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.     

Mean momentum balance analysis of rough-wall turbulent boundary layers

Mean momentum balances (MMB) are carried out for zero pressure gradient rough-wall turbulent boundary layer flows. The balance characterizes the mean dynamical mechanisms and reveals dominant terms in the governing equation, which constitutes a necessary step in the derivation of scaling behaviors. The Reynolds stress profiles in rough-wall boundary layers are, however, quite scattered and the uncertainty in the data poses challenges for educing the MMB. The present study employs a method that invokes theoretical constraints to more reliably reveal Reynolds stress gradient behaviors in the presence of data scatter.Properties of the rough-wall mean momentum balances are compared to those of the smooth-wall case. Important qualitative features of the layer structure that exists for the smooth-wall are shown to also exist for rough-wall boundary layers. Specifically, the present analysis reveals the existence of a stress gradient balance layer, and thus the importance of the viscous force term well above the roughness crests. The smooth-wall Reynolds stress peak position scales in proportion with the geometric mean of inner-outer characteristic lengths. Roughness, however, imposes new dynamical length scales and evidence is provided to indicate that the scale separations between the inner length, roughness length, peak Reynolds stress length and outer length are important. The failure of the rough-wall Reynolds stress profiles to merge under smooth-wall meso-scalings clearly reveals the additional richness of the problem.Although more data are required to gain a complete characterization, the present results provide evidence that the combined roughness-Reynolds number problem exhibits significantly greater complexity than captured by the prevalent scheme for characterizing and classifying roughness regimes.     

Inflow conditions for spatial direct numerical simulation of turbulent boundary layers

The inflow conditions for spatial direct numerical simulation (SDNS) of turbulent boundary layers should reflect the characteristics of upstream turbulence, which is a puzzle. In this paper a new method is suggested, in which the flow field obtained by using temporal direct numerical simulation (TDNS) for fully developed turbulent flow (only flow field for a single moment is sufficient) can be used as the inflow of SDNS with a proper transformation. The calculation results confirm that this method is feasible and effective. It is also found that, under a proper time-space transformation, all statistics of the fully developed turbulence obtained by both temporal mode and spatial mode DNS are in excellent agreement with each other, not only qualitatively, but also quantitatively. The normal-wise distributions of mean flow profile, turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses of the fully developed turbulence obtained by using SDNS, bear similarity in nature. Supported by the National Natural Science Foundation of China (Grant No. 90205021), the China Postdoctoral Science Foundation (Grant No. 20060400707), and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200328), and partially supported by Liu-Hui Center of Applied Mathematics, Nankai University and Tianjin University     

High-order generalisation of the diagnostic scaling for turbulent boundary layers

The diagnostic scaling concept, introduced for the streamwise turbulence intensity in wall-bounded turbulent flows (Alfredsson, Segalini and Örlü, Phys. Fluids 2011;23:041702), is here extended and generalised not only for the higher even-order central statistical moments, but also for the odd moments and thereby the probability density distribution of the streamwise velocity fluctuations. Turbulent boundary layer data up to a friction Reynolds number of 60,000 are employed and demonstrate the feasibility of the diagnostic scaling for the data throughout the logarithmic and wake regions. A comparison with the generalised logarithmic law for even-order moments by Meneveau and Marusic (J. Fluid Mech. 2013;719:R1) based on the attached-eddy hypothesis, is reported. The diagnostic plot provides an apparent Reynolds-number-independent scaling of the data, and is exploited to reveal the functional dependencies of the constants needed in the attached-eddy-based model. In particular, the invariance of the lowest order diagnostic scaling poses an intriguing incompatibility with the asymptotic constancy of the Townsend–Perry constant.     

Effect of wall temperature on hypersonic turbulent boundary layer

Turbulent boundary layers at Mach 4.9 with the ratio of wall temperature to recovery temperature from 0.5 to 1.5 are investigated by means of direct numerical simulation. Various fundamental properties relevant to the influence of wall temperature on Morkovin’s scaling, standard and modified strong Reynolds analogies, and coherent vortical structures have been studied. It is identified that the scaling relations proposed for cool and adiabatic wall conditions, such as Morkovin’s scaling and the modified strong Reynolds analogy, are also applicable for hot wall condition. Moreover, the relation between the density and temperature fluctuations under the second-order approximation is derived and verified to provide a reliable prediction. Based on the analysis of coherent vortical structures, it is found that the orientation of vortex core can be quantitatively determined by means of the vector with its direction and modulus using the local strain direction and the imaginary part of the eigenvalue of velocity gradient tensor, respectively. As the increase of wall temperature, the spanwise distance between the two legs of hairpin vortex increases, and the mean swirling strength and the angle of vortical structure with respect to the wall plane also increase in the inner layer. The statistical properties relevant to vortical structures are nearly insensitive to the wall temperature in the outer layer.     

Spectral energy balance in dry convective boundary layers

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 1152²×400) were used, an inertial range with a ?5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to ?4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.     

不同光线入射角度下超声速湍流边界层气动光学效应的实验研究

利用基于纳米粒子的平面激光散射技术获取超声速(Ma=3.0)湍流边界层的密度分布,采用光线追迹方法计算其对应的光程差分布,并结合边界层气动光学相似律验证实验结果的可靠性.着重研究了光线入射角度对超声速湍流边界层气动光学效应的影响,并对其内在机理进行了分析.研究表明,气动光学效应对光线入射角度的依赖性源于光线在流场中的传输路径,传输路径的不同导致了光线在流场中的传输距离以及对应密度脉动互相关结果的差异.光线倾斜入射导致其在流场中传输距离增长,进而气动光学效应出现恶化.光线入射方向与壁面垂直方向之间的夹角越大,气动光学效应越显著,而且不同时刻的差异性增加,气动光学效应校正的难度增加.超声速湍流边界层中大量具有特定方向的涡结构导致了湍流边界层气动光学效应的各向异性.当光线倾斜向下游入射时,光线传播方向与流场中的涡结构具有较好的一致性,体现为此方向上密度脉动互相关系数较大,故气动光学效应比较严重.而当光线倾斜向上游入射时,相关系数较小,故气动光学效应较弱.     

Analysis of the turbulent boundary layer in the vicinity of a self-excited cylindrical Helmholtz resonator

This study investigates the changes in the structure of a turbulent boundary layer downstream of a flow-excited Helmholtz resonator. To this end, a fully developed turbulent boundary layer over a resonator mounted flush with a flat plate was simulated by implementing a large eddy simulation (LES). To assist in understanding the effect of the resonator on the flow structure, a sensitivity study was undertaken by changing the main geometrical parameters of the resonator. The results demonstrated that when the boundary layer thickness equals the orifice length, the cross-stream component of velocity fluctuations penetrates the boundary layer, resulting in a reduction of the turbulence intensity by up to 12%. Therefore, it is concluded that a Helmholtz resonator has the potential to reduce the instabilities within the boundary layer. These investigations also assist in identifying the optimal parameters to delay turbulence events within the grazing flow using Helmholtz resonators.     

A high-resolution code for turbulent boundary layers

A new high-resolution code for the direct simulation of incompressible boundary layers over a flat plate is described. It can accommodate a wide range of pressure gradients, and general time-dependent boundary conditions such as incoming wakes or wall forcing. The consistency orders of the advective and pressure-correction steps are different, but it is shown that the overall resolution is controlled by the higher-order advection step. The formulation of boundary conditions to ensure global mass conservation in the presence of arbitrary forcing is carefully analyzed. Two validation boundary layers with and without a strong adverse pressure gradient are presented, with maximum Reynolds numbers Re_θ≈2000${\mathit{Re}}_{\theta }\approx 2000$. They agree well with the available experiments. Turbulent inflow conditions for the zero-pressure case are implemented by a recycling method, and it is shown that at least the initial 300 momentum thicknesses have to be discarded before the effect of the artificial inflow is forgotten. It is argued that this is not a defect of the method used to generate the inflow, but a property of the boundary layer.     

Interaction between strain and vorticity in compressible turbulent boundary layer

The interaction of strain and vorticity in compressible turbulent boundary layers at Mach number 2.0 and 4.9 is studied by direct numerical simulation(DNS)of the compressible Navier-Stokes equations.Some fundamental characteristics have been studied for both the enstrophy producing and destroying regions.It is found that large enstrophy production is associated with high dissipation and high enstrophy,while large enstrophy destruction with moderate ones.The enstrophy production and destruction are also correlated with the dissipation production and destruction.Moreover,the enstrophy producing region has a distinct tendency to be‘sheet-like’structures and the enstrophy destroying region tends to be‘tube-like’in the inner layer.Correspondingly,the tendency to be‘sheet-like’or‘tube-like’structures is no longer obvious in the outer layer.Further,the alignment between the vorticity vector and the strain-rate eigenvector is analyzed in the flow topologies.It is noticed that the enstrophy production rate depends mainly on the alignment between the vorticity vector and the intermediate eigenvector in the inner layer,and the enstrophy production(destruction)mainly on the alignment between the vorticity vector and the extensive(compressive)eigenvector in the outer layer.     

Temporal evolution of optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the short-exposure optical transfer function.     

Dynamic model of coherent structure in the wall region of a turbulent boundary layer

Based on the theoretical model for a single coherent structure in the wall region of a turbulent boundary layer, we studied the interaction of two coherent structures by direct numerical simulation in order to explain the mechanism for the formation of low-speed streaks.     

Effects of single synthetic jet on turbulent boundary layer

The turbulent boundary layer (TBL) is actively controlled by the synthetic jet generated from a circular hole. According to the datasets of velocity fields acquired by a time-resolved particle image velocimetry (TR-PIV) system, the average drag reduction rate of 6.2% in the downstream direction of the hole is obtained with control. The results of phase averaging show that the synthetic jet generates one vortex pair each period and the consequent vortex evolves into hairpin vortex in the environment with free-stream, while the reverse vortex decays rapidly. From the statistical average, it can be found that a low-speed streak is generated downstream. Induced by the two vortex legs, the fluid under them converges to the middle. The drag reduction effect produced by the synthetic jet is local, and it reaches a maximum value at x⁺=400, where the drag reduction rate reaches about 12.2%. After the extraction of coherent structure from the spatial two-point correlation analysis, it can be seen that the synthetic jet suppresses the streamwise scale and wall-normal scale of the large scale coherent structure, and slightly weakens the spanwise motion to achieve the effect of drag reduction.     

Temporal evolution of the optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of the OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the shortexposure optical transfer function.     

Numerical analysis of shock wave and supersonic turbulent boundary interaction between adiabatic and cold walls

Direct numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a 24° compression ramp with adiabatic and cold-wall temperatures are conducted. The wall temperature effects on turbulence structures and shock motions are investigated. The results are validated against previous experimental and numerical data. The effects of wall cooling on boundary layer characteristics are analysed. Statistical data show that wall cooling has a significant effect on the logarithmic region of mean velocity profile downstream the interaction region. Moreover, the influence of wall temperature on Reynolds stress anisotropy is mainly limited in the near-wall region and has little change on the outer layer. As the wall temperature decreases, the streamwise coherency of streaks increases. Based on the analysis of instantaneous Lamb vector divergence, the momentum transport between small-scale vortices on cold-wall condition is significantly enhanced. In addition, spectral analysis of wall pressure signals indicates that the location of peak of low-frequency energy shifts toward higher frequencies in cold case. Furthermore, the dynamic mode decomposition results reveal two characteristic modes, namely a low-frequency mode exhibiting the breathing motion of separation bubble and a high-frequency mode associated with the propagation of instability waves above separation bubble. The shape of dynamic modes is not sensitive to wall temperature.     

机体表面湍流边界层噪声特性及预测方法研究

湍流边界层噪声是飞机巡航过程中的主要外部噪声源,对舱内噪声水平的影响尤为重要。因此,对飞机机体表面湍流边界层噪声的研究具有重要意义。本文通过试验获得了某型民机巡航过程中的湍流边界层噪声,试飞工况为3500ft/0.78、3500ft/0.7、2500ft/0.67、1500ft/0.66。对实测数据进行分析,发现湍流边界层噪声与动压、边界层厚度等参数有关。同时,利用计算流体力学的方法得到了飞机机体表面的压力分布,并分析了压力梯度对湍流边界层噪声的影响。最后,基于工程预测方法对湍流边界层噪声进行了预测,对于不存在逆压梯度的区域,预测结果与试验结果吻合较好,仅部分频段存在一定偏差。通过对模型的参数进行优化,改善了预测结果。     

DNS of compressible turbulent boundary layer over a blunt wedge

Wall turbulence is more complicated than free turbulence, and the direct numerical simulation (DNS) of wall turbulence is more difficult. In recent years, most of DNS cases for wall turbulence are simplified by using temporal mode, where streamwise pe- riodic boundary condition is imposed. In temporal mode, spatial transition will be con- sidered as an analogue of time-evolving transition. For the channel turbulence, an equivalent body force can substitute for the mean gradient of pressure, …     

Predetermined control of turbulent boundary layer with a piezoelectric oscillator

With a piezoelectric(PZT) oscillator, the predetermined controls of the turbulent boundary layer(TBL) are effective in reducing the drag force. The stream-wise velocities in the TBL are accurately measured downstream of the oscillator driven by an adjustable power source. The mean velocity profiles in the inner and outer scales are reported and the skin friction stresses with different voltage parameters are compared. Reduction of integral spatial scales in the inner region below y+of 30 suggests that the oscillator at work breaks up the near-wall stream-wise vortices responsible for high skin friction. For the TBL at Reθof 2183, the controls with a frequency of 160 Hz are superior among our experiments and a relative drag reduction rate of 26.83% is exciting. Wavelet analyses provide a reason why the controls with this special frequency perform best.