Hypersonic Boundary Layer Receptivity Research Articles

Freestream Temperature Effects on the Receptivity of Hypersonic Boundary Layer Induced by Finite-Amplitude Pulse Entropy Waves

The unsteady hypersonic flow under finite amplitude pulse entropy perturbation at different freestream temperatures was calculated by direct numerical simulation. The flow response characteristics under the perturbation of entropy waves in freestreaming are analyzed. The temperature effect of freestreaming is studied based on the sensitivity of the boundary layer caused by pulse entropy perturbation. The results show that the higher freestream temperature promotes the first growth of the above third-order modes after leaving the head region, and strongly inhibits the first attenuation. The influence of the freestream temperature on the evolution of the induced disturbance wave is more significant than that on the development of the main flow disturbance waves. Low freestream temperature can suppress the attenuation of the modes below the second order. As the disturbance wave evolves downstream, the frequency band of the finite frequency disturbance wave gradually narrows, and the frequency band narrows faster when the temperature of freestreaming is low than when the temperature of freestreaming is high.

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 < 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.

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

High-speed laminar-to-turbulent transition over blunt bodies is relevant to a variety of aerodynamic applications. Experiments have observed that beyond a critical value of the nose radius the initially downstream movement of transition location is reversed. Linear stability and receptivity analyses have been unsuccessful at predicting this reversal. The current Paper uses a random forcing approach in conjunction with the Navier–Stokes equations to understand this phenomenon using blunted flat plates of different nose radii at . Specifically, steady validated base flows are perturbed to generate multiple scales associated with both the boundary layer as well as the entropy layer. The dominant frequencies and corresponding growth rates in the frequency spectrum are identified with spectral decomposition techniques. With increasing nose bluntness, a reversal in growth rate of maximum amplified frequency is observed beyond a critical value. At low bluntness, the invariance of the scaled frequency parameter indicates that the dominant instability is the Mack mode, as confirmed with through dynamic mode decomposition. For nose radii higher than the critical value, the mode associated with the peak frequency is different, with more prominent support in the entropy layer, indicating the presence of non-Mack modes.

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.

Receptivity Study of Hypersonic Boundary Layer under Freestream Finite Amplitude Continuous Entropy Disturbance with Single Frequency

The DNS method is used to calculate the unsteady flowfield around blunt cone under the action of a single frequency finite amplitude continuous entropy wave. The hypersonic flowfield response to single frequency finite amplitude entropy wave is investigated, and the hypersonic boundary layer receptivity features under single frequency finite amplitude disturbance are explored. The results find that the strong disturbance wave is produced by the interaction of freestream wave with shock wave and boundary layer, and there are regular high-entropy and low-entropy regions in the downstream evolution process. The frequency characteristics of boundary layer disturbance wave are directly related to freestream disturbance wave, and the frequency characteristics become weaker as the disturbance wave evolves downstream. During the development of disturbance downstream, the second, third and fourth (f2-f4) order modes in the boundary layer increase relatively. The central disturbance modes of the nose region are the fundamental mode in the boundary layer, and the main disturbance modes in the boundary layer of the downstream region of the flowfield are composed of the fundamental mode (f1) and the second, third and fourth (f2-f4) order modes.

Effect of a Roughness Element on the Hypersonic Boundary Layer Receptivity Due to Different Types of Free-Stream Disturbance with a Single Frequency.

The hypersonic flow field around a blunt cone was simulated using a high-order finite difference method. Fast acoustic waves, slow acoustic waves, entropy waves, and vortical waves were introduced into the free-stream to determine the influence of a free-stream with disturbances on the hypersonic flow field and boundary layer. The effect of disturbance type on the evolution of perturbations in the hypersonic boundary layer was analyzed. Fast Fourier Transform was adopted to analyze the effect of the disturbance type on the evolution of different modes in the boundary layer. A roughness element was introduced into the flow field to reveal the impact of the roughness element on hypersonic boundary layer receptivity. The results showed that a free-stream with disturbances affected the hypersonic flow field and boundary layer; acoustic waves had the greatest influence. The impact of slow acoustic waves on the flow field was mainly concentrated in the region between the shock and the boundary layer, whereas the influence of fast acoustic waves was mainly concentrated in the boundary layer. Multi-mode perturbations formed in the boundary layer were caused by the free-stream with disturbances, wherein the fundamental mode was the dominant mode of the perturbations in the boundary layer caused by fast acoustic waves, entropy waves, and vortical waves. The dominant modes of the perturbations in the boundary layer caused by slow acoustic waves were both the fundamental mode and the second harmonic mode. The roughness element changed the propagation process of different modes of perturbations in the boundary layer. In the downstream region of the roughness element, perturbations in the boundary layer caused by the slow acoustic waves had the greatest influence. The second harmonic mode in the boundary layer was significantly suppressed, and the fundamental mode became the dominant mode. The effects of fast acoustic waves and entropy waves on the boundary layer receptivity were similar, except the amplitude of the perturbations in the boundary layer caused by the fast acoustic waves was larger.

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.

Receptivity of hypersonic boundary layer due to fast-slow acoustics interaction

The objective of receptivity is to investigate the mechanisms by which external disturbances generate unstable waves. In hypersonic boundary layers, a new receptivity process is revealed, which is that fast and slow acoustics through nonlinear interaction can excite the second mode near the lower-branch of the second mode. They can generate a sum-frequency disturbance though nonlinear interaction, which can excite the second mode. This receptivity process is generated by the nonlinear interaction and the nonparallel nature of the boundary layer. The receptivity coefficient is sensitive to the wavenumber difference between the sum-frequency disturbance and the lower-branch second mode. When the wavenumber difference is zero, the receptivity coefficient is maximum. The receptivity coefficient decreases with the increase of the wavenumber difference. It is also found that the evolution of the sum-frequency disturbance grows linearly in the beginning. It indicates that the forced term generated by the sum-frequency disturbance resonates with the second mode.

Receptivity of Hypersonic Boundary Layers over Straight and Flared Cones

The effects of adverse pressure gradients on the receptivity and stability of hypersonic boundary layers were numerically investigated. Simulations were performed for boundary-layer flows over a straight cone and two flared cones. The steady and the unsteady flowfields were obtained by solving the two-dimensional Navier–Stokes equations in axisymmetric coordinates using the fifth-order-accurate weighted essentially nonoscillatory scheme for space discretization and using a third-order total-variation-diminishing Runge–Kutta scheme for time integration. The mean boundary-layer profiles were analyzed using local stability and nonlocal parabolized stability equations methods. After the most amplified disturbances were identified, two-dimensional plane acoustic waves were introduced at the outer boundary of the computational domain and time-accurate simulations were performed. The adverse pressure gradient was found to affect the boundary-layer stability in two important ways. First, the frequency of the most amplified second-mode disturbance was increased relative to the zero-pressure gradient case. Second, the amplification of first- and second-mode disturbances was increased. Although an adverse pressure gradient enhances instability wave growth rates, small nose-tip bluntness was found to delay transition due to the low receptivity coefficient and the resulting weak initial amplitude of the instability waves. The computed and measured amplitude-frequency spectra in all three cases agree very well in terms of frequency and the shape except for the amplitude.

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.

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.

Characterizing Laser-Generated Hot Spots for Receptivity Studies

Simple, well-characterized experimental perturbations are needed to validate CFD simulations of supersonic and hypersonic boundary-layer receptivity. A laser-generated hot-spot perturbation has been characterized and modeled, based on experiments in the Purdue University Mach-4 quiet-flow Ludwieg tube. The model provides a detailed density profile and time evolution for the perturbation, which consists of a hot spot and the surrounding weak shock. The model is validated by comparing simulated optical path differences to measurements from a high-sensitivity, high-bandwidth laser differential interferometer. CFD simulations are compared with receptivity experiments on a hemisphere to illustrate the usefulness of the perturbation model.

Boundary-layer receptivity of Mach 7.99 flow over a blunt cone to free-stream acoustic waves

The receptivity phenomenon, which is the process of environmental disturbances initially entering the boundary layers and generating disturbance waves, is one of the important but not well understood mechanisms involving laminar–turbulent transition of hypersonic flows. This paper presents a numerical simulation study of the receptivity to weak free-stream fast acoustic waves for a Mach 7.99 axisymmetric flow over a half-angle blunt cone. In hypersonic boundary-layer flow over a blunt cone, the process of receptivity to free-stream disturbances is altered considerably by the presence of a bow shock and an entropy layer. In the present study, both steady and unsteady flow solutions are obtained by computing the full Navier–Stokes equations with a fifth-order shock-fitting finite-difference scheme, which is able to account for the effects of bow-shock/free-stream-disturbance interaction accurately. The current numerical results for the steady base flow are compared with previous experimental and numerical results. In addition, a normal-mode linear stability analysis is used to identify the main components of boundary-layer disturbances generated by forcing free-stream fast acoustic waves. It is found that neither the first mode nor the second-mode instability waves are excited by free-stream fast acoustic waves in the early region along the cone surface, although the Mack modes can be unstable there. Instead, the second mode is excited downstream of the second-mode Branch I neutral stability point. The delay of the second-mode excitation is because the hypersonic boundary-layer receptivity is governed by a two-step resonant interaction process: (i) resonant interactions between the forcing waves and a stable boundary-layer wave mode I near the leading-edge region; and (ii) resonant interactions between the induced stable mode I and the unstable second Mack mode downstream. The same receptivity mechanism also explains the results that no first Mack mode components are generated by the current receptivity process because there is no resonant interaction between fast acoustic waves and the first Mack mode.

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.

Receptivity of Hypersonic Boundary Layer to Wall Disturbances

Theoretical analysis of hypersonic boundary-layer receptivity to wall disturbances is conducted using a combination of asymptotic and numerical methods. Excitation of the second mode by distributed and local forcing on a flat-plate surface is studied under adiabatic and cooled wall conditions. Analysis addresses receptivity to wall vibrations, periodic suction/blowing, and temperature disturbances. A strong excitation occurs in local regions where forcing is in resonance with normal waves. It is shown that the receptivity function tends to infinity as the resonance point tends to the branch point of the discrete spectrum that is typical for boundary layers on cool surfaces. Asymptotic analysis resolves this singularity and provides the receptivity coefficient in the branch-point vicinity. Numerical results indicate extremely high receptivity to vibrations and suction/blowing in the vicinity of the branch point located near the lower neutral branch of the Mack second mode.

Leading-edge receptivity to free-stream disturbance waves for hypersonic flow over a parabola

The receptivity of hypersonic boundary layers to free-stream disturbances, which is the process of environmental disturbances initially entering the boundary layers and generating disturbance waves, is altered considerably by the presence of bow shocks in hypersonic flow fields. This paper presents a numerical simulation study of the generation of boundary layer disturbance waves due to free-stream waves, for a two-dimensional Mach 15 viscous flow over a parabola. Both steady and unsteady flow solutions of the receptivity problem are obtained by computing the full Navier–Stokes equations using a high-order-accurate shock-fitting finite difference scheme. The effects of bow-shock/free-stream-sound interactions on the receptivity process are accurately taken into account by treating the shock as a discontinuity surface, governed by the Rankine-Hugoniot relations. The results show that the disturbance waves generated and developed in the hypersonic boundary layer contain both first-, second-, and third-mode waves. A parametric study is carried out on the receptivity characteristics for different free-stream waves, frequencies, nose bluntness characterized by Strouhal numbers, Reynolds numbers, Mach numbers, and wall cooling. In this paper, the hypersonic boundary-layer receptivity is characterized by a receptivity parameter defined as the ratio of the maximum induced wave amplitude in the first-mode-dominated region to the amplitude of the free-stream forcing wave. It is found that the receptivity parameter decreases when the forcing frequency or nose bluntness increase. The results also show that the generation of boundary layer waves is mainly due to the interaction of the boundary layer with the acoustic wave field behind the bow shock, rather than interactions with the entropy and vorticity wave fields.

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

Direct numerical simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies of transition need to consider the effects of bow shocks, entropy layers, surface curvature, and finite-rate chemistry. It is necessary that numerical methods for such studies are robust and high-order accurate both in resolving wide ranges of flow time and length scales and in resolving the interaction between the bow shocks and flow disturbance waves. This paper presents a new high-order shock-fitting finite-difference method for the DNS of the stability and transition of hypersonic boundary layers over blunt bodies with strong bow shocks and with (or without) thermo-chemical nonequilibrium. The proposed method includes a set of new upwind high-order finite-difference schemes which are stable and are less dissipative than a straightforward upwind scheme using an upwind-bias grid stencil, a high-order shock-fitting formulation, and third-order semi-implicit Runge–Kutta schemes for temporal discretization of stiff reacting flow equations. The accuracy and stability of the new schemes are validated by numerical experiments of the linear wave equation and nonlinear Navier–Stokes equations. The algorithm is then applied to the DNS of the receptivity of hypersonic boundary layers over a parabolic leading edge to freestream acoustic disturbances.