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 boundarylayer 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.

Stability analysis method considering non-parallelism:EPSE method and its application

The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory （LST） based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation （PSE） method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation （DNS）. In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.

Extension of e^N method to general three-dimensional boundary layers

In order to extend the eN method to general three-dimensional boundary layers, the conservation law of the imaginary parts for the wave parameters with a fixed wave vector is deduced. The compatibility relationship （CR） and the general theory of ray tracing （RT）, which have been extensively used in conservative systems, are applied to a general three-dimensional boundary layer belonging to non-conservative systems. Two kinds of eN methods, i.e., the eN-CR method and the eN-RT method, are established. Both the two kinds of methods can wavenumber and the amplitude of the be used to predict the evolutions of the spanwise disturbances in general three-dimensional boundary layers. The reliability of the proposed methods is verified and validated by performing a direct numerical simulation （DNS） in a hypersonic general three-dimensional boundary layer over an aircraft model. The results are also compared with those obtained by other eN methods, indicating that the proposed methods have great potential applications in improving the transition prediction accuracy in general three-dimensional boundary layers.

Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

The nth-order expansion of the parabolized stability equation （EPSEn） is obtained from the Taylor expansion of the linear parabolized stability equation （LPSE） in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE （EPSE1） and the second-order EPSE （EPSE2） are used to study the crossflow instability in the swept NLF（2）-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory （LST）, the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient ey prediction tool for the crossflow instability in swept-wing boundary-layer flows.

Improvement for expansion of parabolized stability equation method in boundary layer stability analysis

An improved expansion of the parabolized stability equation(iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient dα/dx are unknown variables. This eigenvalue problem is solved for the eigenvalue dα/dx with an initial α, and the correction of α is performed with the conservation relation used in the PSE. The i EPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the i EPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the i EPSE. As a local non-parallel stability analysis tool, the i EPSE has great potential application in the eNtransition prediction in general three-dimensional boundary layers.

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Nonlinear interactions of the two-dimensional （2D） second mode with oblique modes are studied numerically in a Mach 6.0 fiat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation （PSE） method, which is able to simulate interaction of two modes with different frequen- cies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations.

Global instability of Stokes layer for whole wave numbers

The study on the global instability of a Stokes layer, which is a typical unsteady flow, is usually a paradigm for understanding the instability and transition of unsteady flows. Previous studies suggest that the neutral curve of the global instability obtained by the Floquet theory is only mapped out in a limited range of wave numbers （0.2 ≤ a ≤ 0.5）. In this paper, the global instability is investigated with numerical simulations for all wave numbers. It is revealed that the peak of the disturbances displays irregularity rather than the periodic evolution while the wave number is beyond the above range. A ＂neutral point＂ is redefined, and a neutral curve of the global instability is presented for the whole wave numbers with this new definition. This work provides a deeper understanding of the global instability of unsteady flows.

Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wall cooling effect on the Mack mode instability by numerical methods. It is shown that the wall-cooling can destabilize the Mack mode instability, similar to the previous conclusions with the exception that the Mack mode instability can be stabilized by wall-cooling if the wall temperature is extremely low. The reversed wall temperature is related to a freestream condition. If the Mach number increases to a large enough value, e.g., about 7, the reversed wall temperature will tend to be zero. It seems that the Mack mode instability is determined by the region between the boundary layer edge and the critical layer. When the wall temperature decreases, this region becomes wider, and the boundary layer becomes more unstable. Additionally, a relative supersonic unstable mode can be observed when the velocity of the critical layer is less than 1 - liMa or is cancelled by the wall-cooling effect. These results provide a deeper understanding on the wall-cooling effect in high speed boundary layers.

Chiral Betaine-Mediated Asymmetric Peroxidation-Kinetic Resolution Cascade for the Synthesis of Optically Pure Peroxides

An array of natural products bearing chiral peroxide motifs display antitumor,anticancer,and antiparasitic activities.However,there are very few catalytic asymmetric syntheses of chiral peroxides.Moreover,effective catalysts for asymmetric catalytic peroxidations are limited to chiral amines.To further expand synthetic access to chiral peroxides,the development of new catalysts realizing catalytic asymmetric peroxidation is highly desirable yet challenging.We report here a catalytic asymmetric peroxidation of anα,β-unsaturated triflone-kinetic resolution cascade reaction,which furnishes chiral peroxides in greater than 99.9%ee.The realization of this cascade reaction resulted from the development of two betaines as novel catalysts for chiral peroxide synthesis;one betaine promoted enantioselective peroxidation ofα,β-unsaturated triflones via conjugate addition affording peroxides in 80-92%ee,while the other betaine catalyzed kinetic resolution of the newly generated chiral peroxides to further increase the ee to greater than 99.9%.