Decay Of Kinetic Energy Research Articles

Freely Decaying Saffman Turbulence Experimentally Generated by Magnetic Stirrers.

We investigate experimentally the decay of three-dimensional hydrodynamic turbulence, initially generated by the erratic motions of centimeter-size magnetic stirrers in a closed container. Such zero-mean-flow homogeneous isotropic turbulence is well suited to test Saffman's model and Batchelor's model of freely decaying turbulence. Here, we report a consistent set of experimental measurements (temporal decay of the turbulent kinetic energy, of the energy dissipation rate, and growth of the integral scale) strongly supporting the Saffman model. We also measure the conservation of the Saffman invariant at early times of the decay and show that the energy spectrum scales as k^{2} at large scales and keeps its self-similar shape during the decay. This Letter thus presents the first experimental evidence of the validity of the connection between the Saffman invariant and the k^{2}-energy spectrum of the large scales. The final decay regime closely corresponds to Saffman's model when the container size is sufficiently large.

Pore-pressure-dependent performance of rocking foundations

This study explores the concept of rocking foundations to mitigate damage during seismic events. By weakening the footing intentionally, the foundation acts as a “fuse” to prevent plastic hinges from forming in columns. Shake table experiments were conducted on a lightweight prototype deck mass-column-footing model founded on a fine, medium-dense sand, in two states of nearly dry and saturated. Kinetic energy dissipation, hysteresis, and decay are examined for various structure masses, for two nominal low and high motion frequencies. Findings suggest that energy dissipation is higher in saturated sands ― as compared to nearly dry and despite the absence of liquefaction ― due to fluctuating pore water pressure and a suction effect that evolves beneath foundations’ edge. Where the substrate retains its original porosity, flow of water and subsequent damping becomes pivotal mechanisms to enable the rocking motion. In dry sands, energy dissipation occurs mainly through rotation, and enhances with motion frequency (from testing 3–5 Hz). In saturated sands, energy dissipation occurs predominantly through plastic settlement, and becomes less effective with motion frequency. Lighter structures experience greater rotational movement, especially in the case of dry sands. That enhanced rotational movement is drove by lower rotational stiffness. Overall, lighter structures facilitate the re-centring of the foundation upon rocking motion.

On the role of aortic valve architecture for physiological hemodynamics and valve replacement, Part II: Spectral analysis and anisotropy

Severe aortic valve stenosis can lead to heart failure and aortic valve replacement (AVR) is the primary treatment. However, increasing prevalence of aortic stenosis cases reveal limitations in current replacement options, necessitating improved prosthetic aortic valves. We investigate flow disturbances downstream of severe aortic stenosis and two bioprosthetic aortic valve (BioAV) designs using advanced energy-based analyses. Three-dimensional high-fidelity fluid–structure interaction simulations have been conducted and a dedicated and novel spectral analysis has been developed to characterise the kinetic energy (KE) carried by eddies in the wavenumber space. In addition, new field quantities, i.e. modal KE anisotropy intensity as well as normalised helicity intensity, are introduced. Spectral analysis shows kinetic energy (KE) decay variations, with the stenotic case aligning with Kolmogorov’s theory, while BioAV cases differing. We explore the impact of flow helicity on KE transfer and decay in BioAVs. Probability distributions of modal KE anisotropy unveil flow asymmetries in the stenotic and one BioAV cases. Moreover, an inverse correlation between temporally averaged modal KE anisotropy and normalised instantaneous helicity intensity is noted, with the coefficient of determination varying among the valve configurations. Leaflet dynamics analysis highlights a stronger correlation between flow and biomechanical KE anisotropy in one BioAV due to higher leaflet displacement magnitude. These findings emphasise the role of valve architecture in aortic turbulence as well as its importance for BioAV performance and energy-based design enhancement.

Mixing and inter-scale energy transfer in Richtmyer–Meshkov turbulence

This work investigates the compressible turbulence induced by Richtmyer–Meshkov (RM) instability using high-resolution Navier–Stokes simulations. Special attention is paid to the characteristics of RM turbulence including the mixing width growth, the turbulent kinetic energy (TKE) decay, the mixing degree, inhomogeneity and anisotropy. Three distinct initial perturbation spectra are designed at the interface to reveal the initial condition imprint on the RM turbulence. Results show that cases with initial large-scale perturbations present a stronger imprint on statistical characteristics and also a quicker growth of mixing width, whereas cases with small-scale perturbations present a faster TKE decay, greater mixing level, higher isotropy and homogeneity. A thorough analysis on the inter-scale energy transfer in RM turbulence is also presented with the coarse-graining approach that exposes the two subfilter-scale (SFS) energy fluxes (i.e. deformation work and baropycnal work). A strong correlation between the nonlinear model of baropycnal work (Fluids, 4(2), 2019) and the simulation results is confirmed for the first time, demonstrating its potential in modelling the RM turbulence. Two primary mechanisms of baropycnal work (the straining and baroclinic generation processes) are explored with this nonlinear model. The evolutions of two SFS energy fluxes exhibit distinct behaviours at various filter scales, in different flow regions and under various flow motions (strain and rotation). It is found that all three cases share the common inter-scale energy transfer dynamics, which is important for modelling the RM turbulence.

Cooling of a granular gas mixture in microgravity

Granular gases are fascinating non-equilibrium systems with interesting features such as spontaneous clustering and non-Gaussian velocity distributions. Mixtures of different components represent a much more natural composition than monodisperse ensembles but attracted comparably little attention so far. We present the observation and characterization of a mixture of rod-like particles with different sizes and masses in a drop tower experiment. Kinetic energy decay rates during granular cooling and collision rates were determined and Haff’s law for homogeneous granular cooling was confirmed. Thereby, energy equipartition between the mixture components and between individual degrees of freedom is violated. Heavier particles keep a slightly higher average kinetic energy than lighter ones. Experimental results are supported by numerical simulations.

Developing a digital twin framework for wind tunnel testing: validation of turbulent inflow and airfoil load applications

Abstract. Wind energy systems, such as horizontal-axis wind turbines and vertical-axis wind turbines, operate within the turbulent atmospheric boundary layer, where turbulence significantly impacts their efficiency. Therefore, it is crucial to investigate the impact of turbulent inflow on the aerodynamic performance at the rotor blade scale. As field investigations are challenging, in this work, we present a framework where we combine wind tunnel measurements in turbulent flow with a digital twin of the experimental set-up. For this, first, the decay of the turbulent inflow needs to be described and simulated correctly. Here, we use Reynolds-averaged Navier–Stokes (RANS) simulations with k−ω turbulence models, where a suitable turbulence length scale is required as an inlet boundary condition. While the integral length scale is often chosen without a theoretical basis, this study derives that the Taylor micro-scale is the correct choice for simulating turbulence generated by a regular grid: the temporal decay of turbulent kinetic energy (TKE) is shown to depend on the initial value of the Taylor micro-scale by solving the differential equations given by Speziale and Bernard (1992). Further, the spatial decay of TKE and its dependence on the Taylor micro-scale at the inlet boundary are derived. With this theoretical understanding, RANS simulations with k−ω turbulence models are conducted using the Taylor micro-scale and the TKE obtained from grid experiments as the inlet boundary condition. Second, the results are validated with excellent agreement with the TKE evolution downstream of a grid obtained through hot-wire measurements in the wind tunnel. Third, the study further introduces an airfoil in both the experimental and the numerical setting where 3D simulations are performed. A very good match between force coefficients obtained from experiments and the digital twin is found. In conclusion, this study demonstrates that the Taylor micro-scale is the appropriate turbulence length scale to be used as the boundary condition and initial condition to simulate the evolution of TKE for regular-grid-generated turbulent flows. Additionally, the digital twin of the wind tunnel can accurately replicate the force coefficients obtained in the physical wind tunnel.

Predicting the energy stability limit of shear flows using weighted velocity components

Predicting the subcritical transition in fluid dynamic systems remains a challenging task, but recent advancements utilizing edge tracking methods, polynomial Lyapunov functions, and various energy norms have shown promise. In this study, we propose a novel approach by defining the general kinetic energy through weighted velocity components. The minimal Reynolds number is determined, where the derivative of this generalized energy with respect to time is zero. The procedure is similar to that of the well-known Reynolds–Orr equation. Unlike traditional methods, our approach does not necessitate the monotonic decay of the classic perturbation kinetic energy, resulting in a larger critical Reynolds number and reduced conservativeness of the Reynolds–Orr equation. However, the energy production of the pressure is not negligible, in contrast to the classical Reynolds–Orr equation. The pressure's implicit dependence on the velocity field complicates the variation process. To address this, a method is presented to handle the problem effectively. Our approach is then applied to analyze parallel flows, specifically the plane Couette and plane Poiseuille flows, wherein the problem can be further simplified using the complex Fourier transformation. The weights of velocity components are optimized to maximize the critical Reynolds number, resulting in a significant increase.

Numerical investigation of hydraulic jump for different stilling basins using FLOW-3D

Abstract Stilling basin of the Tuansa barrage is a modified form of the United States Bureau of Reclamation (USBR) Type-III basin, which includes impact baffle and friction blocks. Soon after the barrage's operation, baffle blocks were found to be uprooted. Additionally, previous studies also highlighted the issues of rectangular baffle blocks, i.e., less drag, smaller wake zone, and flow reattachment. On the contrary, the use of wedge-shaped splitter blocks is found limited downstream of diversion barrages. Therefore, this study focuses on the hydraulic effects of wedge-shaped splitter blocks on hydraulic jump (HJ) and energy dissipation using FLOW-3D and confirms its suitability downstream of the diversion barrage. The study mainly investigated the free surface profiles, roller lengths, relative energy losses, velocity profiles, and turbulent kinetic energies for three different stilling basins. The results of free surface profiles indicated that new basins stabilised the HJ and produced smaller lengths of HJ. The results also showed that as the flow increased, the roller lengths decreased in the new basins. Similarly, with an increase in the flow, the relative energy loss increased in new basins. Furthermore, within HJ, and at the basins' end, the results showed higher decay of velocity and turbulent kinetic energy in the new basins.

Expanding Orbitrap Collision Cross-Section Measurements to Native Protein Applications Through Kinetic Energy and Signal Decay Analysis.

The measurement of collision cross sections (CCS, σ) offers supplemental information about sizes and conformations of ions beyond mass analysis alone. We have previously shown that CCSs can be determined directly from the time-domain transient decay of ions in an Orbitrap mass analyzer as ions oscillate around the central electrode and collide with neutral gas, thus removing them from the ion packet. Herein, we develop the modified hard collision model, thus deviating from the prior FT-MS hard sphere model, to determine CCSs as a function of center-of-mass collision energy in the Orbitrap analyzer. With this model, we aim to increase the upper mass limit of CCS measurement for native-like proteins, characterized by low charge states and presumed to be in more compact conformations. We also combine CCS measurements with collision induced unfolding and tandem mass spectrometry experiments to monitor protein unfolding and disassembly of protein complexes and measure CCSs of ejected monomers from protein complexes.

Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence

ABSTRACT Small-scale fluctuating magnetic fields of order nG are observed in supernova shocks and galaxy clusters, where its amplification is likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel 3D magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The configuration used here is currently being tested in the shock tunnel at the National Ignition Facility (NIF). In order to probe the statistical properties of the post-shock turbulent region, we use 384 × 512 × 384 tracers to track its evolution through the Lagrangian framework, thus providing a high-fidelity analysis of the shocked medium. Our simulations indicate that the growth of the magnetic field, which accompanies the near-Saffman kinetic energy decay (Ekin ∝ t−1.15) without turbulence driving, exhibits slightly different characteristics as compared to periodic box simulations. Seemingly no distinct phases exist in its evolution because the shock passage and time to observe the magnetic field amplification during the turbulence decay are very short (∼0.3 of a turbulent turnover time). Yet, the growth rate is still consistent with those expected for compressive (curl-free) turbulence driving in subsonic, compressible turbulence. Phenomenological understanding of the dynamics of the magnetic and velocity fields are also elucidated via Lagrangian frequency spectra, which are consistent with the expected inertial range scalings in the Eulerian–Lagrangian bridge.

Scalings and decay of homogeneous, nearly isotropic turbulence behind a jet array

In the study of dispersed multiphase turbulence, using a jet array has shown promise in creating intense homogeneous, nearly isotropic turbulence with high dissipation rates in water and wind tunnels. However, the scaling of turbulent characteristics with jet nozzle diameter, velocity, and downstream location has not been fully explored. Our research, combined with previous experiments focusing on near-field measurements, offers a comprehensive understanding of the decay of kinetic energy and energy dissipation rate, as well as the flow inhomogeneity and anisotropy generated by a jet array.

The Role of Inertia in the Onset of Turbulence in a Vortex Filament

The decay of the kinetic energy of a turbulent flow with time is not necessarily monotonic. This is revealed by simulations performed in the framework of discrete mechanics, where the kinetic energy can be transformed into pressure energy or vice versa; this persistent phenomenon is also observed for inviscid fluids. Different types of viscous vortex filaments generated by initial velocity conditions show that vortex stretching phenomena precede an abrupt onset of vortex bursting in high-shear regions. In all cases, the kinetic energy starts to grow by borrowing energy from the pressure before the transfer phase to the small turbulent structures. The result observed on the vortex filament is also found for the Taylor–Green vortex, which significantly differs from the previous results on this same case simulated from the Navier–Stokes equations. This disagreement is attributed to the physical model used, that of discrete mechanics, where the formulation is based on the conservation of acceleration. The reasons for this divergence are analyzed in depth; however, a spectral analysis allows finding the established laws on the decay of kinetic energy as a function of the wave number.

Acoustic viscous boundary layer beyond laminar regime: Particle Image Velocimetry measurements

The current study reports an experimental investigation of flow regimes for acoustically oscillating flows in the near-wall region of a resonator. Particle Image Velocimetry (PIV) is used to measure axial and transverse velocity components inside an empty square resonator over the acoustic cycle for a wide range of Reynolds numbers and at a high Womersley number. The measurements are compared with LDV measurements in a circular duct. A good agreement between the PIV and LDV measurements is observed. The measured transverse distribution of the axial velocity agrees well with the Stokes boundary layer expectations up to the Reynolds number (based on acoustic velocity and viscous boundary layer depth) of 240. At higher Reynolds numbers, the measured velocity distribution deviates from the theoretical expectations, suggesting a change of regime at a Reynolds number between 240 and 272. To assert the critical Reynolds number, the velocity fluctuations and Reynolds stress are estimated. At Reynolds number of 272, an increase in the value of the Reynolds stress is observed at the edge of the viscous penetration depth which is regarded as an indication of changing the flow regime. To better qualify the high amplitude acoustic flow, the spectrum of the turbulent kinetic energy and evolution of the integral length scale over the acoustic cycle are investigated. The decay of turbulent kinetic energy with the wavenumber complies with the universal slope (−5/3). The integral length scale increases during the deceleration stage and decreases at the beginning of the acceleration stage.

A new compact active turbulence generator for premixed combustion: Non-reacting flow characteristics

A new compact active turbulence generator is developed, tested, and characterized, which extends the capabilities of such generators used in turbulent premixed combustion research. The generator is composed of two blades that resemble the shape of two bow-ties. Hot-wire anemometry and high-speed imaging are performed to characterize the non-reacting flow produced by the generator and the blades dynamics, respectively. Two mean bulk flow velocities of 5.0 and 7.0 m/s are examined. For comparison purposes, in addition to the developed generator, tests are also performed for a free jet as well as one and two perforated plates. The results show that the centerline root mean square velocity fluctuations can become as large as 1.8 m/s. For the newly developed device, the power-law decay of the one-dimensional kinetic energy is −1.0 and −1.3 for the mean bulk flow velocities of 5.0 and 7.0 m/s, respectively. The normalized energy dissipation rate is relatively small for the newly developed device, while the energy dissipation rate is relatively large. The spectral analysis of the velocity data does not show dominant frequencies equal to the blades rotation frequencies, and the one dimensional kinetic energy and dissipation spectra follow −5/3 and 1/3 power-law relations, respectively. It is shown that the small eddies produced by the newly developed device dissipate the turbulent kinetic energy faster than those corresponding to the rest of the tested turbulence generators.

Influence of the Heliospheric Current Sheet on the Evolution of Solar Wind Turbulence

Abstract The effects of the heliospheric current sheet (HCS) on the evolution of Alfvénic turbulence in the solar wind are studied using MHD simulations incorporating the expanding-box model. The simulations show that, near the HCS, the Alfvénicity of the turbulence decreases as manifested by lower normalized cross-helicity and larger excess of magnetic energy. The numerical results are supported by a superposed-epoch analysis using OMNI data, which shows that the normalized cross-helicity decreases inside the plasma sheet surrounding HCS, and the excess of magnetic energy is significantly enhanced at the center of HCS. Our simulation results indicate that the decrease of Alfvénicity around the HCS is due to the weakening of radial magnetic field and the effects of the transverse gradient in the background magnetic field. The magnetic energy excess in the turbulence may be a result of the loss of Alfvénic correlation between velocity and magnetic field and the faster decay of transverse kinetic energy with respect to magnetic energy in a spherically expanding solar wind.

Dissipation of mesoscale eddies at a western boundary via a direct energy cascade

The fate of mesoscale eddy kinetic energy represents a large source of uncertainty in the global ocean energy budget. Satellite altimetry suggests that mesoscale eddies vanish at ocean western boundaries. However, the fate of the eddies’ kinetic energy remains poorly known. Here we show that the generation of small-scale turbulence as eddy flow impinges on the steep and corrugated slope of an ocean western boundary plays a dominant role in the regional decay of mesoscale eddy kinetic energy. We compare altimetry-based estimates of mesoscale eddy kinetic energy decline with measurements of turbulent dissipation. Mesoscale eddies are found to decay at a rate of 0.016 ± 0.012 GW and 0.023 ± 0.017 GW for anticyclonic and cyclonic eddies, respectively, similar to the observed turbulent dissipation rate of 0.020 ± 0.011 GW. This demonstrates that a major direct transfer of mesoscale eddy kinetic energy to small, dissipative scales can be effectively triggered by the eddies’ interaction with the western boundary topography.

Analysis of Turbulent Flow Structure with Its Fluvial Processes around Mid-Channel Bar

Researchers have recognized that the successive growth of mid-channel bar deposits can be entertained as the raison d’être for the initiation of the braiding process, which is closely interlinked with the growth, decay, and vertical distribution of fluvial turbulent kinetic energy (TKE). Thus, focused analysis on the underlying mechanics of turbulent flow structures in the proximity of a bar deposit occurring in the middle of the channel can afford crucial scientific clues for insight into the initiating fluvial processes that give rise to braiding. In the study reported herein, a physical model of a mid-channel bar is constructed in an experimental flume to analyze the turbulence parameters in a region close to the bar. Notably, the flow velocity plays an important role in understanding the flow behavior in the scour-hole location in the upstream flow divergence zone as well as near the downstream zone of flow convergence in a mid-channel bar. Therefore, the fluctuating components of turbulent flow velocity are herein discussed and analyzed for the regions located close to the bar. In the present study, the impact of the mid-channel bar, as well as its growth in turbulent flow, on higher-order velocity fluctuation moments are investigated. For near-bed locations, the results show the dominance of ejection events in upstream zones and the dominance of sweep events at locations downstream of the mid-channel bar. In scour-hole sections, the negative value of the stream-wise flux of turbulent kinetic energy and the positive value of the vertical flux of turbulent kinetic energy indicate energy transport in downward and forward directions, respectively. The downward and forward energy transport processes lead to scouring at these locations. The maximum turbulent production rate occurs in the wake region of the bar. The high rate of turbulence production has occurred in that region, which can be ascribed to the process of shedding turbulent vortices. The results show that the impact of the presence of the bar is mainly restricted to the lower layers of flow. The turbulent dissipation rate monotonically decreases with an increase in the vertical distance from the bed. The turbulent production rate first increases and then decreases with successive increases in the vertical distance from the bed. The paper concludes with suggestions for the future potential use of the present research for the practical purpose of examining braid bar occurrences in alluvial rivers to develop an appropriate response through training measures.

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.

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.

Large-eddy simulation of droplet-laden decaying isotropic turbulence using artificial neural networks

We propose a model for large-eddy simulation (LES) of decaying isotropic turbulence laden with droplets with diameter of Taylor length-scale. The main challenge in creating LES models for such flow is that the presence of the droplets introduces additional subgrid-scale (SGS) closure terms to the filtered governing equations of motion of the flow. By processing available DNS data (Dodd & Ferrante, J. Fluid Mech. 806:356–412, 2016), we analyze these terms a priori to show that they are all significant enough to warrant modeling. Then, we propose a new modeling approach that we call mixed artificial neural network (MANN) LES because it is a mixed LES model that uses the standard Smagorinsky SGS stress model in the carrier fluid, and artificial neural networks to predict the SGS closure terms at the interface. Such an approach is justified because the SGS energy in the carrier flow away from the droplet interface is practically unaffected by the droplets, as we have previously shown using wavelet analysis of the DNS data (Freund & Ferrante, J. Fluid Mech. 875:914–928, 2019). Furthermore, we have performed the first a posteriori analysis of such flow for droplets of different Weber numbers, and show that our LES method closely reproduces the temporal decay of the filtered-velocity turbulence kinetic energy as well its p.d.f. of the filtered DNS, show that the modeling of the SGS terms at the interface is necessary for reproducing the results of the filtered DNS, and provide both physical- and spectral-space analysis of the LES results. Finally, the MANN LES approach could be applied to a variety of multiphase turbulent flows due to its ease of implementation, adaptability, and performance.