A proposed intermittency measurement method for transitional boundary layer flows

A new turbulent intermittency detector method, based on the Turbulent Energy Recognition Algorithm (TERA), has been proposed. Its performance was compared with two other available methods using the data obtained from hot-wire measurements in a developing boundary layer flow on a concave surface with constant radius of curvature of 2 m. Comparisons show that this new method is better than the other two as a turbulent detector under the same flow conditions, especially in the near-wall and in the outer and outside regions of the boundary layer.     

Statistical modeling of the turbulent transition in the boundary layer

A method of statistical modeling the flow in the boundary-layer transition region is proposed on the basis of experimental data on kinematics and dynamics of turbulent spots (Emmons spots) on a flat plate in an incompressible fluid. This method allows one to determine the intermittency with allowance for overlapping of the spots, the forces on the plate surface, and the flow field in the vicinity of the transition region if the field of the streamwise component of the mean velocity in the developed turbulent boundary layer is known as a function of the Reynolds number. In contrast to multi-parameter models of the transition, this approach makes it possible to avoid the use of physically meaningless parameter values.     

Comparison of Two Unsteady Intermittency Models for Bypass Transition Prediction on a Turbine Blade Profile

The present paper evaluates two unsteady transition modelling approaches: the prescribed unsteady intermittency method PUIM, developed at Cambridge University and the dynamic unsteady intermittency method developed at Ghent University. The methods are validated against experimental data for the N3-60 steam turbine stator profile for steady and for unsteady inlet flow conditions. The characteristic features of the test case are moderately high Reynolds number and high inlet turbulence intensity, which causes bypass transition. The tested models rely both on the intermittency parameter and are unsteady approaches. In the prescribed method, the time-dependent intermittency distribution is obtained from integral relations. In the dynamic method, the intermittency distribution follows from time-dependent differential equations. For unsteady computations, self-similar wake profiles are prescribed at the inlet of the computational domain. Joint validation of the prescribed and the dynamic unsteady intermittency models against experimental data shows that both methods are able to reproduce the global features of the periodical evolution of the boundary layer under the influence of a periodically impinging wake. The overall quality of the dynamic method is better than that of the prescribed method.     

Development of an Intermittency Equation for the Modeling of the Supersonic/Hypersonic Boundary Layer Flow Transition

An intermittency transport equation is developed in this study to model the laminar-turbulence boundary layer transition at supersonic and hypersonic conditions. The model takes into account the effects of different instability modes associated with the variations in Mach numbers. The model equation is based on the intermittency factor γ concept and couples with the well-known SST k–ω eddy-viscosity model in the solution procedures. The particular features of the present model approach are that: (1) the fluctuating kinetic energy k includes the non-turbulent, as well as turbulent fluctuations; (2) the proposed transport equation for the intermittency factor γ triggers the transition onset through a source term; (3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ, which are often cost-ineffective with the modern CFD methods; (4) in the fully turbulent region, the model retreats to SST model. This model is validated with a number of available experiments on boundary layer transition including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition with a reasonably wide range of Mach numbers.     

Extension of an algebraic intermittency model for better prediction of transition in separated layers under strong free-stream turbulence

A constitutive law describing the Reynolds stresses in boundary layers undergoing laminar-to-turbulent transition, constructed in previous work by elastic-net regression on an experimental data base, is used to improve an algebraic intermittency model for cases with transition in a separated layer influenced by a high level of free-stream turbulence. The intermittency model is combined with a k-ω turbulence model and the basic version, developed in previous work, functions well for bypass transition in attached boundary layers and for transition in separated boundary layers under a low free-stream turbulence level. The basic model version is extended by an additional production term in the transport equation for turbulent kinetic energy. A sensor detects the front part of a separated layer and activates the production term. The term expresses the effect of Klebanoff streaks generated upstream of separation on the Kelvin-Helmholtz instability rolls in the separated part of the layer. The Klebanoff streaks cause faster breakdown by the combined effects of a large adverse pressure gradient and an elevated free-stream turbulence level. The extended model does not alter the results of the basic model version for bypass transition in an attached boundary layer and for transition in a separated boundary layer under a low free-stream turbulence level. The extended model significantly improves the predictions of the previous model version for transition in a separated boundary layer under a high free-stream turbulence level.     

Transitional intermittency detection by neural network

 A neural network has been used to predict the flow intermittency from velocity signals in the transition zone in a boundary layer. Unlike many of the available intermittency detection methods requiring a proper threshold choice in order to distinguish between the turbulent and non-turbulent parts of a signal, a trained neural network does not involve any threshold decision. The intermittency prediction based on the neural network has been found to be very satisfactory. Received: 15 December 1997/Accepted: 30 December 1998     

Improved methods for measuring laminar-turbulent intermittency in boundary layers

The last stage of laminar-turbulent transition in boundary layers is commonly described using the spatial distribution of intermittency. Existing methods for computing this laminar-turbulent intermittency from experimental data involve the use of thresholds that are set by the experimentalist using subjective comparisons to the raw signal. These threshold settings cannot be reproduced by other experimentalists using different equipment, so a precise determination of intermittency is not currently possible. This note reports on a new method of determining boundary-layer intermittency that appears to be objective and reproducible. The wall shear was measured in a flat-plate boundary layer using hot-film sensors. Probability density functions (PDF's) of the calibrated wall shear are remarkably consistent. A correlation to the turbulent portion of these PDF's is given. The consistency observed in these PDF's suggests an objective and reproducible setting for the laminar-turbulent cutoff threshold. Intermittencies determined using this method can be compared quantitatively, with any differences being caused only by experimental error or differences in the flows. The universality of the method can be determined through comparisons to measurements in other flows.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

Boundary layer development from transition provoking devices

The results of an experimental investigation of four different, incompressible, transitional boundary layer situations are presented. The experiments were carried out in zero pressure gradient conditions and transition was initiated from two- and from three-dimensional provoking agents.

The measurements of transitional intermittency from two-dimensional tripping agents showed a trend consistent with that reported elsewhere in the literature, with the development of mean and fluctuating component velocity profiles and local skin friction coefficient exhibiting approximate similarity through the transition region.

Disturbance frequency and spread angles for turbulent wedge growth behind isolated roughness elements were similar to those reported by others.

Computer predictions using a transition model based on the present correlations show reasonable agreement with the data.     

Large-Eddy BreakUp Devices – a 40 Years Perspective from a Stockholm Horizon

In the beginning of the 1980’s Large Eddy BreakUp (LEBU) devices, thin plates or airfoils mounted in the outer part of turbulent boundary layers, were shown to be able to change the turbulent structure and intermittency as well as reduce turbulent skin friction. In some wind-tunnel studies it was also claimed that a net drag reduction was obtained, i.e. the reduction in skin-friction drag was larger than the drag on the devices. However, towing-tank experiments with a flat plate at high Reynolds numbers as well as with an axisymmetric body showed no net reduction, but instead an increase in total drag. Recent large-eddy simulations have explored the effect of LEBUs on the turbulent boundary layer and evaluations of the total drag show similar results as in the towing tank experiments. Despite these negative results in terms of net drag reduction, LEBUs manipulate the boundary layer in an interesting way which explains why they still attract some interest. The reason for the positive results in the wind-tunnel studies as compared to drag measurements are discussed here, although no definite answer for the differences can be given.     

自然对流边界层中湍流的发生

自然对流边界层中从层流到湍流的转捩经历了浮力振型、无摩擦振型和黏性振型的三重流动不稳定性相继产生的前转捩过程,以及近壁迅速出现强湍流源,随之平缓地向自模拟的湍流边界层过渡的热转捩过程.浮力振型在修正Grashof数G>40时开始失稳并成为主要振型,在振幅分布中3种振型的临界层位置处出现3个峰值;在G>100时浮力振型消失,无摩擦振型失稳并成为主要振型,振幅分布中在近壁区还出现黏性振型的峰值;在G>170时无摩擦振型经非线性演化在外层形成较弱的湍流,但内层黏性应力仍远高于湍流应力,振幅分布中仅有与黏性振型相应的峰值,在频谱中黏性振型的基频、第一、第二、第三阶亚谐频随G的增加相继出现,此时黏性不稳定波的高频成分已转化为湍流,但低频成分仍按线性规律增长,直至湍流惯性子区开始形成;至G>800时黏性振型消失,并在G=850附近时近壁区出现强湍流源,湍流应力、湍能产生项和近壁湍流热流率剧增.在热转捩后期,湍流应力和湍能产生项明显下降,流动在内外层趋于平衡.     

MODELLING OF BYPASS TRANSITION WITH CONDITIONED NAVIER–STOKES EQUATIONS COUPLED TO AN INTERMITTENCY TRANSPORT EQUATION

A differential method is proposed to simulate bypass transition. The intermittency in the transition zone is taken into account by conditioned averages. These are averages taken during the fraction of time the flow is turbulent or laminar respectively. Starting from the Navier–Stokes equations, conditioned continuity, momentum and energy equations are derived for the laminar and turbulent parts of the intermittent flow. The turbulence is described by a classical k−ϵ model. The supplementary parameter, the intermittency factor, is determined by a transport equation applicable for zero, favourable and adverse pressure gradients. Results for these pressure gradients are given.     

金属丝壁面加热湍流标度律的实验研究

通过在固壁表面的平板湍流边界层沿流向平行放置若干通电加热的金属细丝,在平板表面形成沿展向周期性分布的温度场,利用该温度场引起的空气热对流,在湍流边界层近壁区域产生一组沿湍流边界层展向周期分布的流向涡结构。对壁湍流小尺度结构标度律统计特性的研究表明,金属丝加热后形成的规则流向涡结构将壁湍流各种尺度湍涡结构不规则的脉动有序地组织起来,增强了湍流小尺度结构的层次结构相似性,减小了壁湍流中小尺度结构的间歇性和奇异性,抑制了壁湍流中奇异的湍涡结构。     

The effect of modeled drag reduction on the wall region

The low-dimensional model derived for the wall region of a turbulent boundary layer (Aubry et al., 1988) is applied to a drag-reduced flow. In agreement with some experimental results, drag reduction is modeled by thickening the wall region, which is achieved by applying stretching transformations to the original flow. By application of a Galerkin projection, a set of ordinary differential equations (ODEs) is obtained whose structure is identical to the set corresponding to the unmodified flow. The coefficients of the ODEs are modified in a nontrivial way. The bifurcation diagrams plotted for different values of the stretching parameter are different in detail but the structure is globally the same. In particular, the intermittent behavior which Aubry et al. identified with the cyclic bursting events experimentally observed is still present. The scenario by which intermittency appears through a subcritical Hopf bifurcation in which a heteroclinic cycle is created and disappears through a bifurcation to traveling waves is identical. These results hold for values of the stretching between 1 and 2.65, the value at which the top of the buffer layer reaches the centerline of the pipe. This is in agreement with experimental results for flows whose drag is reduced but which still display intermittency. The bifurcations occur in the stretched flow at increased levels of dissipation (relative to the unstretched flow), consistent with theoretical pictures of drag reduction, in which the increase of scale is due to stabilization by an increase of dissipation in the turbulent part of the flow. Moreover, this method is a systematic way to perturb the coefficients of the ODEs of Aubry et al. (1988). Under this kind of perturbation, the behavior of the solution (in the part of the bifurcation diagram physically relevant) is found to be extremely robust.     

壁湍流边界层奇异标度律的实验研究

采用热线风速仪对平板湍流边界层的流向速度进行测量,用速度结构函数研究不同尺度结构标度律的变化规律,结果显示小尺度区的概率密度曲线尾部明显偏离高斯型,说明高幅值间歇性事件占的份额较多;惯性子区的曲线向高斯型靠近,间歇性事件所占份额减少;大尺度结构的曲线趋于高斯型,间歇性事件所占份额最小。在耗散区、惯性子区和较大的尺度结构区存在大小不同的绝对标度指数,越靠近壁面这些区域的标度指数均越偏离p/3而逐渐变小。绝对标度指数与边界层位置有关,在缓冲层各阶标度指数与线性标度律偏差很大,显示较强的奇异性,当过渡到对数层及外区,标度指数逐渐增大,接近均匀各向同性湍流的状态。缓冲层、对数层及外区具有各异的绝对标度指数增长率,与各层的不同湍流结构特征和运动形式有关。     

湍流能量耗散率标度律实验研究

应用粒子图像测速(PIV)系统对平板湍流边界层内流向和法向的瞬时速度进行了测量。湍流的能量耗散率由轴对称假设得到,同时在研究湍流动能耗散率标度律的过程中采用传统的统计学方法。实验结果显示,对于不同尺度上和不同法向位置湍流耗散率标度律来说,湍流耗散主要发生在小尺度上,也就是说湍动能耗散率标度律在小尺度上具有普适性。另外,根据层次结构理论假设,通过PIV实验数据对最高激发态的标度指数进行了研究,结果发现,最高激发态存在绝对标度指数,并且绝对标度律是由信号中最强耗散涨落的局部结构产生的。     

Direct Numerical Simulation of an Accelerating Channel Flow

Direct Numerical Simulation of a linearly accelerating channel flow starting from an initially statistically steady turbulent flow has been performed. It is shown that the response of the accelerating flow is fundamentally the same as that of the step-change transient flow described in He and Seddighi (J Fluid Mech 715:60–102, 2013). The flow structure again behaves like a boundary layer bypass transition undergoing three distinct phases, namely, (i) initially (pre-transition), the flow is laminar-like and the pre-existing turbulent structures are modulated resulting in elongated streaks leading to a strong and continuous increase in the streamwise fluctuating velocity but little changes in the other two components; (ii) it then undergoes transition when isolated turbulent spots are generated which spread and merge with each other, and (iii) they eventually cover the entire surface of the wall when the flow is fully turbulent. The similarity between the turbulence responses in the two flows is significant noting the contrasting features of the two types of mean flow unsteadiness: in the step-change flow, a sharp boundary layer is resulted in nearly instantly on the wall which closely resembles the spatially developing boundary layer, whereas the linear flow acceleration causes a continuing change of velocity gradient adjacent to the wall which propagates into the flow field with time, resulting in a gradually-developing boundary layer. There are, however, quantitative differences in the detailed behavior of the two flows and especially the transition is much delayed in the accelerating flow. It is also shown that the late pre-transition and early transition stages in both flows are characterised by significantly increased inwards sweep events in the wall region and ejection events in the outer layer. The flatness of the wall-normal velocity increases markedly near the wall around the time of onset of transition as a consequence of the huge intermittency of the velocity fluctuations. That is, there are long periods of quiescent flow coupled with occasional turbulent bursts.     

A three-velocity-component laser-Doppler velocimeter for measurements inside the linear compressor cascade

A 24′′ (610 mm) access laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements in a low speed linear cascade wind tunnel with moving wall simulation. The probe has a 610 mm access length and achieves a measurement spatial resolution of 100 μm by using off-axis optical heads. With the relatively large access length, the LDV probe allows for measurements from the side of a wind tunnel instead of through the tunnel floor, while the high spatial resolution allows for quality near-wall measurements. The probe has been tested in a zero-pressure gradient 2D turbulent boundary layer and the test results agree well with the experimental data measured with different LDV systems and hot-wire anemometery for the boundary layer flows. The energy spectral density was estimated using a slot correlation, and Von Kármán’s model for the energy-spectrum function was used to analyze the measured spectral data to estimate the turbulent kinetic energy dissipation rate, which compares favorably with the measured production values in the log-layer region of the turbulent boundary layer. Measurements are presented for the moving endwall boundary layer at the inlet of the linear compressor cascade facility to validate the capability of this LDV for tip leakage flow measurements. These results indicate that the moving endwall reduces velocity gradients in the near-wall region and results in less production of Reynolds stresses and turbulent kinetic energy compared to the stationary endwall case.     

An investigation of the scales in transitional boundary layers under high free-stream turbulence conditions

The scales in a transitional boundary layer subject to high (initially 8%) free-stream turbulence and strong acceleration (K as high as 9×10^–6) were investigated using wavelet spectral analysis and conditional sampling of experimental data. The boundary layer shows considerable evolution through transition, with a general shift from the lower frequencies induced by the free-stream unsteadiness to higher frequencies associated with near-wall-generated turbulence. Within the non-turbulent zone of the intermittent flow, there is considerable self-similarity in the spectra from the beginning of transition to the end, with the dominant frequencies in the boundary layer remaining constant at about the dominant frequency of the free-stream. The frequencies of the energy-containing scales in the turbulent zone change with streamwise location and are significantly higher than in the non-turbulent zone. When normalized on the local viscous length scale and velocity, however, the turbulent zone spectra also show good self-similarity throughout transition. Turbulence dissipation occurs almost exclusively in the turbulent zone. The velocity fluctuations associated with dissipation are isotropic, and their normalized spectra at upstream and downstream stations are nearly identical. The distinct differences between the turbulent and non-turbulent zones suggest the potential utility of intermittency based transition models in which these zones are treated separately. The self-similarity noted in both energy containing and dissipation scales in both zones suggests possibilities for simplifying the modeling for each zone.

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Large-Eddy Simulation of Transition to Turbulence in Boundary Layers

Large-eddy simulation (LES) results for laminar-to-turbulent transition in a spatially developing boundary layer are presented. The disturbances are ingested into a laminar flow through an unsteady suction-and-blowing strip. The filtered, three-dimensional time-dependent Navier–Stokes equations are integrated numerically using spectral, high-order finite-differences, and a three-stage low-storage Runge–Kutta/Crank–Nicolson time-advancement method. The buffer-domain technique is used for the outflow boundary condition. The localized dynamic model used to parametrize the subgrid-scale (SGS) stresses begins to have a significant impact at the beginning of the nonlinear transition (or intermittency) region. The flow structures commonly found in experiments are also observed in the present simulation; the computed linear instability modes and secondary instability $\Lambda$-vortex structures are in agreement with the experiments, and the streak-like structures and turbulent statistics compare with both the experiments and the theory. The physics captured in the present LES are consistent with the experiments and the full Navier–Stokes simulation (DNS), at a significant fraction of the DNS cost. A comparison of the results obtained with several SGS models shows that the localized model gives accurate results both in a statistical sense and in terms of predicting the dynamics of the energy-carrying eddies, while requiring fewer ad hoc adjustments than the other models. Received: 5 April 1996 and accepted 27 March