Numerical Simulation of Riblet Controlled Spatial Transition in a Zero-Pressure-Gradient Boundary Layer

To analyze the fundamental physical mechanism which determines the damping effect of a riblet surface on three-dimensional transition several numerical simulations of spatial transition in a flat plate zero-pressure-gradient boundary layer above a riblet wall are performed in this study. Two types of forced transition scenarios are investigated. The first type of transition is defined by K-type transition induced by a dominant two-dimensional Tollmien–Schlichting (TS) wave and a weak spanwise disturbance. The second type of transition is purely excited by two oblique waves. By a qualitative analysis of the occurring maximum wall-normal and spanwise velocity components and the Fourier modes of the disturbances the two-dimensional TS waves are found to be amplified by riblets, whereas three-dimensional structures, i.e., Λ-, hairpin, and streamwisely aligned vortices, are damped. At oblique transition the breakdown to turbulence is delayed by the riblets compared to transition on a clean surface. The investigation of the near wall flow structure reveals secondary flows induced by the riblets and reduced wall normal ejections as well as a reduced downwash.     

Nonlinear evolution of Klebanoff type second mode disturbances in supersonic flat-plate boundary layer简

Studying the evolution of 3D disturbances is of crucial theoretical importance for understanding the transition process. The present study concerns the nonlinear evolution of second mode unstable disturbances in a supersonic boundary layer by the numerical simulation, and discusses the selectivity of 3D disturbances and possibility to transition. The results indicate that a Klebanoff type nonlinear interaction between 2D and 3D disturbances with the same frequency may amplify a band of 3D disturbances centered at a finite spanwise wavenumber. That is, certain 3D disturbances can be selectively and rapidly amplified by the unstable 2D disturbances, and certain small-scale 3D structures will appear.     

Vortex-induced vibration and mode transition of a curved flexible free-hanging cylinder in exponential shear flows

This paper presents an experimental study of vortex-induced-vibration (VIV) of a curved flexible free-hanging cylinder in exponential shear flows. The emphasis is on previously unexplained phenomena in our early research and in some cases offers insights on the mode transition of nonlinear vibration behavior of long flexible cylinders. The experimental results illustrate that the cylinder undergoes multi-frequency response and the dominant frequency varies spatially. The IL and CF response and transition are out-of-sync. In the second (2nd) mode response, the spanwise response exhibits a mixed pattern with standing wave and traveling wave. The contribution of traveling wave becomes greater as the reduced velocity increases. Only two distinct branches of response, namely the initial and lower branches, are observed in each mode. The lower branches of the first (1st) and 2nd modes present the same normalized frequency. A phase jump around 180°occurs at the transition between initial branches and lower branches, accompanying with a switch between 2S $\leftrightarrow$ 2P or P+S vortex shedding modes.     

An experimental study of oblique transition in a Blasius boundary layer flow

Transition initiated by a pair of oblique waves was investigated experimentally in a Blasius boundary layer flow by using hot-wire measurements and flow visualisation. The oblique waves were generated by periodic blowing and suction through an array of pipes connecting to the flow through a transverse slit in the flat plate model. The structure of the flow field is described and the amplitude of individual frequency-spanwise wave number modes was determined from Fourier transforms of the disturbance velocity. In contrast to results from investigations of oblique transition at subcritical flow conditions, the transition process at the present conditions suggests the combined effect of non-modal growth of streaks and a second stage with exponential growth of oblique waves to initiate the final breakdown stage.     

Dynamic hydroelastic response of a surface-piercing strut in waves and ventilated flows

The objective of this work is to study the effects of waves and ventilation on the dynamic hydroelastic response of a surface-piercing strut via towing tank studies. The experimental studies are especially designed to test the hypothesis that flow conditions affect the modal response and hence structural dynamics, which in turn affect the hydrodynamic response through fluid–structure interaction, particularly near regions of mode localization such as frequency coalescence. The results showed that the modal frequencies decrease with increasing submergence, and are higher in fully ventilated flow compared to fully wetted flow. Regular, non-breaking waves lead to simple harmonic oscillations about the mean values at the encountered wave frequency for the slowly varying component of the hydrodynamic loads and tip deformations. The spectral response of the fast fluctuating component of the hydrodynamic loads and tip deformations showed peaks at the modal frequencies and vortex shedding frequencies (off the blunt trailing edge of the strut). Significant dynamic load amplifications and flow-induced vibrations were observed when the second and third modal frequencies coalesced at a submerged aspect ratio of two in fully wetted flow. In fully ventilated flow, the second and third modes separated enough to result in drastically reduced dynamic load fluctuations and flow-induced vibrations. When the submergence decreased, the separation between the modal frequencies increased, which avoided frequency coalescence in both fully wetted and fully ventilated flows. The results suggest that for cases where the wave encountered frequency is well separated from the modal frequencies, the spectral response of the fast fluctuating component of the hydrodynamic loads and tip deformations are governed by the structural response, and not by wave conditions.     

Viscous and Inviscid Instabilities of Flow Along a Streamwise Corner

Here we consider the stability of flow along a streamwise corner formed by the intersection of two large flat plates held perpendicular to each other. Self-similar solutions for the steady laminar mean flow in the corner region have been obtained by solving the boundary layer equations for zero and nonzero streamwise pressure gradients. The stability of the mean flow is investigated using linear stability analysis. An eigensolver has been developed to solve the resulting linear eigenvalue problem either in a global mode to obtain an approximation to all the dominant eigenmodes or in a local mode to refine a particular eigenmode. The stability results indicate that the entire spectrum of two-dimensional and oblique viscous modes of a two-dimensional Blasius boundary layer is active in the case of a corner layer as well, but away from the cornerline. In a corner region of finite spanwise extent, the continuous spectrum of oblique modes degenerates to a discrete spectrum of modes of increasing spanwise wave number. The effect of the corner on the two-dimensional viscous instability is small and decreases the growth rate. The growth rate of outgoing oblique disturbances is observed to decrease, while the growth rate of incoming oblique disturbances is enhanced by the corner. This asymmetry between the outgoing and incoming viscous modes increases with increasing obliqueness of the disturbance. The instability of a zero pressure gradient corner layer is dominated by the viscous modes; however, an inviscid corner mode is also observed. The critical Reynolds number of the inviscid mode rapidly decreases with even a small adverse streamwise pressure gradient and the inviscid mode becomes the dominant one. Received 17 March 1998 and accepted 28 April 1999     

连续分层流体中垂直薄板的水动力特性

研究了在线性连续分层流体中水波与半潜式刚性垂直薄板相互作用的问题. 在 Boussinesq近似下，基于分离变量法，导出了具有自由面的平面前进波的色散关系，建立 了半潜式刚性垂直薄板的反射与透射能量、水平波浪力的计算方法. 对给定的频率，当它大 于浮力频率时，流场中只有一种模态的平面前进波，当它小于浮力频率时，流场 中有无数多个模态的平面前进波，并证明了对每一种模态的入射波，其它每个模态水波的反射与透射能量是 相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量，以及作用在薄板上的水平波浪力 进行了数值计算分析，表明了流体的线性连续分层效应对这些水动力的影响是不可忽视 的. 特别地，在入射波频率小于浮力频率时，与第1模态入射波的能量转化量及其对薄板产 生的水平波浪力相比，其它模态入射波的能量转化量及其对薄板产生的水平波浪力都要大得 多.     

PIV- and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus

Already in the 1950s, an elegant laboratory experiment had been designed to understand how the atmospheric circulation transports heat from equatorial to polar latitudes. It consists of a cooled inner and heated outer cylinder mounted on a rotating platform, mimicking the heated tropical and cooled polar regions of the earth’s atmosphere. Depending on the strength of the heating and the rate of rotation, different flow regimes had been identified: wave-regimes that can be classified by pro-grade propagating waves of different wavenumbers and quasi-chaotic regimes where waves and small-scale vortices coexist. In the present paper, we will use multivariate statistical techniques to understand better the variability of the heated rotating flow (i) in the transition region between regular waves with zonal wave number 3 and 4 and (ii) in the transition region to the quasi-chaotic regime. The former regime is studied by applying the complex empirical orthogonal function (CEOF) method to particle image velocimetry data, the latter by applying the multichannel singular spectrum analysis (M-SSA) to laser Doppler velocimetry (LDV) data. In the annulus, interactions between the dominant mode and the so-called weaker modes, explaining less variance than the dominant mode, can lead to low-frequency amplitude and wave structure vacillations. The CEOF analysis reveals the coexistence of a dominant and a weak mode in the 3-4 wave transition region. This finding confirms earlier ideas on wave dispersion in transition regions between regular waves. Increasing the annulus’ rotation leads to a growth of the weak mode until this mode becomes the dominant one. No coexistence of modes could be found for the regular 4-wave regime but a slight structural vacillation was present. The M-SSA was applied to LDV data corresponding with much faster annulus rotation for which the flow becomes more irregular. The analysis reveals a coexistence of a dominant 4 mode and a much weaker 5 mode for this regime. Our results complement previous observations recovered primarily by thermocouple arrangements.     

Nonlinear vibrations of a circular cylindrical shell with multiple internal resonances under multi-harmonic excitation

The nonlinear response of a water-filled, thin circular cylindrical shell, simply supported at the edges, to multi-harmonic excitation is studied. The shell has opportune dimensions so that the natural frequencies of the two modes (driven and companion) with three circumferential waves are practically double than the natural frequencies of the two modes (driven and companion) with two circumferential waves. This introduces a one-to-one-to-two-to-two internal resonance in the presence of harmonic excitation in the spectral neighbourhood of the natural frequency of the mode with two circumferential waves. Since the system is excited by a multi-harmonic point-load excitation composed by first and second harmonics, very complex nonlinear dynamics is obtained around the resonance of the fundamental mode. In fact, at this frequency, both modes with two and three circumferential waves are driven to resonance and each one is in a one-to-one internal resonance with its companion mode. The nonlinear dynamics is explored by using bifurcation diagrams of Poincaré maps and time responses.     

On the application of en-methods to three-dimensional boundary-layer flows

Extension of the eⁿ-method from two-dimensional to three-dimensional boundary-layer flows has not been straightforward. Confusion has centred on whether to use temporal or spatial stability theories, conversion between the two approaches, and the choice of integration path. The aim of this study is to clarify the confusion about the direction and magnitude of maximum growth in convectively unstable three-dimensional non-parallel boundary layers. To this end, the time-asymptotic response of the boundary layer to an impulsive point excitation is considered. Since all frequencies and all wavenumbers are excited by an impulsive point source, the most amplified component of the response is equivalent to the result of maximizing the growth over arbitrary choices of harmonic point excitation; the standard eⁿ-approach. The impulse response is calculated using a spatial steepest-descent method, which is distinct from the earlier Cebeci–Stewartson method. It is necessary to allow both time and spanwise distance to become complex during integration, but with the constraint that both are real at the end point. This method has been applied to the two-dimensional Blasius boundary layer, for which validation of the method is more straightforward, and also to a three-dimensional Falkner–Skan–Cooke (with non-zero pressure gradient and sweep) boundary layer. Dimensional frequencies and spanwise wavenumbers of propagating components are kept constant (although not necessarily real), as is physically relevant to steady flows with spatial inhomogeneity in the chordwise direction only. With this method a spatial approach is taken without having to make a priori choices about the value of disturbance frequency or wavenumber. Further, purely by choosing a downstream observation point, it is possible to find the maximum-amplitude component directly without having to calculate the entire impulse response (or wave packet). If the flow is susceptible to more than one convective instability mode, provided the modes are separated in the frequency–wavenumber space, separate n-factors can be calculated for each mode. Wave-packet propagation in the Ekman layer (a strictly parallel three-dimensional boundary layer) is also discussed to draw comparisons between the conditions for maximum growth in parallel and non-parallel boundary layers.     

Computational studies of inertia-gravity waves radiated from upper tropospheric jets

The generation and physical characteristics of inertia-gravity waves radiated from an unstable forced jet at the tropopause are investigated through high-resolution numerical simulations of the three-dimensional Navier–Stokes anelastic equations. Such waves are induced by Kelvin–Helmholtz instabilities on the flanks of the inhomogeneously stratified jet. From the evolution of the averaged momentum flux above the jet, it is found that gravity waves are continuously radiated after the shear-stratified flow reaches a quasi-equilibrium state. The time–vertical coordinate cross-sections of potential temperature show phase patterns indicating upward energy propagation. The sign of the momentum flux above and below the jet further confirms this, indicating that the group velocity of the generated waves is pointing away from the jet core region. Space–time spectral analysis at the upper flank level of the jet shows a broad spectral band, with different phase speeds. The spectra obtained in the stratosphere above the jet show a shift toward lower frequencies and larger spatial scales compared to the spectra found in the jet region. The three-dimensional character of the generated waves is confirmed by analysis of the co-spectra of the spanwise and vertical velocities. Imposing the background rotation modifies the polarization relation between the horizontal wind components. This out-of-phase relation is evidenced by the hodograph of the horizontal wind vector, further confirming the upward energy propagation. The background rotation also causes the co-spectra of the waves high above the jet core to be asymmetric in the spanwise modes, with contributions from modes with negative wavenumbers dominating the co-spectra. Dedicated to the memory of our colleague Dr. Binson Joseph     

Prehistory of Instability in a Hypersonic Boundary Layer

The initial phase of hypersonic boundary-layer transition comprising excitation of boundary-layer modes and their downstream evolution from receptivity regions to the unstable region (instability prehistory problem) is considered. The disturbance spectrum reveals the following features: (1) the first and second modes are synchronized with acoustic waves near the leading edge; (2) further downstream, the first mode is synchronized with entropy and vorticity waves; (3) near the lower neutral branch of the Mack second mode, the first mode is synchronized with the second mode. Disturbance behavior in Regions (2) and (3) is studied using the multiple-mode method accounting for interaction between modes due to mean-flow nonparallel effects. Analysis of the disturbance behavior in Region 3) provides the intermodal exchange rule coupling input and output amplitudes of the first and second modes. It is shown that Region (3) includes branch points at which disturbance group velocity and amplitude are singular. These singularities can cause difficulties in stability analyses. In Region (2), vorticity/entropy waves are partially swallowed by the boundary layer. They may effectively generate the Mack second mode near its lower neutral branch. Received 17 July 2000 and accepted 23 March 2001     

Hypersonic boundary-layer transition on a flared cone

Transition on a flared cone with zero angle of attack was studied in our newly established Mach 6 quiet wind tunnel (M6QT) via wall pressure measurement and flow visualization. High-frequency pressure transducers were used to measure the second-mode waves’ amplitudes and frequencies. Using pulsed schlieren diagnostic and Rayleigh scattering technique, we got a clear evolution of the second-mode disturbances. The second-mode waves exist for a long distance, which means that the second-mode waves grow linearly in a large region. Strong Mach waves are radiated from the edge of the boundary layer. With further development, the second-mode waves reach their maximum magnitude and harmonics of the second-mode instability appear. Then the disturbances grow nonlinearly. The second modes become weak and merge with each other. Finally, the nonlinear interaction of disturbance leads to a relatively quiet zone, which further breaks down, resulting in the transition of the boundary layer. Our results show that transition is determined by the second mode. The quiet zone before the final breakdown is observed in flow visualization for the first time. Eventual transition requires the presence of a quiet zone generated by nonlinear interactions.     

Boundary element modeling for defect characterization potential in a wave guide

Wave scattering analysis implemented by boundary element methods (BEM) and the normal mode expansion technique is used to study the sizing potential of two-dimensional shaped defects in a wave guide. Surface breaking half-elliptical shaped defects of three opening lengths (0.3, 6.35 and 12.7 mm) and through-wall depths of 10–90% on a 10 mm thick steel plate were considered. The reflection and transmission coefficients of both Lamb and shear horizontal (SH) waves over a frequency range 0.05–2 MHz were studied. A powerfully practical result was obtained whereby the numerical results for the S₀ mode Lamb wave and n₀ mode SH wave at low frequencies showed a monotonic increase in signal amplitude with an increase in the defect through-wall depth. At high frequency (usually above the cut-off frequency of the A₁ mode for Lamb waves and the n₁ mode for SH waves, respectively), the monotonic trend does not hold in general due to the energy redistribution to the higher order wave modes. Guided waves impinging onto an internal stringer-like an inclusion were also studied. Both the Lamb and SH waves were shown to be insensitive to the stringer internal inclusions at low frequency. Experiments with piezoelectric Lamb wave transducers and non-contact SH wave electro-magnetic acoustic transducers (EMAT) verified some of the theoretical results.     

Streamwise streaks and secondary instability in a two-dimensional bent channel

Streamwise streaks generated from a pair of oblique waves and secondary instability of the streaks are studied in a two-dimensional bent channel. Nonlinear parabolized stability equations (NPSE) are employed to investigate streamwise streaks and vortices. A pair of oblique waves from linear stability analysis is imposed as initial disturbances. Generation of streamwise streaks and vortices and subsequent development are described in detail. The case of plane channel is also studied to provide comparable data. Through comparison, the effect of bent region is clearly highlighted. Results of parametric studies to examine the effect of Reynolds number, radius of curvature, and bent angle are also given and discussed in detail. Secondary instability analysis for the modified mean flow due to the streamwise streaks is carried out by solving a two-dimensional eigenvalue problem. Several unstable modes which can be classified into fundamental and subharmonic mode of secondary instability are identified. Among several unstable modes, two modes are turned out to be dominant modes. Details on these two modes including generation mechanism, typical pattern, and dependency on wave number and streak amplitude are discussed. It is found that the presence of bent channel can lead to early oblique-mode breakdown via strong growth of the streamwise streaks due to the curved section. Such large amplitude of streaks and its secondary instability eventually could trigger transition even for small amplitude oblique waves at subcritical channel Reynolds numbers.     

一维与二维爆轰传播的时空关联特性数值研究

一维爆轰传播的理论完备、计算准确, 二维斜爆轰传播由于壁面与黏性效应, 大尺度、高精度预测还有一定难度. 利用Euler方程和H₂-Air基元反应模型, 对二维有限长楔面诱导的斜爆轰和活塞驱动一维非定常正爆轰进行计算比较研究, 从时空两个维度方面, 分析了两者在起爆过程、稀疏波传播、爆轰波面演化中的关联特性. 研究结果表明: 在过驱动度相同的条件下, 经过时空变换的活塞驱动一维爆轰传播与二维驻定斜爆轰在起爆区波系结构、波面演化特征和主要参数分布规律方面无论定性或者定量对比均符合较好, 所以, 一维非定常爆轰和二维驻定斜爆轰具有时空相关性. 两者的差异主要体现在过驱动斜爆轰受稀疏波影响过渡到近Chapman-Jouguet (C-J)爆轰状态所需的弛豫时间不同, 原因可能是起源于活塞和壁面稀疏波强度的差异. 本文提出的一维与二维爆轰传播的时空关联方法不仅有助于认知斜爆轰起爆、过驱爆轰产生、胞格爆轰演化的三阶段规律, 还可以对比揭示壁面、边界层和黏性效应的影响, 应用在斜爆轰发动机燃烧室设计中能够有效节约计算时间和成本, 并降低复杂度.      

Numerical modeling of guided wave interaction with non-axisymmetric cracks in elastic cylinders

A three dimensional (3D) hybrid method combining the classical finite element (FE) method with the semi-analytical finite element (SAFE) technique is developed. This hybrid method is employed to study the interaction of guided waves with non-axisymmetric damages in cylinders. The near field surrounding the damage is analysed with the 3D FE method. The solution is expanded into sums of guided modes on both inlet and outlet cross-sections. Such eigenmode expansions enable separation into ingoing and outgoing waves, i.e., incident, reflected and transmitted waves. Using the SAFE method, elastic guided modes are then computed at the aforementioned cross-sections thus reducing the analysis to two dimensions (2D). The amplitudes of the incident modes are imposed, whereas those of the scattered modes are determined by solving the global system of the 3D hybrid FE-SAFE model. In this paper, a formula is proposed for the calculation of eigenforces and modal power flows from eigendisplacements and SAFE matrices. This has the advantage of simplifying the post-process of load eigenvectors in hybrid FE-SAFE methods. Results obtained for a vertical free-end cylinder are in good agreement with those published in the literature. Moreover, first results of the interaction of the fundamental compressional, flexural and torsional Pochhammer–Chree modes with non-axisymmetric vertical cracks are obtained and discussed. Then, the interactions of the fundamental compressional mode with oblique free-ends and cracks are briefly addressed. The power balance is shown to be satisfied with a good accuracy.     

双自由面溶质?热毛细液层的不稳定性

溶质?热毛细对流是流体界面的浓度和温度分布不均导致的表面张力梯度驱动的流动, 它主要存在于空间微重力环境、小尺度流动等表面张力占主导的情况中, 例如晶体生长、微流控、合金浇筑凝固、有机薄液膜生长等. 对其流动进行稳定性分析具有重要意义. 本文采用线性稳定性理论研究了双自由面溶质?热毛细液层对流的不稳定性, 得到了两种负毛细力比(η)下的临界Marangoni数与Prandtl数(Pr)的函数关系, 并分析了临界模态的流场和能量机制. 研究发现: 溶质?热毛细对流和纯热毛细对流的临界模态有较大的差别, 前者是同向流向波、逆向流向波、展向稳态模态和逆向斜波, 后者是逆向斜波和逆向流向波. 在Pr较大时, Pr增加会降低流动稳定性; 在其他参数下, Pr增加会增强流动稳定性. 在中低Pr, 溶质毛细力使流动更加不稳定; 在大Pr时, 溶质毛细力的出现可能使流动更加稳定; 在其他参数下, 溶质毛细力会减弱流动稳定性. 流动稳定性不随η单调变化. 在多数情况下, 扰动浓度场与扰动温度场都是相似的. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但其中溶质毛细力和热毛细力做功的正负性与参数有关.      

The effect of G?rtler instability on hypersonic boundary layer transition

The evolution of G?rtler vortices and its interaction with other instabilities are investigated in this paper.Both the Mack mode and the G?rtler mode exist in hypersonic boundary-layer flows over concave surfaces, and their interactions are crucially important in boundary layer transition. We carry out a direct numerical simulation to explore the interaction between the G?rtler and the oblique Mack mode.The results indicate that the interaction between the forced G?rtler mode and the oblique Mack mode promotes the onset of the transition. The forced oblique Mack mode is susceptible to nonlinear interaction.Because of the development of the G?rtler mode, the forced Mack mode and other harmonic modes are excited.     

两层流体中水波在垂直薄板上的反射与透射

研究在两层流体中表面波模态和内波模态的波浪与半潜式刚性垂直薄板 相互作用的问题. 基于特征函数展开理论,建立了两种模态入射波作用下,半潜式刚性垂直 薄板的反射与透射能量的计算方法,证明了对每一种模态的入射波,另一种模态波浪的反射 与透射能量是相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量,以及作用在其上的 水平波浪力进行了数值计算分析,表明在某个频率范围内,流体的分层效应对这些水动力 量的影响是不可忽视的. 特别地,当薄板的一端位于两层流体的内界面上时,两种模态波浪 的能量转化是最大的.