Laminar Separation Research Articles

Direct numerical simulation and mode analysis of turbulent transition flow in a compressor blade channel

The separation and turbulent transition of the flow in a compressor blade channel are investigated through direct numerical simulations (DNS) at a Reynolds number of 1.367 × 105. Based on the original DNS data, both time-averaged statistics and instantaneous vortex structures of the flow field are extensively analyzed. The vortices are visualized and studied by the Liutex method, and the streaming dynamic mode decomposition (SDMD), a low-storage variant of conventional DMD, is applied to the large datasets obtained on both pressure and suction sides. The physical quantity analyzed with SDMD is the Liutex magnitude R. The DNS results indicate that flow separation occurs on both sides of the blade. On the pressure surface, the separation is weak and the flow remains in a natural transition dominated by viscous Tollmien–Schlichting instabilities. In contrast, owing to the presence of a large laminar separation bubble, the flow experiences a separation transition governed by inviscid Kelvin–Helmholtz instabilities on the suction surface. The SDMD results suggest that a broad range of vortex frequencies exist in the transition flow, and the scale of the spatial structures is negatively correlated with the frequency of the mode. On the pressure surface, the extracted SDMD modes are primarily related to Kelvin–Helmholtz rolls, whereas on the suction side, influenced by the separated boundary layer, the modal structures exhibit greater diversity.

Study on the application of 3D imaging based on the γ-photon silk thread method for visualisation and detection of flow fields

As a flow display technique, the silk thread method can clearly show the state of the flow field. However, displaying the state of the flow field in industrial closed metal cavities is impossible, and results of the traditional silk thread method fail to present depth information. To address these limitations, we propose a display method based on γ-photon silk thread 3D imaging. Firstly, a flow field visualization experimental platform applicable for industrial closed metal cavity was designed. Then, aiming at the shortcomings of insufficient γ-photon scanning data and limited imaging quality in flow field visualization, an adaptive sinogram interpolation-iterative filtering reconstruction algorithm was proposed to expand the data via the adaptive interpolation processing of the sinogram in image reconstruction. Beltrami filtering was also embedded in the iterative algorithm to effectively reduce noise and artifacts in the imaging image. Finally, the internal flow field inspection of the NACA0018 airfoil and the industrial confinement turbine were used as examples to visualise the wing upper surface flow and turbine blade passage secondary flow, respectively, and the results were consistent with those of the numerical simulation analysis. As the angle of attack of the wing increased, laminar flow separation occurred, and the silk thread structure state changed to the point where the aircraft stalled. After the imaging map analysis, the stall angle ranged between (15°,19°), which is consistent with the simulation results. In the turbine blade passage secondary flow detection, the imaging map formed a horseshoe vortex with airflow separation at the central saddle point and silk threads clearly presenting the structural state of the flow field along different directions.

The Effect of Riblets on the Aerodynamic Performance of NACA 0018 Airfoil

In this numerical study, riblets on the airfoil were utilized to enhance the aerodynamic performance of NACA0018 airfoil. Riblets of identical height and base length are strategically placed on the suction surface of the airfoil with varying spacing ratios along the flow direction (x) and chord length (c), specifically x/c = 0.3 and 0.7. Four distinct riblet airfoil models are subjected to computational fluid dynamics (CFD) analysis within an angle of attack range from 0° to 21° at a Reynolds number of Re=1×105. The obtained results are systematically compared with the performance of the plain airfoil. Numerical analyses reveal the significant influence of the spacing ratio on flow control and the overall aerodynamic performance of the airfoil, establishing a direct relationship with riblet spacing. The presence of riblet structures is observed to increase the lift coefficient, concurrently delaying the stall angle up to 19°. Notably, the ribbed structures effectively mitigate the interaction between the laminar separation bubble and trailing edge separation, leading to a reduction in turbulent kinetic energy values.

Aerodynamic Performance of a Finite-Span Wing in a Time-Varying Freestream

The current study analyzes the dynamic response of a NACA 0015 finite-span wing to a time-varying freestream in an unsteady wind tunnel at a mean Reynolds number of 1.0×105. The aerodynamic response of the wing can be categorized based on the angle of attack and the degree of flow separation on the suction side of the wing. When the suction side is dominated by separated flow, either at low angles of attack with long laminar separation bubbles or at high, poststall, angles of attack, the lift is enhanced by the favorable pressure gradient during freestream acceleration and decremented by the adverse pressure gradient during freestream deceleration. In these cases, the sectional lift coefficient is shown to oscillate by as much as ±0.1 due to the unsteady pressure gradient. Comparatively, regions of attached flow on the wing surface remain largely unaffected by the time-varying conditions, regardless of the reduced frequency. Discrepancies between the measured lift and the estimated response from Isaacs’s theory demonstrate that the coupling between the viscous flow separation and the unsteady conditions dominates the unsteady aerodynamic response.

Swing and reverse swing of a cricket ball: laminar separation bubble, secondary vortex and wing-tip-like vortices

Large eddy simulation of flow past a cricket ball with its seam at $30^\circ$ to the free stream is carried out for $5 \times 10^4 \le Re \le 4.5 \times 10^5$ . Three regimes of flow are identified on the basis of the time-averaged swing force coefficient ( $\bar {C}_Z$ ) – no swing (NS), conventional swing (CS, $\bar {C}_Z>0$ ) and reverse swing (RS, $\bar {C}_Z<0$ ). The effect of seam on the boundary layer is investigated. Contrary to the popular belief, the boundary layer does not transition to a turbulent state in the initial stages of CS. The seam energizes the laminar boundary layer and delays its separation. The delay is significantly larger in a region near the poles, whose extent increases with an increase in $Re$ causing $\bar {C}_Z$ to increase. Here $\bar {C}_Z$ assumes a near constant value in the later stage of CS. The boundary layer transitions to a turbulent state via formation of a laminar separation bubble (LSB) in the equatorial region and directly, without a LSB, in the polar region. The extent of the LSB shrinks while the region of direct transition near the poles increases with an increase in $Re$ . A LSB forms on the non-seam side of the ball in the RS regime. A secondary vortex is observed in the wake bubble. While it exists on the non-seam side for the entire range of $Re$ considered, the mixing in the flow introduced by the seam causes it to disappear beyond a certain $Re$ on the seam side. The pressure difference between the seam and non-seam sides sets up wing-tip-like vortices. Their polarity reverses with the switch from the CS to RS regime.

Propeller-noise reduction by microfiber coating on a blade surface

The popularity of small aerial vehicles has dramatically increased in recent years and propeller noise from such vehicles is a public health concern. Further advancement and utilization of small aerial vehicles require a substantial focus on noise reduction. Microstructures using surface and coating technology are applied in a variety of ways to address this engineering challenge. This study investigates a microfiber coating as a passive means for reducing propeller noise. The microfiber coating is comprised of a fibrous structure and has been previously shown to be a passive mean for reducing drag on a circular cylinder. To begin testing the efficacy of the microfiber coating for propeller noise reduction, microfiber-coated strips are placed at different spanwise locations on propeller blades. The sound pressure level produced by the rotating propeller is measured using a sound-level meter. The microfiber-coated propeller exhibited a lower sound pressure level than that of the uncoated propeller. At a Reynolds number of 7.4 × 104 based on the chord at the 75% spanwise station of the propeller blade, the microfiber-coated propeller achieved a noise reduction of up to 1.6 dBA compared to that of the uncoated propeller. The microfiber coating is effective in reducing broadband noise associated with the interaction of the vortex shedding associated with laminar boundary layer separation. It is found that the noise-reduction performance is a function of the spanwise location of the microfiber-coated strips.

Nonlinear Evolution of Instabilities in a Laminar Separation Bubble at Hypersonic Speeds

The development of both convective stationary perturbation and global instabilities in the vicinity of a laminar separation bubble above an axisymmetric compression corner in hypersonic flow was investigated using numerical simulations. The flow configuration of interest corresponded to the cone–cylinder–flare model used in experimental measurements in the Boeing/U.S. Air Force Office of Scientific Research Mach-6 Quiet Tunnel (BAMQT) at Purdue University. For a flare angle of 10 deg and unit Reynolds number of 11.5×106 m−1, their surface flow visualizations identified the presence of streamwise elongated thermal streaks near the reattachment location that had a dominant azimuthal wave number m=36. Previous linear stability analyses predicted that the amplification characteristics of small-amplitude, unsteady, and convective instabilities within this flow were consistent with the surface pressure fluctuations measured in the experiment. However, their accompanying investigation of global instabilities showed that the separation bubble was weakly unstable at the 10 deg flare angle, with the most unstable global mode corresponding to a stationary disturbance with m≈5–6 (i.e., well below the measured wave number of m=36. Besides characterizing the global instability for selected flare angles, the present numerical simulations quantify the details of the stationary equilibrium state associated with supercritical bifurcation resulting from the nonlinear saturation of the unstable global mode. Although velocity perturbations associated with the saturated global mode are dominated by the fundamental spanwise wavelength associated with the linear global instability, the surface heat flux downstream of the reattachment is dominated by m=36, in agreement with the experimental measurements.

Extraction of geometric features and analysis of flow mechanism of high loaded compressor airfoils at low Reynolds number

When the aircraft cruising at high altitude, the aerodynamic performance of the compressor sharply decreases due to the enhanced boundary layer separation loss. Therefore, it is of great significance to design the high-performance airfoils suitable for low Reynolds numbers (Re) to improve the aerodynamic performance of compressor. In this paper, numerical simulations were carried out on a high-loaded subsonic compressor cascade V103 at low Re. Meanwhile, a multi-objective optimization of blade profile was performed to get optimal solutions, and data mining techniques were applied to extract valuable design knowledge from the optimal database. The results show that the Pareto-optimal airfoils achieve a maximum reduction of 27.32% in total pressure loss coefficient under design condition and 36.71% under near stall condition. Compared with the original airfoil, the curvature distribution law of the camber line with larger values at both ends and smaller values in the middle is advantageous for the performance of the compressor cascade under design condition. This distribution pattern causes a forward shift for the loading distribution of airfoils, accompanied by an earlier transition onset. Additionally, it reduces adverse pressure gradient at the rear part of suction surface, which suppresses the development and growth of laminar separation bubble and delays the separation of turbulent boundary layer. Under near stall condition, maintaining larger leading edge angle and uniform flow diffusion is beneficial for improving the performance of compressor cascade. This is because the larger leading edge angle reduces incidence angle, while the uniform flow diffusion inhibits a great flow separation.

Insights into the transition of separation bubble over a rough surface at varying angles of attack

The evolution of a separated boundary layer on the rough surface in the vicinity of a leading edge of a model airfoil is documented at varying angles of attack. Particle image velocimetry and hotwire data are analyzed to elucidate the flow feature, depicting the manifestation of the shear layer, its rollup, growth of perturbations, spectral response, and intermittency. For a hydrodynamically smooth surface, a laminar separation bubble often appears near the leading edge, where the shear layer becomes inviscidly unstable. Wall roughness amplifies the near-wall perturbations, resulting in earlier transition and reattachment. This leads to a reduction in bubble length and laminar shear layer length compared to the smooth surface at the corresponding angle of attack. Notably, despite the amplification of selective frequency, the inviscid instability is bypassed on the rough surface for varying angles of attack. Moreover, the linear stability analysis proves inadequate in predicting the most amplified frequency and the growth of disturbances. Furthermore, the universal intermittency curve formulated for the bypass transition is valid for the separation-induced transition, illustrating the significance of viscous effect.

Experimental Investigation of the Effect of Bio-Inspired Wavy Leading-Edges on Aerodynamic Performance and Flow Topologies of the Airfoil

The characteristic of delayed airfoil stalls caused by the bio-inspired Wavy Leading-Edges (WLEs) has attracted extensive attention. This paper investigated the effect of WLEs on the aerodynamic performance and flow topologies of the airfoil through wind tunnel experiments, while also discussing the flow control mechanism of WLEs. The result shows that, at small Angle of Attack (AOA), the flow through the WLEs exhibits periodic and symmetrical characteristics, where flow vortices upwash at the trough and downwash at the crest, resulting in flow from the crest to the trough. Upwash leads to the formation of a localized three-dimensional laminar separation bubble (LSB) structure at the leading edge of the trough section. At large AOA after baseline airfoil stall, the flow on the airfoil surface of WLEs presents a two-period pattern along the spanwise direction, and the separation zone and the attachment zone appear alternately, indicating that the control effect of delayed stall is accomplished by reducing the separation zone on the airfoil surface. The alternating occurrence of the separation and attachment zones is the result of intricate interactions among flows passing through multiple WLEs. This interaction causes the convergence of high-momentum attached airflows on both sides, thereby constraining the spread of the separation from the leading edge and enabling the re-attachment of separated air. The research results of this paper provide a reference for researchers to reveal the flow control mechanism of WLEs more comprehensively.

Laminar Separation Control for Eppler 387 Airfoil Based on Resolvent Analysis

By actively controlling laminar separation, the aerodynamic loading can be increased. In the context of turbomachinery, an increased loading allows for more power to be extracted or for a lower part count. Active flow control can be made more effective and efficient if the actuator location and forcing frequency are chosen well. Large-eddy simulations of the flow over an E387 airfoil were carried out for a chord Reynolds number of 100,000. For an angle of attack of zero degrees, the suction-side boundary layer separates laminar to form a large separation bubble. With 1% freestream turbulence intensity, the boundary layer reattaches earlier, and the length of the separated region is in better agreement with available measurements. A resolvent analysis suggests that forcing immediately upstream of separation with an angular frequency of 50 (based on freestream velocity and chord length) provides the maximum forcing-response gain. Guided by the resolvent analysis, active flow control by wall-normal blowing and suction was then investigated in the simulation. Forcing introduces laminar, two-dimensional “rollers” that effectively suppress separation. Without freestream turbulence, transition occurs close to the trailing edge. With freestream turbulence, the flow transitions further upstream and active flow control is less effective.

Aerodynamic and Aeroacoustic Effects of Different Transition Mechanisms on an Airfoil

The paper delves into the detailed sound generation and propagation mechanisms associated with tripping-induced flow perturbations and trailing-edge scattering using wall-resolved large-eddy simulations. Two distinct boundary-layer tripping techniques, namely a geometrically resolved stair strip and an artificially modeled trip using suction and blowing, are investigated. To facilitate comparison, the natural boundary-layer transition is also simulated as a baseline scenario. The analysis takes into account a Reynolds number of 4×105, a Mach number of 0.058, and a nonzero angle of attack of 6.25° over a NACA 0012 airfoil configuration. The mechanisms for sound generation and propagation related to trailing-edge noise remain consistent across the three transition scenarios. However, boundary-layer tripping notably leads to intricate, scenario-specific noise generation: there is an interaction between the laminar separation bubble and tripping for the stair strip case, whereas laminar boundary-layer instability is evident for the suction and blowing scenario. Aerodynamic flowfields involving acoustic noise sources, their propagating natures near the wall, and far-field acoustics are cross-examined in detail. The comprehensive analysis of observed phenomena provides valuable insights for understanding nonlinear flow and acoustic interactions relevant to airfoil noise and designing new types of trips under adverse pressure gradient flows.

Investigation of Transition Flow on Suction Surface of Highly Loaded Compressor Cascade Controlled by Plasma Actuator

A practical method for improving the performance of highly loaded compressor cascades is to delay the onset of transition. Plasma actuators are used on the suction surface to manage the transition from laminar to turbulent by injecting momentum into the boundary layer. An experimental study was conducted in a low-speed wind tunnel to validate the actuator's control capability and the numerical simulation model. Both experimental and numerical results show that actuators located at various positions can improve the performance of the cascade and reduce flow loss to varying degrees. The most effective method is to place the actuator upstream of the separation bubble to delay the onset of the transition from laminar to turbulent flow, which results in a 6.32% decrease in total pressure loss and a 2.5% increase in static pressure rise. The control scheme at the transition position restores laminar flow locally, causing a secondary transition. However, it has the lowest control capability due to the dissipation of the actuator momentum. The downstream control scheme only suppresses the degree of turbulent separation without delaying laminar separation, resulting in weaker control effectiveness compared to the upstream laminar separation scheme. The study also examined the interaction between the plasma actuator on the suction surface and the flow in the endwall region, which showed that the accumulation of low-energy fluid in the corner region increases, resulting in a slight elevation of shear losses between the midspan boundary layer and the corner region.

Experimental Investigation of Additional Loss Associated With Incoming Wakes in Low-Pressure Turbine Cascades

Abstract The present paper aims to experimentally investigate the influence of wake-passing frequency, Reynolds number, and suction surface diffusion rate on the additional loss due to incoming wakes to the profile loss in the low-pressure turbine (LPT) cascades and discuss a design guide for reducing the additional loss. Using a moving-bar mechanism, the unsteady effects of incoming wakes were measured in a low-speed linear turbine cascade facility. The wake-passing frequency was varied by adjusting the moving-bar speed. The different airfoils with different surface velocity distributions were tested to examine the effect of suction surface diffusion rate. For each test case in an unsteady flow condition, the additional loss due to incoming wakes was derived by subtracting the profile loss from the measured total pressure loss across the cascade. Here, the profile loss was estimated by using the friction drag force, which was calculated by the measured surface velocity distribution, and the pressure drag force, which was calculated by the measured surface pressure distribution and the predicted base pressure. The resultant additional loss includes all kinds of losses associated with incoming wakes, such as mixing loss of incoming wakes enhanced in the blade passage and unsteady interaction loss between incoming wakes and surface boundary layers. It was demonstrated that in an unsteady flow condition, a substantial performance improvement was obtained in the entire Reynolds number range by applying the surface velocity distribution with no laminar separation to a low-solidity blade row.

An Experimental Database for the Analysis of Bursting of a Laminar Separation Bubble

The bursting phenomenon consists in the switch of a laminar separation bubble from a short to a long configuration. In the former case, reduced effects on profile pressure distribution are typically observed with respect to the attached condition. On the contrary, long bubbles provoke significant variations in the loading coefficient upstream of the separation position, with increased risk of stall of the lifting surfaces. The present work presents an experimental database describing separated boundary layers evolving under different Reynolds numbers, adverse pressure gradients and free-stream turbulence levels. Overall, more than 80 flow conditions were tested concerning short and long bubbles for the characterization of separated flows under turbine-like conditions. Measurements were performed on a flat plate geometry using a fast-response Particle Image Velocimetry (PIV) system. For each flow case, two sets of 6000 flow records were acquired with an acquisition frequency equal to 300 and 1000 Hz. Based on existing criteria for the identification of the bursting phenomenon, the flow cases were clustered in terms of short and long bubble states. Additionally, the kind of instability (i.e., convective or absolute) developing into the separated boundary layer was identified based on flow statistics. The present data captures the existing link between the bursting of a laminar separation bubble and the onset of the absolute instability of the separated shear layer, with stationary vortices forming in the dead air region.

Experimental investigation of instantaneous lift on NACA 0018 airfoil section due to a non-harmonic pitching motion

In this study, we explore the problem of an airfoil in a harmonic and arbitrary periodic pitching motion and seek to understand how theoretical estimation with first-order potential theory match experiments. We adopt Jones’ approximation for the Wagner function for lift computations in the time domain and Theodorsen’s model in the frequency domain. We experimentally investigate a two-dimensional symmetric NACA 0018 airfoil in pitching motion under attached flow with reduced frequencies up to 0.25 and Reynolds number varying from 1.5×105 to 3×105. To eliminate the influence of the laminar separation bubble, free-stream turbulence intensity was elevated above the baseline level by placing turbulence generating grid, thus, obtaining better compatibility between the flow conditions in the experiments and the theoretical assumptions. Time-resolved sectional lift is determined by simultaneous static pressure measurement with miniature pressure transducers. The transient response is captured with accuracy in the time domain by quantifying the non-circulatory contribution. Excellent agreement is achieved in the time and frequency domains due to the highly accurate measurement of the instantaneous magnitude and phase of the time-resolved surface pressures. We further explore the applicability of the theory for high-pitching amplitudes, which results in a temporary deviation of the measured lift from the theoretical predictions. As the frequency domain unsteady theory is more widely studied than its time domain counterpart, this study provides a unique opportunity to highlight the significance of time-domain analysis in estimating instantaneous lift in non-harmonic motion.

Evaluating the Effects of Pulsed Electrical Stimulation on the Mechanical Behavior and Microstructure of Medulla Oblongata Tissues.

The development of remote surgery hinges on comprehending the mechanical properties of the tissue at the surgical site. Understanding the mechanical behavior of the medulla oblongata tissue is instrumental for precisely determining the remote surgery implementation site. Additionally, exploring this tissue's response under electric fields can inform the creation of electrical stimulation therapy regimens. This could potentially reduce the extent of medulla oblongata tissue damage from mechanical compression. Various types of pulsed electric fields were integrated into a custom-built indentation device for this study. Experimental findings suggested that applying pulsed electric fields amplified the shear modulus of the medulla oblongata tissue. In the electric field, the elasticity and viscosity of the tissue increased. The most significant influence was noted from the low-frequency pulsed electric field, while the burst pulsed electric field had a minimal impact. At the microstructural scale, the application of an electric field led to the concentration of myelin in areas distant from the surface layer in the medulla oblongata, and the orderly structure of proteoglycans became disordered. The alterations observed in the myelin and proteoglycans under an electric field were considered to be the fundamental causes of the changes in the mechanical behavior of the medulla oblongata tissue. Moreover, cell polarization and extracellular matrix cavitation were observed, with transmission electron microscopy results pointing to laminar separation within the myelin at the ultrastructure scale. This study thoroughly explored the impact of electric field application on the mechanical behavior and microstructure of the medulla oblongata tissue, delving into the underlying mechanisms. This investigation delved into the changes and mechanisms in the mechanical behavior and microstructure of medulla oblongata tissue under the influence of electric fields. Furthermore, this study could serve as a reference for the development of electrical stimulation regimens in the central nervous system. The acquired mechanical behavior data could provide valuable baseline information to aid in the evolution of remote surgery techniques involving the medulla oblongata tissue.

A review and reassessment of the aerodynamics of cricket ball swing

This paper reviews 70 years of cricket ball swing literature and reassesses the results in light of new measurements. A comparison of ball tracking data with published experimental results shows that current understanding does not explain the behaviour observed in professional cricket matches. Descriptions of cricket ball boundary layer aerodynamics are updated with new results which show that the seam acts more like a series of vortex generators than a trip and that there is a laminar separation bubble on the seam side of the ball. Previous results for reverse swing are consolidated and compared with new data, showing that different magnitudes of swing occur depending on the condition of both sides of the ball. Variation in pressure and temperature should be included when the Reynolds number, a non-dimensional ball speed, is calculated, while humidity can be neglected. Studies on the effect of wind speed and direction are summarised and results considering the effect of free-stream turbulence are compared with new measurements. Throughout the paper, recommendations for future work are suggested. These include quantitative study of the effect of surface defects and roughness, an assessment of whether atmospheric turbulence can affect swing and investigation into the effect of backspin on swing.

Effect of aero-shaped vortex generators on NACA 4415 airfoil

A parametric study was carried out to investigate the effect of aero-shaped vortex generators (AsVGs) on NACA 4415 airfoil by comparing conventional vortex generators (CVGs). Force and flow visualization experiments were carried out for the CVGs and AsVGs at Re = 1.4 × 105. Six different configurations were selected for the positioning of the CVGs to investigate the best one. The best configuration was applied to the Aero-shaped VGs type, which is generated with the S1223 airfoil model. The results indicated that even if AsVGs did not show better performance to delay the stall angle when compared with the CVGs, in some positions they produced the same stall performance as the CVGs. Moreover, aero-shaped VGs increased the lift coefficient (CL) more than the conventional ones in the pre-stall region. At x/c = 0.1, CL and CD improve by up to 107.7% and 23.39% compared to baseline, respectively. At α = 18° and Re = 0.8 × 105, AeM5 at x/c = 0.1 increased the CL by 102.45% compared to the baseline model. While the CVGs increased the lift coefficient (CL) and postponed the stall (α) angle up to 4° according to the baseline model, the CVGs also caused an overall increase in the drag coefficient (CD). AsVGs decreased the drag coefficient (CD) more than conventional ones. Lift to drag ratio (L/D) of AsVGs is higher than that of the CVGs. The results of the surface oil flow visualization showed that both CVGs and AsVGs segmented the laminar separation bubble (LSB) and formed attached flow zones on the airfoil surface. As a result, AsVGs can be used as an alternative to CVGs in flow control applications.

A data-driven analysis of short and long laminar separation bubbles

This work investigates the statistical response of short and long laminar separation bubbles to external flow parameters, such as Reynolds number, free-stream turbulence intensity and streamwise pressure gradient, known to govern bubble formation and characteristics. A parametric experimental campaign has been performed using particle image velocimetry on a flat plate to provide a comprehensive database for the characterization of separation-induced transition in both short and long separation bubbles. The proper orthogonal decomposition (POD) was applied to the data set of all dividing streamlines commonly used to identify a laminar separation bubble. This provides an optimal state-space basis for the data-driven classification of the state of a laminar separation bubble, with the leading modes capturing the change in length and height of the laminar separation bubble in response to changes in the flow parameters. When projected onto the POD subspace constituted by the first three leading modes, the normalized data from the present study and the results from prior investigations not used in the modal analysis collapse on the same trajectory in the low-dimensional space. The present POD basis can be therefore adopted for the description of the general response of the time-mean shape of a laminar separation bubble to changes in the main influencing parameters. A well-defined pattern was observed in the case of short laminar separation bubbles in the reduced-order space defined by the first three POD coefficients, whereas a higher dispersion in the long-bubble regime indicates an increased sensitivity of long bubbles to the external flow characteristics.