Bypass Transition Research Articles

The near wake of discrete roughness elements on swept wings

This work presents the first experimental characterization of the flow field in the vicinity of periodically spaced discrete roughness elements (DRE) in a swept wing boundary layer. The time-averaged velocity fields are acquired in a volumetric domain by high-resolution dual-pulse tomographic particle tracking velocimetry. Investigation of the stationary flow topology indicates that the near-element flow region is dominated by high- and low-speed streaks. The boundary layer spectral content is inferred by spatial fast Fourier transform (FFT) analysis of the spanwise velocity signal, characterizing the chordwise behaviour of individual disturbance modes. The two signature features of transient growth, namely algebraic growth and exponential decay, are identified in the chordwise evolution of the disturbance energy associated with higher harmonics of the primary stationary mode. A transient decay process is instead identified in the near-wake region just aft of each DRE, similar to the wake relaxation effect previously observed in two-dimensional boundary layer flows. The transient decay regime is found to condition the onset and initial amplitude of modal crossflow instabilities. Within the critical DRE amplitude range (i.e. affecting boundary layer transition without causing flow tripping) the transient disturbances are strongly receptive to the spanwise spacing and diameter of the elements, which drive the modal energy distribution within the spatial spectra. In the super-critical amplitude forcing (i.e. causing flow tripping) the near-element stationary flow topology is dominated by the development of a high-speed and strongly fluctuating region closely aligned with the DRE wake. Therefore, elevated shears and unsteady disturbances affect the near-element flow development. Combined with the harmonic modes transient growth these instabilities initiate a laminar streak structure breakdown and a bypass transition process.

On the laminar–turbulent transition mechanism on megawatt wind turbine blades operating in atmospheric flow

Abstract. Among a few field experiments on wind turbines for analyzing laminar–turbulent boundary layer transition, the results obtained from the DAN-AERO and aerodynamic glove projects provide significant findings. The effect of inflow turbulence on boundary layer transition and the possible transition mechanisms on wind turbine blades are discussed and compared to CFD (computational fluid dynamics) simulations of increasing fidelity (Reynolds-averaged Navier–Stokes, RANS; unsteady Reynolds-averaged Navier–Stokes, URANS; and large-eddy simulations, LESs). From the experiments, it is found that the transition scenario changes even over a single revolution with bypass transition taking place under the influence of enhanced upstream turbulence, for example, such as that from wakes, while natural transition is observed in other instances under relatively low inflow turbulence conditions. This change from bypass to natural transition takes place at azimuthal angles directly outside the influence of the wake indicating a quick boundary layer recovery. The importance of a suitable choice of the amplification factor to be used within the eN method of transition detection is evident from both the RANS and URANS simulations. The URANS simulations which simultaneously check for natural and bypass transition match very well with the experiment. The LES predictions with anisotropic inflow turbulence show the shear-sheltering effect and a good agreement between the power spectral density plots from the experiment and simulation is found in case of bypass transition. A condition to easily distinguish the region of transition to turbulence based on the Reynolds shear stress is also observed. Overall, useful insights into the flow phenomena are obtained and a remarkably consistent set of conclusions can be drawn.

Passive scalar transport in a turbulent spot within a poiseuille flow

A pair of counter-rotating vortices are introduced in a Poiseuille flow to trigger the by-pass transition. The accent is put on the passive scalar transport within the resulting transitional spot. The latter is identified and tracked in time and space using the fluctuating vorticity and temperature fields it induces. The velocity and temperature statistics are determined strictly within the spot. They are scaled by the inner variables, related to the shear velocity and the wall temperature flux induced by the spot. The statistics are compared with those of the corresponding fully developed turbulent channel flow, in order to determine the degree of similarity between the internal structure of the spot and the fully developed wall turbulence. The analysis includes the fine structure of the fluctuating temperature field, its transport equations and the effect of the coherent structures within the spot. It is found that the turbulent part of the spot is closely similar to the turbulent wall flow, both for the fluctuating flow, and the passive scalar fields. The root-mean-square of the temperature fluctuations determined in the entire spot is nearly twice larger than that in the fully developed wall turbulence in the outer part of the flow. The transport is enhanced and the turbulent fluxes increase compared to the fully developed turbulent channel flow. This is due to the wave area of the spot that contains, in their great majority, the structures coming from the breakdown process of waves. The latter is responsible for the increase of the small-scale mixing and of the large peripheral temperature fluctuations, which is rather good news from an application point of view.

Algebraic modifications of the [formula omitted] and Spalart–Allmaras turbulence models to predict bypass and separation-induced transition

Many reliable and robust turbulence models are nowadays available for the Reynolds-Averaged Navier–Stokes (RANS) equations to accurately simulate a wide range of engineering flows. However, turbulence models are not suited to correctly described flows with low to moderate Reynolds numbers, which are characterized by strong transitional phenomena. Therefore, numerical models able to accurately predict transitional flows are mandatory to overcome the limits of turbulence models for the efficient design of many industrial applications. The only ways to describe transition are Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), and transition models, where the computational cost of DNS and LES is still too high for their routine use in industry. A modified version of the k-ω̃ and Spalart–Allmaras turbulence models is here proposed to predict transition due to the bypass and separation-induced modes. The modifications are based on the γk-ω̃ and the SA-BCM models and avoid complex formulations of transport equations ad-hoc defined for transition. Both the transition models are correlation-based algebraic models that rely only on local flow information and an intermittency function, which damps the turbulent production according to some transition onset requirements. The proposed transition models are implemented in a high-order discontinuous Galerkin (dG) solver and validated on benchmark cases from the ERCOFTAC suite to the Eppler 387 airfoil, with different transition mode, freestream Reynolds number and turbulent intensity, and pressure gradient.

Flat plate boundary layer accelerated by shock wave propagation

The flat plate transitional boundary layer response to the acceleration induced by the shock wave propagation is studied using large-eddy simulations. The steady boundary layer global behaviour is first investigated before focusing on the transient response of a turbulent region following the shock wave propagation. It is shown that the transient response of the turbulent region exhibits strong similarities with the spatial transition process to turbulence induced by free-stream turbulence, the so-called bypass transition. The boundary layer does not evolve gradually from the initial turbulence intensity to the final turbulence intensity but undergoes a temporal transition process composed of three distinct phases. These three different phases are comparable with the three stages of a bypass transition (i.e. buffeted laminar flow, transition and fully turbulent) because they are governed by the same physical processes. On the other hand, it is highlighted that this temporal response is identical to that described by He & Seddighi (J. Fluid Mech., vol. 715, 2013, pp. 60–102) during the study of an incompressible boundary layer undergoing an increase of mass flow rate. The boundary layer compression by the shock propagation does not contribute to any significant change in the turbulence dynamic after an unsteady acceleration.

Assessment of implicit LES modelling for bypass transition of a boundary layer

The implicit LES model recently introduced by Dairay et al. (2017), which is based on numerical dissipation introduced via the discretisation of the viscous term, is assessed for the case of a flat plate boundary layer submitted to external turbulence and undergoing bypass transition. The free stream turbulent fluctuations are generated using a recently proposed linear forcing method adapted to control their intensity and length scale. Two configurations are considered, one with the leading edge of the plate taken into account and one without. LES results for the configuration without leading edge are compared with a DNS, and results for the configuration with leading edge are compared with available experimental and numerical reference data from the literature. Global parameters, unconditional and conditional statistics, as well as Reynolds stress budgets are analysed, and good agreements are obtained with reference data, hence confirming the ability of the model to predict accurately transitional flows. In particular, it is shown that, thanks to its action limited to the smallest resolved scales, the model is only active in the transitional and turbulent regions and therefore does not alter the development of the streaks in the laminar region of the boundary layer.

Predicting transition with wall-distance-free SST k-[formula omitted] model

Unlike the correlation-based γ–Reθ transition model, an exceptionally simplified approach is applied to extend the wall-distance-free (WDF) model toward transition predictions. An anisotropic stress-intensity parameter as a function of eddy-to-laminar viscosity ratio is introduced, preserving the “flow-structure-adaptive” characteristic. The prospective parameter is included with the constitutive relation for the eddy-viscosity. The proposed formulation is intrinsically plausible, having a dramatic influence on the prediction of bypass, separation-induced and natural transitions. The newly devised transitional WDF (TWDF) model is further modified to compute separation-induced transition over a low-Reynolds number (LRN) airfoil. The curiosity toward airfoil performance at an LRN has been executed with growing attention to marine autonomous systems. An extra viscous-production term Pklim is added to the turbulent kinetic energy (k) equation to ascertain proper development of k at the viscous sublayer region. Reliance on this Pklim is likely to be suitable for forecasting separation-induced transition over an LRN airfoil. Results illustrate that the TWDF model sustains decent agreement with the four-equation γ–Reθ transition model.

Dynamics of bypass transition behind roughness element subjected to pulses of free-stream turbulence

This study explores the dynamics of bypass transition of a zero pressure gradient boundary layer transitioning under the combined influence of an isolated roughness element with pulses of free-stream turbulence (FST). We consider a hemispherical roughness element placed over a flat plate, while the pulses of FST are introduced at the inlet, which is in contrast to continuous FST largely explored in the literature. For a fixed turbulence intensity and length scale, a series of eddy-resolving simulations are carried out to examine the effect of varying the pulsing frequency of FST. The flow behind the roughness element remains stable in the absence of FST for the subcritical Reynolds number Rek = 400 considered in this study. We observe that with the pulses of FST, the transition is triggered due to the interaction of the FST-induced Klebanoff streaks with the roughness-induced streamwise vortices. With an increase in the frequency of FST pulses, the boundary layer has less time to relax to its unperturbed state resulting in an earlier onset of transition. The transition onset predicted is in favorable agreement with the correlations proposed in the literature. We analyze the growth of disturbance kinetic energy, the shape of secondary instabilities over the streaks, and their phase speeds in detail. The FST pulse convecting over the roughness element triggers the inner varicose modes in its near-wake region. The varicose modes decay rapidly further downstream and the well-known sinuous instabilities (or the outer modes) trigger transition via transient growth associated with convective instabilities. Such clear identification of the sinuous and varicose instabilities is not usually observed in cases with continuous FST, highlighting the importance of our study in applications involving transition under intermittent turbulence.

Capturing transition and non-transition flows with a new shear stress transport model

A new Shear Stress Transport (SST) k-ω model is devised to integrate salient features of both the non-transitional SST k-ω model and correlation-based γ-Reθ transition model. An exceptionally simplified approach is applied to extend the New SST (NSST) model capabilities toward transition/non-transition predictions. Bradshaw’s stress-intensity factor Rb=-uv¯/k can be parameterized with the wall-distance dependent Reynolds numberRey=ky/v; however, as the Rey is replaced by a “flow-structure-adaptive” parameterRμ=vT/v, the resulting Rb is capable of capturing various transition phenomena naturally. The prospective stress-intensity parameter Rb=Rb(Rey,Rμ) is incorporated in the constitutive relations for eddy-viscosity vT and production termPk. The proposed formulation is intrinsically plausible, having a dramatic impact on the prediction of bypass, separation-induced and natural transitions together with non-transitional flows. An extra viscous-production term Pklim is added with the k-equation to ensure proper generation of k at the viscous sublayer when computing separation-induced transition over a Low-Reynolds Number (LRN) airfoil. Results demonstrate that the NSST k-ω model maintains an excellent consistency with both SST k-ω and γ-Reθ models.

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.

Characteristics of boundary-layer transition driven by diverse streamwise vortices

The present direct numerical simulations investigate the dynamics of diverse streamwise vortices in a zero-pressure gradient incompressible laminar boundary layer and the onset of turbulence. Due to the critical role of streamwise vortices in bypass transitions, we compare the transition mechanisms induced by a single vortex and vortex pairs. We initially examine the evolution of a single vortex by employing streamwise vortex profiles at two wall-normal locations. The single streamwise vortex will prompt a more rapid eruption from the bottom part of the boundary layer if moved nearer to the wall, as observed in the experimental study by Manu et al. [“Evolution of isolated streamwise vortices in the late stages of boundary-layer transition,” Exp. Fluids 48, 431–440 (2010)]. In the late stages of boundary-layer transition, the vortex–wall interaction emerges to be particularly pronounced. The second set of simulations triggers flow transition by imposing counter-rotating vortex pairs at the inlet of the computational domain. Streamwise vortex pairs with net upward flows cause intense, sporadic ejections of near-wall fluids into the boundary-layer edge, providing the first signs of inflectional instability in all considered cases. Instead of vortex–wall interactions, flow structures created by vortex pairs penetrate deeply into the inviscid region, resulting in substantial unsteady viscous-inviscid interactions. When counter-rotating vortices accompany to form a net downward flow, the initial formation of each vortex is analogous to that of a single vortex. The instability frequency and wavelength of the transitional flow produced by a vortex introduced in the middle of the boundary layer are lower than those imposed near the wall. The transitional flow generated by the vortex pair exhibits longer-wavelength instability than the single vortex cases.

Capturing transition around low-Reynolds number hydrofoil with zero-equation transition model

Compared with the local correlation-based shear stress transport (SST) γ−Reθ transition model (where SST k−ω transport equations are coupled with intermittency γ and transitional momentum-thickness Reynolds number Reθ transport equations), relatively simple and convenient modifications are applied to the parent SST k−ω model for computing natural and separation-induced transitions over the hydrofoil at a low-Reynolds number (LRN). The curiosity toward hydrofoil performance at an LRN has been enhanced by increasing attention to autonomous marine systems, deserving numerical simulations for transitional flow using computational fluid dynamics. With the newly devised transitional SST (T-SST) model, the viscous sublayer blending function F2 is slightly modified, and a stress-intensity parameter as a function of eddy-to-laminar viscosity ratio RT is introduced; intended formulations are plausible and have significant impacts on the transition prediction. Owing to the inherent potential for predicting bypass transition, two anisotropic versions of the v¯2−f(V2F) turbulence model are selected to evaluate their competencies in capturing separation-induced and natural transitions. Results demonstrate that natural transition prediction is more challenging than separation-induced transition for the V2F model. Nonetheless, the T-SST model performs consistently well in replicating both transitional phenomena.

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.

A Galilean Invariant Variable–Based RANS Closure Model for Bypass and Laminar Separation Bubble–Induced Transition

A one-equation Reynolds-averaged Navier-Stokes (RANS) closure model has been established for bypass transition and laminar separation bubble (LSB)–induced transition. A new local indicator is proposed to describe the influence of turbulence intensities and pressure gradients, which makes the model Galilean invariant. Based on this new indicator, a novel and efficient transition criterion is formulated. For LSB-induced transition, an empirical correlation is developed to modify the intermittency factor and control the size of separation bubbles. Several flow cases, including flat plates with various pressure gradients, flat plates with LSBs, semicircular leading-edge flat plates, National Advisory Committee for Aeronautics (NACA) 0018 airfoil, and SD7003 airfoil, are employed for the model verification. The predictions show good agreement with the experimental data and large-eddy simulation data for different inlet conditions, which indicates the increment of free-stream turbulence intensity leads to the reduction of the size of laminar separation bubbles.

Optimal perturbations and transition in the magnetohydrodynamic boundary layer under the influence of a spanwise magnetic field

Many shear flows exhibit laminar to turbulent transitions at subcritical Reynolds numbers. In this context, the computation of the perturbations that exhibit the largest possible transient growth is of central interest as it often sheds light on the actual bypass transition route. In this work, we consider the effect on the transient growth of a spanwise magnetic field in a boundary layer flow of a liquid metal over an electrically insulating flat plate. We compute the optimal perturbations using non-modal theory and perform a parametric study to measure the influence of the magnetic field on their amplification and orientation with respect to the flow direction. We also perform direct numerical simulations to examine how the optimal perturbations evolve in the nonlinear regime. To assess the influence of the boundary layer development, we consider both a constant Blasius base flow profile and a growing base profile. We show that the properties of the optimal perturbations are not significantly affected by the choice of the base profile, whereas it has a more important impact on their evolution in the nonlinear regime.

Effect of free-stream turbulence properties on different transition routes for a zero-pressure gradient boundary layer

The natural and bypass routes to boundary-layer transition to turbulence are traditionally investigated independently in fluid mechanics applications. Nevertheless, in certain flow regimes both mechanisms could coexist and interact. In this work, large-eddy simulations (LES) were performed for a zero-pressure gradient boundary layer developing over a flat plate to investigate the transition mechanism for variable free-stream turbulent properties. Four different combinations of turbulence intensity and integral length scale were analyzed, and two main transition mechanisms were observed. High free-stream turbulence intensity instigates pure bypass transition through the amplification of a continuous Orr–Sommerfeld (O–S) mode that breaks down after secondary instability. Instead, at low free-stream turbulence intensity, discrete and continuous O–S modes interact and are both involved in the transition process. Visual inspection of the LES snapshots provides a detailed insight in Tollmien–Schlichting (TS) waves–streaks mutual interaction and clearly identifies two main mechanisms involved in turbulence breakdown. On one hand, TS waves trigger varicose instability of streaky structures. On the other hand, streaks cause secondary instability of TS waves with emerging Λ-structure formation. Then, dynamic mode decomposition (DMD) is applied to extract the main stability properties for both types of transition route and to highlight coherent structure dynamics, which is hardly observable in the literature. Specifically, for low-medium free-stream turbulence levels, DMD extracts unstable modes clearly related to streaks–TS waves interaction and leading to the formation of Λ structures. Therefore, the streaks–TS waves interaction is proved to be destabilizing and to trigger secondary instability leading to turbulence breakdown.

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.

Transition induced by wall-normal vibration in flow around a flat plate with roughness

The effects of wall-normal vibration on bypass transition in a boundary-layer flow over a flat plate with roughness elements in the form of circular cylinders are investigated using direct numerical simulations (DNS), linear Floquet analyses and dynamic mode decompositions (DMD). The vibration of the plate strengthens the streamwise vorticity, consequently enhancing the velocity streaks and reducing the critical Reynolds number for transition. A map is constructed to identify the coupling effect of the vibration amplitude and Reynolds number on transition. Among all investigated combinations of height and diameter of roughness, the critical Reynolds numbers at different vibration amplitude $A$ can be unified by a scaling function of $(1-10A)$ . Two instability modes are identified in the vibration-induced transition process: a wake mode immediately downstream of the roughness, related to the inviscid Kelvin–Helmholtz instability of the wall-normal shear in the wake; and a streak mode, in response to the spanwise shear of the streaky flow, occurring further downstream. The first one results in the generation of central hairpin vortices which then feed the second one. Further development of the streak instability leads to two arrays of hairpin vortices. Results from linear Floquet analyses and DMD further confirm the two modes of instability observed in DNS. A quantitative study suggests that the amplification of vibration-induced disturbance by the base shear dominates the production of streamwise vorticity and subsequently the hairpin vortices.

Modeling of surface roughness effects on bypass and laminar separation bubble-induced transition for turbomachinery flows

In a previous study, we developed a one-equation transition model for the bypass and laminar separation bubble (LSB)-induced transition based on local variables. In this paper, distributed surface roughness effects are taken into account by constructing a new transport equation for the roughness amplification factor Ar. Modified criteria taking account of Ar are proposed to describe the roughness effects on the bypass and LSB-induced transitions. Moreover, to predict the flow properties in the laminar–turbulent region more accurately, a modified boundary condition for rough surfaces is employed. The calculations show that, overall, the rough wall promotes the bypass transition and reduces the size, or even causes the disappearance, of the LSBs. Good agreement of the numerical results from the proposed model with the experimental data indicates that the present roughness correction formula is reasonable and accurate.

Predicting transition with algebraic intermittency function

An algebraic intermittency function is developed for “laminar-to-turbulent” transition flow within the framework of Bradshaw stress–intensity factor (ratio of principal shear-stress over turbulent kinetic energy in the boundary layer), which is parameterized with a “flow-structure-adaptive” variable (eddy-to-laminar viscosity ratio). Naturally, the intermittency inherits the “flow-structure-adaptive” character and captures various transition phenomena like bypass, separation-induced, and natural transitions when incorporated in an undamped eddy-viscosity transport equation. An additional viscous-production term is added with the eddy-viscosity transport equation to ensure proper generation of eddy-viscosity at the viscous sublayer when computing separation-induced transition over a low-Reynolds number airfoil. Splitting the intermittency into low and elevated free-stream turbulence intensities has the potential to avoid the “trial-and-error” inconsistency involved in most of the correlation-based transition models for precise computations. The results demonstrate that the proposed algebraic intermittency model is rational and feasible.