Turbulent Kinetic Energy Transport Research Articles

Critical flux Richardson number for Kolmogorov turbulence enabled by TKE transport

In stably stratified flows, the flux Richardson number Ri f is a measure of the ratio between buoyancy destruction and shear production of turbulent kinetic energy (TKE). In flows with local equilibrium between shear production, buoyancy destruction and dissipation of TKE, the critical Ri f,c ≈0.21 corresponds to the limit above which Kolmogorov turbulence can no longer be sustained. Analysis of the TKE and velocity variance budget equations shows that the critical Ri f,c is increased by the presence of positive turbulent transport of TKE. This situation is observed, for example, in the roughness sublayer above plant canopies, as demonstrated using field data from the Amazon rainforest.

Calculation of cavitation evolution and associated turbulent kinetic energy transport around a NACA66 hydrofoil

The physical mechanism of flow unsteadiness is one of the key problems in cavitating flow. Significant efforts have been exerted to explain the cavitation-vortex interaction mechanism. As well, the process of kinetic energy transport during the evolution of unsteady cavitating flow must be elucidated. In this work, 2D calculations of cavitating flow around a NACA66 hydrofoil were performed based on the open source software OpenFOAM. The modified shear stress transport k-ω turbulence model, which considers curvature and turbulent eddy viscosity corrections, was employed to close the governing equations. The Schnerr-Sauer cavitation model was adopted to capture the cavitation phase change process. Numerical results showed reasonable consistency with the results of the experiments conducted by Leroux et al. (2004). The results showed that cavitation promotes turbulence intensity and flow unsteadiness around the hydrofoil. During the attached sheet cavity growth stage, high-value regions of turbulent kinetic energy are located substantially at the interface of the cavity, particularly at the rear portion of the cavity region. During the cloud cavity shed-off stage, the cavity begins to break off and the maximum value of turbulent kinetic energy is observed inside the shed cavity. Finally, the influence of cavitation on the turbulence intensity is illustrated using the turbulent kinetic energy transport equation, which shows that the pressure diffusion and turbulent transport terms dominate as cavitation occurs. In addition, cavitation promotes turbulence production and increases dissipation with fluid viscosity and flow unsteadiness. The viscous transport term only acts in the cavitation shedding stage under large-scale vortex shedding. Overall, these findings are of considerable interest in engineering applications.

Simulation of laboratory experiments for vortex dynamics at shallow tidal inlets using the fine resolution environmental hydrodynamics (Frehd) model

In this paper, we present the results of numerical simulations matched to laboratory experiments of tidal, starting-jet vortices forming at idealized, barotropic inlets. The laboratory experiments are for sinusoidally varying inflow/outflow along a wide, flat basin. Inlet configurations include simple inlets with negligible channel length as well as a longer inlet channels through a long barrier island and jettied inlet. Laboratory observations are made using particle image velocimetry, and we analyze the laboratory and numerical model velocity fields to compare starting-jet trajectory, diameter, and total circulation. The numerical simulations use the Fine Resolution Environmental Hydrodynamic model, solving the three-dimensional, hydrostatic, barotropic equations of motion. Our goal is to identify the minimum model attributes necessary to match the vortex properties. This is accomplished using a third-order upwind scheme for advection, a constant bottom friction drag coefficient, and a one-equation turbulence model for transport of turbulent kinetic energy. The optimal value of the bottom drag coefficient matches the time-average value at the basin inflow/outflow boundaries, and the optimal dissipation coefficient, $$C_{me}$$, was an order of magnitude smaller than literature values for a steady open-channel flow. We show that the drag coefficient mainly affects the advection speeds of the outer coastal waters, which control the penetration of the tidal vortices away from the inlet, and the lower turbulence dissipation rate results from the low turbulent dissipation in the large, shallow starting-jet vortices.

Spatial and temporal distributions of turbulence under bichromatic breaking waves

The present study aims to extend insights of surf zone turbulence dynamics to wave groups. In a large-scale wave flume, bichromatic wave groups were produced with 31.5 s group period, 4.2 s mean wave period, and a 0.58 m maximum wave height near the paddle. This condition resulted in plunging-type wave breaking over a fixed, gravel-bed, barred profile. Optic, acoustic and electromagnetic instruments were used to measure the flow and the spatial and temporal distributions of turbulent kinetic energy (TKE). The measurements showed that turbulence in the shoaling region is primarily bed-generated and decays almost fully within one wave cycle, leading to TKE variations at the short wave frequency. The wave breaking-generated turbulence, in contrast, decays over multiple wave cycles, leading to a gradual increase and decay of TKE during a wave group cycle. In the wave breaking region, TKE dynamics are driven by the production and subsequent downward transport of turbulence under the successive breaking waves in the group. Consequently, the maximum near-bed TKE in the breaking region can lag the highest breaking wave by up to 2.5 wave cycles. The net cross-shore transport of TKE is in the shoaling region primarily driven by short-wave velocities and is shoreward-directed; in the wave breaking region, the TKE transport is seaward-directed by the undertow and the long-wave velocities. Downward transport of TKE is driven by the vertical component of the time-averaged flow. The cross-shore and vertical diffusive transport rates are small relative to the advective transport rates.

Evaluation of curvature correction methods for tip vortex prediction in SST [formula omitted] turbulence model framework

This paper presents and studies effects of curvature correction (CC) methods to improve two equation RANS simulations of tip vortex flows, exemplified using the SST k−ω turbulence model. Performance of the CC models is first evaluated in the classical Rankine vortex flow field, and then extended into the study of tip vortex flows over an elliptical foil. The results have been compared with experimental measurements in terms of the vortex strength and velocity field, and the importance of the turbulence closure in tip vortex simulations is highlighted.Contribution of the CC models in different terms of the turbulent kinetic energy and specific dissipation transport equations are described, and it is discussed why a CC model may have mesh resolution dependent results. By considering the distribution of the CC function, it is shown that although some of the models can predict the location of the tip vortex core accurately, they still do not significantly improve the vortex prediction as the impact on the turbulent viscosity is wrong or not enough. It is further noted that as some of these models have been calibrated on specific vortex flows, they may not be completely applicable for other cases without recalibration. It is shown that some CC models provide accurate tip vortex predictions, primarily the ones based on the sensitization of the turbulent viscosity. Further, it is noteworthy that the successful models are active not only around the vortex, but also change the boundary layer characteristics on the foil, and the boundary layer separation lines, which consequently can provide the required momentum for the vortex core accelerated axial velocity.

Phase evolution of terms of turbulent kinetic energy transport equation in the boundary layer of a pulsating flow

Experimental data on production, dissipation, turbulent and molecular diffusion of turbulent energy have been obtained in the boundary layer of flow with forced freestream velocity fluctuations. The evolution of these terms over the pulsation phase is presented for streamwise and wall-normal velocity components. The presented results have been obtained on the basis of the dynamics of vector fields measured using a new optical SIV method with a spatial resolution comparable to the Kolmogorov scale.

Turbulent flow field in a stirred vessel agitated by an Impeller with flexible blades

In order to reveal the effect of the blades normal vibration on flow turbulence in the stirred vessel, we designed three kinds of blades: the flexible, flat‐rigid and curved‐rigid blades. The flow fields produced by the impellers with these three kinds of blades were measured by two‐dimensional particle image velocimetry. The results showed that the calculated turbulent kinetic energy (TKE) based on the pseudo‐isotropic assumption is slightly higher than that by the three fluctuating velocities for the flexible and curved‐rigid impellers, and the difference between above two calculations is smaller for the former impeller. For the flexible blades, the trailing vortices slightly move outwards in radial direction than those for the curved‐rigid blades, enhancing TKE transport from the blade to the bulk region of the vessel. For the flexible impeller, the phase‐averaged TKE differs slightly from that for the flat‐rigid impeller, but is higher than that for the curved‐rigid impeller. © 2018 American Institute of Chemical Engineers AIChE J, 64: 4148–4161, 2018

Turbulent transport of energy across a forest and a semiarid shrubland

Abstract. The role of secondary circulations has recently been studied in the context of well-defined surface heterogeneity in a semiarid ecosystem where it was found that energy balance closure over a desert–forest system and the structure of the boundary layer was impacted by advection and flux divergence. As a part of the CliFF (“Climate feedbacks and benefits of semi-arid forests”, a collaboration between KIT, Germany, and the Weizmann Institute, Israel) campaign, we studied the boundary layer dynamics and turbulent transport of energy corresponding to this effect in Yatir Forest situated in the Negev Desert in Israel. The forest surrounded by small shrubs presents a distinct feature of surface heterogeneity, allowing us to study the differences between their interactions with the atmosphere above by conducting measurements with two eddy covariance (EC) stations and two Doppler lidars. As expected, the turbulence intensity and vertical fluxes of momentum and sensible heat are found to be higher above the forest compared to the shrubland. Turbulent statistics indicative of nonlocal motions are also found to differ over the forest and shrubland and also display a strong diurnal cycle. The production of turbulent kinetic energy (TKE) over the forest is strongly mechanical, while buoyancy effects generate most of the TKE over the shrubland. Overall TKE production is much higher above the forest compared to the shrubland. The forest is also found to be more efficient in dissipating TKE. The TKE budget appears to be balanced on average both for the forest and shrubland, although the imbalance of the TKE budget, which includes the role of TKE transport, is found to be quite different in terms of diurnal cycles for the forest and shrubland. The difference in turbulent quantities and the relationships between the components of TKE budget are used to infer the characteristics of the turbulent transport of energy between the desert and the forest.

Numerical investigation of the transient cavitating flow and vortical patterns around a hydrofoil

The objective of this work is to investigate the cavitating flow mechanism of a specific hydrofoil, Tulin hydrofoil, and better understand the vortex-cavitation interactions in transient cavitating flows. The numerical investigations are performed using a large eddy simulation method and the Zwart cavitation model. The predicted cavity formation and evolution agree well with the experimental observation. An asymmetric vortex street has been formed, with the upper one (the trailing edge vortex street) has a regular vortex shape and a clear boundary between vortex structures, while the lower one (the leading edge vortex street) has a larger cavitation area due to the low pressure distribution on the suction side of the foil. The turbulent kinetic energy transport equation has been adopted to examine the balance and contribution of different mechanisms. The formation and evolution of the leading and trailing edge vortex structures are responsible for the generation and modification of the turbulent kinetic energy distributions. The convection term varies significantly in the cavity region during the phase change process, and the boundary of the vortex structures enhance the production term of the turbulent kinetic energy.

Inverse Interscale Transport of the Reynolds Shear Stress in Plane Couette Turbulence.

Interscale interaction between small-scale structures near the wall and large-scale structures away from the wall plays an increasingly important role with increasing Reynolds number in wall-bounded turbulence. While the top-down influence from the large- to small-scale structures is well known, it has been unclear whether the small scales near the wall also affect the large scales away from the wall. In this Letter we show that the small-scale near-wall structures indeed play a role to maintain the large-scale structures away from the wall, by showing that the Reynolds shear stress is transferred from small to large scales throughout the channel. This is in contrast to the turbulent kinetic energy transport which is from large to small scales. Such an "inverse" interscale transport of the Reynolds shear stress eventually supports the turbulent energy production at large scales.

The Role of Roughness and Stability on the Momentum Flux in the Marine Atmospheric Surface Layer: A Study on the Southwestern Atlantic Ocean

AbstractFor the first time, in situ turbulence measurements collected in the vicinity of the Brazil‐Malvinas Confluence are used to determine the influence of the ocean waves and atmospheric stability on the Marine Atmospheric Surface Layer. From the analysis of 187 high‐frequency sampled segments of temperature and wind velocity, carefully selected from three ship campaigns of the Air‐Sea Interaction at Brazil‐Malvinas Confluence project, we found a particular behavior of the drag coefficient, with a negative trend for a calm wind speed up to 10 m/s when the significant wave height was lower than 2.5 m, and a continuous decrease of the drag coefficient with increasing wind speed for significant wave height higher than 2.5 m. The results suggest that waves act as roughness elements during high wave conditions, inducing a zero‐plane displacement in the order of 0.1 to 1 m as an indication for a wave‐induced roughness layer. In addition, the analysis of the turbulent kinetic energy (TKE) budget indicates the occurrence of upward TKE transport mainly during stable conditions, while the general patterns of transport and dissipation of TKE are similar to observations taken over land surfaces.

Turbulent boundary layers absent mean shear

We perform an experimental study to investigate the turbulent boundary layer above a stationary solid glass bed in the absence of mean shear. High Reynolds number $(Re_{\unicode[STIX]{x1D706}}\sim 300)$ horizontally homogeneous isotropic turbulence is generated via randomly actuated synthetic jet arrays (RASJA – Variano & Cowen J. Fluid Mech. vol. 604, 2008, pp. 1–32). Each of the arrays is controlled by a spatio-temporally varying algorithm, which in turn minimizes the formation of secondary mean flows. One array consists of an $8\times 8$ grid of jets, while the other is a $16\times 16$ array. Particle image velocimetry measurements are used to study the isotropic turbulent region and the boundary layer formed beneath as the turbulence encounters a stationary wall. The flow is characterized with statistical metrics including the mean flow and turbulent velocities, turbulent kinetic energy, integral scales and the turbulent kinetic energy transport equation, which includes the energy dissipation rate, production and turbulent transport. The empirical constant in the Tennekes (J. Fluid Mech. vol. 67, 1975, pp. 561–567) model of Eulerian frequency spectra is calculated based on the dissipation results and temporal frequency spectra from acoustic Doppler velocimetry measurements. We compare our results to prior literature that addresses mean shear free turbulent boundary layer characterizations via grid-stirred tank experiments, moving-bed experiments, rapid-distortion theory and direct numerical simulations in a forced turbulent box. By varying the operational parameters of the randomly actuated synthetic jet array, we also find that we are able to control the turbulence levels, including integral length scales and dissipation rates, by changing the mean on-times in the jet algorithm.

Experimental investigation of streamwise velocity fluctuation based on the Reynolds-number dependency in turbulent viscoelastic-fluid flow

This paper describes an experimental verification of energy supply mechanisms for the streamwise component of the turbulent kinetic energy (TKE) at different Reynolds numbers in viscoelastic-fluid flow. We investigated the characteristics of the streamwise turbulent velocity fluctuation by analyzing the production and turbulent diffusion terms in the TKE transport equation. In addition, we reported on the Reynolds-number dependency in a high Reynolds-number regime where direct numerical simulation cannot demonstrate changes in fluid properties. Based on the experimental verification, we proposed a conceptual model of the energy-exchange term between the TKE and the elastic energy, with focusing on the dependency of the fluid properties on the shear stress. This model is indirectly reflected in the streamwise TKE, the instantaneous velocity field, and the wave number relevant to energy-containing eddies. The main gain term of the TKE switches between the energy-exchange term and the production term dependently on the Reynolds number: as the Reynolds number exceeds the value which provides the maximum drag reduction rate, the production term becomes dominant and the magnitude of streamwise TKE becomes high compared to the water flow case.

Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

The structure and budget of turbulent kinetic energy in front of a wall-mounted cylinder

We investigate the flow and turbulence structure in front of a cylinder mounted on a flat plate by a combined study using highly resolved large-eddy simulation and particle image velocimetry. The Reynolds number based on the bulk velocity and cylinder diameter is $Re_{D}=39\,000$. As the cylinder is placed in an open channel, we take special care to simulate open-channel flow as the inflow condition, including secondary flows that match the inflow in the experiment. Due to the high numerical resolution, subgrid contributions to the Reynolds stresses are negligible and the modelled dissipation plays a minor role in major parts of the flow field. The accordance of the experimental and numerical results is good. The shear in the approach flow creates a vertical pressure gradient, inducing a downflow in the cylinder front. This downflow, when deflected in the upstream direction at the bottom plate, gives rise to a so-called horseshoe vortex system. The most upstream point of flow reversal at the wall is found to be a stagnation point which appears as a sink instead of a separation point in the symmetry plane in front of the cylinder. The wall shear stress is largest between the main (horseshoe) vortex and the cylinder, and seems to be mainly governed by the strong downflow in front of the cylinder as turbulent stresses are small in this region. Due to a strong acceleration along the streamlines, a region of relatively small turbulent kinetic energy is found between the horseshoe vortex and the cylinder. When passing under the horseshoe vortex, the upstream-directed jet formed by the deflected downflow undergoes a deceleration which gives rise to a strong production of turbulent kinetic energy. We find that pressure transport of turbulent kinetic energy is important for the initiation of the large production rates by increasing the turbulence level in the upstream jet near the wall. The distribution of the dissipation of turbulent kinetic energy is similar to that of the turbulent kinetic energy. Large values of dissipation occur around the centre of the horseshoe vortex and near the wall in the region where the jet decelerates. While the small scales are nearly isotropic in the horseshoe vortex centre, they are anistotropic near the wall. This can be explained by a vertical flapping of the upstream-directed jet. The distribution and level of dissipation, turbulent and pressure transport of turbulent kinetic energy are of crucial interest to turbulence modelling in the Reynolds-averaged context. To the best of our knowledge, this is the first time that these terms have been documented in this kind of flow.

Production and dissipation of turbulent fluctuations close to a stagnation point

In this article, we investigate the production and dissipation of turbulence in a region where the mean flow topology presents a stagnation point. Our goal is to understand the generation of anisotropic fluctuations and their influence on production, dissipation, and transport of turbulent kinetic energy. In order to investigate the local turbulent kinetic energy budget, we use a shadow particle tracking velocimetry technique (S-PTV) to track Lagrangian tracers in a large portion of a turbulent von Karman flow produced by counter-rotating disks. We observe that the flow produced in a square tank is bistable, with each of the two states resembling impinging jets. This stagnation-point topology is responsible for the strong anisotropy of velocity fluctuations observed in these type of flows. The production of turbulence locally exceeds the dissipation rate. As a consequence, the flow is to be considered as strongly inhomogeneous as the fluxes of turbulent kinetic energy are non-negligible when compared to the production and dissipation terms.

Influence of Stokes Drift Decay Scale on Langmuir Turbulence

AbstractAccurately scaling Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) is critical for improving ocean, weather, and climate models. The physical processes by which the structure of LT depends on surface waves’ Stokes drift decay length scale are examined. An idealized model for OSBL turbulent kinetic energy (TKE) provides a conceptual framework with three physical processes: TKE transport, dissipation, and production by the Craik–Leibovich (CL) vortex force (VF) associated with the Stokes drift shear. TKE profiles depend on OSBL depth h, surface roughness length z0, and wavenumber k through the nondimensional parameters kh and kz0. These parameters determine the rate and length scale for the dissipation of TKE produced by the CL-VF. For kz0 ≫ 1, TKE input by the CL-VF is governed by a surface flux with TKE rapidly decaying with depth. Only for kz0 < 1 can TKE penetrate deeper into the OSBL, with the TKE penetration depth controlled by kh. Turbulence-resolving large-eddy simulation results support this conceptual framework and indicate that the dominant Langmuir cell size scales with (kh)−1. Within the depth of dominant Langmuir cells, TKE dissipation is approximately balanced by CL-VF production. Shorter waves contribute less to deeper vertical velocity variance 〈w2〉 because the CL-VF is less effective in generating larger-scale LT. Depth-averaged 〈w2〉 scales with a modified Langmuir number Laϕ = (u*/usϕ)1/2, where u* denotes the water-side surface friction velocity and usϕ is a depth-integrated weighted Stokes drift shear or, equivalently, a spectrally filtered surface Stokes drift.

A Surface-Layer Study of the Transport and Dissipation of Turbulent Kinetic Energy and the Variances of Temperature, Humidity and CO $$_2$$ 2

We discuss scalar similarities and dissimilarities based on analysis of the dissipation terms in the variance budget equations, considering the turbulent kinetic energy and the variances of temperature, specific humidity and specific CO $$_2$$ content. For this purpose, 124 high-frequency sampled segments are selected from the Boundary Layer Late Afternoon and Sunset Turbulence experiment. The consequences of dissipation similarity in the variance transport are also discussed and quantified. The results show that, for the convective atmospheric surface layer, the non-dimensional dissipation terms can be expressed in the framework of Monin–Obukhov similarity theory and are independent of whether the variable is temperature or moisture. The scalar similarity in the dissipation term implies that the characteristic scales of the atmospheric surface layer can be estimated from the respective rate of variance dissipation, the characteristic scale of temperature, and the dissipation rate of temperature variance.

The influence of shear-dependent rheology on turbulent pipe flow

Direct numerical simulations of turbulent pipe flow of power-law fluids at $Re_{\unicode[STIX]{x1D70F}}=323$ are analysed in order to understand the way in which shear thinning or thickening affects first- and second-order flow statistics including turbulent kinetic energy production, transport and dissipation in such flows. The results show that with shear thinning, near-wall streaks become weaker and the axial and azimuthal correlation lengths of axial velocity fluctuations increase. Viscosity fluctuations give rise to an additional shear stress term in the mean momentum equation which is negative for shear-thinning fluids and which increases in magnitude as the fluid becomes more shear thinning: for an equal mean wall shear stress, this term increases the mean velocity gradient in shear-thinning fluids when compared to a Newtonian fluid. Consequently, the mean velocity profile in power-law fluids deviates from the law of the wall $U_{z}^{+}=y^{+}$ in the viscous sublayer when traditional near-wall scaling is used. Consideration is briefly given to an alternative scaling that allows the law of wall to be recovered but which results in loss of a common mean stress profile. With shear thinning, the mean viscosity increases slightly at the wall and its profile appears to be approximately logarithmic in the velocity log layer. Through analysis of the turbulent kinetic energy budget, undertaken here for the first time for generalised Newtonian fluids, it is shown that shear thinning decreases the overall turbulent kinetic energy production but widens the wall-normal region where it is generated. Additional dissipation terms in the mean flow and turbulent kinetic energy budget equations arise from viscosity fluctuations; with shear thinning, these result in a net decrease in the total viscous dissipation. The overall effect of shear thinning on the turbulent kinetic energy budget is found to be largely confined to the inner layers, $y^{+}\lesssim 60$.

Turbulent kinetic energy transport in head-on quenching of turbulent premixed flames in the context of Reynolds Averaged Navier Stokes simulations

This paper investigates the statistical behaviour of the turbulent kinetic energy transport for moderate values of turbulent Renolds number Ret in turbulent premixed flames by using Direct Numerical Simulation (DNS) data in the case of head-on quenching by an isothermal inert wall for different Lewis numbers (i.e. Le=0.8–1.2). The magnitudes of turbulent kinetic energy and the terms of its transport equation have been found to increase with a reduction in global Lewis number. The magnitudes of all the terms except the viscous dissipation rate drops sharply near the wall whereas the magnitude of viscous dissipation rate exhibits a sharp increase in the near-wall region. The statistical behaviours of the terms arising from turbulent transport, pressure fluctuation transport, mean pressure gradient, pressure dilatation and viscous dissipation have been analysed by explicit Reynolds averaging of DNS data. It has been found that the viscous dissipation term acts as a major sink for all cases and all locations. The mean pressure gradient acts as the leading order source for all cases. However, the magnitudes of the mean pressure gradient, pressure dilatation and transport terms diminish with increasing Lewis number. Moreover, turbulent flux of kinetic energy has been found to exhibit counter-gradient transport and its extent diminishes with increasing Lewis number as a result of the weakening of flame normal acceleration. Detailed physical explanations have been provided for the observed behaviour of the turbulent kinetic energy transport. Existing models for the unclosed terms have been modified for accurate prediction of the corresponding terms extracted from DNS data especially in the near-wall region.