There is great difficulty for direct Boltzmann solvers to simulate high Knudsen number flow due to the severe steep slope and high concentration of the gas distribution function in a local particle ...velocity space. Local mesh adaptation becomes necessary in order to make the Boltzmann solver to be a practical tool in aerospace applications. The present research improves the unified gas-kinetic scheme (UGKS) in the following two aspects. First, the UGKS is extended in a physical space with moving mesh. This technique is important to study a freely flying object in a rarefied environment. Second, the adaptive quadtree method in the particle velocity space is implemented in the UGKS. Due to the new improvements in the discretization of a gas distribution function in the six dimensional phase space, the adaptive unified gas kinetic scheme (AUGKS) is able to deal with a wide range of flow problems under extreme flying conditions, such as the whole unsteady flying process of an object from a highly rarefied to a continuum flow regime. After validating the scheme, the capability of AUGKS is demonstrated in the following two challenge test cases. The first case is about the free movement of an ellipse flying at initial Mach number 5 in a rarefied flow at different Knudsen numbers. The force on the ellipse and the unsteady trajectory of the ellipse movement are fully captured. The gas distribution function around the ellipse is analyzed. The second case is about the study of unsteady flight of a nozzle under a bursting process of the compressed gas expanding into a rarefied environment. Due to the strong expansion wave and the huge density difference between interior and exterior regions around the nozzle, the particle distribution function changes dramatically in the particle velocity space. The use of an adaptive velocity space in the AUGKS becomes necessary to simulate such a flow and to control the computational cost to a tolerable level. The second test is a challenge problem for any existing rarefied flow solver.
The free-fall motion of a thin disk with small dimensionless moments of inertia (
${I}^{\ast } \lt 1{0}^{- 3} $
) was investigated experimentally. The transition from two-dimensional zigzag motion to ...three-dimensional spiral motion occurs due to the growth of three-dimensional disturbances. Oscillations in the direction normal to the zigzag plane increase with the development of this instability. At the same time, the oscillation of the nutation angle decreases to zero and the angle remains constant. The effects of initial conditions (release angle) were investigated. Two kinds of transition modes, zigzag–spiral transition and zigzag–spiral–zigzag intermittence transition, were observed to be separated by a critical Reynolds number. In addition, the solution of the generalized Kirchhoff equations shows that the small
${I}^{\ast } $
is responsible for the growth of disturbances in the third dimension (perpendicular to the planar motion).
Abstract
Turbulence is a universal form of fluid motion. It is the key issue in fluid mechanics. Very recently, it has become a bottleneck in some key engineering research of national importance, ...such as aeronautics, astronautics and navigation. Developed turbulence and the onset of turbulence, i.e. transition, are two interrelated parts of turbulence. The hypersonic boundary-layer transition is a strategic focus in the fluid mechanics community. This article reviews recent developments in the study of the hypersonic boundary-layer transition, research facilities and experimental techniques. The hypersonic quiet wind tunnel is introduced as a necessary device to obtain real flight data in near space. Near-wall measurement techniques, such as temperature-sensitive paint, near-wall particle image velocimetry and Rayleigh-scattering visualization, are shown. The most important issues in the recent development of the transition in the hypersonic boundary layer are addressed. The instability and nonlinear interaction of different instability modes are discussed. The recent contributions from China, especially at Peking University, are also introduced.
The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu ...et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Görtler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Görtler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.
Boundary layer transition is usually associated with the amplification and breakdown of three-dimensional waves (3D waves). However, the details of the development of 3D waves in different transition ...regimes are not well resolved. The present study attempts to examine the transition process at early nonlinear stages of K-, N-, and O-regimes by the solution of nonlinear parabolized stability equations (NPSE). The spatial and temporal variations of streamwise velocity are compared at the one-spike stage. Timelines and material surfaces are presented using Lagrangian tracking method. The development of 3D waves are observed to contribute to the upward lift and downward sweep of flow behaviors, causing inflectional regions in the boundary layer. The evolution of material surfaces reveals that the nonlinear 3D wave manifests as a warped wave front in the near-wall region and as a soliton-like structure at the upper region of the boundary layer. The 3D wave structure is hypothesized as a soliton-like coherent structure. Markedly similar flow behaviors are observed between the regimes, which indicates a similar underlying physical mechanism.
Transition and turbulence production in a hypersonic boundary layer is investigated in a Mach 6 wind tunnel using Rayleigh-scattering visualization, fast-response pressure measurements, and particle ...image velocimetry. It is found that the second-mode instability is a key modulator of the transition process. Although the second-mode is primarily an acoustic wave, it causes the formation of high-frequency vortical waves, which triggers a fast transition to turbulence.
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