Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel. Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface in the streamwise direction to investigate the development of the unstable disturbance. Wavelet transform is employed as a mathematical tool to obtain the multi-scale characteristics of fluctuating surfacethermal-flux both in the temporal and spectrum space. The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbance waveform from the fluctuating surface-thermal-flux signals.The generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique. The development of the unstable disturbance in the streamwise direction is assessed both in the temporal and spectrum space. Our study shows that the local unstable disturbance detection method based on wavelet transformation offers an alternative powerful tool in studying the hypersonic unstable mode of laminar-turbulent transition. It is demonstrated that, at hypersonic speeds, the dominant flow instability is the second mode, which governs the course of laminar-turbulent transition of sharp cone boundary layer.
Jian Han.Nan Jiang.Yan Tian Department of Mathematics,Tianjin University,300072 Tianjin,China Department of Mechanics,Tianjin University,300072 Tianjin,China Tianjin Key Laboratory of Modern Engineering Mechanics,300072 Tianjin,China State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences,100190 Beijing,China
The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. W＇avelet transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation position in the boundary layer, and the or breakup of eddies are related to the vertical energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.
We present dynamic mode decomposition (DMD) for studying the hairpin vortices generated by hemisphere protuberance measured by two-dimensional (2D) time-resolved (TR) particle image velocimetry (PIV) in a water channel. The hairpins dynamic information is extracted by identifying their dominant frequencies and associated spatial structures. For this quasi-periodic data system, the resulting main Dynamic modes illustrate the different spatial structures associated with the wake vortex region and the near-wall region. By comparisons with proper orthogonal decomposition (POD), it can be concluded that the dynamic mode concentrates on a certain frequency component more effectively than the mode determined by POD. During the analysis, DMD has proven itself a robust and reliable algorithm to extract spatial-temporal coherent structures.
Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional co- herent structures in the logarithmic region of the turbulent boundary layer in a water tunnel. The Reynolds number based on momentum thickness is Reo = 2 460. The in- stantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low speed fluid, which is flanked on either side by high- speed ones. Statistical support for the existence of hairpins is given by conditional averaged eddy within an increasing spanwise width as the distance from the wall increases, and the main vortex characteristic in different wall-normal re- gions can be reflected by comparing the proportion of ejec- tion and its contribution to Reynolds stress with that of sweep event. The pre-multiplied power spectra and two-point cor- relations indicate the presence of large-scale motions in the boundary layer, which are consistent with what have been termed very large scale motions （VLSMs）. The three dimen-sional spatial correlations of three components of veloc- ity further indicate that the elongated low-speed and high- speed regions will be accompanied by a counter-rotating roll modes, as the statistical imprint of hairpin packet structures, all of which together make up the characteristic of coherent structures in the logarithmic region of the turbulent boundary layer （TBL）.
The streamwise fluctuating velocity in the turbulent boundary layer is measured under approximately medium Reynolds Number by hot wire in order to investigate the scaling properties of the overlapped turbulent spectrum among energy-containing area, inertial subrange and dissipation range based on FFT analysis. The experiment indicates that the high Reynolds flow reported before is not indispensable to produce -1 scaling. So far as the measured position is provided with much higher spatial resolution and enough closing to the wall, -1 scaling is determinate to exist when approaching medium Reynolds. The scaling ranges are supposed to begin at inner scale and end in outer scale, which reveals the local similarity of the energy spectrum over the energy-containing eddies near the wall. In the logarithmic area (y+ > 130), -5/3 scaling occurs in the energy spectrum, while moving away from the wall with Reynolds numbers increasing, the inertial subrange extends to the lower wavenumbers. On the condition k1η 0.1, the curves of the turbulence spectrum in the logarithmic layer are superposed, which expresses the similarity of turbulence energy distributed in Komogorov scaling area and exhibits local isotropy characteristics by virtue of the viscous dissipation.
采用数值模拟的方法,对在重力作用下微管末端液滴缓慢形成及脱落的动力学过程进行分析和研究。采用有限体积法在轴对称坐标系下求解液滴形成与破碎过程的Navier-Stokes方程,采用VOF(volume of fluid)方法以及基于PLIC(piecewise-linear interface construction)的几何重构方法追踪液滴运动过程的自由表面,捕捉气液界面的演化过程。分析了量纲1液滴最小颈宽以及量纲1液滴高度等相关特征量随相对时间的变化规律,并与实验结果进行了比较。分析了液滴形貌与液滴轴心线上流向速度的变化以及液滴内部涡环形成与湮灭的关系。通过研究轴心线上压力随时间的变化,分析了压力与液滴颈部位置及断裂位置的关系。
