Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

The turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u_∞ / v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.     

Large-eddy simulations of temporally accelerating turbulent channel flow

The unsteady turbulent channel flow subject to the temporal acceleration is considered in this study. Large-eddy simulations were performed to study the response of the turbulent flow to the temporal acceleration. The simulations were started with the fully developed turbulent channel flow at an initial Reynolds number of Re₀ = 3500 (based on the channel half-height and the bulk-mean velocity), and then a constant temporal acceleration was applied. During the acceleration, the Reynolds number of the channel flow increased linearly from the initial Reynolds number to the final Reynolds number of Re₁ = 22,600. The effect of grid resolution, domain size, time step size on the simulation results was assessed in a preliminary study using simulations of the accelerating turbulent flow as well as simulations of the steady turbulent channel flow at various Reynolds numbers. Simulation parameters were carefully chosen from the preliminary study to ascertain the accuracy of the simulation. From the accelerating turbulent flow simulations, the delays in the response of various flow properties to the temporal acceleration were measured. The distinctive features of the delays responsible for turbulence production, energy redistribution, and radial propagation were identified. Detailed turbulence statistics including the wall shear stress response during the acceleration were examined. The results reveal the changes in the near-wall structures during the acceleration. A self-sustaining mechanism of turbulence is proposed to explain the response of the turbulent flow to the temporal acceleration. Although the overall flow characteristics are similar between the channel and pipe flows, some differences were observed between the two flows.     

An experimental study of the forerunners of boundary-layer localized disturbances at an enhanced turbulence level

Turbulence production processes in boundary layer at a high level of free-stream turbulence have been studied. The tests were carried out in the MT-324 subsonic wind tunnel of ITAM, SB RAS, on models of straight and 45° swept wings at Reynolds numbers Re_c1 = 97000 and Re_c2 = 137000, and also at low (Tu = 0.18 % U _∞) and high (Tu = 0.79 and 2.31 % U _∞) levels of free-stream turbulence. The longitudinal localized disturbances developing in the boundary layer under the action of free-stream turbulence were artificially modeled using local air suction through a slot on the model surface. Wave packets, or forerunners, produced in the boundary layer, in the region preceding the abrupt local change of flow velocity near the localized-disturbance fronts, were examined. The high level of free-stream turbulence was found to accelerate the downstream evolution of the wave packets and their transformation into turbulent spots.     

On mean flow universality of turbulent wall flows. II. Asymptotic flow analysis

Understanding of the structure of turbulent flows at extreme Reynolds numbers (Re) is relevant because of several reasons: almost all turbulence theories are only valid in the high Re limit, and most turbulent flows of practical relevance are characterized by very high Re. Specific questions about wall-bounded turbulent flows at extreme Re concern the asymptotic laws of the mean velocity and turbulence statistics, their universality, the convergence of statistics towards their asymptotic profiles, and the overall physical flow organization. In extension of recent studies focusing on the mean flow at moderate and relatively high Re, the latter questions are addressed with respect to three canonical wall-bounded flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Main results reported here are the asymptotic logarithmic law for the mean velocity and corresponding scale-separation laws for bulk flow properties, the Reynolds shear stress, the turbulence production and turbulent viscosity. A scaling analysis indicates that the establishment of a self-similar turbulence state is the condition for the development of a strict logarithmic velocity profile. The resulting overall physical flow structure at extreme Re is discussed.     

Constrained large-eddy simulation of supersonic turbulent boundary layer over a compression ramp

A supersonic turbulent boundary layer over a compression ramp is numerically investigated using the constrained large-eddy simulation (CLES) method. The compression corner is characterised by a deflection angle of 24°. The free-stream Mach number is Ma_∞ = 2.9, and the Reynolds number based on the momentum thickness of inlet boundary layer is Re_θ = 2300. The mean and statistical quantities, such as mean velocity, wall pressure and Reynolds stresses, are thoroughly analysed and compared with those from traditional large-eddy simulation (LES), experimental measurement and direct numerical simulation (DNS). It turns out that CLES can predict the friction coefficient, wall-pressure distribution, size of separation bubble, Reynolds stresses, etc. more accurately than traditional LES, and the results are in reasonable agreement with the experimental and/or DNS data. Also discussed are the effects of specific parameterisations of the Reynolds constraint and interfacial positions separating the constrained and unconstrained regions on the performance of the CLES method.     

POD-based wall boundary conditions for the numerical simulation of turbulent channel flows

Simulation of turbulent wall-bounded flows requires a high spatial resolution in the wall region, which limits the range of Reynolds numbers which can be effectively reached. In previous work, we proposed proper orthogonal decomposition (POD) based wall boundary conditions to bypass the simulation of the inner wall region. Tests were carried out for direct numerical simulation at a low Reynolds number Re_τ = 180. The boundary condition is based on the POD spatial eigenfunctions which are determined a priori in the full channel. It consists of a three-component velocity field on the plane y⁺ = 50 which is reconstructed at each instant from a combination of selected eigenfunctions. The coefficients of the combination are estimated from the simulation in the reduced domain using the threshold-based reconstruction method described in Podvin et al. The study is now extended to large-eddy simulation at higher Reynolds numbers Re_τ = 295 and Re_τ = 590. Two versions of the reconstruction method are considered. In the first version, both the phases and the moduli of the coefficients are allowed to vary. In the second version, only the phases are adjusted. We find that the latter method is associated with improved statistics and is relatively robust with respect to the reconstruction threshold. However, it is sensitive to the details of the numerical simulation, unlike the former method, which is associated with less accurate statistics and is more dependent on the reconstruction threshold.     

Numerical simulation of transitional flow on a wind turbine airfoil with RANS-based transition model

This paper presents a numerical investigation of transitional flow on the wind turbine airfoil DU91-W2-250 with chord-based Reynolds number Re_c = 1.0 × 10⁶. The Reynolds-averaged Navier–Stokes based transition model using laminar kinetic energy concept, namely the k ? k_L ? ω model, is employed to resolve the boundary layer transition. Some ambiguities for this model are discussed and it is further implemented into OpenFOAM-2.1.1. The k ? k_L ? ω model is first validated through the chosen wind turbine airfoil at the angle of attack (AoA) of 6.24° against wind tunnel measurement, where lift and drag coefficients, surface pressure distribution and transition location are compared. In order to reveal the transitional flow on the airfoil, the mean boundary layer profiles in three zones, namely the laminar, transitional and fully turbulent regimes, are investigated. Observation of flow at the transition location identifies the laminar separation bubble. The AoA effect on boundary layer transition over wind turbine airfoil is also studied. Increasing the AoA from ?3° to 10°, the laminar separation bubble moves upstream and reduces in size, which is in close agreement with wind tunnel measurement.     

Study on the dynamic characteristics of flow over building cluster at high Reynolds number by large eddy simulation

In this paper,the dynamic characteristics of building clusters are simulated by large eddy simulation at high Reynolds number for both homogeneous and heterogeneous building clusters.To save the computational cost a channel-like flow model is applied to the urban canopy with free slip condition at the upper boundary.The results show that the domain height is an important parameter for correct evaluation of the dynamic characteristics.The domain height must be greater than 8h(h is the average building height)in order to obtain correct roughness height while displacement height and roughness sublayer are less sensitive to the domain height.The Reynolds number effects on the dynamic characteristics and flow patterns are investigated.The turbulence intensity is stronger inside building cluster at high Reynolds number while turbulence intensity is almost unchanged with Reynolds number above the building cluster.Roughness height increases monotonously with Reynolds number by 20%from Re*=103 to Re*=105 but displacement height is almost unchanged.Within the canopy layer of heterogeneous building clusters,flow structures vary between buildings and turbulence is more active at high Reynolds number.     

Near-surface turbulence in the atmospheric boundary layer

Measurements of the near-surface turbulence in the atmospheric boundary layer have been made using hot-wire probes above the salt flats of northwestern Utah, where the momentum thickness Reynolds number, R_θ, is O(10⁶), and the surface is smooth and nearly devoid of flow obstructions. The measurements were made with arrays of up to 24 parallel straight sensors and with a modular 12-sensor probe capable of measuring all of the components of the instantaneous velocity vector and velocity gradient tensor. Measurements were also made in a laboratory wind tunnel at R_θ=1730 using 22 straight sensors. The data analysis focuses on the effects of the Reynolds number on turbulence properties and on the physics of the dissipation rate of turbulent kinetic energy.Some properties are found to be dependent on the Reynolds number when normalized with inner variables, while others are not. Among those that show the significant Reynolds number dependence are the rms and the skewness factor of the streamwise velocity fluctuations.Significant differences in flow structure, particularly those related to high rates of dissipation, are implied by the data. The joint PDF and covariance integrand of streamwise and wall normal vorticity fluctuations show less preferred orientation of the vorticity vector in the buffer layer at R_θ of O(10⁶) than at R_θ=1070. The largest contribution to the dissipation rate, at O(10⁶) is by the ∂w/∂z velocity gradient, while this term makes a quite small contribution to the dissipation rate at low R_θ. Here w and z are the spanwise velocity fluctuations and direction, respectively. Conditional analysis in the streamwise-wall normal (x−y) plane based on high instantaneous dissipation rate shows that the typical high dissipation rate events are generally similar at high and low Reynolds numbers, but display some significant differences.     

Characterizing the relative role of low-frequency and turbulent processes in the nocturnal boundary layer through the analysis of two-point correlations of the wind components

The study presents an analysis of two-point correlations between time series of nocturnal atmospheric wind, obtained from two micrometeorological towers, 45 m horizontally apart, each equipped with two sonic anemometers, 2.5 m vertically apart. It focuses on the scale dependence of the two-point correlations obtained from sensors vertically and horizontally separated. In particular, the role of low-frequency non-turbulent processes in the correlations is assessed, and compared to that of the turbulent scales of motion. The vertical correlations of the streamwise and vertical wind components show little dependence on the turbulence intensity, but those of the spanwise component decrease appreciably as it gets more turbulent. Multiresolution decomposition shows that the two-point correlations become increasingly dominated by low-frequency scales as it gets less turbulent, and that such large-scale processes are largely reduced in fully turbulent conditions. It is also shown that the vertical correlations of the spanwise wind component is negative for very small time scales. Horizontal two-point correlations obtained at the 45 m separation distance between the towers are almost entirely dominated by low-frequency motions, regardless of the turbulence intensity, but the magnitude of such correlations decreases with increasing turbulence intensity for any wind components. A comparison between the horizontal two-point correlations and autocorrelations taken with a time lag given by the ratio of the horizontal separation to the mean wind component in the direction that connects the two towers leads to the conclusion that the statistical properties of turbulence are often preserved over the horizontal distance, despite the lack of turbulence correlations for that separation.     

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.     

低速压气机叶栅附面层分离的实验研究

本文利用表面热膜对某高负荷压气机叶片吸力面附面层的分离过程进行了实验研究,捕捉到了边界层分离点的位置及其随攻角的变化情况,给出了利用表面热膜测量的准壁面剪切应力米预判分离先兆和分离点位置的判据.同时,分析了 Re数对附面层分离特性的影响.结果表明:准壁面剪切应力及其均方根极小值对应的位置点是进入分离泡内的第一个测量点;在所有测量的工况条件下,表面热膜都捕捉到了吸力面附面层的长分离泡,并能准确捕捉到攻角所引起的分离点位置变化;低Re数下,Re数对附面层分离影响较小.     

Vorticity,backscatter and counter-gradient transport predictions using two-level simulation of turbulent flows

The two-level simulation (TLS) method evolves both the large-and the small-scale fields in a two-scale approach and has shown good predictive capabilities in both isotropic and wall-bounded high Reynolds number (Re) turbulent flows in the past. Sensitivity and ability of this modelling approach to predict fundamental features (such as backscatter, counter-gradient turbulent transport, small-scale vorticity, etc.) seen in high Re turbulent flows is assessed here by using two direct numerical simulation (DNS) datasets corresponding to a forced isotropic turbulence at Taylor’s microscale-based Reynolds number Re_λ ≈ 433 and a fully developed turbulent flow in a periodic channel at friction Reynolds number Re_τ ≈ 1000. It is shown that TLS captures the dynamics of local co-/counter-gradient transport and backscatter at the requisite scales of interest. These observations are further confirmed through a posteriori investigation of the flow in a periodic channel at Re_τ = 2000. The results reveal that the TLS method can capture both the large- and the small-scale flow physics in a consistent manner, and at a reduced overall cost when compared to the estimated DNS or wall-resolved LES cost.     

Study of Automatic Transmission Fluid in a Serpentine Minichannel Heat Exchanger: An Experimental Approach

An experimental investigation was conducted on automatic transmission fluid cooling in a minichannel heat exchanger using a closed-loop integrated thermal wind tunnel test facility. Effects of automatic transmission fluid Reynolds number (Re_L) on heat transfer coefficient and Nusselt number were examined within the Re_L of 3–30 for air-flow Re of 1,450–5,200. Effects of serpentine on heat transfer enhancement and flow characteristics were evaluated through Dean number analysis. The analysis of Eckert number and Brinkman number showed a contribution to the viscous heating even for a low Re_L in the minichannel. The study showed enhanced heat transfer characterizations of the multi-port minichannel heat exchanger.     

The investigation of coherent structures in the wall region of a supersonic turbulent boundary layer based on DNS database

Through temporal mode direct numerical simulation, flow field database of a fully developed turbulent boundary layer on a flat plate with Mach number 4.5 and Reynolds number Reθ =1094 has been obtained. Commonly used detection meth- ods in experiments are applied to detecting coherent structures in the flow field, and it is found that coherent structures do exist in the wall region of a supersonic turbulent boundary layer. The detected results show that a low-speed streak is de- tected by using the Mu-level method, the rising parts of this streak are detected by using the second quadrant method, and the crossing regions from a low-speed streak to the high-speed one are detected by using the VITA method respectively. Notwithstanding that different regions are detected by different methods, they are all accompanied by quasi-stream-wise vortex structures.     

Intermittency,Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.     

Characterisation of backflow events over a wing section

Rare backflow (negative wall-shear stress) events have recently been found and quantified in the near-wall region of canonical wall-bounded turbulent flows. Although their existence and correlation with large-scale events have been established beyond numerical and measurement technique uncertainties, their occurrence at numerically high Reynolds numbers is still rare (less than 1 per thousand and 1 per million at the wall and beyond the viscous sublayer, respectively). To better quantify these rare events, the turbulent boundary layer developing over the suction side of a wing section, experiencing an increasing adverse pressure gradient (APG) without separation along its chord c, is considered in the present work. We find that the backflow level of 0.06% documented in turbulent channels and zero-pressure-gradient (ZPG) turbulent boundary layers is already exceeded on the suction side for x/c > 0.3, at friction Reynolds numbers three times lower, while close to the trailing edge the backflow level reaches 30%. Conditional analysis of extreme events indicates that for increasing Clauser pressure-gradient parameters (reaching β ? 35), the flow reaches a state in which the extreme events are more likely aligned with or against the freestream, and that the otherwise strong spanwise component of the wall-shear stress reduces towards the vicinity of the trailing edge. Backflow events subjected to moderate up to strong APG conditions (0.6 < β < 4.1) exhibit an average width of Δz⁺ ? 20, and an average lifetime of Δt⁺ ? 2. This directly connects with the findings by Lenaers et al., and implies that there is a connection between high-Re ZPG and strong APG conditions.     

圆形射流中心线上小尺度湍流的统计特性及其受高频噪声的影响

本文采用热线风速仪测量了出口雷诺数为Re (≡ U_jd/ν) = 20100的圆形射流的中心线轴向速度,其中U_j为动量平均出口速度,d为喷嘴出口直径,ν为运动黏性系数.在有效去除热线测量数据中的高频噪声后,作者对射流中心线上小尺度湍流统计量的变化规律进行了系统的分析.研究发现,射流在经过一定距离的发展后,其小尺度统计量逐渐进入自相似状态,湍动能平均耗散率ε随下游距离的增加以指数形 关键词： 恒温热线 圆形湍射流 耗散率 小尺度     

Scaling the characteristic time of the bursting process in the turbulent boundary layer

Characteristic time scales associated with bursting events in the turbulent boundary layer were examined over a very large range of Reynolds numbers based on momentum thickness of 1010, 2870, 4850, and 5×10⁶. Well-resolved hot-wire measurements were obtained at the lowest three Reynolds numbers in a low-speed wind tunnel with a long development length and compared to hot-wire and sonic anemometer measurements in the near-neutral atmospheric surface layer over the salt flats of Utah’s western desert. Bursting events were detected using the modified U-level threshold-crossing algorithm outlined by Luchik and Tiederman (1987) [1]. The same procedure and codes were used to analyze all time series records from both the wind tunnel and field experiments. The time between events, T_e, and the event duration, ΔT, were calculated and normalized using four different types of scalings: inner, outer, mixed, and Taylor microscales. It was found that both Reynolds number and wall-normal trends in the mode of T_e were eliminated when scaled by the Taylor microscale. Furthermore, constant (Reynolds number independent) values of the nondimensional meanT_e and ΔT were found in a narrow wall-normal region near the top of the buffer layer when the data were normalized by the Taylor microscale.     

Harbingers and latecomers – the order of appearance of exact coherent structures in plane Poiseuille flow

The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. We here discuss a variety of different structures that are relevant for the transition, compare the critical Reynolds numbers and optimal wavelengths for their appearance, and explore the differences between flows operating at constant mass flux or at constant pressure drop. The Reynolds numbers quoted here are based on the mean flow velocity and refer to constant mass flux. Reynolds numbers based on constant pressure drop are always higher. The Tollmien–Schlichting (TS) waves bifurcate subcritically from the laminar profile at Re = 5772 at wavelength 6.16 and reach down to Re = 2610 at a different optimal wave length of 4.65. Their streamwise localised counter part bifurcates at the even lower value Re = 2334. Three-dimensional exact solutions appear at much lower Reynolds numbers. We describe one exact solutions that has a critical Reynolds number of 316. Streamwise localised versions of this state require higher Reynolds numbers, with the lowest bifurcation occurring near Re = 1018. The analysis shows that the various branches of TS-waves cannot be connected with transition observed near Re ≈ 1000 and that the exact coherent structures related to downstream vortices come in at lower Reynolds numbers and prepare for the transition.