Kinetic Energy Transport Research Articles

Three-dimensional evolution and turbulent kinetic energy transport of tip vortex from an elliptical hydrofoil

A non-cavitating tip vortex generated by an elliptical hydrofoil is investigated utilizing tomographic particle image velocimetry (TPIV). Focus is placed on its three-dimensional evolution over a relatively large streamwise region, as well as the transport process of turbulent kinetic energy (TKE). Based on the variations in vortex structure and related vortex properties, three main stages of tip vortex evolution can be identified: formation stage, persistence stage, and decay stage. The boundary between the formation and persistence stages is the position where tip vortex cavitation (TVC) is more prone to incept, attributed to the rapid growth in vortex circulation and vortex-center axial velocity, along with high turbulent fluctuations. During the tip vortex evolution, its swirling momentum significantly influences the axial flow pattern, likely by altering the pressure gradient along the vortex path. TKE transport equation is employed to analyze the turbulent properties of the tip vortex. Flow near the hydrofoil tip is highly turbulent and unsteady, with the local TKE at an excessive level. The local high TKE tends to diffuse into surrounding flow rather than being concentrated within the tip vortex as it moves downstream. TKE is mainly produced on the suction side of hydrofoil, potentially due to local boundary-layer behaviors, and is subsequently transported into the vortex core. As the tip vortex propagates further downstream, the in-core TKE exhibits a decreasing trend, and a relaminarization process appears to occur in far wake region. The flow topology of the tip vortex is examined with the invariants of velocity gradient tensor, providing insights into the topological features during the vortex evolution.

Turbulence modulation in liquid–liquid two-phase Taylor–Couette turbulence

We investigate the coupling effects of the two-phase interface, viscosity ratio and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor–Couette turbulence at a system Reynolds number of $6\times 10^3$ and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, whereas light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. In addition, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the physics of turbulence modulation by the dispersed phase in two-phase turbulence systems.

Aerodynamic Performance and Numerical Validation Study of a Scaled-Down and Full-Scale Wind Turbine Models

Understanding the aerodynamic performance of scaled-down models is vital for providing crucial insights into wind energy optimization. In this study, the aerodynamic performance of a scaled-down model (12%) was investigated. This validates the findings of the unsteady aerodynamic experiment (UAE) test sequence H. UAE tests provide information on the configuration and conditions of wind tunnel testing to measure the pressure coefficient distribution on the blade surface and the aerodynamic performance of the wind turbine. The computational simulations used shear stress transport and kinetic energy (SST K-Omega) and transitional shear stress transport (SST) turbulence models, with wind speeds ranging from 5 m/s to 25 m/s for the National Renewable Energy Laboratory (NREL) Phase VI and 4 m/s to 14 m/s for the 12% scaled-down model. The aerodynamic performance of both cases was assessed at representative wind speeds of 7 m/s for low, 10 m/s for medium, and 20 m/s for high flow speeds for NREL Phase VI and 7 m/s for low, 9 m/s medium, and 12 m/s for the scaled-down model. The results of the SST K-Omega and transitional SST models were aligned with experimental test measurement data at low wind speeds. However, the SST K-Omega torque values exhibited a slight deviation. The transitional SST and SST K-Omega models yielded aerodynamic properties that were comparable to those of the 12% scaled-down model. The torque values obtained from the simulation for the full-scale NREL Phase VI and the scaled-down model were 1686.5 Nm and 0.8349 Nm, respectively. Both turbulence models reliably predicted torque and pressure coefficient values that were consistent with the experimental data, considering specific flow regimes. The pressure coefficient was maximum at the leading edge of the wind turbine blade on the windward side and minimum on the leeward side. For the 12% scaled-down model, the flow simulation results bordering the low-pressure region of the blade varied slightly.

Momentum and kinetic energy transport in supersonic particle-laden turbulent boundary layers

Momentum and kinetic energy transport in supersonic particle-laden turbulent boundary layers

Interfacial modulation of Ti3C2Tx MXene using functionalized cellulose nanofibrils for enhanced electrochemical actuation

Electrochemical actuators (ECAs) with low voltage actuation and large deformation ranges generally require electrode materials with high ion kinetic energy transport, high charge storage, and excellent electrochemical-mechanical properties. However, the fabrication of such actuators remains a major challenge. In the present work, hybrid electroactive films were fabricated by self-assembling one-dimensional functionalized cellulose nanofibrils (CNFs) with two-dimensional MXene (Ti3C2Tx). The obtained ECA actuators fabricated by carboxymethylated cellulose nanofibrils (consisting of -CH2COO−surface groups) with Ti3C2Tx integrate excellent curvature (0.1041 mm−1), mechanical strength (21.68 MPa), a bending strain of 0.50 %, and a good actuation displacement of 9.3 mm at a low voltage range of −0.6 to 0.3 V. This may be attributed to the enlarged layer spacing (15.34 Å), which makes the embedding and transport of H+ easier, and excellent adaptivity of mechanical properties achieved by molecular-scaled strong hydrogen bonding, leading to better actuation performance. This study provides a potential research direction for the preparation of ECAs with large actuation deformation.

Flow Field Characteristics at the Spanwise Edge of a Vegetative Canopy Model

This study investigates the complex flow field across a spanwise vegetative model canopy edge focusing on turbulent transport processes. Utilizing stereoscopic particle image velocimetry, the three velocity components were measured in wall-parallel planes at various elevations within canopy across the spanwise canopy edge. Conventional ensemble averaged results were contrasted with those obtained by conditionally averaged flow properties across instantaneous internal interfaces in the flow to understand their contribution to the ensemble average. The conditional average captured the strong gradients in mean velocities, Reynolds stresses, vorticity, swirling strength, and turbulent kinetic energy production across the dynamically changing instantaneous interface. In contrast, the conventional ensemble average smeared out the strong gradients. Small magnitudes of advective terms in the turbulent kinetic energy transport equation suggested weak secondary transverse flows in the present model canopy. The turbulent flow structure across the spanwise canopy edge was further investigated using Quadrant-Hole analysis for both averaging approaches. Conventional ensemble averaged results indicated a shift from sweep to ejection dominance when moving from canopy into the open patch, while the conditional average showed only sweep dominated transport. In contrast to a homogeneous canopy layout, below canopy height at the canopy edge, sweeps and ejections lose their dominance in vertical turbulent transport. The present results show that the dynamics of internal interfaces govern the ensemble averaged results and a possible implementation into existing models is proposed. The present results are expected to increase understanding of spanwise turbulent transport and aid in developing strategies to mitigate desertification.

Direct numerical simulation of laminar boundary layer interaction with a wall-mounted circular cylinder at low-Reynolds number

In our current study, we employ direct numerical simulation to investigate the interaction between a laminar boundary layer flow and a wall-mounted circular cylinder with an aspect ratio of 4 and a Reynolds number of 750, based on the cylinder diameter and free-stream velocity. As highlighted in recent works by Morton et al. [Int. J. Heat Fluid Flow 72, 109–122 (2018)] and Crane et al. [J. Fluid Mech. 931, R1 (2022)], understanding of flow at low-Reynolds number around wall-mounted circular cylinders remains limited, motivating our study to contribute to this knowledge gap. Our objectives include exploring flow topology, analyzing first- and second-order statistics to characterize the turbulent wake flow, and investigate turbulent kinetic energy transport budgets to comprehend energy transfer mechanisms behind the cylinder. Our spectral analysis of velocity content reveals a low-frequency peak, consistent with recently published literature. However, we observe certain discrepancies between our findings and those of similar studies conducted at lower Reynolds numbers, particularly regarding the frequency content of the wake region. We employ dynamic mode decomposition to unravel the flow dynamics associated with the highest-amplitude mode. Our results indicate that the low-frequency mode reported in the above-mentioned references primarily correlates with the incoming boundary layer and is prominently evident in the lateral force coefficient, in contrast to scenarios at higher Reynolds numbers.

Plant Morphology Impacts Bedload Sediment Transport

AbstractBedload sediment transport plays an important role in the evolution of rivers, marshes and deltas. In these aquatic environments, vegetation is widespread, and plant species have unique morphology. However, the impact of real plant morphology on flow and sediment transport has not been quantified. This study used model plants with real plant morphology, based on the aquatic species Phragmites australis, Acorus calamus and Typha latifolia. The frontal area of these species increases away from the bed, which leads to higher near‐bed velocity than would be predicted from depth‐average frontal area. A plant morphology coefficient was defined to quantify the impact of vertically‐varied plant frontal area. Laboratory experiments confirmed that the plant morphology coefficient improved the prediction of near‐bed velocity, near‐bed turbulent kinetic energy and bedload transport rate in canopies with realistic morphology. Plant morphology can alter transport rates by up to an order of magnitude, relative to the assumption of uniform morphology.

Direct numerical simulation of shock wave/boundary layer interaction controlled by steady microjet in a compression ramp

Shock wave/boundary layer interaction in a 24° turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation. Three different jet spacings which are termed as sparse, moderate and dense are considered, and the induced vortex system and shock structures are compared. A moderate jet spacing configuration is found to generate counter-rotating vortex pairs that transport high-momentum fluid towards the vicinity of wall and strengthen the boundary layer to resist separation, reducing the separation region. The dense jet spacing configuration creates a larger momentum deficit region, reducing the friction downstream of the corner. Analysis of pressure and pressure gradient reveals that dense jet spacing configuration reduces the intensity of separation shock. The impact of varying jet spacings on the turbulent kinetic energy transport mechanism is also investigated by decomposing the budget terms in the transport equation. Furthermore, the spectral characteristics of the separation region are studied using power spectral density and dynamic mode decomposition methods, revealing that moderate jet spacing configuration suppresses low-frequency fluctuations in the separation region.

Erosion rate of lunar soil under a landing rocket, part 1: Identifying the rate-limiting physics

Multiple nations are planning activity on the Moon's surface, and to deconflict lunar operations we must understand the sandblasting damage from rocket exhaust blowing soil. Prior research disagreed over the scaling of the erosion rate, which determines the magnitude of the damage. Reduced gravity experiments and two other lines of evidence now indicate that the erosion rate scales with the kinetic energy flux at the bottom of the laminar sublayer of the gas. Because the rocket exhaust is so fast, eroded particles lifted higher in the boundary layer do not impact the surface for kilometers (if at all; some leave the Moon entirely), so there is no saltation in the vicinity of the gas. As a result, there is little transport of gas kinetic energy from higher in the boundary layer down to the surface, so the emission of soil into the gas is a surprisingly low energy process. In low lunar gravity, a dominant source of resistance to this small energy flux turns out to be the cohesive energy density of the lunar soil, which arises primarily from particles in the 0.3 to 3 μm size range. These particles constitute only a tiny fraction of the mass of lunar soil and have been largely ignored in most studies, so they are poorly characterized.

A modification of production term for the shear stress transport turbulence model based on a new wall-law for adverse pressure gradient

This paper presents an attempt to improve the predictive accuracy of the Menter shear stress transport (SST) turbulence model for adverse pressure gradient (APG) flows. The foundation of this work lies in the newly modified law of the wall and turbulent kinetic energy (TKE) transport equation within the APG turbulent boundary layer. The modification of the law of the wall is achieved through a newly proposed variable λ, which is derived theoretically and calibrated using direct numerical simulation data. Based on the new law of the wall, we analyze the TKE transport equation of the SST model at APG and demonstrate that the analytical solution satisfying the law of the wall cannot achieve equilibrium in the current SST model. Further theoretical analysis reveals that this imbalance is caused by the TKE production term Pk, and the decomposition of the wall friction coefficient Cf indicates that Pk directly affects the prediction of flow separation. Based on the analysis and the new law of the wall, an additional term for Pk is suggested to correct Pk and improve the model's predictive accuracy for APG flows. Numerical validation results show that the correction leads to an increase in Pk within the APG turbulent boundary layer, resulting in more accurate predictions of Cf and the mean velocity profile in the inner layer of the turbulent boundary layer.

Numerical modeling of self-aerated flows: Turbulence modeling and the onset of air entrainment

Numerical modeling of self-aerated flows is essential for understanding water systems and designing hydraulic structures. This work discusses and extends a theoretical/numerical model to represent air entrainment in self-aerated flows, which includes a criterion to define the occurrence of air entrainment, based on a balance between disturbing and stabilizing energies. The impact of the turbulence closure on the modeling of the onset of air entrainment and the distribution of bubble concentration is studied with particular emphasis. This work shows that uniform-density formulations of Reynolds-averaged Navier–Stokes closures lead to severe overprediction of air entrainment due to unphysical transport of turbulent kinetic energy generated in the air phase to the water phase. In contrast, combining variable-density turbulence closures with the energy balance criterion enables accurate prediction of the regions where air is entrained for stepped spillways and plunging jets. The choice of turbulence closure significantly influences the proposed criterion, emphasizing the importance of selecting an appropriate closure for an accurate description of the air entrainment process. Based on the conducted tests, the standard k−ε and buoyancy modified k−ε models better predict the onset of air entrainment and bubble distribution in stepped spillways, while the k−ω SST model proves to be more effective in capturing air entrainment at the impingement point in plunging jets. This study expands the capabilities of numerical models in predicting air entrainment and provides valuable insights into the effects and interrelations of the turbulence modeling, the air entrainment occurrence criteria, and the bubble transport equations.

Turbulent transports in the flow around a rectangular cylinder with different aspect ratios

The flow around a rectangular cylinder exhibits intricate features, encompassing phenomena such as separation, reattachment, boundary layer transition, and relaminarization. This study explores the intense transport of turbulent fluctuations in these complex flow phenomena, including momentum and turbulent kinetic energy (TKE) transport, for three aspect ratios (L/D=5,10 and 15) at a medium Reynolds number (Re=1000). The connection between these transports and crucial vortical structures is elucidated for the first time. On the lateral side of the cylinder, strong momentum transport occurs, dominated by ejection and sweep events associated with the hairpin vortex. The generation of the LE vortex also leads to active TKE production. The existence of the LE separation bubble, as well as the relaminarization of the downstream boundary layer at L/D=10 and 15, affects the distribution of production terms. This perspective offers an effective yet novel approach that has not been previously addressed in prior researches. The redistribution of TKE results in a disturbance growth, linked to boundary layer transition. The source term reveals that streamwise TKE carried into the recirculating region is closely related to the frequency prior amplified by the LE shear layer. In the wake behind TE, turbulent transports are influenced by vortex shedding patterns.

Data-driven approach for modeling Reynolds stress tensor with invariance preservation

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) (Ling et al., 2016) are involved and applied. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier–Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user’s defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.

Turbulent kinetic energy transport in high-speed turbulence subject to wall disturbances

Wall disturbances in high-speed turbulent boundary layers induce large-scale motions in the outer region even when the Reynolds number is not sufficiently high for their existence in the case of smooth wall flows. In the present study, we investigate the dynamics of these outer region large-scale motions by exploiting the scale-by-scale energy transport in the spectral space. By scrutinizing the disparity in the budget terms of the turbulent kinetic energy spectra between turbulence over smooth and disturbed walls, we found that the intensification of the large-scale motions in the outer region is statistically correlated with the stronger interaction between the Reynolds stress and the mean shear, i.e. the production term of the turbulent kinetic energy. The corresponding turbulent kinetic energy is then transferred to smaller-scale motions and dissipated by viscosity, whereas the effects of spatial diffusion and mean convection are insignificant and are dimly affected by the wall disturbances. These dynamic processes are roughly irrelevant to the Mach numbers, and processes related directly to the genuine compressibility effects, namely the dilatational motions and mass flux, are trivial. The outer large-scale motions contribute to the skin friction by approximately 19% ∼45% compared with 4% in smooth wall cases in terms of the mean kinetic energy transport, suggesting that the drag increment in turbulent boundary layers in the presence of wall disturbances should be partly attributed to their intensification.

Improvements in the Prediction of Steady and Unsteady Transition and Mixing in Low-Pressure Turbines by Means of Machine-Learnt Closures

Abstract In this article, novel machine-learnt transition and turbulence models are applied to the prediction of boundary-layer transition and wake mixing in a low-pressure turbine (LPT) cascade, including unsteady inflow cases with incoming wakes. A laminar kinetic energy (LKE) transport approach is employed as baseline transition framework. The application of the machine-learnt explicit algebraic Reynolds stress models (EARSMs) takes advantage of a zonal strategy based on a newly developed sensing function that allows automated wake demarcation. This work compares the performance of several approaches that are based on the application of improved transition models without machine learnt EARSMs, baseline transition model with EARSMs trained for improved wake mixing, and new transition and turbulence closures that are simultaneously developed in a fully coupled way and aimed at improving both transition and wake mixing predictions in LPTs. The investigation is carried out on a cascade of industrial footprint, representative of modern LPT bladings. First, the various modeling frameworks are evaluated, without bar wakes (steady conditions), over a wide range of Reynolds number values. Unsteady Reynolds-averaged Navier–Stokes (URANS) analyses have also been carried out to investigate the predictive capabilities of machine-learnt closures in the presence of incoming bar wakes. Reynolds-averaged Navier–Stokes (RANS)/URANS results are scrutinized against large eddy simulation (LES) calculations and experimental data. It will be demonstrated that machine-learnt EARSMs are capable of producing realistic wake mixing when simply applied on top of the baseline transition models. However, the most accurate predictions will be shown to be provided by fully integrated machine-learnt transition/turbulence closures.

Analysis of Near-wall Coherent Structure of Spiral Flow in Circular Pipe Based on Large Eddy Simulation

Based on the large eddy simulation method, this study performed the three-dimensional transient numerical analysis of the near-wall flow field of the spiral flow in a circular pipe and applied the sub-grid model of the kinetic energy transport. The low-speed bands, streamwise vortices and hairpin vortices of the spiral flow in the near-wall region of the circular pipe are determined using the Q criterion. The ejection and sweeping of coherent structures are identified using the velocity vector of the near-wall region; moreover, the two methods of creating the hairpin vortices are established by the image time series. The results demonstrate that the development directions of the near-wall bands, streamwise vortices and hairpin vortices of the spiral flow in the circular pipe develop along the path of the spiral line. The average spanwise period of the low-speed bands in the near-wall region is approximately 120 wall units, the length is more than 900 wall units and the height is not more than 40 wall units. The separation distance of the streamwise vortices is about 119 wall units. It has a certain angle with the wall (approximately 22°). The average burst period of a hairpin vortices is less than 0.015 s.

Fluctuation characteristics induced by energetic coherent structures in air-core vortex: The most complex vortex in the tidal power station intake system

The air-core vortex is the most complex vortex in the intake system of tidal power stations. Nearly all power plants prohibit the operation of units with air-core vortices, as these vortices not only contain air but also induce significant inflow fluctuations that can potentially lead to significant damage to the units. The current understanding of the fluctuation characteristics and mechanisms induced by energetic coherent structures in the air-core vortex flow is very limited. To address this, the coupled level-set and volume-of-fluid large-eddy simulations are conducted to investigate the energetic coherent structures that cause power output fluctuations. Two critical frequencies have been identified in the energy spectra of the velocity field: the air-core vortex meandering frequency and the shear vortex shedding frequency. The level and trend of the spectrum density at low frequencies are determined by the large-scale energy structure represented by the air-core vortex. The shear vortices are initially formed from a shear separation layer that eventually evolves into streamwise vortices downstream. When the air-core vortex enters the pipe, it breaks up and merges with the near-wall coherent structures. The enhanced velocity and pressure fluctuations, induced by air-core vortices and coherence structures, are analyzed using the turbulent kinetic energy transport equation, revealing that the production term dominates the development of turbulent kinetic energy. Moreover, the diffusion term is responsible for transferring energy through the evolution of turbulent structures. The energy loss induced by fluctuations is investigated using the entropy production method. We find that the direct dissipation of entropy production is mainly induced by air-core vortices, while the side-wall coherent structures in the pipe contribute to the turbulent dissipation.

The Role of Multiscale Interaction in the Maintenance and Propagation of MJO in Boreal Winter

Abstract The multiscale interaction and its role in the maintenance and propagation of the Madden–Julian oscillation (MJO) has been investigated using the newly developed multiscale window transform (MWT), the theory of canonical transfer, and the MWT-based multiscale energetics analysis (here particularly for this study, dry energetics analysis). The field variables are reconstructed/filtered with MWT onto three scale windows, namely a high-frequency window, intraseasonal window, and low-frequency window. Compositing the intraseasonal fields with respect to the real-time multivariate MJO (RMM) index unambiguously shows that the zonal extents of the easterlies and westerlies of MJO vary with the RMM phases, among which phases 4 and 2 are representative. In the former phase, the MJO has easterlies and westerlies within the same extent, while in the latter their extents are quite different. In phase 4, besides the previously discovered mechanisms such as pressure work and buoyancy conversion, the MJO is also energized by the canonical kinetic energy (KE) transfer from the low-frequency window to the intraseasonal window (signifying barotropic instability) on the west of its convection. But on the eastern side, MJO loses KE to the low-frequency window. The KE transport also functions like an energy sink. In phase 2, the MJO variabilities can be divided into an eastern part and a western part. The former is essentially the same as that in phase 4; for the latter, barotropic instability dominates. On the available potential energy (APE) budget, baroclinic instability and intraseasonal APE transport help produce and maintain the temperature anomalies. In contrast to previous energetics studies, our findings highlight the essential role played by multiscale interactions.

Turbulent boundary layer flow over a three-dimensional sinusoidal surface

The sinusoidal roughness effect is investigated using a direct numerical simulation (DNS) of a spatially developing turbulent boundary layer (TBL) over three-dimensional sinusoidal roughness. The validity of Townsend's outer-layer similarity hypothesis is assessed based on comparisons of mean and second-order flow statistics, with a DNS of smooth-wall TBL data set at a similar Reynolds number. The total, Reynolds and dispersive stress tensors are calculated using the double-averaging procedure. The mean and second-order statistical similarities in the outer layer between rough-wall and smooth-wall TBLs are generally observed. The transport between total, turbulent and dispersive kinetic energy is investigated utilising triple-decomposed kinetic energy transports equations. The transport behaviour of turbulent kinetic energy (TKE) is significantly affected by the local mean shear induced by the surface roughness. However, the TKE transport shows good collapse with the smooth-wall case in the outer region of the flow. On the other hand, the transport of dispersive kinetic energy, including local production, redistribution and dissipation, are confined within the roughness sublayer. The intercomponent transfer between TKE and dispersive kinetic energy is quantified from the triple-decomposed kinetic energy transport equations. The intercomponent energy transfer is associated with the local spatial gradients of the turbulent momentum fluxes generated near the roughness canopy.