Wavelet Cross-Spectrum Analysis of Multi-Scale Disturbance Instability and Transition on Sharp Cone Hypersonic Boundary Layer

Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean andfluctuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in thefrequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance are demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.     

高超声速条件下7°直圆锥边界层转捩实验研究

在Ma=6低噪声风洞中开展了半锥角7?的直圆锥边界层转捩相关实验研究.利用响应频率达到MHz量级的高频压力传感器对圆锥壁面脉动压力进行了测量,研究了高超声速圆锥边界层中扰动波的发展过程.结果表明:高超声速圆锥边界层中第二模态扰动波产生的位置以及扰动波特征频率和波长等参数受雷诺数影响较大,当单位雷诺数从2×106m~(-1)增加到8×106m~(-1)时,第二模态波的特征频率从55 k Hz增加到226 k Hz;随着单位雷诺数增加,边界层中扰动增长速度加快,第二模态波出现在圆锥表面更靠近上游的位置;相同单位雷诺数条件下,随着第二模态波的向下游传播,其特征频率逐渐减小.通过对比发现自由来流湍流度对边界层中扰动波的发展同样有较大影响,自由来流湍流度降低,边界层中的第二模态波的特征频率明显减小.利用互相关分析得出第二模态扰动波在边界层中的传播速度大约为当地主流速度的0.8—0.9倍.在1?小攻角条件下,圆锥迎风面和背风面边界层发展呈现出明显的差异,背风面边界层中扰动发展提前,第二模态波出现在更靠近上游的位置,而迎风面中扰动发展受到抑制,第二模态波特征频率更大.     

Receptivity to free-stream disturbance waves for hypersonic flow over a blunt cone

A high-order shock-fitting finite difference scheme is studied and used to do direction numerical simulation (DNS) of hypersonic unsteady flow over a blunt cone with fast acoustic waves in the free stream, and the receptivity problem in the blunt cone hypersonic boundary layers is studied. The results show that the acoustic waves are the strongest disturbance in the blunt cone hypersonic boundary layers. The wave modes of disturbance in the blunt cone boundary layers are first, second, and third modes which are generated and propagated downstream along the wall. The results also show that as the frequency decreases, the amplitudes of wave modes of disturbance increase, but there is a critical value. When frequency is over the critial value, the amplitudes decrease. Because of the discontinuity of curvature along the blunt cone body, the maximum amplitudes as a function of frequencies are not monotone. Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 10502052)     

激光聚焦扰动作用下高超声速边界层稳定性实验研究

在马赫数6、单位雷诺数3.1×10⁶/m的条件下对半锥角7°直圆锥边界层稳定性开展了实验研究.以激光聚焦于流场中局部空间而产生的膨胀冲击波作为人工添加的小扰动,分析了该扰动对高超声速圆锥边界层流动稳定性的影响.实验中利用响应频率达到兆赫兹量级的高频压力传感器对圆锥壁面脉动压力进行测量,通过对压力数据进行短时傅里叶分析和功率谱分析发现,相比于不添加激光聚焦扰动的结果,添加激光聚焦扰动使边界层中第二模态波的出现位置提前,且扰动波的幅值大幅度地增加,在相同的流向范围内,激光聚焦扰动将边界层中的扰动波从线性发展阶段推进到非线性发展阶段,其对边界层中扰动波发展的促进效果明显.同时,激光聚焦位置的不同对边界层中扰动波的发展也具有不同的影响.当激光直接聚焦于圆锥壁面X=100 mm位置时,边界层中频率为90 kHz的扰动波幅值增长最快,在X=500 mm的位置处其幅值放大倍数为3.81,相比而言当激光聚焦位置位于圆锥前方自由来流中时,边界层幅值增长最快的扰动波频率大幅减小为73 kHz,相同范围内,其幅值放大倍数为4.51倍.由此可见,当激光聚焦位置位于圆锥上游的自由来流中时,其对边界层中扰动波的影响更为显著.     

Improved algorithm for solving nonlinear parabolized stability equations

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations(NPSE) approach has been widely used to study the stability and transition mechanisms. However,it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation(DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers.     

Stability of supersonic boundary layer under the influence of heavy gas injection: experimental study

Experiments were performed on the influence of distributed injection of a heavy gas (elegas SF₆) into the near-wall region of the supersonic (freestream Mach number М_∞ = 2) boundary layer on its stability in relation to natural disturbances. Heavy gas injection for the case of linear development of disturbance field results in boundary layer stabilization. It was experimentally proved that the elegas injection can suppress disturbances at the frequencies higher than 15 kHz for the tested range of the streamwise coordinate.     

合成冷/热射流控制超声速边界层流动稳定性

为了探究超声速边界层流动稳定性及其转捩控制机理,提出基于合成冷/热射流的边界层速度-温度耦合控制方法,并通过数值模拟研究了Ma=4.5超声速平板边界层不稳定波的传播,采用线性稳定性理论中的时间模式分析了壁面吹吸、射流温度、扰动频率、扰动振幅等对不稳定波控制效果的影响.结果表明:无射流控制时,边界层内同时存在不稳定的第一模态扰动波和第二模态扰动波,且二维波形式的第二模态占主导地位;壁面吹吸作用下,仅出现更加不稳定的第二模态,第一模态被抑制;速度-温度耦合控制下,射流温度对扰动模态的不稳定区域大小及扰动增长率影响显著,射流温度与来流温度不同时,温度的脉动使得流动转捩为湍流的速度加快,边界层速度型更加饱满,抗干扰能力增强,流动稳定性提高;高频的吹吸扰动对流场的控制效果优于低频扰动,扰动频率超过400 Hz时,第二模态扰动波时间增长率降低,扰动分量对边界层速度剖面和温度剖面的修正加快,第二模态更加稳定;扰动振幅减小为主流速度的1%时,仅出现时间增长率较小的第二模态,控制效果较好,进一步减小时,第一模态重新出现,并且波数范围与第二模态先重合后分离,对应的时间增长率先增加后减小.研究结果为边界层转捩控制技术提供了新的思路.     

Competition of the multiple Grtler modes in hypersonic boundary layer flows

Competition of multiple Grtler modes in hypersonic boundary layer flows are investigated with the local and marching methods.The wall-layer mode(mode W)and the trapped-layer mode(mode T)both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge.The mode T has the largest growth rate at a lower Grtler number while the mode W dominates at larger Grtler numbers.These two modes are both responsible for the flow transition in the hypersonic flows especially when Grtler number is in the high value range in which the crossover of these two modes takes place.Such high Grtler numbers are virtually far beyond the neutral regime.The nonparallel base flows,therefore,cease to influence the stability behavior of the Grtler modes.The effects of the Mach number on the multiple Grtler modes are studied within a chosen Mach number of 0.95,2,4 and 6.When the flow Mach number is sufficiently large,e.g.,Ma 4,the growth rate crossover of the mode T and mode W occurs both in the conventional G-βmap as well as on the route downstream for a fixed wavelength disturbance.Four particular regions(Region T,T-W,W-T and W)around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis.The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.     

高超声速圆锥边界层转捩实验研究

在高超声速静音风洞内, 通过基于纳米粒子示踪的平面激光散射(nano-tracer-based planar laser scattering, NPLS)技术、高频压力传感器和温敏漆(temperature sensitive paints, TSP)技术开展了0°攻角条件下7°直圆锥高超声速边界层转捩相关实验研究, 得到了圆锥边界层由层流发展至湍流完整过程的NPLS图像, 清晰地展示了第2模态波的"绳状"结构, 尖锥与钝锥边界层的NPLS结果表明尖锥边界层转捩中第2模态波占主导, 而钝锥边界层在转捩前出现波长约为第2模态波波长5倍(甚至更长)、特征频率不高于31 kHz的狭长涡结构; 采用功率谱密度(power spectrum density, PSD)分析、互相关和N值计算对高频脉动压力数据进行分析, 得到了边界层内扰动波的发展规律, 在尖锥和钝锥中均观察到了沿流向第2模态波幅值先增大后减小、特征频率逐渐降低, 低频成分逐渐增加, 表明边界层发展过程中第2模态率先发展达到饱和, 而后逐渐衰减, 而低频模态则逐渐发展; 通过TSP技术得到了不同单位Reynolds数下的圆锥表面温升分布, 结果表明, 随单位Reynolds数增大, 边界层转捩阵面前移.      

高超声速椭圆锥边界层横流转捩特性大涡模拟

横流效应显著影响高超声速飞行器的三维边界层转捩过程, 深化对该流动机制的认识有助于提升和改善飞行器气动性能及热力学环境. 针对HIFiRE5椭圆锥绕流问题, 采用大涡模拟方法计算分析了超声速边界层横流转捩特性, 并揭示其中的流动机理. 参考HIFiRE5风洞模型试验条件, 数值模拟中椭圆锥来流入口处施加人工速度扰动以激发边界层内不稳定扰动波, 进而预测了高超声速边界层流动横流失稳、转捩过程等基本流动特征, 并基于转捩热流分布形态对比, 获得了与试验数据基本吻合的计算结果. 研究发现, 椭圆锥中心线流动汇聚形成的流向涡结构非常容易失稳, 另外在中心线及侧缘之间的中部区域存在较强的横流不稳定性, 两种机制共同作用影响边界层转捩过程. 此外, 分析了来流扰动幅值对边界层横流失稳转捩的影响, 并发现静来流条件下, 横流区域出现两组独立的定常横流涡结构, 而强噪声来流条件下, 中心线主涡和中部横流涡均发生失稳转捩, 且在椭圆锥表面形成多峰状的转捩阵面. 最后, 深入分析流场的压力脉动动力学特性, 揭示了三维边界层发生失稳转捩的非线性演化机制.      

Generation of nonstationary Görtler vortices by localized surface nonuniformities. Receptivity coefficients

The mechanism of production of nonstationary Görtler vortices in a boundary layer on concave wall by surface nonuniformities (vibrations and roughness) has been experimentally examined. The nonuniformities were produced by a specially developed disturbance source. They were controlled, localized along the streamwise coordinate, and periodic over the span of the experimental model. Tests in a low-turbulence wind tunnel have proved that the disturbance source is an efficient means of experimental study of the receptivity and stability problem for boundary layers dominated by Görtler instability. The operation of the disturbance source leads to the production of small-amplitude nonstationary Görtler vortices (tenth or hundredth fractions of a per cent of the free-stream velocity) with predefined characteristics (frequency and spanwise wavelength). In our experiments, we quantitatively examined the problem of linear receptivity of boundary layer to surface nonuniformities in a broad range of frequencies for the most dangerous spanwise scales of Görtler vortices. The values of the amplitudes and phases of the receptivity coefficients were determined. The amplitudes proved to be much smaller in magnitude in comparison with the excitation of modes of hydrodynamic instabilities of other types (Tollmien-Schlichting waves and cross-flow-instability modes). It was found that, with increasing the frequency, the amplitudes of the receptivity coefficients showed a distinct growth while for high frequencies those amplitudes also exhibited a growth with the spanwise scale of perturbations, although for stationary surface roughness no effect due to this scale was observed. It was found that the dependences on frequency of the efficiency of the mechanisms of stability and receptivity showed opposing behaviors, were in competition, and could partially compensate each other, promoting, thus, the production of boundary-layer Görtler vortices in a broad range of frequencies.     

前缘形状对钝三角翼边界层稳定性及转捩的影响

选择典型高速流动条件,基于线性稳定性理论研究了不同前缘几何特征对典型大后掠角平板钝三角翼外形高速边界层流动稳定性及转捩的影响.研究表明,椭前缘(截面为椭圆)形状的变化仅影响前缘附近的流场特征和边界层流动稳定性;前缘截面长短轴比(形状因子)变大,前缘形状变尖,则横流速度变大,扰动波增长率变大;对于横流模态和第1模态,不同...     

基于Ludwieg管的高超声速边界层转捩实验

高超声速边界层层/湍流转捩是高超声速飞行器气动力和气动热设计中的难点和热点问题.为了降低开展高超声速边界层不稳定性与转捩实验研究的门槛,研究基于Ludwieg管原理设计并建造了一座Mach 6高超声速管风洞,重点对Ludwieg管风洞的启动和运行过程开展了数值模拟,分析了储气段弯管布局对试验段流场的影响;之后,对该高超...     

Investigation of weakly-nonlinear development of unsteady Görtler vortices

We have examined, both experimentally (using fully controlled disturbances) and theoretically, the weakly-nonlinear development stages of unsteady (in general) Görtler instability of a boundary layer over a concave surface. Primary attention was given to early manifestations of nonlinearity in the development of unsteady Görtler vortices belonging to the first, most rapidly growing, mode in the discrete spectrum of the stability problem. We have investigated the manifestations of instability versus the frequency of the fundamental (primary) Görtler mode and the initial disturbance amplitude. The weakly-nonlinear stage of development of unsteady Görtler vortices was found to display the following characteristic features: (a) nonlinear interaction among the combination modes in the frequency-wavenumber spectrum, (b) distortion of the wall-normal profiles of disturbance amplitudes and phases, (c) reduction of the growth rate of the fundamental Görtler mode and the majority of combination modes, and (d) a decrease in the phase velocities of unsteady disturbances. It was found that the disturbances enter the region of weakly-nonlinear development after the amplitude of the fundamental frequency-wavenumber mode reaches a threshold of 4–6 %, this value being much greater than that for Tollmien — Schlichting waves (1–2 %) but significantly lower than that for the cross-flow instability modes in three-dimensional boundary layer (more than 10 %).     

The gravitational faraday rotation for cylindrical gravitational solitons

By using cylindrical soliton solutions, the nonlinear behavior of gravitational waves in vacuum is studied in terms of a rotation of the polarization vector between two independent modes. This effect was emphasized by Piran, Safier, and Stark as a gravitational analogue of the Faraday rotation. The polarization of the soliton wave is calculated, and it is found that the+mode which was dominant near the axis of symmetry is fully converted to the×mode at some interaction region and then the disturbance propagating along a light cone like a gravitational wave pulse contains both polarizations.     

Influence of an unfavourable pressure gradient on the breakdown of boundary layer streaks

Breakdown of boundary layer streaks is studied experimentally and compared at zero and adverse (positive) streamwise pressure gradients on a wing under fully controlled experimental conditions. The varicose mode of streak breakdown is found to be a dominant mode in the case of the adverse pressure gradient. A strong influence of pressure gradient upon the development of the streak and the secondary instability is revealed. The unfavourable pressure gradient is shown to alter the critical streak amplitude, the dispersion properties of the streak and the secondary disturbance, as well as attained maximum amplitudes for both the streak and the secondary disturbance.     

多孔表面推迟高超声速边界层转捩的机理

利用线性稳定性理论分析（LST）结合直接数值模拟（DNS）研究高超声速多孔表面边界层流动的失稳特征,分析多孔表面推迟高超声速边界层转捩的机理.在Ma=6,Re=2.0×10⁴（参考长度为入口处边界层位移厚度）条件下获得平板边界层及不同孔隙排列情形下平板边界层的典型流动特征,并采用LST方法分析光滑平板及多孔平板扰动的增长率及累计放大率.研究表明三维顺排及错排多孔表面都可以抑制第二模扰动的发展,推迟高超声速边界层转捩,但顺排多孔表面推迟高超声速边界层转捩能力更强.     

气动光学效应湍流脉动模型系数修正

以光学窗口的气动光学效应研究为背景,研究影响光学传输预测的流场湍流脉动量预测.选取平板、压缩拐角、凹腔流动模型,采用大涡模拟（LES）方法研究超声速湍流脉动工程预测模型的系数修正.结果表明：LES方法能够获得无激波干扰、强激波干扰及底部大分离条件下,湍流密度脉动的定量分布,并据此给出脉动工程模型的系数修正,结果已经应用于型号飞行器的光学窗口气动光学效应预测.     

连续波激光器腔内倍频晶体半解析分析方法的研究

连续波激光器系统腔内倍频非线性光学晶体吸收基频光辐射产生谐波的同时,也会在晶体内部产生非均匀温升,引起折射率变化,破坏位相匹配条件,影响激光器谐波转换效率.解决问题的关键是准确得出晶体内部温度场.由于激光器中激光模式和边界条件的复杂性,无法得到温度场的解析解.利用半解析热分析方法得出了晶体工作在TEM00模式下产生的温度场计算公式,分析了对温度场分布的各种影响.所得结果对连续波腔内倍频激光系统设计将起到指导作用.     

相邻双侧边盖驱动方腔流动的三维线性整体稳定性

文章考察了相邻双侧边盖驱动方腔流动（即上壁面向右运动和左侧壁面向下运动）的三维线性整体稳定性.首先,采用Taylor-Hood有限元方法并经由Newton迭代过程计算得到双侧边盖驱动方腔流动的二维稳态基本流.其次,Taylor-Hood有限元在Chebyshev Gauss配置点上进行离散,同时Gauss配置点也可以用于线性稳定性方程的高阶有限差分格式离散.然后,离散得到的矩阵形式的广义特征值问题可以结合shift-and-invert算法采用隐式重启Arnoldi方法计算.最后,通过对线性稳定性方程特征值的计算,发现了一个最不稳定的驻定模态和两对对称行波模态.最不稳定的三维驻定模态的临界Reynolds数为Re_c=261.5,远远小于二维不稳定的临界Reynolds数Re_c2d=1 061.7.通过画出这3类三维不稳定模态的流向扰动速度和扰动涡量的空间等值面图像,可以发现不稳定扰动位于稳态基本流的两个主涡区域,因此可以认为主涡区域是三维扰动失稳的主要能量来源地.