Slow Acoustic Waves Research Articles

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.

Effects of Mach number on space-time characteristics of wall pressure fluctuations beneath turbulent boundary layers

Wall pressure fluctuations beneath turbulent boundary layers are a fundamental source of aerodynamic noise by exciting the wall structure, with their space-time characteristics serving as the basic ingredient for predicting the wall structural response. To this end, direct numerical simulations of fully developed compressible turbulent boundary layers at Mach numbers of 0.5, 1.2, and 2.0 are conducted to investigate wall pressure fluctuations comprehensively. The effects of Mach number on the single-point statistics of wall pressure fluctuations, such as the root mean square, skewness and flatness factors, probability density function, and frequency spectrum, are assessed to be very weak. Regarding the space-time characteristics, the convection velocity Uc determined by the space-time correlation of wall pressure fluctuations increases slightly with the Mach number, which only reflects the convective behavior of turbulent vortices. On the wavenumber–frequency spectrum, characteristic peaks of both the acoustic wave and convective vortices are identified. At Mach 0.5, the peaks of the fast (Uc+c) and slow (Uc−c) acoustic waves are unattached to others with c denoting acoustic speed, while only the peak of the fast acoustic wave is distinguishable from the convective peak at Mach 1.2 and 2.0. Due to the aerodynamic heating at supersonic conditions, the thermal effect on acoustic speed should be taken into account in determining the acoustic wavenumber. By introducing a convective Prandtl–Glauert parameter, a refined relation is proposed to provide a more accurate depiction of the acoustic domain in the wavenumber–frequency spectrum.

Evaluation of the Tellurium Dioxide Crystal Shear Acoustic Wave Attenuation at 40-140 MHz Frequency.

The attenuation of slow shear acoustic waves in the (110) plane of tellurium dioxide (TeO2) crystals was investigated. The strong acoustic anisotropy of TeO2 crystals results in a non-uniform acoustic power distribution, which can introduce errors in conventional acousto-optic testing methods. In this study, we propose a general method to measure the acoustic power distribution along the propagation direction of acoustic waves in non-collinear acousto-optic tunable filters (AOTFs). Additionally, we analyze the errors introduced by the non-uniform acoustic field resulting from strong acoustic anisotropy in acousto-optic testing methods. The measurements were carried out for a crystal cutoff angle of 6.5° from the [110] axis, for the ultrasound frequency range from 40 to 140 MHz. The attenuation coefficients were determined and their quadratic dependence on ultrasound frequency was confirmed.

Three-dimensional receptivity of a high-speed blunt cone to different types of freestream disturbances

Receptivity to freestream disturbances is the initial stage of the boundary-layer transition process, which can determine the final path of boundary-layer disturbance triggering transition. At present, researches on the receptivity of two-dimensional boundary layer to disturbances with zero incident angles, are relatively sufficient. In fact, the freestream disturbances often propagate into the boundary layer in the form of non-zero incident angles, resulting in a component of spatial disturbances in the circumferential direction of rotating bodies (such as a cone). It is a receptivity problem with a distinct three-dimensional feature. However, research on this three-dimensional receptivity problem is relatively scarce. The preliminary work only studied the three-dimensional receptivity to low-frequency incident slow acoustic waves. There has not been a systematic study on the three-dimensional receptivity to different types of freestream disturbances. The paper conducts a study on the three-dimensional receptivity of a blunt cone to different freestream disturbances. Firstly, a high-resolution numerical simulation method is used to compute the three-dimensional receptivity process by introduce freestream disturbances with 15 degree incident angles. The freestream disturbances include fast acoustic wave, slow acoustic wave, entropy wave, and vortex wave. Their frequencies are selected as dimensionless 1.1 and 5, corresponding to the frequencies of the first mode and second mode, respectively. Then, the phase velocity and shape function of the boundary-layer disturbances at each circumferential position for the numerical results are obtained by Fourier transform. To interpret the receptivity mechanisms, the corresponding results by linear stability analysis are obtained for comparisons. It is found that, the first and second modes of the boundary layer can be effectively excited by the incident slow acoustic waves; It is difficult for the incident fast acoustic waves to excite unstable modes in the boundary layer; The incident entropy wave and vortex wave are difficult to excite the first mode at low frequency, but can excite the second mode at high frequency. Furthermore, the incident angle of the freestream disturbances can cause the differences in the receptivity at different circumferential positions of the cone, which can be reflected in two ways. One is the difference in the dominant disturbance form at different circumferential positions; The second is the difference in the amplitude of boundary-layer disturbances. Under different disturbance types and frequencies, these differences between different circumferential positions exhibit different results. The strongest receptivity may occur on the incident front, the incident back, and the incident side. These phenomena may be the result of the combined action of the upstream head disturbances and the disturbances on the incident front.

Numerical simulation of laminar-turbulent transition in a supersonic boundary layer under the action of acoustic disturbances

In low disturbance environment, laminar-turbulent transition (LTT) is associated with excitation of unstable normal modes of small initial amplitudes (receptivity problem). These modes grow exponentially to a critical amplitude in accord with the linear stability theory (LST) and trigger the nonlinear breakdown. In the current study numerical simulation of laminar-turbulent transition (LTT) in the boundary layer on the upper surface of a flat plate in a supersonic free stream of Mach number M∞=3 and Reynolds number Re∞=2 × 107 is carried out. The flow is perturbed by fast or slow acoustic waves of low intensity, which excite unstable waves of the first mode. The latter have frequencies corresponding to the integral amplification N ≈ 9.16 typical for flight conditions. Two cases are considered: the angle of attack AoA=0° at which acoustic waves pass through a weak shock induced by viscous-inviscid interaction; AoA=5° at which acoustic waves pass through the expansion fan emanating from the plate leading edge. A holistic modeling of all stages of the transition from receptivity to the birth of turbulent spots is performed using direct numerical simulations. Linear stability theory is used to interpret the results. Feasibility of practical implementation of the amplitude method for predictions of the LTT onset in the considered and similar cases is discussed. It has been shown that to realize the amplitude method in the considered and similar cases, it is sufficient: to calculate the initial amplitudes of instability in a small vicinity of the leading edge and the propagation of instability from the leading edge to the station where the instability reaches the critical amplitude u′max≈4%. Analysis of known numerical and experimental data showed that this criterion weakly depends on the local Mach number in the range 0<Me<7, and it is acceptable for practical predictions of the transition onset points.

Biorthogonal decomposition of the disturbance flow field generated by particle impingement on a hypersonic boundary layer

The disturbance flow field in a hypersonic boundary layer excited by particle impingement was investigated with a focus on the first stage of the laminar-to-turbulent transition process, namely the receptivity process. A previously validated direct numerical simulation approach adopting disturbance flow tracking is used to simulate the particle-induced transition process. Particle impingement generates a highly complex disturbance flow field that can be characterised by a wide range of frequencies and wavenumbers. After providing some insight about the spectral characteristics of the disturbance flow field in the frequency and wavenumber domains, biorthogonal decomposition is employed to reveal the composition of the disturbance flow field consisting of different continuous and discrete eigenmodes that are triggered through particle impingement. The disturbance flow characteristics for different frequency and wavenumber pairs are discussed where large contributions in the disturbance flow spectrum are observed in the vicinity of the impingement location. A significant amount of the disturbance energy is diverted into the free stream leading to large coefficients of projection for the slow and fast acoustic branches while contributions to the entropy and vorticity branches are negligible. In addition to the continuous acoustic spectra, the first-, second- and other higher-order Mack modes are activated and provide large contributions to the disturbance flow field inside the boundary layer. Finally, it is demonstrated that the disturbance flow field in the vicinity of the impingement location can be reconstructed with a maximum relative error of $2.3\,\%$ by employing a theoretical biorthogonal eigenfunction system expansion and by considering contributions from fast and slow acoustic waves and at most four discrete modes only.

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 &amp;lt; 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.

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.

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.

HTR approach to the asymptotic solutions of supersonic boundary layer problem: the case of slow acoustic waves interacting with streamwise isolated wall roughness

HTR approach to the asymptotic solutions of supersonic boundary layer problem: the case of slow acoustic waves interacting with streamwise isolated wall roughness

Receptivity of a hypersonic flow over a blunt wedge to a slow acoustic wave

The receptivity of the second mode for Mach 6 flow over a blunt wedge with a nose radius of 0.258 mm is investigated numerically. When a plane slow acoustic wave is imposed on the freestream, the receptivity process of the boundary layer goes through three stages, with the development of an entropy-layer mode, a fast mode, and nonmodal external disturbances, before exciting the second mode. The first two dominant modes can be obtained by linear stability theory in the entropy layer and the boundary layer, respectively, whereas the third is a complicated type of disturbance whose shape function peaks in the entropy layer. The results show that the nonmodal disturbances in the entropy layer play a leading role in the excitation of the second mode, which suggests that the growth of nonmodal disturbances could dominate nonmodal amplification, eventually leading to boundary-layer transition.

Numerical study of shock-disturbances interaction in hypersonic inviscid flows with real gas effects using high-order WENO scheme

In the present study, the shock-disturbances interaction in hypersonic inviscid flows with real gas effects is studied by applying a high-order accurate numerical method with the shock capturing technique. To consider real gas effects, the equilibrium air model is utilized here. The strong conservative form of the unsteady compressible Euler equations in the 2D generalized curvilinear coordinates is formulated and the resulting system of equations for the equilibrium air model is discretized by using the fifth-order finite-difference WENO scheme in space and the explicit third-order TVD Runge–Kutta scheme in time to provide a highly accurate and robust equilibrium airflow solver. The solution methodology adopted based on the high-order WENO scheme with the shock capturing technique can reasonably simulate the strong discontinuities in the solution domain without needing any numerical artifact and this feature makes the solution method suitable for the shock-disturbances interaction in hypersonic flows in which real gas effects are to be considered. To study the physical phenomenon of the shock-disturbances interaction problem in high-speed inviscid equilibrium airflows, two test cases are simulated by applying the solution methodology adopted. In the first test case, the interaction between the incoming fast acoustic wave with the bow shock formed around a cylinder with the nose radius of RN=0.0381 m at M∞=8.03 and T∞=182.333 K is simulated. In the second test case, the cylinder radius is taken RN=2.54×10−2 m and the upstream velocity and temperature are u∞=5590m/s and T∞=1833 K, respectively, and all kinds of free stream disturbances, including the entropy wave and the fast and slow acoustic waves, for different wave numbers are considered. The computations are carried out for both the perfect gas and equilibrium air models and the effects of real gas on both the mean and disturbances fields are also studied. The present study introduces the first-known numerical investigation of the shock-disturbances interaction in hypersonic flow over blunt noses with real gas effects in which the numerical results obtained are thoroughly validated by the analytical/theoretical ones and good agreement is found.

Instability of Supersonic Radiation Mode in Hypersonic Boundary Layers

The supersonic mode in hypersonic flows is studied numerically. The radiation characteristics of this mode in a flat-plate boundary layer with cooled walls are focused on. The linear stability analysis and a marching investigation using a parabolized stability equations approach are performed. Unlike the traditional bounded freestream boundary condition, a more physical boundary condition was proposed based on the group velocity direction of the supersonic mode. Two classes of the supersonic modes, the radiation mode and the incoming mode, are distinguished according to their different group velocities in wall-normal direction. The radiation mode is more unstable than the incoming one, for which it is the dominant instability. It is also found that both the stable and unstable radiation modes can radiate slow acoustic waves into the freestream, and no coalescence occurs between the radiation mode and the wave of the slow acoustic spectrum. This process can only be predicted by the linear stability theory with the new boundary condition. The slow acoustic wave has no effect on the supersonic radiation mode.

Hypersonic boundary layer receptivity on flat plate with blunt leading edge due to acoustic disturbance

In the process of hypersonic boundary layer transition, the leading edge receptivity due to free-stream acoustic disturbance provides unstable perturbations in boundary layer with initial amplitudes, which is one of hot issues in the study about transition mechanism. The receptivity of leading edge is influenced by many factors, involving geometry parameters, disturbance types, etc., among which the bluntness plays a key role for generating disturbances. In order to reveal the mechanism of bluntness influence on the boundary layer transition, investigations into the acoustic receptivity on flat plates with sharp and blunt leading edge are carried out. The flow conditions are as follows: Mach number 6, Reynolds number 1e7/m, adiabatic wall. By introducing two-dimensional plane fast and slow acoustic waves into the free-stream, the whole receptivity process of free-stream disturbances passing through shock wave into boundary layer is simulated with high-order accuracy DNS method. With sharp leading edge as a reference, the generation mechanism of the perturbations near blunt leading edge and its influence on the boundary layer downstream are analyzed. Some conclusions are obtained: for acoustic disturbances in hypersonic free-streams, the receptivity mechanism of blunt leading edge is different from that of sharp leading edge; both the fast and the slow mode can be produced respectively near the sharp leading edge by the fast and the slow acoustic wave, while only fast mode appears near the blunt leading edge; the receptivity of blunt leading edge due to the fast acoustic is stronger than that due to slow acoustic, and is also stronger than that of the sharp leading edge in a certain region of boundary layer downstream.

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.

Slow Surface Acoustic Waves via Lattice Optimization of a Phononic Crystal on a Chip

Strategically reducing the speed of waves, which greatly improves both the energy density and information capacity of carrier signals in space, is a key enabling factor for signal-processing devices. Among these devices, especially in the prosperous wireless communication industry, surface acoustic wave (SAW) devices based on interdigital transducers (IDTs) currently hold an essential status. However, velocity reduction in traditional IDT-based SAW devices can be achieved only by using specific substrate materials that are generally of lower hardness, which inevitably leads to an increase in device size and less-optimal electromechanical coupling coefficients. Here, we demonstrate a technological means of realizing slow on-chip SAWs that is relevant for practical rf signal processing, gyrometers, sensing, and transduction. This method takes advantage of the gradual flattening of a Rayleigh-type dispersion band due to the spatial lattice evolution of a surface phononic crystal. In our experiment, the speed of an ultraslow SAW is measured to be approximately 200 m/s, which is even slower than the speed of sound in air and equivalent to 1/17.4 of the speed of the original Rayleigh waves in ${\mathrm{Li}\mathrm{Nb}\mathrm{O}}_{3}$. Such ultraslow SAWs may have promising applications in time-dependent SAW modulation, high-sensitivity SAW sensors, and SAW nonlinear even quantum-dynamic systems. Additionally, our technique can be similarly applied to a broad range of other two-dimensional or quasi-two-dimensional wave structures, e.g., in electronic, optical, acoustic, and thermal systems.

Shear acoustic wave attenuation influence on acousto-optic diffraction in tellurium dioxide crystal.

The slow shear acoustic wave attenuation in a tellurium dioxide crystal (11¯0) plane is examined. The measurements were carried out for two crystal cutoff angles: 7° and 10.5° from the [110] axis. The ultrasound attenuation was examined in the frequency range of 80 to 300 MHz by the acousto-optic (AO) method. The attenuation coefficients were determined for both acoustic wave propagation directions for the frequency range of 200 to 300 MHz. The influence of ultrasound attenuation on the AO cell transmission functions was examined for the 10.5° AO cell both theoretically and experimentally. It is shown that acoustic wave absorption affects mainly the AO diffraction efficiency. The attenuation influence on the AO cell transmission function shape and its half-width is not significant.

Receptivity of a Hypersonic Blunt Cone: Role of Disturbances in Entropy Layer

The boundary-layer receptivity of the second mode to a slow acoustic wave is investigated using direct numerical simulation for a Mach 6 flow over a blunt cone with the nose radius of 5.08 mm. The mean flow behind the shock can be divided into three layers: outer layer, entropy layer, and boundary layer. With the forcing of an acoustic wave, the excited disturbances at downstream locations close to the nose include the fast mode in the boundary layer and the disturbances in the entropy layer and outer layer. Direct numerical simulations show that the disturbance in the entropy layer actually plays a key role in exciting the second mode. The whole process of receptivity is found to follow a three-stage route. In the first stage, the fast mode is excited in the boundary layer. Although it has a dominant amplitude initially, it experiences a significant decay. In the second stage, it is overtaken by the disturbance in the entropy layer. In the third stage, the latter enters the boundary layer and excites the second mode near the lower branch, which is due to a different mechanism of synchronism.

Generation of first Mack modes in supersonic boundary layers by slow acoustic waves interacting with streamwise isolated wall roughness

This paper investigates the receptivity of a supersonic boundary layer to slow acoustic waves whose characteristic frequency and wavelength are on the triple-deck scales, and the phase speed is thus asymptotically small. Acoustic waves on these scales are of special importance as they have the interesting property that a perturbation with a magnitude of in the free stream generates much larger, , velocity fluctuations inside the boundary layer, where is the Reynolds number based on the distance to the leading edge. Their interaction with streamwise localized roughness elements, leading to stronger receptivity, is studied using triple-deck theory and direct numerical simulations (DNS). The receptivity coefficient, defined as the ratio of the streamwise-velocity amplitude of the instability mode excited to that of the incident free-stream acoustic wave, serves to characterize receptivity efficiency. Its dependence on the roughness width, the Reynolds number , the free-stream Mach number and the incident angle of the acoustic wave is examined. The theoretical predictions, obtained assuming , are found to be in quantitative agreement with the DNS results at moderate values of when the roughness elements are located near the lower branch of the instability. The receptivity is sensitive to the incident angle (or the phase speed) of the acoustic wave, being highly effective within a small range of angles close to and for downstream and upstream propagating sound waves, respectively. The amplitude of the instability mode excited is proportional to the streamwise-velocity amplitude of the acoustic signature inside the boundary layer, and scales with the roughness height as , where is the boundary-layer thickness.

Linear interaction of two-dimensional free-stream disturbances with an oblique shock wave

The problem of interaction between disturbances and shock waves was solved by a theoretical approach called linear interaction analysis in the mid-twentieth century. More recently, great progress has been made in analysing shock–turbulence interactions by direct numerical simulation. However, an unsolved theoretical problem remains: What happens when no acoustic waves are stimulated behind the shock wave? The concept of a damped wave is introduced, which is a type of excited plane wave. Based on this, the dispersion and amplitude relationships between any incident plane wave and resulting stimulated waves are constructed analytically, systematically and comprehensively. The physical essence of damped waves and the existence of critical angles are clarified. It is demonstrated that a damped wave is a complex number space solution to the acoustic dispersion relationship under certain conditions. It acts as a bridge connecting fast and slow acoustic waves at the position where the $x$ component of the group velocity is zero. There are two critical angles that can excite fast and slow acoustic waves, which determine the conditions that stimulate a damped wave. Our results show good agreement with theoretical and simulation results. The contribution of each excited wave to the transmission coefficient is evaluated, the distribution of the transmission coefficient is analysed and application to an engineering wedge model is performed.