Wave Packet Model Research Articles

Subsonic Jet Noise Prediction in Near and Far Field with Optimized Wave-Packet Approach

In this study, the parameters of a wave-packet model for subsonic jet noise prediction are systematically optimized by leveraging near- and far-field data obtained from the large-eddy simulation (LES) of a free jet at a Mach number of 0.9 across various radial distances. The utilization of near-field information is justified by the observation that the scattering surfaces are typically situated within a few nozzle diameters from the jet axis in the radial direction, both in the current and in innovative aircraft configurations. The far-field information is used to guarantee the correct subdivision between the wave-packet radiating noise and the hydrodynamic components. The results show a notable agreement between the LES data and the wave-packet solutions, consistent with findings documented in the existing literature. This agreement underscores the validity and applicability of the implemented methodology, offering an effective method for obtaining an equivalent jet noise acoustic source, easily implementable in acoustic scattering codes, and accounting for the directional behavior of jet noise.

Eduction of coherent structures from schlieren images of twin jets using SPOD informed with momentum potential theory in the spectral domain

Abstract This work presents a methodology to extract coherent structures from high-speed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequency-wavenumber domain instead of the time-space domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twin-jet configuration with a small jet separation at two supersonic operation conditions: a perfectly-expanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation, together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lower-rank decomposition than schlieren-based SPOD and provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twin-jet wavepacket models available in the literature than those originally obtained with direct schlieren-based SPOD, facilitating their interpretation and comparison against theoretical analyses. Graphical abstract

On the application of acoustic liners for the reduction of jet-flap installation noise

In this work, an experimental and numerical analysis of the feasibility of using acoustic liners to reduce the acoustic far-field radiation of a subsonic jet near a flat plate is presented. The Boundary Element Method (BEM) with a wavepacket model of the jet noise and considering an acoustic impedance boundary condition was used to calculate the far-field noise for different conditions. A parametric optimization was performed in order to find an optimum impedance in terms of the Overall Sound Pressure Level reduction. Semi-empirical models of acoustic liners were then used to design a liner with an impedance as close as possible to the optimum impedance. The liners were built using additive manufacturing and tested in terms of their acoustic impedance and the resulting noise reduction when applied to a region of the flat plate. The BEM simulations, considering the impedance, showed good agreement with experimental data. Overall, by means of the BEM model, optimization and liner semi-empirical models, it was possible to design an acoustic liner which significantly reduced the installation noise at the far-field, with the overall noise reduction between 2 dB to 4 dB depending on observation angle.

Development of a new quantum trajectory molecular dynamics framework.

An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Potential energy surfaces for electron dynamics from a model of localized Gaussian wave packets with valence-bond spin-coupling: High-harmonic generation spectra from H and He atoms

Potential energy surfaces of electron dynamics (ePES) are constructed from a model of localized electron wave packets (eWP) with non-orthogonal valence-bond (VB) spin coupling and applied to quantum dynamics simulations of high harmonic generation (HHG) spectra of hydrogen and helium atoms induced by intense laser pulses. The dynamics of the single electron on the ePES is calculated by numerically solving the time-dependent Schrödinger equation. The results reasonably reproduce previous studies. The dynamics of the electron wave function, dipole moment and dipole acceleration were analyzed by comparing one- and two-dimensional calculations. It was found that the main part of the wave function remains within a few Bohrs of the nuclear position, while the part of the wave function that is several orders of magnitude smaller in probability density, which escapes the laser-induced potential barrier by quantum tunneling effect, mainly contributes to the HHG.

Prediction of Installed Jet Noise from Wave-Packet Models Tuned with Freejet Data

In this work, a kinematic wave-packet model is used to predict installed-jet noise. Large-eddy simulation results of freejets, for Mach numbers 0.4 and 0.9, are used to obtain parameters of wave packets representing large-scale turbulent structures, which were used to provide a model source for the Lighthill analogy used to predict far-field noise spectra. The source amplitude in the model is calibrated using noise measurements for a freejet, and such a wave-packet source is used to predict noise of the same jet in an installed configuration using a tailored Green’s function. Results from the prediction model are compared to installed-jet experimental data for four different observer positions and a large range of frequencies. Overall, the model predicts both directivities and amplitudes similar to the experimental data, with a hump in the generated noise for lower Strouhal numbers and a clear peak near a Strouhal number of 0.2. This low-order model is fast and flexible, and it is expected to be helpful in preliminary aircraft design.

Stopping power of plasma free and bound electrons using dielectric formalism

In this work, a method is proposed that accounts for the stopping power of free and bound electrons of a partially ionized plasma. To formulate this method, the well-known dielectric formalism is used, combining a dielectric function of quantum plasmas, which includes temperature, for free electrons, and the shellwise local plasma approximation (SLPA) for bound electrons. Since few experimental data are available for plasmas, our method calculations at T=0 for solids are compared with SRIM code. The agreement with experimental data is excellent. Also, a cold gas target is considered at different ionization states; results show the expected behavior, but with a little overestimation of the stopping peak and underestimation in the low energy region. Finally our results for plasmas at diverse conditions of temperature are compared with other methods from the literature that contemplate bound electrons explicitly: Mehlhorn, Zimmerman and Unified Wave Packet models. Differences observed between our method, and Mehlhorn and Zimmerman models can be explained by the limited range of application of these old models. In contrast better agreement is obtained when our method is compared with Unified Wave Packet model. These comparisons also serve to prove the validity of our method in different elements.

Real-time supersonic jet noise predictions from near-field sensors with a wavepacket model.

Parabolized stability equations (PSE) have been shown to model wavepackets and, consequently, the near-field of turbulent jets with reasonable accuracy. In this work, PSE were employed to obtain a reduced-order model that could estimate both the fluid-dynamic and the acoustic fields of a supersonic jet in a computationally efficient approximation for resolvent-based estimation based on a single input. From the unsteady pressure data at an input position, the time-domain pressure field was estimated using transfer functions obtained using PSE and a data-driven method based on a well-validated large-eddy simulation (LES). The prediction scheme employed is a single-input single-output, linear model. The unsteady pressure predicted by the PSE showed good agreement with the LES results, especially if the input position is outside the mixing layer, where the prediction capabilities of the PSE are comparable to those of the data-driven transfer functions. The good agreement indicates that PSE could not only be used to predict the sound generation but also to open up different potentialities to attenuate the noise by flow control. The exploration of the regions where the method displayed good agreement, which are presented in this work, can guide the positioning of the sensors for experimental implementation of closed-loop control in a jet.

Approximate neutrino oscillations in the vacuum

It is well known that neutrino oscillations may damp due to decoherence caused by the separation of mass eigenstate wave packets or by a baseline uncertainty of order the oscillation wave length. In this note we show that if the particles created together with the neutrino are not measured and do not interact with the environment, then the first source of decoherence is not present. This demonstration uses the saddle point approximation and also assumes that the experiment lasts longer than a certain threshold. We independently derive this result using the external wave packet model and also using a model in which the fields responsible for neutrino production and detection are treated dynamically. Intuitively this result is a consequence of the fact that the neutrino emission time does not affect the final state and so amplitudes corresponding to distinct emission times must be added coherently. This fact also implies that oscillations resulting from mass eigenstates which are detected simultaneously arise from neutrinos which were not created simultaneously but are nonetheless coherent, realizing the neutrino oscillation paradigm of Kobach, Manohar and McGreevy.

A Quantum Mechanical Financial Time Series Model

This paper introduces a time series model derived from the reverse engineering of the Schrodinger equation. The model is a wave packet model which has a stochastic drift as a superposition of trigonometric functions. The model can be thought of as a financial time series model that includes a model of a real-world measure that allows the opportunity to profit from market timing strategies and a model of an efficient market hypothesis that does not allow it.

Photodissociation of the methyl radical: the role of nonadiabatic couplings in enhancing the variety of dissociation mechanisms.

The nonadiabatic photodissociation dynamics of the CH3 (and CD3) radical from the 3pz and 3s Rydberg states is investigated by applying a one-dimensional (1D) wave packet model that uses recently calculated ab initio 1D electronic potential-energy curves and nonadiabatic couplings. Calculated predissociation lifetimes are found to be too long as compared to the experimental ones. The 1D dynamical model, however, is able to predict qualitatively and explain the fragmentation mechanisms that produce the hydrogen-fragment translational energy distributions (TED) measured experimentally for the ground vibrational resonance of the 3pz and 3s Rydberg states (CH3(v = 0, 3pz) and CH3(v = 0, 3s)). The CH3(v = 0, 3pz) TED found experimentally displays a rather large energy spreading, while the experimental CH3(v = 0, 3s) TED is remarkably more localized in energy. The present model also predicts a widely spread CH3(v = 0, 3pz) TED, produced by a complex dissociation mechanism which involves predissociation to one dissociative valence state through a nonadiabatic coupling, as well as transfer of population to a second valence state through three conical intersections. Also in agreement with experiment, the model predicts a rather localized CH3(v = 0, 3s) TED because the conical intersections no longer operate in this photodissociation process, and predissociation occurs only into a single valence state. Another complex dissociation mechanism is predicted by the model for initial CH3(v > 0, 3s) and CD3(v > 0, 3s) resonances. In this case the mechanism is gradually activated, as vibrational excitation increases, by the interplay between the two nonadiabatic couplings connecting the 3s and 3px,y Rydberg states with the dissociative 2A1 valence state, and produces complex TEDs with signals from several resonances of both 3s and 3px,y. Thus the present 1D quantum model reveals a rich photodissociation dynamics of methyl, where a variety of complex fragmentation mechanisms is favored by the presence of different nonadiabatic couplings between the electronic states involved.

A modal wave-packet model for the multi-mode Richtmyer–Meshkov instability

A model for multimode perturbations subject to the Richtmyer–Meshkov (RM) instability is presented and compared with simulations and experiments for conditions relevant to inertial confinement fusion. The model utilizes the single mode response to the RM impulse whereby its amplitude h(k, t) first grows with an initial velocity V0 ∝ kh(k, 0) that eventually decays in time as 1/kV0t. Both the growth and saturation stages are subject to nonlinearities since they depend explicitly on the initial amplitude. However, rather than using the individual mode amplitude h(k, t), nonlinearity is taken to occur when the root-mean-square amplitude hrms(k, t) of a wave-packet within wavenumbers k ± δk becomes comparable to 1/k. This is done because nearby sidebands can act in unison for an auto-correlation distance 1/δk beyond nonlinearity as observed in the beam-plasma instability. Thus, the nonlinear saturation amplitude for each mode is reduced from the usual 1/k by a phase space factor that depends on the physical dimensionality, as in the Haan model for the Rayleigh–Taylor instability. In addition, for RM, the average value of khrms for the initial spectrum is used to calculate a nonlinear factor FNL that reduces V0, as observed for single modes. For broadband perturbations, the model describes self-similar growth ∝tθ as successively longer wavelength modes reach saturation. The growing and saturated modes must be discerned because only the former promote θ and are enhanced by reshock and spherical convergence. All of these flows are described here by the model in good agreement with simulations and experiments.

Single-electron quantum dynamics in high-harmonic generation spectrum from LiH molecule: Analysis of potential energy surfaces for electrons constructed from a model of localized Gaussian wave packets with valence-bond spin-coupling.

A high-harmonic generation (HHG) spectrum from a LiH molecule induced by an intense laser pulse is computed and analyzed with potential energy surfaces for electron motion (ePES) constructed from a model of localized electron wave packets with valence-bond spin-coupling. The molecule has two valence ePES with binding energies of 0.39 hartree and 1.1 hartree. The HHG spectrum from an electron dynamics on the weaker bound valence ePES, virtually assigned to Li 2s, exhibits a dominant peak at the first harmonic without plateau and cutoff. This compares with the free electron spectrum under an oscillating laser field and is comprehensive with the shape and depth of the ePES. The other valence ePES, assigned to H 1s, is deeper bound such that the overall profile of the wave function is well approximated by a Gaussian of the width comparable to the Li-H bond length. However, a small fraction, less than 10-3, of the probability density amplitude tunnels out from the bound potential with high wave number and spreads over tens of nm with parts recombining to the molecule due to the laser field oscillation. This minor portion of the electronic wave function is the major origin of the HHG extending up to 50 harmonic orders. Nonlinear dynamics within the potential well induced by the laser field oscillation also contributes to the HHG up to 30 harmonic orders.

A pressure decomposition framework for aeroacoustic analysis of turbulent jets

Aeroacoustic analyses of jet flows have benefited greatly from a decomposition of turbulent pressure fluctuations into hydrodynamic and acoustic components. This is typically accomplished using signal processing techniques based on phase speeds, coherence properties or spectral analyses. We present an approach, building on the Momentum Potential Theory (MPT) approach of (Doak, 1989), to split pressure fluctuations into their hydrodynamic, acoustic and entropic, collectively designated fluid-thermodynamic (FT), components. Key advantages are that the approach is applicable everywhere in the jet i.e, not restricted to the near-acoustic field, and does not need user-defined thresholds. The effectiveness of the technique is demonstrated by analyzing the flowfields of three simulated jets, to encompass moderate-compressible to supersonic conditions. The statistical properties and wavepacket dynamics of each pressure component, and their relationships with the unsplit pressure are elaborated. The acoustic pressure field has the form of a wavepacket that attenuates downstream and whose modal analysis reveals low-rank behavior. At each Mach number examined, the acoustic pressure also identifies the relative prominence of each of three components: i) waves with upstream propagating energy content (negative group velocity), ii) supersonically traveling radiating downstream waves, and iii) subsonically convected evanescent waves, which follow the convection pattern of hydrodynamic eddies in the turbulent region. With increasing Mach number, the radiating and convected bands of energy move closer to each other. The hydrodynamic pressure also displays a wavepacket structure, but its features are different: it displays large-scale subsonically convected structures even past the core collapse region. Thus, in the turbulent region of the jet, the acoustic pressure displays smaller integral time scales of fluctuations than the hydrodynamic component. The acoustic pressure field, which includes a zero-crossing in its radial profiles, displays larger wavelengths than the hydrodynamic pressure field, correlates better with the near-field pressure signal and captures the radiated component of noise, especially at shallow angles. These properties make it a suitable field for informing pressure-based wavepacket models for jet noise.

Theoretical models of stopping and ionization of metallic targets and oxydes bombarded by H2 + molecules

SynopsisWe study the vicinage effects in the interaction of H2 + projectiles with C, Al, Si, Al2O3 and SiO2 targets considering the excitation of inner shells. On one side we extend the use of the semiclassical impact-parameter model for the excitation of atomic shells, considering quantum corrections and the role of target screening in the vicinage effects. On the other hand, we adapt our extended wave packet model (EWPM) [3] to the calculation of stopping ratios and ionization cross sections for correlated ions. Lindhard model is used to evaluate valence electrons contributions.

Exact Solutions of Two Nonlinear Partial Differential Equations by the First Integral Method

In recent years, many methods have been used to find the exact solutions of nonlinear partial differential equations. One of them is called the first integral method, which is based on the ring theory of commutative algebra. In this paper, exact travelling wave solutions of the Non-Boussinesq wavepacket model and the (2 + 1)-dimensional Zoomeron equation are studied by using the first integral method. From the solving process and results, the first integral method has the characteristics of simplicity, directness and effectiveness about solving the exact travelling wave solutions of nonlinear partial differential equations. In other words, tedious calculations can be avoided by Maple software; the solutions of more accurate and richer travelling wave solutions are obtained. Therefore, this method is an effective method for solving exact solutions of nonlinear partial differential equations.

On the modelling of wavepacket scattering noise with coherence effects.

An investigation of a wavepacket model for free-jet and jet-surface interaction noise was conducted. The source term for the axisymmetric mode was extracted from a Mach 0.9 jet large eddy simulation and employed to adjust the parameters of a simple source model. Streamwise coherence decay, in particular, was considered. The source model was propagated with both the free-field and tailored Green's function for a semi-infinite flat plate positioned at a distance of r/D = 1 from the jet axis. Significant deviations were observed in the prediction of the low-angle directivity of the isolated jet as well as in the reproduction of the characteristics of the source field. However, the effects of trailing edge noise were well reproduced. The installed jet case, at the region dominated by trailing-edge scattering, showed very little sensitivity to the coherence decay, a crucial feature in the isolated jet case. In this sense, the modelling of the installed-jet case proved to be much simpler.

Two-point wavepacket modelling of jet noise

This paper is focused on the study of a kinematic wavepacket model for jet noise based on two-point statistics. The model contains physical parameters that define its structure in terms of wavenumber, envelope shape and coherence decay. These parameters, which are necessary to estimate the sound pressure levels radiated by the source, were educed from a large-eddy simulation database of a Mach 0.4, fully turbulent jet. The sound pressure levels predicted by the model were compared with acoustic data and the results show that when the parameters are carefully educed from the data, the sound pressure levels generated are in good agreement with experimentally measured values for low Strouhal numbers and polar angles. Furthermore, here we show that a correct representation of both coherence decay and wavepacket envelope shape are key aspects to an accurate sound prediction. A Spectral Proper Orthogonal Decomposition (SPOD) of the model source was also performed motivated by the search for a low-rank model capable of capturing the acoustic efficiency of the full source. It is shown that only a few SPOD modes are necessary to recover acoustically important wavepacket traits.

Isotopic Fractionation in Photolysis of Ozone in the Hartley and Chappuis Bands

AbstractThe isotopic enhancement of atmospheric ozone (O3) is mainly determined by two processes of formation and photolytic decomposition. The formation is known to be associated with isotopic fractionation which can be as high as 120‰ relative to the parent oxygen. Photolysis‐induced isotopic fractionation in O3, however, is not known accurately. Absorption cross sections of various ozone species have been calculated by Zero Point Energy‐based model and quantum mechanical wave packet model. But their predictions pertaining to isotopic fractionations have not been verified experimentally. In the present work, we performed irradiation experiments of O3 at several wavelengths in the Hartley and Chappuis bands and determined the dissociative isotopic fractionation factors by a Rayleigh distillation model. In laboratory conditions, photolysis of ozone produces reactive atomic and/or molecular oxygen which influence the dissociative process through secondary chemistry. The complex interplay of primary photolysis and secondary chemistry was tracked by a kinetic model, and isotopic fractionation factors associated with photolysis alone were derived within a range of uncertainties. The fractionations are found to depend on the photon wavelength and deviate significantly at some wavelengths from the predicted values. For example, at 254 nm the zero point energy‐based models predict lower photolysis rate coefficients for the lighter isotopic species; the present data show about 50‰ higher values.

Resonance Raman Characterization of Tetracene Monomer and Nanocrystals: Excited State Lattice Distortions With Implications For Efficient Singlet Fission.

The characterization of specific phonon modes and exciton states that lead to efficient singlet fission (SF) may be instrumental in the design of the next generation of high-efficiency photovoltaic devices. To this end, we analyze the absolute resonance Raman (RR) cross sections for tetracene (Tc) both as a monomer in solution and as a crystalline solid in an aqueous suspension of nanocrystals. For both systems, a time-dependent wavepacket model is developed that is consistent with the absolute RR cross sections, the magnitude of the absorption cross sections, and the vibronic line shapes of the fluorescence. In the monomer, the intramolecular reorganization energy is between 1500 and 1800 cm-1 and the solvent reorganization energy is 70 cm-1. In nanocrystals, the total reorganization is diminished to less than 600 cm-1. The lowest energy exciton has an estimated intramolecular reorganization energy between 300 and 500 cm-1 while intermolecular librational phonons have a reorganization energy of about 130 cm-1. The diminished reorganization energy of the nanocrystal is interpreted in the context of the delocalization of the band-edge exciton onto about ∼7 molecules. When electron and electron-hole correlations are included within many-body perturbation theory, the polarized absorption spectra of crystalline Tc are calculated and found to be in agreement with experiment. The low-lying exciton states and optically active phonons that contribute to the polarized crystal absorption are identified. The likely role of coherent exciton phonon evolution in the SF process is discussed.