Fluid Turbulence Model Research Articles

Development, verification and experimental validation of a 3D numerical model for tubular solar receivers equipped with Raschig Ring porous inserts

This study presents a numerical investigation of gaseous tubular absorbers used in a solar furnace and introduces a 3D model to simulate porous inserts with random packing of metallic Raschig Rings (RR) at pore-scale. A comprehensive verification and validation process was conducted based on the experimental data obtained at Plataforma Solar de Almeria (SF60). The evaluations were carried out on three samples, including a smooth pipe (SP) and two enhanced pipes (20RR and 40RR) with 20 mm and 40 mm RR inserts. The effects of several influential parameters, such as the fluid turbulence model, the effective thermal conductivity of the porous material, and the randomness of the RR in the porous structure, were studied to assess the accuracy and repeatability of the model in predicting thermal and fluidic characteristics of air inside the absorber pipes under different working conditions. A detailed thermo-hydraulic analysis revealed an irregular flow pattern inside the porous zone, while the air recirculation at the porous entrance and exit provides an uneven pressure drop distribution in the azimuthal direction. Moreover, fluid turbulence is enhanced downstream of the porous insert thanks to several stream jets formed by uneven flow discharge at the insert outlet face, which improves heat transfer in that area. The analyses demonstrated a significant improvement in heat transfer, with a maximum enhancement factor of 10–15 than the smooth tube. Additionally, in the evaluation of thermo-hydraulic performance, the enhanced absorbers exhibit Performance Evaluation Criteria up to 2, compared to the tube without RR inserts.

Urban Pollutant Dispersion on a Turbulent Fluid Model

In 2019, more than 90% of the world’s population was living in places where pollutantconcentrations exceeded the air-quality guidelines. Anthropogenic activity has been the main cause of climate change in the last 20 years, especially in urban centres where industrial activities and motorized traffic mainly occur. This article presents a study of air pollutant dispersion by computational fluid dynamics modelling using OpenFOAM for urban street canyon simulations. The aim of this study was to investigate the influence of vegetation on natural ventilation, dispersion and CO2 mitigation. The behavior of pollutants was modeled by the Reynolds-averaged Navier–Stokes equations (RANS) and the k−ε fluid turbulence model. The results indicate that aerodynamic effects are more important at lower pollutant wind velocities, as they reduce turbulent dispersion and allow a higher reduction in the concentration of air pollutants. In addition, the direction of the wind, relative to the main axis of the street, had a significant impact on the results found. In general, in the presence of trees, perpendicular winds can lead to higher concentration of pollutants, while parallel winds allow improve air quality, considerably reducing those pollutant concentrations.

Validation of edge turbulence codes against the TCV-X21 diverted L-mode reference case

Self-consistent full-size turbulent-transport simulations of the divertor and scrape-off-layer (SOL) of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted ohmic L-mode discharges on the tokamak à configuration variable (TCV) tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from five diagnostic systems from the outboard midplane (OMP) to the divertor targets—giving a total of 45 one- and two-dimensional comparison observables in two toroidal magnetic field directions. The experimental dataset is used to validate three flux-driven 3D fluid-turbulence models—GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, individually tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the OMP—both in terms of profile shape and absolute magnitude—while a comparatively poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset and validation analysis, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and SOL.

The Fluid-structure Coupling Analysis of Steel-Wire-Reinforced Flexible Pipe Under Inner Fluid Pressure Impact

Identifying dynamic characteristics of the fluid filled steel-wire-reinforced flexible pipe is vital in controlling the pipe vibration. A direct fluid-structure coupling method based on finite element analysis is proposed and validated by modal simulation of an oil filled T-shape pipe. An innovative way of modeling steel-wire-reinforced rubber pipe is put forward. The modeling method is validated by modal test of the water-filled pipe. The 2nd Mooney-Rivlin constitutive model is used for the rubber material. Transient dynamic simulations of a bending steel-wire-reinforced pipe filled with water under step and sine-shape pressure impact are performed for the first time. Different fluid turbulence models are used to evaluate the influences on pipe vibration. The dynamic characteristics of the water filled flexible pipe is researched under different fluid pressures. The vibration peak frequencies of the water-filled pipe under various impact excitations coincide well with the fluid-structure coupling modes of the pipe.

Effect of spatial dimension on a model of fluid turbulence

A numerical study of the $d$ -dimensional eddy damped quasi-normal Markovian equations is performed to investigate the dependence on spatial dimension of homogeneous isotropic fluid turbulence. Relationships between structure functions and energy and transfer spectra are derived for the $d$ -dimensional case. Additionally, an equation for the $d$ -dimensional enstrophy analogue is derived and related to the velocity derivative skewness. Comparisons are made to recent four-dimensional direct numerical simulation results. Measured energy spectra show a magnified bottleneck effect which grows with dimension whilst transfer spectra show a varying peak in the nonlinear energy transfer as the dimension is increased. These results are consistent with an increased forward energy transfer at higher dimensions, further evidenced by measurements of a larger asymptotic dissipation rate with growing dimension. The enstrophy production term, related to the velocity derivative skewness, is seen to reach a maximum at around five dimensions and may reach zero in the limit of infinite dimensions, raising interesting questions about the nature of turbulence in this limit.

Existence and uniqueness of weak solution to a three-dimensional stochastic modified-Leray-alpha model of fluid turbulence

In this paper, we study the stochastic three-dimensional modified Leray-alpha model arising from the turbulent flows of fluids. We prove the existence of the probabilistic weak solution under the non-Lipschitz condition for the nonlinear forcing terms. We also discuss its uniqueness.

Coarse-grid simulations of full-loop gas-solid flows using a hybrid drag model: Investigations on turbulence models

The effect of fluid turbulence models on the coarse-grid simulation for the mesoscale gas-solid flow system is not as clear as that for gas-liquid/single flows. In this study, the effect of different turbulence models on predictions of riser-only, turbulent and bubbling flow hydrodynamics is quantified. Then the selected turbulence models are examined by coarse-grid simulations in a full-loop circulating fluidized bed (CFB) with a proposed hybrid drag model which integrates two SGMs and Hulin-Gidaspow model. Results show that the standard k-epsilon and k-omega models fail to capture a correct fluidization pattern in riser. Meanwhile, the RNG and realizable k-epsilon models and SST k-omega model enable satisfactory predictions which are highly comparable to discrete model predictions and experiments over different flow regimes. However, the realizable k-epsilon model produces more pronounced flow fluctuations causing computational instability. Using superior turbulence closures, full-loop simulations with the proposed hybrid model can predict desirable hydrodynamics.

Towards a self-consistent Boltzmann's kinetic model of fluid turbulence

A closure for the effective relaxation time of the Boltzmann–BGK kinetic equation for fluid turbulence is presented, based on a double-averaging procedure over both kinetic and turbulent fluctuations. The resulting effective relaxation time appears to agree with values obtained via a renormalisation group treatment of the Navier–Stokes equation only at low values of k/T, the ratio of turbulent kinetic energy to fluid temperature. For the kinetic treatment delivers a significantly longer effective relaxation time.

ПРОФИЛЬ КОНЦЕНТРАЦИИ ВЫСОКОИНЕРЦИОННЫХ ЧАСТИЦ В ПРИСТЕННОЙ ТУРБУЛЕНТНОСТИ ПРИ БОЛЬШИХ ЧИСЛАХ РЕЙНОЛЬДСА

Актуальность работы обусловлена многочисленными применениями турбулентных газодисперсных потоков во многих аппаратах и устройствах, применяемых в добыче полезных ископаемых, при транспортировке природных ресурсов, в энергетике, химической технологии и других отраслях промышленности. В качестве примеров можно привести технологии и установки пневмотранспорта порошкообразных материалов, штреки горных выработок, вентиляционные каналы для помещений различных типов, системы газоочистки и т. д. Течения со взвешенными частицами также широко распространены в природе и являются объектами исследований в метеорологии, геоморфологии, гидравлике русловых процессов и речных наносов и др. Взаимодействие инерционных частиц с неоднородными пристенными турбулентными потоками является весьма сложным явлением, требующим детального моделирования на основе глубокого понимания механизмов взаимодействия частиц с многомасштабными турбулентными вихревыми структурами. Цель: моделирование распределения и статистических параметров движения высокоинерционных частиц в пристенной зоне турбулентного потока при больших числах Рейнольдса на основе стохастической лагранжевой модели турбулентности среды. Методы: статистическое моделирование методом Монте-Карло движения частиц на основе стохастической лагранжевой модели турбулентности среды и теории подобия пристенной турбулентности. Результаты. Стохастическое лагранжево моделирование динамики высокоинерционных частиц в логарифмическом слое пристенной турбулентности при больших числах Рейнольдса показало существенную неравновесность статистики скорости частиц вблизи стенки. Показано, что вблизи стенки имеет место вызванная турбофорезом аккумуляция частиц, вследствие которой концентрация частиц на стенке более чем в 3 раза превышает концентрацию частиц в ядре потока при условии упругого отскока частиц от стенки. В то же время интенсивность пульсаций нормальной к стенке компоненты скорости частиц не равна нулю на стенке и составляет примерно 1/3 от интенсивности пульсаций скорости в ядре потока.

Modelling of the landslide-induced impulse waves in the Artvin Dam reservoir by empirical approach and 3D numerical simulation

Due to the burgeoning energy demand in Turkey, there has been a significant increase in the number of dams and hydroelectric power plants constructed; >250 dams have been built in the past 10 years. Consequently, various engineering problems were encountered due to landslides near reservoirs, both during and after the construction. Generally, two-dimensional (2D) and three-dimensional (3D) empirical equations have been used to calculate the physical properties and propagation of the landslide-induced impulse waves; however, 3D numerical simulation-based methodologies are rarely used, although they can model the complex geometry of dam reservoirs better, using detailed topographic data. In this study, therefore, 3D numerical analysis is carried out for a potential generation of impulse waves, using the data of paleo-landslide at the Artvin Dam reservoir (NE Turkey), and the results are compared with the calculated results by empirical equations. A finite element method-based shear strength reduction analysis (FEM-SSR) was performed to analyse the slope stability. After the establishment of the correct propagation model, the equations were utilised with different input parameters and 3D numerical analysis-based simulations to evaluate the characteristics of the impulse waves. In the numerical model created using the FLOW-3D software, the ‘drift-flux model’ was used to simulate the probable landslides. The Reynolds-averaged Navier–Stokes equations were used in a free-surface modelling technique together with the volume of fluid (VOF) model for simulating the wave generation. The renormalised group model (RNG) for viscous flow and k-ε turbulence model for fluid–fluid coupled condition, were used as the boundary conditions. The results indicated that the values obtained from the proposed empirical equations and 3D numerical analysis were not similar. Thus, if the reservoir geometry is very complex and the wave propagation distance is more than a few kilometers (as in this study), highly detailed engineering geological studies should be performed to accurately define the boundary conditions, and three-dimensional numerical analyses should be performed to construct the impulse wave model.

ON MODELLING THE TRANSITION TO TURBULENCE IN PIPE FLOW

As a possible model for fluid turbulence, a Reiner–Rivlin-type equation is used to study Poiseuille–Couette flow of a viscous fluid in a rotating cylindrical pipe. The equations of motion are derived in cylindrical coordinates, and small-amplitude perturbations are considered in full generality, involving all three velocity components. A new matrix-based numerical technique is proposed for the linearized problem, from which the stability is determined using a generalized eigenvalue approach. New results are obtained in this cylindrical geometry, which confirm and generalize the predictions of previous recent studies. A possible mechanism for the transition to turbulent flow is discussed.

Investigation of the interaction between competing types of nondiffusive transport in drift wave turbulence

Radial transport in turbulence dominated tokamak plasmas has been observed to deviate from classical diffusion in certain regimes relevant for magnetic confinement fusion. These situations at least include near-marginal turbulence, where radial transport becomes superdiffusive and mediated by elongated radial structures (or avalanches) and transport across radially sheared poloidal flows, where radial subdiffusion often ensues. In this paper, the interaction between very different physical ingredients responsible for these two types of nondiffusive dynamics (namely, turbulent profile relaxation close to a local threshold and the interaction with radially sheared zonal flows) is studied in detail in the context of a simple two-dimensional electrostatic plasma fluid turbulence model based on the dissipative trapped electron mode. It is shown that, depending on the relative relevance of each of these ingredients, which can be tuned in various ways, a variety of non-diffusive radial transport behaviors can be found in the system. The results also illustrate the fact that the classical diffusion paradigm is often insufficient to describe turbulent transport in systems with self-generated flows and turbulent profile relaxations.

On the Convergence of the Uniform Attractor for the 2D Leray-α Model

We consider a nonautonomous 2D Leray-α model of fluid turbulence. We prove the existence of the uniform attractor Aα. We also study the convergence of Aα as α goes to zero. More precisely, we prove that the uniform attractor Aα converges to the uniform attractor of the 2D Navier-Stokes system as α tends to zero.

Information Theory Analysis of Cascading Process in a Synthetic Model of Fluid Turbulence

The use of transfer entropy has proven to be helpful in detecting which is the verse of dynamical driving in the interaction of two processes, X and Y . In this paper, we present a different normalization for the transfer entropy, which is capable of better detecting the information transfer direction. This new normalized transfer entropy is applied to the detection of the verse of energy flux transfer in a synthetic model of fluid turbulence, namely the Gledzer–Ohkitana–Yamada shell model. Indeed, this is a fully well-known model able to model the fully developed turbulence in the Fourier space, which is characterized by an energy cascade towards the small scales (large wavenumbers k), so that the application of the information-theory analysis to its outcome tests the reliability of the analysis tool rather than exploring the model physics. As a result, the presence of a direct cascade along the scales in the shell model and the locality of the interactions in the space of wavenumbers come out as expected, indicating the validity of this data analysis tool. In this context, the use of a normalized version of transfer entropy, able to account for the difference of the intrinsic randomness of the interacting processes, appears to perform better, being able to discriminate the wrong conclusions to which the “traditional” transfer entropy would drive.

Statistics of the Navier–Stokes-alpha-beta regularization model for fluid turbulence

We explore one-point and two-point statistics of the Navier–Stokes-αβ regularization model at moderate Reynolds number (Re ≈ 200) in homogeneous isotropic turbulence. The results are compared to the limit cases of the Navier–Stokes-α model and the Navier–Stokes-αβ model without subgrid-scale stress, as well as with high-resolution direct numerical simulation. After reviewing spectra of different energy norms of the Navier–Stokes-αβ model, the Navier–Stokes-α model, and Navier–Stokes-αβ model without subgrid-scale stress, we present probability density functions and normalized probability density functions of the filtered and unfiltered velocity increments along with longitudinal velocity structure functions of the regularization models and direct numerical simulation results. We highlight differences in the statistical properties of the unfiltered and filtered velocity fields entering the governing equations of the Navier–Stokes-α and Navier–Stokes-αβ models and discuss the usability of both velocity fields for realistic flow predictions. The influence of the modified viscous term in the Navier–Stokes-αβ model is studied through comparison to the case where the underlying subgrid-scale stress tensor is neglected. Whereas, the filtered velocity field is found to have physically more viable probability density functions and structure functions for the approximation of direct numerical simulation results, the unfiltered velocity field is found to have flatness factors close to direct numerical simulation results.

Boundary conditions for plasma fluid models at the magnetic presheath entrance

The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with Ti≪Te and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v||i, v||e, n, ϕ, Te, and for the vorticity ω=∇⊥2ϕ. The effects of E × B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.

Universality of scaling and multiscaling in turbulent symmetric binary fluids

We elucidate the universal scaling and multiscaling properties of the nonequilibrium steady states in a driven symmetric binary fluid (SBF) mixture in its homogeneous miscible phase in three dimensions. We show, via direct numerical simulations (DNSs) that structure functions of the velocity and the concentration gradient exhibit multiscaling in three dimensions (3D) and extended self-similarity. We also find that, in contrast to the well-known passive scalar turbulence problem, structure functions of the concentration show simple scaling. We propose a shell model for SBF turbulence that preserves all the invariances in the ideal limit of the SBF equations and reduces to a well-known shell model for fluid turbulence in the zero concentration field limit. We show that the shell model has the same scaling properties as the three-dimensional SBF equations. Our combined results from our DNSs of the SBF equations and shell-model studies consistently bring out the multiscaling of the velocity and concentration gradient fields and simple scaling of the concentration field.

Reduced model simulations of the scrape-off-layer heat-flux width and comparison with experiment

Reduced model simulations of turbulence in the edge and scrape-off-layer (SOL) region of a spherical torus or tokamak plasma are employed to address the physics of the scrape-off-layer heat-flux width. The simulation model is an electrostatic two-dimensional fluid turbulence model, applied in the plane perpendicular to the magnetic field at the outboard midplane of the torus. The model contains curvature-driven-interchange modes, sheath losses, and both perpendicular turbulent diffusive and convective (blob) transport. These transport processes compete with classical parallel transport to set the SOL width. Midplane SOL profiles of density, temperature, and parallel heat flux are obtained from the simulation and compared with experimental results from the National Spherical Torus Experiment [S. M. Kaye et al., Phys. Plasmas 8, 1977 (2001)] to study the scaling of the heat-flux width with power and plasma current. It is concluded that midplane turbulence is the main contributor to the SOL heat-flux width for the low power H-mode discharges studied, while additional physics is required to fully explain the plasma current scaling of the SOL heat-flux width observed experimentally in higher power discharges. Intermittent separatrix-spanning convective cells are found to be the main mechanism that sets the near-SOL width in the simulations. The roles of sheared flows and blob trapping versus emission are discussed.

ON THE HIGH ACCURACY NS-ALPHA-DECONVOLUTION TURBULENCE MODEL

We analyze the mathematical and physical properties of, and present numerical experiments for, the recently proposed NS-α-deconvolution model of fluid turbulence. This family of models has the well-known NS-α model as its zeroth-order model, and applies the Nth van Cittert deconvolution operator to the filtered terms in NS-α to create the Nth-order NS-α-deconvolution model. This model is proposed in Ref. 29, where it is shown to have consistency error O(α2N + 2). Herein we prove that the model admits unique regular solutions, is frame invariant, and improves the consistency error of NS-α from O(α2) to O(α2N + 2) while requiring (N + 1)1/2 times more (typically 1 ≤ N ≤ 5) degrees of freedom for complete resolution. Numerical experiments show that adding approximate deconvolution to NS-α significantly improves accuracy in computations.

The universality of dynamic multiscaling in homogeneous, isotropic Navier–Stokes and passive-scalar turbulence

We systematize the study of dynamic multiscaling of time-dependent structure functions in different models of passive-scalar and fluid turbulence. We show that, by suitably normalizing these structure functions, we can eliminate their dependence on the origin of time at which we start our measurements and that these normalized structure functions yield the same linear bridge relations that relate the dynamic-multiscaling and equal-time exponents for statistically steady turbulence. We show analytically, for both the Kraichnan model of passive-scalar turbulence and its shell model analogue, and numerically, for the Gledzer–Ohkitani–Yamada (GOY) shell model of fluid turbulence and a shell model for passive-scalar turbulence, that these exponents and bridge relations are the same for statistically steady and decaying turbulence. Thus, we provide strong evidence for dynamic universality, i.e. dynamic-multiscaling exponents do not depend on whether the turbulence decays or is statistically steady.