Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets

Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.

Super-resolution with a nonlinear thin film: Beam reshaping via internal multi-interference

In laser applications, the size of the focus spot can be reduced beyond the diffraction limit with a thin film of strong nonlinear optical Kerr effect. We present a concise theoretical simulation of the device. The origin of the super-resolution is found to be mainly from the reshaping effect due to the strongly nonlinear refraction mediated multi-interference inside the thin film. In addition, both diffraction and self-focusing effects have been explored and found negligible for highly refractive and ultrathin films in comparison with the reshaping effect. Finally, the theoretic model has been verified in experiments with single Ge2Sb2Te5 film and SiN/Si/SiN/Ge2Sb2Te2 multilayer structures. (c) 2006 American Institute of Physics.

A comparison of methods for the coupled analysis of floating structures

The dynamic analysis of a deepwater floating platform and the associated mooring/riser system should ideally be fully coupled to ensure a reliable response prediction. It is generally held that a time domain analysis is the only means of capturing the various coupling and nonlinear effects accurately. However, in recent work it has been found that for an ultra-deepwater floating system (2000m water depth), the highly efficient frequency domain approach can provide highly accurate response predictions. One reason for this is the accuracy of the drag linearization procedure over both first and second order motions, another reason is the minimal geometric nonlinearity displayed by the mooring lines in deepwater. In this paper, the aim is to develop an efficient analysis method for intermediate water depths, where both mooring/vessel coupling and geometric nonlinearity are of importance. It is found that the standard frequency domain approach is not so accurate for this case and two alternative methods are investigated. In the first, an enhanced frequency domain approach is adopted, in which line nonlinearities are linearized in a systematic way. In the second, a hybrid approach is adopted in which the low frequency motion is solved in the time domain while the high frequency motion is solved in the frequency domain; the two analyses are coupled by the fact that (i) the low frequency motion affects the mooring line geometry for the high frequency motion, and (ii) the high frequency motion affects the drag forces which damp the low frequency motion. The accuracy and efficiency of each of the methods are systematically compared. Copyright © 2007 by ASME.

The nonlinear heat release response of stratified lean-premixed flames to acoustic velocity oscillations

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to high-amplitude acoustic forcing in a laboratory-scale stratified burner operated with CH4 and air at atmospheric pressure. The double-swirler, double-channel annular burner was specially designed to generate high-amplitude acoustic velocity oscillations and a radial equivalence ratio gradient at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the response are not considered in the present investigation. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a constant temperature anemometer and photomultiplier tubes with narrow-band OH*/CH* interference filters. Time-averaged and phase-synchronized CH* chemiluminescence intensities were measured using an intensified CCD camera. The measurements show that flame stabilization mechanisms vary depending on equivalence ratio gradients for a constant global equivalence ratio (φg=0.60). Under uniformly premixed conditions, an enveloped M-shaped flame is observed. In contrast, under stratified conditions, a dihedral V-flame and a toroidal detached flame develop in the outer stream and inner stream fuel enrichment cases, respectively. The modification of the stabilization mechanism has a significant impact on the nonlinear response of stratified flames to high-amplitude acoustic forcing (u'/U∼0.45 and f=60, 160Hz). Outer stream enrichment tends to improve the flame's stiffness with respect to incident acoustic/vortical disturbances, whereas inner stream stratification tends to enhance the nonlinear flame dynamics, as manifested by the complex interaction between the swirl flame and large-scale coherent vortices with different length scales and shedding points. It was found that the behavior of the measured flame describing functions (FDF), which depend on radial fuel stratification, are well correlated with previous measurements of the intensity of self-excited combustion instabilities in the stratified swirl burner. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, its effect on flame location and the interaction with unsteady flow structures. © 2011 The Combustion Institute.

Two-orbit switch-pitch structures

The Hoberman 'switch-pitch ' ball is a transformable structure with a single folding and unfolding path. The underlying cubic structure has a novel mechanism that retains tetrahedral symmetry during folding. Here, we propose a generalized class of structures of a similar type that retain their full symmetry during folding. The key idea is that we require two orbits of nodes for the structure: within each orbit, any node can be copied to any other node by a symmetry operation. Each member is connected to two nodes, which may be in different orbits, by revolute joints. We will describe the symmetry analysis that reveals the symmetry of the internal mechanism modes for a switch-pitch structure. To follow the complete folding path of the structure, a nonlinear iterative predictor-corrector algorithm based on the Newton method is adopted. First, a simple tetrahedral example of the class of two-orbit structures is presented. Typical configurations along the folding path are shown. Larger members of the class of structures are also presented, all with cubic symmetry. These switch-pitch structures could have useful applications as deployable structures.

The interaction of elasticity and rocking in flexible structures allowed to uplift

Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified 'equivalent' oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. © 2012 John Wiley & Sons, Ltd.

A flexural crack model for damage detection in reinforced concrete structures

The use of changes in vibration data for damage detection of reinforced concrete structures faces many challenges that obstruct its transition from a research topic to field applications. Among these is the lack of appropriate damage models that can be deployed in the damage detection methods. In this paper, a model of a simply supported reinforced concrete beam with multiple cracks is developed to examine its use for damage detection and structural health monitoring. The cracks are simulated by a model that accounts for crack formation, propagation and closure. The beam model is studied under different dynamic excitations, including sine sweep and single excitation frequency, for various damage levels. The changes in resonant frequency with increasing loads are examined along with the nonlinear vibration characteristics. The model demonstrates that the resonant frequency reduces by about 10% at the application of 30% of the ultimate load and then drops gradually by about 25% at 70% of the ultimate load. The model also illustrates some nonlinearity in the dynamic response of damaged beams. The appearance of super-harmonics shows that the nonlinearity is higher when the damage level is about 35% and then decreases with increasing damage. The restoring force-displacement relationship predicted the reduction in the overall stiffness of the damaged beam. The model quantitatively predicts the experimental vibration behaviour of damaged RC beams and also shows the damage dependency of nonlinear vibration behaviour. © 2011 Published under licence by IOP Publishing Ltd.

Constructive Nonlinear Control

In this book several streams of nonlinear control theory are merged and di- rected towards a constructive solution of the feedback stabilization problem. Analytic, geometric and asymptotic concepts are assembled as design tools for a wide variety of nonlinear phenomena and structures. Di®erential-geometric concepts reveal important structural properties of nonlinear systems, but al- low no margin for modeling errors. To overcome this de¯ciency, we combine them with analytic concepts of passivity, optimality and Lyapunov stability. In this way geometry serves as a guide for construction of design procedures, while analysis provides robustness tools which geometry lacks.

The effect of an electric field on the nonlinear response of InAs/GaAs quantum dots

The refractive nonlinearities of InAs/GaAs quantum dots under a dc electric field at photon energies above its band gap energy have been studied using the reflection Z-scan technique. The effect of the dc electric field on the nonlinear response of InAs/GaAs quantum dots showed similar linear and quadratic electro-optic effects as in the linear response regime at low fields. This implies that the electro-optic effect in the nonlinear regime is analogous to the response in the linear regime for semiconductor quantum dots. Our experimental results show the potential for voltage tunability in InAs quantum dot-based nonlinear electro-optic devices.

Quantum-confinement-effect-driven type-I-type-II transition in inhomogeneous quantum dot structures

We investigate the electronic structures of the inhomogeneous quantum dots within the framework of the effective mass theory. The results show that the energies of electron and hole states depend sensitively on the relative magnitude 77 of the core radius to the capped quantum dot radius. The spatial distribution of the electrons and holes vary significantly when the ratio eta changes. A quantum-confinement-driven type-II-type-I transition is found in GaAs/AlxGa1-xAs-capped quantum dot structures. The phase diagram is obtained for different capped quantum dot radii. The ground-state exciton binding energy shows a highly nonlinear dependence on the innner structures of inhomogeneous quantum dots, which originates from the redistribution of the electron and hole wave functions.

Pockels effect in GaN/Al-x,Gal(1-x)N superlattice with different quantum structures - art. no. 69841G

The linear electro-optic (Pockels) effect of wurtzite gallium nitride (GaN) films and six-period GaN/AlxGa1-xN superlattices with different quantum structures were demonstrated by a polarization-maintaining fiber-optical Mach-Zehnder interferometer system with an incident light wavelength of 1.55 mu m. The samples were prepared on (0001) sapphire substrate by low-temperature metalorganic chemical vapor deposition (MOCVD). The measured coefficients of the GaN/AlxGa1-xN superlattices are much larger than those of bulk material. Taking advantage of the strong field localization due to resonances, GaN/AlxGa1-xN SL can be proposed to engineer the nonlinear responses.

Theoretical studies of nonlinear optical properties of compounds K(4)Ln(2)(CO3)(3)F-4 (Ln=Pr, Nd, Sm, Eu, Gd)

K(4)Ln(2)(CO3)(3)F-4 (Ln=Pr, Nd, Sm, Eu, Gd) is a special type of frequency doubling compound, whose crystal structure exhibits a scarcity of fluorine ions. This leads to two different coordination polyhedrons in the general position of K(2) atoms: [K(2)O6F(1)(2)F(2)] and [K(21)O6F(1)(2)] in a 2/1 ratio. The chemical bonding structures of all constituent atoms of the compound K4Gd2(CO3)(3)F-4 (KGCOF) are comprehensively studied; moreover, the relationship between the chemical bonding structure and the nonlinear optical (NLO) properties is investigated from the chemical bond viewpoint. The theoretical prediction of the NLO tensor coefficient d(11) of KGCOF is in agreement with experimental observation. Theoretical analyses show that the nonlinearity of this crystal type mainly originates from K-O bonds. In addition, the correlation between the NLO tensor d(11) and the refractive index n(0) of KGCOF is discussed. (C) 2000 American Institute of Physics. [S0021-8979(00)07506-X].

Chemical bond analysis of the correlation between crystal structure and nonlinear optical properties of complex crystals

Second order nonlinear optical (NLO) properties of single crystals with complex structures are studied, from the chemical bond viewpoint. Contributions of each type of constituent chemical bond to the total linearity and nonlinearity are calculated from the actual crystal structure, using the chemical bond theory of complex crystals and the modified bond charge model. We have quantitatively proposed certain relationships between the crystal structure and its NLO properties. Several relations have been established from the calculation. Our method makes it possible for us to identify, predict and modify new NLO materials according to our needs. (C) 1999 Elsevier Science B.V. All rights reserved.