} for some c 0 > 0 c_0>0 independent of R e Re , then the solution of the 3D Navier-Stokes equations is global in time and does not transit away from the Couette flow in the L ∞ L^\infty sense, and rapidly converges to a streak solution for t ≫ R e 1 3 t\gg Re^{\frac 13} due to the mixing-enhanced dissipation effect. This result confirms the threshold result obtained by Chapman via an asymptotic analysis(JFM 2002). The most key ingredient of the proof is the resolvent estimates for the full linearized 3D Navier-Stokes system around the flow ( V ( y , z ) , 0 , 0 ) (V(y,z), 0,0) , where V ( y , z ) V(y,z) is a small perturbation(but independent of R e Re ) of y y .

Synthetic Lagrangian turbulence by generative diffusion models

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, biofluids, the atmosphere, oceans and astrophysics. Despite exceptional theoretical, numerical and experimental efforts conducted over the past 30 years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pretraining various downstream applications of Lagrangian turbulence.

Fast fluid–structure interaction simulation method based on deep learning flow field modeling

The rapid acquisition of high-fidelity flow field information is of great significance for engineering applications such as multi-field coupling. Current research in flow field modeling predominantly focuses on low Reynolds numbers and periodic flows, exhibiting weak generalization capabilities and notable issues with temporal inferring error accumulation. Therefore, we establish a reduced order model (ROM) based on Convolutional Auto-Encoder (CAE) and Long Short-Term Memory (LSTM) neural network and propose an unsteady flow field modeling method for the airfoil with a high Reynolds number and strong nonlinear characteristics. The attention mechanism and weak physical constraints are integrated into the model architecture to improve the modeling accuracy. A broadband excitation training strategy is proposed to overcome the error accumulation problem of long-term inferring. With only a small amount of latent codes, the relative error of the flow field reconstructed by CAE can be less than 5‰. By training LSTM with broadband excitation signals, stable dynamic evolution can be achieved in the time dimension. CAE-LSTM can accurately predict the forced response and complex limit cycle behavior of the airfoil in a wide range of amplitude and frequency under subsonic/transonic conditions. The relative errors of predicted variables and integral force are less than 1%. The fluid–structure interaction framework is built by coupling the ROM and motion equations of the structure. CAE-LSTM predicts the time series response of pitch displacement and moment coefficient at different reduced frequencies, which is in good agreement with computational fluid dynamics, and the simulation time savings exceed one order of magnitude.

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

Large eddy simulations of turbulent pipe flows at moderate Reynolds numbers

Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we investigate fully developed turbulent pipe flows at moderate-to-high friction velocity Reynolds numbers (361≤Reτ≤2000), corresponding to bulk velocity-based Reynolds numbers of 11 700≤Reb≤82 500, using wall-modeled large eddy simulations (LES) in OpenFOAM. A grid convergence study is performed for Reτ=361, followed by an investigation of the accuracy of various subgrid-scale stress models for the same Reynolds number. Results show that the wall-adapting local eddy (WALE) model performs well compared to experiments and direct numerical simulations, while one-equation eddy-viscosity model and Smagorinsky are too dissipative. LES utilizing WALE is then performed for four different Reynolds numbers with gradually refined grids, revealing excellent agreement with DNS data in the outer region. However, a significant deviation from DNS data is observed in the sub-viscous layer region, indicating the need for further mesh refinement in the wall-normal direction to accurately capture the smallest-scale motions' behavior. Additional mesh sensitivity analysis uncovered that, as the Reτ value rises, it becomes crucial for a grid to adhere to the condition of Δx+≤20−25 and Δz+≤10 in order to precisely capture substantial large and small-scale fluctuations. Overall, the WALE model enables accurate numerical simulations of high-Reynolds number, wall-bounded flows at a fraction of the computational cost required for temporal and spatial resolution of the inner layer.

Assessment of the influence of flushing on the wear and morphological properties of the tool during electrical discharge machining

The present study is an integrated approach of experimental and simulation processes to investigate the influences of the flushing on the wear, textural feature, heat dissipation, tool-tip temperature, and elemental contents of the electrical discharge machining-tool. The general heat transfer equation in cylindrical coordinates is used to explain the thermal phenomenon through the tool, where the boundary conditions are influenced by convective interactions and dimensionless numbers. The inter-electrode flushing is considered a micro-channel flow, and the used model is conceptualized from “Hazen–Poiseuille observation.” It is observed that the adopted model has a prediction error of 8.503% and can accurately explain the thermal consequences of the process. The study reveals that tool wear is influenced by flushing velocity and flushing pressure. The tool-tip temperature reduces with the Reynolds number, and effectual expelling of the debris can be ensued with a flushing of a higher Reynolds number (Re). However, the increment of Re beyond 4500 provides rapid heat dissipation, which produces extensive residual stress and creates cracks on the surface.

Forgetfulness of turbulent energy cascade associated with different mechanisms

The small scales of high Reynolds number turbulence exhibit the statistical universality by forgetting about the large scales during the energy cascade. In this study, we revisit this schematic description with an information-theoretic point of view. Our objective is to understand the importance of different cascade mechanisms in this process. To this end, we compute the “information flux”, the information-theoretic measure of causality formulated by one of the authors, of the decomposed inter-scale energy transfer. For the kinetics, the ratio of the inertial-range inter-scale energy transfer between the strain self-amplification (SSA) and the vortex stretching (VS) mechanisms is 5 : 3. However, for the information-flux, the VS contribution is roughly twice as large as the SSA. We also find several deviations between the kinetics and the informatics, highlighting the nontrivial nature of information distributed among different scales and mechanics in turbulence. This result infers that the SSA is a less efficient mechanism than the VS in terms of information transfer, and contributes to losing the large-scale information.

Karhunen–Loéve decomposition of high Reynolds number turbulent pipe flows: a Voronoi analysis

We perform the Karhunen–Loéve decomposition of the data from direct numerical simulations pertaining to incompressible turbulent pipe flow at various Reynolds numbers, in order to identify large-scale coherent structures. A novel approach based on the Voronoi diagram is introduced to estimate the energy distribution along the radial direction as a function of the geometrical properties of the modes. In contrast to previous classifications, no user-defined criterion, threshold or ad-hoc separation of the eddies is required since the two most energetic branches are inherently present as the Reynolds number increases. Details about the Voronoi analysis are provided, together with a comprehensive validation and comparison with previous classifications at low Reynolds numbers. We discuss the results and potential of the presented approach at Reτ = 180 and 5200, commenting on the two classes of coherent structures with a varying and constant size in the radial direction appearing at Reτ = 5200.

Aerodynamic Design and Performance Analysis of Mars Ascent Vehicles

The mid-lift-to-drag ratio vehicle possesses larger dimensions and enhanced aerodynamic characteristics compared to the conventional sphere-cone reentry vehicle, suggesting its suitability for crewed missions to Mars. This research employs Computational Fluid Dynamics (CFD) simulations to investigate the influence of varying geometries on the aerodynamic properties of mid-lift-to-drag ratio vehicles. The aerodynamic analysis of four distinct configurations demonstrates that a bow shock wave forms on the windward side, leading to a reduction in flow velocity and subsequent increases in pressure and temperature after the shock wave. The simulation results for the four configurations in both laminar and turbulent flow conditions, specifically using the Shear-Stress Transport (SST) model, reveal that turbulence results in higher aerodynamic heating compared to laminar flow. Moreover, the aerodynamic heating is greater at a 40° angle of attack than at 30°. In this study, the transition phenomena of four geometric configurations are examined using the k-ω-γ transition model. The findings indicate a pronounced transition to turbulence on the windward side of the Ellipsled 2.00-0.25 and Hammerhead-Nominal configurations under conditions of high Reynolds numbers, transitioning from laminar to turbulent flow. The investigation into the aerodynamic characteristics of mid-lift-to-drag ratio vehicles holds substantial importance for ensuring the safety and success of Martian reentry missions, highlighting the critical nature of aerodynamic behavior in the context of space exploration.

Numerical study of heat transfer and fluid flow in the offset strip-fin heat exchanger: A fin-by-fin analysis

Heat transfer and fluid flow in the offset strip-fin heat exchanger are studied numerically, fin by fin. The impact of the offset strip-fin geometry on j/f performance is also evaluated. The mathematical model is validated against j- and f-factor correlations from the literature. The numerical analysis revealed that the offset strip-fin heat exchanger achieves best j/f performance in the laminar flow region (Redh < 700). At higher Reynolds numbers, the j/f factor deteriorates under the impact of flow recirculations, oscillatory wakes and the contribution of form drag. Compared to the continuous rectangular fin, the offset strip-fin increases the air-side heat transfer coefficient by 50% at Redh = 100 and by 120% at Redh = 4000 while the pressure drop increases by a factor of 3–5. Generally, the offset strip-fin achieves j/f performance between 0.20 and 0.30, with maximum values found in the laminar flow region (Redh 〈1000). Offset strip-fin geometries with reduced fin space and increased wall thickness strongly affect the form drag, which reduces the j/f performance, especially for Redh > 1000. The fin height weakly influences the performance, and the j/f factor is between 0.22 and 0.23 for a wide range of fin heights.

Thermal performance augmentation in a pipe employing hybrid nanofluid and a plate as turbulator with V-shaped double-winglet ribs

This article employs a plate with V-shape ribs inside a tube as turbulator to augment the heat transfer rate. The utilized vortex generators are double-winglets arranged in a V-shape placed on both sides of the plate. The proposed system’s suggested working fluids are water-based hybrid nanofluids, including Al2O3–Cu/water, Cu–CuO/water, and Cu–TiO2/water. This work involves a numerical evaluation of the effects of the type and volume concentration of the examined hybrid nanofluids on the enhancement of heat transfer. The experimental results are used to validate the numerical model. It is worth mentioning that all the obtained numerical results are compared with the simple tube, without any turbulator (vortex generator) and in the presence of water instead of the hybrid nanofluids. Based on the numerical results, it can be concluded that all employed hybrid nanofluids showed improved thermal performance compared to pure water. Furthermore, the differences between the models are more substantial for higher Reynolds numbers than for lower Reynolds numbers. In Re = 30,000, the Cu–TiO2/water exhibits the lowest thermal performance improvement (augmentation of about 0.3%), while the Cu–CuO/water at Re = 50,000 exhibits the largest thermal performance improvement (augmentation of approximately 5.7%), in the case of ∅1 = ∅2 = 0.5%. For ∅1 = ∅2 = 1%, the Cu–TiO2/water at Re = 30,000 has the lowest thermal performance improvement (augmentation of around 1.1%), while the Cu–CuO/water at Re = 50,000 has the most thermal performance improvement (augmentation of roughly 8.7%). According to the augmentation of around 2.8% at Re = 30,000 for Cu–TiO2/water and approximately 10.8% at Re = 50,000 for Cu–CuO/water, the thermal performance increase in the scenario of ∅1 = ∅2 = 1.5% is the lowest. In Conclusion, the Cu–CuO/water hybrid nanofluid with a volume concentration of ∅1 = ∅2 = 1.5% has the greatest thermal performance value of all the hybrid nanofluids studied.

Convergence analysis of high-order IMEX-BDF schemes for the incompressible Navier–Stokes equations

In this paper, we consider developing high-order temporal integration schemes for the unsteady incompressible Navier–Stokes equations in bounded two-dimensional domain subjected to the periodic boundary conditions. Utilizing the k-step (k=3,4,5) backward differentiation formula (BDF) coupled with the implicit–explicit (IMEX) treatment of the nonlinear convective term in an anti-symmetry form, a class of IMEX-BDFk schemes up to fifth-order in time are constructed and analyzed. By imposing a zero-mean constrain on the finite-dimensional space for the pressure, the proposed numerical schemes are proven to be uniquely solvable. Based on the recent theoretical framework consisting of a class of discrete orthogonal convolution kernels, rigorous L2 norm error estimates for both the velocity and the pressure are established by using a novel divergence free projection system. The proposed schemes are then implemented in two benchmark experiments, including a Taylor–Green vortex problem and a double shear layer flow at various high Reynolds numbers. Numerical results demonstrate the expected solution accuracy and the computational effectiveness in simulating the realistic flow dynamics.

Effect of network architecture on physics-informed deep learning of the Reynolds-averaged turbulent flow field around cylinders without training data

Unsupervised physics-informed deep learning can be used to solve computational physics problems by training neural networks to satisfy the underlying equations and boundary conditions without labeled data. Parameters such as network architecture and training method determine the training success. However, the best choice is unknown a priori as it is case specific. Here, we investigated network shapes, sizes, and types for unsupervised physics-informed deep learning of the two-dimensional Reynolds-averaged flow around cylinders. We trained mixed-variable networks and compared them to traditional models. Several network architectures with different shape factors and sizes were evaluated. The models were trained to solve the Reynolds-averaged Navier-Stokes equations incorporating Prandtl’s mixing length turbulence model. No training data were deployed to train the models. The superiority of the mixed-variable approach was confirmed for the investigated high Reynolds number flow. The mixed-variable models were sensitive to the network shape. For the two cylinders, differently deep networks showed superior performance. The best fitting models were able to capture important flow phenomena such as stagnation regions, boundary layers, flow separation, and recirculation. We also encountered difficulties when predicting high Reynolds number flows without training data.