Decay Of Turbulence Research Articles

Modeling Bubble Entrainment and Transport for Ship Wakes: Progress Using Hybrid RANS/LES Methods

This article presents progress on modeling bubble entrainment and transport around ships using hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/ LES) methods. Previous results using a Boltzmann-based polydisperse bubbly flow model show that LES perform better than RANS in predicting transport of bubbles to depth, a very important process to predict bubbly wakes. However, standard DES-type models fail to predict proper turbulent kinetic energy (TKE) and dissipation, needed by bubble entrainment, breakup, and coalescence models. We propose different approaches to obtain TKE and dissipation in LES regions and evaluate them for cases of increasing complexity, including decay of isotropic turbulence, a flat plate boundary layer, and the flow in the wake of the research vessel Athena. An exponential weighted average is used to estimate statistics and obtain the averaged quantities in regions with resolved turbulence. The TKE is satisfactorily predicted in the cases tested. A modified ω equation in the SST model is proposed to implicitly compute the dissipation, showing superior results than the standard DES models, although further improvements are necessary. A hybrid RANS/LES approach is proposed, which focused at conserving total TKE as the flow crosses RANS/LES interfaces, as previously performed for zonal approaches but attempting a DES-like detection of regions suitable for LES, critical for large-scale computations of bubbly flows involving complex geometries. A general form of a dynamic forcing term is derived to transfer the modeled TKE to resolved TKE with a controller to guarantee proper conservation of the energy transferred. It was verified that the model is not sensitive to grid size or time step. Improvements to DDES and the proposed TKE-conserving hybrid RANS/ LES method show encouraging results, although remaining challenges are discussed.

High-Order Delayed Detached Eddy Simulation of Separated Flow with Self-Adaptive Dissipation

A self-adaptive dissipation method based on a fifth-order dissipative compact scheme is proposed to reduce the numerical dissipation in separated flow. The method involves a self-adaptive operating parameter to adjust the weight of upwind part, which is a major source of numerical dissipation. Cooperated with delayed detached eddy simulation, the method can perform with less numerical dissipation in a large-eddy simulation region to resolve more small-scale structures, and return to normal dissipation in a Reynolds-averaged Navier–Stokes region to stabilize simulation. Firstly, the decay of isotropic turbulence is simulated to study the influence of the method over the energy spectrum and resolution of turbulent structures. Secondly, the plane channel flow is simulated to test the stability under the pressure gradient and turbulent fluctuation. Finally, the typical separated flow over NACA0021 airfoil and circular cylinder is investigated, and the results are compared with experimental data.

Analysis of turbulent kinetic energy decay power law in atmospheric boundary layer models

The transitional periods that take place in the atmospheric boundary layer are challenging to model due to their non-stationary nature. Large-eddy simulation (LES) models have proven to be sufficiently accurate for modeling the evening transitions, and now a possibility to adapt turbulent kinetic energy (TKE) closure models for calculations in single-column models appears to be very plausible. In this study, evening transition modeling is analysed with emphasis on the pattern of a TKE decay which follows the power law. E(t) α t −αThe effects of different parameters on the results of the simulations are explored, along with the geostrophic wind effect on the model. It is shown that the model presented here behaves in a manner similar to that of a LES model, thus showing that the above adaptation is possible and worth being investigated further.

An Examination of the Dependency between Maximum Equilibrium Local Scour Depth and the Grain Size/Structure Size Ratio

This paper begins by demonstrating how the Florida Department of Transportation (FDOT) local scour equations take the ratio between grain size and structure size into account when computing equilibrium local scour depth and contrasts this with the well-known Colorado State University (CSU) equation that does not take sediment information into account. Then, a relatively recent empirical formulation from the J-L. Briaud research group for computing local equilibrium scour depth is presented that appears to take the structure size/grain size ratio into account indirectly. Next, a possible explanation for the dependency between local equilibrium scour depth and the structure/grain size ratio is presented that was originally developed by D. Max Sheppard in 2004. This explanation shows that superimposing the pressure gradient around a particle with the pressure gradient around a pile leads to the dependency between equilibrium scour depth and the grain size/structure size ratio. Finally, a new formulation for local equilibrium scour depth based upon turbulent energy spectrum decay is presented. This new formulation reduces the local scour problem to a problem whereby turbulent diffusivity must be better understood. However, this new formulation also appears to show a dependency between equilibrium scour depth and the grain size/structure size ratio. Overall, the analysis presented herein provides several reasons, explanations, and pieces of evidence to suggest that the grain/structure size ratio is an important parameter to consider when computing local equilibrium scour depth.

Comparison analysis of analytical and lattice Boltzmann methods for simulation of turbulence decay in flows in converging and diverging channels

AbstractThe paper focuses on a study of turbulence decay in flow with streamwise gradient. For the first time, an analytical solution of this problem was obtained based on the k‐ε model of turbulence in one‐dimensional (1D) approximation, as well as on the symmetry properties of the system of differential equations. Lie group technique enabled reducing the problem to a linear differential equation. The analytical solution enabled parametric studies, which are computationally cheap in comparison to CFD based simulations. The lattice Boltzmann method (LBM) in two‐dimensional approximation (2D) was used to validate the analytical results. Large eddy simulation (LES) Smagorinsky approach was used to close the LBM model. Computations revealed that the rate of turbulence decay is significantly different for the cases of positive and negative streamwise pressure gradient. The further comparisons showed that the analytical solution underpredicts the predictions by the numerical methodology, which can be attributed to the simplified problem statement used to derive the closed‐form analytical solution. Comparisons of calculations with experiments revealed that the theoretical models used in the study underpredict the measurements for flows with a positive pressure gradient. Hence it can be concluded that the LBM technique combined with the LES Smagorinsky model requires the further modification.

Zero Net Flux MRI Turbulence in Disks: Sustenance Scheme and Magnetic Prandtl Number Dependence

Abstract We investigate sustenance and dependence on magnetic Prandtl number (Pm) for magnetorotational instability (MRI)-driven turbulence in Keplerian disks with zero net magnetic flux using standard shearing box simulations. We focus on the turbulence dynamics in Fourier space, capturing specific/noncanonical anisotropy of nonlinear processes due to disk flow shear. This is a new type of nonlinear redistribution of modes over wavevector orientations in Fourier space—the nonlinear transverse cascade—which is generic to shear flows and fundamentally different from the usual direct/inverse cascade. The zero flux MRI has no exponentially growing modes, so its growth is transient, or nonmodal. Turbulence self-sustenance is governed by constructive cooperation of the transient growth of MRI and the nonlinear transverse cascade. This cooperation takes place at small wavenumbers (on the flow size scales) referred to as the vital area in Fourier space. The direct cascade transfers mode energy from the vital area to larger wavenumbers. At large Pm, the transverse cascade prevails over the direct one, keeping most of modes’ energy contained in small wavenumbers. With decreasing Pm, however, the action of the transverse cascade weakens and can no longer oppose the action of the direct cascade, which more efficiently transfers energy to higher wavenumbers, leading to increased resistive dissipation. This undermines the sustenance scheme, resulting in the turbulence decay. Thus, the decay of zero net flux MRI turbulence with decreasing Pm is attributed to the topological rearrangement of the nonlinear processes when the direct cascade begins to prevail over the transverse cascade.

Theory and verification of a new 3D RANS wake model

Abstract. This paper details the background to the WakeBlaster model: a purpose-built, parabolic three-dimensional RANS solver, developed by ProPlanEn. WakeBlaster is a field model, rather than a single turbine model; it therefore eliminates the need for an empirical wake superposition model. It belongs to a class of very fast (a few core seconds, per flow case) mid-fidelity models, which are designed for industrial application in wind farm design, operation, and control. The domain is a three-dimensional structured grid, a node spacing of a tenth of a rotor diameter, by default. WakeBlaster uses eddy viscosity turbulence closure, which is parameterized by the local shear, time-lagged turbulence development, and stability corrections for ambient shear and turbulence decay. The model prescribes a profile at the end of the near wake, and the spatial variation of ambient flow, by using output from an external flow model.

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction.

In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capability of the approach to approximate an optimal value for eddy viscosity with different measurement configurations. Specifically, we show that our approach can sufficiently assimilate information either through full-field or sparse noisy measurements to estimate eddy viscosity closure to cure standard Galerkin reduced order model (GROM) predictions. Therefore, our approach provides a modular framework to correct forecasting error from a sparse observational network on a latent space. We highlight that the proposed GROM-FSM framework is promising for emerging digital twin applications, where real-time sensor measurements can be used to update and optimize surrogate model's parameters.

Unsteady Flow Field Characterization of Effusion Cooling Systems with Swirling Main Flow: Comparison Between Cylindrical and Shaped Holes

The presence of injectors with strongly swirled flows, used to promote flame stability in the combustion chambers of gas turbines, influences the behaviour of the effusion cooling jets and consequently of the liner’s cooling capabilities. For this reason, unsteady behaviour of the jets in the presence of swirling flow requires a characterization by means of experimental flow field analyses. The experimental setup of this work consists of a non-reactive single-sector linear combustor test rig, scaled up with respect to the real engine geometry to increase spatial resolution and to reduce the frequencies of the unsteadiness. It is equipped with a radial swirler and multi-perforated effusion plates to simulate the liner cooling system. Two effusion plates were tested and compared: with cylindrical and with laid-back fan-shaped 7-7-7 holes in staggered arrangement. Time resolved Particle Image Velocimetry has been carried out: the unsteady characteristics of the jets, promoted by the intermittent interactions with the turbulent mainstream, have been investigated as their vortex structures and turbulent decay. The results demonstrate how an unsteady analysis is necessary to provide a complete characterization of the coolant behaviour and of its turbulent mixing with mainflow, which affect, in turn, the film cooling capability and liner’s lifetime.

Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation

Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions -- (i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in a sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic felicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe.

Role of rigid boundary on the decay of turbulence generated by passive-grid for free surface flow

The present study aims to investigate the flow characteristics of grid-generated turbulence under the consideration of solid boundary in free surface flow. To understand the nature of isotropy and anisotropy in the flow, the turbulent intensity is evaluated at the downstream of the grid for different mesh sizes. The energy spectrums based on the Fast Fourier and marginal Hilbert–Huang transform are presented to understand the decay of energy in the associated spectral frequency domain. It is observed that the peak of energy associated with the Fourier spectrum decreases in the near-field region of the grid with the increase in mesh size of the grid. Further, to characterise the concentrated velocity fluctuations, the paper strives to analyse the joint probability distribution function and the local intermittency measure in the close and far stream of the grid. The autocorrelation functions and the magnitude of integral length scale of the stream-wise fluctuating velocity components are also presented at two different vertical levels from the solid boundary. The normalised Shannon entropy is also evaluated to characterise the degree of the orderness or disorderness in the flow due to the interaction of grid and rigid boundary.

Non-thermal line broadening due to braiding-induced turbulence in solar coronal loops

Aims.Emission line profiles from solar coronal loops exhibit properties that are unexplained by current models. We investigate the non-thermal broadening associated with plasma heating in coronal loops that is induced by magnetic field line braiding.Methods.We describe the coronal loop by a 3D magnetohydrodynamic model of the turbulent decay of an initially-braided magnetic field. From this, we synthesised the Fe XIIline at 193 Å that forms around 1.5 MK.Results.The key features of current observations of extreme ultraviolet (UV) lines from the corona are reproduced in the synthesised spectra: (i) Typical non-thermal widths range from 15 to 20 km s−1. (ii) The widths are approximately independent of the size of the field of view. (iii) There is a correlation between the line intensity and non-thermal broadening. (iv) Spectra are found to be non-Gaussian, with enhanced power in the wings of the order of 10–20%.Conclusions.Our model provides an explanation that self-consistently connects the heating process to the observed non-thermal line broadening. The non-Gaussian nature of the spectra is a consequence of the non-Gaussian nature of the underlying velocity fluctuations, which is interpreted as a signature of intermittency in the turbulence.

PTV measurements of oscillating grid turbulence in water and polymer solutions

Particle Tracking Velocimetry (PTV) is applied to measure the flow in an oscillating grid stirred tank filled with either water or shear thinning dilute polymer solutions (DPS) of Xanthan Gum (XG). There are many interests of studying turbulence in such complex non-Newtonian fluids (e.g. in the pharmaceutical, cosmetic, or food industry), and grid stirred tanks are commonly used for fundamental studies of turbulence in Newtonian fluids. Yet the case of oscillating grid flows in shear thinning solutions has been addressed recently by Lacassagne et al. (Exp Fluids 61(1):15, Phys Fluids 31(8):083102, 2019a, b), with only a single two dimensional (2D) Particle Image Velocimetry (PIV) characterization of mean flow and turbulence properties in the central vertical plane of the tank. Here, PTV data processed by the Shake The Box algorithm allows for the time resolved, three dimensional (3D) 3 components (3C) measurement of Lagrangian velocities for a large number of tracked particles in a central volume of interest of the tank. The possibility of projecting this Lagrangian information on an Eulerian grid is explored, and projected Eulerian results are compared with 2D PIV data from the previous work. Even if the mean flow is difficult to reproduce at the lowest polymer concentrations, a good agreement is found between measured turbulent decay laws, thus endorsing the use of this 3D-PTV metrology for the study of oscillating grid turbulence in DPS. The many possibilities of further analysis offered by the 3D3C nature of the data, either in the original Lagrangian form or in the projected Eulerian one, are finally discussed.Graphic

First characterization of a new perturbation system for gust generation: the chopper

Abstract. We present a new system for the generation of rapid, strong flow perturbations in the aerodynamic wind tunnel at École Centrale de Nantes. The system is called the chopper, and it consists of a rotating bar cutting through the inlet of a wind tunnel test section, thus generating an inverse gust that travels downstream. The flow generated by the chopper is investigated with respect to the rotational frequency using an array equipped with hot-wires that is traversed downstream in the flow field. It is found that the gust can be described as a superposition of the mean gust velocity, an underlying gust shape, and additional turbulence. Following this approach, the evolution of the mean gust velocity and turbulence intensity are presented, and the evolution of the underlying inverse gust shape is explained. The turbulence is shown to be characterized by an integral length scale of approximately half the chopper blade width and a turbulence decay according to E(f)∝f-5/3.

Turbulent boundary layer subjected to a sonic transverse jet in a supersonic flow

Particle Image Velocimetry (PIV) technology, oil flow visualization and Nanoparticle-based Planar Laser Scattering (NPLS) technology are used to investigate the turbulent boundary layer (BL) of a sonic jet injected into a supersonic flow at Ma=2.95. Instantaneous and averaged NPLS images display detailed structures of the bow shock, the horseshoe vortex, separation zones and the collision shock. Root Mean Square (RMS) values of flow quantities calculated from NPLS images and PIV data reveal that turbulent fluctuations are suppressed downstream of the horseshoe separation zone in the jet lateral region and a 33%-35% reduction of the density fluctuation magnitude across the boundary layer is observed, while it is enhanced in the jet wake by 34%-50%. Further away from the wall, the influences of the λ shock system, the expansion process, and the reflected shock on turbulence intensity and velocities of the crossflow BL is weakened. A three-dimensional schematic diagram of the interaction between the sonic jet and the turbulent BL is presented, explaining the formation of the turbulence decay zone in the jet lateral region.

Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows

Author(s): Motheau, E; Wakefield, J | Abstract: The aim of the present paper is to provide a comparison between several finitevolume methods of different numerical accuracy: the second-order Godunov method with PPM interpolation and the high-order finite-volume WENO method. The results show that while on a smooth problem the high-order method performs better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.

CFD-DPM and experimental study of the dynamics of wheat starch powder/pyrolysis gases hybrid mixtures in the 20-L Sphere

This study comprises an assessment of the behaviour of wheat starch/pyrolysis gases hybrid mixtures under different operating conditions of Ignition Delay Time (tv) and nozzle geometry in the context of the 20-L Sphere Test. The behaviour of the system was determined through the study of the interaction between the chemical reactions of the phases and the turbulence levels produced by the different operating configurations. For these purposes, CFD simulations based on a coupled Eulerian-Lagrangian formulation were developed considering the two main steps of the test: i) Dispersion of the powder, and ii) Pyrolysis/gas-oxidation reactions. The CFD model included a few important improvements to other computational methodologies proposed in previous studies, such as the incorporation of more rigorous kinetic mechanisms for the devolatilization reactions of the starch particles and the combustion reactions of the pyrolysis gases. In parallel, experimental tests were performed in order to validate the CFD model and characterize the powder samples. In particular, the composition of the pyrolysis gases emitted by the particles was determined by a modified setup of the Godbert-Greenwald furnace, and the Particle Size Distribution (PSD) was measured through laser diffraction techniques. The performance of the CFD model was satisfactory in terms of predicting parameters related to the hydrodynamic or reaction-kinetic behaviour of the system, such as the pressure evolution during dispersion and the (dP/dt)m (average deviations from experimental values of ~4.0% and 11.9%, respectively). Furthermore, the results suggest that the combined effect of the dust-phase and gas-phase reactions have a distinctive dissipative effect on the turbulence levels and that higher turbulence decay levels during the explosion step of the test are related to higher explosion severities.

Non-linear instability analysis of the three-dimensional Navier–Stokes equations: Taylor–Green vortex problem

The three-dimensional (3D) Taylor–Green vortex (TGV) flow is one of the simplest systems to study the generation of different scales of vortices due to the growth of disturbances via effects of different physical mechanisms, including vortex-stretching as an additional source for instability, showing not only the creation of turbulence but also turbulent decay. The strong anisotropic and well-organized flow becomes unstable at early time due to transfer of energy to small scales. The analysis of instability of the periodic 3D TGV flow for the Reynolds number of Re = 2000 is reported here. The direct numerical simulation of the periodic 3D TGV flow is carried out using high accuracy numerical methods for the (vector-potential, vorticity)-formulation, which exactly satisfy the solenoidality condition for vector-potential and vorticity in the computational domain. The evolution of disturbances is examined using the instability theories of the disturbance mechanical energy of the Navier–Stokes equation and the role of rotationality by the disturbance enstrophy transport equation (DETE), which is derived from the enstrophy transport equation. The 3D TGV flow exhibits a tornado-type structure at the center of the domain at intermediate stages of transition to turbulence, which is analyzed using the vortex-identification method of λ2-criteria and the DETE method, as described by Sengupta et al. [“Tracking disturbances in transitional and turbulent flows: Coherent structures,” Phys. Fluids 31(12), 124106 (2019)]. Here, it is observed that the coherent structure is diffused in the λ2-contours. Third generation vortex-identification methods are analyzed for capturing the transient, rotating vortex. The combination of new Omega- and the Liutex/Rortex-methods, as reviewed by C. Liu et al. [“Third generation of vortex identification methods: Omega and Liutex/Rortex based systems,” J. Hydrodyn. 31(2), 205–223 (2019)], captures the evolution of the transient vortex, but the structure identified by these methods appears to be diffused, while the DETE method clearly captures the vortex geometry and highlights the formation of the vortex at early times to aid in predicting the flow evolution.

Numerical simulation of 3D magnetohydrodynamic liquid metal flow in a spatially varying solenoidal magnetic field

Abstract Motivated by experiments currently under investigation in the MEKKA laboratory at KIT, numerical simulations have been performed for a liquid metal pipe flow entering a strong magnetic field. Magnetohydrodynamic (MHD) flows in non-uniform magnetic fields are relevant in blanket engineering, in regions where the liquid breeder PbLi enters or exits the magnetic field confining the fusion plasma. Simulations provide insight into 3D phenomena near the non-uniform region of the magnetic field in particular velocity distribution and electric current pattern that cannot be directly observed in the experiments. Moreover, simulations describe the transition from a highly turbulent hydrodynamic entrance flow to a fully established laminar MHD flow. The present work addresses in particular a conservative formulation of the magnetic field, generation and decay of inlet turbulence by means of direct numerical simulation, as well as fluid–wall interaction by electric currents that are exchanged between the liquid metal and the thick electrically conducting pipe wall.

Characteristics of Decaying Convective Boundary Layers Revealed by Large-Eddy Simulations

The decay of the Convective Boundary Layer (CBL) is studied using large-eddy simulations of free and advective CBLs, in which surface heat supply is suddenly cut off. After the cutoff, coherent convective circulations last about one convective time scale and then fade away. In the mixed layer, the decay time scale increases with height, indicating that nonlocal eddies decay slower than near-surface local eddies. The slower decay of turbulence in the middle of CBL than near-surface turbulence is reconfirmed from the analysis of pattern correlations of perturbations of vertical velocity. Perturbations of potential temperature and scalar concentration decay faster and slower than vertical velocity perturbations, respectively. A downward propagation of negative heat flux and its oscillation are found and a quadrant analysis reveals that warmer air sinking events are responsible for the downward propagation. The fourth quadrant events seem to be induced by demixing of air parcels, entrained from above the CBL. The advective CBL simulation with geostrophic wind illustrates that near-surface eddies are mechanically generated and they decelerate flow from the bottom up in the CBL/residual layer. The two-dimensional spectra show the height- and scale-dependent characteristics of decaying convective turbulence again in the free and advective boundary layer simulations.