Turbulent Kinetic Energy Budget Research Articles

Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity

New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$ . The experiments covered energetic sediment transport conditions (Shields number of $0.35 < \theta < 1.2$ ) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 < {w_s}/{u_\ast } < 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and dp/η > 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.

A generalized curvilinear solver for spherical shell Rayleigh-Bénard convection

Summary A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 105 and 107 while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.

Direct Numerical Simulation Database of High-Speed Flow over Parameterized Curved Walls

This study presents a direct numerical simulation (DNS) database of high-speed turbulent boundary layers (TBLs) subject to pressure gradients due to parametrically varied backward-facing and forward-facing wall curvatures, with an inflow Mach number of 4.9 and a friction Reynolds number of Reτ≃1000 immediately before the onset of wall curvature. The Mach and Reynolds numbers are significantly higher than those reported in the literature for the DNS of pressure-gradient TBLs. The flow conditions and baseline wall geometries are representative of experiments in the high-speed blowdown wind tunnel at the National Aerothermochemistry Laboratory at Texas A&M University. The wall steepness of the baseline geometry for both the backward-facing and forward-facing walls was systematically varied to cause attached, incipiently separated, and fully separated flows. Precomputed flow statistics, including turbulent kinetic energy budgets, are available on the website of the Turbulence Modeling Resource of the NASA Langley Research Center, allowing other investigators to query any property of interest.

Manipulation of a turbulent boundary layer using sinusoidal riblets

We investigate experimentally the effects of micro-grooves on the development of a zero pressure gradient turbulent boundary layer at two different values of the friction Reynolds number. We consider both the well-known streamwise aligned riblets as well as wavy riblets, characterized by a sinusoidal pattern in the mean flow direction. Previous investigations by the authors showed that sinusoidal riblets yield larger values of drag reduction with respect to the streamwise aligned ones. We perform new particle image velocimetry experiments on wall-parallel planes to get insights into the effect of the sinusoidal shape on the near-wall organisation of the boundary layer and the structures responsible for the friction drag reduction and the turbulence generation. Conditional averages, aimed at identifying the topology of the low-speed streaks in the turbulent boundary layer, reveal that the flow is highly susceptible to wall manipulation. This is particularly evident in the cases that are associated with greater values of drag reduction. The results suggest a fragmentation and/or weakening of the streaks in the sinusoidal cases, that is triggered by the larger values of the wall-normal vorticity found at the streaks’ edges. The results are also confirmed by applying the variable interval spatial averaging events eduction technique. The turbulent kinetic energy budget also shows that the sinusoidal geometry significantly attenuates the turbulence production, hence supporting the idea of the manipulation of the turbulence regeneration cycle.

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

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

Analysis and Modeling of Turbulence Anisotropy of a Swirled Hot Streak Flow

Abstract This study is carried out in the context of hot streak flows in high-pressure turbines, for which a correct prediction of the temperature evolution is required. The present work particularly focuses on the turbulence anisotropy analysis of a swirled hot streak flow in a bent channel representative of a nozzle guide vane (NGV) passage of a high-pressure turbine. Large-eddy simulations are conducted with the in-house solver IC3 in order to measure and characterize the anisotropy of turbulence. Moreover, to evaluate turbulence modeling, steady simulations of the bent channel are performed with the elsA software, which solves the Reynolds-averaged Navier–Stokes (RANS) equations. LES is first used to complete a turbulent kinetic energy (TKE) budget that enables to understand the energetic transfers associated with turbulence. This budget reveals two distinct zones where turbulence activity is impacted when the curvature is reached. The analysis of the anisotropy of turbulence based on two metrics highlights a misalignment of the Reynolds stress tensor and the mean strain-rate tensor (Schmitt's criterion), and a strong anisotropy developing inside the bent duct (Lumley's analysis) that may cause the failure of the classical RANS turbulence models based on Boussinesq's hypothesis. To check this hypothesis, RANS is positioned against LES with different turbulence models that accounts or not for the anisotropy of turbulence. Both turbulence activity (TKE budgets, Lumley's analysis) and aerothermal fields (radial distributions) are compared. Results show that Explicit Algebraic Reynolds Turbulence Models (EARSM) enable to better account for the anisotropy of turbulence, which in turn promote a better prediction of temperature, both in terms of intensity and trajectory.

Profiling the molecular destruction rates of temperature and humidity as well as the turbulent kinetic energy dissipation in the convective boundary layer

Abstract. A simultaneous deployment of Doppler, temperature, and water-vapor lidars is able to provide profiles of molecular destruction rates and turbulent kinetic energy (TKE) dissipation in the convective boundary layer (CBL). Horizontal wind profiles and profiles of vertical wind, temperature, and moisture fluctuations are combined, and transversal temporal autocovariance functions (ACFs) are determined for deriving the dissipation and molecular destruction rates. These are fundamental loss terms in the TKE as well as the potential temperature and mixing ratio variance equations. These ACFs are fitted to their theoretical shapes and coefficients in the inertial subrange. Error bars are estimated by a propagation of noise errors. Sophisticated analyses of the ACFs are performed in order to choose the correct range of lags of the fits for fitting their theoretical shapes in the inertial subrange as well as for minimizing systematic errors due to temporal and spatial averaging and micro- and mesoscale circulations. We demonstrate that we achieve very consistent results of the derived profiles of turbulent variables regardless of whether 1 or 10 s time resolutions are used. We also show that the temporal and spatial length scales of the fluctuations in vertical wind, moisture, and potential temperature are similar with a spatial integral scale of ≈160 m at least in the mixed layer (ML). The profiles of the molecular destruction rates show a maximum in the interfacial layer (IL) and reach values of ϵm≃7×10-4 g2 kg−2 s−1 for mixing ratio and ϵθ≃1.6×10-3 K2 s−1 for potential temperature. In contrast, the maximum of the TKE dissipation is reached in the ML and amounts to ≃10-2 m2 s−3. We also demonstrate that the vertical wind ACF coefficient kw∝w′2‾ and the TKE dissipation ϵ∝w′2‾3/2. For the molecular destruction rates, we show that ϵm∝m′2‾w′2‾1/2 and ϵθ∝θ′2‾w′2‾1/2. These equations can be used for parameterizations of ϵ, ϵm, and ϵθ. All noise error bars are derived by error propagation and are small enough to compare the results with previous observations and large-eddy simulations. The results agree well with previous observations but show more detailed structures in the IL. Consequently, the synergy resulting from this new combination of active remote sensors enables the profiling of turbulent variables such as integral scales, variances, TKE dissipation, and the molecular destruction rates as well as deriving relationships between them. The results can be used for the parameterization of turbulent variables, TKE budget analyses, and the verification of large-eddy simulations.

Impact of Momentum Perturbation on Convective Boundary Layer Turbulence

AbstractMesoscale‐to‐microscale coupling is an important tool for conducting turbulence‐resolving multiscale simulations of realistic atmospheric flows, which are crucial for applications ranging from wind energy to wildfire spread studies. Different techniques are used to facilitate the development of realistic turbulence in the large‐eddy simulation (LES) domain while minimizing computational cost. Here, we explore the impact of a simple and computationally efficient Stochastic Cell Perturbation method using momentum perturbation (SCPM‐M) to accelerate turbulence generation in boundary‐coupled LES simulations using the Weather Research and Forecasting model. We simulate a convective boundary layer (CBL) to characterize the production and dissipation of turbulent kinetic energy (TKE) and the variation of TKE budget terms. Furthermore, we evaluate the impact of applying momentum perturbations of three magnitudes below, up to, and above the CBL on the TKE budget terms. Momentum perturbations greatly reduce the fetch associated with turbulence generation. When applied to half the vertical extent of the boundary layer, momentum perturbations produce an adequate amount of turbulence. However, when applied above the CBL, additional structures are generated at the top of the CBL, near the inversion layer. The magnitudes of the TKE budgets produced by SCPM‐M when applied at varying heights and with different perturbation amplitudes are always higher near the surface and inversion layer than those produced by No‐SCPM, as are their contributions to the TKE. This study provides a better understanding of how SCPM‐M reduces computational costs and how different budget terms contribute to TKE in a boundary‐coupled LES simulation.

Direct Observation of Wave-Coherent Pressure Work in the Atmospheric Boundary Layer

Abstract Surface waves grow through a mechanism in which atmospheric pressure is offset in phase from the wavy surface. A pattern of low atmospheric pressure over upward wave orbital motions (leeward side) and high pressure over downward wave orbital motions (windward side) travels with the water wave, leading to a pumping of kinetic energy from the atmospheric boundary layer into the waves. This pressure pattern persists above the air–water interface, modifying the turbulent kinetic energy in the atmospheric wave-affected boundary layer. Here, we present field measurements of wave-coherent atmospheric pressure and velocity to elucidate the transfer of energy from the atmospheric turbulence budget into waves through wave-coherent atmospheric pressure work. Measurements show that the phase between wave-coherent pressure and velocity is shifted slightly above 90° when wind speed exceeds the wave phase speed, allowing for a downward energy flux via pressure work. Although previous studies have reported wave-coherent pressure, to the authors’ knowledge, these are the first reported field measurements of wave-coherent pressure work. Measured pressure work cospectra are consistent with an existing model for atmospheric pressure work. The implications for these measurements and their importance to the turbulent kinetic energy budget are discussed. Significance Statement Surface waves grow through a pattern of atmospheric pressure that travels with the water wave, acting as a pump against the water surface. The pressure pumping, sometimes called pressure work, or the piston pressure, results in a transfer of kinetic energy from the air to the water that makes waves grow larger. To conserve energy, it is thought that the pressure work on the surface must extract energy from the mean wind profile or wind turbulence that sets the shape of the wind speed with height. In this paper, we present direct measurements of pressure work in the atmosphere above surface waves. We show that the energy extracted by atmospheric pressure work fits existing models for how waves grow and a simple model for how waves reduce energy in the turbulent kinetic energy budget. To our knowledge, these are the first reported field measurements of wave-coherent pressure work.

Direct numerical simulation of temporally evolving stratified wakes with ensemble average

Direct numerical simulations are conducted for temporally evolving stratified wake flows at Reynolds numbers from $10\,000$ to $50\,000$ and Froude numbers from $2$ to 50. Unlike previous studies that obtained statistics from a single realization, we take ensemble averages among 80–100 realizations. Our analysis shows that data from one realization incur large convergence errors. These errors reduce quickly as the number of statistical samples increases, with the benefit of ensemble average diminishing beyond 40–60 realizations. The data with ensemble average allow us to test the previously established scalings and arrive at new scaling estimates. Specifically, the data do not support power-law scaling in the centreline velocity deficit $U_0$ beyond the near wake. Its decay rate increases continuously from 0.1 at the onset of the non-equilibrium regime until the end of our calculations without reaching any asymptote. Additionally, while no power-law scalings could be found in the wake width ( $L_H$ ) and wake height ( $L_V$ ) in the late wake, $L_H\sim (Nt)^{1/3}$ is a good working approximation of the wake's horizontal size, where $N$ is buoyancy frequency and $t$ is time. Besides the low-order statistics, we also report the transverse integrated terms and the vertically integrated terms in the turbulent kinetic energy budget equation as a function of the vertical and transverse coordinates. The data indicate that there are two peaks in the vertically integrated production and transport terms, and one peak when the two terms are integrated horizontally.

Effects of Viscosity Law on High-Temperature Supersonic Turbulent Channel Flow for Chemical Equilibrium

Direct numerical simulations of temporally evolving high-temperature supersonic turbulent channel flow for chemical equilibrium were conducted with a Mach number of 3.0, a Reynolds number of 4880, and a wall temperature of 1733.2 K to investigate the influence of the viscosity law. The mean and fluctuating viscosity for the mixture rule is higher than that for Sutherland’s law, whereas an opposite trend is observed in the mean temperature, mean pressure, and dissociation degree. The Trettel and Larsson transformed mean velocity, the Reynolds shear stress, the turbulent kinetic energy budget, and the turbulent Prandtl number are insensitive to the viscosity law. The semilocal scaling that take into account local variation of fluid characteristics better collapses the turbulent kinetic energy budget. The modified strong Reynolds analogies provide reasonably good results for the mixture rule, which are better than those for Sutherland’s law. The streamwise and spanwise coherencies for the mixture rule are stronger and weaker than those for Sutherland’s law, respectively. The relationship between viscosity and species components can help to identify the traveling wave packet.

Numerical investigation of mixed-phase turbulence induced by a plunging jet

In nature and engineering applications, water jet plunging acts as a key process causing interface breaking and generating mixed-phase turbulence. In this paper, high-resolution numerical simulations of the plunging of a water jet into a quiescent pool were performed to investigate the statistical properties of mixed-phase turbulence, with a special focus on the closure problem of the Reynolds-averaged equation. We conducted phase-resolved simulations, with the air–water interface captured using a coupled level-set and volume-of-fluid method. Various cases were performed to analyse the effects of the Froude number and Reynolds number. The simulation results showed that the turbulence statistics are insensitive to the Reynolds number under investigation, while the Froude number influences the flow properties significantly. To investigate the closure problem of the mean momentum equation, the turbulent kinetic energy (TKE) and turbulent mass flux (TMF) and their transport equations were analysed further. It was discovered that the balance relationship of the TKE budget terms remained similar to many single-phase turbulent flows. The TMF is an additional unclosed term in mixed-phase turbulence over the single-phase turbulence. Our simulation results showed that the production term in its transport equation was highly correlated to TKE. Based on this finding, a closure model for the production term of TMF was further proposed.

Impact of urban canopy characteristics on turbulence dynamics: Insights from large eddy simulation

In this study, a series of large-eddy simulations are conducted to explore the dynamics of turbulence within the urban canopy. Two idealized urban-like geometries (staggered and aligned arrays of cubes) and one real urban region (located on the Southern University of Science and Technology campus in China) are simulated under neutral atmospheric conditions. The results show a significant difference in the dispersive momentum fluxes between OpenFOAM and PALM within the ultra-dense arrays. Furthermore, it is found that the spatial layout does not exert a significant effect on the budget of turbulent kinetic energy. Instead, it mainly depends on the ratio of the building surface area to the total surface area, i.e., packing density. In addition, a multi-scale coupled inflow boundary condition is introduced in this study to simulate the flow in a real urban area. This boundary condition yields a better match to the LiDAR measurements than the Weather Research and Forecasting model data. Finally, this study shows that the mean velocity obtained from the campus of SUSTech is in satisfactory agreement with the data from low-density idealized cube arrays and the corresponding urban canopy model. This observation suggests that mean wind speeds within partially occupied urban areas are relatively independent of wind direction, thus greatly improving the application of urban canopy models to such scenarios.

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

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

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 = 1000 to 10 000 and a Prandtl number of = 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.