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.     

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.     

Modeling ExB drift transport in conceptual slot divertor configurations

At DIII-D, a slot divertor concept, called small-angle-slot (SAS), is under development, aiming to enable detachment at relatively low plasma edge density. We report on simulations using the SOLPS-ITER two-dimensional edge code to examine the performance of conceptual “SAS 2” slot configurations. The focus of the analysis is on E  ×  B drift effects on upstream density at detachment (UDD), with detachment marked by electron temperature T_e ≤ 3 eV at the outer strike point (OSP). With toroidal field such that radial E  ×  B drift carries particles from the OSP towards the private flux region (PFR), placing the OSP near the inner slot wall gives ≈20% lower UDD than having the OSP near the outer wall. The inner wall effectively traps the radial E  ×  B drift flux, resulting in low T_e and associated radial electric field in the PFR, and thus small losses from the slot to the inner target via poloidal E  ×  B drift flux. With toroidal field reversed such that radial E  ×  B drift is reversed, OSP placement near the inner wall gives ≈10% lower UDD than OSP placement near the outer wall. Although radial E  ×  B flux is from the OSP towards the outer wall, this flux largely escapes the slot, raising the UDD. A change in the slot shaping is suggested with the goal of eliminating such E  ×  B -driven particle losses from the slot.     

Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces

Rough surfaces are usually characterised by a single equivalent sand-grain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles show a good collapse. Profile peaks of the turbulent kinetic energy also vary depending on the surface. We then consider which surface properties are important and how new properties can be incorporated into an empirical model, the accuracy of which can then be tested. Optimised models with several roughness parameters are systematically developed for the roughness function and profile peak turbulent kinetic energy. In determining the roughness function, besides the known parameters of solidity (or frontal area ratio) and skewness, it is shown that the streamwise correlation length and the root-mean-square roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and root-mean-square roughness height, along with the mean forward-facing surface angle and spanwise effective slope. The results suggest feasibility of relating rough-wall flow properties (throughout the range from hydrodynamically smooth to fully rough) to surface parameters.     

Large-eddy simulation of impinging jets on smooth and rough surfaces

We performed large-eddy simulations (LES) of forced impinging jets over smooth and rough surfaces, containing large-scale, azimuthal vortices generated by the enhanced primary instability in the jet shear layer. The interaction between these vortices and the turbulence in the wall jet that is formed downstream of the impingement region determines their rate of decay. To explore the surface-roughness effects on the evolution of the vortices, sand-grain-like surfaces are generated using uniformly distributed but randomly oriented ellipsoids. The flow is compared to our previous LES of jets impinging on a smooth surface. In spite of the severe modification caused by the roughness on the near-wall flow, the vortex development is not significantly altered. Slightly faster decay of the primary vortices is observed in the rough-wall case compared to the smooth-wall one; the secondary vortex that detaches from the wall and is lifted up has larger vorticity. The highly disturbed near-wall flow is advected outward and affects the evolution of the primary vortex for a longer period during the vortex interaction. The robust turbulent generation mechanism in the outer shear layer, however, mitigates the changes in vortex behaviour. The momentum deficit and the enhancement of turbulence due to the surface roughness play a key role during this process.     

An Extension of Spherically Symmetric Self-Similar Inhomogeneous Cosmological Models

An inhomogeneous cosmological solution with partial similarity is derived by extending the self-similar solutions in spherically symmetric spacetime containing pressureless matter. To show their physical difference from the previous self-similar one, we consider inhomogeneous cosmological models with inner and outer homogeneous regions and an intermediate inhomogeneous region, and derive the relations between observational quantities in them. It is found as a result that the models have different z-dependence of the local density parameter.     

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.     

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.     

Characteristics and structure of inverse flames of natural gas

Characteristics and structure of nominally non-premixed flames of natural gas are investigated using a burner that employs simultaneously two distinct features: fuel and oxidiser direct injection, and inverse fuel and oxidiser delivery. At low exit velocities, the result is an inverse diffusion flame that has been noted in the past for its low NO_x emissions, soot luminosity, and narrow stability limits. The present study aimed at extending the burner operating range, and it demonstrated that the inverse flame exhibits a varying degree of partial premixing dependent on the discharge nozzle conditions and the ratio of inner air jet and outer fuel jet velocities. These two variables affect the flame length, temperature distributions, and stability limits. Temperature measurements and Schlieren visualisation show areas of enhanced turbulent mixing in the shear region and the presence of a well-mixed reaction zone on the flame centreline. This reaction zone is enveloped by an outer diffusion flame, yielding a unique double-flame structure. As the fuel–air equivalence ratio is decreasing with an increase in the inner jet velocity, the well-mixed reaction zone extends considerably. These findings suggest a method for establishing a flame of uniform high temperature by optimising the coaxial nozzle geometry and flow conditions. The normalised flame length is decreasing exponentially with the air/fuel velocity ratio. Measurements demonstrate that the inverse flame stability limits change qualitatively with varying degree of partial premixing. At the low premixing level, the flame blow-out is a function of the inner and outer jet velocities and the nozzle conditions. The flame blow-out at high degree of partial premixing occurs abruptly at a single value of the inner air jet velocity, regardless of the fuel jet velocity and almost independent of the discharge nozzle conditions.     

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.     

气体-表面相互作用的分子动力学模拟研究

采用分子动力学模拟方法研究了气体分子Ar在光滑和粗糙Pt表面上的散射规律.提出了一种速度抽样方法,计算了不同温度条件下气体分子对光滑和粗糙表面的切向动量适应系数和吸附概率.结果显示：光滑表面条件下,气体分子的切向动量系数和吸附概率都随着温度的升高而降低;粗糙度对气体分子切向动量与表面的适应具有极大的促进作用,当粗糙度足够大时,切向动量适应系数的大小趋近于1.0,对温度的敏感性也逐渐降低.采用粒子束方法对气体分子在光滑和粗糙表面上的散射规律进行了定量分析.总结了散射过程中气体分子的典型轨迹和动量变化规律,将气体分子在光滑表面的散射分为两种类型：单次碰撞后散射和多次碰撞后散射.单次碰撞后散射的气体分子平均切向动量有所减小,而经过多次碰撞后散射的气体分子则倾向于保持原有的平均切向动量.对于粗糙表面,粗糙度的存在使气体分子与表面间的动量和能量适应更加充分,导致气体分子在较粗糙表面上散射后的平均切向动量大幅减小并接近于0,且气体分子在表面上经历的碰撞次数越多,其散射后的能量损失越严重.     

基于蚯蚓背孔射流的仿生射流表面减阻性能研究

为了减小流体对固体壁面的阻力, 基于蚯蚓生物学特征, 对蚯蚓背孔射流特性进行分析, 建立仿蚯蚓背孔射流的仿生射流表面计算模型, 采用SST k-ω 湍流模型对仿生射流表面的减阻特性进行数值模拟, 同时对数值模拟结果进行实验验证, 并以此研究了仿蚯蚓背孔射流表面的减阻机理.结果表明, 在一定条件下, 仿蚯蚓背孔射流的仿生射流表面具有较好的减阻效果; 在同一射流方向角下, 随着射流速度的增加, 减阻率逐渐增大; 在同一射流速度下, 随着射流方向角的增加, 减阻率呈先减小后增大的变化趋势; 数值模拟与实验均在射流速度为1 m·s^-1、射流方向角为-30°时达到最大, 分别为8.69%, 7.86%; 射流表面改变了原有光滑壁面的边界层结构, 对壁面边界层进行了有效的控制, 减小了壁面的剪应力, 降低了壁面边界层的速度.     

Self-similar turbulent boundary layer with imposed pressure gradient. Velocity-defect law

Self-similar flows in a turbulent boundary layer when the free-stream velocity is specified as a power function of the longitudinal coordinate are investigated. The self-similar formulation not only simplifies solving the problem by reducing the equations of motion to ordinary differential equations but also provides a mean for formulating the closure conditions for these equations. It is shown that for the class of flows under consideration that depend on three governing parameters, the dimensionless mixing length in the outer region is a function of the normalized distance from the wall and the exponent m of the power law. In calculations, this function is assumed to be independent of pressure gradient, which gives the results very close to experimental data. As a result of an exact asymptotic solution of the problem, we establish the characteristic scale of the velocity defect in the outer region (the velocity-defect law) valid in the entire range of variation of the Clauser similarity parameter.     

Large Eddy Simulation of Turbulent Channel Flow with 3D Roughness Using a Roughness Element Model

Large eddy simulation of turbulent channel flow with dense and small 3D roughness elements is carried out using a roughness element model Profiles of mean Reynolds stress, mean velocity and rms velocity as well as turbulent structures near the wall are obtained. The shear stress in the rough wall is larger than that in the smooth wall side and the rough wall has a larger influence on the channel flow. Profiles of mean streamwise velocity near the wall have logarithmic velocity distributions for both smooth and roughness walls, while there is a velocity decrease for the rough wall due to larger fractional drag. All the three components of rms velocities in the rough wall region are larger than that in the smooth wall region, and the roughness elements on the wall increase turbulent intensity in all directions. The s~reak spacing and average diameter of near wall quasi-s~reamwise vortices increase with the presence of roughness elements on the wall and it is shown that the rough wall induces complex and strong streamwise vortices. Results of dense and small 3D roughness elements in both turbulent statistics and structure, obtained with a relatively simple method, are found to be comparable to related experiments.     

Thin-film electroluminescent structures on substrates with rough surfaces

It is shown that the use of substrates with inner rough and outer diffusely scattering surfaces in film electroluminescent structures makes it possible to substantially increase the coefficient of radiation extraction (by a factor of 1.3–2.5) and the brightness of luminescence (by a factor of 1.2–3.5) as compared to the structure on a smooth surface, which can be employed to enhance the brightness of individual colors of the luminescence of electroluminescent emitters. The results of the investigations indicate a substantial decrease in the constant of the time of brightness buildup (by a factor of 6–8 for MDSDM structures and by a factor of ∼3.8 for MDSCM structures) and the appearance of two segments of brightness decay for MDSMD structures with different constant decay times in going from the structure on a smooth substrate to the structures built on substrates with an inner rough surface. Unlike this, MDSCM structures have two segments of brightness decay on both a smooth substrate and a rough substrate. Ul’yanovsk State University, 42, L. Tolstoi St., Ul’yanovsk, Russia, 432700. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 5, pp. 787–793, September–October, 1998.     

Experimental study on the local similarity scaling of the turbulence spectrum in the turbulent boundary layer

The streamwise fluctuating velocity in the turbulent boundary layer is measured under approximately medium Reynolds Number by hot wire in order to investigate the scaling properties of the overlapped turbulent spectrum among energy-containing area, inertial subrange and dissipation range based on FFT analysis. The experiment indicates that the high Reynolds flow reported before is not indispensable to produce −1 scaling. So far as the measured position is provided with much higher spatial resolution and enough closing to the wall, −1 scaling is determinate to exist when approaching medium Reynolds. The scaling ranges are supposed to begin at inner scale and end in outer scale, which reveals the local similarity of the energy spectrum over the energy-containing eddies near the wall. In the logarithmic area (y ⁺ > 130), −5/3 scaling occurs in the energy spectrum, while moving away from the wall with Reynolds numbers increasing, the inertial subrange extends to the lower wavenumbers. On the condition k ₁ η ≫ 0.1, the curves of the turbulence spectrum in the logarithmic layer are superposed, which expresses the similarity of turbulence energy distributed in Komogorov scaling area and exhibits local isotropy characteristics by virtue of the viscous dissipation. Supported by the National Natural Science Foundation of China (Grant Nos. 10832001 and 10872145), the Program for New Century Excellent Talents in Universities of Education Ministry of China, and the Plan of Tianjin Science and Technology Development (Grant No. 06TXTJJC13800)     

影响空心旋转液体射流初始阶段运动的无量纲参数的分析

本文以描述空心旋转时流初始阶段运动规律的理论模型[1]为依据,重点讨论了影响射流运动的无量纲参数：韦伯数,液膜内外压力差,液膜初始内外环半径比,初始旋流度;初始径向速度等。从而进一步加深了对旋流喷嘴所产生的空心旋转射流初始阶段运动及发展规律的认识。     

Large eddy simulations and parameterisation of roughness element orientation and flow direction effects in rough wall boundary layers

We conduct a series of large eddy simulations (LES) of turbulent boundary layers over arrays of cuboidal roughness elements at arbitrary orientation angles (non-frontal orientations with the incident flow). Flow response to changing roughness orientation is systematically studied at two ground coverage densities, λ_p = 0.06 and 0.11. As expected, the effective roughness heights z_o measured from LES are higher for λ_p = 0.11 than for λ_p = 0.06, although appreciable changes both in z_o and wall shear stress (friction velocity) are observed at both ground coverage densities as the roughness orientation angle changes. This suggests the necessity of accounting for detailed rough wall topology (including more information than just λ_p, λ_f) when relating rough wall morphology to its aerodynamic properties. To this end, a recently developed analytical rough wall parameterisation is used to predict the aerodynamic properties of the simulated rough surfaces. In this rough wall model, wake interactions among roughness elements are explicitly modelled using the concept of sheltering height and exponential attenuation coefficient. As a result, the parameterisation is responsive to detailed ground roughness arrangements and flow conditions, including roughness height variations, element orientation, incident flow direction, transverse displacements, etc. Model-predicted effective roughness heights, wall stress, mean velocity at the height of the roughness, and in some cases displacement height, are compared against the LES measurements from this study as well as numerical/experiment measurements from other authors. The predictions from the model are found to agree well with the measurements both in trends and in absolute values, thus extending the applicability of the analytical rough wall model to more general surfaces than those previously tested.     

Screening effects in flow through rough channels

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome of numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. Finally, the effects on the flow behavior of the channel symmetry and aspect ratio are also investigated.     

Inner–outer interactions in rough-wall turbulence

Here we revisit the inner–outer interaction model (IOIM) of Marusic et al. (Science, vol. 329, 2010, pp. 193–196) that enables the prediction of statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows from a large-scale velocity signature measured in the outer region of the flow. The model is characterised by two empirically observed inner–outer interactions: superposition of energy from outer region large-scale motions; and amplitude modulation by these large-scale motions of a small-scale ‘universal’ signal (u^*), which in smooth-wall flows is Reynolds number invariant. In the present study, the inner–outer interactions in rough-wall turbulent boundary layers are examined within the framework of the IOIM. Simultaneous two-point hot-wire anemometry measurements enable quantification, via the model parameters, of the strengths of superposition and amplitude modulation effects in a rough-wall flow, and these are compared to a smooth-wall flow. It is shown that the present rough-wall significantly reduces the effects of superposition, while increasing the amplitude modulation effect. The former is true even in flows that exhibit outer region similarity. Using the model parameters obtained from the two-point measurements, predictions of inner region streamwise velocity statistics and spectra are compared to measurements over a range of friction and roughness Reynolds numbers. These results indicate that the u^* signal does depend on roughness Reynolds number (k⁺_s), but is robust to changes in friction Reynolds number (δ⁺). Additionally, the superposition strength is shown to be relatively independent of both roughness and friction Reynolds number. The implications of the present results on the suitability of the IOIM as a predictive tool in rough-wall turbulence are discussed.