Vortex dynamics of turbulence–coherent structure interaction

We study the interaction between a coherent structure (CS) and imposed external turbulence by employing direct numerical simulations (DNS) designed for unbounded flows with compact vorticity distribution. Flow evolution comprises (i) the reorganization of turbulence into finer-scale spiral filaments, (ii) the growth of wave-like perturbations within the vortex core, and (iii) the eventual arrest of production, leading to the decay of ambient turbulence. The filaments, preferentially aligned in the azimuthal direction, undergo two types of interactions: parallel filaments pair to form higher-circulation “threads”, and anti-parallel threads form dipoles that self-advect radially outwards. The consequent radial transport of angular momentum manifests as an overshoot of the mean circulation profile—a theoretically known consequence of faster-than-viscous vortex decay. It is found that while the resulting centrifugal instability can enhance turbulence production, vortex decay is arrested by the dampening of the instability due to the “turbulent mixing” caused by instability-generated threads. Ensemble-averaged turbulence statistics show strong fluctuations within the core; these are triggered by the external turbulence, and grow even as the turbulence decays. This surprising growth on a normal-mode-stable vortex results from algebraic amplification through “linear transient growth”. Transient growth is examined by initializing DNS with the “optimal” modes obtained from linear analysis. The simulations show that the growth of transient modes reproduces the prominent dynamics of CS-turbulence interaction: formation of thread-dipoles, growth of core fluctuations, and appearance of bending waves on the column’s core. At the larger Reynolds numbers prevailing in practical flows, transient growth may enable accelerated vortex decay through vortex column breakdown.     

Drag coefficients of spherical liquid droplets Part 2: Turbulent gaseous fields

The drag of non-evaporating, spherical, liquid droplets was measured in turbulent flow fields at parametric ranges relevant to spray combustion, characterized by the droplet Reynolds number, and the intensity and spatial scales of turbulence. The experimental apparatus comprised a wind-tunnel and a piezo-electric droplet generator. The procedure was to inject water droplets of uniform size co-currently and continuously with vertical turbulent air flows while droplet velocity was measured at different elevations using laser-Doppler velocimetry. Turbulence was characterized using hot-wire anemometry prior to droplet injection. Drag coefficients were calculated using these main measurements and the law of conservation of mechanical energy. Reynolds numbers were investigated in the range 10–100, in terms of the equivalent spherical diameter of a droplet, and the mean relative speed between the ambient gaseous field and the droplets. Weber numbers were much less than unity so droplets were effectively spherical. Relative intensities of turbulence were investigated in the range 20–65 percent, in terms of the mean relative speed. Spatial scales of turbulence were large in comparison to the droplets; the ratio between the spatial integral scale and the droplet diameter was in the range 11–38, and the Kolmogorov scale was comparable in size or smaller than the droplet diameter. Experimental data showed that the drag in turbulent fields under these conditions is not significantly different than that of solid spheres in a quiescent field at the same Reynolds number.The financial support of the Natural Sciences and Engineering Research Council of Canada and the Manufacturing Research Corporation of Ontario is gratefully acknowledged.     

Vortices for computing: the engines of turbulence simulation

Vortices have been described as the “sinews of turbulence”. They are also, increasingly, the computational engines driving numerical simulations of turbulence. In this paper, I review some recent advances in vortex-based numerical methods for simulating high Reynolds number turbulent flows. I focus on coherent vortex simulation, where nonlinear wavelet filtering is used to identify and track the few high energy multiscale vortices that dominate the flow dynamics. This filtering drastically reduces the computational complexity for high Reynolds number simulations, e.g. by a factor of 1000 for fluid–structure interaction calculations (Kevlahan and Vasilyevvon in SIAM J Sci Comput 26(6):1894–1915, 2005). It also has the advantage of decomposing the flow into two physically important components: coherent vortices and background noise. In addition to its computational efficiency, this decomposition provides a way of directly estimating how space and space–time intermittency scales with Reynolds number, Re ^α . Comparing α to its non-intermittent values gives a realistic Reynolds number upper bound for adaptive direct numerical simulation of turbulent flows. This direct measure of intermittency also guides the development of new mathematical theories for the structure of high Reynolds number turbulence.     

A method to estimate turbulence intensity and transverse Taylor microscale in turbulent flows from spatially averaged hot-wire data

A new approach to evaluate turbulence intensity and transverse Taylor microscale in turbulent flows is presented. The method is based on a correction scheme that compensates for probe resolution effects and is applied by combining the response of two single hot-wire sensors with different wire lengths. Even though the technique, when compared to other correction schemes, requires two independent measurements, it provides, for the same data, an estimate of the spanwise Taylor microscale. The method is here applied to streamwise turbulence intensity distributions of turbulent boundary layer flows but it is applicable generally in any turbulent flow. The technique has been firstly validated against spatially averaged DNS data of a zero pressure-gradient turbulent boundary layer showing a good capacity to reconstruct the actual profiles and to predict a qualitatively correct and quantitatively agreeing transverse Taylor microscale over the entire height of the boundary layer. Finally, the proposed method has been applied to available higher Reynolds number data from recent boundary layer experiments where an estimation of the turbulence intensity and of the Taylor microscale has been performed.     

A volume-agglomeration multirate time advancing for high Reynolds number flow simulation

A frequent configuration in computational fluid mechanics combines an explicit time advancing scheme for accuracy purposes and a computational grid with a very small portion of much smaller elements than in the remaining mesh. Two examples of such situations are the travel of a discontinuity followed by a moving mesh, and the large eddy simulation of high Reynolds number flows around bluff bodies where together very thin boundary layers and vortices of much more important size need to be captured. For such configurations, multistage explicit time advancing schemes with global time stepping are very accurate but very CPU consuming. In order to reduce this problem, the multirate (MR) time stepping approach represents an interesting improvement. The objective of such schemes, which allow to use different time steps in the computational domain, is to avoid penalizing the computational cost of the time advancement of unsteady solutions that would become large due to the use of small global time steps imposed by the smallest elements such as those constituting the boundary layers. In the present work, a new MR scheme based on control volume agglomeration is proposed for the solution of the compressible Navier-Stokes equations equipped with turbulence models. The method relies on a prediction step where large time steps are performed with an evaluation of the fluxes on macrocells for the smaller elements for stability purpose and a correction step in which small time steps are employed. The accuracy and efficiency of the proposed method are evaluated on several benchmarks flows: the problem of a moving contact discontinuity (inviscid flow), the computation with a hybrid turbulence model of flows around bluff bodies like a flow around a space probe model at Reynolds number 10⁶, a circular cylinder at Reynolds number 8.4 × 10⁶, and two tandem cylinders at Reynolds number 1.66 × 10⁵ and 1.4 × 10⁵.     

Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGS model. The resulting so-called adaptive local deconvolution method (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper, ALDM is evaluated for the separated flow through a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2,808 and Re = 10,595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered physically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.      

蜿蜒边界下平面流的线性流动稳定性

为便于数值分析,蜿蜒河流水动力和演变模型中一般隐性假设二次时均流-二次涡的关系与明渠流时均流-明渠湍流的关系相同,但由于高雷诺数下的DNS算力限制和实验尺度限制,这种隐含假设是否成立目前尚无相关湍流研究来支撑.文章试图通过分析明渠湍流和二次湍流发展初期的研究,侧面揭示其湍流结构的异同.通过对曲线正交坐标系下的平面二维NS方程使用双参数摄动的方法,建立了一种求解蜿蜒边界弱非线性层流的摄动解法,并推导得出一个适用于蜿蜒边界的EOS方程以及其特征值问题的解法.蜿蜒边界下弱非线性层流解为一系列蜿蜒谐波分量的叠加,其中线性部分使得两壁产生流速差,非线性部分随着雷诺数增大呈指数增长.水流的扰动增长率特征谱的第一模态与直道流相似,由3条曲线、4个波段合成,但其长波段和短波段的扰动流场与直道流不同,所有短波段的扰动流速近似于KH涡.蜿蜒边界对内部水流扰动有一定的选择性.偏角幅值越大扰动增长越快;蜿蜒波数的影响则为先增后减,有一个使扰动增长最快的蜿蜒波数.扰动流场由一个典型的TS波和一对波包形式的二次涡叠加而成,波包只有纵向流速分量,包络线由蜿蜒波数控制,波包内是与直道扰动波参数相同的TS波.     

A low Reynolds number variant of partially-averaged Navier-Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier-Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k-ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results - at a reduced CPU time - as compared to the Dynamic Smagorinsky model.     

Direct numerical simulation of a particle-laden low Reynolds number turbulent round jet

Direct numerical simulation method is used for the investigating of particle-laden turbulent flows in a spatially evolution of low Reynolds number axisymmetric jet, and the Eulerian–Lagrangian point-particle approach is employed in the simulation. The simulation uses an explicit coupling scheme between particles and the fluid, which considers two-way coupling between the particle and the fluid. The DNS results are compared well with experimental data with equal Reynolds number (R_e = 1700). Our objects are: (i) to investigate the correlation between the particle number density and the fluctuating of fluid streamwise velocity; (ii) to examine whether the three-dimensional vortex structures in the particle-laden jet are the same as that in the free-air jet and how the particles modulate the thee-dimensional vortex structures and turbulence properties with different Stokes number particles; (iii) to discover the particle circumferential dispersion with different Stokes number particles. Our findings: (i) all the particles, regardless of their particle size, tend to preferentially accumulate in the region with large-than-mean fluid streamwise velocity; (ii) the small Stokes number particles take an important part in the modulation of three-dimensional vortex structures, but for the intermediate and larger sized particles, this modulation effect seems not so apparent; (iii) the particle circumferential dispersion is more effective for the smaller and intermediate sized particles, especially for the intermediate sized particles.     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

A two‐scale low‐Reynolds number turbulence model

In this study, a two‐scale low‐Reynolds number turbulence model is proposed. The Kolmogorov turbulence time scale, based on fluid kinematic viscosity and the dissipation rate of turbulent kinetic energy (ν, ε), is adopted to address the viscous effects and the rapid increasing of dissipation rate in the near‐wall region. As a wall is approached, the turbulence time scale transits smoothly from a turbulent kinetic energy based (k, ε) scale to a (ν, ε) scale. The damping functions of the low‐Reynolds number models can thus be simplified and the near‐wall turbulence characteristics, such as the ε distribution, are correctly reproduced. The proposed two‐scale low‐Reynolds number turbulence model is first examined in detail by predicting a two‐dimensional channel flow, and then it is applied to predict a backward‐facing step flow. Numerical results are compared with the direct numerical simulation (DNS) budgets, experimental data and the model results of Chien, and Lam and Bremhorst respectively. It is proved that the proposed two‐scale model indeed improves the predictions of the turbulent flows considered. Copyright © 2000 John Wiley & Sons, Ltd.     

Measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging

We present the first measurements of relative velocity statistics of inertial particles in a homogeneous isotropic turbulent flow with three-dimensional holographic particle image velocimetry (holographic PIV). From the measurements we are able to obtain the radial relative velocity probability density function (PDF) conditioned on the interparticle separation distance, for distances on the order of the Kolmogorov length scale. Together with measurements of the three-dimensional radial distribution function (RDF) in our turbulence chamber, these statistics, in principle, can be used to determine interparticle collision rates via the formula derived by Sundaram and Collins (1997). In addition, we show temporal development of the RDF, which reveals the existence of an extended quasi-steady-state regime in our facility. Over this regime the measured two-particle statistics are compared to direct numerical simulations (DNS) with encouraging qualitative agreement. Statistics at the same Reynolds number but different Stokes numbers demonstrate the ability of the experiment to correctly capture the trends associated with particles of different inertia. Our results further indicate that even at moderate Stokes numbers turbulence may enhance collision rates significantly. Such experimental investigations may prove valuable in validating, guiding and refining numerical models of particle dynamics in turbulent flows.     

Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall

Periodic wall oscillations in the spanwise or circumferential direction can greatly reduce the friction drag in turbulent channel and pipe flows. In a concentric annulus, the constant rotation of the inner cylinder can intensify turbulence fluctuations and enhance skin friction due to centrifugal instabilities. In the present study, the effects of the periodic oscillation of the inner wall on turbulent flows through concentric annulus are investigated by the direct numerical simulation (DNS). The radius ratio of the inner to the outer cylinders is 0.1, and the Reynolds number is 2 225 based on the bulk mean velocity U_m and the half annulus gap H. The influence of oscillation period is considered. It is found that for short-period oscillations, the Stokes layer formed by the circumferential wall movement can effectively inhibit the near-wall coherent motions and lead to skin friction reduction, while for long-period oscillations, the centrifugal instability has enough time to develop and generate new vortices, resulting in the enhancement of turbulence intensity and skin friction.     

无壁面参数低雷诺数非线性涡黏性模式研究

建立了一个低雷诺数的非线性涡黏性湍流模式,该模式的一个显著特性是它不包含壁面参数（如y^ ,n等）,因而特别适用于复杂几何流场的计算,本模式在几种包括回流、分离、激波等典型流动中进行了验证,结果令人满意。     

Hydrodynamic and thermal fields analysis in gas-solid two-phase flow

The present work aims to investigate numerically the flowfield and heat transfer process in gas-solid suspension in a vertical pneumatic conveying pipe. The Eulerian-Lagrangian model is used to simulate the flow of the two-phases. The gas phase is simulated based on Reynolds Average Navier-Stokes equations (RANS) with low Reynolds number k-ε model, while particle tracking procedure is used for the solid phase. An anisotropic model is used to calculate the Reynolds stresses and the turbulent Prandtl number is calculated as a function of the turbulent viscosity. The model takes into account the lift and drag forces and the effect of particle rotation as well as the particles dispersion by turbulence effect. The effects of inter-particles collisions and turbulence modulation by the solid particles, i.e. four-way coupling, are also included in the model. Comparisons between different models for turbulence modulation with experimental data are carried out to select the best model. The model is validated against published experimental data for velocities of the two phases, turbulence intensity, solids concentration, pressure drop, heat transfer rates and Nusselt number distribution. The comparisons indicate that the present model is able to predict the complex interaction between the two phases in non-isothermal gas-solid flow in the tested range. The results indicate that the particle-particle collision, turbulence dispersion and lift force play a key role in the concentration distribution. In addition, the heat transfer rate increases as the mass loading ratio increases and Nusselt number increases as the pipe diameter increases.     

The 3D Transition to Turbulence in Wake Flows by Means of Direct Numerical Simulation

The three-dimensional transition to turbulence in flows around bodies of non-rectangular configuration has been analysed physically by performing direct numerical simulation to solve the system of Navier-Stokes equations. The successive stages of 3D transition, beyond the first bifurcation, have been detected first in the incompressible regime, for a circular cylinder configuration. The generation of streamwise vorticity, organised according to spanwise periodic cells has been associated with the development of large-scale coherent spanwise undulations of the originally rectilinear (nominally 2D) alternating vortex rows. The wavelengths of these undulations have been determined as a function of Reynolds number. As this parameter increases, a further inherent change of the flow transition is obtained and analysed, the natural vortex dislocations pattern. Beyond this change, the increase of Reynolds number yields an abrupt shortening of the spanwise wavelength and the flow undergoes another transition step, whose critical Reynolds number is evaluated by the present DNS approach in association with the Ginzburg-Landau model. Therefore, the linear and non-linear parts of the flow transition have been quantified by means of the amplitude evolution versus time obtained by the present DNS, in conjunction with the mentioned global oscillator model. This revised version was published online in July 2006 with corrections to the Cover Date.     

Direct numerical simulation of fluid flow in a 5x5 square rod bundle

Characterization of parallel flow through rod bundles is of key importance in assessing the performance and safety of several engineering systems, including a majority of nuclear reactor concepts. Inhomogeneities in the bundle cross-section can present complex flow phenomena, including varying local conditions of turbulence. With the ever-increasing capabilities of high-performance computing, Direct Numerical Simulation (DNS) of turbulent flows is becoming more feasible. Through resolving all scales of turbulence, DNS can serve as a “numerical experiment,” and can provide substantial insight into flow physics, but at considerable computational cost. Thus to date, the DNS in open literature for rod bundle flows is relatively scarce, and largely limited to unit-cell domains. Since wall effects are important in rod bundle flows, a multiple-pin DNS study can expand understanding of rod bundle flows while providing valuable reference data for evaluating reduced-resolution techniques. In this work, DNS of a 5x5 square bare rod bundle representative of typical light water reactor fuel dimensions was performed using the spectral element code Nek5000. Turbulent microscales based on an advanced Reynolds-Averaged Navier–Stokes model were used to establish the required DNS resolution. Velocity and Reynolds stress fields are analyzed in detail, and invariant analysis is used for further investigation into flow physics. The results show stark changes in the structure of turbulence in the edge gaps, suggesting the presence of gap vortices in these regions. In addition, turbulent kinetic energy budgets are presented to more fully illustrate the various turbulent processes. These data can prove useful for rigorous evaluation of lower-fidelity turbulence modeling approaches.     

Comparisons and applications of numerical simulation methods for predicting aerodynamic heating around complex configurations

Numerical simulation methods of aerodynamic heating were compared by considering the inuence of numerical schemes and turbulence models,and attempting to investigate the applicability of numerical simulation methods on predicting heat flux in engineering applications. For some typical cases provided with detailed experimental data,four spatial schemes and four turbulence models were adopted to calculate surface heat flux. By analyzing and comparing,some inuencing regularities of numerical schemes and turbulence models on calculating heat flux had been acquired. It is clear that AUSM+-up scheme with rapid compressibilitymodified high Reynolds number k-ω model should be appropriate for calculating heat flux. The numerical methods selected as preference above were applied to calculate the heat flux of a 3-D complex geometry in high speed turbulent flows. The results indicated that numerical simulation can capture the complex flow phenomena and reveal the mechanism of aerodynamic heating. Especially,the numerical result of the heat flux at the stagnation point of the wedge was well in agreement with the prediction of Kemp-Riddel formula,and the surface heat flux distribution was consistent with experiment results,which implied that numerical simulation can be introduced to predict heat flux in engineering applications.     

Resolution-optimised nonlinear scheme for secondary derivatives

A 5-point-stencil optimised nonlinear scheme with spectral-like resolution within the whole wave number range for secondary derivatives is devised. The proposed scheme can compensate for the dissipation deficiency of traditional linear schemes and suppress the spurious energy accumulation that occurs at high wave numbers, both of which are frequently encountered in large eddy simulation. The new scheme is composed of a linear fourth-order central scheme term and an artificial viscosity term. These two terms are connected by a nonlinear weight. The proposed nonlinear weight is designed based on Fourier analysis, rather than Taylor analysis, to guarantee a spectral-like resolution. Moreover, the accuracy is not affected by the optimisation, and the new scheme reaches fourth-order accuracy. The new scheme is tested numerically using the one-dimensional diffusion problem, one-dimensional steady viscous Burger’s shock, two-dimensional vortex decaying, three-dimensional isotropic decaying turbulence and fully developed turbulent channel flow. All the tests confirm that the new scheme has spectral-like resolution and can improve the accuracy of the energy spectrum, dissipation rate and high-order statistics of turbulent flows.     

Evaluation of linear and nonlinear convection schemes on multidimensional non‐orthogonal grids with applications to KVLCC2 tanker

Almost all evaluations of convection schemes reported in the literature are conducted using simple problems on uniform orthogonal grids; thus, having limited contribution when solving industrial computational fluid dynamics (CFD), where the grids are usually non‐orthogonal with distortions. Herein, several convection schemes are assessed in uniform and distorted non‐orthogonal grids with emphasis on industrial applications. Linear and nonlinear (TVD) convection schemes are assessed on analytical benchmarks in both uniform and distorted grids. To evaluate the performance of the schemes, four error metrics are used: dissipation, phase and L₁ errors, and the schemes' effective order of accuracy. Qualitative and quantitative deterioration of these error metrics as a function of the grid distortion metrics are investigated, and rigorous verifications are performed. Recommendations for effective use of the convection schemes based on the range of grid aspect ratio (AR), expansion ratio (ER) and skewness (Q) are included. A ship hydrodynamics case is studied, involving a Reynolds averaged Navier–Stokes simulation of a bare‐hull KVLCC2 tanker using linear and nonlinear convection schemes coupled with isotropic and anisotropic Reynolds‐stress (ARS) turbulence models using CFDShip‐Iowa v4. Predictions of local velocities and turbulent quantities from the midships to the nominal wake plane are compared with experimental fluid dynamics (EFD), and rigorous verification and validation analyses for integral forces and moments are performed for 0° and 12° drift angles. Best predictions are observed when coupling a second‐order TVD scheme with the anisotropic turbulence model. Further improvements are observed in terms of prediction of the vortical structures for 30° drift when using TVD2S‐ARS coupled with DES. Copyright © 2009 John Wiley & Sons, Ltd.