Disturbances In Boundary Layer Research Articles

Unsteady disturbances in a swept wing boundary layer due to plasma forcing

This work investigates the response of a transitional boundary layer to spanwise-invariant dielectric barrier discharge plasma actuator (PA) forcing on a 45° swept wing at a chord Reynolds number of 2.17×106. Two important parameters of the PA operation are scrutinized, namely, the forcing frequency and the streamwise location of forcing. An array of passive discrete roughness elements is installed near the leading edge to promote and condition a set of critical stationary crossflow (CF) instability modes. Numerical solutions of the boundary layer equations and linear stability theory are used in combination with the experimental pressure distribution to provide predictions of critical stationary and traveling CF instabilities. The laminar–turbulent transition front is visualized and quantified by means of infrared thermography. Measurements of velocity fields are performed using hotwire anemometry scans at specific chordwise locations. The results demonstrate the inherent introduction of unsteady velocity disturbances by the plasma forcing. It is shown that, depending on actuator frequency and location, these disturbances can evolve into typical CF instabilities. Positive traveling low-frequency type III modes are generally amplified by PA in all tested cases, while the occurrence of negative traveling high-frequency type I secondary modes is favored when PA is operating at high frequency and at relatively downstream locations, with respect to the leading edge.

Transitional hypersonic flow over slender cone/flare geometries

Experiments are performed in a Mach-6 shock tunnel to examine the laminar-to-turbulent transition process associated with a sudden increase in surface angle on a slender body. A cone/flare geometry with a 5 $^\circ$ frustum and compression angles ranging from 5 $^\circ$ to 15 $^\circ$ allow a range of mean flow configurations, spanning an attached shock-wave/boundary-layer interaction to a fully separated one; the unit Reynolds number of the flow is also varied to modify the state of incoming second-mode boundary-layer disturbances. Ultra-high-speed schlieren visualizations provide a global picture of the flow development, supplemented by high-frequency surface pressure measurements. For the 5 $^\circ$ compression, the unsteady flow field is dominated by the second-mode waves, whose breakdown to turbulence is generally accelerated (compared with the straight-cone configuration) by encountering the angle change. As the compression angle is increased to induce separation, lower-frequency disturbances appear along the separated shear layer that exhibit much larger amplification rates than the incoming second-mode waves; the latter effectively freeze in amplitude downstream of the separation point before rapidly breaking down upon reattachment. The shear-layer disturbances become dominant at the largest compression angle tested. Radiation of disturbance energy to the external flow is consistently observed: this generally occurs along mean flow features (flare, separation or reattachment shocks) for the second-mode disturbances and spontaneously for the shear-layer waves. The combined application of spectral proper orthogonal decomposition and a global bispectral analysis allows the identification of important unsteady flow structures and the association of these with prominent nonlinear interactions in the various configurations.

Non-modal growth of finite-amplitude disturbances in oscillatory boundary layer

The essence of sub-critical transition of oscillatory boundary-layer flows is the non-modal growth of finite-amplitude disturbances. The current understanding of the mechanisms of the orderly and bypass transitions of oscillatory boundary-layer flows is limited. The present study adopts optimisation approaches to predict the maximum energy amplification of two- and three-dimensional perturbations in response to the optimal initial disturbance with or without external forcing. A series of direct numerical simulations are also performed to compare with the results obtained from the stability analyses. In particular, the optimal initial perturbation similar to a Tollmien–Schlichting (T–S) wave yields the largest transient growth under the combined effects of the Orr mechanism and inflectional point instability. With a considerable level of two-dimensional disturbance, the vortex tube nonlinearly develops from the T–S-like wave, and then either deforms into a $\varLambda$ -vortex in the near-wall region or rolls up to the free shear region. The further burst of turbulence can follow the first pathway as K-type transition or the second one as vortex tube breakdown due to the elliptical instability. Additionally, non-modal growth can initiate the inception of streaky structures by favourable three-dimensional initial perturbations and/or forcing. The secondary instabilities responsible for the streak breakdown are classified as the varicose (symmetric) and sinuous (anti-symmetric) modes. Under a sufficiently high level of three-dimensional disturbance, the bypass transition is predominantly characterised by the formation of the sinuous mode and turbulent spots, which leads to the suppression of inflection point instability.

Bluntness-Dependent Hypersonic Boundary-Layer Modes’ Excitation

Boundary-layer disturbances on a cone in a hypersonic flow are investigated by heat flux sensors. The cone has a half-angle of 10.9 deg and is situated with a 0 deg angle of attack in a Mach 10 region of a conical nozzle in a shock-tunnel facility. There are three atomic layer thermopile heat flux sensors mounted at different chordwise positions in order to investigate the receptivity to freestream disturbances and the emergence of unstable modes of the boundary layer, that is, Mack first and second modes. The cone’s nose is exchangeable, and there are three differently sized radii to investigate the bluntness effect on transition with respect to entropy/boundary-layer displacement. It is found that each nose type tested shows a different set of amplified spectral bands in the receptivity region of the first two sensors, as well as at the third sensor’s location downstream of the critical point. There is a unique wavelength, scaling with boundary-layer height, that is most receptive to disturbances. For the two sharper cones, this excitation lies in the range of Mack second modes, which are observed in the unstable region. For the blunter cone, this excitation lies near the first mode frequency; as a result, only first modes are amplified and detected at sensor 3, although linear stability theory predicts higher growth rates for second modes.

The effects of nose bluntness on broadband disturbance receptivity in hypersonic flow

While nose bluntness is known to have a large impact on the stability of hypersonic vehicles, its influence on the freestream receptivity process has not been fully characterized for a wide range of conditions. This paper investigates the effects of nose bluntness on the second mode receptivity coefficients and the development of boundary layer disturbances over two 7° half-angle circular blunt cones at Mach 10 after perturbation with broadband freestream pulses of different types. The cones have nose radii of 9.525 mm (case B) and 5.08 mm (case I). Unsteady direct numerical simulation (DNS) and linear stability theory (LST) results compare well and predict stronger second mode growth for case I in all pulse cases. Unsteady DNS also shows variations in extramodal excitation between the cones depending on freestream disturbance type. Spectral receptivity coefficients are generated by decomposing the unsteady DNS data into discrete frequency Fourier modes, which are then corrected with LST N-factors. Fast acoustic disturbances demonstrate minimal variation in receptivity coefficients, while temperature and vorticity disturbances have much higher coefficients in case I. Planar slow acoustic pulses induce stronger disturbances outside of the second mode in case I, resulting in higher peak receptivity coefficients. Results show significant variation in receptivity response based on nose bluntness, pulse geometry, and the type of incident perturbation.

Heat Transfer of Ferrofluid in Fluted Tubes with an Electromagnetic Field

The present study considers the effects of the electromagnetic field and pulsating flow on nanofluids heat transfer and flow characteristics in the three-start helically fluted tube. The experiments are performed using anofluids with the Reynolds number varying from 8000 to 13000, and with an Fe3O4/water nanofluids (Ferrofluid) concentration of 0.005% by volume with and without an electromagnetic field effect. The measured results are verified with the predicted results from the proposed correlations and the published experimental results. As a result of the disturbed flow boundary layer, higher swirling Brownian motion, higher local thermal conductivity, and the mixing of turbulent intensity, the heat transfer performance also increases. For a given pulsating flow of 30 Hz, the Nusselt number enhancement increases significantly to 137.7% and 156.7% for the helical depth ratios of 0.028 and 0.093, respectively. The helically fluted tube with a helical depth ratio of 0.093 and a helical pitch ratio of 0.93 yields the highest Nusselt number improvement. The Nusselt number under the electromagnetic field effect increases by 19.0% and 14.4% for the pulsating flow of 30 Hz and 20 Hz, respectively. Finally, a comprehensive evaluation index is applied to estimate thermo-hydraulic performance. It is found that the comprehensive evaluation index increases with the increasing Reynolds number at first and then decreases as the Reynolds number increases further.

Experimental Measurements of Hypersonic Instabilities over Ogive-Cylinders at Mach 6

Hypersonic boundary-layer instability disturbance and transition experiments were performed in the Air Force Research Laboratory Mach-6 Ludwieg Tube on a 1-m-long ogive-cylinder model with interchangeable nose-tip geometries of varying ogive radii and nose bluntnesses. Boundary-layer disturbances were measured via focused laser differential interferometry, surface-mounted pressure sensors, and high-speed schlieren videography at unit Reynolds numbers ranging from to . Three primary disturbance structures were observed that were dependent on ogive radius and nose bluntness. Each disturbance structure exhibits unique characteristics that are closely tied to the leading-edge geometry of the model. The addition of nose bluntness is shown to have an overall delay in transition onset, and a possible blunt nose transition reversal is observed as bluntness is further increased. It is also shown that the effects of the ogive radius in addition to nose bluntness alter the flow instability disturbance and transition behaviors and are likely tied to a modification of the entropy layer structure. A novel curvature-based Reynolds number is proposed that successfully correlates the effects of multiple leading-edge radii of curvature to dominant downstream boundary-layer disturbances and transition onset locations.

Control of roughness-induced transition under the influence of inflow disturbance

Control of roughness-induced transition influenced by two- or three-dimensional inflow disturbances using spanwise-uniform wall blowing is investigated from the perspective of unstable modal growth with direct numerical simulations. Visualization of flow structures for two-dimensional disturbances indicates that the counter-rotating vortex pair in the wake bends the high-shear layer, which is related to both symmetric and antisymmetric unstable modes. The interaction of these structures is found to be responsible for the initial growth of the symmetric mode, which dominates the transition process. Both upstream and downstream position wall blowing are effective for transition control. Upstream position blowing works by lifting up the boundary layer and diminishing the wake structures, resulting in inhibition of the symmetric mode. Downstream position blowing has an even better effect, attributable to reconfiguration of the streamwise vorticity field in the wake and further distortion of the high-shear layer. When the inflow disturbance is a three-dimensional wave, the antisymmetric mode becomes dominant in the near-wake region, resulting in more rapid initial growth of the symmetric mode. As oblique waves have higher growth rates in a compressible boundary layer, the background disturbance is obviously stronger. Therefore, transition occurs earlier than for two-dimensional disturbances. When upstream position blowing is introduced, the spanwise shear related to the antisymmetric mode is reduced, and the background disturbance is suppressed as the disturbed boundary layer is pushed away from the roughness. Downstream position blowing can still inhibit the symmetric mode, but the antisymmetric mode is barely influenced, since this blowing is less effective in suppressing the counter-rotating vortex pair.

Buoyancy-driven algebraic (localised) boundary-layer disturbances

We show that a new class of steady linear eigenmodes exist in the Falkner–Skan boundary layer, associated with an algebraically developing, thermally coupled three-dimensional perturbation that remains localised in the spanwise direction. The dominant mode has a weak temperature difference that decays (algebraically) downstream, but remains sufficient (for favourable pressure gradients that are below a critical level) to drive an algebraically growing disturbance in the velocity field. We determine the critical Prandtl number and pressure gradient parameter required for downstream algebraic growth. We also march the nonlinear boundary-region equations downstream, to demonstrate that growth of these modes eventually gives rise to streak-like structures of order-one aspect ratio in the cross-sectional plane. Furthermore, this downstream flow can ultimately become unstable to a two-dimensional Rayleigh instability at finite amplitudes.

Numerical simulation of the interaction of the disturbed boundary layer with an incident shock

Interaction of the disturbed supersonic boundary layer with an incident oblique shock wave is studied numerically with eddy-resolving numerical simulations. Eigenmodes of the linear stability theory are used to generate the inflow boundary layer disturbances. The evolution of unstable boundary-layer disturbances, effects of the incident shock on the disturbances, effects of the disturbances on the boundary layer separation, flow dynamics in the separation zone, and laminar-turbulent transition are studied.

Evolution of artificial disturbances in a shear layer at M=1.43

The evolution of artificial disturbances in a laminar boundary layer on a flat plate model in the presence of an incident shock wave is considered. The flow is supersonic with the freestream Mach number M = 1.43. The study is carried out by hot-wire anemometry. A dielectric barrier discharge is used to generate disturbances. Data on the distribution in space of the average and non-stationary components of the mass flow are obtained. Disturbances created by the discharge and their evolution along the separation zone are recorded.

Effects of Surface Waviness on Fan Blade Boundary Layer Transition and Profile Loss—Part I: Methodology and Computational Results

AbstractThis two-part paper describes a new approach to determine the effect of surface waviness, arising from manufacture of composite fan blades, on transition onset location movement and hence fan profile losses. The approach includes analysis and computations of unsteady disturbances in boundary layers over a wavy surface, assessed and supported by wind tunnel measurements of these disturbances and the transition location. An integrated framework is developed for analysis of surface waviness effects on natural transition. The framework, referred to as the extended eN method, traces the evolution of disturbance energy transfer in flow over a wavy surface, from external acoustic noise through exponential growth of Tollmien–Schlichting (TS) waves, to the start and end of the transition process. The computational results show that surface waviness affects the transition onset location due to the interaction between the surface waviness and the TS boundary layer instability and that the interaction is strongest when the geometric and TS wavelengths match. The condition at which this occurs, and the initial amplitude of the boundary layer disturbances that grow to create the transition onset is maximized, is called receptivity amplification. The results provide first-of-a-kind descriptions of the mechanism for the changes in transition onset location as well as quantitative calculations for the effects of surface waviness on fan performance due to changes in surface wavelength, surface wave amplitude, and the location at which the waviness is initiated on the fan blade.

An adjoint approach for computing the receptivity of the rotating disc boundary layer to surface roughness

An adjoint approach is developed to compute the receptivity of the rotating disc boundary layer to surface roughness. The adjoint linearised Navier–Stokes equations, in cylindrical coordinates, are derived and receptivity characteristics are computed for a broad range of azimuthal mode numbers using a fully equivalent velocity–vorticity formulation. For each set of flow conditions (i.e. azimuthal mode number), the adjoint method only requires that the linear and adjoint solutions be computed once. Thus, the adjoint approach offers significant computational and time advantages over alternative receptivity schemes (i.e. direct linearised Navier–Stokes) as they can be used to instantaneously compute the receptivity of boundary layer disturbances to many environmental mechanisms. Stationary cross-flow disturbances are established by randomly distributed surface roughness that is periodic in the azimuthal direction and modelled via a linearisation of the no-slip condition on the disc surface. Each roughness distribution is scaled on its respective root-mean-square. A Monte-Carlo type uncertainty quantification analysis is performed, whereby mean receptivity amplitudes are computed by averaging over many thousands of roughness realisations with variable length and wavelength filters. The amplitude of the cross-flow instability is significantly larger for roughness distributions near the conditions for neutral linear instability, while roughness elements radially outboard have a negligible effect on the receptivity process. Furthermore, receptivity increases sharply for roughness distributions that encompass wavelength scales equivalent to that associated with the cross-flow instability. Finally, mean receptivity characteristics are used to predict the radial range that stationary cross-flow vortices achieve amplitudes sufficient to invalidate the linear stability assumptions.

Experimental Analysis of the Performance of a Wind-Turbine Airfoil Using Temperature-Sensitive Paint

Knowledge on the boundary-layer transition location at large chord Reynolds numbers is essential to evaluate the performance of airfoils designed for modern wind-turbine rotor blades. In the present work, a temperature-sensitive paint was used to systematically study boundary-layer transition on the suction side of a DU 91-W2-250 airfoil. The experiments were performed in the High-Pressure Wind Tunnel Göttingen at chord Reynolds numbers up to 12 million and angles of attack from to 20°. The coefficients of airfoil lift, drag, and pitching moment were also obtained after integration of the pressure distributions measured on the surface and in the wake of the wind-tunnel model. The global information obtained via temperature-sensitive paint not only enabled the analysis of the change in the transition location with varying angle of attack and chord Reynolds number, but also provided an explanation for the evolution of the aerodynamic coefficients measured at stall and poststall conditions. The stability of the laminar boundary layers investigated in the experiments was analyzed according to linear stability theory. The results of the stability computations supported the experimentally observed variations in the transition location. The amplification factors of boundary-layer disturbances at transition were also determined by correlating the experimental and numerical results.

Numerical study of heat transfer of laminar air flow in perforated trapezoidal corrugated plate-fin ducts

A novel trapezoidal corrugated perforated fin core is proposed in this study. The porosity of the fin surface, or perforations, is indicated to promote the unusual behavior of increasing the heat transfer coefficient, while reducing the friction factor with respect to its non-perforated counterpart, primarily due to surface transpiration, which leads to better flow mixing and successive boundary layer disturbances. This allows the heat exchanger to be built much more compact with a smaller volume and a front area. To highlight this, the results of the computational simulations for velocity and temperature fields in typical trapezoidal corrugated perforated plate-fin ducts are presented. Constant property, fully or periodically developed laminar airflow [Formula: see text] with Reynolds number [Formula: see text] passing through inter-fin passages, with fins at constant wall temperature T, in which the fin walls have perforations equally spaced along the length of the duct, is considered and a parametric study of the effects of the duct geometry, including the variation of the inclination angle [Formula: see text] of the diverging plane, the aspect ratio of the channel or period length and fin density effects [Formula: see text] and the converging-diverging ratio of the plate [Formula: see text], is performed. The results of the Fanning friction factor and the Nusselt number over the wide range of the Reynolds number, which was treated in this study, show the improved performance. The improvement is assessed quantitatively by the area goodness factor ( j/ f) relative to Re, comparison with simple flat channels. It is seen that increasing ϕ to [Formula: see text] improves the core performance; As ϕ increases beyond [Formula: see text], performance starts to decrease. j/ f increases with increasing λ; and λ = 3.6 acts as an inflection point. It is better to have a large λ value for lower Re range and vice versa. As ε increases, the performance increases; so, the highest area goodness factor value occurs at [Formula: see text]. In case 11, with [Formula: see text], [Formula: see text], and [Formula: see text] at Re = 200, compared to the non-perforated channel, the friction factor decreases about 11%, and the area goodness factor increases about 72%. Thus, the area goodness factor of the perforated case reaches 0.37.

Experiments on the development of natural disturbances in a hypersonic boundary layer on surfaces with microgrooves

Experiments on the development of natural disturbances in a hypersonic boundary layer on surfaces with microgrooves

Numerical study of disturbances generated by localized impulse action in a flat-plate boundary layer at Mach 2

The work is devoted to the numerical simulation of the excitation and development of localized disturbances in the supersonic boundary layer of a plate with a sharp leading edge at a Mach number of 2 in a two-dimensional formulation. Artificial disturbances are generated with the help of localized in time and space by changing the boundary conditions to the velocity component normal to the surface. The studies for two intensities of the impulse action were carried out. It was found that with an increase in the intensity of the action on the boundary layer, the amplitude of the generated disturbances increases. The development of disturbances of various amplitudes is similar. The ratio of the level of total temperature pulsations to the level of mass flow pulsations was estimated for the investigated disturbances. It was found that at small distances from the source of disturbances, this ratio increases downstream, at the same time in the far field, it reaches a constant value.

Pressure gradient effects on the secondary instability of Mack mode disturbances in hypersonic boundary layers

In hypersonic boundary layers, Mack mode disturbances play an important role in laminar–turbulence transition. Understanding the secondary instability mechanism of Mack mode disturbances will provide physical insight into turbulence generation for the researchers, which is also meaningful for transition control. According to the previous studies over straight cones and flared cones, it seems that a pressure gradient may affect the primary instability and secondary instability of Mack mode disturbances obviously. In this paper, we are trying to make it clear that what the pressure gradient effect on the secondary instability of Mack modes is and what the influence rule is. Four hypersonic flat plate cases with various pressure gradients at Mach 6 are analyzed through linear stability theory, non-linear parabolized stability equations, and spatial secondary instability theory methods. We found that the essence of the pressure gradient influence on the secondary instability mechanism is by affecting the primary amplitude of Mack modes, rather than other routes or factors. An adverse pressure gradient can enlarge both the primary instability and secondary instability growth rates and advance the transition. Moreover, an adverse pressure gradient will form a larger primary amplitude of the Mack mode, leading to a fundamental resonance dominated secondary instability. In contrast, the favorable pressure gradient will suppress the primary amplitude so that the subharmonic resonance may dominate the secondary instability. Therefore, it is very meaningful and valuable for transition prediction and turbulence generation to conduct the present study of pressure gradient effects on the secondary instability of Mack mode disturbances.

Numerical Investigation on the Response Characteristics of Hypersonic Boundary Layer under Different Types of Finite Amplitude Pulse Disturbance Waves

The hypersonic transient flow pass a blunt cone under three types of pulse disturbances is calculated using DNS. The response characteristic of hypersonic boundary layer among different types of pulse disturbance is compared. The distribution and evolution characteristics of disturbance modes are investigated by mode analysis. Results indicate that the receptivity characteristics induced by freestream pulse wave have both similarities and differences with that induced by freestream continuous wave. The interactions of different types of pulse waves with boundary layer and bow shock present different characteristics. The boundary layer thermodynamic characteristics under pulse fast acoustic wave are sensitive to mainstream disturbance wave, and that under pulse slow acoustic wave are sensitive to residual reflection wave. The type of pulse disturbance wave has a great influence on the production and mode distribution of boundary layer disturbance wave. In general, the disturbance amplitude in the pulse fast acoustic wave situation is the largest, the case of entropy wave is the second, and the case of slow acoustic wave is the smallest. For regional influence, the type of pulse disturbance has a huge impact on the disturbance modes in both the head and the non-head. For the three cases of pulse wave, the main mode group attenuation phenomenon which narrows the disturbance frequency band exists in the boundary layer. This group attenuation is the fastest for freestream slow acoustic wave, followed by entropy wave, and then fast acoustic wave. Under the action of pulse slow acoustic waves, the disturbance wave evolution of each order mode in the boundary layer along the streamwise is relatively stable, followed by entropy wave, and the case of fast acoustic wave is the most active.

Improved nonlinear parabolized stability equations approach for hypersonic boundary layers* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12072232 and 11672351) and the National Key Project of China (Grant No. GJXM92579).

The nonlinear parabolized stability equations (NPSEs) approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency. However, divergence of the NPSEs will occur when disturbances imposed at the inlet no longer play a leading role or when the nonlinear effect becomes very strong. Two major improvements are proposed here to deal with the divergence of the NPSEs. First, all disturbances are divided into two types: dominant waves and non-dominant waves. Disturbances imposed at the inlet or playing a leading role are defined as dominant waves, with all others being defined as non-dominant waves. Second, the streamwise wavenumbers of the non-dominant waves are obtained using the phase-locked method, while those of the dominant waves are obtained using an iterative method. Two reference wavenumbers are introduced in the phase-locked method, and methods for calculating them for different numbers of dominant waves are discussed. Direct numerical simulation (DNS) is performed to verify and validate the predictions of the improved NPSEs in a hypersonic boundary layer on an isothermal swept blunt plate. The results from the improved NPSEs approach are in good agreement with those of DNS, whereas the traditional NPSEs approach is subject to divergence, indicating that the improved NPSEs approach exhibits greater robustness.