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

The receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate to acoustic disturbances is investigated on the basis of a numerical solution of the 2D Navier-Stokes equations. Numerical results obtained for fast and slow acoustic waves impinging on the plate at zero angle agree qualitatively with asymptotic theory. Calculations carried out for other angles of incidence of the acoustic waves reveal new features of the perturbation field in the neighborhood of the leading edge of the plate. It is shown that, due to visco-inviscid interaction, the shock formed near the leading edge may significantly affect the acoustic field and the receptivity.     

Response of a hypersonic blunt cone boundary layer to slow acoustic waves with assessment of various routes of receptivity

The hypersonic boundary-layer receptivity to slow acoustic waves is investigated for the Mach 6 flow over a 5-degree half-angle blunt cone with the nose radius of 5.08 mm. The plane acoustic wave interacts with the bow shock, and generates all types of disturbances behind the shock, which may take various routes to generate the boundary-layer unstable mode. In this paper, two routes of receptivity are investigated in detail. One is through the disturbance in the entropy layer. The other is through the slow acoustic wave transmitted downstream the bow shock, which can excite the boundary-layer mode due to the synchronization mechanism. The results show that, for a low frequency slow acoustic wave, the latter route plays a leading role. The entropy-layer instability wave is able to excite the first mode near the neutral point, but its receptivity efficiency is much lower.     

Disturbance evolution in the leading-edge region of a blunt flat plate in supersonic flow

The spatio-temporal dynamics of small disturbances in viscous supersonic flow over a blunt flat plate at freestream Mach number M_∞=2.5 is numerically simulated using a spectral approximation to the Navier–Stokes equations. The unsteady solutions are computed by imposing weak acoustic waves onto the steady base flow. In addition, the unsteady response of the flow to velocity perturbations introduced by local suction and blowing through a slot in the body surface is investigated. The results indicate distinct disturbance/shock-wave interactions in the subsonic region around the leading edge for both types of forcing. While the disturbance amplitudes on the wall retain a constant level for the acoustic perturbation, those generated by local suction and blowing experience a strong decay downstream of the slot. Furthermore, the results prove the importance of the shock in the distribution of perturbations, which have their origin in the leading-edge region. These disturbance waves may enter the boundary layer further downstream to excite instability modes.     

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 to a Steady Free-Stream Vortex Disturbance

A single trailing vortex developed behind a micro-wing immersed in a free stream was used to study the vortex receptivity of a swept-wing boundary layer. As a result of the interaction, longitudinal-velocity disturbances develop in the boundary layer. On the swept wing, disturbance transformation occurs near the leading edge and is accompanied by the formation of a wave packet consisting of waves typical of cross-flow instability. Disturbances with other characteristics are also detected. These disturbances may be attributable to distributed boundary-layer receptivity to the free-stream vortex disturbance considered.     

Experimental study of evolution of disturbances in a supersonic boundary layer on a swept-wing model under controlled conditions

Experimental data on stability of a three-dimensional supersonic boundary layer on a swept wing are presented. Evolution of artificial wave trains was studied. The experiments were conducted for Mach numberM=2.0 and unit Reynolds numberRe ₁=6.6·10⁶m⁻¹ on a swept-wing model with a lenticular profile and a40° sweep angle of the leading edge at zero incidence. Excitation of high-frequency disturbances caused by secondary-flow instability at a high initial amplitude was observed. It is shown that the evolution of disturbances at frequencies of10, 20, and30 kHz is similar to the development of travelling waves for the case of subsonic velocities. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 50–56, January–February, 2000.     

Inflow broadband noise from an isolated symmetric airfoil interacting with incident turbulence

Inflow noise from a symmetric airfoil interacting with homogeneous and isotropic turbulence is investigated focusing on the effects of airfoil geometry. The numerical method employed is based on computational aeroacoustic techniques using the high-order dispersion-relation-preserving finite-difference schemes for solving two-dimensional linearized Euler equations. Effects on inflow noise of the airfoil thickness, leading-edge radius, and freestream Mach number are examined by comparing the acoustic power spectrum of the airfoils and their flow field characteristics. Acoustic power levels of airfoils are found to exponentially decrease in the high-frequency range as airfoil thickness increases because incident turbulent velocities are more distorted in the larger stagnation region near the leading edge. This distortion is shown to be related to the slope angle of the streamline of steady mean flow near the leading edge. However, this high-frequency reduction weakens as the Mach number increases due to the decreasing slope angle. In addition, the chordwise velocity component in the incident turbulence contributes more to the radiating acoustic pressure level as the freestream Mach number increases, which also results in less high-frequency reduction at higher freestream Mach number. At fixed airfoil thickness, increasing the leading-edge radius leads to decreases in the acoustic power level, which may also be explained by size variation of the stagnation region around the leading edge. An approximate algebraic formula for acoustic power spectra is derived on the basis of these observations. Acoustic power spectra predicted using this formula are shown to closely follow the numerical results. Finally, the applicability of the algebraic formula and the current numerical methods to more realistic problems are confirmed by comparing their predictions with the measured data.     

高超声速边界层中模态转化的数值研究

在高超声速边界层中,第一模态和第二模态是与转捩有关的两个主要不稳定模态.除了不稳定模态,还存在一类稳定模态,其相速度在前缘接近快声波的相速度称为快模态.在感受性过程中,这类模态对激发边界层中不稳定模态起着很重要的作用.前缘感受性理论解释了边界层外扰动激发边界层中第一模态波的机理.针对高超声速平板边界层,利用相似性解剖面作为基本流,采用线性稳定性理论和直接数值模拟的方法研究了快模态和慢模态的稳定性行为.研究发现模态转化的位置与马赫数有关.根据线性稳定性理论的结果定义了临界频率.当扰动频率高于临界频率,第一模态与第二模态同支;而当扰动频率低于临界频率,第一模态与第二模态的共轭模态同支.借助稳定性方程的伴随方程分析了直接数值模拟的结果.直接数值模拟结果表明不论上游是快模态还是慢模态,当它们经过第二模态的不稳定区,它们都会演化成第二模态. 这可用模态在非平行流中传播的特征来解释.      

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. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 84–91, May–June, 2007.     

Interaction between an Inclined Shock and Boundary and High-Entropy Layers on a Flat Plate

The flow structure and heat exchange in the zone of interference between an inclined shock and the surface of a flat plate are investigated experimentally and theoretically as functions of many parameters, the interference being studied in both the presence and the absence of bluntness of the leading edge. The experiments were carried out at Mach numbers M = 6, 8, and 10 and the Reynolds numbers Re _L , calculated using the plate length L = 120 mm and the free-stream parameters, varied over the range from 0.24 ? 10⁶ to 1.31 ? 10⁶. The bluntness radius of the leading edge of the plate, the intensity of the impinging shock, and its location with respect to the leading edge were varied. The numerical simulation was carried out by solving the complete two-dimensional Navier-Stokes equations and averaged Reynolds equations using the q-ω turbulence model. The laminar boundary layer became turbulent inside the separation zone induced by the shock. It is shown that the plate bluntness significantly reduces the heat exchange intensity in the interference zone, this effect intensifying with increase in the Mach number.     

Receptivity of the inclined-cylinder attachment-line boundary layer to vortex perturbations

The receptivity of the boundary layer in the neighborhood of the attachment line of a cylinder inclined to the flow with respect to periodic vortex perturbations frozen into the stream is investigated. The problem considered simulates the interaction between external turbulence and the leading-edge swept wing boundary layer. It is shown that if the direction of the external perturbation vector is almost parallel to the leading edge, then the external perturbations are considerably strengthened at the outer boundary layer edge. This effect can cause laminar-turbulent transition on the attachment line at subcritical Reynolds numbers.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 72–85. Original Russian Text Copyright © 2004 by Ustinov.     

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.     

Evolution of disturbances in a laminarized supersonic boundary layer on a swept wing

Experimental data on stability of a three-dimensional supersonic boundary layer on a swept wing are presented. The experiments are performed on a swept wing model with a lenticular profile with a 40° sweep angle of the leading edge at a zero angle of attack. The supersonic boundary layer on the swept wing was laminarized with the use of distributed roughness. A pioneering study of interaction of traveling and stationary disturbances is performed. Some specific features of this interaction are identified. The main reason for turbulence emergence in a supersonic boundary layer on a swept wing is demonstrated to be secondary crossflow instability. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 40–46, March–April, 2008.     

Effect of the cone nose bluntness and the ultrasonically absorptive coating on transition in a hypersonic boundary layer

The effect of an ultrasonically-absorptive coating on laminar-turbulent transition on cones with different nose bluntnesses is experimentally investigated. The experiments were performed with a cone with the semi-vertex angle of 7° set at zero incidence in the Mach 8 flow for three Reynolds numbers. A material with a chaotic micropore structure was used as the ultrasonically-absorptive coating. One side of the model, along its generator, was coated with the porous material, while the second represented a rigid surface. The laminar-turbulent transition location was determined from the results of heat flux distribution measurements. The heat flux fluctuations were also measured on the model surface. It was found that the laminar region length increased with an increase in the bluntness radius. The ultrasonically-absorptive coating with a chaotic microstructure effectively stabilizes the boundary layer for all bluntness radii considered, increasing the laminar region length by 30 to 85%.     

On the mechanism by which nose bluntness suppresses second-mode instability

A physical mechanism by which nose bluntness suppresses second-mode instability is proposed.Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm,5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well.Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.     

Stability analysis and transition prediction of hypersonic boundary layer over a blunt cone with small nose bluntness at zero angle of attack

Stability and transition prediction of hypersonic boundary layer on a blunt cone with small nose bluntness at zero angle of attack was investigated. The nose radius of the cone is 0.5 mm; the cone half-angle is 5°, and the Mach number of the oncoming flow is 6. The base flow of the blunt cone was obtained by direct numerical simulation. The linear stability theory was applied for the analysis of the first mode and the second mode unstable waves under both isothermal and adiabatic wall condition, and eN method was used for the prediction of transition location. The N factor was tentatively taken as 10, as no experimentally confirmed value was available. It is found that the wall temperature condition has a great effect on the transition location. For adiabatic wall, transition would take place more rearward than those for isothermal wall. And despite that for high Mach number flows, the maximum amplification rate of the second mode wave is far bigger than the maximum amplification rate of the first mode wave, the transition location of the boundary layer with adiabatic wall is controlled by the growth of first mode unstable waves. The methods employed in this paper are expected to be also applicable to the transition prediction for the three dimensional boundary layers on cones with angle of attack.     

Interaction of intersecting shocks with a flat-plate boundary layer in the presence of an entropy layer

Gas flow and heat transfer on the surfaces of sharp and blunt plates is experimentally investigated in the presence of two forward-looking wedges at the Mach numbers M = 5, 6, and 8 and the Reynolds numbers up to Re_∞L = 27×10⁶. It is shown that the entropy layer generated by a small bluntness of the leading edge of the plate can considerably change the heat transfer, the gas pressure, and the friction in the zone of interference of the shock with the plate boundary layer. Under certain conditions a small plate bluntness can also lead to a qualitative change in the flow structure. The effect of constriction of the channel between the wedges on the interference flow is studied.     

Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow

The influence of small cylindrical bluntness of the leading edge of a flat plate on formation of spatial structures in a nominally two-dimensional supersonic compression corner flow at the Mach number M∞ ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperature-sensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 · 10⁶–2.55 · 10⁶) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces spanwise oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum deviations of the Stanton number reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of spanwise oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of three-dimensional Navier–Stokes equations are obtained for some test conditions. The computed results are in good agreement with experimental data, which points to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.     

Hypersonic boundary-layer transition on a flared cone

Transition on a flared cone with zero angle of attack was studied in our newly established Mach 6 quiet wind tunnel (M6QT) via wall pressure measurement and flow visualization. High-frequency pressure transducers were used to measure the second-mode waves’ amplitudes and frequencies. Using pulsed schlieren diagnostic and Rayleigh scattering technique, we got a clear evolution of the second-mode disturbances. The second-mode waves exist for a long distance, which means that the second-mode waves grow linearly in a large region. Strong Mach waves are radiated from the edge of the boundary layer. With further development, the second-mode waves reach their maximum magnitude and harmonics of the second-mode instability appear. Then the disturbances grow nonlinearly. The second modes become weak and merge with each other. Finally, the nonlinear interaction of disturbance leads to a relatively quiet zone, which further breaks down, resulting in the transition of the boundary layer. Our results show that transition is determined by the second mode. The quiet zone before the final breakdown is observed in flow visualization for the first time. Eventual transition requires the presence of a quiet zone generated by nonlinear interactions.     

Leading-edge receptivity of boundary layer to three-dimensional free-stream turbulence

The laminar-turbulent transition has always been a hot topic of fluid mechanics. Receptivity is the initial stage and plays a crucial role in the entire transition process. The previous studies of receptivity focus on external disturbances such as sound waves and vortices in the free stream, whereas those on the leading-edge receptivity to the three-dimensional free-stream turbulence(FST), which is more general in the nature,are rarely reported. In consideration of this, this work is devoted to investigating the receptivity process of three-dimensional Tollmien-Schlichting(T-S) wave packets excited by the three-dimensional FST in a flat-plate boundary layer numerically. The relations between the leading-edge receptivity and the turbulence intensity are established, and the influence of the FST directions on the propagation directions and group velocities of the excited T-S wave packets is studied. Moreover, the leading-edge receptivity to the anisotropic FST is also studied. This parametric investigation can contribute to the prediction of laminar-turbulent transition.