Law-of-the-wall in a boundary-layer over regularly distributed roughness elements

As opposed to the log-region, the roughness sublayer present above rough surfaces is still poorly understood due to the complex interaction between wakes developing behind roughness elements. To investigate the spatially averaged flow velocity in this region, a data-set has been collected from several direct numerical simulations and wind-tunnel experiments available in the literature. A generalised law-of-the-wall has been derived, applicable to a roughness sublayer present over regularly distributed roughness elements. The key roughness parameter of this new law is the effective height ?, which characterises the interaction between the roughness and the outer flow in a temporally and spatially averaged sense. A morphometric study reveals that ? is closely related to a new roughness density parameter, λ₂, that accounts for the roughness element shape and the inter-element spacing. This allows ? to be a universal parameter on roughness characterisation. The derived values of the classical roughness length z₀ of the log-law compare well with previous experimental data and geometrical model predictions. Finally, the main properties of the roughness sublayer such as its height are discussed using the geometrical and the roughness parameters proposed in the study.     

On the effect of an anisotropy-resolving subgrid-scale model on large eddy simulation predictions of turbulent open channel flow with wall roughness

A large eddy simulation (LES) was conducted of turbulent flow in a channel with a rough wall on one side and a free surface on the other by adopting an anisotropy-resolving subgrid-scale (SGS) model. A shear Reynolds number of Re_τ = 395 was used based on the mean friction velocity and channel height. To investigate the grid dependency of the LES results caused by the SGS model, three grid resolutions were tested under the same definition of a roughness shape by using the immersed boundary method. The results obtained were compared with direct numerical simulation data with and without the wall roughness and those without the extra anisotropic term. The primary focus was on how the present anisotropic SGS model with coarser grid resolutions can properly provide the effects of roughness on the mean velocity and turbulent stresses, leading to a considerable reduction of the computational cost of LES.     

Effects of upstream roughness and Reynolds number on separated and reattached turbulent flow

This paper presents experimental investigation of upstream roughness and Reynolds number effects on the recirculation region over a smooth forward facing step. The upstream rough wall was produced from 1.5 mm sand grains and the Reynolds number based on step height, Re_h, was varied from 2040 to 9130 for both the upstream smooth and rough walls. For the smooth wall, the reattachment length increased monotonically with Re_h to an asymptotic value of 2.2 step heights for Re_h ≥ 6380. Upstream roughness reduced the reattachment length by 44% because of larger momentum deficit and higher turbulence level in the rough wall boundary layer. The mean velocities and Reynolds stresses were also reduced by roughness. The Reynolds shear stress and production of turbulent kinetic energy showed high negative values at the leading edge of the step indicating counter-gradient diffusion. The implications of these results for standard eddy viscosity models are discussed.     

Estimation and prediction of the roughness function on realistic surfaces

Large-eddy simulations are carried out in turbulent open-channel flows to determine the roughness function and the equivalent sand-grain roughness height, k_s, over sand-grain roughness and different types of realistic roughness replicated from hydraulic turbine blades. A range of Reynolds numbers and mean roughness heights is chosen, leading to both transitionally and fully rough regimes. The start of the fully rough regime is shown to depend on the roughness type, and k_s depends strongly on the surface topography. We then examine several existing correlations that predict k_s based on the information of the surface geometry. In the cases where the surface slope is an important parameter, the moments of surface height statistics do not predict the roughness function, while the existing forms of slope-based correlations perform well. The range of applicability of various correlations is shown to vary with the roughness topography, as the critical value of the effective slope, separating the waviness and roughness regimes, is shown to be higher for a realistic surface, compared to the value for the more regular types of roughness that were previously studied.     

Large-scale flow structures in a planar offset attaching jet with a co-flowing wall jet

Conditional averaging techniques were used to examine the periodic motions that were observed in flows consisting of an offset planar jet and a co-flowing planar wall jet. The offset jet is one jet height (H_j) away from the wall and has a Reynolds number of approximately 40, 000, based on H_j and flow-rate averaged velocity U_o; for the co-flowing jets, different heights (i.e., 0.18H_j and 0.5H_j) and velocities (i.e., 0.56U_o and 0.36U_o) were considered. The flows had periodic motions with frequencies fH_j/U_o = 0.28 and 0.49 or fH_c/U_o = 0.23 and 0.25, where H_c is the distance between the jets. The periodic motions were present in both the inner shear layer of the offset jet above the re-circulation region and the outer shear layer of the wall jet below the re-circulation region. The motions from the inner shear layer of the offset jet persisted in the shear layer that formed downstream of the re-circulating region. There were periodic motions in the outer shear layer of the offset jet particularly in the flow with the smaller wall jet. The relative contribution of the motions to the total fluctuations increased as the flow evolved downstream reaching a maximum approximately 4H_c downstream of the flow exit. The relative contribution of the periodic motions to the turbulent fluctuations was similar in the two flows but the periodic motions had a much larger impact on the near-wall velocity and pressure fluctuations in the flow with the smaller wall jet due to the trajectory of the periodic structures, the distance of the periodic structures to the wall and the size of these structures.     

Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ₂ criterion, swirling strength (λ_ci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λ_ci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.     

Mean flow scaling along smooth and rough wall boundary layers

Effects of the upstream conditions and the degree of the wall roughness on the mean velocity profiles and some integral flow parameters in two dimensional zero-pressure-gradient boundary layer were characterized experimentally. The results were analyzed utilizing conventional and recent scaling flow parameters for 245< Re _θ ≤ 11·10³, where Re _θ is the Reynolds number based on the free stream velocity (Ū _∞) and the momentum thickness (θ). Good correlation of the quantity ΔŪ ⁺ as a function of the roughness parameter k ⁺ was obtained for sand roughness of 1.7 < k ⁺ ≤ 172, revealing a universality of the roughness effect, where ΔŪ ⁺ = = (Ū _∞ − Ū)/u _τ and K ⁺ = ku _τ /v.The mean flow structure of the outer flow was observed not to be influenced by the degree of the wall roughness, i. e., the outer flow of either the smooth or the rough surfaces scales similarly with the various scaling parameters regardless the degree of the wall roughness. However, it made flow confined to the wall region away from the classical universality, allowing similarity hypothesis not to be identical in the wall region at least for the current range of the Reynolds number.     

Turbulent plane wall jets over smooth and rough surfaces

Large-eddy simulations were carried out to study the effects of surface roughness on a plane wall-jet using the Lagrangian dynamic eddy-viscosity subgrid-scale model, at Re = 7500 (based on the jet bulk velocity and height). Results over both smooth and rough surfaces were validated by experimental data at the same Reynolds number. As the jet is injected into the still environment, large-scale rollers are generated in the shear layer between the high-momentum fluid of the jet and the surrounding and are convected downstream with the flow. To understand the extent to which the outer-layer structures modify the flow in the inner layer and the extent to which the effect of roughness spreads away from the wall, both instantaneous and mean flow fields were investigated. The results revealed that, for the Reynolds number and roughness height considered in this study, the effect of roughness is mostly confined to the near-wall region of the wall jet. There is no structural difference between the outer layer of the wall jet over the smooth and rough surfaces. Roughness does not affect the size of the outer-layer structures or the scaling of the profiles of Reynolds stresses in the outer layer. However, in the inner layer, roughness redistributes stresses from streamwise to wall-normal and spanwise directions toward isotropy. Contours of joint probability-density function of the streamwise and wall-normal velocity fluctuations at the bottom of the logarithmic region match those of the turbulent boundary layer at the same height; while the traces of the outer-layer structure were detected at the top of the logarithmic region, indicating that they do not affect the flow very close to the wall, but still modify a major portion of the inner layer. This modification must be taken into consideration when the inner layer of a wall jet is compared with the conventional turbulent boundary layer.     

The beryllium atom and beryllium positive ion in strong magnetic fields

The ground and a few excited states of the beryllium atom in external uniform magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for field strengths ranging from zero up to 2.35×10⁹ T. With changing field strength the ground state of the Be atom undergoes three transitions involving four different electronic configurations which belong to three groups with different spin projections S _z = 0, - 1, - 2. For weak fields the ground state configuration arises from the 1s ²2s ², S _z = 0 configuration. With increasing field strength the ground state evolves into the two S _z = - 1 configurations 1s ²2s2p _-1 and 1s ²2p _-13d _-2, followed by the fully spin polarised S _z = - 2 configuration 1s2p _-13d _-24f _-3. The latter configuration forms the ground state of the beryllium atom in the high field regime γ > 4.567. The analogous calculations for the Be ⁺ ion provide the sequence of the three following ground state configurations: 1s^22s and 1s ²2p _-1 (S _z = - 1/2) and 1s2p _-13d _-2 (S _z = - 3/2). Received 2 October 2000 and Received in final form 8 January 2001     

Measurements of roughness noise

Experiments have been performed on the roughness noise produced by a two-dimensional turbulent wall jet boundary layer flowing over short fetches of sandpaper roughness. A range of rough surface sizes were studied from hydrodynamically smooth through fully rough. Velocity measurements were made to document the form of the wall jet boundary layer and the influence of the roughness upon it. Acoustic measurements showed background noise levels to be very low so that the sound produced by the rough surfaces could be clearly detected with signal to noise ratios as large as 20 dB. Even hydrodynamically smooth roughness was found to produce noise, conclusively indicating the presence of scattering as a source mechanism. Variations of the roughness noise spectra with flow speed and roughness size are found to be inconsistent with any simple parameter scaling. Boundary layer wall pressure fluctuation measurements made within the roughness fetches reveal a spectral form quite different than the roughness noise, and fluctuation levels some 50-70 dB higher. Despite these differences the wall pressure and roughness noise are found to be very simply related, at least at lower frequencies (<6 kHz). The roughness noise spectrum varies closely as the product of the wall pressure spectrum, the frequency squared, and the mean-square roughness height. This is the scaling predicted by scattering theory and implies a major simplification to the problem of roughness noise prediction for stochastic surfaces.     

Estimation of the micrometeorological parameters using on-site instrumentation

Summary Semi-empirical formulae, which have been proposed to estimate the Monin-Obukhov lengthL, are used to derive equations predicting the surface roughness lengthz ₀ and the potential temperature θ₀ at heightz ₀, using routine meteorological measurements. The friction velocityu _* is obtained from the computed values ofL andz ₀.     

Recycling inflow method for simulations of spatially evolving turbulent boundary layers over rough surfaces

The technique by Lund et al. to generate turbulent inflow for simulations of developing boundary layers over smooth flat plates is extended to the case of surfaces with roughness elements. In the Lund et al. method, turbulent velocities on a sampling plane are rescaled and recycled back to the inlet as inflow boundary condition. To rescale mean and fluctuating velocities, appropriate length scales need be identified and for smooth surfaces, the viscous scale l_ν = ν/u_τ (where ν is the kinematic viscosity and u_τ is the friction velocity) is employed for the inner layer. Different from smooth surfaces, in rough wall boundary layers the length scale of the inner layer, i.e. the roughness sub-layer scale l_d, must be determined by the geometric details of the surface roughness elements and the flow around them. In the proposed approach, it is determined by diagnosing dispersive stresses that quantify the spatial inhomogeneity caused by the roughness elements in the flow. The scale l_d is used for rescaling in the inner layer, and the boundary layer thickness δ is used in the outer region. Both parts are then combined for recycling using a blending function. Unlike the blending function proposed by Lund et al. which transitions from the inner layer to the outer layer at approximately 0.2δ, here the location of blending is shifted upwards to enable simulations of very rough surfaces in which the roughness length may exceed the height of 0.2δ assumed in the traditional method. The extended rescaling–recycling method is tested in large eddy simulation of flow over surfaces with various types of roughness element shapes.     

横向粗糙元壁面槽道湍流的大涡模拟研究

采用大涡模拟和浸没边界法相结合对不同高度和不同间距横向粗糙元壁面槽道湍流进行了模拟,得到了光滑壁面和粗糙壁面湍流的流向平均速度分布,雷诺剪切应力,脉动速度均方根和近壁区拟序结构。结果发现横向粗糙元降低了流向平均速度,增大了流动阻力,粗糙壁面湍流的雷诺剪切应力大于光滑壁面。粗糙元降低了流向脉动速度,增强了展向和法向脉动速度。粗糙元高度越高,对湍流流动影响越大,而粗糙元间距对湍流统计特性的影响不大。粗糙壁面仍然存在着和光滑壁面类似的条带结构。     

On the relationship between the gradient and the bulk Richardson number for the atmospheric surface layer

Summary Semi-empirical formulations which have been proposed to describe the wind and potential temperature profiles are used to derive relationships between the gradient Richardson number, Ri, the finite-difference layer Richardson number, Ri_b, the surface layer Richardson number, Ri_s, and the bulk Richardson number,B, through the atmospheric surface layer. The theoretical analysis for stable conditions indicates that Ri (z ₃)=Ri_b, wherez ₃=(z ₂−z ₁)/ln(z ₂/z ₁), andz ₂;z ₁=upper and lower levels at which temperature and wind speed are specified. It is also found that, during stable conditions, the wind profile power law exponent,p, is computed at the heightz ₃, instead of the widely used geometric mean height,z _m, between top (z ₂) and bottom (z ₁) of the layer considered.     

TE- and TM-polarization-resolved spectroscopy on quantum wells under normal incidence

We present TE- and TM-polarization-resolved photocurrent measurements on quantum well pin diodes under normal incidence. Usually, optical experiments performed in such a geometry yield information only about transitions involving in-plane (p_x and p_y) components of the hole wave functions because of the in-plane (TE) polarization of the light. Information on transitions sensitive to the p_z components can be obtained by focussing a radially polarized laser beam through a microscope objective with high numerical aperture (NA=0.9). With our setup, the electrical field vector at the focal tail has a significant component along the optical axis (TM-polarization!) which enables excitation of transitions sensitive to p_z components also. Additionally, the existence of a degenerate (azimuthally polarized) optical mode enables switching these p_z components on and off easily.Experimental evidence of these features has been achieved by exploiting the selection rules for e–hh and e–lh transitions in a quantum well structure. We present a comparison of our recorded spectra with theoretical predictions obtained from simple geometric optics assumptions. For our quantum wells the polarization effects are small because our measurement averages the intensity distribution of the whole focal plane. We plan to extend our measurements to polarization resolved single quantum dot spectroscopy. By restricting the detection region to the spatial extent of a single dot, one can exploit the almost pure TM-polarization on the optical axis for obtaining high contrast between heavy- and light-hole exciton absorption.     

Large eddy simulation of a pulverized coal jet flame ignited by a preheated gas flow

Large eddy simulation (LES) is applied to a pulverized coal jet flame ignited by a preheated gas flow. The simulation results are compared to experimental data obtained for the inlet stoichiometric ratios of 0.14, 0.22, and 0.36. An accurate and computationally inexpensive devolatilization model suitable for combustion simulation in LES is proposed and incorporated into the LES. The numerical results of gas temperature and coal burnout on the centerline show good agreement with the experimental data. Two kinds of lift-off heights are introduced to verify the combustion simulation. One is the height from the primary nozzle exit to the starting point of the growing flame region. The other is the height from the primary nozzle exit to the starting point of the continuous flame region. The calculated results of the two lift-off heights show good agreement with the experimental data. In contrast to LES, the standard k–ε model overestimates the lift-off heights because it calculates time-averaged temperature which does not contain information about local flame structure. The stoichiometric ratio in the gas phase at the starting point of the growing flame region is found to be independent of the inlet stoichiometric ratio in the range from 0.14 to 0.36.     

Drag reduction by herringbone riblet texture in direct numerical simulations of turbulent channel flow

A bird-feather-inspired herringbone riblet texture was investigated for turbulent drag reduction. The texture consists of blade riblets in a converging/diverging or herringbone pattern with spanwise wavelength Λ_f. The aim is to quantify the drag change for this texture as compared to a smooth wall and to study the underlying mechanisms. To that purpose, direct numerical simulations of turbulent flow in a channel with height L_z were performed. The Fukagata-Iwamoto-Kasagi identity for drag decomposition was extended to textured walls and was used to study the drag change mechanisms. For Λ_f/L_z ? O(10), the herringbone texture behaves similarly to a conventional parallel-riblet texture in yaw: the suppression of turbulent advective transport results in a slight drag reduction of 2%. For Λ_f/L_z ? O(1), the drag increases strongly with a maximum of 73%. This is attributed to enhanced mean and turbulent advection, which results from the strong secondary flow that forms over regions of riblet convergence/divergence. Hence, the employment of convergent/divergent riblets in the texture seems to be detrimental to turbulent drag reduction.     

粗糙微通道内液体流动的多尺度耦合模拟

采用分子动力学与有限容积法多尺度耦合算法对粗糙微通道内的液体Poiseuille流动进行了模拟。分析了粗糙元高度、分布以及几何形状对通道内流动速度和边界滑移长度的影响。结果表明：随着粗糙元高度的增加,流动速度和粗糙元间隙底部壁面上滑移长度均减小;粗糙元分布越密或不同几何形状粗糙元所对应的固壁原子数越多,滑移长度越小,但...     

Zonal PANS: evaluation of different treatments of the RANS–LES interface

The partially Reynolds-averaged Navier–Stokes (PANS) model can be used to simulate turbulent flows either as RANS, large eddy simulation (LES) or DNS. Its main parameter is f_k whose physical meaning is the ratio of the modelled to the total turbulent kinetic energy. In RANS f_k = 1, in DNS f_k = 0 and in LES f_k takes values between 0 and 1. Three different ways of prescribing f_k are evaluated for decaying grid turbulence and fully developed channel flow: f_k = 0.4, f_k = k^3/2 _tot/? and, from its definition, f_k = k/k_tot where k_tot is the sum of the modelled, k, and resolved, k_res, turbulent kinetic energy. It is found that the f_k = 0.4 gives the best results. In Girimaji and Wallin, a method was proposed to include the effect of the gradient of f_k. This approach is used at RANS– LES interface in the present study. Four different interface models are evaluated in fully developed channel flow and embedded LES of channel flow: in both cases, PANS is used as a zonal model with f_k = 1 in the unsteady RANS (URANS) region and f_k = 0.4 in the LES region. In fully developed channel flow, the RANS– LES interface is parallel to the wall (horizontal) and in embedded LES, it is parallel to the inlet (vertical). The importance of the location of the horizontal interface in fully developed channel flow is also investigated. It is found that the location – and the choice of the treatment at the interface – may be critical at low Reynolds number or if the interface is placed too close to the wall. The reason is that the modelled turbulent shear stress at the interface is large and hence the relative strength of the resolved turbulence is small. In RANS, the turbulent viscosity – and consequently also the modelled Reynolds shear stress – is only weakly dependent on Reynolds number. It is found in the present work that it also applies in the URANS region.     

XANES studies of monosubstituted benzhydrazide complexes of copper

K x‐ray absorption near‐edge structure (XANES) studies were carried out on nine samples of monosubstituted benzhydrazide complexes of copper, viz. copper(II) benzhydrazide, o‐, m‐ and p‐hydroxybenzhydrazide, o‐, m‐ and p‐nitrobenzhydrazide and o‐ and p‐chlorobenzhydrazide. These complexes are known for their pharmacological activity as antitubercular agents, antibacterial agents and as fungicides. In the three categories of substituted benzhydrazides the ionicity is found to increase in the order para > meta > ortho. Our studies revealed that the substituted complexes are less ionic than the parent complex. Among the three groups, hydroxy‐substituted complexes are more ionic than nitro‐ and chloro‐substituted hydrazides. Splitting of the principal absorption maximum (1s → 4p) takes place in most of these complexes. The splitting into two components has been assigned to the transitions 1s → A*(4p_z) and 1s → B*(4p_x, 4p_y). The estimated bandgap values for these complexes decrease in the order ortho > meta > para. The present studies indicate that as the chemical shift values increase in all the three groups, the bandgap energy values decrease. Copyright © 2004 John Wiley & Sons, Ltd.