Turbulent Kinetic Energy Generation Research Articles

Observations of Elevated Mixing and Periodic Structures Within Diurnal Warm Layers

AbstractSurface drifters (SWIFTs) equipped with down‐looking high‐resolution acoustic doppler current profilers (ADCPs) were used to estimate the turbulent kinetic energy (TKE) dissipation rate within highly stratified diurnal warm layers (DWLs) in the Southern California Bight. Over a 10‐day period, five instances of DWLs were observed with strong surface temperature anomalies up to 3°C and velocity anomalies up to 0.3 m . Profiles of in the upper 5 m suggest turbulence is strongly modulated by the DWL stratification. Burst‐averaged (8.5 min) is stronger than predicted by law‐of‐the‐wall boundary layer scaling within the DWLs and suppressed below. Predictions for within the DWLs are improved by a shear‐production scaling using observed shear and linearly decaying turbulent stress. However, is still under‐predicted. Examination of the un‐averaged acoustic backscatter data suggests elevated is related to the presence of turbulent structures in the DWLs which span the layer height and strongly modulate TKE. Evolution in the bulk Richardson number each day suggests the DWLs become unstable to layer‐scale overturning and entrainment each afternoon, thus the turbulent structures may result from shear‐driven instability. This interpretation is supported by a conditional average of the data during a burst characterized by strongly periodic structures. The structures resemble high‐frequency internal waves with strong asymmetry in the along‐flow direction (steepening) which suggests they are unstable. Coincident asymmetric patterns in upwelling/downwelling and corresponding regions of strong vertical convergence/divergence suggest that both vertical transport and local TKE generation are plausible sources of elevated in the DWLs.

Research on the Influence of Particles and Blade Tip Clearance on the Wear Characteristics of a Submersible Sewage Pump

A submersible sewage pump is designed for conveying solid–liquid two-phase media containing sewage, waste, and fiber components, through its small and compact design and its excellent anti-winding and anti-clogging capabilities. In this paper, the computational fluid dynamics–discrete element method (CFD-DEM) coupling model is used to study the influence of different conveying conditions and particle parameters on the wear of the flow components in a submersible sewage pump. At the same time, the energy balance equation is used to explore the influence mechanism of different tip clearance sizes on the internal flow pattern, wear, and energy conversion mechanism of the pump. This study demonstrates that increasing the particle volume fraction decreases the inlet particle velocity and intensifies wear in critical areas. When enlarging the tip clearance thickness from 0.4 mm to 1.0 mm, the leakage vortex formation at the inlet is enhanced, leading to increased wear rates in terms of the blade and volute. Consequently, the total energy loss and turbulent kinetic energy generation increased by 3.57% and 2.25%, respectively, while the local loss coefficient in regard to the impeller channel cross-section increased significantly. The findings in this study offer essential knowledge for enhancing the performance and ensuring the stable operation of pumps under solid–liquid two-phase flow conditions.

Temporal-spatial and energy dissipation characteristics of vortex evolutions in Francis turbine during load reduction

This study numerically investigates the load reduction effects, on a model Francis turbine, combining cavitation model and structured dynamic grid technique. The results indicate that the vapor volume in the draft tube undergoes two rapid increases and decreases until cavitation ceases. The precessing vortex rope transitions from a strong helical structure to axial contraction as ellipticity increases, ultimately forming a discrete band before disappearing. Initially, vapor volume in the runner increases gradually and linearly, followed by continued growth with a consistent pulsation amplitude. The inter-blade vortex (IBV) first appears at the blade trailing edge and then develops into a complete structure extending from the runner crown to the blade trailing edge, driven by pulsating vapor volume growth. Axial force extracted by the runner changes significantly and correlates closely with variations in the vapor volume in the runner. Flow separation in the runner occurs near the runner crown, forming dual separation lines that enhance IBV formation, which highlights the significant influence of crown-proximal flow separation on IBV development. Regarding energy loss, initial decreases followed by increases are observed in both the draft tube and runner, with draft tube losses consistently exceeding 57.4% and runner losses exceeding 27.1%. Turbulent kinetic energy generation and Reynolds stress are the primary forms of energy dissipation, with high-value regions corresponding to vortex locations, underscoring the substantial role of vortices in energy dissipation. This study provides new insights into the evolution of vortices and energy dissipation characteristics during load reduction in Francis turbines.

Numerical assessment of transient flow and energy dissipation in a Pelton turbine during startup

The Pelton turbine, known for its high application water head, wide efficient operating range, and rapid start-stop capability, is ideal for addressing intermittent and stochastic load issues. This study numerically analyzes the transient two-phase flow and energy dissipation during the startup of a Pelton turbine. Dynamic mesh technology controlled nozzle opening changes, and momentum balance equations managed runner rotation. Findings showed that the runner speed initially increased rapidly and then more slowly, and flow rate matched the nozzle opening variations. Runner torque first rose linearly, then decreased, with the fastest decline during nozzle closing. Hydraulic efficiency peaked early in nozzle reduction but then dropped sharply. Strong vortices formed due to upstream inflow and downstream backflow impact in the distributor pipe. The jet needle and guide vane improved flow in the converging section of nozzle, but flow began to diffuse with increased stroke. Initially, the jet spread fully on the bucket surface, but later only affected the bucket tips. Pressure fluctuations in the water supply mechanism were primarily due to jet needle motion, with higher amplitude during movement and lower when stationary. These fluctuations propagated upstream, weakening over distance. Reynolds stress work and turbulent kinetic energy generation, respectively, dominated energy transmission and energy dissipation, with their maximum contribution exceeding 96% and 70%. High-energy clusters corresponded to jet impact positions, highlighting jet-bucket interference as crucial for energy transport. This study established a performance evaluation method for Pelton turbine startups, supporting further investigation into characteristic parameters, flow evolution, and energy dissipation patterns.

The investigation on the flow characteristics during the continuous development of the tip leakage vortex cavitation in an axial pump-jet propulsion

The continuous deterioration and development of tip leakage vortex (TLV) cavitation in the pump-jet propulsion significantly affect propulsion performance and operational stability. Larger eddy simulation and cavitation tunnel experiment are utilized to investigate the temporal and spatial evolution characteristics of TLV cavitation under varying cavitation conditions. The results reveal that the continuous development of TLV cavitation prompts the TLV to gradually move away from the blade suction surface due to increasing pressure difference at the blade tip surface. Furthermore, the development of TLV cavitation amplifies the effect of the radial outward Coriolis force and makes the TLV even more unstable. Under the influence of the tip leakage flow, primary generation of turbulent kinetic energy (TKE) persistently migrates to the TLV core center and subsequently travels downstream. Despite the large magnitude of TKE that occurs at the TLV core center, the TKE generation remains low. With the inception of TLV cavitation, the transport of TKE between the TLV core center and the surrounding flow gradually intensifies, followed by a subsequent weakening of this transport effect. It increases again as the breakdown of TLV becomes more severe.

Numerical study on thermal–hydraulic performance of hydrocarbon fuel under trans-critical states and supercritical CO2 in a zigzag printed circuit heat exchanger

The supercritical CO2 closed-Brayton-cycle (CBC) is a highly promising integrated scheme for cooling and power generation in hypersonic vehicles. However, the CO2-fuel printed circuit heat exchanger (PCHE) in the CBC faces extreme heat loads and fuel consumption constraints, leading to complex heat transfer phenomena including trans-critical processes and buoyancy effects. In this study, the coupled heat transfer process between the large-molecule hydrocarbon fuel and supercritical CO2 inside the zigzag-type PCHE is investigated using a numerical simulation, based on the practical constraints of the onboard CBC system. The results demonstrate that the distributions of eddy viscosity and specific heat within the boundary layer are significantly improved by the turbulence-enhancing effect of the zigzag channel, thus avoiding local heat transfer deterioration caused by trans-critical processes. Additionally, numerous small-scale vortex structures are found to increase the source term of turbulent kinetic energy generation, effectively suppressing the weakening effect of buoyancy on turbulence. Finally, an optimization study is conducted on the resistance of the zigzag channel starting from the power generation performance of the CBC system. The findings indicate a 71% reduction in pressure loss coupled with only a 7% reduction in volume heat transfer rate compared to the original configuration.

Forest density is more effective than tree rigidity at reducing the onshore energy flux of tsunamis

Communities around the world are increasingly interested in nature-based solutions to the mitigation of coastal risks by coastal forests, but it remains unclear how much protective benefits vegetation provides, particularly in the limit of highly energetic flows after tsunami impact. The current study, using a three-dimensional incompressible computational fluid dynamics model with a fluid–structure interaction approach, aims to quantify how energy reflection and dissipation vary with different degrees of rigidity and vegetation density of a coastal forest. We represent tree trunks as cylinders and use the elastic modulus of hardwood trees such as pine or oak to characterize the rigidity of these cylinders. The numerical results show that energy reflection increases with rigidity only for a single cylinder. In the presence of multiple cylinders, the difference in energy reflection created by varying rigidity diminishes as the number of cylinders increases. Instead of rigidity, we find that the blockage area created by the presence of multiple tree trunks dominates energy reflection. As tree trunks are deformed by the hydrodynamic forces, they alter the flow field around them, causing turbulent kinetic energy generation in the wake region. As a consequence, trees dissipate flow energy, highlighting coastal forests reducing the onshore energy flux of tsunamis by means of both reflection and dissipation.

On the Lateral Entrainment Instability in the Inner Core Region of Tropical Cyclones

AbstractEntrainment of dry moat air with low equivalent potential temperature laterally into the eyewall and rainbands is a unique turbulent process in the inner‐core region of a tropical cyclone (TC). By analyzing in‐situ aircraft measurements collected by the reconnaissance flights that penetrated the eyewalls and rainbands of Hurricanes Rita (2005), Patricia (2015), Harvey (2017), and Michael (2018), as well as numerical simulations of Hurricanes Patricia (2015), and Michael (2018), we show that the moat air entrained into the eyewall and rainbands meets the instability criterion, and therefore, sinks unstably as a convective downdraft. The resultant positive buoyancy fluxes are an important source for the turbulent kinetic energy (TKE) in the eyewall and rainband clouds. This mechanism of TKE generation via lateral entrainment instability should be included in the TKE‐type turbulent mixing schemes for a better representation of turbulent transport processes in numerical forecasts of TCs.

Direct numerical simulation of the fully developed turbulent free convection flow in an asymmetrically heated vertical channel

We report direct numerical simulations of the fully developed turbulent natural convection flow of a Boussinesq fluid (Pr = 0.71) in a vertical channel. One wall is heated with a constant heat flux and the other is assumed to be perfectly insulated. Simulations were performed at three different Rayleigh numbers (Ra = 5 × 105, 106 and 5 × 106). Predictions of the time averaged velocities, temperatures and intensities of the fluctuations agree with experiments reported in the literature. Under the fully developed flow conditions considered in this study the shear stress is greater on thermally active wall than that on the adiabatic wall, but the turbulent intensities and the turbulent shear stress are greater near the insulated wall. Conversely, the intensities of the temperature fluctuations and turbulent heat fluxes are higher near the thermally active wall than those near the adiabatic wall. Contrary to the vertical channel with constant but different wall temperatures, where buoyancy and turbulent shear dominate the generation of turbulent kinetic energy, in the asymmetrically heated channel the turbulent shear stress is the principal mechanism of turbulent kinetic energy production as in a forced convection channel flow.

Numerical investigations of vortex dynamics and loss generation in the corner separation region of a high subsonic compressor blade

Three-dimensional corner separation seriously deteriorates the aerodynamic performance of a compressor blade. In this study, the complicated vortex dynamics and loss mechanism in the corner region of a high subsonic compressor blade (the inlet Mach number is 0.67) are investigated using large eddy simulations (LESs) at a Reynolds number (Re) of 5.6 × 105. The results show that the predicted total pressure loss and outlet flow angle match well with the experimental data, indicating that the LES method can accurately predict the size and strength of corner separation in the compressor blade. With the passage vortex rolling up and further interacting with the low-momentum fluids originating from the end wall boundary layers and the local blade boundary layers, strong shear strain induces a large-scale concentrated shedding vortex (CSV) near the spanwise location of x/H = 0.3. The formation and rolling-up of the CSV not only cause the strongest flow blockage but also strengthen the turbulence anisotropy. As the CSV moves toward the trailing edge, the strong interaction with a pair of counter-rotating vortices shed in the wake region (wake shedding vortex) further accelerates the local generation of turbulent kinetic energy (TKE). Detailed TKE budget analysis shows that the streamwise Reynolds normal stress (w′w′¯) plays the most decisive role in the TKE production term. Furthermore, we demonstrate that the strength of turbulence anisotropy is positively correlated with the TKE budget. Therefore, turbulence anisotropy should be considered carefully in predicting the loss level in the corner region of a compressor blade.

Componentwise influence of upstream turbulence on the far-wake dynamics of wind turbines

Wake meandering and turbulent kinetic energy (TKE) generation in the far-wake region of wind turbines significantly affect the power production and aerodynamic loads of wind farms. This work thus aims at understanding the componentwise influence of upstream turbulence and roles of different mechanisms on the far-wake dynamics to guide the development of wind-farm wake models. We find that the wake meandering is mainly caused by the upstream spanwise (v′) and vertical (w′) velocity fluctuations, supporting the passive wake meandering mechanism. However, our results also show a scale-dependence of the wake meandering that should be accounted in wake models. We find that v′ and w′ cause greater TKE generation than the streamwise velocity fluctuations (u′). We then use simulation- and resolvent-based componentwise input–output analyses to explain that this is because the shear instability in turbine wakes is more receptive to the transverse forcing relative to the streamwise forcing. This highlights the importance of implementing the shear instability mechanism in wake models for accurate TKE estimations. Finally, we find that u′ cause the thrust fluctuations, which can lead to near-wake corrections and hence influence the far-wake evolution.

Influence of sidewalls on three-dimensional turbulent wall jet: An experimental and numerical approach

In this study, with the help of with and without sidewall configurations, experimental and numerical approaches are utilised to investigate the sidewall influence on a three-dimensional turbulent wall jet. The mean flow profile of the three-dimensional turbulent wall jet is measured through experimental method and compared with the numerical results. In addition, the numerical method is used to characterise the turbulence characteristics of the wall jet for both the configurations. A 200 mm square nozzle (height h=20 ± 0.5 mm) is used to generate the developing jet exit profile for the experimental results. The Reynolds number based on the jet exit velocity and nozzle height is 25,000. The numerical results are obtained by solving the Reynolds Average Navier stokes (RANS) equations with low Reynolds number k−ε turbulence models proposed by Yang and Shih and Launder and Sharma. The experimental results are obtained by a single probe hotwire anemometer and a K-type thermocouple. It is observed that the sidewall affects the temperature distribution just after the potential core region x/h=5 whereas the velocity distribution is affected in the fully developed region after the downstream location x/h=22.5. Sidewalls drastically influenced the thermal and velocity decay in wall-normal and lateral directions. It is found from the numerical simulation that the decay of maximum streamwise velocity is increased by 9%, whereas centerline temperature decay is decreased by 25% in sidewall configuration as compared to without sidewall configuration. The contour plots of temperature and velocity also exhibit the sidewall effect on the whole domain. The Reynolds shear stress <u′v′> dominates in the vertical jet centerline plane atz=0, whereas <u′w′> dominates in the lateral direction at ymax plane in both the configurations. On the vertical jet centerline plane at z=0, Reynolds shear stress <u′v′> is nearly increased by 10% in the presence of sidewall compared to without sidewall configuration. The entrainment of the ambient fluid initially decreases, but after the downstream location x/h=22.4, it increases for the case of the sidewall compared to the corresponding case without the sidewall. This happens owing to an increase in maximum turbulent kinetic energy generation inside the flow domain by 10%. The turbulent heat flux <T′V′> dominates in lateral and wall-normal shear layers in both the configurations. The correlations of decay of temperature and velocity are also suggested through numerical techniques.

The coastal front modulates the timing and magnitude of spring phytoplankton bloom in the Yellow Sea

Major seasonal quasi-stationary fronts on shelves play an important role in regulating the spatiotemporal variations in the phytoplankton community. However, knowledge of their effects on the timing and magnitude of spring phytoplankton bloom (SPB) remains limited. Here, based on decadal satellite data (2003–2020), we examine the climatological relationship between the Shandong coastal front (SCF) and SPB in the Yellow Sea. The results show that the onset of SPB occurs either in March (∼56% of the seasons examined) or in April (44%). The peak of SPB most often occurs in April (∼56% of the seasons examined) or is advanced to March (16%) or delayed to May (28%), and that the peak ranges from 1.04 to 2.54 mg Chl-a m−3. The onset of SPB matches with lower turbulence, particularly when the rate of generation of turbulent kinetic energy (TKERT) reaches zero. A higher magnitude of bloom is associated with a greater change in front and a lower TKERT. The in situ observations along the SCF transects in the Yellow Sea indicate that weakened SCF in spring associated with a shallower mixing layer enhances the transport of nutrients from the coastal to the shelf waters. Weakened frontal structure and atmospheric forcing in spring can further increase the water stability and decrease turbulence in the upper waters. The variation in hydrodynamic conditions allows shelf phytoplankton to stay longer in the upper waters with sufficient light and nutrients and consequently generate a Chl-a peak. The results suggest that the seasonal changes in front intensity and structure and turbulence are important prerequisites for initiating SPB on the shelf, and that further determines the magnitude of SPB.

Numerical investigation of cavitation-vortex structures around a sphere with boundary data immersion method

The boundary data immersion method (BDIM) coupled with the artificial compressibility method is applied to investigate the interaction of the cavitation-vortex dynamics around a sphere. The convolution of governing equation with a nascent delta kernel is employed to smooth the transition region between the solid and the fluid subdomain. Therefore, the BDIM addresses a key problem with smooth immersion boundary method in representing the discontinuity of the velocity gradient ∂u/∂y at the wall when considering flows with intermediate to high Reynolds numbers. In addition, a pseudo-time derivative of the pressure multiplied by an artificial-compressibility factor is added to the continuity equation. The developed coupling algorithm can accurately capture the unsteady cavitation characteristics, which is consistent with the previous experimental data. Subsequently, the typical vortex identification methods and the turbulent kinetic energy (TKE) transport equation are applied to analyze the interaction between the cavitation dynamics and turbulence vortices structures. A series of turbulent vortices are captured with the cloud cavity shedding. Moreover, it is found that the unsteady cavity topology will promote the generation of TKE.

On the unexplored relationship between kinetic energy and helicity in prosthetic heart valves hemodynamics

Surgical replacement of the diseased aortic valve consists in the implantation of a prosthetic heart valve (PHV), either biological or mechanical (BHV and MHV, respectively). Risks of complication have been linked to high levels of turbulence and consequent energy dissipation induced by the PHV.As helicity is an emergent feature in cardiovascular flows, deemed to impact blood flow organization, stability and the turbulent energy cascade, in this study the interplay between the production/decay of phase-averaged and turbulent kinetic energy and helicity in the presence of a BHV or MHV was investigated. Technically, direct numerical simulations of the coupled fluid–structure interaction problem were conducted using the immersed boundary method. A quantitative description of phase-averaged and fluctuating helicity, mean and turbulent kinetic energy was adopted to explore the nature of the kinetic energy vs. helicity relationship.A clear PHV-type dependence of the helicity production/decay in the downstream hemodynamics emerged, with MHVs hemodynamics presenting larger phase-averaged and fluctuating helicity than BHVs. For both heart valve types strong linear correlations were found between volume-average kinetic energy and helicity when based on phase-averaged or fluctuating quantities (Pearson's correlation coefficient r up to 0.98, p<0.001). The generation of turbulent kinetic energy or fluctuating helicity for both heart valve types was delayed with respect to the inflow waveform or the generation of both mean kinetic energy and phase-averaged helicity (up to 5.4% of the cardiac cycle). The exploration of the link between helical and turbulent hemodynamic flow features expands the current understanding of the PHV hemodynamic features associated with clinical complications, potentially translating into improvements of the design of PHVs.

Comparative analysis of drag reduction characteristics of two-type riblets based on numerical simulation

Turbulent drag reduction has always been a hot issue in fluid mechanics. Among various turbulent drag reduction methods, riblets has attracted wide attention due to its simple structure and convenient application. In order to investigate the effect of the riblets shape on the drag reduction, the effect of the triangular and trapezoidal riblets on the turbulent boundary layer flow field and drag reduction characteristics has been studied numerically by adopting the CFD method and based on the large eddy simulation (LES). The numerical simulation of turbulent channel flow was conducted by RANS, DES and LES methods respectively, and their results were compared with the results of direct numerical simulation (DNS) to verify the accuracy and feasibility of the large eddy simulation method. According to the experimental results in references, the flow field parameters such as integral statistics, first-order statistics and second-order statistics of the triangular and trapezoidal riblets on the turbulent boundary layer flow fields were compared and analyzed. The drag reduction characteristics of two-type riblets were investigated by studying the variation in physical parameters such as drag reduction rate, time-averaged velocity, root mean square velocity fluctuation, shear stress, turbulent kinetic energy generation and contour of spanwise velocity fluctuation, and it was concluded that the trapezoidal riblets have better drag reduction effect than the triangular riblets under the same dimensionless condition.

A case study of wind farm effects using two wake parameterizations in the Weather Research and Forecasting (WRF) model (V3.7.1) in the presence of low-level jets

Abstract. While the wind farm parameterization by Fitch et al. (2012) in the Weather Research and Forecasting (WRF) model has been used and evaluated frequently, the explicit wake parameterization (EWP) by Volker et al. (2015) is less well explored. The openly available high-frequency flight measurements from Bärfuss et al. (2019a) provide an opportunity to directly compare the simulation results from the EWP and Fitch scheme with in situ measurements. In doing so, this study aims to complement the recent study by Siedersleben et al. (2020) by (1) comparing the EWP and Fitch schemes in terms of turbulent kinetic energy (TKE) and velocity deficit, together with FINO 1 measurements and synthetic aperture radar (SAR) data, and (2) exploring the interactions of the wind farm with low-level jets (LLJs). This is done using a bug-fixed WRF version that includes the correct TKE advection, following Archer et al. (2020). Both the Fitch and the EWP schemes can capture the mean wind field in the presence of the wind farm consistently and well. TKE in the EWP scheme is significantly underestimated, suggesting that an explicit turbine-induced TKE source should be included in addition to the implicit source from shear. The value of the correction factor for turbine-induced TKE generation in the Fitch scheme has a significant impact on the simulation results. The position of the LLJ nose and the shear beneath the jet nose are modified by the presence of wind farms.

A Review on Analysis of Heat Transfer Coefficient in Internal Rib Tube

The rate of heat transfer is increased by a fin arrangement applied to the rectangular duct. In order to save energy, many industrial heat exchange devices use various techniques to improve heat transfer, such as: B. fins, dimples, vortex chamber and ribbed tabs. The most common technique used to improve heat transfer is to add fins to the flow channel. The ribs are of simple construction and are widely used in many industries. Turbulent kinetic energy generation increases turbulent heat transfer in the duct due to flow disturbances caused by fin arrangements. The shape of the fin plays an important role in improving heat transfer as it affects the formation of bubble separation behind the fin and the amount of turbulent kinetic energy generated.

Numerical analysis of heat transfer and hydraulic resistance during an upward turbulent flow of supercritical pressure carbon dioxide in a heated tube

This paper presents the wall temperature distribution, averaged velocity, turbulent statistics, and hydraulic resistance investigated using large eddy simulation for CO2 at supercritical pressure flowing upward in a heated vertical tube for the deteriorated heat transfer regimes simulated by Bae et al. using a direct numerical simulation (DNS). Numerical simulations were performed using the “in-house” computational fluid dynamics code ANES. We discuss the reasons for certain inconsistencies in wall temperature distribution between the DNS data of Bae et al. and others, the mechanism of formation of an M-shaped profile of the averaged axial velocity, and the features of turbulent kinetic energy generation due to deformation of the averaged velocity field and buoyancy forces. We show that the return to the normal heat transfer regime after the wall temperature reaches its local peak is due to the action of buoyancy forces.

Experimental investigation of turbulent flows through a boulder array placed on a permeable bed

AbstractGlass beads were used to model permeable beds and boulders (simulated by plastic spherical balls) placed on the centre section of the bed. Flume experiments were conducted to investigate the hydrodynamics through a boulder array over impermeable and permeable beds (i.e. IMPB and PB). For background reference, hydrodynamics investigation was made over smooth beds (SB) with the boulder array. Through measuring the instantaneous velocity field, the major flow characteristics such as mean flow velocity, turbulence intensity, turbulent kinetic energy (TKE) and instantaneous Reynolds stresses (through quadrant analysis) were presented. The results show that the increase in bed permeability through decreasing the exposure height of boulders has little impact on the magnitude of streamwise velocity, but tends to decrease the near-bed velocity gradient, thus affecting the bed shear-stress. For turbulence, similar to the previous studies, the bed permeability is identified to enable a downward shift of the peak of turbulence intensity. The TKE budget analysis shows that bed permeability tends to inhibit the transport and diffusion processes of TKE generation. Finally, the quadrant analysis of turbulence structure clearly shows that the ejections (Q2) and sweeps (Q4) with and without the boulder array are dominated by turbulence structure of different scales.