Turbulent Kinetic Energy Transport Research Articles

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.

Vertical Energy Fluxes Driven by the Interaction Between Wave Groups and Langmuir Turbulence

Abstract Data from an air-sea interaction tower are used to close the turbulent kinetic energy (TKE) budget in the wave-affected surface layer of the upper ocean. Under energetic wind forcing with active wave breaking, the dominant balance is between the dissipation rate of TKE and the downward convergence in vertical energy flux. The downward energy flux is driven by pressure work, and the TKE transport is upward, opposite to the downgradient assumption in most turbulence closure models. The sign and the relative magnitude of these energy fluxes are hypothesized to be driven by an interaction between the vertical velocity of Langmuir circulation (LC) and the kinetic energy and pressure of wave groups, which is the result of small-scale wave-current interaction. Consistent with previous modeling studies, the data suggest that the horizontal velocity anomaly associated with LC refracts wave energy away from downwelling regions and into upwelling regions, resulting in negative covariance between the vertical velocity of LC and the pressure anomaly associated with the wave groups. The asymmetry between downward pressure work and upward TKE flux is explained by the Bernoulli response of the sea surface, which results in groups of waves having a larger pressure anomaly than the corresponding kinetic energy anomaly, consistent with group-bound long wave theory.

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.

Turbulent kinetic energy redistribution in a gravity current interacting with an emergent cylinder

Gravity currents are flows driven by density gradients between two or more contacting fluids and play a key role in nature and industrial environments via global ocean circulations, climate variability and the distribution of airborne pollutants. In the present work, we study, experimentally, the changes induced by an emergent vertical PVC cylinder on the mean and turbulent flow fields of an unsteady bottom-generated lock release gravity current. Tests were carried out, with and without the cylinder, in refractive index matching conditions and instantaneous velocities were acquired with a Particle Image Velocimetry system. The mean velocity field, Reynolds stresses and terms of turbulent kinetic energy (TKE) budget for the currents head were presented and discussed. The results show that the adverse pressure gradient generated by the cylinder induces a uniform deceleration of the current head. Hence, there are no appreciable differences on the spatial distribution of the mean velocities in the current head, compared to the undisturbed current. On the other hand, the changes on the turbulent flow field are remarkable. The total diffusion of TKE decays in the inner part of the head while becoming stronger at the interface between the two fluids, as the current approaches the cylinder. This is associated to an increase of the diffusion term due to pressure fluctuations, that acts against diffusion due to velocity fluctuations and contributes to disrupt the transport of TKE from the interface between the fluids and the inner part of the current. As a result, in the presence of an obstacle, Reynolds stresses are suppressed in the inner part of the current head and enhanced at the interface.

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.

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.

Compressible Rayleigh–Taylor instability subject to isochoric initial background state

The effect of compressibility on the single-mode Rayleigh–Taylor instability is examined using two (2D) and three-dimensional (3D) direct numerical simulations. To isolate compressibility from background stratification effects, this work employs a constant density profile on each side of the interface. The numerical simulations are performed at various Reynolds numbers using the gas kinetic method for static Mach numbers up to M = 0.4. The most important finding is that compressibility acting in isolation enhances the instability and perturbations grows faster with increasing Mach number, unlike previous results with background isothermal state, which show suppression of the instability at higher static Mach numbers. In addition, compressibility is also shown to increase the bubble-spike asymmetry. While the instability grows faster for the 3D case, the findings are qualitatively similar in 2D and 3D. The dynamical reasons underlying the effect of compressibility are elucidated by examining the evolution of vorticity and turbulent kinetic energy transport equations.

A new composite modelling strategy for engineering computation of turbulence modulation in dilute solid-liquid two-phase flows

Turbulence modulation is an important physical phenomenon in solid-liquid two-phase flows, including two co-effects of wake enhancement and resistance dissipation. This physical phenomenon is usually modelled in an integrated way by adding two corresponding source terms to the turbulent kinetic energy (TKE) transport equation. However, this modelling strategy may easily cause the problem of explicit interference between the two co-effects, while the influencing factors of turbulence modulation are also not fully reflected, affecting the prediction accuracy of turbulence intensity. A new composite modelling strategy for turbulence modulation in dilute solid-liquid two-phase flows is proposed in this article. In the Euler-Euler framework, the two co-effects of turbulence modulation are modelled in a separate way to avoid the explicit interference. The resistance dissipation term is independently added to the TKE transport equation as a TKE change rate, while the wake enhancement term is independently added to the eddy viscosity as a TKE increment. On this basis, the appropriate mathematical expressions are determined, the influencing factors of the two effects are considered individually to reflect the dynamic characteristics of particles as fully as possible, and the empirical coefficients are calibrated for the condition of dilute solid-liquid two-phase flows to improve the applicability to the flow medium. Four typical flow cases are tested, and it is demonstrated that the new composite modelling strategy can better reflect the modulation of particles on the TKE of liquids, thereby providing higher-precision simulation results without significant increase in computational cost for dilute solid-liquid two-phase flows.

Large eddy simulation of plunging solitary wave: Understanding the breaking and turbulent mechanisms along shoaling region

A large eddy simulation (LES) is conducted to investigate the distribution of turbulence kinetic energy (TKE) under a plunging solitary wave over a 1:15 slope. This study provides a novel contribution to the field by examining the roles of resolved and sub-grid scale TKE in plunging solitary waves at the different stages of wave breaking. Furthermore, comparing the performances of two sub-grid scale (SGS) models in simulating the distribution of TKE was carried out to identify their performances. The separate investigation of these components in the context of wave breaking and recognizing the importance of an appropriate sub-grid scale model to consider the effects of small-scale eddies provide a significant advancement in understanding coastal morphological changes and nearshore sediment transport. Both the zero-equation and one-equation SGS models demonstrated acceptable performance in simulating water surface and kinematic properties. The one-equation SGS model, however, provided more accurate results on TKE transport during the breaking process and as the wave approaches its collapsing point. The study’s results reveal that an SGS model’s inability to simulate TKE transport (such as in the zero equation model) leads to inaccurate simulations of the TKE level and breaking location in the breaking zone. Additionally, the results of the one-equation model demonstrated that the maximum horizontal fluid velocity around the wavefront surface is a better predictor of breaking wave onset than the horizontal fluid velocity at the wave crest.

High-resolution simulations of a turbulent boundary layer impacting two obstacles in tandem

We created a new publicly available data set of high-fidelity numerical simulations for two obstacles in tandem invested by a fully resolved turbulent boundary layer. In the three configurations of skimming flow, wake interference, and isolated roughness, we identify the regions of intense turbulent fluctuations, production and transport of turbulent kinetic energy, and examine the anisotropy-invariants map.

Effects of groove distributions on supersonic turbulent channel flows

This paper investigates the influences of the distribution of the grooves on the wall on the turbulent statistics, transport of turbulent kinetic energy, and flow structures in supersonic turbulent channel flows at the bulk Mach number of 3.0 by performing direct numerical simulations. It is found that the existence of the grooves leads to the enhancement of the turbulent kinetic energy close to the wall and the abatement thereof above the buffer layer. The density and temperature fluctuations are also enhanced, but only within the buffer layer, above which the influences of the grooves can be disregarded. The pressure fluctuations, however, are significantly increased, which is attributed to the radiated acoustic waves from the wall generated by the disturbances on the wall. Such inference is substantiated by the fact that the inclination angles of the phase averaged pressure are related to the Mach number. Nevertheless, the acoustic and dynamic processes seem to be decoupled, leading to insignificant pressure-dilatation terms in the transport of turbulent kinetic energy.

Coupling heat transfer study of liquid sodium and supercritical carbon dioxide in a PCHE straight channel based on a four-equation model

The Brayton cycle using supercritical carbon dioxide (S-CO2) as the working fluid is expected to be a thermo-power conversion technology for sodium-cooled fast reactors. Printed Circuit Heat Exchanger (PCHE) is the key heat transport structure to realize the above technology. The study of conjugate heat transfer characteristics of sodium (Na) with low Prandtl number turbulent heat transfer characteristics and S-CO2 with supercritical convective heat transfer behaviors in a PCHE channel are of great significance. However, the constant turbulent Prandtl number (Prt) model obtained by the general Reynolds analogy hypothesis may affect the conjugate heat transfer assessment between Na and S-CO2. Compared with the constant Prt model, the fluid’s Prt distribution can be obtained by four-equation models, introducing the transport of turbulent kinetic energy k, dissipation rate ε of k, temperature fluctuation kθ, and dissipation rate εθ of kθ. The four-equation model is expected to obtain more effective conjugate heat transfer characteristics between Na andS-CO2, while there are no available commercial codes. Therefore, in this paper, two kinds of four-equation model, which can effectively evaluate the heat transport performance of Na with low-Prandtl number and S-CO2 away from the pseudo-critical region, respectively, are first introduced into the conjugate heat transfer solver of OpenFOAM. Then the conjugate heat transfer experiment data of Na in a pipe and the simulation data of S-CO2 in a PCHE straight channel are used to verify the validity of the numerical model in this paper. The results show that the present calculation method can effectively reproduce the numerical conjugate heat transfer process of Na and S-CO2. Finally, based on four-equation models, the coupling heat exchange performance of Na/S-CO2 are studied to obtain the effects of mass rate and temperature on the conjugate heat transfer process between Na and S-CO2 in a PCHE straight channel.

Features of turbulence during wildland fires in forested and grassland environments

Fire-induced turbulence and the feedback into the fire, following ambient changes, differ for forested (sub-canopy) and grassland environments. Here, we synthesize observations from multiple experimental surface fires: two sub-canopy backing fires, one sub-canopy heading fire, and a grassland heading fire. We identify and compare the most essential coherent structures and processes of each case from the turbulent momentum fluxes and turbulent kinetic energy (TKE) budget terms. In the sub-canopy burns, turbulent eddies are strongest near the canopy top: high streamwise turbulent flux accompanies low cross-stream turbulent flux and vice versa. In the grassland fire, both streamwise and cross-stream eddies strengthen simultaneously until a certain height, informing a vertical length scale for the fire-influence. Moreover, the forward sweep from streamwise eddies assists in the fire spread by pushing hot gases towards unburnt fuel. In the sub-canopy fires, shear production and buoyancy production are more substantial near the canopy top for more intense fires, while their magnitudes decrease with decreasing fire intensity. At mid-canopy-height scales, buoyancy production dominates shear production, becoming the key mechanism for vertical transport of TKE. In the grassland fire, shear production dominates buoyancy production near the surface and is insignificant beyond a certain height relative to the flame length, while buoyancy production increases with height, becoming substantial further away from the surface. Turbulent transport terms are also active in both environments. For intense sub-canopy fires, there is a loss in TKE due to its expulsion to the boundary layer aloft via the transport term, compensated by a reversal process: TKE influx via the transport term. In the grassland fire, the transport term mimics this behavior until a certain height. The insights into the relative significance of the respective turbulent fluxes and TKE budget terms in each environment can help simplify the complex system of equations governing fire physics.

Production and transport of turbulent kinetic energy from premixed flames subjected to mean pressure gradients

The influence of mean favorable pressure gradients on the production and transport of turbulent kinetic energy is experimentally investigated in a premixed bluff-body combustor. The combustor wall geometry is modified into converging, straight, or diverging configurations to experimentally alter the mean pressure gradient in the reacting flow field. For each configuration, turbulent kinetic energy production and transport dynamics are characterized with high-speed particle image velocimetry and simultaneous CH* chemiluminescence imaging. For all cases, the premixed reaction increases the turbulent kinetic energy and integral length scales in the flow. However, increasing the magnitude of the mean favorable pressure gradient increases the turbulent kinetic energy produced by the flame. The source of increased turbulent fluctuations from reactants to products is first investigated with a steady flow energy analysis, and is accompanied with a Reynolds decomposed investigation of the kinetic energy in the flow. As the mean pressure gradient increases, the turbulent kinetic energy in the flow increases due to stronger magnitudes of flame-generated turbulence in the form of baroclinic torque. The evolution of the flame-generated turbulence is examined by decomposing the transport equation of turbulent kinetic energy. Increasing the mean favorable pressure gradient augments the largest magnitude transport terms, and the budget of turbulent kinetic energy is primarily driven by pressure gradient work and viscous dissipation. The results here differ from previous direct numerical simulation (DNS) studies, and should ultimately motivate additional research to aid the development of computational models which can better predict turbulent flame-flow dynamics in confined environments with mean pressure gradients.

Effects of swirl number and bluff body on swirling flow dynamics

Bluff-body swirling flows have been widely employed in gas-turbine combustors to achieve flame stabilization. Meanwhile, considerable efforts have been made to understand swirling flow dynamics, the effects of swirl number and bluff body on flow structure and dynamics are still not well understood. To this end, a series of direct numerical simulations of isothermal swirling flows have been conducted in this work in order to investigate the impact of swirl numbers and bluff-body diameters on the flow structure, Reynolds stresses, and turbulent kinetic energy (TKE) transport. It is found that a change in the swirl number can affect the inner recirculation zone (IRZ) and hence momentum transport. Specifically, as the swirl number increases, the vortex core formed at downstream locations can merge with the IRZ. Moreover, including the bluff body not only contributes to the formation of the IRZ but also serves as a disturbance source for the flow, which is favorable for the formation of large-scale vortex structures. Then, the impact of swirl number and bluff body on Reynolds shear stresses and anisotropy invariants is investigated to identify the locations of the inter shear layer (ISL), the outer shear layer (OSL), and the main swirling zone (MSZ). The results show that as the swirl number increases, both the ISL and MSZ shift to the wall, indicating a large IRZ. Furthermore, the analysis of TKE indicates that for cases with a bluff body, TKE mainly occurs in the ISL and OSL, featuring a dual peak distribution. However, for cases without a bluff body, the distribution of TKE is primarily concentrated in the ISL. These results suggest that both increasing the swirl number and/or including the bluff body could help with TKE transport, which can lead to a wide range of TKE distribution.

Effects of wall disturbances on the statistics of supersonic turbulent boundary layers

In the present study, we perform direct numerical simulations to investigate the spatial development and basic flow statistics in the supersonic turbulent boundary layers at the free-stream Mach number of 2.0 over smooth and disturbed walls, the latter of which enforces extra Reynolds shear stress in the streamwise direction to emulate the drag increment and mean streamline curvature effects of rough walls. Such disturbances escalate the growth rate of turbulent boundary layer thickness and the shape factor. It is found that under the rescaled global coordinate, the mean velocity, Reynolds stress, and pressure fluctuation variance manifest outer-layer similarity, whereas the average and fluctuation variances of temperature and density do not share such a property. Compressibility effects are enhanced by the wall disturbances, yet not sufficiently strong to directly impact the turbulent kinetic energy transport under the presently considered flow parameters. The generalized Reynolds analogy that relates the mean velocity and temperature can be satisfied by incorporating the refinement in modifying the generalized recovery coefficient, and that associates the fluctuating velocity and temperature work reasonably well, indicating the passive transport of temperature fluctuations. The dispersive motions are dominant and decay exponentially below the equivalent sand grain roughness height ks, above which the wall disturbances are distorted to form unsteady motions responsible for the intensified density and pressure fluctuations in the free-stream traveling isentropically as the acoustic radiations.

An improved combination of ruler and local electromagnetic brakes for continuous casting process

In the present study, using computational fluid dynamics, we aim to systematically propose an improved combination of local and ruler ElectroMagnetic Brakes (EMBr) to reduce the surface and internal defects in the thin-slab steel continuous casting. To achieve this goal, first, each of governing submodels, including turbulent fluid flow and heat transfer, solidification, and electromagnetics, is carefully validated. Then, the model is used to evaluate the performance of different EMBr design configurations in terms of six flow metrics, i.e., the flow pattern, solidified shell thickness, surface velocity, turbulent kinetic energy, level fluctuation, and superheat transport. The results manifest that the braking effect, imposed by the combinations of ruler and local EMBrs, effectively resolves the problem of uneven solidified shell growth, especially for SEN-type casters. On the other hand, using local EMBrs on the thin wall midway the SEN and meniscus can result in unstable flow structures which are prone to change to the detrimental single-roll pattern under the perturbations in the operating conditions. Finally, the best performance is achieved by the combination of a single-ruler EMBr below the SEN and a couple of local EMBrs near the center of the meniscus. This configuration substantially increases the superheat transport to the surface and decreases surface mean and fluctuating velocities, especially at the meniscus near the walls, and can effectually prevent the formation of defects.

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent riblets

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent (C–D) riblets at a Reynolds number of Reb=2800 are presented. It is found that, with a fixed normalized riblet height of h+=5, as the ratio of the riblet spacing and the height, s/h, increases from 2 to 10, the strength of the large-scale secondary flow motion Γ generated by the C–D riblets peaks around s/h=4 when the C–D riblets behavior lies between d- and k-type roughness. Compared to the baseline case with smooth walls, the turbulent activities and energy level increase significantly and peak at s/h=4 when Γ is the highest. It is shown that while the intense local turbulent kinetic energy (TKE) production occurring in the diverging region is caused by the high local velocity gradient due to the downwelling of the secondary flow, the strong local TKE production occurring in the converging region is caused by the high turbulent shear stress associated with upwelling. Furthermore, the TKE transport characteristics are significantly altered by the secondary flow motion, especially over the converging and diverging regions. The secondary flow is not caused by the local imbalance between turbulent kinetic energy production and dissipation but by the yawed riblets. It is then more appropriate to classify this flow as a Prandtl’s secondary flow of the first kind, also known as the geometry-driven secondary flow. Finally, in comparison with the baseline case, the drag increases for all the riblet cases examined, and a direct correlation between the amount of drag and intensity of the secondary flow exists, both peaking at s/h=4.