High Reynolds Number Research Articles

Numerical investigation of vortex-induced forces on a wind turbine tower segment at very high Reynolds numbers

The vortex-induced forces on an extruded cylinder with a span of two diameters representative of a finite segment of a non-tapered wind turbine tower at a very high Reynolds number (Re = 8.0×106) are numerically investigated using an incompressible Navier-Stokes flow solver with an Improved Delayed Detached Eddy Simulation (IDDES) turbulence model and correlation-based boundary layer transition modelling. The solution shows spanwise correlated structured vortex shedding with the Strouhal number St = 0.48. The boundary layer transition is found to occur at θ transition = 70 ◦ , and boundary layer separation is found to occur at θ separation = 120 ◦ . Results from the grid dependency study strongly imply that when using IDDES, the Strouhal number converges to higher values than previously reported by the literature as the grid is refined, with results ranging from St ∼ 0.44 using a grid with 4.2 × 106 cells, to St = 0.48 for the finest considered grid with 33 × 106 cells. This behaviour is not seen for URANS, where St = 0.33 for the finest grid.

Study of implicit CFD modeling of riblets on wind turbine airfoil in transitional flow

The study introduces a novel hybrid boundary condition, derived from existing literature, crafted for predicting the impact of riblets on airfoils in transitional flow. In contrast to models tailored for fully turbulent flow, the hybrid approach successfully captures the operational dynamics of riblets, as demonstrated through meticulous testing. The boundary condition integrates slip length and a modified specific dissipation rate (ω) boundary to encompass the entire riblet regime. Adjusting the model to match measured drag behavior enables predictions of riblet effects at higher Reynolds numbers pertinent to wind turbine blades. Validation reveals the model’s proficiency in capturing the order of magnitude in drag reduction and aligns the change in drag in the correct direction for diverse riblet heights, yet highlights discrepancies in replicating absolute drag reduction values, particularly at smaller angles of attack. This underscores the imperative for further refinement and tuning, necessitating additional experimental data at higher Reynolds numbers and across various angles of attack to ensure the model’s robust applicability across a broader spectrum of conditions.

Virtual physical framework reveals vortex-induced vibration “Soar” and “Death” for a bluff body at high Reynolds numbers

Vortex-induced vibration (VIV) of a bluff body is well known as a canonical phenomenon in complex fluid–structure interactions (FSI). However, our understanding and physical theories of this phenomenon are still restricted to a lower Reynolds number (Re) range owing to the limitations of experimental fluid mechanics. Herein, we describe a virtual physical framework (VPF) capable of editing and controlling the physical parameters of an actual physical system with high fidelity by combining numerical disciplinary and mechanical actuators. We demonstrated the effectiveness of applying a VPF to address the experimental fluid mechanical challenges of vortex-induced vibration (VIV) for a bluff body at a high Re by virtualizing a large, flexibly mounted rigid cylindrical system. We observed the VIV evolution of the bluff body at different Re values. Notably, the VIV appears in its “soar” stages with unexpected amplitudes of 2.4 D, nearly 200% higher than the traditionally acknowledged value at approximately Re = 2.0E5, while suddenly entering into its “death” stages with no vibrations over the critical Re region. The dissynchrony changes in the energy dissipation and input with Re caused by drag and excitation forces in the fluid system were further found to result in these VIV phenomena. This discovery upsets previous perceptions of VIVs and raises profound questions regarding related engineering projects. The VPF also opens a promising paradigm in experimental research for accelerating scientific discovery and investigating unaddressed classical physical phenomena.

Study of surface roughness on flow past a wind turbine tower section

The flow around wind turbine towers usually reaches very high Reynolds numbers greater than a million. Understanding the flow around the towers under these conditions is crucial, as it may lead to vibrations due to the vortices formed. Investigating aerodynamic characteristics at such high Reynolds numbers, both numerically and experimentally, is challenging. The current study validates such an experimental study, where a rough surface is employed to increase the effective Reynolds numbers and accelerate the laminar-turbulent transition in the boundary layer. Unsteady Reynolds-Averaged Navier-Stokes (RANS) simulations are carried out using OpenFOAM for a Reynolds number range of 1.36·105 to 6.8·105. The constant (a 1) used to calculate the eddy viscosity is varied to simulate the flow separation during adverse pressure gradients. A force partitioning method is implemented in OpenFOAM and various force contributions are analysed for this Reynolds number range. It is seen that the RANS simulations overpredict the aerodynamic characteristics and the extent of flow separation unless the value of a 1 is varied as a function of the Reynolds number. Furthermore, it is observed that the only force contributor is the vorticity-induced force, as the simulations are performed for a fixed cylinder.

Comparison of Pressure-based and Skin Friction-based Methods for the Determination of Flow Separation of a Circular Cylinder with Roundness Imperfection

Introduction: A delayed detached eddy simulation in Open FOAM was performed to study flow separation of a circular cylinder with roundness imperfection up to 4% of its diameter at Reynolds numbers of 100, 3900, and 104 in normal flow. Methods: The flow was considered to be Newtonian and incompressible. The separation position was determined independently based on surface pressure distribution and skin friction. Results: Results show that the patterns of these distributions depend on both Reynolds number and roundness imperfection level, and flow separation in an imperfectly round cylinder may be induced by either an adverse pressure gradient or a Gentle Bend (GB) introduced by the roughness. For the separation point determined by the pressure-based method, its accuracy can be affected by the characteristic of pressure distribution near the separation point at low Reynolds numbers, and, thus, its physical validity needs to be verified by flow visualization at high Reynolds numbers. Conclusion: The skin friction-based method can accurately predict separation point for both perfectly and imperfectly round cylinders without additional information. When the roundness imperfection ratio reaches 2% and the Reynolds number reaches 3900, both approaches indicate that the flow separation point converges to the location of GB on the cylinder surface and the two sets of predicted separation points agree well.

Numerical analysis of static and dynamic wind turbine airfoil characteristics in transonic flow

This study performed an aerodynamic characterization of the FFA-W3-211 wind turbine tip airfoil in transonic flow using Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations, for both steady and dynamic operational conditions. First, the boundary between subsonic and supersonic flow in static conditions was identified, depending on the angle of attack, the approach flow Mach number, and the Reynolds number. The analysis points out that higher Reynolds numbers promote the occurrence of local supersonic flow. Thereafter, to investigate the dynamic behavior in the transonic flow regime, a sinusoidal pitching motion with representative values was imposed. A hysteresis, similar to but distinct from dynamic stall, was observed for entering and leaving the supersonic and subsonic regions. Elevated reduced frequencies widened the hysteresis loop, resulting in increased normal forces on the airfoil. The study indicated that an increase in reduced frequency leads to an earlier onset of transonic flow. In conclusion, the risk of transonic flow occurring during normal operation of the next generation wind turbines predicted in earlier studies could be corroborated. Moreover, dynamic effects and Reynolds number dependencies can be significant.

A posteriori study on wall modeling in large eddy simulation using a nonlocal data-driven approach

The feasibility of wall modeling in large eddy simulation (LES) using convolutional neural network (CNN) is investigated by embedding a data-driven wall model developed using CNN into the actual simulation. The training dataset for the data-driven wall model is provided by the direct numerical simulation of turbulent channel flow at Reτ=400. The data in the inner layer, excluding y+≤10, are used in the training process. The inputs of the CNN wall model are the velocity components, and the outputs of the wall model are the streamwise and spanwise components of the wall shear stress. An a priori test has already been carried out in our previous study to assess the potential of CNN in establishing a wall model, and the results have shown the reasonable accuracy of the CNN model in predicting the wall shear stress. In this study, the focus is on the a posteriori test, and the performance of the CNN wall model is investigated in the actual LES under various conditions. Initially, the model is used in a simulation with the same specifications as those used for obtaining the training dataset, and the effect of the wall-normal distance of the CNN model inputs is investigated. Then, the model is tested for coarser grid sizes and higher Reynolds number flows to check its generalizability. The performance of the model is also compared with one of the commonly used existing wall models, called ordinary differential equation (ODE)-based wall model. The results show that the CNN wall model has better accuracy in predicting the wall shear stress in the a posteriori test compared to the ODE-based wall model. Moreover, it is able to predict the flow statistics with reasonable accuracy for the wall-modeled LES under various conditions different from those of the training dataset.

Errors and uncertainties in CFD validation for non-equilibrium turbulent boundary layer flows at high Reynolds numbers

NATO AVT-RTG-349 was dedicated to the validation of computational fluid dynamics (CFD) methods based on the Reynolds-Averaged Navier-Stokes (RANS) equations and statistical turbulence models for non-equilibrium turbulent-boundary-layer flows at high Reynolds numbers. This paper describes and discusses the errors and uncertainties arising in the comparison of RANS simulation results with experimental data from wind-tunnel experiments. These errors and uncertainties are associated with the CFD grid and the discretization, the physical modelling, the measurement accuracy, and the differences in the flow conditions between the experimental facility and the computational set-up. The results show the need for a grid-convergence study using systematically-refined families of CFD grids. The two major sources of errors are the RANS turbulence model and the uncertainty originating from the differences between the computational set-up and the wind-tunnel. Then two possible paths for future research are described: future CFD mesh generation, and future validation experiments at high Reynolds numbers.

Tip shape effects on the axial-flow-induced vibration of a cantilever rod

The influence of tip shape on flow-induced vibration of a cantilever rod subjected to axial water flow is experimentally investigated, through optical tracking of the rod movement and mapping of the instantaneous flow field around the rod tip. The experimental setup consists of a vertical cantilever rod housed within a tube. The rod tip shapes considered in this study include a blunt tip and cones with height-to-diameter ratios of 0.5, 1, and 2. The experiments were conducted across a Reynolds number range between 20k to 100k in both clamped-free and free-clamped configurations, representing opposite flow directions. The rod tip motion was captured using fast video image tracking, whereas the flow field near the rod tip was obtained using particle image velocimetry (PIV). The rod vibration dynamics exhibited a primarily fuzzy period-1 behavior, characterized by a periodic motion with a chaotic component. Flutter-like oscillation and buckling were also observed at higher Reynolds numbers, depending on the flow direction. The mechanisms of fluid-structure interaction involved turbulent buffeting and movement-induced excitations. Unsteady flow separation around the rod tip was identified as a further contributing mechanism to flow excitation. In the clamped-free configuration, unsteady flow separation was more pronounced for the cone tips due to the increased rod surface area in the wake region, leading to larger vibration amplitude. In the free-clamped configuration, flow separation effects were more prominent for the blunt tip, as the streamlined cone shapes were less prone to flow separations. Overall, the rod with a blunt tip resulted in smaller displacement in the clamped-free configuration, while the rods with cone tips led to smaller displacement in the free-clamped configuration.

Effects of roughness on non-equilibrium turbulent boundary layers

The effects of roughness were considered as part of a NATO Advanced Vehicle Technology effort titled ‘Non-Equilibrium Turbulent Boundary Layers at High Reynolds Numbers’ (NATO AVT-349). This paper comments on the current state of understanding of the flow physics and modelling efforts to predict rough-wall boundary layer behaviour. Outer layer similarity to smooth wall flows and Reynolds number effects are discussed for zero, favourable, and adverse pressure gradients based on the results of experiments and numerical simulations. Various types of modelling are considered including Reynolds averaged Navier-Stokes (RANS) models with different roughness and turbulence models, wall-modelled large eddy simulations (WMLES), and resolvent models. Current needs and gaps in present understanding are discussed along with recommendations for future experiments and computations.

Energy-conserving finite difference scheme based on velocity interpolation applicable to unsteady flows using collocated grids

The collocation method uses the Rhie–Chow scheme to find the cell interface velocity by pressure-weighted interpolation. The accuracy of this interpolation method in unsteady flows has not been fully clarified. This study constructs a finite difference scheme for incompressible fluids using a collocated grid in a general curvilinear coordinate system. The velocity at the cell interface is determined by weighted interpolation based on the pressure difference to prevent pressure oscillations. The Poisson equation for the pressure correction value is solved with the cross-derivative term omitted to improve calculation efficiency. In addition, simultaneous relaxation of velocity and pressure is applied to improve convergence. Even without the cross-derivative term, calculations can be stably performed, and convergent solutions are obtained. In unsteady inviscid flow, the conservation of kinetic energy is excellent even in a non-orthogonal grid, and the calculation result has second-order accuracy to time. In viscous analysis at a high Reynolds number, the error decreases compared with that of the Rhie–Chow interpolation method. The present numerical scheme improves calculation accuracy in unsteady flows. The possibility of applying this computational method to high Reynolds number flows is demonstrated through several analyses.

Electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid through a rough circular microchannel with surface charge-dependent slip.

This research examines the electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid in a rough circular microchannel while considering the effect of surface charge on slip. The channel wall corrugations are described as periodic sinusoidal waves with small amplitudes. The perturbation method is employed to derive solutions for velocity and volumetric flow rate, and a combination of three-dimensional (3D) and two-dimensional (2D) graphical representations is utilized to effectively illustrate the impacts of relevant parameters on them. The significance of the Reynolds number in investigations of EMHD flow is particularly emphasized. Furthermore, the effect of wall roughness and wave number on velocity and the influence of wall roughness and surface charge density on volumetric flow rate are primarily focused on, respectively, at various Reynolds numbers. The results suggest that increasing the wall roughness leads to a reduction in velocity at low Reynolds numbers ( ) and an increment at high Reynolds numbers ( ). For any Reynolds number, a roughness with an odd multiple of wave number ( ) will result in a more stable velocity profile compared to one with an even multiple of wave number ( ). Decreasing the relaxation time while increasing the retardation time and Hartmann number can diminish the impact of wall roughness and surface charge density on volumetric flow rate, independent of the Reynolds number. Interestingly, in the existence of wall roughness, further consideration of the effect of surface charge on slip leads to a 15% drop in volumetric flow rate at and a 32% slippage at . However, in the condition where the effect of surface charge on slip is considered, further examination of the presence of wall roughness only results in a 1.4% decline in volumetric flow rate at and a 1.6% rise at . These findings are crucial for optimizing the EMHD flow models in microchannels.

Effect of hemispherical ash slag simulants on the thickness distribution and fluctuation characteristics of turbulent liquid film

To explore the influence of ash slag adhering to the scrubbing-cooling tube on the turbulent falling film flow, three hemispheres with different radii (R = 2 mm, 4 mm, and 6 mm) were used to simulate the slag. Ultrasonic Doppler Velocimetry was used to investigate the liquid film’s thickness distribution and fluctuation characteristics under Reynolds number of liquid film Ref ≈8.75 × 103 ––2.63 × 104. The liquid film thickness distribution at low Reynolds numbers exhibits an isosceles triangle when subjected to R = 4 mm and 6 mm hemispheres. At high Reynolds numbers, the average thickness of the liquid film is smaller downstream of the three simulants. The simulants can enhance the liquid film’s perturbations. A mathematical model has been established to predict the mean liquid film thickness on hemispherical simulants, and the relative difference is within 10 %. The probability density distribution curves of the instantaneous liquid film thickness on the simulant exhibit multimodality.

Experimental Parametric Study on Flow Separation Control Mechanisms around NACA0015 Airfoil Using a Plasma Actuator with Burst Actuation over Reynolds Numbers of 105–106

Dielectric barrier discharge plasma actuators (DBD-PAs) have the potential to improve the performance of fluid machineries such as aircrafts and wind turbines by preventing flow separation. In this study, to identify the multiple flow control mechanisms in high Reynolds number flow, parametric experiments for an actuation parameter F+ with a wide range of Re values (105–106) for NACA0015 airfoil was conducted. We conducted wind tunnel tests by applying a DBD-PA to the flow field around a wing model at the leading edge. Lift characteristics, turbulent kinetic energy in the flow field, shear layer height, and the separation point of the boundary layer were evaluated based on pressure distributions on the wing surface and velocity of the flow field, with the effect of DBD-PA on the post-stall flow around the wing and the mechanism behind the increase in the lift coefficient CL analyzed based on these evaluation results. The following phenomena contributed to the increase in CL: (1) increase in turbulent kinetic energy; (2) increase in circulation; and (3) acceleration of the flow near the leading edge. Thus, this study effectively investigated the dependence of the increase in lift on F+ and the lift-increasing mechanism for a wide range of Re values.

Observations of airflow around a supertall curved building and its impact on temperature and humidity in Houston's urban center

Characterization of realistically shaped skyscrapers embedded in non-uniform neighbourhoods experiencing intricate weather patterns remains inadequately investigated. Aiming to close this gap, the Center for Multiscale Applied Sensing team deployed its mobile observatory in the street canyons around the curved Wells Fargo Plaza skyscraper in downtown Houston, TX. Three deployments allowed airflow observations under different inflow wind and thermodynamic stability conditions. Doppler lidar measurements reveal that when inflow hits the curved wall of the skyscraper, perpendicular canyons experience similar vortex configurations creating two windward and two leeward circulations. Windsond measurements support that buoyancy within the deep street canyons can generate thermal updrafts as strong as 2 m s−1 which is sufficient to overturn the mechanical downwash under gentle wind conditions. Canyons experiencing venting during the daytime were observed to be more thermodynamically stable at night while thermodynamically stable canyons during the day were observed to be more thermodynamically unstable at night owing to the accumulation of heat near street-level. Fourier decomposition of the vertical velocity measurements shows that in all cases flow exhibited high Reynolds numbers and was composed of turbulent eddies of predominantly 6 and 15 min periods. This observational dataset provides insights to assess wind load, pedestrian comfort, urban air mobility, and natural ventilation and may be used as a benchmark for numerical model and wind tunnel studies attempting to represent realistically complex urban conditions.

Triad interactions investigated by dual wave component injection

The study of the exchange of momentum and energy between wave components of the turbulent velocity field, the so-called triad interactions, offers a unique way of visualizing and describing turbulence. Most often, this study has been carried out by direct numerical simulations or by power spectral measurements. Due to the complexity of the problem and the great range of velocity scales in high Reynolds number developed turbulence, direct measurements of the interaction between the individual wave components have been rare. In the present work, we present measurements and related computations of triad interactions between controlled wave components injected into an approximately laminar and uniform flow from an open wind tunnel by vortex shedding from two rods suspended into the flow. This results in two-dimensional interactions of three-dimensional turbulence, which makes the analysis of the triadic interactions considerably less complex to analyze than in a fully developed three-dimensional flow. With the information obtained from the computations, we are able to isolate the individual triad interactions contributing to the generated frequency components as the flow develops downstream as well as understanding, mapping out and predicting the strengths of these interactions. The analysis also provides the time constants governing the development of higher order frequency components. We are thus able to see the pattern of frequency combinations, the strengths of the individual mode combinations and the time sequence in which they occur. Any of the higher order combinations is not just the result of a single term in the Navier–Stokes Equation, but a combination of various previous combinations occurring with different strengths and in a varied pattern of generation. The combination of these experiments and computations thus provide unique insight into the inner workings of turbulence and shows how the nonlinear term in the Navier–Stokes equation on average forces the energy towards higher frequencies, which is the reason for the so-called energy cascade.

Hybrid aeroacoustic investigation of turbulent 90° pipe bend flow with source terms from Large-Eddy Simulation

The internal, low Mach number, turbulent flow-induced acoustic field of a cylindrical 90° pipe bend with a curvature radius Rm/D=1.02 is investigated using hybrid Computational Aero-Acoustics (CAA). Incompressible Large-Eddy Simulation (LES) is used to computationally describe the turbulent flow field at bulk Reynolds numbers ReB=5000,12000,26000 and 66000. The incompressible LES predicts all salient flow features, like the separation from the inner wall of the bend followed by a turbulent recirculation zone, in good agreement with literature. The internal flow-induced noise is predicted by Acoustic Propagation Simulations (APS) applying Lighthill’s Equation (LE), Ribner’s Dilatation Equation (RDE) and the Perturbed Convective Wave Equation (PCWE), provided with acoustic source terms obtained from the incompressible LES. The turbulent recirculation zone is the most active region for generating acoustic sources. Among the two constituent components of the PCWE source term, the local pressure time derivative term turned out as clearly dominant in this region, so that PCWE and RDE predicted similar acoustic fields. The sub-grid scale (SGS) model applied in LES notably contributes only at high frequencies to the total LE source term, starting from f=2000 Hz for the lower Reynolds numbers and beyond for the higher. The mapping of source terms from the boundary layer resolving LES grid onto the typically coarser preferably uniform APS grid leads to lower high-frequency signal amplitudes for coarser APS mesh size in regions with small turbulent structures. The impact of this amplitude reduction on the predicted acoustics sound power levels was still very small, exhibiting relative differences less than 0.7% for the different APS meshes. Despite the LES-specific limitations expected from the decrease of directly resolved content for higher Reynolds numbers, the use of increasingly underresolved source terms did not significantly lower the accuracy of finally predicted acoustics. The comparison of the acoustic results against data from dedicated measurements generally showed very good agreement for all Reynolds numbers.

Behind the Non-Uniform Breakup of Bubble Slug in Y-Shaped Microchannel: Dynamics and Mechanisms.

Bubble flow in confined geometries is a problem of fundamental and technological significance. Among all the forms, bubble breakup in bifurcated microchannels is one of the most commonly encountered scenarios, where an in-depth understanding is necessary for better leveraging the process. This study numerically investigates the non-uniform breakup of a bubble slug in Y-shaped microchannels under different flow ratios, Reynolds numbers, and initial bubble volumes. Overall, the bubble can either breakup or non-breakup when passing through the bifurcation and shows different forms depending on flow regimes. The flow ratio-Reynolds number phase diagrams indicate a power-law transition line of breakup and non-breakup. The bubble takes longer to break up with rising flow ratios yet breaks earlier with higher Reynolds numbers and volumes. Non-breakup takes less time than the breakup patterns. Flow ratio is the origin of non-uniform breakup. Both the Reynolds number and initial volume influence the bubble states when reaching the bifurcation and thus affect subsequent processes. Bubble neck dynamics are analyzed to describe the breakup further. The volume distribution after breaking up is found to have a quadratic relation with the flow ratio. Our study is hoped to provide insights for practical applications related to non-uniform bubble breakups.

A three-dimensional pseudo-potential multiphase model with super-large density ratio and adjustable surface tension

In this paper, an improved three-dimensional pseudo-potential multiphase flow model is proposed. A high-precision difference scheme is employed to improve the computational accuracy of the interaction forces to achieve super-large density ratio. The present model is verified to obtain two-phase density ratio up to hundreds of thousands for all selected equations of state, and the spurious currents can be suppressed to a relatively low level. A modification pressure tensor is introduced to implement a wide range of surface tension adjustments independently of the density ratio. The model is applied to simulate droplet impacts on a liquid film as well as droplet impacts on a dry surface. Numerical results show that the model still has good numerical stability in simulating complex fluid problems with very large density ratio, adjustable surface tension, high Reynolds number, or containing the wettable surface. In addition, to improve the computational efficiency, an efficient parallel algorithm based on graphics processing unit (GPU) is designed for the present model. A maximum speedup ratio of 687 times is obtained compared to the corresponding CPU-based serial algorithm, which can significantly accelerate the numerical simulation study.

Turbulent vortex pair at equilibrium and its interaction with the ground at

A turbulent two-vortex system (T-2VS) is obtained by inserting analytical model wake vortices into very weak homogeneous isotropic turbulence (HIT) and by evolving them in time using large-eddy simulation until a turbulent state at statistical equilibrium is reached. The T-2VS is characterised as follows: circulation distribution of the vortices; energy of the mean and fluctuating fields; energy dissipation rate. It is also verified that essentially the same T-2VS is obtained when varying the initial model or initial HIT perturbation. A wall-resolved simulation of the T-2VS further interacting with a smooth ground is then performed at $Re_\varGamma = 2 \times 10^5$ ; this is $10 \times$ higher than in previous works, which allows us to better capture the high Reynolds number behaviour. The high release height of the T-2VS also ensures a physically correct approach to the ground. The results are compared with the literature and also to what is obtained for the case of non-turbulent vortices interacting with the same ground at the same Reynolds number. The flow topologies are discussed, and significant differences are highlighted regarding the separation of the boundary layer generated at the ground, and the way this secondary vorticity interacts with the primary vortices and makes them decay. The vortex trajectories are also measured, together with their circulation distribution and global circulation evolution, and the differences are discussed.