Streaky Structures Research Articles

Identification of coexisting dynamics in boundary layer flows through proper orthogonal decomposition with weighting matrices

A different version of the classic proper orthogonal decomposition (POD) procedure introducing spatial and temporal weighting matrices is proposed. Furthermore, a newly defined non-Euclidean (NE) inner product that retain similarities with the POD is introduced in the paper. The aim is to emphasize fluctuation events localized in spatio-temporal regions with low kinetic energy magnitude, which are not highlighted by the classic POD. The different variants proposed in this work are applied to numerical and experimental data, highlighting analogies and differences with respect to the classic and other normalized variants of POD available in the literature. The numerical test case provides a noise-free environment of the strongly organized vortex shedding behind a cylinder. Conversely, experimental data describing transitional boundary layers are used to test the capability of the procedures in strongly not uniform flows. By-pass and separated flow transition processes developing with high free-stream disturbances have been considered. In both cases streaky structures are expected to interact with other vortical structures (i.e. free-stream vortices in the by-pass case and Kelvin–Helmholtz rolls in the separated type) that carry a significant different amount of energy. Modes obtained by the non-Euclidean POD (NE-POD) procedure (where weighted projections are considered) are shown to better extract low energy events sparse in time and space with respect to modes extracted by other variants. Moreover, NE-POD modes are further decomposed as a combination of Fourier transforms of the related temporal coefficients and the normalized data ensemble to isolate the frequency content of each mode.

Time-resolved wake dynamics of finite wall-mounted circular cylinders submerged in a turbulent boundary layer

Abstract

Infrared high-speed thermography of combustion chamber wall impinged by diesel spray flame

As a demonstration of a new method to examine the extremely unsteady and spatially varying wall heat transfer phenomena on diesel engine combustion chamber wall, high-speed imaging of infrared thermal radiation from the wall surface impinged by a diesel spray flame was attempted using a high-speed infrared camera. A 35 mm-diameter chromium-coated quartz window surface was impinged by a diesel spray flame with an impinging distance of 27 mm from the nozzle orifice in a constant volume combustion chamber. The infrared thermal radiation from the back surface of the 0.6 µm thick chromium layer was successfully visualized at 10 kHz frame rate and 128 × 128 pixel resolution through the quartz window. The infrared radiation exhibited coherent and streaky structure with radial stripes extending and waving from the stagnation point. The width of the radial stripes, spatial amplitude and the period of the waving movement were comparable to the ones for turbulent heat transfer on the engine cylinder wall previously measured with a heat flux sensor, suggesting that they are resulting from the turbulent structure in the wall-impinging diesel flame. The radiation intensity was calibrated to temperature and converted to heat flux via 3-D numerical analysis of transient thermal conduction in the quartz window. The peak-to-peak variation amplitudes of temperature and heat flux among the radial stripes during the diesel spray flame impingement were about 20 K and 2.3 MW/m2, corresponding to 13% of 150 K maximum temperature swing amplitude and 18 MW/m2 maximum heat flux, respectively.

Inspection of structures interaction in laminar separation bubbles with extended proper orthogonal decomposition applied to multi-plane particle image velocimetry data

This work reports the application of an extended proper orthogonal decomposition (E-POD) procedure to multi-plane particle image velocimetry (PIV) measurements describing the evolution of laminar separation bubbles (LSBs). Measurements were performed over a flat plate installed between adjustable end-walls providing a prescribed adverse pressure gradient for two Reynolds numbers (Re = 70 000, 150 000) and free-stream turbulence intensity levels (Tu = 1.5%, 2.5%). A wall-normal and two wall-parallel measuring planes located at different distance from the wall were considered. POD was applied to the entire PIV planes as well as on their sub-domains, showing the main flow features occurring in the different regions of the LSB. Then, the application of E-POD on different plane partitions revealed the existing correlation between the main dynamics observed in the forward part of the bubble and the breakup events occurring in the reattachment region. The E-POD modes computed in the breakup region resemble streaky structures when PIV snapshots are projected onto the POD eigenvectors of the near wall plane. Otherwise, Kelvin–Helmholtz rolls dominate the E-POD modes obtained by projection of the snapshot matrices on the basis computed in the plane located far from the wall. The main scales of the coherent structures highlighted by the E-POD modes were also characterized by means of the streamwise and spanwise autocorrelation functions of E-POD filtered fields. Data in this work clearly highlight the similarity properties of the main flow features observed in LSBs once scaled with the momentum thickness of the boundary layer at the separation position.

Mechanisms of entrainment in a turbulent boundary layer

Data from direct numerical simulation of a zero-pressure-gradient incompressible turbulent boundary layer (TBL) [You and Zaki, “Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances,” J. Fluid Mech. 866, 526 (2019)] are analyzed to examine the entrainment process. The two mechanisms by which the outer irrotational flow can be entrained into the turbulent region and their relative contribution to the growth of the spatially developing boundary layer are evaluated: (i) nibbling is the enstrophy transport across the turbulent/non-turbulent interface (TNTI), and (ii) engulfment is the entrapment of pockets of irrotational flow inside the TBL prior to finally breaking apart. The relative importance of the two mechanisms depends on the normalized vorticity threshold adopted to identify the TNTI. Our choice of this threshold highlights the structure of the TNTI and entrainment within this layer by engulfment of irrotational pockets. The sizes of the engulfed pockets are of the same order as the heads of the hairpin vortices underneath the TNTI. The vortices straddle larger streaky structures of internal layers and cause handle shaped deformations on the TNTI, which leads to engulfment as they fold onto themselves and entrap the external potential flow. Three dynamical regions are distinguished: a TNTI region (interface layer), an adjustment region, and the turbulent core. The first of these is further sub-divided into a viscous superlayer and a turbulent sublayer. It is shown as the irrotational fluid elements cross the interface layer toward the turbulent core, a smooth transition from the non-focal topology to the well-known primarily focal topology of fully developed turbulence occur. The viscous superlayer is similar to previously studied flow configurations, such as jets and mixing layers. In contrast, vorticity stretching in the turbulent sublayer is significantly weaker in the boundary layer relative to free-shear flows, which results in a smaller rate of entrainment by nibbling.

On dispersion relation for Faraday waves in a near-critical fluid under weightlessness

One reports experiments and numerical simulations of Faraday waves at the liquid - vapor interface of fluids (typically CO2 and H2) near its critical point when submitted to vibration in a weightlessness environment. It is known that in such a system striation is formed under the action of vibrations. The boundary between the liquid and gas phases is located perpendicular to the direction of vibrations, and a streaky structure in the form of periodic stripes (striations) is formed in the cavity. It is shown that under vibrations of sufficient intensity an instability develops on the striation interface perpendicular to the direction of vibrations, leading to Faraday waves. A theoretical and numerical study of this instability is carried out, the critical parameters of the appearance of Faraday waves are determined taking into account the interaction of waves on adjacent striations. Dispersion relations for Faraday waves are obtained numerically. It is shown that in the vicinity of the critical point there is a significant deviation of the dispersion relation from the classical theoretical dependence.

Flow visualization and skin friction determination in transitional channel flow

The present study experimentally determines the transitional Reynolds number range for plane channel flow and characterizes its transitional state. The pressure along the channel is measured to determine the skin friction coefficient as function of Reynolds number from the laminar state, through the transitional region into the fully turbulent state. The flow structure was studied through flow visualisation which shows that as the Reynolds number increases from the laminar state the transitional region starts showing randomly occurring turbulent spots. With increasing Reynolds number the spots shift into oblique patches and bands of small scale turbulence that form across the channel width, together with large-scale streaky structures found in areas between the turbulent regions. An image analysing technique was used to determine the intermittency factor, i.e. the turbulence fraction in the flow, as function of Reynolds number. It is found that the skin friction coefficient reaches its turbulent value before the flow is fully turbulent (the intermittency factor is still below one). This suggests that the observed streaky structures in non-turbulent regions contribute to the enhancement of the wall-normal transfer of momentum. Also above the Reynolds numbers where the turbulent skin friction coefficient has been established large-scale features consisting of irregular streaky structures are found. They have an oblique shape similar to the non-turbulent and turbulent patches in the transitional flow indicating that the transition process is not fully complete even above the Reynolds number where the skin friction reaches its turbulent level.Graphic abstractProcessing of flow visualization images to determine the turbulenceintermittency in the transitional region. Flow is from left to right, (a)unprocessed, (b) filtered (c) standard deviation of (b), (d) binary picture

Исследование развития локализованных возмущений в пограничном слое плоской пластины в условиях повышенной степени турбулентности набегающего потока за уступом поверхности

In a wind tunnel on a flat plate in a separated flow behind a rectangular step, the emergence and development of localized disturbances generated by low-frequency impulse deviations of the local surface section under conditions of low and moderate degrees of the incoming flow turbulence is studied. The results were obtained by hot-wire anemometry at low subsonic flow velocity. It was found that impulse deviations of the wall generate disturbances, which are socalled Streaky structures and wave packets of oscillations. The separation of the laminar boundary layer accelerates the growth of wave packets with subsequent turbulization of the near-wall flow. The specific features of the behavior of localized disturbances under conditions of moderate degree of free-stream turbulence are revealed.

Investigation on the boundary layer transition with the effects of periodic passing wakes

The boundary layer transition caused by wake is a problem related to basic fluid mechanics and engineering applications. In this paper, the interaction between the periodic passing wakes induced by moving cylinders and the boundary layer of the plate is investigated by large eddy simulation, and experiments in a low-speed water tunnel are designed to verify the simulations. The flow field velocity is measured by high-resolution pressure sensors and two-dimensional particle image velocimetry. The effects of wake passing frequencies fN = 0.63, 1, and 1.26 on the time average and statistical average characteristics of the boundary layer transition and the instantaneous flow structure are studied. The influence of large-scale wakes on the integral parameters of boundary layer thickness, skin friction coefficients, time-averaged velocity distributions, and velocity fluctuations is addressed. The results show that the onset of transition moves to the leading edge of the plate as the wake passing frequency increases, while the location of transition completion moves to the end of the plate. The specific boundary layer transition process is analyzed through the spanwise pocket and streamwise streaky structure propagation. The vortex structures in the boundary layer are extracted by the Q criterion, and the results show that the spanwise secondary vortex on the pressure side induced by the large-scale wake gradually loses its stability and results in transition. Moreover, the hairpin vortex in the suction surface continually lifts up the wall-normal location of the breakdown event. Thus, it turns the turbulence spot arrowhead pointing downstream into pointing upstream.

Spatial characteristics of turbulent organized structures within the roughness sublayer over idealized urban surface with obstacle-height variability

The effects of obstacle-height variability on spatial characteristics of turbulent organized structures were investigated with the use of a large-eddy simulation technique for airflows over roughness obstacles. Two-types simulation cases were considered: one is uniform-height case in which uniform-height obstacles are aligned in streamwise direction, the other is height-variability case with staggered higher-height obstacles. Streaky structures were observed above the roughness sublayer (RSL) regardless of obstacle-height variability. When obstacles are uniform, flow fields within the RSL contain low- and high-speed regions along the streamwise streets. When obstacle heights vary, airflow within the RSL collides with the front-facing surfaces of taller obstacles. The statistical features of low- and high-speed structures were examined using the spatial correlations of flow fields centering on strong ejection and sweep, respectively. The ejection– and sweep–center spatial correlations extend forward and backward in the streamwise direction, respectively. Length scales were obtained from the ejection–center and sweep–center spatial correlations. The streamwise lengths vary significantly below the canopy height when obstacles are uniform. In contrast, the streamwise length scales remain nearly constant when obstacle heights vary. The horizontal aspect ratios below the canopy heights indicate that turbulent organized structures over obstacles with variable heights are more isotropic than those over uniform obstacles. The inclination angles of the organized structures were also deduced using the spatial correlations. The angles of sweep–center structures are steeper than those of the ejection–center structures. The angles of the ejection–center structures at the RSL heights become larger with obstacle-height variability.

Feedback control of chaotic systems using multiple shooting shadowing and application to Kuramoto-Sivashinsky equation.

We propose an iterative method to evaluate the feedback control kernel of a chaotic system directly from the system's attractor. Such kernels are currently computed using standard linear optimal control theory, known as linear quadratic regulator theory. This is however applicable only to linear systems, which are obtained by linearizing the system governing equations around a target state. In the present paper, we employ the preconditioned multiple shooting shadowing (PMSS) algorithm to compute the kernel directly from the nonlinear dynamics, thereby bypassing the linear approximation. Using the adjoint version of the PMSS algorithm, we show that we can compute the kernel at any point of the domain in a single computation. The algorithm replaces the standard adjoint equation (that is ill-conditioned for chaotic systems) with a well-conditioned adjoint, producing reliable sensitivities which are used to evaluate the feedback matrix elements. We apply the idea to the Kuramoto-Sivashinsky equation. We compare the computed kernel with that produced by the standard linear quadratic regulator algorithm and note similarities and differences. Both kernels are stabilizing, have compact support and similar shape. We explain the shape using two-point spatial correlations that capture the streaky structure of the solution of the uncontrolled system.

On the effect of free-stream turbulence on boundary-layer transition

Abstract

Wall-shear stress fluctuations in a supersonic turbulent boundary layer over an expansion corner

The effect of wall expansion on the structural and statistical characteristics of wall-shear stress (WSS) fluctuations was investigated by direct numerical simulations of a supersonic turbulent boundary layer over a sharp expansion corner with various deflection angles (β = 00, 20, 50 and 100). It is found that the two-dimensional fields of WSS are characterised as streamwise-elongated streaky structures being aligned in the spanwise direction, resembling low- and high-speed streaks in the buffer region of the flow. Due to the relaminarization effect, these WSS steaks experience a sudden weakening shortly after the expansion corner, but present gradual regrowth with their length scales even exceeding those of the flat-plate case in the far downstream. A strong streamwise-alignment of the instantaneous WSS vector is evident in the case of the largest deflection angle, suggesting a distinct reduction of the intermittency in the relaminarization process. Furthermore, the characteristic time scale of the spanwise component of WSS is quasi-invariant to the expansion effect, while the peak frequency of the streamwise component increases with the increase of the deflection angle.

Interaction of Stationary Disturbances with Tollmien—Schlichting Waves in a Supersonic Boundary Layer

The possibility of controlling unsteady disturbances, traveling Tollmien—Schlichting waves, and stationary streamwise structures is studied. The investigation is performed for the flat-plate boundary layer at the freestream Mach number M = 2. The possible enhancement and suppression of the growth of these waves by stationary streaky structures of the stability eigenproblem of supersonic boundary layer is studied. The problem is solved in the local-parallel approximation within the framework of the three-wave resonance interaction. The pumping wave is a stationary, near-streaky formation. It is shown that even in the stability domain Tollmien—Schlichting waves grow under the influence of the streamwise structures. It is established that under certain conditions the effect of stationary disturbances on these waves can be considerable also in the instability domain and the Reynolds number ranges in which the steady disturbances suppress traveling waves are determined.

Influence of domain size on direct numerical simulation of turbulent flow in a moderately curved concentric annular pipe

Direct numerical simulation (DNS) of turbulent flow in a concentric annular pipe was performed using a pseudo-spectral method computer code. In order to study the effects of computational domain size on the turbulence statistics, 12 test cases of different domain sizes are compared. The characteristics of the velocity field are examined at two different Reynolds numbers. It is observed that the predictive accuracy of the first- and second-order statistics is sensitive to the axial and azimuthal domain sizes. It is also found that the scales and dynamics of turbulence structures vary with the surface curvature of the concave and convex walls. The characteristic length scales of the turbulence structures are identified through a spectral analysis, and it is observed that a minimum computational domain is required in order to accurately capture the near-wall streaky and hairpin structures of a concentric annular pipe flow using DNS.

Recognition of Structures Leading to Transition in a Low-Pressure Turbine Cascade: Effect of Reduced Frequency

Abstract The boundary layer developing over the suction side of a low-pressure turbine cascade operating under unsteady inflow conditions has been experimentally investigated. Time-resolved particle image velocimetry (PIV) measurements have been performed in two orthogonal planes, the blade-to-blade and a wall-parallel plane embedded within the boundary layer, for two different wake-reduced frequencies. Proper orthogonal decomposition (POD) has been used to analyze the data and to provide an interpretation of the most significant flow structures for each phase of the wake passing cycle. Detailed information on the most energetic turbulent structures at a particular phase is obtained with a newly developed procedure that overcomes the limit of classical phase average. The synchronization of the measurements in the two planes allows the computation of the characteristic dimension of boundary layer streaky structures that are responsible for transition. The largest and most energetic structures are observed when the wake centerline passes over the rear part of the suction side, and they appear practically the same for both reduced frequencies. The passing wake forces transition leading to the breakdown of the boundary layer streaks. Otherwise, the largest differences between the low and high reduced frequency are observed in the calmed region. The postprocessing of these two planes allowed computing the spacing of the streaky structures and making it nondimensional by the boundary layer displacement thickness observed for each phase. The nondimensional value of the streaks spacing is about constant, irrespective of the reduced frequency.

Large-Eddy Simulation of Neutrally-Stratified Turbulent Flow Within and Above Plant Canopy Using the Central-Moments-Based Lattice Boltzmann Method

A central-moments-based lattice Boltzmann model for large-eddy simulation of neutrally-stratified turbulent flows is described. Through comparative simulations of the airflow within and above a homogeneous plant canopy, the performance of the model is evaluated with respect to a conventional large-eddy-simulation model based on the incompressible Navier–Stokes equations. Simulated turbulence statistics, such as the mean velocity, velocity variances, velocity skewness, and power spectra, are shown to be almost identical between the two models. The spatial structure of coherent eddies and their maintenance processes are also confirmed to be properly represented by the lattice Boltzmann method through analysis of the turbulence kinetic energy budget and spatial two-point correlation functions. Using the simulated results, the energetics of the streamwise-elongated streaky structures commonly observed over vegetation and urban canopies are examined. While the short-wavelength components of the shear-generated streamwise kinetic energy are redirected rapidly by pressure to the lateral and vertical velocity components, long-wavelength energy tends to remain in the streamwise velocity component, which is dissipated in relatively slower processes. Consequently, the streaky structures persist in the streamwise velocity component.

Uncovering Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence

A growing body of studies supports the existence of Townsend’s wall-attached eddies in wall turbulence under the condition of sufficiently high Reynolds numbers. In the present work, we uncover the signature of Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence. To this end, we use a three-dimensional clustering methodology to identify the wall-attached structures of intense streamwise and spanwise velocity fluctuations in turbulent channel flows at four Reynolds numbers ( , 358, 547 and 934). The statistical properties of the structures, such as their geometric self-similarity, population density and statistical moments, are investigated and compared with the predictions of the attached-eddy model. Particular attention is paid to the asymmetries between high- and low-speed wall-attached streaky structures, and we show that the former are a closer representation of the wall-attached eddies. This observation is ascribed to the differences between the sweep and ejection events associated with the streaks. We also examine the Reynolds-number effects on the statistical properties of the structures, and find that the signature of attached eddies can be observed within the Reynolds-number range under scrutiny. Our approach paves the way to cost-efficient model development and flow prediction using computationally more affordable simulations at low Reynolds numbers.

Quantitative Evaluation of Cascade Process Due to Secondary Instability Generated in Streaky Structure Excited in Turbulent Channel Flow

Quantitative Evaluation of Cascade Process Due to Secondary Instability Generated in Streaky Structure Excited in Turbulent Channel Flow

On the role of actuation for the control of streaky structures in boundary layers

This work deals with the closed-loop control of streaky structures induced by free-stream turbulence in a zero-pressure gradient, transitional boundary layer, by means of localized sensors and actuators. A linear quadratic gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator which aims to induce the exact structures which are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition mode, and an actuator that maximizes the energy of induced downstream structures. Two free-stream turbulence levels were evaluated, corresponding to 3.0% and 3.5%, and closed-loop control is applied in large-eddy simulations of transitional boundary layers. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the free-stream turbulence levels. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer. However, it is shown that even with the actuator located downstream of the input measurement it may become impossible to cancel incoming disturbances in a causal way, depending on the wall-normal position of the output and on the actuator considered, which limits sensor and actuator placement capable of good closed-loop performance.