Abstract:In this paper, we continue to study the mechanisms of the receptivity of the supersonic boundary layer to free-stream disturbances by using both direct numerical simulation and linear stability theory. Specifically, the receptivity of a Mach 4.5 flow over a flat plate to free-stream fast acoustic waves is studied. The receptivity to free-stream slow acoustic waves, entropy waves and vorticity waves will be studied in the future. The oblique shock wave induced by the boundary-layer displacement plays an importa… Show more
“…DNS investigations by Ma & Zhong (2003b, 2005 and by Balakumar (2003Balakumar ( , 2005) have indicated too that planar acoustic, vortical and entropy disturbances alone can excite instability modes in a supersonic flat-plate boundary layer. These careful numerical studies have provided much important information about supersonic boundary-layer receptivity.…”
This paper analyses the response and receptivity of the hypersonic boundary layer over a wedge to free-stream disturbances including acoustic, vortical and entropy fluctuations. Due to the presence of an attached oblique shock, the boundary layer is known to support viscous instability modes whose eigenfunctions are oscillatory in the far field. These modes acquire a triple-deck structure. Any of three elementary types of disturbances with frequency and wavelength on the triple-deck scales interacts with the shock to generate a slow acoustic perturbation, which is reflected between the shock and the wall. Through this induced acoustic perturbation, vortical and entropy free-stream disturbances drive significant velocity and temperature fluctuations within the boundary layer, which is impossible when the shock is absent. A quasi-resonance was identified, due to which the boundary layer exhibits a strong response to a continuum of high-frequency disturbances within a narrow band of streamwise wavenumbers. Most importantly, in the vicinity of the lower-branch neutral curve the slow acoustic perturbation induced by a disturbance of suitable frequency and wavenumbers is in exact resonance with a neutral eigen mode. As a result, the latter can be generated directly by each of three types of free-stream disturbances without involving any surface roughness element. The amplitude of the instability mode is determined by analysing the disturbance evolution through the resonant region. The fluctuation associated with the eigen mode turns out to be much stronger than free-stream disturbances due to the resonant nature of excitation and in the case of acoustic disturbances, to the well-known amplification effect of a strong shock. Moreover, excitation at the neutral position means that the instability mode grows immediately without undergoing any decay, or missing any portion of the unstable region. All these indicate that this new mechanism is particularly efficient. The boundary-layer response and coupling coefficients are calculated for typical values of parameters.
“…DNS investigations by Ma & Zhong (2003b, 2005 and by Balakumar (2003Balakumar ( , 2005) have indicated too that planar acoustic, vortical and entropy disturbances alone can excite instability modes in a supersonic flat-plate boundary layer. These careful numerical studies have provided much important information about supersonic boundary-layer receptivity.…”
This paper analyses the response and receptivity of the hypersonic boundary layer over a wedge to free-stream disturbances including acoustic, vortical and entropy fluctuations. Due to the presence of an attached oblique shock, the boundary layer is known to support viscous instability modes whose eigenfunctions are oscillatory in the far field. These modes acquire a triple-deck structure. Any of three elementary types of disturbances with frequency and wavelength on the triple-deck scales interacts with the shock to generate a slow acoustic perturbation, which is reflected between the shock and the wall. Through this induced acoustic perturbation, vortical and entropy free-stream disturbances drive significant velocity and temperature fluctuations within the boundary layer, which is impossible when the shock is absent. A quasi-resonance was identified, due to which the boundary layer exhibits a strong response to a continuum of high-frequency disturbances within a narrow band of streamwise wavenumbers. Most importantly, in the vicinity of the lower-branch neutral curve the slow acoustic perturbation induced by a disturbance of suitable frequency and wavenumbers is in exact resonance with a neutral eigen mode. As a result, the latter can be generated directly by each of three types of free-stream disturbances without involving any surface roughness element. The amplitude of the instability mode is determined by analysing the disturbance evolution through the resonant region. The fluctuation associated with the eigen mode turns out to be much stronger than free-stream disturbances due to the resonant nature of excitation and in the case of acoustic disturbances, to the well-known amplification effect of a strong shock. Moreover, excitation at the neutral position means that the instability mode grows immediately without undergoing any decay, or missing any portion of the unstable region. All these indicate that this new mechanism is particularly efficient. The boundary-layer response and coupling coefficients are calculated for typical values of parameters.
“…This method makes it possible to obtain detailed information on the perturbation field, which is difficult in experimental studies. A numerical simulation of the receptivity of a two-dimensional boundary layer on a flat plate with a sharp leading edge to acoustic waves was carried out in [10] by using a numerical scheme of a high order of approximation with the separation of the head jump. This scheme is not applicable in a small region near the leading edge of the plate, where a shock wave is formed.…”
Section: Introductionmentioning
confidence: 99%
“…This scheme is not applicable in a small region near the leading edge of the plate, where a shock wave is formed. This region was not considered in [10], although it can play an important role in the receptivity process. In [10], only fast acoustic waves with a positive inclination angle (12 different angles) were investigated with M =4.5.…”
Section: Introductionmentioning
confidence: 99%
“…This region was not considered in [10], although it can play an important role in the receptivity process. In [10], only fast acoustic waves with a positive inclination angle (12 different angles) were investigated with M =4.5. In [11] for the same regime, other types of perturbations in the incoming flow (slow acoustic waves, entropy waves and vorticity) are considered.…”
Abstract. Based the direct numerical simulation in the paper the supersonic flow around of the infinitely thin plate, which was perturbed by the acoustic wave, was investigated. Calculations carried out in the case of small perturbations at the Mach number M=2 and Reynold's numbers Re<600. It is established that the velocity perturbation amplitude within the boundary layer is greater than the amplitude of the external acoustic wave in several times, the maximum amplitude growth is reached 10. At the small sliding and incidence angles the velocity perturbations amplitude increased monotonously with Reynold's numbers. At rather great values of these angles there are maxima in dependences of the velocity perturbations amplitude on the Reynold's number. The oscillations exaltation in the boundary layer by the sound wave more efficiently if the plate is irradiated from above. At the fixed Reynolds's number and frequency there are critical values of the sliding and incidence angles (χ, φ) at which the disturbances excited by a sound wave are maxima. At M=2 it takes place at χ≈ φ ≈30°. The excitation efficiency of perturbations in the boundary layer increases with the Mach number, and it decreases with a frequency.
“…The VSL consists of a thick boundary layer and a thin layer of an inviscid §ow behind the SW. Like the boundary layer, the laminar shock layer is unstable, and perturbations developed in this layer induce its transition to the turbulent §ow regime. The evolution of perturbations in supersonic §ows with Mach numbers 6 and 10 was studied by Egorov et al [1,2] and Ma and Zhong [3,4]. However, mechanisms governing emergence and development of perturbations in the VSL with higher Mach numbers may di¨er from those investigations with lower Mach numbers.…”
This is a brief review of the investigations of receptivity and control of hypersonic shock layers. The present paper describes comprehensive numerical and experimental investigations of evolution of disturbances generated in the hypersonic viscous shock layer (VSL) on a §at plate by external acoustic waves and by perturbations introduced into the shock layer from the surface of model. The active control of intensity of pulsations is possible because both external acoustic waves and the periodic controlled disturbances introduced on the plate surface generate, in a shock layer, entropy-vorticity disturbances with identical spatial distributions and phase velocities.
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