Turbulent Kinetic Energy Transport Research Articles

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.

A Simple Criterion for Estimating the Grid Level of Detail for RANS Methods

A simple criterion for evaluating the grid resolution needed to obtain a grid-independent solution of turbulent flow problems in the framework of statistical approach to turbulence simulation is proposed. The criterion is derived on the basis of an a posteriori estimate of the local interpolation error of the field of turbulent kinetic energy. A good resolution should ensure a small local interpolation error of the discrete turbulent kinetic energy. The equation for the transport of turbulent kinetic energy and realizability conditions for the turbulent stress tensor made it possible to reduce the estimation of relative interpolation error to an explicit formula for the estimate of the maximal grid step required for obtaining a grid-independent solution. The proposed criterion is applied to a steady problem for a flow past a backward facing step and to the problem of unsteady flow around a half-circular profile arranged at a zero angle of attack for the Reynolds number Re = 45 000. A numerical study showed that the proposed criterion gives a good estimate of the grid resolution required for obtaining a grid-independent solution away from a wall. This criterion can be used both for estimating the grid independence of the solution and for adapting the computation grid.

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.

Turbulent kinetic energy evolution in turbulent boundary layers during head-on interaction of premixed flames with inert walls for different thermal boundary conditions

The statistical behaviour of turbulent kinetic energy, and its transport in turbulent boundary layers during premixed flame-wall interaction for isothermal and adiabatic chemically inert walls have been analysed using a Direct Numerical Simulation (DNS) database. The terms due to the mean velocity gradient (commonly known as the production term) and viscous dissipation remain leading order contributors to the turbulent kinetic energy transport when the flame is away from the wall, similar to that in the corresponding non-reacting turbulent boundary layer, but in addition to these terms, the pressure dilatation and pressure transport contributions play leading order roles when the flame interacts with the wall. It has been found that the gradient hypothesis-based Reynolds stress closures in the context of the k−ε model may yield an inaccurate prediction of the mean velocity gradient term due to the counter-gradient behaviour of Reynolds stresses in the premixed flame cases considered in this analysis. The thermal boundary condition at the wall does not have a major influence apart from a higher wall friction velocity for adiabatic boundary condition than in the case of isothermal boundary condition. The assumption of local equilibrium of production and dissipation of turbulent kinetic energy has been found to be rendered invalid when the flame is either near to the wall or interacting with the wall. This invalidates the conventional log-law for mean streamwise velocity variation, and the wall functions derived based on production-dissipation balance equipped by the usual gradient hypothesis in the context of the standard k−ε model for premixed flame-wall interaction in turbulent boundary layers. Therefore, improved wall functions are necessary for Reynolds averaged Navier-Stokes simulations of premixed flame-wall interaction in turbulent boundary layers.

Understanding of turbulence modulation and particle response in a particle-laden jet from direct numerical simulations

Abstract Point-particle direct numerical simulations have been employed to quantify the turbulence modulation and particle responses in a turbulent particle-laden jet in the two-way coupled regime with an inlet Reynolds number based on bulk velocity and jet diameter $({D_j})$ of ~10 000. The investigation focuses on three cases with inlet bulk Stokes numbers of 0.3, 1.4 and 11.2. Special care is taken to account for the particle–gas slip velocity and non-uniform particle concentrations at the nozzle outlet, enabling a reasonable prediction of particle velocity and concentration fields. Turbulence modulation is quantified by the variation of the gas-phase turbulent kinetic energy (TKE). The presence of the particle phase is found to damp the gas-phase TKE in the near-field region within $5{D_j}$ from the inlet but subsequently increases the TKE in the intermediate region of (5–20)Dj. An analysis of the gas-phase TKE transport equation reveals that the direct impact of the particle phase is to dissipate TKE via the particle-induced source term. However, the finite inertia of the particle phase affects the gas-phase velocity gradients, which indirectly affects the TKE production and dissipation, leading to the observed TKE attenuation and enhancement. Particle response to the gas-phase flow is quantified. Particles are found to exhibit notably stronger response to the gas-phase axial velocity than to the radial velocity. A new dimensionless figure is presented that collapses both the axial and radial components of the particle response as a function of the local Stokes number based on their respective integral length scales.

Mode vortex and turbulence in ventilated cavitation over hydrofoils

In this paper, the complex interaction of gas-vortex-turbulence in ventilated cavitation over a NACA0015 hydrofoil is investigated by using large eddy simulation. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used for analyzing the three-dimensional fluctuation modes of gas-liquid interfaces induced by turbulent coherent structures in ventilated cavitation. The results show that among the first four dominant POD modes possessing 99.5% modal kinetic energy in the ventilated cavitating flow, and the turbulent POD mode 2 contains the multi-scale coherent structures and acts as a bridge for the energy scale transition from mode 1 to mode 3 through the gas-liquid interface oscillations. The DMD modal structures are reconstructed from the roller-shaped energetic structure captured by POD mode 2, which further reveal the process of breaking down near the hydrofoil leading edge, changing into the hairpin shape and finally stretching into the horseshoe shape above the hydrofoil trailing edge for the turbulent coherent structures on the cavity interfaces. Such low-frequency wake structures are energetic but sustained by means of the high-frequency turbulent fluctuations, with the interfacial oscillation amplitude changed through the formation and transition of the multi-scale coherent structures. Further, the modal turbulent kinetic energy transport theory is introduced to describe the ventilated coherent structures. It is worth noting that the large-scale energetic structures in POD mode 2 are mainly drawing energy from mean flows through the Reynolds stress, and the modal turbulent energy stored by shedding vortex and air cavities in the ventilated wake flow is redistributed and balanced due to the turbulent and pressure diffusion effects. Besides, the uneven spatial distribution of turbulent energy caused by the vortex structures of different modal scales is proved to promote the spatial oscillation level of the ventilated cavity interfaces. This study is helpful to understand the interaction mechanism between turbulence and gas-liquid interfacial fluctuations for the ventilated wake flow.

Wall-cooling effects on pressure fluctuations in compressible turbulent boundary layers from subsonic to hypersonic regimes

Pressure fluctuations play an essential role in the transport of turbulent kinetic energy and vibrational loading. This study focuses on examining the effect of wall cooling on pressure fluctuations in compressible turbulent boundary layers by high-fidelity direct numerical simulations. Pressure fluctuations result from the vorticity mode and the acoustic mode that are both closely dependent on compressibility. To demonstrate the effects of wall cooling at various compressibility intensities, three free-stream Mach numbers are investigated, i.e. $M_\infty =0.5$ , 2.0 and 8.0, with real gas effects being absent for $M_\infty =8.0$ due to a low enthalpy inflow. Overall, opposite effects of wall cooling on pressure fluctuations are found between the subsonic/supersonic cases and the hypersonic case. Specifically, the pressure fluctuations normalized by wall shear stress $p^\prime _{rms}/\tau _w$ are suppressed in the subsonic and supersonic cases, while enhanced in the hypersonic case near the wall. Importantly, travelling-wave-like alternating positive and negative structures (APNS), which greatly contribute to pressure fluctuations, are identified within the viscous sublayer and buffer layer in the hypersonic cases. Furthermore, generating mechanisms of pressure fluctuations are explored by extending the decomposition based on the fluctuating pressure equation to compressible turbulent boundary layers. Pressure fluctuations are decomposed into five components, in which rapid pressure, slow pressure and compressible pressure are dominant. The suppression of pressure fluctuations in the subsonic and supersonic cases is due to both rapid pressure and slow pressure being suppressed by wall cooling. In contrast, wall cooling strengthens compressible pressure for all Mach numbers, especially in the hypersonic case, resulting in increased wall pressure fluctuations. Compressible pressure plays a leading role in the hypersonic case, mainly due to the APNS. Essentially, the main effects of wall cooling can be interpreted by the suppression of the vorticity mode and the enhancement of the acoustic mode.

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.

Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the stabilized mixed model (SMM). In this paper, we try to increase the convenience of the SMM by replacing the modeled transport equation for the SGS energy with an algebraic model. The SMM quantitatively adequately predicts the total turbulent kinetic energy of the direct numerical simulation (DNS) even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy simulation (LES), the statistically averaged production term balances with the dissipation in the region away from the wall in the SGS energy transport equation. In contrast, we reveal that the correlation coefficient between the production and dissipation terms is high for the modeled transport equation in LES, whereas that for the fDNS is low. Based on the high correlation or local equilibrium between the production and dissipation observed in the LES, we demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We construct a new damping function based on the grid-scale Kolmogorov length to reproduce the near-wall behavior of the algebraic model for the SGS energy. The ZE-SMM provides quantitatively the same performance as the original SMM that employs the SGS energy transport model. This result suggests that the local equilibrium model for the SGS energy provides the equivalent performance as the transport model in wall-bounded turbulent flows even in coarse grid cases.

Analysis of turbulence generation and dissipation in shear layers of methane–oxygen diffusion flames using direct numerical simulations

A turbulent methane–oxygen diffusion flame is studied using a direct numerical simulation setup. The operating regime and turbulence characteristics are chosen to resemble those of a modern methane rocket combustor. Local flame characteristics and dimensionless numbers are defined and evaluated, and their relationship with the turbulent kinetic energy transport budget is studied. Positive net turbulence generation is observed in the reaction shear layer. It is found that the underlying mechanisms for these results are similar to those encountered in premixed flames, with pressure terms acting as the primary turbulent kinetic energy sources. Models for predicting turbulent transport through mean pressure gradients, fluctuating pressure gradients, and turbulent flux of turbulent kinetic energy are adapted. The accuracy of the proposed formulations is assessed, and the involved challenges are discussed.

Effects of Body Forces on Turbulent Kinetic Energy Transport in Premixed Flames

The effects of buoyancy on turbulent premixed flames are expected to be strong due to the large changes in density between the unburned and fully burned gases. The present work utilises three-dimensional direct numerical simulations of statistically planar turbulent premixed flames under decaying turbulence to study the influence of buoyancy on the evolution of turbulent kinetic energy within the flame brush. Four sets of turbulence parameters have been studied, with four different values of Froude number for each set. It is found that for a given set of turbulence parameters, flame wrinkling increases with an increase in body force magnitude in the case of unstable stratification, which is also reflected in the increased values of turbulent burning velocity and flame surface area. An increase in body force magnitude in the case of stable stratification acts to reduce the extent of flame wrinkling. Turbulent kinetic energy and its dissipation rate are found to be affected by both the magnitude and direction of the body force. For low turbulence intensities considered here, turbulent kinetic energy increases from the leading edge of the flame brush before decaying eventually towards the product side of the flame brush. For high turbulence intensities, the turbulent kinetic energy is found to decay across the flame brush, and it is also found that the effect of body force on the evolution of turbulent kinetic energy is marginal in the case of high turbulence intensities. The effects of body force magnitude and direction on the statistical behaviours and closures of the various terms of the turbulent kinetic energy transport equation are analysed, and existing models have been modified to account for Froude number effects, where necessary.

The structure of turbulence in rotating rough-channel flows

Direct numerical simulation (DNS) of rib-roughened turbulent channel flow rotating about its spanwise axis, by Narasimhamurthy and Andersson [Turbulence statistics in a rotating ribbed channel. International Journal of Heat and Fluid Flow 51, 29–41. (2015)], is revisited to seek complementary insights into the combined effects of roughness and Coriolis force on the turbulence. Flow in the channel was maintained at a friction Reynolds number, Reτ=400 and the non-inertial reference frame was rotated at different speeds quantified by the dimensionless rotation number, Ro=0, 2 and 6. Both the aforementioned parameters are based on the friction velocity uτ and half-height of the channel h. The channel walls were symmetrically mounted with transverse square ribs with cross-section of side k=0.1h and pitch λ=8k. Rotation causes preferential aligning of the near-wall vortical structures. The Taylor-Görtler–like roll-cells similar to those found in the rotating smooth-channel flows, survive the presence of the transverse ribs, but exhibit transient behavior. Increased transport of turbulent kinetic energy from the pressure side at higher Ro is evident from the variation of the vertical transport velocity Vk. The rotational production rates assume increasingly significant roles in distributing the kinetic energy in different directions. Anisotropy invariant maps and Taylor microscales show that the structure of turbulence is affected by rotation in a significant manner.

Turbulence structure in a very sharp thermally stratified open-channel meander

Direct numerical simulation (DNS) results for turbulent open-channel flow through an idealized sine-generated meander with and without an internal heat source that models radiative heating from above are used to analyze the effect of a very sharp meander configuration and thermal stratification on the turbulence structure in the channel with friction Reynolds number Reτ=200. Spatial distributions of temperature, mean velocities, vorticity, mean-flow kinetic energy, and turbulent kinetic energy (TKE) are presented. In both cases, the cross-sectional motion is characterized by three circulation cells: a center-region cell and two weaker outer bank and inner bank cells. However, there is also a small cell observed near the corner of the channel bed inner bank at the channel outlet and the channel bed outer bank at the channel inlet. The tri-cellular cross-stream motions control the distributions of temperature and kinetic energy. In the stratified case, two separated shear layers (SSLs) are found: the first one is formed before the bend apex, and the second one is observed in the wake after the bend apex. In the neutral case, only the first SSL is observed. Turbulent amplification can be seen in both cases; however, in the stratified case, the second SSL stretches out to the channel outlet and is introduced back to the channel inlet by an anti-symmetric periodic boundary condition and then follows the outer bank line. The two SSLs converge in the region before the bend apex and amplify the turbulence more strongly there than in the neutral case. The turbulence kinetic energy budget terms for the stratified case are analyzed to determine the characteristics of production, dissipation and transport of TKE in thermally stratified meandering flow.

Amplification of turbulence by sharp meanders on thermally stratified open channel flow

In order to unravel the effects of meander bends on the mechanism by which the turbulence kinetic energy (TKE) is produced, redistributed and dissipated in a thermally stratified curved open-channel flow, Direct Numerical Simulation (DNS) was carried out through an idealized sharp meander with and without an internal heat source. The heat source models radiative heating from above and varies with height due to progressive absorption. In both cases, we find a pronounced local increase in TKE starting in the region approximately 25% of the distance through the bend. Here a local extremum of TKE is found near the channel bed at the inner bank and close to the free surface at the outer bank. This grows to a more generalised increase in turbulence that starts at a location approximately 35% of the distance through the bend and peaks at the meander apex before gradually weakening in the downstream part of the bend. However, while only showing a marked increase in the mid-depth region near the inner bank in the neutral case, turbulence is amplified more strongly in the stratified case with the high TKE values spread out across the whole channel width. This is due to the two observed separated shear layers converging in the bend apex in this case. There is only one SSL observed in the neutral case. An investigation of the TKE budget terms for the stratified case at the turbulence amplification location was undertaken to elucidate the mechanisms leading to the production, dissipation and transport of TKE in these regions.