2D Turbulence Research Articles

Numerical simulation of turbulent thermal convection based on LBM

The two-dimensional (2D) turbulent thermal convection is numerically investigated by using Lattice Boltzmann Method. The 2D turbulence is considered as 2D channel flow where the flow is forced by the arrays of adiabatic cylinders placed in the inlet and wall boundary of 2D channel, which is heated uniformly from the inlet as to inspire the paradigmatic motion of thermal convection. It is found that the spacing vortex number density distribution in the large-scale range [Formula: see text], based on the Liutex vortex definition criterion, which is in fair agreement with the Benzi prediction. The energy spectrum of the Liutex field [Formula: see text]. The scaling behavior of full-field energy spectrum in the large scale is [Formula: see text]. The temperature spectrum in the large-scale range is found to be approximate to [Formula: see text], which is according with the Bolgiano theory of 2D buoyancy driven turbulence. The energy flux cascades to the large scale, the enstrophy cascades to small scale. The moments of the energy dissipation field [Formula: see text] coarse grained at the scale [Formula: see text] have the power-law behaviors with the scale [Formula: see text]. The velocity intermittency measured by PDF exists in large-scale range of 2D turbulent thermal convection. The measured scaling exponents [Formula: see text] are determined by a lognormal formula. The measured intermittency parameter is [Formula: see text], which denotes the strong intermittency in the large-scale range of 2D turbulent thermal convection.

Spatio-temporal deep learning models of 3D turbulence with physics informed diagnostics

Direct Numerical Simulations (DNSs) of high Reynolds number turbulent flows, encountered in engineering, earth sciences, and astrophysics, are not tractable because of the curse of dimensionality associated with the number of degrees of freedom required to resolve all the dynamically significant spatio-temporal scales. Designing efficient and accurate Machine Learning (ML)-based reduced models of fluid turbulence has emerged recently as a promising approach to overcoming the curse of dimensionality challenge. However, to make the ML approaches reliable one needs to test their efficiency and accuracy, which is recognised as important but so far incomplete task. Aiming to improve this missing component of the promising approach, we design and evaluate two reduced models of 3D homogeneous isotropic turbulence and scalar turbulence based on state-of-the-art ML algorithms of the Deep Learning (DL) type: Convolutional Generative Adversarial Network (C-GAN) and Compressed Convolutional Long-Short-Term-Memory (CC-LSTM) Network. Quality and computational efficiency of the emulated velocity and scalar distributions is juxtaposed to the ground-truth DNS via physics-rich statistical tests. The reported results allow to uncover and classify weak and strong aspects of C-GAN and CC-LSTM. The reported results, as well as the physics-informed methodology developed to test the ML-based solutions, are expected to play a significant role in the future for making the DL schemes trustworthy through injecting and controlling missing physical information in computationally tractable ways.

Convectively Driven 3D Turbulence in Massive Star Envelopes. I. A 1D Implementation of Diffusive Radiative Transport

Abstract Massive (M > 30 M ⊙) stars exhibit luminosities that are near the Eddington limit for electron scattering, causing the increase in opacity associated with iron at T ≈ 180 , 000 K to trigger supersonic convection in their outer envelopes. Three-dimensional radiative hydrodynamics simulations by Jiang and collaborators with the Athena++ computational tool have found order-of-magnitude density and radiative flux fluctuations in these convective regions, even at optical depths ≫ 100 . We show here that radiation can diffuse out of a parcel during the timescale of convection in these optically thick parts of the star, motivating our use of a “pseudo” Mach number to characterize both the fluctuation amplitudes and their correlations. In this first paper, we derive the impact of these fluctuations on the radiative pressure gradient needed to carry a given radiative luminosity. This implementation leads to a remarkable improvement between 1D and 3D radiative pressure gradients, and builds confidence in our path to an eventual 1D implementation of these intrinsically 3D envelopes. However, simply reducing the radiation pressure gradient is not enough to implement a new 1D model. Rather, we must also account for the impact of two other aspects of turbulent convection: the substantial pressure and the ability to transport an appreciable fraction of the luminosity, which will be addressed in upcoming works. This turbulent convection also arises in other instances where the stellar luminosity approaches the Eddington luminosity. Hence, our effort should apply to other astrophysical situations where an opacity peak arises in a near Eddington-limited, radiation pressure-dominated plasma.

Simulation of EAST edge plasma using SOLPS-ITER/BOUT++ coupling

The self-consistent simulation of transport and turbulence in tokamak edge plasma on the EAST tokamak is performed by coupling the fluid plasma/neutral 2D transport code SOLPS-ITER and the fluid 3D turbulence code BOUT++. The convergence of the coupling is validated. The changing rates between the two consecutive profiles of density, electron temperature and ion temperature are close to zero in the last several iteration steps, and the variations of the transport coefficients Dr, χe and χi also show the tendency to diminish as the iteration step increases, indicating that the coupling tends to be in a quasi-steady state. The edge plasma at the time t = 3400 ms in shot 36 780 with deuterium discharge on EAST is simulated by the SOLPS-ITER/BOUT++ coupling. The MHD equilibrium at the shot time with the lower single-null configuration is used for the production of the computational meshes for SOLPS-ITER and BOUT++, respectively. The computational profiles of electron density and temperature, particle and heat fluxes at the divertor targets from the SOLPS-ITER/BOUT++ coupling simulation are compared with the measured profiles, and it is found that the computational and measured profiles are similar.

Spectral Anisotropy in 2D plus Slab Magnetohydrodynamic Turbulence in the Solar Wind and Upper Corona

Abstract The 2D + slab superposition model of solar wind turbulence has its theoretical foundations in nearly incompressible magnetohydrodynamics (NI MHD) in the plasma beta ∼1 or ≪1 regimes. Solar wind turbulence measurements show that turbulence in the inertial range is anisotropic, for which the superposition model offers a plausible explanation. We provide a detailed theoretical analysis of the spectral characteristics of the Elsässer variables in the 2D + NI/slab model. We find that (1) the majority 2D component has a power spectrum in perpendicular wavenumber k ⊥; (2) the strongly imbalanced minority NI/slab turbulence has power spectra and , where k z is aligned with the mean magnetic field; (3) NI/slab turbulence can exhibit a double-power-law spectrum, with the steeper part being G*(k) ∼ k −5/3 and corresponding to strong turbulence and the flatter spectrum satisfying G*(k) ∼ k −3/2 and corresponding to weak turbulence; (4) there is a critical balance regime for NI/slab turbulence that satisfies and ; and (5) the forward and backward Elsässer power spectra can have different spectral forms provided that the triple-correlation times for each are different. We use the spectral analysis to compute the total power spectra in frequency parallel to the solar wind flow for the superposition model, showing that strongly imbalanced turbulence yields an f −5/3 spectrum for all angles between the mean flow and magnetic field, and that double power laws are possible when the nonlinear and Alfvén timescales are both finite.

Numerical simulation of three dimensional flow in Yazidang Reservoir based on image processing

In order to study the water flow movement of the Yazidang Reservoir, this paper generates the initial terrain for the researched water area with the image stitching technology and image edge detection technology, establishes a 3D k - ɛ mathematical model, solves the equations discretely by FVM and SIMPLEC algorithms, studies the numerical simulation of the water flow movement of the reservoir under four working conditions, and analyzes the flow field on the surface and at the bottom of the reservoir. The results show the improved terrain pre-processing accuracy and efficiency of the researched water area and the rationality of the water flow field and rate simulation results, which means that the established 3D turbulence mathematical model can be applied to the numerical simulation of the reservoirs similar to the Yazidang Reservoir. The numerical simulation of 3D turbulence in Yazidang Reservoir provides a theoretical basis and practical application value for the numerical simulation of similar reservoirs.

Renormalized Onsager functions and merging of vortex clusters

This paper is devoted to an heuristic discussion of the merging mechanism between two clusters of point vortices, supported by some numerical simulations. A concept of renormalized Onsager function is introduced, elaboration of the solutions of the mean field equation. It is used to understand the shape of the single cluster observed as a result of the merging process. Potential implications for the inverse cascade 2D turbulence are discussed.

A Study of Modified Infotaxis Algorithms in 2D and 3D Turbulent Environments.

Emergency response to hazardous gases in the environment is an important research field in environmental monitoring. In recent years, with the rapid development of sensor technology and mobile device technology, more autonomous search algorithms for hazardous gas emission sources are proposed in uncertain environment, which can avoid emergency personnel from contacting hazardous gas in a short distance. Infotaxis is an autonomous search strategy without a concentration gradient, which uses scattered sensor data to track the location of the release source in turbulent environment. This paper optimizes the imbalance of exploitation and exploration in the reward function of Infotaxis algorithm and proposes a mobile strategy for the three-dimensional scene. In two-dimensional and three-dimensional scenes, the average steps of search tasks are used as the evaluation criteria to analyze the information trend algorithm combined with different reward functions and mobile strategies. The results show that the balance between the exploitation item and exploration item of the reward function proposed in this paper is better than that of the reward function in the Infotaxis algorithm, no matter in the two-dimensional scenes or in the three-dimensional scenes.

Simulation of a dense gas chlorine release with a Lagrangian particle dispersion model (LPDM)

In 2015, 2016, nine chlorine releases experiments took place at Dugway Proving Ground (Utah, USA). Five trials conducted in 2015 featured a grid of CONEX shipping containers around the release tank to simulate an idealized urban area. The trials were a great occasion to collect data describing the dynamics of “high molecular weight” species in an idealized urban environment.This paper proposes a comparison of the PMSS (Parallel Micro-Swift Micro-Spray) suite against the experimental data from four of the trials, following the choice made by an international model inter-comparison team. PMSS combines two MPI parallelized urban modelling subsystems: (1) PSWIFT phenomenologically accounts for 3D wind flow and turbulence around buildings, and (2) PSPRAY simulates air-based contaminant dispersion in urban areas using a stochastic Lagrangian Particle Dispersion Model.For this comparison, PMSS is deployed first on a hypothetic configuration and compared to the Code_Saturne CFD model, and then using the data of the trials 1, 5, 6 and 7 performed during JRII (Jack Rabbit II) 2015 and 2016. The initial momentum due to the tank discharge and the dense gas and droplet effects of the pressurized chlorine release are modelled using a dedicated radial source term jet and the Glendening equations. In trials 1 and 5, the influence of the CONEX shipping containers on the wind flow and the dispersion is explicitly considered. While spread through a large interval, the chlorine concentrations are computed both in the near field and in the far field (up to 11 km) using PMSS nesting capabilities. The results of the model are compared with the experimental data and sensitivity tests are also presented.

Analysis and improvement of a mathematical turbine model

A mathematical turbine model is necessary for dynamic and transient analysis of hydro power plants, also in the early stages of a project. Such models can be based on a first principles approach or on empirical data, many models are a combination. A first principles approach is practical when specific laboratory data are unavailable, for example in the design phase of a new plant. These models can easily be simplified and linearized without losing physical correctness or generality, even though accuracy may vary when applied to a specific system.The model studied in this work, was developed several years ago from the Euler turbine equation and the opening degree definition, and has later been modified and linearized for simple implementation into simulation software. The model captures losses for varying rotational speed quite well, but struggles to capture losses for varying flow rate. The hydraulic efficiency is over-predicted for flow far off the design point, because irreversible hydraulic loss phenomena such as 3D turbulence and dissipation are not inherently included in this 1D model. Empirical relations or Hill charts for exact fit to a measured turbine can be included, however generality is then lost.This paper analyzes and discusses the mathematical model compared to laboratory measurements, highlighting its performance in predicting the efficiency off best efficiency point (BEP). A mathematical improvement based on turbine data is presented and implemented for three specific Francis turbines. The possibility to generalize the procedure is also discussed.

Simulation of pollutant dispersion in urban street canyons using hybrid rans-les method with two-phase model

In this study, to simulate the pollution treatment as a separated phase a 3D incompressible turbulence model under isothermal conditions was considered. The hybrid RANS-LES method with a sub-grid scale(SGS) technique within the framework of two-phase flow was used to study pollution distribution in urban street canyons. An area source of pollutant with a constant concentration, located in the ground of the street canyon, was used to simulate vehicular emissions. The near-wall regions were simulated using the RANS(k-ε) turbulence model and the rest of the domain was simulated with the LES model. To measure the effect of building height on pollutant dispersion, the parameter AR(Aspect Ratio) was calculated. Also to determine the effect of street width, a new parameter SWV(Street Width Value) was introduced. Governing equations were discretized using the well-known finite volume method on a staggered grid. To increase the accuracy, the second-order Van Leer Method(VLM) was applied and the Volume of Fluid(VOF) method was employed for the description of the interfaces. The Iterative line-by-line TDMA solution procedure and the Strongly Implicit Procedure(SIP) was used for the Pressure Correction Equation. A fine comparison of the results revealed that by increasing SWV, the number of vertical vortices in the canyon streets generally decreased and the vortices grew larger. In addition, increasing AR caused a rise in the pollution volume fraction in the first canyon street. The current numerical results indicate that the AR and SWV influence the flow field and volume fraction of phases inside an isolated street canyon, significantly.

Wind Profile Satellite Observation Requirements and Capabilities

Abstract The Aeolus mission objectives are to improve numerical weather prediction (NWP) and enhance the understanding and modeling of atmospheric dynamics on global and regional scale. Given the first successes of Aeolus in NWP, it is time to look forward to future vertical wind profiling capability to fulfill the rolling requirements in operational meteorology. Requirements for wind profiles and information on vertical wind shear are constantly evolving. The need for high-quality wind and profile information to capture and initialize small-amplitude, fast-evolving, and mesoscale dynamical structures increases, as the resolution of global NWP improved well into the 3D turbulence regime on horizontal scales smaller than 500 km. In addition, advanced requirements to describe the transport and dispersion of atmospheric constituents and better depict the circulation on climate scales are well recognized. Direct wind profile observations over the oceans, tropics, and Southern Hemisphere are not provided by the current global observing system. Looking to the future, most other wind observation techniques rely on cloud or regions of water vapor and are necessarily restricted in coverage. Therefore, after its full demonstration, an operational Aeolus-like follow-on mission obtaining globally distributed wind profiles in clear air by exploiting molecular scattering remains unique.

Studying subcritical opposing channel flows

This study investigates the hydraulics of opposing open channel flow (OCF) by using computational fluid dynamics software – Fluent. The model is validated with the velocity fields, flow separation zone, and water surface elevation obtained from experimental study available in the literature. 3D flow structures and turbulence characteristics of the validation problem are also discussed. In total, 81 cases of opposing flows are studied varying the discharge ratio, Froude number at the exit, the width ratio, and the aspect ratio of the exit channel. Simulated results are used to develop empirical equations for contraction coefficient, flow depth ratio, and minimum water depth in the contracted section of the OCF. The energy loss coefficient is computed from the simulated results. Contraction coefficient, flow depth ratio, and energy loss coefficient of OCF and corresponding values of right-angled channel junction flows are compared.

Numerical Investigation of 2D Turbulent Flow past a Circular Cylinder at Lower Subcritical Reynolds Number

The main objective of the present study is to evaluate the applicability of the standard k-ε turbulence model in engineering practice in the subcritical flow regimes. Also, examine the influence of Reynolds number variation on the flow characteristics are considered. The numerically simulation of the flow characteristics over a smooth uniform cross section circular cylinder with a diameter of 50 mm and 400mm span, placed horizontally perpendicular to the main flow direction at four different Reynolds numbers (Re) based on the cylinder diameter (D) and the undisturbed free-stream velocity in the range Re=(0.5,0.7,0.85 and 1.0) ×105 were performed. The simulated results of the flow properties such as flow stream velocity components, pressure distribution contours, pressure coefficient (Cp) and drag coefficient(CD) around the circular cylinder were consider. The numerical analysis obtain by CFD using ANSYS FLUNET (19.1) with K-ε turbulence model, for solving the 2D (ANSE) governing equation for tested model were consider. The present simulation results validation is obtained by comparing the converged results with published numerical and experimental data.

Dynamics of a long chain in turbulent flows: impact of vortices.

We show and explain how a long bead-spring chain, immersed in a homogeneous isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of three-dimensional (3D) turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In the 3D case on the contrary, the chain is extended even in vortical regions, which suggests that the chain follows axially stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly flexible, inextensible chain also shows preferential sampling in three dimensions, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in two dimensions is considerably reduced. In three dimensions, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Numerical verification of a non-residual orthogonal term-by-term stabilized finite element formulation for incompressible convective flow problems

The modeling of turbulent flows is relevant in many engineering applications and, is an active field of research on numerical methods. Convergence and stability of proposed formulations are crucial to predict transitional flows from laminar to turbulent flows. In this work, a recently developed stabilized finite element formulation is used as a powerful tool to describe such kind of problems. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual based formulations, the introduction of two velocity subscale components. The theoretical rate of convergence of the method is verified numerically using linear and quadratic equal-order finite element discretizations. To this end, a standard convergence test of L2-norm is presented where the computed solutions are compared when manufactured solutions are imposed at Gauss-point level. Moreover, the Hopf bifurcation is studied for two well-known benchmark problems: flow past a cylinder and the three-dimensional lid-driven cavity flow. For the flow past a cylinder case, the Hopf bifurcation is verified using dynamic subscales and is assessed so that they do not disturb the solution. In particular, a dominant convective problem (Re=4000) is solved using both the quasistatic and dynamic versions of the method, evaluating the performance of each one in the quality of the solution and in the CPU time needed to obtain a converged solution. For the 3D lid-driven cavity flow problem, the Hopf bifurcation is determined using two different boundary conditions, analyzing their effect on the dynamics of the problem and on the thickness and shape of the boundary layer. The final test case is the turbulent 3D lid-driven cavity problem (Re=12000), where velocity profiles are compared with experimental, LES and DNS reference solutions. Additionally, pressure and velocity spectra are shown at certain representative points of the domain, as well as phase diagrams, correlation function graphs, the Poincaré map, and the Lyapunov exponent, typical mathematical tools used in dynamical system analysis. From the results, the method is robust and accurate for all the numerical tests both in viscous dominant problems as in dominant convective ones.

Effect of magnetic perturbations on turbulence-flow dynamics at the L-H transition on DIII-D

Detailed 2D turbulence measurements from the DIII-D tokamak provide an explanation for how resonant magnetic perturbations (RMPs) raise the L-H power threshold PLH [P. Gohil et al., Nucl. Fusion 51, 103020 (2011)] in ITER-relevant, low rotation, ITER-similar-shape plasmas with favorable ion ∇B direction. RMPs simultaneously raise the turbulence decorrelation rate ΔωD and reduce the flow shear rate ωshear in the stationary L-mode state preceding the L-H transition, thereby disrupting the turbulence shear suppression mechanism. RMPs also reduce the Reynolds stress drive for poloidal flow, contributing to the reduction of ωshear. On the ∼100 μs timescale of the L-H transition, RMPs reduce Reynolds-stress-driven energy transfer from turbulence to flows by an order of magnitude, challenging the energy depletion theory for the L-H trigger mechanism. In contrast, non-resonant magnetic perturbations, which do not significantly affect PLH, do not affect ΔωD and only slightly reduce ωshear and Reynolds-stress-driven energy transfer.

Testing of 3D Printed Turbulence Promoters for Membrane Filtration

Membrane filtration process can be intensified by using static mixers inside tubular membranes. Most of commercial static mixers are optimized for mixing fluids, not for membrane filtration. We have developed new turbulence promoter geometries designed for intensification of permeate flux and retention without significant pressure drop along the membrane. In previous experiments, we used metallic turbulence promoters, but in this work, FDM 3D printing technology was used to create these improved geometries, which are new in membrane filtration and they have the same geometry as existing metallic versions. New 3D printed objects were tested with filtration of stable oil-in-water emulsion. Our experiments proved that 3D printed static mixers might be as effective as metallic versions. The effect on initial flux and retention of oil was very similar. Pressure drop along membrane was slightly higher (but significantly lower from pressure drop along the membrane resulted by commercial static mixers, designed only for mixing fluids). Higher pressure drop may be the result of rougher surface due the layer-technology of 3D printing. This negative effect can be reduced by using a smaller nozzle (which will produce smaller layers) or smoothing the surface. PLA is material easier for printing, but from these two materials, PETG is a better choice due its higher operating temperature and better water-resist properties too.

Skew-Symmetric Splitting for Multiscale Gas Dynamics and MHD Turbulence Flows

The objective of this work is to improve nonlinear stability and to minimize aliasing error by applying high order central discretizations to skew-symmetric splitting forms of the inviscid flux derivative without added high order numerical dissipation for both shock-free compressible turbulence and turbulence with weak shocks. Skew-symmetric splittings of the inviscid flux derivative for high order central schemes are studied and developed for gas dynamics and MHD systems. For problems containing discontinuities and multiscale turbulence fluctuations the Yee and Sjogreen (Proceedings of the ICOSAHOM09, Trondheim, 2016) high order nonlinear filter approach is utilized at isolated computational regions, while maintaining high accuracy almost everywhere for direct numerical simulation and large eddy simulations of turbulence computations. Three skew-symmetric splittings are considered for a wide range of compressible flow speeds and flow types, including a 3D forced turbulence simulation. Not all of the skew-symmetric splittings used for gas dynamics can be extended to the non-strictly hyperbolic conservation laws of ideal magnetohydrodynamics (MHD) governing equations. In this work, the Ducros et al. (J Comput Phys 161:114–139, 2000) splitting variants are constructed for MHD. Four formulations of the MHD equations are considered. The different formulations of the equations in conjunction with the variants of Ducros et al. type skew-symmetric splitting will be shown to have a strong effect on the stability of non-dissipative approximations.

Scaling of L-mode heat flux for ITER and COMPASS-U divertors, based on five tokamaks

This contribution aims to improve existing scalings of the L-mode power decay length , especially for plasma configurations with strike points at the ITER-relevant location—closed vertical divertor targets. We propose 13 new scalings based on data from the tokamaks JET, EAST, MAST, Alcator C-mod and COMPASS, and validate them against the output of the 2D turbulence code HESEL. The analysis covers 500 divertor heat flux profiles (obtained by probes or IR cameras), measured in L-mode discharges with varying 12 global plasma parameters (all well predictable). We find that the two previously published scalings (Eich 2013 J. Nucl. Mat. 438 S72) and (Scarabosio 2013 J. Nucl. Mat. 438 S426), which were based on outer target data from AUG and JET, describe the JET, C-mod and COMPASS profiles well. This holds not only at the outer horizontal and vertical targets, but surprisingly also at the inner vertical targets. In contrast, EAST, HESEL and especially MAST data are poorly described by these two scalings. We therefore derive 13 new scalings, which account for 85–92 % of the measured variability across all five tokamaks. Although each of the scalings is based on a different parameter combination, their predictions for the ITER and COMPASS-Upgrade tokamaks are very similar. Just before the L-H transition in the ITER baseline scenario, the presented scalings predict values mm. For the COMPASS-Upgrade tokamak, all the scalings predict mm with a single exception of the scaling based on the stored plasma energy which predicts only 1.2 mm for both tokamaks. We encourage the reader to use as many of these scalings as possible, depending on available data. In attached plasma and using significant assumptions, our results imply steady-state surface-perpendicular heat flux around 10 MW/m2 for ITER, and 20 MW/m2 for COMPASS-Upgrade.