Receptivity Of Boundary Layer Research Articles

Two-dimensional boundary layer receptivity to finite periodic disturbances

Receptivity is the focus and frontier of the research on boundary layer transition and flow drag reduction, but the temporal and spatial evolution of Tollmien–Schlichting waves (T-S waves) is not yet fully investigated, limiting the development of highly efficient laminar flow control techniques. In the present study, the local receptivity problem of the laminar boundary layer on a zero-pressure-gradient flat plate is investigated by using the direct numerical simulation, considering both the temporal and spatial evolution characteristics of the T-S waves. External disturbances at fixed frequencies are introduced in the form of velocity pulsations with different periods to excite T-S waves. The temporal and spatial evolution characteristics of the T-S waves excited by different forms and periods of disturbances are studied. It is found that the amplitude, frequency, and wave velocity of the T-S wave induced by the external multi-period disturbances are different from those induced by the constant disturbances. These conclusions are the same as those of T-S wave induced by wall inhalation. After a further investigation on this particular phenomenon, the influence mechanism of external disturbances on the receptivity process is revealed. This new research finding enriches the instability theory and provides a reference for more efficient applications on active laminar flow control technologies.

Slip effects on the receptivity of supersonic flat-plate boundary layer to freestream acoustic waves

The receptivity phase located upstream from the neutral point might be significantly affected by local rarefaction effects (especially surface slip effects) in terms of the boundary-layer transition of near-space hypersonic vehicles. In this paper, the receptivity of a supersonic flat-plate boundary layer to freestream acoustic waves in no-slip and slip flows is analyzed using direct numerical simulations and linear stability theory. The Maxwell–Smoluchowski velocity-slip and temperature-jump boundary conditions are adopted at the wall to account for surface slip effects. A Mach 4.5 flow at different wall-cooling degrees is mainly analyzed, and another Mach-6 case is presented, both with freestream unit Reynolds number on the order of 1×106/m. The main goal is to clarify the qualitative and quantitative influence of surface slip effects on the receptivity phase under different conditions. The results show that the receptivity mechanism in the slip flow is similar to that in the no-slip flow. That is, the mode S or F is excited near the leading edge due to synchronization with slow or fast acoustic waves, and the Mack second mode is excited further downstream after synchronization between modes S and F. However, the slip effects lead to distinctly quantitative differences in receptivity. The slip effects have little influence on the excitation of mode S or F near the leading edge but largely affect the evolution (intermodal exchange) of modes S and F as propagating downstream. Consequently, as for the receptivity to slow acoustic waves, the slip effects play a stabilizing role in receptivity when mode S is stable while a destabilizing role when mode S converts to the first mode in the upstream. As for receptivity to fast acoustic waves, as slip degree increases, the slip effects initially stabilize and then destabilize the receptivity, where the receptivity coefficient of the tested slip case can increase by 25% compared with the no-slip case.

Linear stability analysis of compressible boundary layer over an insulated wall using compound matrix method: Existence of multiple unstable modes for Mach number beyond 3

The linear spatial stability of a parallel two-dimensional (2D) compressible boundary layer on an adiabatic plate is investigated by considering both 2D and three-dimensional (3D) disturbances. The compound matrix method is employed here, for the first time, for compressible flows, which, unlike other conventional techniques, can efficiently eliminate the stiffness of the equations governing the spectral amplitudes. The method is first validated with published results in the literature corresponding to spatial and temporal instability of flows ranging from low subsonic to high supersonic Mach numbers (M), which shows a good match depending upon the proper choice of free-stream temperature and the wall dispersion relation. Subsequently, flow compressibility effects and the spanwise variation of disturbances are also investigated for M ranging from low subsonic to high supersonic cases (from M = 0.1 to 6). Mack (AGARD Report No. 709, 1984) reported the existence of two unstable modes for M > 3 from viscous calculations (the so-called “second mode”) that subsequently fuse to create only one unstable zone when M increases. Our calculations show a series of higher-order unstable modes for M > 3 in addition to the findings of Ma and Zhong [“Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions,” J. Fluid Mech. 488, 31–78 (2003)], where such higher-order modes for supersonic boundary layers are all noted to be spatially stable. The number and the frequency extent of the corresponding unstable zones increase with an increase in M beyond 3 while propagating downstream at a higher speed than those corresponding to incompressible, subsonic, and low supersonic (M < 2) cases.

Freestream Temperature Effects on the Receptivity of Hypersonic Boundary Layer Induced by Finite-Amplitude Pulse Entropy Waves

The unsteady hypersonic flow under finite amplitude pulse entropy perturbation at different freestream temperatures was calculated by direct numerical simulation. The flow response characteristics under the perturbation of entropy waves in freestreaming are analyzed. The temperature effect of freestreaming is studied based on the sensitivity of the boundary layer caused by pulse entropy perturbation. The results show that the higher freestream temperature promotes the first growth of the above third-order modes after leaving the head region, and strongly inhibits the first attenuation. The influence of the freestream temperature on the evolution of the induced disturbance wave is more significant than that on the development of the main flow disturbance waves. Low freestream temperature can suppress the attenuation of the modes below the second order. As the disturbance wave evolves downstream, the frequency band of the finite frequency disturbance wave gradually narrows, and the frequency band narrows faster when the temperature of freestreaming is low than when the temperature of freestreaming is high.

Receptivity of compressible boundary layers over porous surfaces

Receptivity of compressible boundary layers over porous surfaces

Receptivity of high-speed boundary layer on a flat plate at angles of attack: entropy and vorticity waves

Receptivity of high-speed boundary layer on a flat plate at angles of attack: entropy and vorticity waves

Excitation of crossflow modes in a swept-airfoil boundary layer, Part 2: Surface-vortex receptivity

An extensive experimental investigation of two receptivity mechanisms of localized excitation of unsteady (in general) Cross-Flow (CF) instability modes in a three-dimensional (3D) swept-airfoil boundary layer has been carried out within one extended set of measurements. Two mechanisms of the boundary-layer receptivity have been investigated: (i) to surface nonuniformities (vibrations, in general) and (ii) to scattering of freestream vortices on surface nonuniformities. All obtained results are deeply processed and analyzed. Part 1 of the present study (Borodulin et al., 2023), was devoted to description of the results obtained for problem (i). Meanwhile, results of detailed investigation of problem (ii) are presented in Part 2 of this study (the present paper).

Excitation of crossflow modes in a swept-airfoil boundary layer. Part 1. Surface receptivity

An extensive experimental investigation of two receptivity mechanisms of localized excitation of unsteady (in general) Cross-Flow (CF) instability modes in a three-dimensional (3D) swept-airfoil boundary layer has been carried out within one extended set of measurements. Two mechanisms of the boundary-layer receptivity have been investigated: (i) to surface nonuniformities (vibrations, in general) and (ii) to scattering of freestream vortices on surface nonuniformities. All obtained results are deeply processed and analyzed. Part 1 of the present study (this paper) is devoted to description of the results obtained for problem (i). Meanwhile, results of detailed investigation of problem (ii) are presented in Part 2 of this study (the next paper Borodulin et al. (2023)).

TRANSITION OF SUPERSONIC BOUNDARY LAYER OVER AN UPSWEPT WING DUE TO ACOUSTIC NOISE

Results of direct numerical simulation of the receptivity of the supersonic boundary layer over an upswept wing with a thin parabolic profile to acoustic noise of various intensity are presented. Acoustic noise is shown to be capable of triggering laminar-turbulent transition over the upswept wing of supersonic transport.

Receptivity and its influence on transition prediction of a hypersonic boundary layer over a small bluntness cone

Hypersonic boundary-layer receptivity is investigated using direct numerical simulation for Mach 6 flow over a 0.79 mm nose radius, 5° half-angle cone to slow acoustic waves. Two ways of exciting the second mode are discovered: For a low-frequency forcing (region I where f < 370 kHz), the first mode is initially excited and subsequently evolves into the second mode, whereas for a high-frequency forcing (region II where f≥ 370 kHz), the second mode is excited through the disturbances in the entropy layer. The receptivity mechanisms corresponding to the first and second modes are consistent with those of a previously investigated large bluntness cone. The receptivity coefficient shows a dramatical decrease with the frequency for disturbances in region I while a slight increase for disturbances in region II. The results show that the correlation between the receptivity coefficient of the first mode and the frequency proposed for large bluntness cones also applies to the current case. Furthermore, with receptivity and the measured freestream noise spectra taken into account, it is found that at the measured transition location, the disturbance predicted by the traditional eN method is no longer the most amplified disturbance, since the disturbances with lower frequencies can acquire larger amplitudes due to their large receptivity coefficients despite their smaller growth rates.

Effect of environmental disturbances on crossflow instability

Wind tunnel experiments on the receptivity of three-dimensional boundary layers were performed in a range of freestream turbulence intensities, Tu, from 0.01%—the lowest level ever achieved in this type of work—up to 0.41%. This work confirms that for Tu=0.01%, and presumably below this level, the transition process is dominated by stationary modes. These are receptive to surface roughness and generate Type-I and Type-II secondary instabilities that eventually cause the transition to turbulence. The saturation amplitude of these stationary waves is highly sensitive to the level of environmental disturbances; the former is here recorded to be the highest in the literature, with the latter being the lowest. Travelling modes are still present; however, their influence on the transition process is marginal. At matched surface roughness levels, when the level of environmental disturbance is enhanced to Tuge 0.33%, the travelling modes acquire more importance, strongly influencing the laminar/turbulent transition process, whilst the initial amplitude and growth of the stationary modes are hindered. For this level of Tu, is the interaction of steady and unsteady disturbances that produces highly amplified waves (Type-III), that quickly lead to nonlinear growth and anticipated turbulence. Finally, a simple rule of thumb is proposed, where the transition front was found to move forward by roughly 10% chord for an increase in one order of magnitude in the Tu levels.Graphical abstract

Hypersonic Boundary-Layer Receptivity over Circular Cones with Ellipsoidal/Spherical Noses

The hypersonic boundary-layer receptivity to planar and axisymmetric freestream slow acoustic waves is investigated for a Mach 6 flow over a 5 deg half-angle circular cone with three different ellipsoidal/spherical noses. To fully characterize the boundary-layer response, a wide frequency range of the first and second instability modes is considered. The results show that the receptivity mechanisms for both instability modes are similar to those for a previously investigated sphere-nosed cone. Furthermore, the variation of the receptivity coefficient with the frequency is obtained. For the second mode, the nose effect on the receptivity coefficient is dependent on the forcing frequency; whereas for the first mode, the receptivity coefficient monotonously decreases with increasing bluntness. An empirical similarity parameter is identified to collapse the receptivity coefficient of the first mode for the cones investigated. Considering that the receptivity coefficient of the first mode is nearly two orders of magnitude higher than that of the second mode, the traditional method, which ignores receptivity, may underestimate the role of the first mode in causing transition.

In-flight measurement of free-stream turbulence in the convective boundary layer

Natural laminar flow airfoils have achieved such a level of refinement that further optimisation and subsequent wind tunnel testing need to regard the specific free-stream turbulence to be expected during operation. This requires the characterisation of this turbulence in terms of those properties which are relevant for boundary layer receptivity and subsequent transition. These parameters of turbulence change with environmental conditions and, in case of aircraft, along the flight profile. This study investigates the free-stream turbulence relevant for the case of sailplane airfoils. In-flight measurements with a constant temperature anemometer x-wire probe were conducted during cross-country flights in Central Europe and provided 22 h of flight data, covering thermalling phases as well as straight flight legs. Longitudinal and transversal velocity fluctuations were recorded well into the dissipation range. The special challenges of operating a constant temperature anemometer probe continuously for several hours are addressed. The permanent unsteadiness of the inflow poses challenges for the evaluation, but also provides a broad database of measured turbulence levels. The quality of the measurements is shown by verifying some of the predictions of Kolmogorov's inertial range theories. Free-stream turbulence in thermalling phases is sufficiently homogeneous to be described accurately, as the dissipation range fluctuates only in a limited range and follows a log-normal distribution. On the straight flight legs, the turbulence depends on the convective activity along the flight path. In general, within the convective part of the atmosphere, turbulence levels are found to be significantly larger than in low-turbulence wind tunnels.Graphical abstract

Investigation on transition correlation of conical boundary layer in hypersonic wind tunnel experiments

The wind tunnel experiment is an important approach to studying boundary layer transition. In this study, the effects of bluntness, unit Reynolds number, and wall temperature ratio on hypersonic conical boundary layer transition were studied using numerical simulations and linear stability analyses based on the wind tunnel experimental data. Through the flow similarity principle, the treatment of the bluntness-varying problem was determined. Combining the experimental transition data and theoretical analysis results of sharp and blunt cones at home and abroad, the relation between the transition factor Ntr and the unit Reynolds number before ‘N factor reversal’, as well as the relation between the transition value Rtr and the unit Reynolds number from ‘N factor reversal’ to ‘transition reversal’ were determined too. Finally, according to the wind tunnel test data of China Aerodynamics Research and Development Center, the effect of wall temperature ratio on the receptivity of blunt-cone boundary layer was stated out, and the correlation of transition Reynolds number under different wall temperature ratios was determined. The influence law of parameters in this correlation was also determined.

On transonic boundary-layer receptivity over a vibrating flat plate coated with a thin liquid film

In this paper we study the generation of Tollmien–Schlichting waves initiated by vibrations of a wall where the wall is coated with a thin liquid film in a transonic flow regime. Motion of fluids are described by the two-dimensional Navier–Stokes equations assuming the Reynolds number is large. To find asymptotic solutions of the transonic boundary layer, we conduct an inspection analysis on the affine transformations of the triple-deck model for a subsonic flow and the unsteady full potential equations, with the intention of obtaining the order quantity of the free-stream Mach number in the transonic flow. We construct a modified triple-deck model for the transonic flow by considering the scalings of the perturbations that lead to the viscous–inviscid interaction problem for the flow in a subsonic regime. In particular, we are interested in the region where the subsonic scalings become invalid as the flow approaches transonic regime. We assume the wall oscillates in the vertical direction to the oncoming flow and these vibrations are periodic in time. We outline the process where the flow in the boundary layer converts the wall vibration perturbations into the instability modes which are measured by the receptivity coefficient. The viscous–inviscid interaction problem describes the stability of the boundary layer on the lower branch of the neutral curve. We show that the governing equations for the air viscous sublayer and the film flow are quasi-steady. The equation describing the inviscid layer of the airflow is unsteady and its referred to as the unsteady Kàrmàn–Guderley equation. The influence of the film surface tension is expressed through normal shear stress condition at the interface. We present an analytic formula for the amplitude of the Tollmien–Schlichting waves that are formed in the boundary layer. We analysed our model with different values of surface tension, initial film thickness and Kàrmàn–Guderley parameter. Depending on the value of these parameters, the initial amplitude of the instability waves may grow or decay.

Acoustic receptivity of high-speed boundary layers on a flat plate at angles of attack

Acoustic receptivity of high-speed boundary layers on a flat plate at angles of attack

On subsonic boundary-layer receptivity to acoustic waves over an aircraft wing coated by a thin liquid film

This work is concerned with the laminar–turbulent transition in the boundary layer on an aircraft wing covered by a water film. We consider the initial stage of the transition process known as the receptivity of the boundary layer, namely, we study the generation of the interfacial instability waves by the unsteady free-stream acoustic noise interacting with a small roughness on the wing surface. For effective receptivity, the ‘forcing’ should obey the so-called ‘double-resonance’ principle. According to this principle, both the frequency and the wavenumber of the external perturbations should be in tune with the natural instability modes of the flow. Correspondingly, we choose the frequency of the acoustic wave to coincide with that of the interfacial instability wave. However, this makes the wavelength of the acoustic wave significantly larger than wavelength of the instability wave. Thus, the second resonance condition is not satisfied, which means that the acoustic wave alone cannot produce the instability waves in the boundary layer. Instead, the Stokes layer is created in the boundary layer just above the liquid film. As far as the film is concerned, it also experiences wave-like motion caused by the varying shear stress on the interface. The generation of the interfacial instability waves takes place when the Stokes layer encounters a wall roughness that is short enough for an appropriate scale conversion to take place. To describe the flow in the vicinity of the roughness, a suitably modified triple-deck theory is used.

Three-Dimensional Receptivity of a Blunt-Cone Boundary Layer to Incident Slow Acoustic Waves

The effects of the incident angle of a freestream slow acoustic wave on the three-dimensional receptivity of a first mode are investigated in the case of a hypersonic boundary layer over a blunt cone. When the incident wave strikes the bow shock, the postshock slow acoustic wave on the leeward side of the incident wave is generated at an earlier location than that on the windward side. Therefore, the excited first mode, dominated by the postshock slow acoustic wave, is stronger on the leeward side of the incident wave. Furthermore, the larger the incident angle is, the stronger the first mode on the leeward side is; whereas the mode on the windward side is weaker.

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.

Identification of free-stream and boundary layer correlating events in free-stream turbulence-induced transition

Boundary layer receptivity to free-stream disturbances plays a crucial role in forming coherent structures, whose breakup drives the laminar to turbulent flow transition. In the present work, an extended proper orthogonal decomposition (E-POD) procedure is applied to particle image velocimetry (PIV) data to identify correlating events between the free-stream velocity field and transitional boundary layers for flow configurations typical of low-pressure turbine blades. Data collected in two wall-parallel planes were ordered along the homogeneous spanwise coordinate so that the dominant POD coefficients provide the most energetic spanwise wavelengths in the free-stream and the near-wall regions. Then, the cross-correlation matrix of the POD spanwise coefficients computed independently in both measuring planes directly identifies the free-stream scales showing the highest degree of correlation with the boundary layer structures. Low-order reconstructions of the original PIV data show that the most correlating events are directly linked to the formation and the successive breakup process of streaky structures. Otherwise, larger-scale structures which are not involved in the transition process are filtered out. Interestingly, free-stream disturbances appear as organized wave packets with significant elongation in the streamwise direction when the velocity fields are reconstructed considering only the most correlating modes. The effect due to the Reynolds numbers, the pressure gradient, and the free-stream turbulence variation on the free-stream modes affecting the formation of coherent structures in the boundary layer is discussed in the paper.