Boundary Plasma Turbulence Simulations for Tokamaks

The boundary plasma turbulence code BOUT models tokamak boundaryplasma turbulence in a realistic divertor geometry usingmodified Braginskii equations for plasma vorticity,density(ni),electron and ion temperature(Te,Ti)and parallelmomenta.The BOUT code solves for the plasma fluid equations in a three dimensional(3D)toroidal segment(or a toroidal wedge),including the region somewhat inside the separatrix and extending into the scrape-off layer;the private flux region is also included.In this paper,a description is given of the sophisticated physical models,innovative numerical algorithms,and modern software design used to simulate edgeplasmas in magnetic fusion energy devices.The BOUT code’s unique capabilities and functionality are exemplified via simulations of the impact of plasma density on tokamak edge turbulence and blob dynamics.

A DIGITAL SIMULATION TECHNIQUE FOR DRYDEN ATMOSPHERIC TURBULENCE MODEL

Dryden model is usually used in studying the response of flight vehicle to atmospheric turbulence. For a modern flight simulator,it is necessary to generate random winds ( in Dryden model or sometimes others) with a digital computer.In this paper,a theoretically strict new method to meet this purpose is proposed.By this method,we can acquire a three-dimensional atmospheric turbulence which contains three components of wind velocity and three components of wind velocity gradient.The reliability of this method is checked by comparing the obtained autocorrelation value with the theoretical one.A numerical example has shown a satisfactory result.Finally,some proposals about how to use this mathematical model in flight simulator are given.

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation

Direct numerical simulations（DNSs） of purely elastic turbulence in rectilinear shear flows in a three-dimensional（3D） parallel plate channel were carried out,by which numerical databases were established.Based on the numerical databases,the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns,the wall effect on the turbulent kinetic energy spectrum,and the local relationship between the flow motion and the microstructures＇ behavior.Moreover,to address the underlying physical mechanism of elastic turbulence,its generation was presented in terms of the global energy budget.The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length,and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched.In addition,the patterns of microstructures＇ elongation behave like a filament.From the results of the turbulent kinetic energy budget,it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.

A Reynolds mass flux model for gas separation process simulation:Ⅱ.Application to adsorption on activated carbon in a packed column

Simulations of adsorption process using the Reynolds mass flux model described in Part I of these serial articles are presented. The object of the simulation is the methylene chloride adsorption in a packed column(0.041 m id,packed with spherical activated carbon up to a length of 0.2 m). With the Reynolds mass flux model,breakthrough/regeneration curves, concentration and temperature as well as the velocity distributions can be obtained. The simulated results are compared with the experimental data reported in the literature and satisfactory agreement is found both in breakthrough/regeneration curves and temperature curves. Moreover,the anisotropic turbulent mass diffusion is characterized and discussed.

Unsteady RANS and detached eddy simulation of the multiphase flow in a co-current spray drying

A detached eddy simulation(DES) and a k-ε-based Reynolds-averaged Navier–Stokes(RANS) calculation on the co-current spray drying chamber is presented. The DES used here is based on the Spalart–Allmaras(SA) turbulence model, whereas the standard k-ε(SKE) was considered here for comparison purposes. Predictions of the mean axial velocity, temperature and humidity profile have been evaluated and compared with experimental measurements. The effects of the turbulence model on the predictions of the mean axial velocity, temperature and the humidity profile are most noticeable in the(highly anisotropic) spraying region. The findings suggest that DES provide a more accurate prediction(with error less than 5%) of the flow field in a spray drying chamber compared with RANS-based k-ε models. The DES simulation also confirmed the presence of anisotropic turbulent flow in the spray dryer from the analysis of the velocity component fluctuations and turbulent structure as illustrated by the Q-criterion.

Digital simulation of 3D turbulence wind field of Sutong Bridge based on measured wind spectra

Time domain analysis is an essential implement to study the buffeting behavior of long-span bridges for it can consider the non-linear effect which is significant in long-span bridges. The prerequisite of time domain analysis is the accurate description of 3D turbulence winds. In this paper, some hypotheses for simplifying the 3D turbulence simulation of long-span cable-stayed bridges are conducted, considering the structural characteristics. The turbulence wind which is a 3D multivariate stochastic vector process is converted into four independent 1D univariate stochastic processes. Based on recorded wind data from structural health monitoring system (SHMS) of the Sutong Bridge, China, the measured spectra expressions are then presented using the nonlinear least-squares fitting method. Turbulence winds at the Sutong Bridge site are simulated based on the spectral representation method and the Fast Fourier transform (FFT) technique, and the relevant results derived from target spectra including measured spectra and recommended spectra are compared. The reliability and accuracy of the presented turbulence simulation method are validated through comparisons between simulated and target spectra (measured and recommended spectra). The obtained turbulence si-mulations can not only serve further analysis of the buffeting behavior of the Sutong Bridge, but references for structural anti-wind design in adjacent regions.

THREE-DIMENSIONAL TURBULENCE NUMERICAL SIMULATION OF A STEPPED SPILLWAY OVERFLOW

In this paper, the k ε turbulence model is used to simulate the three dimensional turbulence flow over the stepped spillway at the Yubeishan reservoir. In order to solve the curved free water surface and to handle the complex boundary conditions, the fractional Volume Of Fluid (VOF) model that is applicable to the solution of the stratified two phase flow is introduced along with k ε turbulence model and the unstructured grid is used for the discretization of the irregular simulation domain. By these methods, the turbulence flow field of the stepped spillway is simulated successfully. The location of the free surface along the spillway, the magnitude and distribution of the velocity, the pressure on the step surface, the turbulence kinetic energy and turbulence dissipation rate are obtained by simulation. The changes and distributions of these characteristics along the width of the spillway are also obtained. The energy dissipation ratio of the stepped spillway is calculated according to the upstream and downstream water depth and velocities

Selection of the Relevant Turbulence Model in a CFD Simulation of a Flow Disturbed by Hydraulic Elbow--Comparative Analysis of the Simulation with Measurements Results Obtained by the Ultrasonic Flowmeter

The article is an attempt to compile the results of CFD liquid flow simulation through pipeline section containing hydraulic elbow with the results of ultrasonic flow measurements. To carry out the measurements behind the flow disturbing element(hydraulic elbow), an ultrasonic flowmeter with applied head set in accordance with the Z-type system was used. For comparative purposes, a flow simulation for 3 different turbulence models(k-epsilon, SST and SSG) was performed. It was found that with a proper ultrasonic flowmeter heads configurations, it is possible to measure the flow rate disturbed by the hydraulic elbow at any distance from the source of the disturbance. It has to use appropriate correction factor that can be determined by knowing the flow velocity profile equation. Based on comparison of CFD simulation results with experimental data, the accuracy/purposefulness of using individual turbulence models in the case of discussed hydraulic installation was evaluated.

THREE-DIMENSIONAL TURBULENCE NUMERICAL SIMULATION OF A STEPPED SPILLWAY OVERFLOW

In this paper, the k-ε two-equation turbulence model was used to simulatethe three-dimensional turbulent flow of the stepped spillway at the Yubeishan reservoir. In order tosolve the curved free water surface and to handle the complex boundary conditions, the fractionalVolume Of Fluid (VOF) model that is applicable to the solution of the stratified two-phase flow wasintorduced to the k-ε turbulence model and the unstructured grid was used for the discretization ofthe irregular simulation domain. By these methods, the turbulent flow field of the stepped spillwaywas simulated successfully. The location of the free surface along the spillway, the magnitude anddistribution of the velocity, the pressure distribution on the step surface, the turbulence kineticenergy and turbulence dissipation rate were obtained by simulation. The changes and distributions ofthese characteristics along the width of the spillway were also obtained. The energy dissipationratio of the stepped spillway was calculated according to the upstream and downstream water depthand velocities.

Experimental investigation on the wake interference among wind turbines sited in atmospheric boundary layer winds

We examined experimentally the effects of incoming surface wind on the turbine wake and the wake interference among upstream and downstream wind turbines sited in atmospheric boundary layer（ABL） winds. The experiment was conducted in a large-scale ABL wind tunnel with scaled wind turbine models mounted in different incoming surface winds simulating the ABL winds over typical offshore/onshore wind farms. Power outputs and dynamic loadings acting on the turbine models and the wake flow characteristics behind the turbine models were quantified. The results revealed that the incoming surface winds significantly affect the turbine wake characteristics and wake interference between the upstream and downstream turbines. The velocity deficits in the turbine wakes recover faster in the incoming surface winds with relatively high turbulence levels. Variations of the power outputs and dynamic wind loadings acting on the downstream turbines sited in the wakes of upstream turbines are correlated well with the turbine wakes characteristics. At the same downstream locations, the downstream turbines have higher power outputs and experience greater static and fatigue loadings in the inflow with relatively high turbulence level, suggesting a smaller effect of wake interference for the turbines sited in onshore wind farms.

A Lagrangian Particle Random Walk Model for Simulating A Deep-Sea Hydrothermal Plume with both Buoyant and Non-Buoyant Features

This paper presents a computational model of simulating a deep-sea hydrothermal plume based on a Lagrangian particle random walk algorithm. This model achieves the efficient process to calculate a numerical plume developed in a fluid-advected environment with the characteristics such as significant filament intermittency and significant plume meander due to flow variation with both time and location. Especially, this model addresses both non-buoyant and buoyant features of a deep-sea hydrothermal plume in three dimensions, which significantly challenge a strategy for tracing the deep-sea hydrothermal plume and localizing its source. This paper also systematically discusses stochastic initial and boundary conditions that are critical to generate a proper numerical plume. The developed model is a powerful tool to evaluate and optimize strategies for the tracking of a deep-sea hydrothermal plume via an autonomous underwater vehicle （AUV）.

Numerical study on evolution of subharmonic varicose low-speed streaks in turbulent channel flow

The evolution of two spanwise-aligned low-speed streaks in a wall turbulent flow, triggered by the instability of the subharmonic varicose （SV） mode, is studied by a direct numerical simulation （DNS） method in a small spatial-periodic channel. The results show that the SV low-speed streaks are self-sustained at the early stage, and then transform into subharmonic sinuous （SS） low-speed streaks. Initially, the streamwise vortex sheets are formed by shearing, and then evolve into zigzag vortex sheets due to the mutual induction. As the intensification of the SV low-speed streaks becomes prominent, the tilted streamwise vortex tubes and the V-like streamwise vortex tubes can be formed simultaneously by increasing ＋~. When the SV low-speed streaks break down, new zigzag streamwise vortices will be generated, thus giving birth to the next sustaining cycle of the SV low-speed streaks. When the second breakdown happens, new secondary V-like streamwise vortices instead of zigzag streamwise vortices will be generated. Because of the sweep motion of the fluid induced by the secondary V-like streamwise vortices, each decayed low-speed streak can be divided into two parts, and each part combines with the part of another streak, finally leading to the formation of SS low-speed streaks.

Modeling of drag reduction in turbulent channel flow with hydrophobic walls by FVM method and weakly-compressible flow equations

In this paper the effects of hydrophobic wall on skin-friction drag in the channel flow are investigated through large eddy simulation on the basis of weaklycompressible flow equations with the MacCormack’s scheme on collocated mesh in the FVM framework. The slip length model is adopted to describe the behavior of the slip velocities in the streamwise and spanwise directions at the interface between the hydrophobic wall and turbulent channel flow. Simulation results are presented by analyzing flow behaviors over hydrophobic wall with the Smagorinky subgrid-scale model and a dynamic model on computational meshes of different resolutions. Comparison and analysis are made on the distributions of timeaveraged velocity, velocity fluctuations, Reynolds stress as well as the skin-friction drag. Excellent agreement between the present study and previous results demonstrates the accuracy of the simple classical second-order scheme in representing turbulent vertox near hydrophobic wall. In addition, the relation of drag reduction efficiency versus time-averaged slip velocity is established. It is also foundthat the decrease of velocity gradient in the close wall region is responsible for the drag reduction. Considering its advantages of high calculation precision and efficiency, the present method has good prospect in its application to practical projects.

Numerical investigation on flow and heat transfer characteristics of corrugated tubes with non-uniform corrugation in turbulent flow

Based on finite volume method, the pressure drop and heat transfer characteristics of one smooth tube and ten different axisymmetric corrugated tubes, including two with uniform corrugation and eight with non-uniform corrugation, have been studied. A physical model of the corrugated tube was built, then the numerical simulation of the model was carried out and the numerical simulation results were compared with the empirical formula.The results show that: the friction factor decreases with the increase of Reynolds number ranging from 6000 to 57000, the value of which in the corrugated tubes with non-uniform corrugation(tube 03–10) are smaller than those with uniform corrugation(tube 01–02). The geometry parameters of tube(01) have advantages on the heat transfer enhancement in low Reynolds number flow region(from 6000 to 13000) and tube(07–08)have advantages on the heat transfer enhancement in high Reynolds number flow region(from 13000 to 57000). The vortex, existed in each area between two adjacent corrugations called second flow region, is the root of the enhancement on heat transfer in the corrugated tubes. The effectiveness factor decreases with the increasing of Reynolds number and the performances of the corrugated tubes with pitch of 12.5 mm have advantages than these of 10 mm under the same corrugation geometric parameter.

Constrained large-eddy simulation and detached eddy simulation of flow past a commercial aircraft at 14 degrees angle of attack

With the development of computational power and numerical algorithms,computational fluid dynamics(CFD) has become an important strategy for the design of aircraft,which significantly reduces the reliance on wind-tunnel and flight tests.In this paper,we conducted a numerical investigation on the flow past a full commercial aircraft at Mach number 0.2 and 14 degrees angle of attack by means of Reynolds-averaged Navier-Stokes(RANS),detached-eddy simulation(DES) and our newly developed constrained large-eddy simulation(CLES).The objective of this paper is to study the capability of these models in simulating turbulent flows.To our knowledge,this is the first large-eddy simulation method for full commercial aircraft simulation.The results show that the CLES can predict the mean statistical quantities well,qualitatively consistent with traditional methods,and can capture more small-scale structures near the surface of the aircraft with massive separations.Our study demonstrates that CLES is a promising alternative for simulating real engineering turbulent flows.

LARGE-EDDY SIMULATION OF TURBULENT FLOW CONSIDERING INFLOW WAKES IN A FRANCIS TURBINE BLADE PASSAGE

Turbulent flow in a 3-D blade passage of a Francis hydro turbine was simulated with the Large Eddy Simulation （LES） to investigate the spatial and temporal distributions of the turbulence when strongly distorted wakes in the inflow sweep over the passage, In a suitable consideration of the energy exchanging mechanism between the large and small scales in the complicated passage with a strong 3-D curvature, one-coefficient dynamic Sub-Grid-Scale （SGS） stress model was used in this article. The simulations show that the strong wakes in the inflow lead to a flow separation at the leading zone of the passage, and to form a primary vortex in the span-wise direction. The primary span-wise vortex evolves and splits into smaller vortex pairs due to the constraint of no-slip wall condition, which triggers losing stability of the flow in the passage. The computed pressures on the pressure and suction sides agree with the measured data for a working test turbine model.

Large-eddy simulation: Past, present and the future

Large-eddy simulation（LES） was originally proposed for simulating atmospheric flows in the 1960 s and has become one of the most promising and successful methodology for simulating turbulent flows with the improvement of computing power. It is now feasible to simulate complex engineering flows using LES. However, apart from the computing power, significant challenges still remain for LES to reach a level of maturity that brings this approach to the mainstream of engineering and industrial computations. This paper will describe briefly LES formalism first, present a quick glance at its history, review its current state focusing mainly on its applications in transitional flows and gas turbine combustor flows, discuss some major modelling and numerical challenges/issues that we are facing now and in the near future, and finish with the concluding remarks.

Scale adaptive simulation of vortex structures past a square cylinder

The scale adaptive simulation（SAS） turbulence model is evaluated on a turbulent flow past a square cylinder using the open-source CFD package OpenF OAM 2.3.0. Two and three-dimensional simulations are performed to determine global quantities like drag and lift coefficients and Strouhal number in addition to mean and fluctuating velocity profiles in the recirculation and wake regions. SAS model is evaluated against the Shear Stress Transport k-ω（SST） model and also compared with previously reported results based on DES, LES and DNS turbulence approaches. Results show that global quantities along with mean velocity profiles are well-captured by 2-D SAS model. The 3-D SAS model also succeeded in providing comparable results with recently published DES study on Reynolds shear stress and velocity fluctuation components using about 12 times lower computational cost. It is shown that large values of the SAS model constant result in too dissipative behavior, so that proper calibration of the SAS model constant for different turbulent flows is vital.

CFD simulation of solid-liquid stirred tanks for low to dense solid loading systems

The hydrodynamics of suspension of solids in liquids are critical to the design and performance of stirred tanks as mixing systems. Modelling a multiphase stirred tank at a high solids concentration is complex owing to particle-particle and particle-wall interactions which are generally neglected at low concentra- tions. Most models do not consider such interactions and deviate significantly from experimental data. Furthermore, drag force, turbulence and turbulent dispersion play a crucial role and need to be precisely known in predicting local hydrodynamics. Therefore, critical factors such as the modelling approach, drag, dispersion, coefficient of restitution and turbulence are examined and discussed exhaustively in this paper. The Euler-Euler approach with kinetic theory of granular flow, Syamlal-O＇Brien drag model and Reynolds stress turbulence model provide realistic predictions for such systems. The contribution of the turbulent dispersion force in improving the prediction is marginal but cannot be neglected at low solids volume fractions. Inferences drawn from the study and the finalised models will be instrumen- tal in accurately simulating the solids suspension in stirred tanks for a wide range of conditions. These models can be used in simulations to obtain precise results needed for an in-depth understanding of hydrodynamics in stirred tanks.

Numerical study on three-dimensional CJ detonation waves interacting with isotropic turbulence

The three-dimensional structures of a cellular detonation wave interacting with different turbulent flows were investigated using a one-step irreversible Arrhenius kinetics model. High-resolution bandwidth-optimized WENO scheme of spatial discretization and total variation diminishing temporal integration are used to solve the three dimensional chemically reactive Navier-Stokes equations. The turbulent vertical and entropic forcing effects on the three dimensional detonation wave structures and dynam- ics are analyzed, as well as the detonation effects on tur- bulent vortex structures. It has been found that the turbulence field imposed has created small scale wrinkles embedded in the detonation front, apart from the large scale features of detonation without turbulence. The deto- nation propagating velocity over the leading shock front varies from 0.8 to 1.6 times of CJ velocity and its proba- bility density function （pdf） skews towards sub-CJ velocity and peaks at about 0.9. The recorded detonation velocity always preferentially decays with time, with very rapid accelerations through triple point interactions. Its pdf also skews to sub-CJ velocity, while its overall shape agrees well with W3. The reaction zone is greatly influenced by the vortex, much more irregular and elongated for the turbulent cases. Distributed burning pockets are more likely to be found there. The turbulent kinetic energy is amplified across the detonation, and periodically oscillates downstream the detonation. The off-diagonal components of Reynolds stress also show a rapid rise across the deto- nation and present to be non-zero downstream of detona- tion. Vortex structures are compound results of the convected vortex and the generated vortex by the collision of triple points. The convection term and baroclinic gen- eration term in the transport equation of enstrophy are compared in detail.