The spanwise spectra in wall-bounded turbulence

The pre-multiplied spanwise energy spectra of streamwise velocity fluctuations are investigated in this paper. Two distinct spectral peaks in the spanwise spectra are observed in low-Reynolds-number wall-bounded turbulence.The spectra are calculated from direct numerical simulation(DNS) of turbulent channel flows and zero-pressure-gradient boundary layer flows. These two peaks locate in the nearwall and outer regions and are referred to as the inner peak and the outer peak, respectively. This result implies that the streamwise velocity fluctuations can be separated into large and small scales in the spanwise direction even though the friction Reynolds number Reτ can be as low as 1000. The properties of the inner and outer peaks in the spanwise spectra are analyzed. The locations of the inner peak are invariant over a range of Reynolds numbers. However, the locations of the outer peak are associated with the Reynolds number,which are much higher than those of the outer peak of the pre-multiplied streamwise energy spectra of the streamwise velocity.     

An experimental study into the effects of streamwise and spanwise acceleration in a turbulent boundary layer

We compare two turbulent boundary layers produced in a low-speed water channel experiment. Both are subjected to an identical streamwise pressure gradient generated via a lateral contraction of the channel, and an additional spanwise pressure gradient is imposed on one of the layers by curving the contraction walls. Despite a relatively high streamwise acceleration, hot-film probe measurements of the mean-velocity distributions show that the Reynolds number increases whilst the coefficient of friction decreases downstream. Visualization of the viscous layers using hydrogen bubbles reveal an increase in the non-dimensional streak spacing in response to the acceleration. Changes in statistical moments of the streamwise velocity near the wall suggest an increased dominance of high-velocity fluctuations. The near-wall streaks and velocity statistics have little sensitivity to the boundary layer three-dimensionality induced by the spanwise pressure gradient, with the boundary-layer crossflow velocity reaching 11 % that of the local freestream velocity.     

The effect of aspect ratio on the flow over a rearward-facing step

In this study, we investigate the effect of the spanwise width on the mixing layer behind a rearward-facing step. Results for aspect ratios (tunnel width/step height) of 10 and 4 and Reynolds numbers of 11,000 and 5,000 are presented. A frequency shifted, single component LDV system was used to obtain mean streamwise velocity profiles, turbulence intensity profiles, and normal velocity spectra at four streamwise and three spanwise positions for each test case. The mean velocity and turbulence intensity profiles are constant across the width of the test section for either of the Reynolds numbers considered, but there are significant differences among the cases studied. At a distance greater than three step heights down-stream of the step, the peak turbulence intensity is greater for higher aspect ratio and is relatively insensitive to Reynolds number. The peak frequency is lower and the spectrum is narrower for a higher aspect ratio in the region near the step.     

大涡模拟研究展向旋转槽道湍流流动

本文用大涡模拟预测了以不同转速做展向旋转的槽道湍流流动,统计平均的流向速度型在壁面附近与已有实验数据符合很好,在通道中部的预测差异也能给出合理解释,对比不同转速的计算结果,表明展向旋转通道的湍流应力和壁面摩擦力在压力面附近提高、在吸力面附近降低,这些高阶湍流统计量的变化规律可以结合湍流应力输运方程加以解释,漩涡识别技术显示了近壁条带结构,其形态和猝发率受旋转附加力的影响发生改变,进而影响壁面摩擦速度的数值和分布,进一步考察垂直流动方向的截面内速度分布,发现旋转引起了垂直壁面方向的流动,形成正负相间排列的流向涡对,并随着转速的增加向压力面靠近。      

The influence of temperature on the measurements of Reynolds stresses in shear free turbulence near a wall

 Temperature changes have a significant influence on the measurements of Reynolds stresses in turbulent boundary layers. As compared to the spanwise velocity fluctuations the streamwise turbulence intensity is especially sensitive to temperature deviations. Although this is a general statement its importance is clearly elucidated in a shear-free turbulence near a solid wall, since the mixing due to turbulence production is minimized in this flow. A consequence of temperature influence on hot-wire measurements is that frictional heating from the wall has produced contradictory results in different experiments on shear-free turbulence. In the current paper, measurements of streamwise and spanwise turbulence intensities have been conducted at different wall temperatures, thereby simulating the contradictory results mentioned above. A simple model has been developed showing that the turbulence intensities are affected by both the rms. value of the temperature fluctuations and the correlation between fluctuating temperature and velocity. These correlations are measured and the developed model is used to explain deviations in earlier measurements on shear-free turbulence. Moreover, the individual magnitudes of the two correlations in the temperature correction are estimated and their individual importance is discussed. Received: 17 February 1997 / Accepted: 18 January 1998     

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.     

Effects of coincidence window and measuring volume size on laser Doppler velocimetry measurement of turbulence

The effects of coincidence window and measuring volume size on two-component laser velocimeter measurement of turbulence in an isothermal liquid flow through a concentric annular channel were studied. Three different coincidence windows (100–500 μs) and three different measuring volume sizes (diameter, 5–9 wall units; spanwise length, 24–91 wall units) were used in a flow of Reynolds number 31,500 and data density spanning the high end of intermediate to the low end of high (3–6). While no significant effects of the coincidence window and measuring volume size were found on the time-mean velocity and turbulence intensities, the streamwise Reynolds shear stress measured near a wall was found to be markedly affected by both. The smallest feasible measuring volume along with an appropriate coincidence window provides good measurement of the shear stress. Received: 8 September 1999/Accepted: 11 July 2000     

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

The direct numerical simulation(DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.     

Development of a turbulent near-wall temperature model and its application to channel flow

A numerical study of fluid flow and heat transfer in a two-dimensional channel under fully developed turbulent conditions is reported. A computer program which is capable of treating both forced and natural convection problems under turbulent conditions has been developed. The code uses the high-Reynolds-number form of the two equation turbulent model(k-?) in which a turbulent kinetic energy near-wall model is incorporated in order to accurately represent the behavior of the flow near the wall, particularly in the viscous sublayer where the turbulent Reynolds number is small. A near-wall temperature model has been developed and incorporated into the energy equation to allow accurate prediction of the temperature distribution near the wall and, therefore, accurate calculation of heat transfer coefficients. The sensitivity of the prediction of flow and heat transfer to variations in the coefficients used in the turbulence model is investigated. The predictions of the model are compared to available experimental and theoretical results; good agreement is obtained. The inclusion of the near-wall temperature model has further improved the predictions of the temperature profile and heat transfer coefficient. The results indicate that the turbulent kinetic energy Prandtl number should be a function of Reynolds number.     

Influence of a wavy boundary on turbulence.

Measurements of turbulence with laser Doppler velocimetry (LDV) are compared for turbulent flows over a flat surface and a surface with sinusoidal waves of small wavelength. The wavy boundary was highly rough in that the flow separated. The Reynolds number based on the half-height of the channel and the bulk velocity was 46,000. The wavelength was 5 mm and the height to wavelength ratio was 0.1. The root-mean-squares of the velocity fluctuations are approximately equal if normalized with the friction velocity. This can be explained as a consequence of the approximate equality of the correlation coefficients of the Reynolds shear stress. Calculations with a direct numerical simulation (DNS) are used to show that the fluid interacts with the wall in quite different ways for flat and wavy surfaces. They show similarity in that large quadrant 2 events in the outer flow, for both cases, are associated with plumes that emerge from the wall region and extend over large distances. Measurements of skewness of the streamwise and wall-normal velocity fluctuations and quadrant analyses of the Reynolds shear stresses are qualitatively similar for flat and wavy surfaces. However, the skewness magnitudes and the ratio of the quadrant 2 to quadrant 4 contributions are larger for the wavy surface. Thus, there is evidence that turbulent structures are universal in the outer flow and for quantitative differences in the statistics that reflect differences in the way in which the fluid interacts with the wall.     

Direct numerical simulation of turbulent heat transfer over fully resolved anisotropic porous structures

Lattice Boltzmann direct numerical simulations of turbulent heat transfer over and inside anisotropic porous media are performed. This study considers turbulent plane channel flows whose bottom walls are made from the porous media at the bulk Reynolds number of 2900 with isothermal and conjugate heat transfer wall conditions. Four different porous walls are considered. They are walls with only the wall-normal permeability, with the wall-normal and spanwise permeabilities, with the wall-normal and streamwise permeabilities, and with the isotropic wall-normal, spanwise and streamwise permeabilities. The porosity of the porous walls ranges from 0.6 to 0.8. Discussions on the effects of the anisotropic permeability on turbulent thermal fields are carried out by the instantaneous flow visualizations and the statistical quantities. In particular, temperature fluctuations, turbulent and dispersion heat fluxes are examined both inside and outside the porous walls. Finally, the heat transfer performance is discussed considering the effects of the anisotropic permeability.     

壁面展向周期振动的槽道湍流减阻机理的研究

利用直接数值模拟研究了带有壁面展向周期振动的槽道湍流.壁面在展向的周期运动使湍流受到抑制,并使壁面摩擦阻力减小.通过对雷诺应力输运方程的分析研究了壁面展向周期振动的减阻机理,进一步揭示了压力变形项在湍流抑制中的关键作用.     

Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall

Direct numerical simulations have been performed to study the effect of an oscillating segment of the wall on a turbulent boundary layer flow. Two different oscillation amplitudes with equal oscillation period have been used, which allows a direct comparison between a relatively weak and strong forcing of the flow. The weaker forcing results in 18% drag reduction while the stronger forcing, with twice the amplitude, yields 29% drag reduction. The downstream development of the drag reduction is compared with earlier simulations and experiments. In addition, a simulation with identical oscillation parameters as in previous numerical and experimental investigations allows for an estimation of the effect of the Reynolds number on the drag reduction.Reductions in the Reynolds stresses and the important role that the edge of the Stokes layer has is explained.An estimation of the idealized power consumption shows that a positive energy budget is only possible for the weaker wall velocity case.Spatial and temporal transients are investigated and a transformation between spatial and temporal coordinates via a convection velocity is shown to facilitate a comparison between the two transients in a consistent manner. The streamwise shear exhibits a similar monotonic behavior in the spatial and temporal transients, while the non-monotinic temporal transient of the longitudinal Reynolds stress has no counterpart in the spatial development. Furthermore, the evolution in time of the spanwise Reynolds stress is very similar to previously reported channel flow data.The instantaneous spanwise velocity profile (only averaged in the homogeneous spanwise direction) will for the first time be presented from a boundary layer over an oscillating wall, and comparisons with the analytical solution to the laminar Navier–Stokes equations show very good agreement.     

Turbulence structure in non-equilibrium boundary layers with favorable and adverse pressure gradients

An experimental study was conducted to document the turbulence in boundary layers on smooth walls subject to a favorable pressure gradient followed by a zero pressure gradient recovery and an adverse pressure gradient. Two component velocity profiles were acquired along the spanwise centerline of the test section, and velocity fields were obtained at the same locations in streamwise wall-normal and streamwise–spanwise planes using PIV. The FPG was shown to reduce the turbulence in the outer part of the boundary layer, reducing the transport of this turbulence and the effect of sweeps toward the wall. This reduced the inclination angle of the large structures and increased their length scale, particularly in the streamwise and spanwise directions. Recovery from the FPG to a ZPG was rapid. The APG reduced the near wall shear, resulting in a reduced effect of ejections relative to sweeps. The APG had an opposite but smaller effect on the shape and size of structures compared to the FPG.     

等热流密度加热垂直下降液膜的研究

利用等热流密度加热条件下降膜流动的三维模型方程进行线性稳定性分析和数值模拟。线性稳定性分析表明,模型方程在小到中等Reynolds数下都适用,并且流向不稳定性增长率随着Reynolds数和Marangoni数增加而增加,展向不稳定性增长率则随着Marangoni数增加而增加,随着Reynolds数增加而减小,流向和展向对扰动波数都存在一个不稳定区间。三维数值模拟表明,在等热流密度加热条件下,液膜在随机扰动的情况下最终会形成带孤立波的三维溪流状结构,液膜与气体的换热也因溪流状结构的出现而加强;在随机扰动的基础上引入占优势地位的展向最不稳定扰动会使得换热增强,液膜会提前破裂;在随机扰动的基础上引入占优势地位的流向最不稳定扰动时,液膜的换热会增强,但不会提前破裂;在随机扰动的基础上同时引入占优势地位的流向和展向最不稳定扰动时,换热会加强且液膜会提前破裂。     

The effect of streamwise vortices on the turbulence structure of a separating boundary layer

A high Reynolds number flat plate turbulent boundary layer is investigated in a wind-tunnel experiment. The flow is subjected to an adverse pressure gradient which is strong enough to generate a weak separation bubble. This experimental study attempts to shed some new light on separation control by means of streamwise vortices with emphasize on the change in the boundary layer turbulence structure. In the present case, counter-rotating and initially non-equidistant streamwise vortices become and remain equidistant and confined within the boundary layer, contradictory to the prediction by inviscid theory. The viscous diffusion cause the vortices to grow, the swirling velocity component to decrease and the boundary layer to develop towards a two-dimensional state. At the position of the eliminated separation bubble the following changes in the turbulence structure were observed. The anisotropy state in the near-wall region is unchanged, which indicates that it is determined by the presence of the wall rather than the large scale vortices. However, the turbulence in the outer part of the boundary layer becomes overall more isotropic due to an increased wall-normal mixing and a significantly decreased production of streamwise fluctuations. The turbulent kinetic energy is decreased as a consequence of the latter. Despite the complete change in mean flow, the spatial turbulence structure and the anisotropy state, the process of transfer of turbulent kinetic energy to the spanwise fluctuating component seems to be unchanged. Local regions of anisotropy are strongly connected to maxima in the turbulent production. For example, at spanwise positions in between those of symmetry, the spanwise gradient of the streamwise velocity cause significant production of turbulent fluctuations. Transport of turbulence in the spanwise direction occurs in the same direction as the rotation of the vortices.     

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

A numerical investigation of wall effects in three‐dimensional,laminar flow over a backward facing step with a constant aspect and expansion ratio

The wall effects are investigated in the three‐dimensional laminar flow over a backward‐facing step. For this purpose, a numerical experiment is designed under actual laboratory conditions. The aspect ratio of the computational domain is 1:40 and the expansion ratio is 1:2. The Reynolds number ranges from 100 to 950. The governing equations are the steady state, isothermal and incompressible Navier–Stokes equations for Newtonian fluids. They are solved with a homemade Galerkin finite element code. The computations are validated with data from available laboratory and numerical experiments. The results focus on the variation of both velocity profiles and lengths of eddies along the lower and upper wall in the spanwise direction. Calculated streamlines in the streamwise and transverse direction show how the flow is distorted near the lateral wall and how it develops up to the plane of symmetry. The study of skin friction lines along the top and bottom wall of the domain reveals a flow that takes place in the spanwise direction. This spanwise component of the flow becomes more dominant with increasing Reynolds number and is impossible to be sustained at steady state for Reynolds numbers higher than 950 for this particular geometry. Copyright © 2012 John Wiley & Sons, Ltd.     

Transverse-roll global modes in a Rayleigh–Bénard–Poiseuille system with streamwise variable heating

The effect of a spatially inhomogeneous heating of the bottom wall in Rayleigh–Bénard–Poiseuille convection is studied for slow streamwise variations of the temperature profile. The problem is defined by the constant Reynolds number of the Poiseuille through flow, assumed to be low (typically 10), the constant Prandtl number, and the spatial evolution of the Rayleigh number , assumed to be subcritical everywhere except in a limited region around its single maximum . In this initial study, all spanwise inhomogeneities such as side walls or spanwise variable heating are neglected to obtain two-dimensional (transverse roll) global mode solutions by means of WKBJ asymptotics. The resulting frequency selection yields, at leading order, a global mode frequency equal to the local absolute frequency ω^t at the streamwise location where the Rayleigh number is maximum, with higher-order corrections for non-parallelism. These allow the determination of critical values of for global instability as a function of the profile of the local Rayleigh number and of Prandtl and Reynolds numbers.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.