Turbulent Kinetic Energy Budget Research Articles

LDA measurements in a one-sided ribbed square channel at Reynolds numbers of 50,000 and 100,000

Laser Doppler anemometry (LDA) measurements in the fully developed turbulent flow through a one-sided rib-roughened square channel with a rib-height-to-channel-height ratio of k/H = 0.0667 and a rib-pitch-to-rib-height ratio of p/k = 9 were carried out at Reynolds numbers (based on the channel height H and the mean bulk velocity u_B) of {Re}_H = 5.0 cdot 10^4 and 1.0 cdot 10^5. Mean velocities, Reynolds normal, and shear stresses were determined. The first- and second-order statistical moments of the velocity differed slightly between both Reynolds numbers when normalized by the bulk velocity and the channel height. Deviations were attributed to a minor elongation increase in the large recirculation region behind the rib with increasing Reynolds numbers. The crucial role of turbulent diffusion was reflected in the non-coincidence of the maximum primary mean shear and the Reynolds normal stress as well as outward drifts of the Reynolds stress peaks along the rib crest. Turbulent diffusion contributed significantly to the turbulence kinetic energy (TKE) budget near the rib crest and within the separated shear layer, while mean convection made a remarkable contribution only at the rib leading edge. The detailed first- and second-order moments provide a basis for the validation of computational methods and turbulence models.Graphic abstract

The Dynamical Coupling of Wind-Waves and Atmospheric Turbulence: A Review of Theoretical and Phenomenological Models

When wind blows over the ocean, short wind-waves (of wavelength smaller than 10 m) are generated, rapidly reaching an equilibrium with the overlying turbulence (at heights lower than 10 m). Understanding this equilibrium is key to many applications since it determines (i) air–sea fluxes of heat, momentum and gas, essential for numerical models; (ii) energy loss from wind to waves, which regulates how swell is generated and how energy is transferred to the ocean mixed layer and; (iii) the ocean surface roughness, visible from remote sensing measurements. Here we review phenomenological models describing this equilibrium: these models couple a turbulence kinetic energy and wave action budget through several wave-growth processes, including airflow separation events induced by breaking waves. Even though the models aim at reproducing measurements of air–sea fluxes and wave growth, some of the observed variability is still unexplained. Hence, after reviewing several state-of-the-art phenomenological models, we discuss recent numerical experiments in order to provide hints about future improvements. We suggest three main directions, which should be addressed both through dedicated experiments and theory: (i) a better quantification of the variability wind-wave growth and of the role played by the modulation of short and breaking wind-waves by long wind-waves; (ii) an improved understanding of the imprint of wind-waves on turbulent coherent structures and; (iii) a quantification of the interscale interactions for a realistic wind-wave sea, where wind-and-wave coupling processes coexist at multiple time and space scales.

Turbulent Channel Flow With Spatially Dependent Viscosity: A Numerical Study

Abstract In this study, we examine in detail the effect of spatially dependent viscosity on wall-bounded flow. For this purpose, direct numerical simulations (DNS) are performed considering a channel flow with a viscosity change along the streamwise direction. The DNS were performed using nek5000, a computational fluid dynamics code developed at Argonne National Laboratory. The channel is divided into three different regions: in the first one, the flow is at a constant Reynolds number of Re = 5000; in the second region, the Reynolds number is imposed to linearly increase as viscosity decreases through a ramp; and finally, in the third region, the flow is again at a constant Reynolds number, this time at Re = 10,000. Since the temperature field is not evaluated, the proposed setup is a simplification of a heated channel. Nevertheless, the outcomes of this study may be valuable for future works considering variable-viscosity effects, especially for cooling and heating applications. Four test cases with different ramp inclinations were analyzed. The results from this study were compared with a correlation available in the literature for the friction Reynolds number as a function of the Reynolds number. We observe that in all cases the ramp does not cause an immediate change in the characteristics of turbulent structures, and a delay is in fact observed in both wall shear and friction. Finally, in order to characterize and understand these effects, streaks from the viscous region and turbulence statistics for the turbulent kinetic energy (TKE) budget terms are analyzed.

Compressibility in suddenly expanded subsonic flows

This paper concerns implicit large eddy simulations of subsonic flows through a symmetric suddenly expanded channel. We aim at shedding light on the flow physics at a relatively high Reynolds number of 10 000, based on the inlet bulk velocity and the step height of the channel, and examine the compressibility effects for two Mach numbers, Ma = 0.1 and Ma = 0.5. Comparisons with experimental measurements are provided. In addition, we investigate the structure of the separated regions, turbulence structures—through the Reynolds stress anisotropy componentality—and turbulence kinetic energy budgets. The results reveal that compressibility influences particular flow physics.

Spatially Evolving Turbulent Boundary-Layer Flow over a Wall-Mounted Cube

Turbulent flow over a wall-mounted cube presents an important canonical problem with applications in circuit design, urban building design, or aerodynamics. Flow over a cube placed in a fully developed turbulent channel flow has long been the preferred problem of investigation for researchers. However, a more relevant practical scenario is flow over a cube placed in a spatially evolving turbulent boundary layer (SETBL). In this work, wall-resolved large-eddy simulations of flow over a wall-mounted cube placed in an SETBL on a flat plate are performed at a Reynolds number of 19,600 based on the mean velocity and the inlet boundary-layer thickness. The incompressible Navier–Stokes equations are solved using a second-order finite-volume approach with a dynamic -equation eddy-viscosity model. At this Reynolds number, the key nondimensional parameter governing this problem is the ratio of cube height to boundary-layer thickness, . This paper investigates the dependence of the turbulence wake characteristics on . Specifically, this paper analyzes the vortical structures and the separation and reattachment lengths. It is further examined how the turbulent kinetic energy budget varies with . It is found that the size of the horseshoe vortex roughly scales with the size of the cube, and that the decay of turbulent kinetic energy per unit area over streamwise distance in the near wake exhibits a power-law behavior.

Coherent Velocity Structures in the Mixed Layer: Characteristics, Energetics, and Turbulent Kinetic Energy Budget

AbstractVelocity, hydrographic, and microstructure observations collected under moderate to high winds, large surface waves, and significant ocean-surface heat losses were utilized to examine coherent velocity structures (CVS) and turbulent kinetic energy (TKE) budget in the mixed layer on the outer shelf in the northern Gulf of Mexico in February 2017. The CVS exhibited larger downward velocities in downwelling regions and weaker upward velocities in broader upwelling regions, elevated vertical velocity variance, vertical velocity maxima in the upper part of the mixed layer, and phasing of crosswind velocities relative to vertical velocities near the base of the mixed layer. Temporal scales ranged from 10 to 40 min, and estimated lateral scales ranged from 90 to 430 m, which were 1.5–6 times as large as the mixed layer depth. Nondimensional parameters, Langmuir and Hoenikker numbers, indicated that plausible forcing mechanisms were surface-wave-driven Langmuir vortex and destabilizing surface buoyancy flux. The rate of change of TKE, shear production, Stokes production, buoyancy production, vertical transport of TKE, and dissipation in the TKE budget were evaluated. The shear and Stokes productions, dissipation, and vertical transport of TKE were the dominant terms. The buoyancy production term was important at the sea surface, but it decreased rapidly in the interior. A large imbalance term was found under the unstable, high-wind, and high–sea state conditions. The cause of this imbalance cannot be determined with certainty through analyses of the available observations; however, our speculation is that the pressure transport is significant under these conditions.

Turbulent flow characteristics over an abrupt step change in bed roughness

Turbulent flow characteristics over an abrupt step change in bed roughness from smooth to rough are studied measuring the flow field by a Particle Image Velocimetry (PIV) system. The smooth and rough beds are referred to as the upstream and downstream beds, respectively. The velocity color maps and profiles show that an abrupt step change in bed roughness causes flow retardation in the downstream bed owing to the combined effects of roughness-induced and separated flows. The results of the Reynolds stresses reveal that the profiles in the downstream bed exhibit discriminable bulges, whose size increases with an increase in the streamwise distance. The stress color maps illustrate the creation of a roughness-induced layer that grows over the downstream bed as the streamwise distance increases. The bed shear stress evidences an overshooting behavior immediate downstream of the abrupt step change in bed roughness to reach its peak magnitude. The third-order correlations indicate that the effects of the abrupt step change in bed roughness produce an inrush of rapidly moving fluid streaks in the near-bed flow and arrival of slowly moving fluid streaks in the away-bed flow. Regarding the turbulent kinetic energy (TKE) budget, the enhanced magnitudes of the TKE budget terms within the roughness-induced layer are prevalent. The TKE dissipation rate lags the production rate, and the negative TKE diffusion rate implies an addition in the TKE production. Bursting analysis endorses that the sweeps govern the near-bed flow on the downstream bed and the ejections prevail far from the bed.

Nonlinear evolutions of streaky structures in viscoelastic pipe flows

The dynamics of streaky structures in a viscoelastic pipe flow of FENE-P fluids is studied numerically. The values of Weissenberg number ( W i , polymer relaxation time over flow turn-over time) and viscosity ratios are varied to evaluate the effects of viscoelasticity in the pipe. For Reynolds numbers 3000 ∼ 3500 (based on pipe radius and maximum laminar velocity) near the transition boundary, we select finite-amplitude two-dimensional rolls as initial conditions and add infinitesimal three-dimensional perturbations to trigger the transition. The 2D streamwise rolls are highly unstable to small 3D disturbances, which helps to better understand the evolution of large scale structures. The stronger temporal intermittency in viscoelastic flows makes it more difficult to identify a successful transition; we found that quantities directly related to viscoelasticity can serve as better indicators of transition to turbulence. The role of polymer stress is studied through the kinetic energy budget and it is found that polymer torque opposes the vorticity and become more dominant for higher W i , consistent with previous studies. The results show that the secondary instability of the streaky structures can be enhanced by viscoelasticity at low W i , while at high W i viscoelasticity delays the transition to turbulence, sometimes leading to relaminarization. • Direct numerical simulations of viscoelastic pipe flow of FENE-P fluids are conducted. • Viscoelasticity changes the evolution of streaks and causes strong intermittency. • Polymer stress is studied via turbulent kinetic energy budget in streak breakdown. • Non-monotonic influence of Weissenberg number on threshold boundary of transitions.

CFD simulations of two opposing plane wall jets in a generic empty airplane cabin: Comparison of RANS and LES

Accurate computational fluid dynamics (CFD) simulations of the ventilation flow in airplane cabins are important for ventilation design optimisation regarding passenger health, thermal comfort and energy efficiency. The complex unsteady flow phenomena inside the cabin are challenging in numerical modelling and therefore dedicated validation of the simulation outcomes is required. The majority of airplane ventilation studies performed steady Reynolds-averaged Navier-Stokes (RANS) simulations and focused mainly on global flow field characteristics. This paper presents both steady RANS and transient simulations, including unsteady RANS and large eddy simulations (LES), of the flow driven by opposing plane wall jets in a reduced-scale isothermal water-filled generic airplane cabin. A detailed analysis of the mean velocity and turbulence characteristics (including Reynolds stresses) of the cabin flow is outlined, encompassing a thorough investigation of the fundamental flow components such as the opposing jets and the merged jet. Specific attention is devoted to LES grid sensitivity and the performance of different RANS turbulence and LES subgrid-scale (SGS) models is assessed by comparison with particle image velocimetry (PIV) measurements. It is shown that LES in general performs much better than RANS, the latter being incapable of providing accurate mean flow characteristics within the interaction zone and merged jet due to the underlying dynamic opposing jet interaction. Unsteady RANS partly covers the unsteadiness, however, turbulence levels remain systematically underpredicted and LES is required for a correct representation. Differences between the LES SGS model predictions are limited to the SGS kinetic energy budget of the total turbulent kinetic energy.

The influence of aspect ratio on flow states in the buoyancy-driven turbulence with free slip boundaries

Buoyancy driven turbulence with free-slip top and bottom plates in a confined box is studied via direct numerical simulations (DNS). The Rayleigh number is fixed to Ra=108 and the Prandtl number is Pr=10. The length/height aspect ratio Γy is fixed to 2, while the depth/height aspect ratio Γx varies from 0.125 to 0.3. With the variation of Γx, the hysteresis-like behavior of the heat and momentum transfer is found due to the emergence of two stable states of flow organization. For small Γx, the sheared flow occurs with disordered plumes occupying the entire bulk region, while it is replaced by convection rolls with increasing Γx. The striking feature is that the heat and momentum transport is greatly suppressed in the shear flow (SF) state, compared with that in the convection roll (CR) state. The turbulent kinetic energy budget is performed to delineate the relative contributions of physical processes that govern energy transport. It is found that the kinetic energy in the SF state is mainly produced by the buoyancy force, while it is dominated by the shear production near the plates in the CR state. During energy transport, it seems that the buoyancy force plays a more important role in the SF state than in the CR state, particularly in the bulk. Furthermore, through the analysis of dynamic mode decomposition of temperature fields, we illustrate that the flow in the SF state is dominated by the cloud-like spatially coherent structures with low frequencies, while the low-frequency roll structures play a leading role in the CR state. The flow state transition from SF to CR corresponds to the process that the cloud-like coherent structures form roll structures.

Influence of Form-Induced Shear Stress on Turbulent Kinetic Energy Budget Distributions Above and Within the Flow-Gravel-Bed Interface in Permeable Gravel Bed Stream—a Comparative Study

Influence of Form-Induced Shear Stress on Turbulent Kinetic Energy Budget Distributions Above and Within the Flow-Gravel-Bed Interface in Permeable Gravel Bed Stream—a Comparative Study

Turbulent Kinetic Energy and Budget of Heterogeneous Open Channel with Gravel and Vegetated Beds

Turbulent kinetic energy (TKE) and budget are indispensable hydraulic parameters to determine turbulent scales and processes resulting from various and different natural hydraulic features in open channels. This paper focuses on experimental investigation of turbulent kinetic energy and budget in a heterogeneous open channel flow with gravel and vegetated beds. Results indicate the turbulent kinetic energy (TKE) value over gravel region of the heterogeneous bed remains approximately constant with flow depth. The highest turbulent kinetic energy was calculated for flexible vegetation arrangement compared to the rigid vegetation. The estimation of the turbulent kinetic energy budget shows the higher values of turbulence production recorded over the flexible vegetated bed, consequently, the dissipation rate exhibits faster decay of turbulence kinetic energy over the vegetated bed in comparison to the gravel bed.

Direct numerical simulation of fluid flow in a 5x5 square rod bundle

Characterization of parallel flow through rod bundles is of key importance in assessing the performance and safety of several engineering systems, including a majority of nuclear reactor concepts. Inhomogeneities in the bundle cross-section can present complex flow phenomena, including varying local conditions of turbulence. With the ever-increasing capabilities of high-performance computing, Direct Numerical Simulation (DNS) of turbulent flows is becoming more feasible. Through resolving all scales of turbulence, DNS can serve as a “numerical experiment,” and can provide substantial insight into flow physics, but at considerable computational cost. Thus to date, the DNS in open literature for rod bundle flows is relatively scarce, and largely limited to unit-cell domains. Since wall effects are important in rod bundle flows, a multiple-pin DNS study can expand understanding of rod bundle flows while providing valuable reference data for evaluating reduced-resolution techniques. In this work, DNS of a 5x5 square bare rod bundle representative of typical light water reactor fuel dimensions was performed using the spectral element code Nek5000. Turbulent microscales based on an advanced Reynolds-Averaged Navier–Stokes model were used to establish the required DNS resolution. Velocity and Reynolds stress fields are analyzed in detail, and invariant analysis is used for further investigation into flow physics. The results show stark changes in the structure of turbulence in the edge gaps, suggesting the presence of gap vortices in these regions. In addition, turbulent kinetic energy budgets are presented to more fully illustrate the various turbulent processes. These data can prove useful for rigorous evaluation of lower-fidelity turbulence modeling approaches.

Turbulent and wave kinetic energy budgets in the airflow over wind-generated surface waves

Abstract

Non-explicit large eddy simulations of turbulent channel flows from [formula omitted] up to [formula omitted

This numerical study based on high-order finite-difference schemes presents LES-NWR (Large Eddy Simulation with near-wall resolution) of turbulent channel flows up to Reτ=5200 using non-explicit approaches for which numerical dissipation is introduced via the discretisation of viscous terms of the Navier-Stokes equations. These models are cheaper than explicit LES models as no extra terms are needed in the equations to account for the contribution of the unresolved scales. The Approximate Deconvolution Method with Relaxation Term (ADM-RT) approach is also assessed and the present LES data are compared with reference Direct Numerical Simulations (DNS) data for first and second order moments as well as for the turbulent kinetic energy budget. Even if the viscous sublayer is not resolved, the proposed non-explicit LES approaches are in excellent agreement with the reference DNS data and to a certain extent with the ADM-RT model, for a fraction of the cost of the DNS. The proposed non-explicit models, for which the possibility to locally adjust the added numerical dissipation is investigated, are straightforward to implement and come with a negligible additional computational cost while the ADM-RT model is 30% more expensive than the non-explicit models.The parameters of the models are defined before the simulations and no modifications of the parameters are needed when the Reynolds number and the mesh resolution are changed. It is shown that a modulation of the magnitude of the numerical dissipation in time and in space is not necessarily needed, at least for the mesh resolutions and Reynolds numbers considered in the present study. The main conclusion is that non-explicit models can replace advantageously explicit models when high-order finite-difference methods are used. They can generate accurate LES-NWR of turbulent channel flows over a wide range of Reynolds numbers at a fraction of a cost of DNS.

Higher-Order Turbulence Around Different Circular Cylinders Using Particle Image Velocimetry

Abstract Wakes and higher-order turbulence around circular cylinders of different diameters are investigated using particle image velocimetry measurements. The cylinder Reynolds number (Red) is defined by the depth-averaged velocity, cylinder diameter, and kinematic viscosity. The influence of Red on third-order moment of velocity fluctuations, turbulent kinetic energy (TKE) flux, TKE budget, and turbulent length scales are presented. The intermittency factor (IF) and quadrant analysis around the cylinders are discussed for Red values ranging from 12,600 to 21,000. The energy budget mostly near free surface upstream and near-bed downstream is changed due to Red. Stream-wise and transverse TKE fluxes decreased significantly with Red, but not the vertical flux. Stream-wise skewness changed sign from positive to negative at a certain critical distance downstream, while vertical skewness showed reversed effect with Red. Negative stream-wise skewness and positive vertical skewness indicate the occurrence of ejection events. On the downstream, the production and dissipation rates increased with Red, whereas an opposite trend was observed for dissipation only on the upstream. Increase of Red led to an increase in the Kolmogorov length-scale much higher on the upstream than the downstream, whereas it showed depleting effect on Taylor's length-scale on the upstream and an increasing effect on the downstream. Ejection and sweep events were more prominent in the downstream near the cylinder than upstream with higher values of shear stress on the downstream. The sum of the shear stress contributions of all quadrant events increased consistently with an increase in Red near the cylinder.

Reynolds, Mach, and Freestream Turbulence Effects on the Flow in a Low-Pressure Turbine

Abstract This article presents the large-eddy simulation (LES) of a low-pressure turbine (LPT) nozzle guide vane (NGV) for different Reynolds (Re) and Mach (Ma) numbers with or without inlet turbulence prescribed. The analysis is based on a slice of an LPT blading representative of a midspan flow, where secondary flows, hub, and shroud effects are lower. The characteristic Re of the LPT can vary by a factor of four between take-off and cruise conditions. In addition, the LPT operates at different Ma values, and the incident flow can have significant levels of turbulence due to upstream blade wakes. This article investigates numerically using LES the flow around an LPT blading with three different Reynolds number Re = 175,000 (cruise), 280,000 (mid-level altitude), and 500,000 (take-off) keeping the same characteristic Mach number Ma = 0.2 and three different Mach number Ma = 0.2, 0.5, and 0.8 keeping the same Reynolds number Re = 280,000. These different simulations are performed with 0% freestream turbulence (FST) followed by inlet turbulence (6% FST). The study focuses on the influence of these three parameters (Re, Ma, and upstream turbulence) on different flow characteristics: pressure distribution around the blade, near-wall flow behavior, loss generation, and turbulent kinetic energy (TKE) budget. The results show an earlier boundary layer separation on the aft region of the blade suction side when the Re is increased, while the increase of the Ma delays separation, similar to freestream turbulence. The TKE budget led on the different cases shows the predominant effect of the turbulent production and diffusion in the wake, the axial evolution of these different terms being relatively insensitive to Re and Ma.

Impact of bubble size on turbulent statistics in bubble plumes in unstratified quiescent water

We report an experimental investigation of turbulence in bubble plumes released in unstratified quiescent water. The focus is to study the detailed turbulent statistics and the budget terms in the equations of turbulent kinetic energy (TKE), particularly about their distributions in the radial direction of bubble plumes compared to those in the single-phase momentum jets and buoyant plumes. Two types of diffusers were used to generate plumes consisting of different bubble sizes and population at the same source gas discharge. The bubble plumes have different growth behaviors under different combination of sizes and population: the plumes with many small bubbles show decreasing centerline velocities along the vertical direction; the plumes with larger but fewer bubbles have a tighter bubble core, a smaller spreading ratio, and almost constant centerline velocities. The ratio of turbulence-to-mean in momentum flux is strongly affected by bubble sizes and population, demonstrated in the profiles of normalized turbulent velocity correlations using mean flow parameterizations. Velocity fluctuations show a strong vertical-to-horizontal anisotropy in bubble plumes compared to those in single-phase jets and plumes. Strong vertical fluctuating velocity component contributes a significant role in re-shaping the radial profiles of turbulent stresses and transport terms when the bubble plume is composed of larger but fewer bubbles. Local balance cannot be established in the equation of TKE traditionally used for single-phase flows. A bubble-related source term in the governing equation is needed to close the budget. An empirical equation using drag force and bubble slip velocity is validated for the TKE closure. We provide a diagram of TKE budget to illustrate the pathway of TKE terms in the radial direction, with the magnitude of each term influenced by bubble characteristics.

Experimental study of horizontal heated buoyant jets in a linearly stratified ambience

Horizontal warm buoyant jets injecting into a linearly stratified ambience are common in lakes, estuaries, and oceans. Dynamic features and potential surface temperature signatures of heated buoyant jets are experimentally investigated using particle image velocimetry and an infrared camera. Results reveal that when heated jets are completely underwater, the flow evolution can be classified into the horizontal regime, ascending regime, and collapsing regime, respectively. The maximum rise height and the neutral height both increase linearly with the increasing jet length scale. Based on this relationship, an equation is developed to predict the surface impingement of a horizontal heated buoyant jet. If the surface impingement occurs, staggered vortexes and large meanders caused by mixing between the jet and the free surface are observed on the surface temperature maps. Furthermore, surface temperature fluctuation fields are decomposed using the Karhunen-Loeve method, the first four eigenmodes appear to capture the root mean square temperature fluctuations and the features correlated with the swirling vortexes. In the turbulent kinetic energy budget, mean-flow convection is found to be mainly balanced by turbulent transport. As the heated jet propagates downstream, more kinetic energy is transferred into potential energy rather than into turbulent energy.

Damköhler number scaling of active cascade effects in turbulent premixed combustion

Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damköhler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames. At low Karlovitz numbers, where heat-release effects dominate turbulent kinetic energy budgets, their relative significance scales with the integral Damköhler number in a priori Reynolds-Averaged Navier–Stokes (RANS) statistics and the filter Damköhler number in Large Eddy Simulation (LES). The Damköhler-number scaling of counter-gradient transport in this regime follows theoretical arguments underpinning linear-algebraic turbulence models, which explains their efficacy at low Karlovitz numbers. Conversely, at moderate Karlovitz numbers, LES subfilter turbulence is more strongly influenced by heat-release effects than the analogous large-scale RANS turbulence. This is consistent with the notion of an “active cascade,” which postulates that heat-release-induced volumetric expansion competes on intermediate scales with classical forward-cascade energy transfer. LES exposes these dynamics as dominant subfilter-scale physics, unlike in RANS, where they are secondary to the effects of mean-shear production at the large scales. The significance of subfilter-scale interactions is promoted by the LES filter itself, which modifies the RANS spectral basis by incorporating local flame-normal averaging. This is highlighted by comparing LES fields obtained using a 3D filter to those using a modified 2D filter, excluding the flame-normal direction, which significantly reduces the apparent influence of heat-release effects but is not representative of LES in practice. The subfilter modeling challenges posed by these distinctions at moderate Karlovitz numbers and order-unity Damköhler numbers remain to be understood.