Transitional Flat-plate Boundary Layer Research Articles

Instability and transition control by steady local blowing/suction in a hypersonic boundary layer

The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

Impact of Low Freestream Turbulence and Surface Roughness on the Flat-Plate Boundary Layer Transition Under a High-Lift Airfoil Pressure Gradient

Abstract Effects of low incoming freestream turbulence level (Tu < 1%) and surface roughness on the transition of flat-plate boundary layers under a high-lift airfoil pressure gradient have been investigated. Time-resolved streamwise and wall-normal velocity fields with surface roughness values of Ra/C = 0.065 × 10−5, 4.417 × 10−5, and 7.428 × 10−5 have been measured at a fixed Reynolds number of 5.2 × 105 and freestream turbulence intensity of 0.2%. For the reference smooth surface of Ra/C = 0.065 × 10−5, a laminar separation bubble forms from about 64% to 83% of the chord length. Increasing surface roughness has little impact on the laminar boundary layer separation onset but reduces the height and length of the separation bubble and induces earlier transition. For Ra/C = 4.417 × 10−5, displacement thickness during transition is slightly thinner and the overall momentum deficit is slightly lower than those for Ra/C = 0.065 × 10−5. For Ra/C = 7.428 × 10−5, the separation bubble becomes hardly visible as the transition mode approaches the attached mode, and turbulent mixing by the wall-bounded turbulence becomes dominant. In addition, the portion of turbulent wetted area increases due to earlier transition, and momentum deficit increases more rapidly in the turbulent wetted area. Thus, the overall momentum deficit for Ra/C = 7.428 × 10−5 is larger than that for Ra/C = 0.065 × 10−5.

Numerical Investigation of Hypersonic Flat-Plate Boundary Layer Transition Subjected to Bi-Frequency Synthetic Jet

Transition delaying is of great importance for the drag and heat flux reduction of hypersonic flight vehicles. The first mode, with low frequency, and the second mode, with high frequency, exist simultaneously during the transition through the hypersonic boundary layer. This paper proposes a novel bi-frequency synthetic jet to suppress low- and high-frequency disturbances at the same time. Orthogonal table and variance analyses were used to compare the control effects of jets with different positions (USJ or DSJ), low frequencies (f1), high frequencies (f2), and amplitudes (a). Linear stability analysis results show that, in terms of the growth rate varying with the frequency of disturbance, an upstream synthetic jet (USJ) with a specific frequency and amplitude can hinder the growth of both the first and second modes, thereby delaying the transition. On the other hand, a downstream synthetic jet (DSJ), regardless of other parameters, increases flow instability and accelerates the transition, with higher frequencies and amplitudes resulting in greater growth rates for both modes. Low frequencies had a significant effect on the first mode, but a weak effect on the second mode, whereas high frequencies demonstrated a favorable impact on both the first and second modes. In terms of the growth rate varying with the spanwise wave number, the control rule of the same parameter under different spanwise wave numbers was different, resulting in a complex pattern. In order to obtain the optimal delay effect upon transition and improve the stability of the flow, the parameters of the bi-synthetic jet should be selected as follows: position it upstream, with f1 = 3.56 kHz, f2 = 89.9 kHz, a = 0.009, so that the maximum growth rate of the first mode is reduced by 9.06% and that of the second mode is reduced by 1.28% compared with the uncontrolled state, where flow field analysis revealed a weakening of the twin lattice structure of pressure pulsation.

Time-resolved visualization of coherent structures during supersonic boundary layer transition

The coherent structures arising during flat-plate boundary layer transition at Mach number 3.4 are investigated using a custom-built hyper-rate imaging system. The evolution of transitional structures is investigated in the Eulerian and Lagrangian reference frames. The upstream evolution of transition is dominated by the generation of new hairpin structures, while the interaction among multiple structural types dominates the evolution downstream. The breakdown of the existing structure, which may be caused by interactions among multiple types of structures with similar scales, is also visualized.

Leading-edge pressure gradient effect on boundary layer receptivity to free-stream turbulence

Free-stream turbulence (FST) induced boundary layer transition is an intricate physical process that starts already at the leading edge (LE) with the LE receptivity process dictating how the broad spectrum of FST scales is received by the boundary layer. The importance of the FST integral length scale, apart from the turbulence intensity, has recently been recognized in transition prediction but a systematic variational study of the LE pressure gradient has still not been undertaken. Here, the LE pressure gradient is systematically varied in order to quantify its effect on the transition location. To this purpose, we present a measurement technique for accurate determination of flat-plate boundary layer transition location. The technique is based on electret condenser microphones which are distributed in the streamwise direction with high spatial resolution. All time signals are acquired simultaneously and post-processed giving the full intermittency distribution of the flow over the plate in a few minutes. The technique is validated against a similar procedure using hot-wire anemometry measurements. Our data clearly shows that the LE pressure gradient plays a decisive role in the receptivity process for small integral length scales, at moderate turbulence intensities, leading to variations in the transitional Reynolds number close to 40 %. To our knowledge, this high sensitivity of LE pressure gradient to transition has so far not been reported and our experiments were therefore partly repeated using another LE to ensure set-up independence and result repeatability.

Predictive Simulation of Two-dimensional Flat Plate Boundary Layer Transition

The laminar-turbulent transition is an old but still not a fully solved problem, which is mainly studied from the following aspects: (1) how the perturbation is generated and the receptivity problems (2) linear and nonlinear problems during the evolution of the perturbation (3) numerical simulation of the transition problem and the actual prediction. Considering that the power system of the vehicle is working in a low Reynolds number environment for a long time when flying at high altitudes. In this article, the research focuses on the turbulence model with the introduction of the AGS transition model is used to simulate the two-dimensional flat plate boundary layer transition in the low Reynolds number case, and to predict the transition location by combining the stability of different positions of the flow process, and to evaluate the accuracy of the transition model in comparison with other numerical simulation methods.

The effect of concave roughness on the hypersonic flat-plate boundary-layer transition

In order to reveal the effect of aircraft surface concave roughness on the transition, several hypersonic quiet wind tunnel tests were carried out on the flat-plate model with independent concave roughness on the surface. The experimental Mach number was 6.5 and the total temperature was 430 K. Using infrared thermal imaging technology, a general rule of the effect of concave roughness on the boundary layer transition was obtained. The flow visualization results and the PCB pressure measurement results showed that the concave roughness promotes the transition by increasing the growth of the first mode wave rather than the growth of the second mode wave.

Numerical simulation of nonlinear interactions in a naturally transitional flat plate boundary layer

This paper presents numerical simulations of the natural laminar-turbulent transition in a flat plate boundary layer. Natural transition occurs in low disturbance environments and is triggered by the growth of boundary layer instabilities or disturbances. This contribution specifically aims at investigating the interaction of multiple disturbances and their effect on the transition mechanism. The numerical simulations employ a lattice Boltzmann method (LBM) in conjunction with a highly accurate cumulant collision operator and a shared memory multi-GPU framework. The numerical approach is validated by comparing the growth of single Tollmien-Schlichting (T-S) waves with results of the linear stability theory (LST) prior to transition. Moreover, a comprehensive comparison with available direct numerical simulation results (DNS) for the post transition and the fully turbulent regime confirms the validity of the employed numerical approach. Subsequently, the influence of disturbances on the transition process are investigated in detail and for different disturbance frequencies and amplitudes. Two types of natural transition scenarios (H- & K-type transition) are analyzed and the LBM results are compared to predictions of the classical eN-method. Both approaches are found to reproduce a similar frequency influence. Higher frequency T-S waves trigger an earlier transition until a critical frequency is reached, above which the boundary layer is stable. In addition, it is observed that in case of multiple interacting disturbances, the laminar-turbulent transition occurs earlier than predicted by simplified methods that ignore the nonlinear interactions between disturbances. A spectral analysis of the velocity field confirms that secondary disturbances are crucial for the resonance transition and can significantly accelerate the transition process. The paper offers a comparison of linear and nonlinear results using a classical LST map and furthermore the laminar-turbulent natural transition is comprehensively investigated using the LBM.

Experimental study on effect of transverse groove with/without discharge hole on hypersonic blunt flat-plate boundary layer transition

Experiments are carried out on the <i>Φ</i>2 m Shock Tunnel (FD-14A) at the China Aerodynamics Research and Development Center to study the effect of the transverse groove with/without discharge hole on the hypersonic blunt flat-plate boundary layer transition, and the preliminary computational and theoretical research are carried out. The inflow Mach number of the test is 6, the unit Reynolds number is 3.3 × 10<sup>7</sup>/m, the leading edge radius of the flat-plate is 1 mm, and the angle of attack is –4°. Three different sets of two-dimensional transverse grooves are arranged at 110 mm away from the leading edge of the flat-plate. The width and depth of the grooves are, respectively, 2.5 mm and 1 mm for groove 1, 3.75 mm and 1.5 mm for groove 2, and 5 mm and 2 mm for groove 3, at the same time, both ends of the groove 1 can open the discharge hole (the discharge hole has a size of 2.5 mm × 5.0 mm and a width the same as that of groove 1). The discharge hole is denoted as the groove 4, and the smooth flat-plate when the groove is not included is denoted as groove 5 or the flat. The <i>Φ</i>2-mm-diameter cylindrical heat flux sensor is used to measure the heat flux distributions of the center line of the flat-plate under different conditions, and thus we can judge the transition of the boundary layer. The measurement results show that the smooth plate starts to transit at <i>x</i> ≈ 340 mm, and the transition is nearly completed at <i>x</i> ≈ 425 mm. The groove causes the transition position of the boundary layer of the plate to advance, and as the width and depth of the groove increase, the promoting effect on the transition is enhanced, and the transition position moves upstream. After the groove 1 is added to the discharge hole (groove 4), the heat flux distribution and the transition position are substantially the same as those of the smooth plate. After the boundary layer flow completely transits into turbulent flow, the difference in heat flux for each case is small, which indicates that the grooves of different specifications affect only the heat flux distribution in the transition process, but have little effect on the heat flux of the turbulent wall after the transition. The computational fluid dynamic results show that the discharge holes cause passive suction, and the test results show that the suction effect of the discharge holes at both ends of the groove counteracts the effect of the groove on the transition of the center line boundary layer, but it may be just a coincidence, and further research is needed. The linear stability theory (LST) and the optimal perturbation method are used to analyze the flow instability mechanism of the smooth blunt plate. The LST results show that there is no first mode instability nor second mode instability in the blunt plate flow. The modal instability mechanism cannot explain the observed transition in the test. The optimal disturbance calculation shows that the blunt plate flow suffers strong non-modal instability, which can qualitatively explain the observed transition phenomenon.

Supersonic boundary layer transition induced by self-sustaining dual jets**Project supported by the National Natural Science Foundation of China (Grant Nos. 11602299, 11872374, and 51809271).

To promote high-speed boundary layer transition, this paper proposes an active self-sustaining dual jets (SDJ) actuator utilizing the energy of supersonic mainflow. Employing the nanoparticle-based planar laser scattering (NPLS), supersonic flat-plate boundary layer transition induced by SDJ is experimentally investigated in an Ma-2.95 low-turbulence wind tunnel. Streamwise and spanwise NPLS images are obtained to analyze fine flow structures of the whole transition process. The results reveal the transition control mechanisms that on the one hand, the jet-induced shear layer produces unstable Kelvin–Helmholtz instabilities in the wake flow, on the other hand, the jets also generates an adverse pressure gradient in the boundary layer and induce unstable streak structures, which gradually break down into turbulence downstream. The paper provides a new method for transition control of high-speed boundary layer, and have prospect both in theory and engineering application.

Measurement of Transitional Surface Roughness Effects on Flat-Plate Boundary Layer Transition

An experimental study has been conducted to investigate the effects of transitionally rough surface on the flat-plate boundary layer transition. Transitional boundary layers with three different flat plates (ks+ = 0.07 ∼ 0.19, 2.71 ∼ 7.05, and 13.65 ∼ 41.09) have been measured with a single-sensor hot-wire probe. All of the measurements have been conducted under zero pressure gradient (ZPG) at the fixed Reynolds number (ReL) and freestream turbulence intensity (Tu) of 3.05 × 106 and 0.2%. Transitionally, rough surface does not affect the sigmoidal distribution of turbulence intermittency model; but induces earlier transition onset and shortens the transition length. For all surfaces, streamwise turbulence intensity profiles with similar values of turbulence intermittency are similar for the transition length less than 60%. Therefore, mean velocity profiles with the similar values of turbulence intermittency are similar regardless of surface conditions. However, downstream of 60% of the transition length, mean velocity defect increases as the surface roughness increases. Enhanced diffusion of turbulent kinetic energy from the near wall (y/δ < 0.1) to the outer part (y/δ ≈ 0.4) of the boundary layer due to the surface roughness is responsible for the increased momentum deficit.

Numerical Simulation of Flat Plate Boundary Layer Transition with Synthetic Inlet Turbulence

A large-eddy simulation (LES) of a flat plate boundary layer undergoing transition to turbulence, i.e., ERCOFTAC’s test case T3B, is performed with synthetic inlet turbulent fluctuations. Generated by Billson and Davidson’s method, the isotropic and homogeneous synthetic turbulence is imposed on a uniform flow directly at the inlet of the computational domain without a precursor adaptation region. The issue of the maximum-contained number (MCN) is specified, which aims at the determination of mesh distribution to maintain and strengthen the correlation between neighboring cells. The numerical results are realistic under the original synthetic turbulence if the MCN is suitably set. For further improvement of the prediction, a correction based on the Poisson equation is adopted to make the synthetic turbulence divergence-free, which is the basic requirement of incompressible flow. It is shown that with the divergence correction, the simulation results are better, and in particular, the decay of free stream turbulence near the upper boundary is more reasonable.

Nonlinear PSE Simulation of a flat plate boundary layer transition

In this paper, I present results from nonlinear parabolized stability equations (NPSE) of a flat plate boundary layer transition. I used a Finite different method in the streamwise direction, a Fourier Galerkin method in the spanwise direction and time, and a Chebyshev Collocation method in the wall-normal direction. I compute K-type transition and H-type transition. In both the case, NPSE results are in good agreement with the spatial Direct Numerical Simulation (SDNS) results.

Numerical investigation of hypersonic flat-plate boundary layer transition mechanism induced by different roughness shapes

The roughness-induced laminar-turbulent boundary layer transition is significant for high-speed aerospace applications. The transition mechanism is closely related to the roughness shape. In this paper, high-order numerical method is used to investigate the effect of roughness shape on the flat-plate laminar-to-turbulent boundary layer transition. Computations are performed in both the supersonic and hypersonic regimes (free-stream Mach number from 3.37 up to 6.63) for the square, cylinder, diamond and hemisphere roughness elements. It is observed that the square and diamond roughness elements are more effective in inducing transition compared with the cylinder and hemisphere ones. The square roughness element has the longest separated region in which strong unsteadiness exists and the absolute instability is formed, thus resulting in the earliest transition. The diamond roughness element has a maximum width of the separated region leading to the widest turbulent wake region far downstream. Furthermore, transition location moves backward as the Mach number increases, which indicates that the compressibility significantly suppresses the roughness-induced boundary layer transition.

Evolution of Lagrangian coherent structures in a cylinder-wake disturbed flat plate boundary layer

Evolution of Lagrangian coherent structures (LCS) in a flat plate boundary layer transition induced by the wake of a circular cylinder is investigated. Both hydrogen bubble visualization and particle image velocimetry (PIV) techniques are used. It is found that downstream of the cylinder, the disturbance in the boundary layer experiences a fast growth followed by a slow decay in the transition. Lagrangian coherent structures are revealed by qualitative hydrogen bubble visualizations and quantitative finite-time Lyapunov exponents (FTLE) fields derived from the PIV data. The evolution of the LCS is considered from the very beginning of the transition up to when the boundary layer becomes fully developed turbulent flow. The mean convection velocity and average inclination angle of the LCS are first extracted from the FTLE fields. The streamwise length of the low-speed streaks seems to increase, while their spanwise distance decreases in the boundary layer transition. Proper orthogonal decomposition (POD) of the PIV data shows that low-speed streaks associated with the hairpin vortices and hairpin packets are the dominant coherent structures close to the wall in the transitional and turbulent boundary layer. The POD modes also reveal a variety of scales in the turbulent boundary layer. Moreover, it is found that large-scale coherent structures can modulate the amplitude of the small-scale ones.

Flat plate boundary layer transition induced by a controlled near-wall circular cylinder wake

The flat plate boundary layer transition induced by the wake of a circular cylinder close to the wall is experimentally investigated using particle image velocimetry (PIV) and hydrogen bubble visualization techniques. The wake of the circular cylinder is controlled by a slot synthetic jet at the rear stagnation point of the circular cylinder. It is found that when the synthetic jet is actuated, the wake can be greatly modified. When the excitation frequency of the synthetic jet is set at the natural shedding frequency of the cylinder wake, the symmetrical shedding pattern can be observed. While the excitation frequency increases to be twice of the natural shedding frequency, the wake appears to be antisymmetrical again, but with the shedding frequency locked onto half of the excitation frequency. Flow visualizations show that spanwise secondary vortices can be induced in the near wall region by these large scale vortices in the wake. It is found that the secondary vortices destabilize into streamwise stretched Λ vortices as they convect downstream. After the introduction of the synthetic jet, the destabilization process is promoted. By investigating the disturbance growth inside the boundary layer, it reveals that the synthetic jet can cause earlier initialization of the disturbance growth, thus promoting the transition process of the boundary layer. An explanation is provided that the low frequency components of the wake disturbances, which interact with the boundary layer, are enhanced by the introduction of the synthetic jet. Therefore, the destabilization of the secondary vortices is promoted, and disturbance growth in the boundary layer initiates earlier.

A Dynamic Observer to Capture and Control Perturbation Energy in Noise Amplifier Flows

In this article, we present a technique to extract a reduced-order model of a transitional flat-plate boundary layer from simultaneous velocity snapshots and wall-shear stress measurements. The proposed approach combines a reduction of the degrees of freedom of the system by a projection of the velocity snapshots onto a POD basis together with a system-identification technique to obtain a state-space model of the flow. Such a model is then used in an optimal control framework to reduce the kinetic energy of the perturbation field and therefore delay transition.

Numerical Investigation of Wall Cooling and Suction Effects on Supersonic Flat-Plate Boundary Layer Transition Using Large Eddy Simulation

Reducing friction resistance and aerodynamic heating has important engineering significance to improve the performances of super/hypersonic aircraft, so the purpose of transition control and turbulent drag reduction becomes one of the cutting edges in turbulence research. In order to investigate the influences of wall cooling and suction on the transition process and fully developed turbulence, the large eddy simulation of spatially evolving supersonic boundary layer transition over a flat-plate with freestream Mach number 4.5 at different wall temperature and suction intensity is performed in the present work. It is found that the wall cooling and suction are capable of changing the mean velocity profile within the boundary layer and improving the stability of the flow field, thus delaying the onset of the spatial transition process. The transition control will become more effective as the wall temperature decreases, while there is an optimal wall suction intensity under the given conditions. Moreover, the development of large-scale coherent structures can be suppressed effectively via wall cooling, but wall suction has no influence.

A dynamic observer to capture and control perturbation energy in noise amplifiers

AbstractIn this article, we introduce techniques to build a reduced-order model of a fluid system that accurately predicts the dynamics of a flow from local wall measurements. This is particularly difficult in the case of noise amplifiers where the upstream noise environment, triggering the flow via a receptivity process, is not known. A system identification approach, rather than a classical Galerkin technique, is used to extract the model from time-synchronous velocity snapshots and wall shear-stress measurements. The technique will be illustrated for the case of a transitional flat-plate boundary layer, where the snapshots of the flow are obtained from direct numerical simulations. Particular attention is directed to limiting the processed data to data that would be readily available in experiments, thus making the technique applicable to an experimental set-up. The proposed approach combines a reduction of the degrees of freedom of the system by a projection of the velocity snapshots onto a proper orthogonal decomposition basis combined with a system identification technique to obtain a state-space model. This model is then used in a feedforward control set-up to significantly reduce the kinetic energy of the perturbation field and thus successfully delay transition.

Evolution of vortex structure in boundary layer transition induced by roughness elements

The particle image velocimetry (PIV) and hydrogen-bubble visualization technique are used to investigate the flat-plate boundary layer transition induced by an array of roughness elements. The streamwise evolutions of the mean and fluctuation velocity are analyzed, and the critical Reynolds number Rek,c is determined between 339 and 443 under current experimental setup. The hairpin vortices shed from supercritical roughness elements are visualized by swirling strength, in which two pairs of counter-rotating vortices can be observed: one vortex pair is the manifestation of the neck of the hairpin vortices shed from the top of the roughness; the other vortex pair, which originates from the lower part of the roughness, comes from the streamwise vortices that are constantly perturbed by the hairpin vortex shedding.