Vortex structure of turbulence over permeable walls

In order to understand the effect of the wall permeability on the turbulent vortex structure near porous walls, based on PIV experimental data, a probability density analysis of fluctuating velocities, statistical quadrant and quadrant-hole analyses of the Reynolds shear stress are performed. The investigated flow fields are turbulent channel flows whose bottom walls are made of porous media. The porous media used are three kinds of foamed ceramics which have almost the same porosity (∼0.8) but different permeability. From the discussions on those analyses, a conceptual scenario of the development of the vortex structure near a permeable wall is proposed for a moderate permeability Reynolds number case. It explains the reason why the near-wall long streaky structure tends to vanish near a porous wall with increasing wall permeability.     

Experimental investigation on turbulence modification in a horizontal channel flow at relatively low mass loading

Particle-laden flows in a horizontal channel were investigated by means of a two-phase particle image velocimetry (PIV) technique. Experiments were performed at a Reynolds number of 6 826 and the flow is seeded with polythene beads of two sizes, 60 μm and 110 μm. One was slightly smaller than and the other was larger than the Kolmogorov length scale. The particle loadings were relatively low, with mass loading ratio ranging from 5×10⁻⁴ to 4×10⁻² and volume fractions from 6×10⁻⁷ to 4.8×10⁻⁵, respectively. The results show that the presence of particles can dramatically modify the turbulence even under the lowest mass loading ratio of 5×10⁻⁴. The mean flow is attenuated and decreased with increasing particle size and mass loading. The turbulence intensities are enhanced in all the cases concerned. With the increase of the mass loading, the intensities vary in a complicated manner in the case of small particles, indicating complicated particle-turbulence interactions; whereas they increase monotonously in the case of large particles. The particle velocities and concentrations are also given. The particles lag behind the fluid in the center region but lead in the wall region, and this trend is more prominent for the large particles. The streamwise particle fluctuations are larger than the gas fluctuations for both sizes of particles, however their varying trend with the mass loadings is not so clear. The wall-normal fluctuations increase with increasing mass loadings. They are smaller in the 60 μm particle case but larger in the 110 μm particle case than those of the gas phase. It seems that the small particles follow the fluid motion to certain extent while the larger particles are more likely dominated by their own inertia. Finally, remarkable non-uniform distributions of particle concentration are observed, especially for the large particles. The inertia of particles is proved to be very important for the turbulence modification and particles behaviors and thus should be considered in horizontal channels. The project supported by the National Natural Science Foundation of China (50276021), and Program for New Century Excellent Talents in University, Ministry of Education (NCET-04-0708) The English text was polished by Yunming Chen.     

2D numerical flow modeling in a macro‐rough channel

A 2D numerical flow model, developed at the Research unit of Hydrology, Applied Hydrodynamics and Hydraulic Constructions at ULg, has been applied to flows in a macro‐rough channel. The model solves the shallow water equations (SWE) with a two length scale, depth‐integrated k‐type approach for turbulence modeling. Data for the comparison have been provided by experiments conducted at the Laboratory of Hydraulic Constructions at EPFL. In the experiments with different non‐prismatic channel configurations, namely large‐scale cavities at the side walls, three different 2D flow characteristics could be observed in cavities. With the used numerical model features, especially regarding turbulence and friction modeling, a single set of bottom and side wall roughness could be found for a large range of discharges investigated in a prismatic channel. For the macro rough configurations, the numerical model gives an excellent agreement between experimental and numerical results regarding backwater curves and flow patterns if the side wall cavities have low aspect ratios. For configurations with high aspect ratios, the head loss generated by the preservation of important recirculation gyres in the cavities is slightly underestimated. The results of the computations reveal clearly that the separation of turbulence sources in the mathematical model is of great importance. Indeed, the turbulence related to 2D transverse shear effects and the 3D turbulence, generated by bed friction, can have very different amplitude. When separating these two effects in the numerical models, most of the flow features observed experimentally can be reproduced accurately. Copyright © 2009 John Wiley & Sons, Ltd.     

A semi-implicit lagrangian scheme for 3D shallow water flow with a two-layer turbulence model

A semi-implicit Lagrangian finite difference scheme for 3D shallow water flow has been developed to include an eddy viscosity model for turbulent mixing in the vertical direction. The α-co-ordinate system for the vertical direction has been introduced to give accurate definition of bed and surface boundary conditions. The simple two-layer mixing length model for rough surfaces is used with the standard assumption that the shear stress across the wall region at a given horizontal location is constant. The bed condition is thus defined only by its roughness height (avoiding the need for a friction formula relating to depth-averaged flow, e.g. Chezy, used previously). The method is shown to be efficient and stable with an explicit Lagrangian formulation for convective terms and terms for surface elevation and vertical mixing handled implicitly. The method is applied to current flow around a circular island with gently sloping sides which produce periodic recirculation zones (vortex shedding). Comparisons are made with experimental measurements of velocity using laser Doppler anemometry (time histories at specific points) and surface particle-tracking velocimetry.     

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.     

Examination of wall damping for the k-ε turbulence model using direct simulations of turbulent channel flow

Handler, Hendricks and Leighton have recently reported results for the direct numerical simulation (DNS) of a turbulent channel flow at moderate Reynolds number. These data are used to evaluate the terms in the exact and modelled transport equations for the turbulence kinetic energy k and the isotropic dissipation function ε. Both modelled transport equations show significant imbalances in the high-shear region near the channel walls. The model for the eddy viscosity is found to yield distributions for the production terms which do not agree well with the distributions calculated from the DNS data. The source of the imbalance is attributed to the wall-damping function required in eddy viscosity models for turbulent flows near walls. Several models for the damping function are examined, and it is found that the models do not vary across the channel as does the damping when evaluated from the DNS data. The Lam-Bremhorst model and the standard van Driest model are found to give reasonable agreement with the DNS data. Modification of the van Driest model to include an effective origin yields very good agreement between the modelled production and the production calculated from the DNS data, and the imbalance in the modelled transport equations is significantly reduced.     

A hybrid k-ε turbulence model of recirculating flow

This investigation deals with the modification of streamline curvature effects in the k-ε turbulence model for the case of recirculating flows. Based upon an idea that the modification of curvature effects in C₂ should not be made in regions where the streamline curvature is small, a hybrid k-ε model extended from the modification originally proposed by Srinivasan and Mongia is developed. A satisfactory agreement of model predictions with experimental data reveals that the hybrid k-ε model can perform better simulation of recirculating turbulent flows.     

Interfacial instability in turbulent flow over a liquid film in a channel

We revisit the stability of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. Although this problem has received considerable attention previously, a model that requires no fitting parameters and that uses a base-state profile that has been validated against experiments is, as yet, unavailable. Furthermore, the significance of wave-induced perturbations in turbulent stresses remains unclear. To address these outstanding issues, we investigate this problem and introduce a turbulent base-state velocity that requires specification of a flow rate or a pressure drop only; no adjustable parameters are necessary. This base state is validated extensively against available experimental data as well as the results of direct numerical simulations. In addition, the effect of perturbations in the turbulent stress distributions is investigated, and demonstrated to be small for cases wherein the liquid layer is thin. The detailed modelling of the liquid layer also elicits two unstable modes, ‘interfacial’ and ‘internal’, with the former being the more dominant of the two. We show that it is possible for interfacial roughness to reduce the growth rate of the interfacial mode in relation to that of the internal one, promoting the latter, to the status of most dangerous mode. Additionally, we introduce an approximate measure to distinguish between ‘slow’ and ‘fast’ waves, the latter being the case for ‘critical-layer’-induced instabilities; we demonstrate that for the parameter ranges studied, the large majority of the waves are ‘slow’. Finally, comparisons of our linear stability predictions are made with experimental data in terms of critical parameters for onset of wave-formation, wave speeds and wavelengths; these yield agreement within the bounds of experimental error.     

Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls

Interest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo-spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant-property, turbulent fluid in a two-dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions. Calculations were made for a Prandtl number of 0·72 and Reynolds number based on friction velocity and channel half-height of 180 or 2800 based on channel half-height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two-point velocity correlations are given. Deficiencies are that the calculation requires many hours on a fast computer with a large high-speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.     

Near-wall measurements of turbulence statistics in a fully developed channel flow with a novel laser Doppler velocity profile sensor

This paper reports on the measurements of the near-wall turbulence statistics in a fully developed channel flow. The flow measurements were carried out with a novel laser Doppler velocity profile sensor with a high spatial resolution. The sensor provides both the information of velocity and position of individual tracer particles inside the measurement volume. Hence, it yields the velocity profile inside the measurement volume, in principle, without the sensor being mechanically traversed. Two sensor systems were realized with different techniques. Typically the sensor has a relative accuracy of velocity measurement of 10⁻³ and the spatial resolution of a few micrometers inside the measurement volume of about 500 μm long. The streamwise velocity was measured with two independent sensor systems at three different Reynolds number conditions. The resulting turbulence statistics show a good agreement with available data of direct numerical simulations up to fourth order moment. This demonstrates the velocity profile sensor to be one of the promising techniques for turbulent flow research with the advantage of a spatial resolution more than one magnitude higher than a conventional laser Doppler technique.     

Numerical study of an oscillatory turbulent flow over a flat plate

Oscillatory turbulent flow over a flat plate is studied using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model is employed in LES and Saffman's turbulence model is used in RANS. The flow behaviors are discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime are also investigated for different Reynolds numbers. The project supported by the Youngster Funding of Academia Sinica and by the National Natural Science Foundation of China     

Dynamical eigenfunction decomposition of turbulent channel flow

The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loéve(K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re,= 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90% of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, posses viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher-order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.     

Numerical solution of 2D and 3D turbulent internal flow problems

The paper describes a method for solving numerically two-dimensional or axisymmetric, and three-dimensional turbulent internal flow problems. The method is based on an implicit upwinding relaxation scheme with an arbitrarily shaped conservative control volume. The compressible Reynolds-averaged Navier-Stokes equations are solved with a two-equation turbulence model. All these equations are expressed by using a non-orthogonal curvilinear co-ordinate system. The method is applied to study the compressible internal flow in modern power installations. It has been observed that predictions for two-dimensional and three-dimensional channels show very good agreement with experimental results.     

Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method

Interaction between turbulence and particles is investigated in a channel flow. The fluid motion is calculated using direct numerical simulation (DNS) with a lattice Boltzmann (LB) method, and particles are tracked in a Lagrangian framework through the action of force imposed by the fluid. The particle diameter is smaller than the Kolmogorov length scale, and the point force is used to represent the feedback force of particles on the turbulence. The effects of particles on the turbulence and skin friction coefficient are examined with different particle inertias and mass loadings. Inertial particles suppress intensities of the spanwise and wall-normal components of velocity, and the Reynolds shear stress. It is also found that, relative to the reference particle-free flow, the overall mean skin-friction coefficient is reduced by particles. Changes of near wall turbulent structures such as longer and more regular streamwise low-speed streaks and less ejections and sweeps are the manifestation of drag reduction.     

The effect of two-way coupling and inter-particle collisions on turbulence modulation in a vertical channel flow

Turbulence modulation due to its interaction with dispersed solid particles in a downward fully developed channel flow was studied. The Eulerian framework was used for the gas-phase, whereas the Lagrangian approach was used for the particle-phase. The steady-state equations of conservation of mass and momentum were used for the gas-phase, and the effect of turbulence on the flow-field was included via the standard k–ε model. The particle equation of motion included the drag, the Saffman lift and the gravity forces. Turbulence dispersion effect on the particles was simulated as a continuous Gaussian random field. The effects of particles on the flow were modeled by appropriate source terms in the momentum, k and ε equations. Particle–particle collisions and particle–wall collisions were accounted for in these simulations. Gas-phase velocities and turbulence kinetic energy in the presence of 2–100% mass loadings of two particle classes (50 μm glass and 70 μm copper) were evaluated, and the results were compared with the available experimental data and earlier numerical results. The simulation results showed that when the inter-particle collisions were important and was included in the computational model, the fluid turbulence was attenuated. The level of turbulence attenuation increased with particle mass loading, particle Stokes number, and the distance from the wall. When the inter-particle collisions were negligible and/or was neglected in the model, the fluid turbulence was augmented for the range of particle sizes considered.     

Effect of secondary flow on droplet distribution and deposition in horizontal annular pipe flow

In horizontal annular dispersed pipe flow the liquid film at the bottom is thicker and rougher than at the top of the pipe. A turbulent pipe flow experiencing a variation of roughness along the pipe wall will show a secondary flow. Such secondary flow, consisting of two counter-rotating cells in the cross-section of the tube, can change the distribution of the droplets inside the pipe and their deposition at the wall. Here, we compare the behaviour of the droplets (dispersed phase) with and without secondary flow, using large-eddy simulations. It is shown that the presence of secondary flow increases the droplet concentration in the core of the pipe and the droplet deposition-rate at the top of the pipe.     

Numerical simulation of cavitating flow in 2D and 3D inducer geometries

A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two‐phase flow phenomena. The initial model is a time‐marching algorithm devoted to compressible flow, associated with a low‐speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two‐phase flow areas as weakly compressible single‐phase flow conditions. The numerical model is applied to time‐accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three‐dimensional rotating inducer geometry is then considered, and its quasi‐static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

高超声速三维热化学非平衡流场的数值模拟

对三维高超声速热化学非平衡流场进行数值模拟,采用双温度热化学非平衡、11组元空气模型,考虑振动-离解耦合．差分格式采用沈清博士提出的“迎风型NND”格式,用熵修正方法消除了高超声速流数值模拟中的“carbuncle现象”．与LU-SGS方法结合,提高了单步计算效率和收敛性．数值模拟结果与文献结果进行了对比,并在弹道靶中进行了钢质圆球的弓形激波位置实验验证．计算结果与文献、实验的对比说明,三维热化学非平衡流计算程序可以精确地捕捉到强弓形激波,得到合理的空气动力系数．