Receptivity Of Boundary Layer Research Articles

S054053 2次元翼と噴流を組み合わせて生成した局所外部攪乱に対する平板境界層の受容性([S054-05]噴流、後流およびはく離流れ現象の探求と技術革新(5))

The effect of localized external disturbances on the receptivity of a fla plate boundary layer is investigated by a wind tunnel experiment. The disturbances are introduced in the free stream using the combination of the optimally designed airfoil and the jet ejections from the trailing edge. The experimental results show that the velocity fluctuatio in the boundary layer grows up rapidly when the disturbances comes close to the outer edge of the boundary layer. When the jet is pulsated at 10 Hz and 30 Hz, the velocity fluctuation of the same frequency is observed in the boundary layer.

Generation of nonstationary Görtler vortices by localized surface nonuniformities. Receptivity coefficients

The mechanism of production of nonstationary Gortler vortices in a boundary layer on concave wall by surface nonuniformities (vibrations and roughness) has been experimentally examined. The nonuniformities were produced by a specially developed disturbance source. They were controlled, localized along the streamwise coordinate, and periodic over the span of the experimental model. Tests in a low-turbulence wind tunnel have proved that the disturbance source is an efficient means of experimental study of the receptivity and stability problem for boundary layers dominated by Gortler instability. The operation of the disturbance source leads to the production of small-amplitude nonstationary Gortler vortices (tenth or hundredth fractions of a per cent of the free-stream velocity) with predefined characteristics (frequency and spanwise wavelength). In our experiments, we quantitatively examined the problem of linear receptivity of boundary layer to surface nonuniformities in a broad range of frequencies for the most dangerous spanwise scales of Gortler vortices. The values of the amplitudes and phases of the receptivity coefficients were determined. The amplitudes proved to be much smaller in magnitude in comparison with the excitation of modes of hydrodynamic instabilities of other types (Tollmien-Schlichting waves and cross-flow-instability modes). It was found that, with increasing the frequency, the amplitudes of the receptivity coefficients showed a distinct growth while for high frequencies those amplitudes also exhibited a growth with the spanwise scale of perturbations, although for stationary surface roughness no effect due to this scale was observed. It was found that the dependences on frequency of the efficiency of the mechanisms of stability and receptivity showed opposing behaviors, were in competition, and could partially compensate each other, promoting, thus, the production of boundary-layer Gortler vortices in a broad range of frequencies.

Swept wing boundary-layer receptivity to localized surface roughness

AbstractThe receptivity to localized surface roughness of a swept-wing boundary layer is studied by direct numerical simulation (DNS) and computations using the parabolized stability equations (PSEs). The DNS is laid out to reproduce wind tunnel experiments performed by Saric and coworkers, where micron-sized cylinders were used to trigger steady crossflow modes. The amplitudes of the roughness-induced fundamental crossflow wave and its superharmonics obtained from nonlinear PSE solutions agree excellently with the DNS results. A receptivity model using the direct and adjoint PSEs is shown to provide reliable predictions of the receptivity to roughness cylinders of different heights and chordwise locations. Being robust and computationally efficient, the model is well suited as a predictive tool of receptivity in flows of practical interest. The crossflow mode amplitudes obtained based on both DNS and PSE methods are 40 % of those measured in the experiments. Additional comparisons between experimental and PSE data for various disturbance wavelengths reveal that the measured disturbance amplitudes are consistently larger than those predicted by the PSE-based receptivity model by a nearly constant factor. Supplementary DNS and PSE computations suggest that possible natural leading-edge roughness and free-stream turbulence in the experiments are unlikely to account for this discrepancy. It is more likely that experimental uncertainties in the streamwise location of the roughness array and cylinder height are responsible for the additional receptivity observed in the experiments.

Numerical modeling of the receptivity of a supersonic boundary layer to entropy disturbances

Numerical modeling of the receptivity of a two-dimensional flat-plate boundary layer to entropy disturbances is carried out at the freestream Mach number M∞ = 6. Low-intensity perturbations considered are in the form of temperature spots of various shapes and with different initial positions downstream of the shock. They are shown to be able to generate unstable disturbances in the boundary layer. This receptivity mechanism is relatively weak as compared with the receptivity to acoustic waves. When the entropy perturbations are introduced upstream of the bow shock, they first pass across the shock. Downstream of the shock this interaction generates acoustic waves which, in turn, penetrate into the boundary layer thus exciting unstable disturbances of a considerably greater amplitude than the temperature spots. Thus, the bow shock can change the receptivity mechanism.

Swept-wing boundary-layer receptivity

AbstractAdjoint solutions of the linearized incompressible Navier–Stokes equations are presented for a cross-flow-dominated swept-wing boundary layer. For the first time these have been computed in the region upstream of the swept leading edge and may therefore be used to predict receptivity to any disturbances of the incoming free stream as well as to surface roughness. In this paper we present worst-case scenarios, i.e. those external disturbances yielding maximum receptivity amplitudes of a steady cross-flow disturbance. In the free stream, such an ‘optimal’ disturbance takes the form of a streak which, while being convected downstream, penetrates the boundary layer and smoothly turns into a growing cross-flow mode. The ‘worst-case’ surface roughness has a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the boundary layer is more receptive to surface roughness than to incoming free stream disturbances.

Direct Numerical Simulation on the Receptivity, Instability, and Transition of Hypersonic Boundary Layers

The prediction of the laminar-turbulent transition of boundary layers is critically important to the development of hypersonic vehicles because the transition has a first-order impact on aerodynamic heating, drag, and vehicle operation. The success of transition prediction relies on a fundamental understanding of the relevant physical mechanisms. In the 20 years since the review by Kleiser & Zang (1991) on the direct numerical simulation (DNS) of the boundary-layer transition, significant progress has been made on DNS in the hypersonic flow regime and in the spatial DNS approach. Many high-order shock-capturing and shock-fitting finite-difference methods have been developed and extensively applied to numerical simulations of the hypersonic boundary-layer transition. DNS has become a powerful research tool and has led to discoveries of new transition mechanisms. This article reviews the recent progress of DNS on hypersonic boundary-layer receptivity, instability, and transition. The current status and future directions are also presented.

Nonlinear receptivity to oblique vortical modes in flow past an elliptic leading edge

Nonlinear boundary-layer receptivity to pairs of unsteady oblique freestream vortical modes is studied in direct numerical simulation of flow over a flat plate with an elliptic leading edge. The freestream is perturbed by three types of oblique Fourier modes, differing in the magnitude of the three vorticity components. The vortical modes excite steady boundary-layer streaks. The associated receptivity mechanism, described in detail, is quadratic in the forcing amplitude. Elliptic leading edges with two different aspect ratios are considered. We find that – and explain why – the streak amplitudes in nonlinear receptivity are largely unaffected by the leading-edge bluntness for the types of external disturbances studied. As linear receptivity is the predominant mechanism at low forcing frequencies, the nonlinear mechanism comes into play when high-frequency vortices are present in the freestream. Nonlinear receptivity is therefore expected to contribute to the excitation of boundary-layer streaks by freestream turbulence.

DNS and the theory of receptivity of a supersonic boundary layer to free-stream disturbances

Direct numerical simulation (DNS) of receptivity of a boundary layer over flat plate is carried out. The free stream Mach number is equal to 6. The following two-dimensional disturbances are introduced into the free-stream flow: fast and slow acoustic waves, temperature spottiness. A theoretical model describing the excitation of unstable waves in the boundary layer is developed using the biorthogonal eigenfunction decomposition method. The DNS results agree with the theoretical predictions.

Boundary-layer receptivity to surface non-uniformities leading to generation of Görtler vortices

The paper is devoted to experimental investigation of receptivity of a Blasius boundary layer over a concave wall to surface non-uniformities. This receptivity mechanism is responsible for excitation of either unsteady or steady Görtler vortices by surface vibrations and roughness. As the result of this study quantitative receptivity characteristics are obtained, including the coefficients of the corresponding localized receptivity mechanism. These coefficients are obtained in Fourier space and are independent of the particular shape of the surface non-uniformities.

Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability over Cones

The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variation-diminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement.

Transition prediction of the supersonic boundary layer on a cone under the consideration of receptivity to slow acoustic waves

Transition prediction of the supersonic boundary layer on a cone with small angle of attack and Mach number 3.5 is investigated under the consideration of receptivity to slow acoustic waves, as the acoustic waves are the main environmental disturbances in a conventional, i.e. non-quiet, wind tunnel. It is shown that the e-N method can still yield fairly satisfactory results in comparison with those obtained in wind tunnel experiments, provided that the boundary layer receptivity to slow acoustic waves is properly taken into account, including the dependence of the amplitude of disturbances on the frequency and stream-wise location. Neither the conventional e-N method nor the improved e-N method can yield correct result of transition prediction, because the receptivity mechanisms considered there are not in accord with the real situation in the wind tunnel.

Boundary layer receptivity to free-stream turbulence and surface roughness over a swept flat plate

An experimental study of the receptivity of disturbances and their subsequent development into a three-dimensional boundary layer has been carried out. The three-dimensional boundary layer was set up using a flat plate with a swept leading edge and a pressure gradient using a displacement body at the ceiling of the test section. Low level free-stream turbulence was generated with five different screens and was shown to generate traveling crossflow modes for all but the lowest turbulence level, i.e., for Tu>0.2%, where instead a stationary crossflow disturbance dominated. Stationary crossflow disturbances were triggered by small cylindrical roughness elements arranged in an array. For high enough roughness Reynolds number (Rek) stationary disturbances growing exponentially were seen and their amplitude seems to scale with Rek2.3.

Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge

Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien–Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15% of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.

Continuous spectrum analysis of roughness-induced transient growth

Continuous spectrum amplitude distributions are calculated for transiently growing roughness-induced perturbations in a flat-plate boundary layer. A direct method is employed when the complete flow is known via direct numerical simulation. A new method using regularizing functionals is developed for calculating the distributions when only partial experimental data are available. These amplitude distributions provide a way of rigorously characterizing the boundary layer receptivity to surface roughness. Contrasting the present results to optimal theory results conclusively demonstrates that roughness-induced disturbances cannot be described by optimal disturbance calculations. The continuous spectrum analysis demonstrates the linearity of the perturbations by correctly reproducing the flow evolution over the measurement domain. Extracting the continuous spectrum amplitudes using the partial data technique reveals the underlying vortex behavior that creates transient growth. The method described is amenable to future work with realistic distributed roughness and complex surface geometries.

Receptivity of a Supersonic Boundary Layer to Acoustic Disturbances

The boundary layer receptivity process generated by the interaction of 3-D slow and fast acoustic disturbances with a blunted flat plate, is numerically investigated at a freestream Mach number of 3.5, and at a high Reynolds number of 39 * 10 6 /m. The computations are performed with and without a 2-D isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the fifth-order accurate weighted essentially nonoscillatory scheme for space discretization and using the third-order total-variation-diminishing Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien-Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the freestream disturbances for the slow and fast waves, respectively. It was also revealed that a small isolated roughness element does not enhance the receptivity process for the given nose bluntness.

Effect of wall perturbations on the receptivity of a hypersonic boundary layer

The receptivity of a Mach 5.92 flat plate boundary layer to periodic two-dimensional wall perturbations is studied by numerical simulations and linear stability theory (LST). Free stream flow conditions are the same as the leading edge receptivity experiment of Maslov et al., J. Fluid Mech. 426, 73 (2001). Steady base flow is simulated by solving compressible Navier–Stokes equations with a combination of a fifth-order shock-fitting method and a second-order total variation diminishing scheme. The accuracy of the steady base flow is validated by comparisons with the experimental measurements of Maslov et al. and self-similar boundary-layer solution. In receptivity simulations, streamwise velocity perturbation, blowing suction, and temperature perturbation are introduced to the steady base flow with a forcing slot on flat plate. A model of wall perturbation is proposed based on physical properties of the electric pulse generator used in the experiment of Maslov et al. Stability characteristics of boundary-layer waves are identified and evaluated by comparing the results of LST and numerical simulation. Numerical simulation results show that all three types of wall perturbations eventually result in the same type of instability wave (mode S) in the boundary layer, which indicates that receptivity mechanism of the hypersonic boundary layer to wall perturbation is independent of specific perturbation type. On the other hand, the hypersonic boundary layer is found to be most sensitive to blowing-suction and least sensitive to temperature perturbation.

Receptivity of a Hypersonic Flat-Plate Boundary Layer to Three-Dimensional Surface Roughness

The laminar–turbulent transition of hypersonic boundary layers has a significant effect on drag calculation and aerothermal design of hypersonic vehicles. Recent research has shown that one possible explanation to roughnessinduced bypass transition is transient growth theory. However, it is not known how to generate the optimal disturbances computed by transient growth theory. Furthermore, there has not been any direct numerical simulation study on transient growth in hypersonic boundary layers. The objectives of this paper are to study the receptivity of a Mach 5.92 flow over a flat plate to three-dimensional surface roughness and the effect of spanwise wave number on the receptivity. Steady base flow is computed by solving compressible Navier–Stokes equationswith a combination of a fifth-order shock-fitting method and a second-order total variation diminishing scheme. In receptivity simulations, small surface roughness is introduced on the plate. The numerical results show that counterrotating streamwise vortices and transient growth are induced by surface roughness, however, transient growth is generally weak due to the small height of roughness. For the six cases considered, surface roughness with the spanwise wave number being 0.0101 has the strongest excitation of transient growth.

Receptivity of a hypersonic boundary layer over a flat plate with a porous coating

Two-dimensional direct numerical simulation (DNS) of receptivity to acoustic disturbances radiating onto a flat plate with a sharp leading edge in the Mach 6 free stream is carried out. Numerical data obtained for fast and slow acoustic waves of zero angle of incidence are consistent with the asymptotic theory. Numerical experiments with acoustic waves of non-zero angles of incidence reveal new features of the disturbance field near the plate leading edge. The shock wave, which is formed near the leading edge owing to viscous–inviscid interaction, produces a profound effect on the acoustic near field and excitation of boundary-layer modes. DNS of the porous coating effect on stability and receptivity of the hypersonic boundary layer is carried out. A porous coating of regular porosity (equally spaced cylindrical blind micro-holes) effectively diminishes the second-mode growth rate in accordance with the predictions of linear stability theory, while weakly affecting acoustic waves. The coating end effects, associated with junctures between solid and porous surfaces, are investigated.

Acoustic receptivity of Mach 4.5 boundary layer with leading-edge bluntness

Boundary layer receptivity to two-dimensional slow and fast acoustic waves is investigated by solving Navier–Stokes equations for Mach 4.5 flow over a flat plate with a finite-thickness leading edge. Higher order spatial and temporal schemes are employed to obtain the solution whereby the flat-plate leading edge region is resolved by providing a sufficiently refined grid. The results show that the instability waves are generated in the leading edge region and that the boundary-layer is much more receptive to slow acoustic waves (by almost a factor of 20) as compared to the fast waves. Hence, this leading-edge receptivity mechanism is expected to be more relevant in the transition process for high Mach number flows where second mode instability is dominant. Computations are performed to investigate the effect of leading-edge thickness and it is found that bluntness tends to stabilize the boundary layer. Furthermore, the relative significance of fast acoustic waves is enhanced in the presence of bluntness. The effect of acoustic wave incidence angle is also studied and it is found that the receptivity of the boundary layer on the ‘windward’ side (with respect to the acoustic forcing) decreases by more than a factor of four when the incidence angle is increased from 0° to 45°. However, the receptivity coefficient for the ‘leeward’ side is found to vary relatively weakly with the incidence angle.

Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Direct numerical simulations of the evolution of disturbances in a viscous shock layer on a flat plate are performed for a free-stream Mach number M ∞ = 21 and Reynolds number Re L = 1.44 · 105. Unsteady Navier-Stokes equations are solved by a high-order shock-capturing scheme. Processes of receptivity and instability development in a shock layer excited by external acoustic waves are considered. Direct numerical simulations are demonstrated to agree well with results obtained by the locally parallel linear stability theory (with allowance for the shock-wave effect) and with experimental measurements in a hypersonic wind tunnel. Mechanisms of conversion of external disturbances to instability waves in a hypersonic shock layer are discussed.