Turbulent Kinetic Energy Budget Research Articles

The NexGen burner: Non-Reacting gaseous and spray dynamics

This paper reports the results of a comprehensive investigation to identify turbulent multiphase fluid dynamics through the NexGen burner used for fireworthiness certifications by the Federal Aviation Administration. The burner geometry consists of a draft tube, a stator to swirl the incoming air, a turbulator that is placed immediately downstream of the stator to increase the turbulence intensity of the swirling flow, and a burner cone that exhausts into the atmosphere. A Delavan type-W fuel nozzle, attached downstream of the turbulator injects Jet A into the burner cone, where it mixes with the turbulent swirling air, vaporizes and subsequently burns. The operating conditions consist of air and fuel mass flow rates of 0.0384 kg/s and 2.5 Gph at room temperature and pressure conditions. In this paper, we report on non-reacting fluid dynamics; the reacting flow analysis will be presented in a subsequent manuscript. To systematically analyze the flow configuration, three calculations are conducted. First, to validate our large eddy simulation-based framework, a case without the burner cone is conducted—our results are in reasonable agreement with experimental measurements. In the second configuration, to isolate the effect of liquid injection on turbulent flow physics, simulations are conducted with the burner cone but without fuel spray. Detailed analyses are conducted, including identification of flow structures, swirl generation, and the turbulent kinetic energy budget. Finally, Jet A is injected into the burner, and the spray and gaseous flow fields are quantified and compared with the flow structures developed without spray injection.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Direct Numerical Simulation of Heat Transfer in a 7-Pin Wire-Wrapped Rod Bundle

The Sodium-Cooled Fast Reactor (SFR) is a promising concept chosen in the Generation IV International Forum as a possible design for pursuing the sustainable use of nuclear energy. Its core consists of multiple hydraulically isolated assemblies, with a tightly packed triangular lattice array of fuel pins enclosed in a hexagonal duct present within each assembly. Helical wire spacers are wrapped along the axis of the rods to maintain a gap between them, inducing a secondary flow, increasing the channel mixing, and enhancing convective heat transfer. In this study, a direct numerical simulation campaign is conducted for a simplified 7-pin wire wrapper geometry, with Reynolds numbers ranging from Re = 1000 to 10 000 and a Prandtl number of Pr = 0.005, to investigate heat transfer in low-flow conditions. The wire wrapper case is compared to a bare bundle case with seven pins. The results are discussed, and heat transfer predictions are compared between our numerical results and classic correlations. An anisotropy invariant map is obtained for the above-mentioned cases, and turbulent kinetic energy and turbulent heat flux budgets are computed and analyzed. Our findings provide unique insights into the flow behavior within a wire-wrapped bundle.

Higher-order turbulent characteristics of sinuous alluvial river

Sinuous channels with movable banks were examined for flow patterns in laboratory experiments. The velocity, Turbulent kinetic energy (TKE) budget, TKE flux, and bursting events were analyzed to examine the turbulent flow behavior. Quadrant analysis is performed to determine the contribution of bursting events to Reynold shear stress. At the apex of the sinuous channel, quadrant analysis reveals a mixing of events. On the other hand, as the hole size increases, the contribution of events decreases. The TKE (turbulent kinetic energy) flux is greater near the riverbed and diminishes as it approaches the bed surface. The TKE flux is higher at the river bend's exit than at the entry point. Examining the TKE budget, the TKE production and TKE dissipation indicate that TKE dissipation surpasses the production near the riverbed and the surface. These terms are uniformly distributed and decrease as they approach the surface.

Compressibility effects in turbulent channel with weak spanwise rotation using direct numerical simulations

Direct numerical simulations of temporally evolving turbulent channel flows with a weak spanwise rotation are conducted at a rotation number of 0.05 and Mach numbers of 0.3, 1.5, and 3.0 to investigate the influence of compressibility effects on turbulent statistics and large-scale structures. The corresponding Reynolds numbers are 2820, 3000, and 4880. Investigation shows that many asymmetric characteristics for incompressible flow also hold for compressible flow. The mean and fluctuating turbulent statistics distributions are similar to those for incompressible flows and shift from the suction side toward the pressure side. Weak spanwise rotation alters the mean the Mach number. The recovery enthalpy collapses between the pressure and suction sides and is independent of the Mach number. The Reynolds shear stress distributions are similar for compressible flows but with larger slopes than incompressible flows. When introducing semi-local scaling, the turbulent kinetic energy budget at pressure side is insensitive to compressibility effects. The average spanwise spacing of near-wall streaks increases as with the Mach number. The number of Taylor–Görtler vortex pairs is determined primarily by the aspect ratio of the computational domain, and is independent of the compressibility effects.

High-subsonic boundary-layer flows of an organic vapour

Boundary layers of Novec649, a low-global-warming potential fluid of interest for low-grade heat recovery, are investigated numerically by means of linear stability theory, direct numerical simulation (DNS) and large-eddy simulations (LES). This organic vapour is of interest in organic Rankine cycle (ORC) turbines and realistic thermodynamic conditions are selected. Under these conditions, the vapour behaves as a dense gas and, due to its high molecular complexity, real-gas effects occur. In addition, the fluid exhibits large and highly variable heat capacities and density- as well as temperature-dependent transport properties. More specifically we report the first direct and LES of transitional and turbulent boundary layers of Novec649 at high-subsonic conditions$M=0.9$. A controlled transition is performed by using oblique modes determined by linear stability theory extended to dense gases. An oblique-type transition is obtained as in low-speed air flows, where sinuous streaks develop by the lift-up mechanism and break down into turbulence. In the turbulent state, the profiles of dynamic flow properties (velocities, turbulent intensities, turbulent kinetic energy budgets) are little affected by the gas properties and remain very close to incompressible DNS, despite the high-subsonic flow speed. The fluctuations levels for thermodynamic properties have been quantified with respect to air flows. Notwithstanding a drastic reduction, genuine compressibility effects are present. For example, the fluctuating Mach number and the acoustic mode are characteristic of high-speed flows. The influence of forcing frequency and amplitude on the established turbulent state has been investigated using LES. An analysis of integral quantities shows a slow relaxation towards a canonical equilibrium turbulent state for all cases due to the high Reynolds numbers typical of dense gas flows. Overall the present DNS constitutes a valuable reference not only for forthcoming experiments but also for future studies of free-stream transition and loss mechanisms in ORC turbines.

Estimation of the turbulent kinetic energy in vegetated channels from the perspective of vortex dynamics

Turbulence has been recognized as the main driver of sediment incipient motion in vegetated regions, where the turbulent kinetic energy (TKE) linked to stem wakes exceeds that associated with bed shear and the classical bed shear-based model is no longer valid. Presently, the vegetation-generated turbulence within the emergent canopy of rigid cylinders is described from the perspective of vortex dynamics (i.e., how plant-induced eddies drain kinetic energy from the mean flow and feed it directly into turbulence), instead of the TKE budget balance generally in use. A few theoretical hypotheses on stem wake flow (including the volume, turbulence density, and turbulent energy of Karman vortices) are proposed, based on which a new model is proposed to predict the TKE in vegetated regions. The reasonable performance of this new model, compared with previous research data, indicates the feasibility of the new formula and associated theoretical hypotheses.

LES of natural convection along a side-heated vertical wall in a water cavity applied for the scale of Small Modular Reactor ([formula omitted

The passive safety concept of Small Modular Reactors (SMR) is based on the transfer of residual heat from the reactor to a water pool. Since the height of the reactor vessel reaches approximately 15 m, this leads to a strong heat exchange between the wall and the water by the way of natural convection. The maximum Rayleigh number (Ra) reaches 1014 or 1015. Reliable heat transfer correlations exist only up to Ra≈1012, still along with uncertainties in the extrapolation to higher Rayleigh number values. To improve the understanding of natural convection at high Rayleigh number values, the turbulent natural convection boundary layer (TNCBL) along a 15 m high, side-heated vertical wall in a water tank is simulated by employing the Large Eddy Simulation method with the CEA in-house code Triocfd (Angeli et al., 2015). The numerical results in terms of heat transfer correlation, mean temperature and mean velocity, second moment variables show a reasonable agreement with available experimental data in the range of Ra < 1012. It is observed in the simulation that the powers of the heat transfer correlations in the laminar (Nuy=0.56Gry∙Pr0.25) and the turbulent regimes (Nuy=0.114Gry∙Pr1/3) correspond well to the classical regimes at Ra<2×1012. A slight deviation from the classical exponent (1/3) is found at higher Rayleigh number (2×1012 <Ra<1.8×1015), namely Nuy=0.114(Gry∙Pr)0.33 . Through the analysis of turbulent kinetic energy budget, it is found that turbulent contribution from shear stress increases continuously with the increase of Rayleigh number. However, the turbulence contribution from buoyancy keeps increasing until Ra≈6.6×1013, then decreases gradually at higher Rayleigh number. The behavior of the maximum buoyant force shifts slowly from the inner boundary layer to the outer boundary layer may indicate the potential transition of the buoyancy-dominated regime to the shear stress dominated regime, thus confirming previous theoretical prediction (Wells Andrew and Worster, 2008). The increasing scale of the streak-like turbulent structures with the increase of Rayleigh number are clearly demonstrated through visualization process.

Momentum boundary layers in transcritical channel flows

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. We apply a physically consistent subgrid-scale turbulence model, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. In total seven cases are computed covering different Reynolds numbers, pseudo-boiling positions and pressure values. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum layer thicknesses. All cases feature a turbulent mass flux which is essential in turbulence modelling. Furthermore, we analyse the turbulent kinetic energy budgets, perform a quadrant and octant analysis of the Reynolds shear stress and employ an invariant map to study the anisotropy in transcritical turbulent channel flows.

Kinetic Energy Budget in Turbulent Flows of Dilute Polymer Solutions

Direct numerical simulation of a turbulent pipe flow of a realistic solution of 108\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^8$$\\end{document} polymers, modelled as finitely extensible nonlinear elastic (FENE) dumbbells, and directly momentum coupled with the incompressible Navier–Stokes equations, are performed by means of an Eulerian-Lagrangian approach. Besides the drag reduction, the polymers significantly modify mean and turbulent kinetic energy budgets. The polymer backreaction to the solvent reduces the Reynolds stress and thus decreases the turbulent production and, at large Weissenberg number, the polymers act as a source of turbulent kinetic energy for y+>40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y^+> 40$$\\end{document}, leading to an increase in the dissipation. This effect is peculiar to large Weissenberg polymers and it is particularly apparent at a small Reynolds number. At a smaller Weissenberg number, the effect of the polymers remains confined in the buffer layer, with the kinetic energy budget not significantly altered elsewhere.

Large-eddy simulation of free-surface turbulent channel flow over square bars

The results of large-eddy simulations of free-surface turbulent channel flow over spanwise-aligned square bars are used to investigate the effects of bed roughness and water surface deformations on the root-mean-squared velocity fluctuations, dispersive shear stress, double-averaged Reynolds shear stress, wake kinetic energy and double-averaged turbulent kinetic energy. Two bar spacings, corresponding to transitional and k-type roughness, at similar Reynolds and Froude numbers are considered. The main peak of all statistical quantities occurs at the bar crest height. The effects of a standing wave at the water surface in flow over k-type roughness is marked by a local peak under the water surface for all statistical quantities considered here except wall-normal and spanwise velocity fluctuations. Quadrant analysis shows that sweeps and ejections are the strongest events contributing to both dispersive and double-averaged Reynolds shear stress but their contributions are different for the two bar spacings. Examining the budgets of dispersive and double-averaged Reynolds shear stress reveals that the dominant terms of these stresses are pressure–strain correlation and pressure transport and the contribution of wake production is similar for both of these stresses but with opposite sign. In addition to the main role of the bars in consuming or producing wake kinetic energy through production and transport and convection, the standing wave at the water surface in flow over k-type roughness induces large convection in the bulk flow too. The dominant terms in the double-averaged turbulent kinetic energy budget are similarly production, transport and convection. Large shear production renders large temporal fluctuations than spatial fluctuations of flow variables. The interaction of bars, bed and water surface is seen in the convection term in flow over k-type roughness.

Direct Numerical Simulation and Large Eddy Simulation of a 67-Pebble-Bed Experiment

An in-depth understanding of the flow physics in packed beds is critical for developing simulation tools for pebble bed reactors. Advances in computing power have now made the full-core pebble-resolved computational fluid dynamics simulation of these systems possible. This work presents validation of the velocity and pressure predictions made by the spectral element code NekRS followed by a study of the turbulent kinetic energy and turbulent heat flux budgets. Two cases with corresponding experiments are considered: a bed of 67 pebbles with Re = 1460 and a bed of 789 pebbles with 324 < Re < 1024. Velocity and pressure drop comparisons are performed with the two cases, respectively. Good agreement is found between the experiments and their respective NekRS simulations. The 67-pebble case was then used to perform a direct numerical simulation to extract the turbulent kinetic energy and turbulent heat flux budget terms. Analysis of the turbulent kinetic energy production revealed large areas of negative production near the bottom surfaces of the pebbles. Further investigation revealed a trend between the average amount of negative turbulent kinetic energy production and the local porosity. These results continue to suggest that inertial effects play a large role in differentiating near-wall flow from bed-interior flow.

Turbulence in a wall-wake flow downstream of two horizontal cylinders

Experimental investigations of flow past two (one above other) horizontal cylinders have been presented in this paper. The experimental data captured over a rough-bed with double cylinders having three different diameters, were used for the analysis. Firstly, general characteristics such as streamwise velocity, Reynolds shear stress and turbulence intensity profiles have been elucidated at different downstream locations from cylinder position; then some advanced analysis such as length scales, turbulent kinetic energy (TKE) fluxes and budget have been investigated to exhibit their variations. Length scale profiles exhibit higher values in near bed; indicating comparatively larger eddies’ downstream of both cylinders. TKE budget profiles indicate highly negative pressure energy diffusion rate together with a sufficient TKE production rate, stabilized by the amplified TKE diffusion and dissipation rates. To determine one of the most prime behaviors of turbulence characteristics, namely TKE dissipation rate more accurately, the concept of structure function has been employed. Primarily velocity gradient method elucidates TKE dissipation rate, then it has been verified by Kolmogorov’s two-thirds law using second order structure function and Kolmogorov’s − 5/3 law using the method of power spectra.

Behavioral patterns of turbulent kinetic energy budget and quadrant analysis for flows over bedform under the influence of downward seepage

Seepage is one of the important factors involved in natural flow conditions, contributing to changes in flow turbulence patterns and morphological changes due to the transport of sediments. This transport of sediment particles influences the development of fluvial bedforms in any river channel. However, previous research on fluvial dynamics has not considered the influence of seepage on the flow field over the fluvial bedforms. The present experimental research aims to explore the behavioral patterns of turbulent kinetic energy, the turbulent kinetic energy (TKE) budget, and quadrant analysis for flows over two-dimensional dune shaped bedforms in the absence and presence of downward seepage. Results from the study illustrate that at the measurement locations on the initial and lee side sections of a dune, the TKE increases with the introduction of downward seepage, leading to an increase in turbulence production near the bed-surface region. The flow energy under both no seepage and seepage conditions contributes mainly to the turbulent production. Turbulence diffusion and dissipation rates have been found to decline in the near-bed region of the initial and lee side sections of the dune. However, turbulent production has been found to be significantly higher in the presence of downward seepage than under the no seepage condition. Similarly, turbulent kinetic energy flux increases in the streamwise direction, while it reduces in the vertical direction at initial sections and lee side sections of the dune under seepage conditions. However, at the middle sections and crest portion of the dune, opposite behavioral patterns are observed for all the aforementioned turbulent entities. Quadrant analysis reveals that the sweep and ejection event increases while inward and outward interaction reduces in the near bed zone. Although the contribution of both sweep and ejection events increases in the presence of downward seepage, sweep events have clear dominance in the near bed region, suggesting the possibility of a higher rate and amount of sediment transportation than under the no seepage condition.

Spectral turbulence kinetic energy budget and scale-based velocity decomposition for turbulence in bubble plumes

We conducted a spectral analysis of the turbulence kinetic energy (TKE) budget in a bubble plume using particle image velocimetry with fluorescent particles. Our findings confirmed the hypothesis of an inverse energy cascade in the bubble plume, where TKE is transferred from small to large eddies. This is attributed to direct injection of TKE by bubble passages across a wide range of scales, in contrast to canonical shear production of TKE in large scales. Turbulence dissipation was identified as the primary sink of the bubble-produced TKE and occurred at all scales. The decomposition of velocities using the critical length scale of inter-scale energy transfer allowed us to distinguish between large- and small-scale motions in the bubble plume. The large-scale turbulent fluctuations exhibited a skewed distribution and were likely associated with the return flow after bubble passage and the velocities induced by the bubble wake. The small-scale turbulent fluctuations followed a Gaussian distribution relatively well. The large-scale motions contributed to over half of the Reynolds stresses, while there were significant small-scale contributions to the normal stresses near the plume center but not to the shear stress. The large-scale motions in the vorticity field induced a street of vertically elongated vortex pairs, while the small-scale vortices exhibited similar sizes in both horizontal and vertical directions.

The turbulence development of a vertical natural convection boundary layer

Results from direct numerical simulations of a vertical natural convection boundary layer (NCBL) with $Pr=0.71$ reveal that the turbulence development of such a thermally driven convective flow has two distinct stages: at relatively low Grashof number, the bulk flow is turbulent while the near-wall region is laminar-like or weakly turbulent; at sufficiently high Grashof number, the entire flow becomes turbulent in the sense of von Kármán (cf. Grossmann &amp; Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56, for the ultimate turbulent regime). Investigations on the turbulence statistics show that the near-wall Reynolds shear stress is negligible in the weakly turbulent regime but will grow in magnitude as the flow transitions to the ultimate regime at higher Grashof number. Similar behaviour is also seen in the streamwise turbulence intensity, where it develops from a mono-peak profile into a dual-peak structure as the Grashof number increases. At higher Grashof number, the near-wall energetic site is shown to have an energy distribution similar to that of a canonical wall-bounded turbulence (e.g. Hutchins &amp; Marusic, Phil. Trans. R. Soc.A, vol. 365, 2007, pp. 647–664), with a peak centred at fixed location and wavelength ( $y^+=18$ and $\lambda ^+_x=1000$ ) in viscous coordinates. Investigation on the spanwise spectra also suggests that the turbulent near-wall streaks emerge only at sufficiently high Grashof number, with constant spacing $\lambda _z^+\approx 130$ . The extent of the weakly turbulent regime is identified using the maximum velocity location $\delta_m$ and a laminar length scale $\delta_u$ . The development of near-wall turbulence is also investigated by examining the turbulence kinetic energy budget. In the weakly turbulent regime, the near-wall turbulence is sustained predominantly by the pressure transport in addition to the shear production. At higher Grashof number, the flow becomes fully turbulent, and both turbulent transport and shear production become stronger, while the pressure transport is decreased. These results also reveal that the production–dissipation ratio $P/\varepsilon$ of the NCBL would follow a fundamentally different trend to the canonical wall-bounded flows, which further supports that the near-wall turbulence generation is affected by the bulk flow.

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.

Editorial: Celebrating the contributions of Professor Guieppe Marrucci to rheology and non-Newtonian fluid mechanics

Direct numerical simulations (DNS) of generalized Newtonian fluids in a rectangular channel at a friction velocity of 180 are performed using OpenFOAM. The simulations are performed for a Newtonian fluid, a power-law fluid, and a Herschel-Bulkley (HB) fluid. Two-point correlations of the streamwise velocity reveal that a significant increase in the computational domain size is required to avoid statistical correlation due to the shear-thinning and yield stress. The analogous Kolmogorov scale shows that the dissipative structures may be orders of magnitude larger with these two non-Newtonian behaviors. This is demonstrated to be linked to the significant increase in the viscosity. The mean streamwise velocity field integrates to a larger bulk velocity with increased shear-thinning as compared with the Newtonian fluid flow. The addition of the yield stress does the same with respect to the power-law fluid flow. The difference in the velocity profiles is more pronounced in the outer layer. It, however, is observed that the rheology does not play a significant role in the outer layer for the mean streamwise velocity. It is shown that an HB fluid flow does not necessarily show an increase in the fluctuating streamwise velocity with respect to a power-law fluid flow. It is also shown that low power index and high Hedstrom number lead to strong turbulence anisotropy due to the weakening of turbulence. The turbulent kinetic energy (TKE) budget reveals that the studied non-Newtonian behavior mainly affects the inner layer of the flow. The yield stress is also seen to show small variations in the TKE budget in the outer layer. This is attributed to the weakening turbulence as a result of the increased viscosity near the center. It is also demonstrated that the studied HB fluid flow results can be successfully reproduced by under-resolved DNS.

Influence of channel bend angle on the turbulent statistics in sharply bent channel flows

Turbulence in wall-bounded flows shows a wide range of regimes, where the interaction between scales significantly occur. Reynolds number is used to characterize the dynamics of fluid corresponding to single phase channel flows. Meanwhile, different flow behavior exists in curved channels even at fixed Reynolds number, where the curvature varies as shown by Brethouwer [“Turbulent flow in curved channels,” J. Fluid Mech. 931, A21 (2022)]. In the present study, we show how wall-bounded turbulent flow behaves on sharply bending the channel by investigating the time averaged velocity profiles at the straight section, at the bend, and in the inclined section. The well-known logarithmic behavior of the time averaged normalized velocity profile is retained, where the von Kármán and the additive constants assume altered values depending on the sharp bend inclination. The near-wall fluctuations at the bend are enhanced, which is due to diffusion of counter-rotating vortices leading to increased turbulent activity. In terms of spatial structure of the random fluctuating field, the two-point correlation statistics suggest that multiple high speed and low speed streak pairs are generated, and there are multiple streamwise vortices of different sizes when bend inclination is increased. Budgets of turbulent kinetic energy are presented for various inclinations of the bend at different sections of the bend channel, which depicts that turbulent kinetic energy is modulated at the bend.

The Effect of Advection on the Three Dimensional Distribution of Turbulent Kinetic Energy and Its Generation in Idealized Tropical Cyclone Simulations

AbstractThe distribution of turbulent kinetic energy (TKE) and its budget terms is estimated in simulated tropical cyclones (TCs) of various intensities. Each simulated TC is subject to storm motion, wind shear, and oceanic coupling. Different storm intensities are achieved through different ocean profiles in the model initialization. For each oceanic profile, the atmospheric simulations are performed with and without TKE advection. In all simulations, the TKE is maximized at low levels (i.e., below 1 km) and ∼0.5 km radially inward of the azimuthal‐mean radius of maximum wind speed at 1‐km height. As in a previous study, the axisymmetric TKE decreases with height in the eyewall, but more abruptly in simulations without TKE advection. The largest TKE budget terms are shear generation and dissipation, though variability in vertical turbulent transport and buoyancy production affect the change in the azimuthal‐mean TKE distribution. The general relationships between the TKE budget terms are consistent across different radii, regardless of storm intensity. In terms of the asymmetric distribution in the eyewall, TKE is maximized in the front‐left quadrant where the sea surface temperature (SST) is highest and is minimized in the rear‐right quadrant where the SST is the lowest. In the category‐5 simulation, the height of the TKE maximum varies significantly in the eyewall between quadrants and is between ∼400 m in the rear‐right quadrant and ∼1,000 m in the front‐left quadrant. When TKE advection is included in the simulations, the maximum eyewall TKE values are downwind compared to the simulations without TKE advection.