Turbulent Spots Research Articles

Numerical Simulation of the Evolution of Turbulent Spots in a Supersonic Boundary Layer over a Plate

Numerical Simulation of the Evolution of Turbulent Spots in a Supersonic Boundary Layer over a Plate

Self-similar temporal turbulent boundary layer flow

Direct numerical simulations of temporally evolving boundary layer flows are considered with solutions restricted to self-similar profiles. A new set of modified Navier–Stokes equations is solved with periodic boundary conditions in the streamwise direction, and solutions reach statistically steady states, independent of the initial conditions. The results are presented for different cases, with and without a pressure gradient, and found to be in agreement with existing results of spatial turbulent boundary layer flows. Thus, self-similar temporal solutions are able to reproduce the general features of turbulent boundary layer flows. Finally, the model is applied to simulate a turbulent spot in equilibrium, which is difficult to obtain otherwise.

Investigation of pressure feedback technique to control ramp based SWBLI

Shock wave boundary layer interaction (SWBLI) and associated boundary layer separation create undesirable phenomena such as enhanced aero-thermodynamic loads, localized turbulent spots, unsteadiness, drag enhancement, pressure recovery losses in high-speed flow applications. It necessitates an investigation on the control of shock-induced boundary layer separation. Therefore, a pressure feedback technique (PFT) to control the boundary layer separation has been studied numerically on a two-dimensional flat plate and ramp configuration. PFT consists of a channel that drains fluid from the separated region and reintroduces it in the core flow under the influence of pressure difference. The effect of various freestream, wall, and geometric conditions on the separation controllability of the PFT is examined. It has been observed that PFT with injection located near the upstream influence point and suction at the ramp foot reduces the length of the separation bubble by 12.15%. Variation of injection location marginally affects the separation reduction capability of PFT, while the performance of PFT is greatly dependent on suction location. The parametric study noted that the optimum suction location, for which the separation size is minimum, shifts downstream with increasing freestream Mach number, wall temperature, and ramp angle. Again the optimum suction location shifts upstream as freestream stagnation temperature to wall temperature ratio increases. Reynolds number is seen to have no impact on the optimum suction location. Moreover, freestream stagnation temperature to wall temperature ratio, which is a governing parameter in SWBLI studies, is also a relevant factor in the mechanism of PFT. Finally, the present limited investigation revealed that the suction end of the PFT positioned between Xsu/L = 1.12 to 1.194 provides a minimum size of shock-induced separation for varying freestream and wall conditions.

New Insights into Turbulent Spots

Transitional–turbulent spots bridge the deterministic laminar state with the stochastic turbulent state and affect the transition zone length in engineering flows. Turbulent spot research over the past four decades has expanded from incompressible flat-plate boundary layer and pipe flow to hypersonic boundary layer flow, turbomachinery flow, channel flow, plane Couette flow, and a range of more complex flows. Progress has been made on the origination, composition, demarcation, growth, mutual interaction, reproduction, sustainability, and self-organization of turbulent spots. The hypothesis that transitional–turbulent spots are a basic module of the fully turbulent boundary layer has been proven through the discovery of locally generated turbulent–turbulent spots dominating the wall layer. Splitting of transitional–turbulent spots in pipe flow has been linked to a life cycle localized in the spot frontal section. This review discusses these advances and outlines future research directions.

Mitigation of turbulent noise sources by riblets

A feasibility study is presented on the application of riblets to suppress turbulent pressure sources leading to a reduction in the generation of aerofoil self-noise. It is shown that riblets can reduce skin friction as well as the turbulence intensity inside the boundary layer. In addition, near-wall turbulence structures were found to be dissipated quite rapidly when crossing the riblets surface. It is found that riblets (1) slightly reduce the wall fluctuating pressure power spectral density level at the low and high frequency ranges, but cause an increase at the mid frequency range, and (2) reduce the lateral turbulence coherence length scale across a large frequency range. As a result, riblets have the potential to reduce trailing edge noise at the low and high frequency regions. The fundamental mechanism by which riblets reduce the turbulent intensity level inside the boundary layer is investigated by studying the spatio-temporal evolution of turbulent spots, which are commonly regarded as the building blocks of a turbulent boundary layer. In this paper two mechanisms are proposed. First, the enhanced momentum achieved at the becalmed region of each turbulent spot will lead to a reduction in the overall turbulence intensity obtained when turbulent spots merge downstream. Second, the internal turbulence level at the rear part of a turbulent spot can be reduced directly by an enhanced re-laminarisation effect.

Performance of different inflow turbulence methods for wind engineering applications

Defining the correct inlet boundary conditions for large eddy simulations is a critical issue in computational wind engineering. Since synthetic inflow turbulence does not require costly prior flow simulations like recycling or precursor methods, it is a preferable approach. In this study, different synthetic turbulence generator methods are considered to investigate their performance in wind engineering applications. The considered methods are a) Digital Filter Methods (DFM), b) Synthetic eddy methods (SEM) with different shape functions, c) Divergence Free Synthetic Eddy Method (DFSEM), and d) two types of Anisotropy Turbulent Spot Method (ATSM). These methods are provided in Turbulence Inflow Tool (TInF) from the SimCenter (https://simcenter.designsafe-ci.org/backend-components/tinf/). Additionally, velocity spectrum at the inlet and building location is compared to the Von Karman spectrum for different inflow methods to determine how well the energy is carried from the inlet to the building location. Furthermore, different methods are evaluated to see whether they produce spurious pressure in the domain. It is concluded that spurious pressure exists in all the considered methods except SEM method with the Gaussian shape function (SEM-G). In addition, SEM-G is found to be a suitable method for peak pressure prediction on buildings with upmost 30% error.

A procedure for computing the spot production rate in transitional boundary layers

The present work describes a method for the computation of the nucleation rate of turbulent spots in transitional boundary layers from particle image velocimetry (PIV) measurements. Different detection functions for turbulent events recognition were first tested and validated using data from direct numerical simulation, and this latter describes a flat-plate boundary layer under zero pressure gradient. The comparison with a previously defined function adopted in the literature, which is based on the local spanwise wall-shear stress, clearly highlights the possibility of accurately predicting the statistical evolution of transition even when the near-wall velocity field is not directly available from the measurements. The present procedure was systematically applied to PIV data collected in a wall-parallel measuring plane located inside a flat plate boundary layer evolving under variable Reynolds number, adverse pressure gradient (APG) and free-stream turbulence. The results presented in this work show that the present method allows capturing the statistical response of the transition process to the modification of the inlet flow conditions. The location of the maximum spot nucleation is shown to move upstream when increasing all the main flow parameters. Additionally, the transition region becomes shorter for higher Re and APG, whereas the turbulence level variation gives the opposite trend. The effects of the main flow parameters on the coefficients defining the analytic distribution of the nucleation rate and their link to the momentum thickness Reynolds number at the point of transition are discussed in the paper.Graphical abstract

A spatially accelerating turbulent flow with longitudinally contracting walls

This paper describes a study of spatially accelerating turbulent flow based on the direct numerical simulation of a flow with longitudinally accelerating moving walls to create a relative acceleration between the fluid and the wall without inducing streamline curvature. The results show a broad similarity to those of previous investigations of spatial acceleration, albeit with some differences. A new interpretation has been proposed considering this spatially accelerating flow to be characterised by the formation of a new boundary layer superimposed on the pre-existing turbulent flow. This is followed by the transition of the flow in response to the development of this new boundary layer. This can be seen as an extension of the transition theory for temporally accelerating turbulent flows (He & Seddighi, J. Fluid Mech., vol. 715, 2013, pp. 60–102). The existing turbulent structures act as disturbances for the new boundary layer similar to the role of free-stream turbulence in bypass transition. This boundary layer modulates the pre-existing near-wall structures, amplifying and elongating the streaks. Some streaks eventually become unstable in a sinuous mechanism reminiscent of streak breakdown in near-wall turbulence, resulting in the formation localised turbulent spots which spread until the entire wall is covered in new turbulence. This interpretation naturally splits the flow into a new boundary layer region and a core (or free-stream) flow with interactions between the two dominating a significant length of the flow development and potentially offers a new explanation for the slow evolution of the turbulent stresses observed previously.

Effects of streamwise oriented riblets on spot nucleation in free-stream turbulence induced transition

The effects due to streamwise oriented riblets on the free-stream turbulence (FST) induced transition of a flat plate boundary layer (BL) are studied by means of Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV). The experiments are performed on a flat plate installed between adjustable endwalls providing an adverse pressure gradient typical of turbine blades for aeronautical applications. Four different ribbed surfaces are compared with a smooth reference case to test the effects of riblet dimension and location on turbulent spot nucleation. Riblets are installed in the laminar, the transitional, and the fully turbulent BL. Their effects are studied for three Reynolds numbers (Re=70000, 150000, 220000) under fixed pressure gradient and free-stream turbulence intensity (Tu=5%). Varying the flow Reynolds number leads to different non-dimensional riblet height and spacing values, providing an overall test matrix of 13 different conditions.LDV measurements allowed the computation of the wall shear stress and the BL statistical moments at selected spatial positions. On the other hand, PIV data are used to characterize the riblet effects on turbulent spot nucleation and transition: the higher the non-dimensional riblet height, the more the breakup events occur upstream with respect to the smooth case. Momentum losses significantly increase when the non-dimensional riblet spacing becomes larger than 30 wall-units. Otherwise, beneficial effects are obtained for smaller riblet spacing, regardless of their streamwise extension and position with respect to the BL transition region.

Disturbance growth on a NACA0008 wing subjected to free stream turbulence

The stability of an incompressible boundary layer flow over a wing in the presence of free stream turbulence (FST) has been investigated by means of direct numerical simulations and compared with the linearised boundary layer equations. Four different FST conditions have been considered, which are characterised by their turbulence intensity levels and length scales. In all cases the perturbed flow develops into elongated disturbances of high and low streamwise velocity inside the boundary layer, where their spacing has been found to be strongly dependent on the scales of the incoming free stream vorticity. The breakdown of these streaks into turbulent spots from local secondary instabilities is also observed, presenting the same development as the ones reported in flat plate experiments. The disturbance growth, characterised by its root mean squares value, is found to depend not only on the turbulence level, but also on the FST length scales. Particularly, higher disturbance growth is observed for our cases with larger length scales. This behaviour is attributed to the preferred wavenumbers that can exhibit maximum transient growth. We study this boundary layer preference by projection of the flow fields at the leading edge onto optimal disturbances. Our results demonstrate that optimal disturbance growth is the main cause of growth of disturbances on the wing boundary layer.

Non-modal growth of finite-amplitude disturbances in oscillatory boundary layer

The essence of sub-critical transition of oscillatory boundary-layer flows is the non-modal growth of finite-amplitude disturbances. The current understanding of the mechanisms of the orderly and bypass transitions of oscillatory boundary-layer flows is limited. The present study adopts optimisation approaches to predict the maximum energy amplification of two- and three-dimensional perturbations in response to the optimal initial disturbance with or without external forcing. A series of direct numerical simulations are also performed to compare with the results obtained from the stability analyses. In particular, the optimal initial perturbation similar to a Tollmien–Schlichting (T–S) wave yields the largest transient growth under the combined effects of the Orr mechanism and inflectional point instability. With a considerable level of two-dimensional disturbance, the vortex tube nonlinearly develops from the T–S-like wave, and then either deforms into a $\varLambda$ -vortex in the near-wall region or rolls up to the free shear region. The further burst of turbulence can follow the first pathway as K-type transition or the second one as vortex tube breakdown due to the elliptical instability. Additionally, non-modal growth can initiate the inception of streaky structures by favourable three-dimensional initial perturbations and/or forcing. The secondary instabilities responsible for the streak breakdown are classified as the varicose (symmetric) and sinuous (anti-symmetric) modes. Under a sufficiently high level of three-dimensional disturbance, the bypass transition is predominantly characterised by the formation of the sinuous mode and turbulent spots, which leads to the suppression of inflection point instability.

Opposition control of turbulent spots

Opposition control of artificially initiated turbulent spots in a laminar boundary layer was carried out in a low-turbulence wind tunnel with the aim to delay transition to turbulence by modifying the turbulent structure within the turbulent spots. The timing and duration of control, which was carried out using wall-normal jets from a spanwise slot, were pre-determined based on the baseline measurements of the transitional boundary layer. The results indicated that the high-speed region of the turbulent spots was cancelled by opposition control, which was replaced by a carpet of low-speed fluid. The application of the variable-interval time-averaging technique on the velocity fluctuation signals demonstrated a reduction in both the burst duration and intensity within the turbulent spots, but the burst frequency was increased.

Generation of streamwise helical vortex loops via successive reconnections in early pipe transition

We extend the vortex-surface field (VSF), a Lagrangian-based structure identification method, to investigate the vortex reconnection in temporally evolving transitional pipe flows. In the direct numerical simulation (DNS) of round pipe flows, a radial wave-like velocity disturbance is imposed on the inlet region to trigger the transition. The VSF isosurfaces are vortex surfaces composed of vortex lines, and they are concentric tubes with different wall distances at the initial time. The VSF evolution is calculated by the two-time method based on the DNS velocity field, and it is effective to identify the vortex reconnection. In the early stage of transition, the vortex surfaces are first corrugated with streamwise elongated bulges. The escalation and descent of vortex surfaces characterize the generation of high- and low-speed streaks and streamwise vortex pairs, along with the surge of the wall-friction coefficient. The resultant highly coiled and stretched vortex loops then reconnect with each other under the viscous cancelation mechanism. Subsequently, successive vortex reconnections occur via a “greedy snake” mechanism. The streamwise vortex loops consecutively capture the secondary vortex rings pinched off with self-reconnection, forming long helical vortex loops spanning over ten pipe radii in the streamwise direction. Finally, the Kelvin–Helmholtz instability of the shear layer at the trailing edge breaks down the streamwise helical vortex loops into turbulent spots.

Analysis of interscale energy transfer in a boundary layer undergoing bypass transition

The Kármán–Howarth–Monin–Hill equation is employed to study the production and interscale energy transfer in a boundary layer undergoing bypass transition due to free-stream turbulence. The energy flux between different length scales is calculated at several streamwise locations covering the laminar, transitional and turbulent regimes. Maps of scale energy production and flux vectors are visualised on two-dimensional planes and three-dimensional hyper-planes that comprise both physical and separation spaces. In the transitional region, the maps show strong inverse cascade in the streamwise direction near the wall. The energy flux vectors emanate from a region of strong production and transfer energy to larger streamwise scales. To provide deeper insight into the origin of the inverse cascade process, we decompose the energy flux vector into components arising from nonlinear interactions between velocity fluctuations, mean flow inhomogeneity, pressure and viscous effects. The inverse cascade is mainly due to the nonlinear interaction component, and in the earliest stages of transition this component competes with that due to mean flow inhomogeneity. By superposing the instantaneous velocity fields and the energy flux vectors, we relate the inverse cascade process to the growth of turbulent spots. Once the transition process is complete, the maps become very similar to those observed in other fully developed turbulent flows, such as channel flow. Finally we characterise the nonlinear interaction term using probability density functions (PDFs) evaluated at different wall-normal heights. The PDFs are asymmetric and wide-skirted as in homogeneous isotropic turbulence, but are skewed towards positive values reflecting the inverse cascade.

Turbulent spot transit of a hypersonic laminar separation

This paper presents an experimental study of the interaction of turbulent spots with an initially laminar separation, using schlieren visualisation and dynamic measurements of surface heat transfer and pressure. The separation is generated on a blunt cylinder-flare body, tested at Mach 9, and entropy layer effects result in a boundary layer edge Mach number of 3.43 at separation. A single roughness element is used to produce isolated spots, defined such that separation collapse and re-establishment is completed before arrival of the next spot. On average the spot axial length, at the start of the interaction, is 2.5 times the separation length, growing to 6.8 times as the spot base passes the original reattachment position. As such the spot comprises a large perturbation. The local separation responds almost immediately with passage of the spot, so that the downstream region may be unaffected while the upstream part has already collapsed. Re-establishment of separation is slow, taking up to four times the total transit time of the spot. A basic model is presented to explore the transient wave processes during spot passage.

Passive Scalar Transport in a Turbulent Spot within a Poiseuille Flow

Passive Scalar Transport in a Turbulent Spot within a Poiseuille Flow

Selection and Impact of an Aerofoil Leading Edge on Boundary Layer Transition

The choice of leading-edge aspect ratio (AR) plays a crucial role when planning boundary layer wind tunnel tests on a flat plate. Poor selection of the leading-edge profile hampers effectiveness of the experiment and increases testing costs associated with interchanging of leading edges to attain accurate results. Thus, the appropriate selection of the leading edge is a very crucial part of the wind tunnel experiment process. It is argued that the curvature of the leading edge and thus the AR is of paramount importance to achieve accurate results from the wind tunnel testing. In this project, seven different elliptical leading edges were tested, and their performance was compared with an ideal leading edge with zero thickness. Experiments and computation have been done for leading edges ranging from AR6 to AR20. Results were evaluated for boundary layer transition onset location, and it was found that AR20 has the least influence on the flow structure when compared to the ideal leading edge. A study of the flow structure at the stagnation point indicates an increase in adverse pressure gradient with an increase in the AR but also shows a decrease in the size of the stagnation region. The presence of a higher AR leading edge reduces the turbulent spot production rate, which is one of the primary causes of boundary layer transition. This paper presents a correlation that enables aerodynamicists to quantify the impact of the leading-edge AR on transition. A typical case is also presented to compare the relative performance of a wedge and the higher AR leading edge, which provides a choice between an elliptical or a wedge-shaped leading edge.

Transition in an infinite swept-wing boundary layer subject to surface roughness and free-stream turbulence

The instability of an incompressible boundary-layer flow over an infinite swept wing in the presence of disc-type roughness elements and free-stream turbulence (FST) has been investigated by means of direct numerical simulations. Our study corresponds to the experiments by Örlü et al. (Tech. Rep., KTH Royal Institute of Technology, 2021, http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291874). Here, different dimensions of the roughness elements and levels of FST have been considered. The aim of the present work is to investigate the experimentally observed sensitivity of the transition to the FST intensity. In the absence of FST, flow behind the roughness elements with a height above a certain value immediately undergoes transition to turbulence. Impulse–response analyses of the steady flow have been performed to identify the mechanism behind the observed flow instability. For subcritical roughness, the generated wave packet experiences a weak transient growth behind the roughness and then its amplitude decays as it is advected out of the computational domain. In the supercritical case, in which the flow transitions to turbulence, flow as expected exhibits an absolute instability. The presence of FST is found to have a significant impact on the transition behind the roughness, in particular in the case of a subcritical roughness height. For a height corresponding to a roughness Reynolds number $Re_{hh}=461$ , in the absence of FST the flow reaches a steady laminar state, while a very low FST intensity of $Tu =0.03\,\%$ causes the appearance of turbulence spots in the wake of the roughness. These randomly generated spots are advected out of the computational domain. For a higher FST level of $Tu=0.3\,\%$ , a turbulent wake is clearly visible behind the element, similar to that for the globally unstable case. The presented results confirm the experimental observations and explain the mechanisms behind the observed laminar–turbulent transition and its sensitivity to FST.

Unsupervised modelling of a transitional boundary layer

A data-driven approach for the identification of local turbulent-flow states and of their dynamics is proposed. After subdividing a flow domain in smaller regions, the $K$ -medoids clustering algorithm is used to learn from the data the different flow states and to identify the dynamics of the transition process. The clustering procedure is carried out on a two-dimensional (2-D) reduced-order space constructed by the multidimensional scaling (MDS) technique. The MDS technique is able to provide meaningful and compact information while reducing the dimensionality of the problem, and therefore the computational cost, without significantly altering the data structure in the state space. The dynamics of the state transitions is then described in terms of a transition probability matrix and a transition trajectory graph. The proposed method is applied to a direct numerical simulation dataset of an incompressible boundary layer flow developing on a flat plate. Streamwise–spanwise velocity fields at a specific wall-normal position are referred to as observations. Reducing the dimensionality of the problem allows us to construct a 2-D map, representative of the local turbulence intensity and of the spanwise skewness of the turbulence intensity in the observations. The clustering process classifies the regions containing streaks, turbulent spots, turbulence amplification and developed turbulence while the transition matrix and the transition trajectories correctly identify the states of the process of bypass transition.

Surface Roughness Impact on Boundary Layer Transition and Loss Mechanisms Over a Flat-Plate Under a Low-Pressure Turbine Pressure Gradient

Abstract An experimental study has been conducted to investigate the effects of surface roughness on the profile loss of a flat-plate with a contoured wall. All of the measurements have been conducted for the suction side pressure gradient of a high-lift low pressure turbine airfoil at the fixed freestream turbulence intensity (Tu) of 3.2% under Reynolds numbers of Rec = 1. 2 · 105 (cruise) and Rec = 5.2 · 105 (take-off). The time-resolved streamwise and wall-normal velocity fields for three different surface roughness values of Ra/C · 105 = 0.065, 4.417, and 7.428 have been measured with a 2D hot-wire probe. At the take-off condition (Rec = 5.2 · 105), attached flow transition occurs, and increased surface roughness increases the loss. For all of the surfaces, momentum deficits in the laminar to early transition region (γ ≈ 0.05) are similar. For the intermediate transition (γ ≈ 0.5), increased roughness reduces the Reynolds stress and accelerates the breakdown of large-scale turbulent spots into small-scale turbulent eddies. Therefore, turbulent energy and momentum deficit are decreased for rough surfaces. For the late transition (γ > 0.9), transitional boundary layers become similar to turbulent boundary layers, and increased surface roughness increases turbulent mixing, boundary layer thickness, and, hence, the momentum deficit. On the other hand, at the cruise condition (Rec = 1.2 · 105), separated flow transition occurs and increased surface roughness decreases loss. Since the portion of turbulent flow is relatively small, the overall profile loss is mainly determined by the momentum deficit generated during transition. Increased roughness decreases the maximum height and length of the separation bubble but does not affect the separation bubble onset location. The beneficial effects of increased surface roughness on the profile loss appear in the separated shear layer and reattachment. Increased surface roughness increases turbulent mixing in the separated shear layer, reducing the shear layer thickness and momentum deficit. In addition, increased surface roughness reduces the length scale and turbulence intensity of the shed vortices. Consequently, turbulent mixing and momentum deficit during the reattachment of boundary layers are decreased, resulting in a lower profile loss.