Integral Length Scale Research Articles

A critical analysis of turbulence modulation in particulate flow systems: a review of the experimental studies

Abstract In multiphase particulate systems, the turbulence of the continuous phase (gas or liquid) is modulated due to interactions between the continuous phase and the suspended particles. Such phenomena are non-trivial in the essence that addition of a dispersed phase to a turbulent flow complicates the existing flow patterns depending on the physical properties of the particles leading to either augmentation or attenuation of continuous phase turbulence. In the present study, this aspect has been comprehensively analysed based on the available experimental data obtained from the well-studied turbulent flow systems such as channel and pipes, free jets and grids. Relevant non-dimensional parameters such as particle diameter to integral length scale ratio, Stokes number, particle volume fraction, particle momentum number, and particle Reynolds number have been utilised to characterise the reported turbulence modulation behavior. Some limitations of these commonly used dimensionless parameters to characterise turbulence modulation are discussed, and possible improvements are suggested.

Separate and joint clustering characteristics of large-Stokes-number sprays subjected to turbulent co-flows

Separate and joint droplets, clusters, and voids characteristics of sprays injected in a turbulent co-flow are investigated experimentally. Simultaneous Mie scattering and interferometric laser imaging for droplet sizing along with separate hotwire anemometry are performed. The turbulent co-flow characteristics are adjusted using zero, one or two perforated plates. The Taylor-length-scale-based Reynolds number varies from 10 to 38, and the Stokes number estimated based on the Kolmogorov time scale varies from 3 to 25. The results show that the mean length scale of the clusters normalized by the Kolmogorov length scale varies linearly with the Stokes number. However, the mean void length scale is of the order of the integral length scale. It is shown that the number density of the droplets inside the clusters is approximately 7 times larger than that in the voids. The ratios of the droplets number densities in the clusters and voids to the total number density are independent of the test conditions and equal 5.5 and 0.8, respectively. The joint probability density function of the droplets diameter and clusters area shows that the droplets with the most probable diameter are found in the majority of the clusters. It is argued that intensifying the turbulence broadens the range of turbulent eddy size in the co-flow which allows for accommodating droplets with a broad range of diameters in the clusters. The results are of significance for engineering applications that aim to modify the clustering characteristics of large-Stokes-number droplets sprayed into turbulent co-flows.

Swash flows generated by a train of solitary waves on a planar slope

Six consecutive solitary waves with identical wave height and separation time are generated to study the flow structures during the uprush–downwash interactions in the swash zone. Using particle image velocimetry, the cross-shore velocity fields are captured. Two different wave conditions are examined with different wave-height-to-water-depth ratios, i.e.$H_o/h=0.11$and 0.22. The uprush–downwash interaction reaches quasi-steady state from the third solitary wave for both cases. For the former case, a weak non-stationary hydraulic jump appears during the downwash flow for all the six consecutive waves. The weak hydraulic jump evolves into a momentarily ‘stationary’ broken bore when the next wave arrives. For the latter case, the larger wave height generates stronger wave breaking. No non-stationary hydraulic jump is observed as the duration of downwash flow is relatively short. The flow reverses to the onshore direction before the downwash Froude number reaches the hydraulic jump condition. The temporal and spatial evolution of turbulence structure at the quasi-steady state is quantified using the spatial spectral analysis, the integral length scale and turbulence eddy viscosity. The results suggest that the large-scale energy generated during the uprush–downwash interaction modified the slope of the turbulence energy spatial spectrum in the inertial subrange from$-$5/3 to$-$1 in the larger length scale region, indicating the energy cascade depends not only on the dissipation rate, but also on the turbulent kinetic energy from the large-scale turbulence structure because of the large-scale energy injection in the inertial subrange.

Measurements of decaying grid turbulence with various initial conditions

The uniform grid, a tool commonly used to generate homogeneous and isotropic turbulence, has been the subject of many studies. Many studies have primarily focused on how initial conditions of uniform square grids, including the Reynolds number, mesh size, bar size, cross-section of bar, and solidities, affect the statistical characteristics of grid turbulence. However, the influence of mesh shape has not been studied extensively. This study deviates from the norm by examining the influence of different mesh shapes, specifically the uniform nonsquare grid, on grid turbulence. This variation in mesh shape can be easily achieved based on the traditional uniform square grid. The findings reveal that when a uniform nonsquare grid is used, the distance required for turbulence to fully develop decreases. Additionally, there is an increase in the low-frequency components of fluctuating velocity, while high-frequency components decrease. This shift leads to a difference in energy distribution. Moreover, using a uniform nonsquare grid reduces the anisotropies of decaying turbulence to a certain extent. The skewness approaches theoretical value of 0 more closely, while the flatness remains largely unchanged. The mesh shape also affects the decay exponents and power-law coefficients obtained, with the decay exponent potentially getting much closer to 1. Furthermore, larger integral length scales can be achieved at the same downstream position, without significantly modifying the turbulence intensity, by using the uniform nonsquare grid. This could better meet the requirements of large-scale turbulence in certain engineering fields, such as wind engineering, compared to the traditional uniform square grid.

Effects of turbulence on variations in early development of hydrogen and iso-octane flame kernels under engine conditions

The understanding and prediction of the early development of flame kernels are of high practical importance for the robust relight of aviation gas turbines and the control of cycle-to-cycle variations (CCV) of spark-ignition engines. CCV are known to correlate strongly with early flame kernel development and complicate the optimization of such engines in terms of safety, thermal efficiency, and engine emissions. The flame kernel initiated by a spark is initially small, in the very early combustion phase typically smaller than the size of the turbulent integral length scales. Therefore, the development of the flame kernel is dominated by local, intermittent flow fluctuations and can vary under the same nominal conditions. In this study, the effects of turbulence on the early development of premixed iso-octane and hydrogen turbulent flame kernels under realistic engine conditions are investigated through direct numerical simulations. Multiple realizations were simulated under the same nominal conditions for both fuels. Significant variations in flame kernel interactions with turbulence can be identified among different realizations. The fuel consumption rate varies by a factor of two, which is remarkable considering that only statistical differences in the local flow field are present between different realizations. Effects of different flow features of the initial flow fields on the flame kernel development were analyzed. It was found that the flow motion on the scale of the ignition radius, specifically the fluid deformation, which is characterized by the invariants of the strain rate tensor, determines the global shape of the kernel, while the variations of the kernel growth rate are mostly driven by the variations of the smallest turbulent scales. In particular, turbulence influences the flame surface area growth mainly through the tangential strain rate at the flame surface, which is shown to result from the small-scale turbulent motion. Due to differential diffusion effects, hydrogen and iso-octane exhibit significantly different flame responses to curvature, which is comprehensively studied for both fuels. The findings in this study will guide the development of combustion models that are capable to capture variations of the early flame kernels based on the local turbulence dissipation rate.

Reducing honeycomb-generated turbulence with a passive grid

Honeycombs are widely used to laminarize fluid streams by inhibiting the lateral components of the fluctuating velocity. However, they also produce additional turbulence by themselves due to the formation of large-scale instabilities and the breakup of the individual velocity profiles stemming from the honeycomb cells. In the present research, we use 2D-planar particle image velocimetry to study how honeycomb-generated turbulence is affected by a downstream grid. It is found that placing a grid near the honeycomb discharge drastically enhances flow uniformity by separating the strong jets stemming from the individual honeycomb cells into many smaller jets that are much more rapidly dissipated. The results show that using a grid reduces the integral length scale by up to a factor 10, and the axial and lateral energy spectra reveal that the grid primarily limits the energy contained in eddies with lower wave numbers. Furthermore, the grid can reduce the magnitude of peak turbulence intensity by as much as 95% and leads to a large reduction of the correlation length, as long as it is positioned upstream of the onset of the large-scale honeycomb-induced instabilities. A downstream grid is highly beneficial for both a laminar and turbulent honeycomb discharge and is most effective when there is a slight offset between the grid and honeycomb. Even though longer honeycombs generally produce more turbulence than short ones due to the larger length-scale of the shear layers, these effects are almost entirely decoupled when using a honeycomb-grid combination. Finally, a honeycomb-grid combination effectively inhibits both axial and lateral turbulence.Graphic abstract

Stabilization Characteristics of Transitional and Weakly Turbulent Lifted Jet Diffusion Flames

ABSTRACT This work reports experimental results from laminar-to-turbulent lifted jet diffusion flames. Characteristics of flame liftoff height, flame base structure, cold and reacting jet flow fields, and velocity fields near the flame base during the transitional process were obtained. The flame transition and stabilization characteristics are the focus of the present study. Results show that the lifted flame transition is mainly caused by the interaction between turbulent jets and flame base. As the transition begins, folding and distortion of the flame base occur. With the increase in Reynolds number (Re), the extent to which flame base is distorted increases constantly due to influences of more vortices. Simultaneously, at this transitional stage, the liftoff height decreases with Re. At different co-flow air velocities (U air ), the mean liftoff height with Re are qualitatively the same. While as U air is increased, the critical transitional Reynolds number (in which the flame transition begins) decreases. In the later transitional regime within a range of Re, both the cold and reacting jets exhibit intermittent breakup. After jet breakup, flame base immediately becomes turbulent. When the intermittent flow in the transitional stage gradually becomes less turbulent, flame base still remains turbulent for some time, within which flame and flow can be evidently decoupled. By statistical analysis, the integral length scale and the root mean square (r.m.s.) velocity fluctuation near the lifted flame base were obtained, and then the turbulent flame speed can be estimated. Experimental evidence provided for stabilization mechanism of the original transitional flames was confirmed by the balance between the local flow velocity and the flame speed. However, the difference between the two velocities gradually increases with the Reynolds number, suggesting some new stabilization characteristics. When the upstream eddy contains flammable fuel/air mixture, the flame base responds with moving upstream after ignition. On the contrary, when the mixture in the eddy is nonflammable, the flame base would move downstream.

Turbulence Effects on the Statistical Behaviour and Modelling of Flame Surface Density and the Terms of Its Transport Equation in Turbulent Premixed Flames

The influence of the ratio of integral length scale to flame thickness on the statistical behaviours of flame surface density (FSD) and its transport has been analysed using a Direct Numerical Simulation database of three-dimensional statistically planar turbulent premixed flames for different turbulence intensities. It has been found that turbulent burning velocity based on volume-integration of reaction rate and flame surface area increase but the peak magnitudes of the FSD and the terms of the FSD transport term decrease with an increase in length scale ratio for a given turbulence intensity. The flame brush thickness and flame wrinkling increase with an increase in length scale ratio for all turbulence intensities. However, the qualitative behaviours of the unclosed terms in the FSD transport equation remain unaltered by the length scale ratio and in all cases the tangential strain rate term and the curvature term act as leading order source and sink, respectively. A decrease in length scale ratio for a given turbulence intensity leads to a decrease in Damköhler number and an increase in Karlovitz number. This has an implication on the alignment of reactive scalar gradient with local strain rate eigenvectors, which in turn increases positive contribution of the tangential strain rate term with a decrease in length scale ratio. Moreover, an increase in Karlovitz number increases the likelihood of negative contribution of the curvature term. Thus, the magnitude of the negative contribution of the FSD curvature term increases with a decrease in length scale ratio for a given turbulence intensity. The model for the tangential strain rate term, which explicitly considers the scalar gradient alignment with local principal strain rate eigenvectors, has been shown to be more successful than the models that do not account for the scalar gradient alignment characteristics. Moreover, the existing model for the curvature and propagation term needed modification to account for greater likelihood of negative values for higher Karlovitz number. However, the models for the unclosed flux of FSD and the mean reaction rate closure are not significantly affected by the length scale ratio.

Self-similar propagation and flame acceleration of hydrogen-rich syngas turbulent expanding flames

In order to investigate the flame self-similar propagation and flame acceleration characteristics of hydrogen-rich syngas turbulent expanding flames, the turbulent combustion experimental studies of H2/CO/air mixtures with XH2 = 55%-95%, φ = 0.6–1.0, P = 1 bar-3 bar, u’=0.809–2.533 were conducted in a fan-stirred turbulent combustion chamber with an inner diameter of 380 mm. Results show that the normalized flame propagation speed ST/SL and turbulent flame Reynolds number ReT,flame could be represented by power-law correlations. With the increase of hydrogen fraction from 55% to 95%, the power exponent decreases from 0.413 to 0.301. The increase of hydrogen fraction makes the flame acceleration weaker because that the enhancing of laminar flame speed is more obvious than the differential-diffusion effect by decreasing Le. With the decrease of equivalence ratio from 1.0 to 0.6, the power exponent increases from 0.304 to 0.411 in this study. The relative high power exponent under low equivalence ratio is due to the coupling between differential-diffusion and the flame stretch on the local wrinkled flame structures. In addition, the influence of turbulence and flame intrinsic instabilities on flame acceleration propagation process of hydrogen-enriched syngas were studied. The acceleration exponent was extracted to quantitatively investigate the flame self-acceleration propagation in the transition stage, and the relationships between acceleration exponent and turbulence intensity (u’), Kovasznay number (Kz), turbulence integral length scale (LT), flame thickness (δ), thermal expansion ratio (ρu/ρb), effective Lewis number (Leeff) were analyzed

Baroclinic interaction of forced shock waves with random thermal gradients

Density gradients aligned at an angle to pressure gradients result in baroclinic torque in fluid flows, generating vorticity. In this work, we study the vorticity generated by the baroclinic torque exerted by the interaction of pressure jumps across random two-dimensional shock waves with density gradients. A field of random two-dimensional shock waves has acoustic spectral energy scaling as Êk∼ε2/3ℓ−1/3k−2, where k is the wavenumber, ε is the energy dissipation, and ℓ is the integral length scale of the field. Since the acoustic energy is broadband, pressure and velocity gradients exist in a wide range of length scales. We study the interaction of these broadband gradients with isobaric thermal gradients localized at a length scale in the spectral space. We show that the method of generating shock waves or injection of wave energy in the system governs the baroclinic interactions. For stochastically forced shock waves, baroclinic terms are negligible. Broadband vorticity with energy at least two orders of magnitude smaller is generated due to continuous variation in curvature of shock waves caused by stochastic forcing. On the other hand, shock waves maintained by energy rescaling result in the generation of coherent vorticity. We also discuss the relative magnitude of the baroclinic torque generated due to total density gradients compared to the one generated due to non-isentropic density gradients within the shock waves interacting with the pressure gradients.

On the impact of waves and turbulence on the power fluctuations and wake structure of a tidal-stream turbine

Anticipating the power output of tidal-stream turbines (TSTs) is relevant for its technological advance and success. Therefore, it is important to clarify the behavior of TSTs under tidal-stream environments, which include both waves and currents. In this study, a scale-model horizontal-axis TST was examined in turbulent conditions and in the presence of waves. The impact of waves on the wake structure and output power fluctuations were analyzed in terms of integral length scales, the turbine's power statistics, and spectral density. Due to wave–current interactions, the distribution of integral length scales is asymmetric at downstream positions behind the rotor's lateral tips. The fluctuations of the wave speed in the wake lead to a homogenized but reduced length scale. In the spectral domain, waves mix with the turbulent cascade, effectively reducing the energy decay from f 0 to f−1 in the low-frequency region and from f−5/3 to f−11/3 in the intermediate-decay region. The bandwidth of the mechanical noise in the high-frequency range, along with the periodic components, intensifies with increasing wave height and length. Although they are preliminary, these findings will prove useful for understanding the disruption of turbine flow and power output in wave–current flows. This is a first step toward assessing the damage caused to ecology and the structural parts of TSTs in real-world conditions.

Effects of crossflow pulsation intensity on wake properties of a circular cylinder

The effects of the crossflow pulsation intensity on the wake flow properties of a circular-cylinder were experimentally studied in a wind tunnel. A rotating plate actuator technique was used to generate periodic crossflow oscillations. The Reynolds number and oscillation Strouhal number of the crossflow were fixed at 3111 and 0.074, respectively. The crossflow pulsation intensities were varied within the range between 0.035 and 0.074. The wake evolution processes were captured by laser-light-sheet-assisted smoke flow visualization method. The wake instability frequencies and instantaneous oscillating turbulent velocities were detected by a one-component hot-wire anemometer along with a high-speed data acquisition system. The triple-decomposition technique was applied to the instantaneous velocities to consider the effects of the crossflow oscillations on turbulence. The statistical turbulence flow properties such as the Lagrangian integral time and length scales were estimated. The time-averaged flow structures and vorticity contours in the wake were obtained to analyze the wake geometric parameters by averaging instantaneously captured PIV images. The results revealed that at a fixed Reynolds number, the wake instability frequency of a circular cylinder in oscillating crossflow would present a value in-between of the natural wake instability frequency and the crossflow oscillating frequency. The turbulence intensity and Lagrangian integral time and length scales in the cylinder wake of the oscillating crossflow were drastically larger than those in the natural crossflow. The time-averaged geometric parameters of the recirculation bubble in the circular-cylinder wake in oscillating crossflow were significantly smaller than those in the natural crossflow. The crossflow oscillations induced large scale flow motions and hence enhanced entrainment and mixing in the wake. These mechanisms expedited turbulent diffusion of momentum in the wake, and therefore the turbulence intensity and turbulence time and length scales were enlarged and the geometric parameters of recirculation bubble were shortened when compared with those in the natural crossflow.

Production and transport of turbulent kinetic energy from premixed flames subjected to mean pressure gradients

The influence of mean favorable pressure gradients on the production and transport of turbulent kinetic energy is experimentally investigated in a premixed bluff-body combustor. The combustor wall geometry is modified into converging, straight, or diverging configurations to experimentally alter the mean pressure gradient in the reacting flow field. For each configuration, turbulent kinetic energy production and transport dynamics are characterized with high-speed particle image velocimetry and simultaneous CH* chemiluminescence imaging. For all cases, the premixed reaction increases the turbulent kinetic energy and integral length scales in the flow. However, increasing the magnitude of the mean favorable pressure gradient increases the turbulent kinetic energy produced by the flame. The source of increased turbulent fluctuations from reactants to products is first investigated with a steady flow energy analysis, and is accompanied with a Reynolds decomposed investigation of the kinetic energy in the flow. As the mean pressure gradient increases, the turbulent kinetic energy in the flow increases due to stronger magnitudes of flame-generated turbulence in the form of baroclinic torque. The evolution of the flame-generated turbulence is examined by decomposing the transport equation of turbulent kinetic energy. Increasing the mean favorable pressure gradient augments the largest magnitude transport terms, and the budget of turbulent kinetic energy is primarily driven by pressure gradient work and viscous dissipation. The results here differ from previous direct numerical simulation (DNS) studies, and should ultimately motivate additional research to aid the development of computational models which can better predict turbulent flame-flow dynamics in confined environments with mean pressure gradients.

Effects of turbulence intensity and integral length scale on the surface pressure on a rectangular 5:1 cylinder

This paper presents the LES of the turbulence effects on the flow over a two-dimensional rectangular 5:1 cylinder. The homogeneous and isotropic inflow turbulence fields are generated by the Iterating-Reshaping based Consistent Discrete Random Flow Generation (IRCDRFG) technique. A total of nine numerical cases with the inflow turbulence intensity equal to 5.0%, 7.5%, and 10.0%, and the ratio of integral length scale to cylinder depth (L/D) equal to 1, 2, and 4 are simulated respectively. The LES tool well reproduces both the instantaneous and time-averaged flow structures in the near cylinder area. The sizes of the mean separation bubble on the cylinder surface are noticed to decrease and be closer to the leading edge with the higher turbulence intensity and the lower L/D, which contributes to the shift of location with the minimum mean value and that with the maximum RMS value of the surface pressure. Besides, the consistent drag force results with different inflow conditions are obtained, which have strong connection with the following correlation results of surface pressure in different directions. Additionally, the PSD analysis shows that the low-frequency energy of the fluctuating pressure is significantly increased with the presence of the incoming large-scale turbulence field.

Influence of freestream turbulence on the near-field growth of a turbulent cylinder wake: Turbulent entrainment and wake meandering

The influence of freestream turbulence (FT) on near-field development of turbulent wakes is assessed with regards to both the entrainment rate of background fluid into the wake and the extent of wake meandering. It is shown that FT increases the entrainment rate into the near wake, and thereby the rate at which the wake spreads. The influence of FT on wake meandering is more complex, but it is shown that the integral length scale is the dominant property affecting meandering. In a novel control experiment, large-scale coherent motion in the wake is suppressed, and the far-wake results are recovered: that is, turbulent entrainment is reduced via the suppression of small-scale nibbling.

A Wavenumber–Frequency Spectrum Model for Sheared Convective Atmospheric Boundary Layer Flows

Abstract Parameterizing turbulence in the atmospheric boundary layer as a function of space and time is essential for weather and climate models. Here, we explore a model for wavenumber–frequency spectra based on a linear random advection approach to characterize sheared convective atmospheric boundary layer flows. Building on previous works, we obtain the wavenumber–frequency spectrum as a product of the wavenumber spectrum and a Gaussian frequency distribution, whose mean and variance are given by the mean advection and random sweeping velocities, respectively. The applicability of the model is tested with direct numerical simulation data in the mixed layer and the entrainment zone for the streamwise and vertical velocity components and buoyancy. To obtain a fully analytical model, we propose using a von Kármán wavenumber spectrum parameterized by the characteristic variances and integral length scales. These parameters are height dependent and vary considerably with the relative balance of buoyancy and shear forces. The introduced analytical model relies on fitting parameters obtained from numerical data in the relevant range of scales. The comparison of the von Kármán–based spectra for velocity and buoyancy to simulation results shows that the main features of the measured spectra are captured by the model.

Inflow turbulence distortion for airfoil leading-edge noise prediction for large turbulence length scales for zero-mean loading.

Turbulence distortion due to airfoil finite thickness is an important but not fully understood phenomenon that affects the airfoil radiated noise, resulting in inaccurate noise predictions. This study discusses the turbulence distortion in the leading edge (LE) region of an airfoil aiming to obtain more accurate LE noise predictions. Wind tunnel experiments were performed for National Advisory Committee for Aeronautics (NACA) 0008 and NACA 0012 airfoils at zero angle of attack subjected to large turbulence length scales (between 10 and 43 times the airfoil LE radius) generated by a grid and a rod. Hot-wire and surface pressure measurements were performed in the LE region. Results show that the root mean square of the velocity fluctuations urms and the turbulence integral length scale Λf at the stagnation line decrease considerably as the LE is approached. Rod-airfoil radiated noise was measured and compared with Amiet's model. The predicted noise overestimates the LE noise for high frequencies. However, the prediction agrees well with measurements when the turbulence spectrum based on the rapid distortion theory is used in Amiet's model, with as inputs the urms and Λf values measured close to the LE. This work's main contribution is to demonstrate that more accurate noise predictions are obtained when the inputs to the model consider the turbulence distortion effects.

A thorough experimental investigation on airfoil turbulence interaction noise

This paper on airfoil turbulence interaction noise reveals the nature of the relation between the distortion type of turbulent structures and radiated far-field noise. The turbulence interaction phenomenon is explored through comprehensive simultaneous hot-wire, surface pressure, and far-field noise measurements. Two grid turbulence cases are utilized to examine the effect of the coherent structure's length scale compared to the airfoil's leading-edge radius. The results show that the turbulent structures with a size comparable to the leading-edge radius disperse into smaller three-dimensional structures, losing their spatial coherence in the vicinity of the stagnation point. In contrast, the structures with larger integral length scales distort into highly coherent two-dimensional structures, yielding an increase in the surface pressure fluctuation energy spectra and the chordwise extent of the affected area by the interaction phenomenon, which is found to be responsible for the increased levels of far-field noise. The turbulence characteristics of the flow far upstream of the stagnation point determine the unsteady loading behavior at the stagnation point yet have little influence on the unsteady loading of the full airfoil chord. The stagnation point velocity fluctuations manifest a strong link to the remainder of the airfoil chord, as well as the near-field hydrodynamic to far-field acoustic signal coherence, while demonstrating no communication with the surface pressure fluctuations at the stagnation point.

A simplified semi-empirical model for long-range low-frequency noise propagation in the turbulent atmosphere

We present a semi-empirical long-range low-frequency acoustic propagation model, which accounts for atmospheric turbulence. Ostashev and Wilson’s scattering model is combined with a ray-theory based refraction model to account for turbulent scattering and refraction via a turbulent absorption coefficient. The coefficient is ascertained via integration of scattered energy. The model is formulated, calibrated, and validated via corresponding experiments conducted within the National Science Foundation Boundary Layer Wind Tunnel. The predictions of the newly proposed ‘bridging model’ match the wind tunnel experimental data with an average error of 11.9%. Example predictions are shown to quantify the effect of turbulent kinetic energy and turbulent integral length scale on long-range infrasound propagation. To demonstrate the approach, we present predictions of the propagation of noise from a tornado and a nonlinear wave.

Disturbance growth in a laminar separation bubble subjected to free-stream turbulence

Experiments were conducted to study the transition and flow development in a laminar separation bubble (LSB) formed on an aerofoil. The effects of a wide range of free-stream turbulence intensity ( $0.15\,\%< Tu<6.26\,\%$ ) and streamwise integral length scale ( $4.6\ {\rm mm}<\varLambda _{u}<17.2\ {\rm mm}$ ) are considered. The co-existence of modal instability due to the LSB and non-modal instability caused by streaks generated by free-stream turbulence is observed. The flow field is measured using hot-wire anemometry, which showed that the presence of streaks in the boundary layer modifies the mean-flow topology of the bubble. These changes in the mean flow field result in the modification of the convective disturbance growth, where an increase in turbulence intensity is found to dampen the growth of the modal instability. For a relatively fixed level of $Tu$ , the variation of $\varLambda _{u}$ has modest effects. However, a slight advancement of the nonlinear growth of disturbances and eventual breakdown with the decrease in $\varLambda _{u}$ is observed. The data show that the streamwise growth of the disturbance energy is exponential for the lowest levels of free-stream turbulence and gradually becomes algebraic as the level of free-stream turbulence increases. Once a critical turbulence intensity is reached, there is enough energy in the boundary layer to suppress the laminar separation bubble, resulting in the non-modal instability taking over the transition process. Linear stability analysis is conducted in the fore position of the LSB. It accurately models incipient disturbance growth, unstable frequencies and eigenfunctions for configurations subjected to turbulence intensity levels up to 3 %, showing that the mean-flow modification due to the non-modal instability dampens the modal instability.