Three-dimensional Situation Research Articles

Localizing aeroacoustic sources in complex geometries: A hybrid method coupling 3D microphone array and time-reversal

Flow-induced noise is widely encountered in engineering domains, and noise source localization is the first step to understand the generation mechanisms. A large part of aeroacoustic noise measurements is performed in wind tunnels by using microphone arrays. A widespread method to identify the noise sources based on these measurements is the beamforming technique. This relies on a Green function, which ideally accounts for source type, flow, and reflecting boundaries. This function is generally not known analytically. An alternative approach is the time-reversal technique considered here. This method consists in propagating the sound field from the microphones back to focus points interpreted as sources. The back propagation can be done numerically with an acoustic propagation solver, which replaces the Green function needed in the beamforming. To date time reversal has been used to localize sound sources with flow in two-dimensions, without considering any reflecting/diffracting boundary. The objective of this work is to consider a three-dimensional situation with flow, and to include the presence of such boundaries to see if this can improve source localization. A synthetic sound source enclosed in a streamlined body is placed in a wind tunnel, and its sound field is diffracted by a nearby airfoil. A three-dimensional antenna with 768 microphones is used to measure the sound field, and time-reversal is performed by solving the three-dimensional linearized Euler equations with a discontinuous Galerkin method. The interest of taking into account the airfoil geometry for source localization is discussed, and some comparisons with the beamforming method are performed.

Thermal convection with a Cattaneo heat flux model

The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one.

Numerical Simulations of Vertical Discrete Gusts Driven by Trailing Edge Blowing

A new type of gust generator generates the airflow oscillation in the wind tunnel through the Coanda effect of the unsteady trailing edge blowing, which has been shown to have strong potential for accurately simulating discrete gusts. It is necessary to study the relationship between the generated gust characteristics and the control parameters of such devices in order to optimize the design performance and improve gust simulation capabilities. By solving the compressible unsteady Reynolds-averaged Navier–Stokes (URANS) equations, the computational fluid dynamics model of the subsonic airflow past the gust generator in the wind tunnel was presented. The effects of jet momentum, frequency, and spanwise blowing ratio on gust intensity, shape, and spatial uniformity were investigated. Results indicate that the intensity of gusts is positively correlated with jet momentum and frequency. The gust shape matches well with the normalized jet momentum coefficient curve. However, when the frequency increases to above 10 Hz, the gust shape differs significantly from expectation due to the appearance of reverse wave peaks. In addition, the mechanism of the impact of the sidewall and partial spanwise blowing on gusts was revealed. In the three-dimensional situation, streamwise vortices are formed on the sidewall and at the spanwise position where the blowing stops, respectively. This results in an increase and noticeable nonuniformity in gust amplitude. When the blowing with a 15% spanwise length near the sidewall is turned off, the gust amplitude at the symmetry plane increases by nearly 40% due to the main vortex being closer to the main flow. The result provides a physical explanation for the availability of this operation to reduce gust attenuation.

The relationship between fuel reactivity and exergy features in combustion process

Fuel reactivity is a flexible and feasible method to control combustion, thus reactivity-controlled compression ignition (RCCI) has the potential to achieve lower emissions and higher thermal efficiency. However, the exergy loss during combustion hinders the further exergy-work transform, which limits the thermal efficiency further improvement. The present work focuses on the relationship between fuel reactivity and exergy which contains exergy loss (EL) and thermomechanical exergy (Exthermo due to the temperature and pressure imbalance between system and reference state). By varying the reactivity of primary reference fuels (PRFs) with different initial boundary conditions, it is found that different PRFs could not reduce EL and change Exthermo under same condition but could change the exergy loss rate as well as the EL structure by influencing low-temperature combustion. In terms of boundary conditions, both high temperature and lean mixture could improve Exthermo but with different mechanism: high temperature saving EL into Exthermo, lean mixture recovering incomplete combustion exergy (Exincom) into Exthermo. By contrast, equivalence ratio more easily affects EL and Exthermo. In three-dimensional situation, it is found that decreasing reactivity of PRFs leads more in-cylinder area below equivalence ratio 1.0 which benefits for the Exthermo improvement, but it would cause Exthermo structure mutation which is unfriendly for the smooth output of work near top dead center. The conversion of fuel exergy to final useful work is indirect, and there exist two sub-processes: fuel exergy to thermomechanical exergy then thermomechanical exergy to useful work. The final exergy-work transform efficiency is influenced by both processes. Therefore, using low reactivity fuel as PRF90 in engine is favor of the exergy from fuel transforming into Exthermo by more lean mixture, adopting high reactivity fuel as PRF0 is favor of the Exthermo sequential structure which is benefit for the combustion control and useful work extract near top dead center. Therefore, there is potential to further improve the thermal efficiency by using a dual-fuel combination, with the low reactivity fuel creating a low equivalence ratio region to improve the thermomechanical exergy, and the high reactivity fuel achieving precise phase control during the combustion.

Boundary triples and Weyl functions for Dirac operators with singular interactions

In this paper, we develop a systematic approach to treat Dirac operators [Formula: see text] with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths [Formula: see text], respectively, supported on points in [Formula: see text], curves in [Formula: see text], and surfaces in [Formula: see text] that is based on boundary triples and their associated Weyl functions. First, we discuss the one-dimensional case which also serves as a motivation for the multidimensional setting. Afterwards, in the two- and three-dimensional situation we construct quasi, generalized, and ordinary boundary triples and their Weyl functions, and provide a detailed characterization of the associated Sobolev spaces, trace theorems, and the mapping properties of integral operators which play an important role in the analysis of [Formula: see text]. We make a substantial step towards more rough interaction supports [Formula: see text] and consider general compact Lipschitz hypersurfaces. We derive conditions for the interaction strengths such that the operators [Formula: see text] are self-adjoint, obtain a Krein-type resolvent formula, and characterize the essential and discrete spectrum. These conditions include purely Lorentz scalar and purely non-critical anomalous magnetic interactions as well as the confinement case, the latter having an important application in the mathematical description of graphene. Using a certain ordinary boundary triple, we also show the self-adjointness of [Formula: see text] for arbitrary critical combinations of the interaction strengths under the condition that [Formula: see text] is [Formula: see text]-smooth and derive its spectral properties. In particular, in the critical case, a loss of Sobolev regularity in the operator domain and a possible additional point of the essential spectrum are observed.

On the Single Layer Boundary Integral Operator for the Dirac Equation

This paper is devoted to the analysis of the single layer boundary integral operator mathcal {C}_z for the Dirac equation in the two- and three-dimensional situation. The map mathcal {C}_z is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator A_0 and z belongs to the resolvent set of A_0. In the case of smooth boundaries fine mapping properties and a decomposition of mathcal {C}_z in a ‘positive’ and ‘negative’ part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.

Improved Design of Architecture of the Battlefield Situation Comprehensive Display System

The traditional chimney software architecture design, which is based on the application object, scale and equipment, is difficult to meet the urgent need of multi-resolution, multi-viewpoint, two-dimensional and three-dimensional consistent battlefield situation comprehensive display. Referring to the idea of U.S. Army's general operational diagram, the architecture of the current battlefield situation integrated display system is upgraded and improved. Aiming at the problems of information splitting and real-time undifferentiated access of multi-domain heterogeneous data, technical means such as spatial analysis and multi-source data integration are put forward, and the problems of fast loading and visualization of 3D models of the large battlefield space are solved by designing force clustering and motion trajectory smoothing algorithms. This method improves the service ability and the level of the battlefield situation comprehensive display system, and has a broad arrange of application.

Spurious currents suppression by accurate difference schemes in multiphase lattice Boltzmann method

Spurious currents are often observed near curved interfaces in multiphase simulations based on diffuse interface methods. These unphysical phenomena negatively affect both computational accuracy and stability. In this paper, the origin and suppression of spurious currents are investigated using the multiphase lattice Boltzmann method driven by a chemical potential. Both the difference error and insufficient isotropy of the discrete gradient operator give rise to directional deviations in the nonideal force, leading to spurious currents. Nevertheless, a high-order finite difference scheme produces far more accurate results than a high-order isotropic difference scheme. We compare several finite difference schemes that have different levels of accuracy and resolution. When a large proportional coefficient is used, the transition region is narrow and steep, and the resolution of the finite difference scheme provides a better indication of the computational accuracy than the formal accuracy. Conversely, for a small proportional coefficient, the transition region is wide and gentle, and the formal accuracy of the finite difference gives a better indication of the computational accuracy than the resolution. Numerical simulations show that the spurious currents calculated in the three-dimensional situation are highly consistent with those in two-dimensional simulations; in particular, the two-phase coexistence densities calculated by the high-order accuracy finite difference scheme are in excellent agreement with the theoretical predictions of the Maxwell equal-area construction down to a reduced temperature of 0.2.

Equation-of-state-dependent surface free-energy density for wettability in lattice Boltzmann method.

In thermodynamic theory, the liquid-vapor fluids can be described by a single multiphase equationof state and the surface wettability is usually characterized by the surface free-energy density. In this work, we propose an equation-of-state-dependent surface free-energy density for the wettability of the liquid-vapor fluids on a solid surface, which can lead to a simple closed-form analytical expression for the contact angle. Meanwhile, the thermodynamically derived equilibrium condition is equivalent to the geometric formulation of the contact angle. To numerically validate the present surface free-energy density, the mesoscopic multiphase lattice Boltzmann model with self-tuning equationof state, which is strictly consistent with thermodynamic theory, is employed, and the two-dimensional wetting condition treatment is extended to the three-dimensional situation with flat and curved surfaces. Two- and three-dimensional lattice Boltzmann simulations of static droplets on flat and curved surfaces are first performed, and the obtained contact angles agree well with the closed-form analytical expression. Then, the three-dimensional lattice Boltzmann simulation of a moving droplet on an inclined wall, which is vertically and sinusoidally oscillated, is carried out. The dynamic contact angles well satisfy the Cox-Voinov law. The droplet movement regimes are consistent with previous experiments and two-dimensional simulations. The dependence of the droplet overall velocity with respect to the dimensionless oscillation strength is also discussed in detail.

Study on the Improved Method for Calculating Traveltime and Raypath of Multistage Fast Marching Method

The traditional Fast Marching Method (FMM) based on the finite-difference scheme can solve the traveltime of first arrivals; however, the accuracy and efficiency of FMM are usually affected by the finite-difference schemes and grid size. The Vidale finite-difference scheme and double-grid technology are adopted to replace the traditional first-order and second-order finite-difference schemes in this paper to improve the computation accuracy and efficiency. The traditional FMM does not provide the corresponding raypath calculation methods, and in view of the interoperability of FMM and the linear travel time interpolation (LTI) method, we introduce the linear interpolation method into FMM ray tracing to compute the raypath and take into consideration the secondary source located inside the grid cell to improve the accuracy and stability of the raypath calculation. With these measures and the application of the multistage approach, we successfully completed the improved Multistage FMM (MFMM) ray tracing, which can track first arrivals and any type of primary and multiple reflection waves. Through the theoretical and actual field model tests, the computation accuracy and efficiency of the improved MFMM are proven to be higher than that under traditional first-order and second-order finite-difference schemes, the correctness and effectiveness of the interpolation method for raypath calculation are verified, and the improved MFMM has demonstrated good adaptability and stability for complex models. The improvements for the MFMM in this paper are successfully applied in two-dimensional cases and need to be extended to three-dimensional situations.

The effect of working memory training on situation awareness in a flight simulator

The close relationship between working memory and situation awareness (SA) has been confirmed and further empirical investigations are lacking. The main aim of this study was to demonstrate the feasibility of working memory training for improving SA. Thirty-eight participants completed a challenging flight scenario in a high-fidelity flight simulator and were randomized into a training group (n = 20) or a control group (n = 18). The training group engaged in an adaptive dual N-back task for 2 weeks, while the control group was given a negative control task. Three-dimensional situation awareness rating technique (3D-SART) scores and situation awareness global assessment technique (SAGAT) scores were recorded to evaluate pretest and posttest SA. The results showed that both situational understanding dimension scores in the 3D-SART and SAGAT scores were significantly increased from the pretest to the posttest in the training group, while the control group showed no significant differences. It was concluded that working memory training can effectively improve individuals’ SA, which has important implication for future research.

Fragile versus stable two-dimensional fermionic quasiparticles

We provide a comprehensive theoretical investigation of the Fermi liquid quasiparticle description in two-dimensional electron gas interacting via the long-range Coulomb interaction by calculating the electron self-energy within the leading-order approximation, which is exact in the high-density limit. We find that the quasiparticle energy is larger than the imaginary part of the self-energy up to very high energies, implying that the basic Landau quasiparticle picture is robust up to far above the Fermi energy. We find, however, that the quasiparticle picture becomes fragile in a small discrete region around a critical wave vector where the quasiparticle spectral function strongly deviates from the expected quasiparticle Lorentzian line shape with a vanishing renormalization factor. We show that such a non-Fermi liquid behavior arises due to the coupling of quasiparticles with the collective plasmon mode. This situation is somewhat intermediate between the one-dimensional interacting electron gas (i.e., Luttinger liquid), where the Landau Fermi liquid theory completely breaks down since only bosonic collective excitations exist, and three-dimensional electron gas, where quasiparticles are well-defined and more stable against interactions than in one and two dimensions. We use a number of complementary definitions for a quasiparticle to examine the interacting spectral function, contrasting two-dimensional and three-dimensional situations critically.

Weak magnetohydrodynamic turbulence

Low-frequency hydromagnetic turbulence is thought to play an important role in charged particle energization in space and astrophysical environments. For understanding large-scale turbulence in magnetized plasmas, low-frequency electromagnetic turbulence has been widely investigated within the theoretical framework of incompressible magnetohydrodynamic (MHD) theory. Among the existing works is the weak turbulence formalism of incompressible MHD turbulence. The present paper revisits the existing formalism under the assumption of zero residual energy. Under the strict assumption of turbulence taking place in a two-dimensional plane, which can be interpolated to a three-dimensional situation with azimuthal symmetry, the well-known steady-state turbulent spectrum of k⊥−2 is recovered, where k⊥ denotes the wave number perpendicular to the ambient magnetic field.

Presence versus absence of two-dimensional Fermi surface anomalies

We theoretically consider Fermi surface anomalies manifesting in the temperature-dependent quasiparticle properties of two-dimensional (2D) interacting electron systems, comparing and contrasting with the corresponding three-dimensional (3D) Fermi liquid situation. In particular, employing microscopic many-body perturbative techniques, we obtain analytically the leading-order and the next-to-leading-order interaction corrections to the renormalized effective mass for three distinct physical interaction models: electron-phonon, electron-paramagnon, and electron-electron Coulomb coupling. We find that the 2D renormalized effective mass does not develop any Fermi surface anomaly due to electron-phonon interaction, manifesting $\mathcal{O}({T}^{2})$ temperature correction and thus remaining consistent with the Sommerfeld expansion of the noninteracting Fermi function, in contrast to the corresponding 3D situation where the temperature correction to the renormalized effective mass has the anomalous ${T}^{2}logT$ behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous $\mathcal{O}(T)$ corrections to the 2D effective mass renormalization in contrast to ${T}^{2}logT$ behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a ${T}^{2}logT$ term could possibly arise in the 2D quasiparticle effective mass from electron-phonon interactions. We also compare results for the temperature-dependent specific heat in the interacting 2D and 3D Fermi systems, using the close connection between the effective mass and specific heat.

Know the enemy: 2D Fermi liquids

We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the phase diagram in the frequency–temperature space separating the collisionless ballistic regime and the collision-dominated hydrodynamic regime for 2D and 3D interacting electron systems. We also provide the temperature corrections up to third order for the renormalized effective mass, and comment on the validity of 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation.

Stationary Response of Nonlinear Vibration Energy Harvesters by Path Integration

Abstract A path integration procedure based on Gauss–Legendre integration scheme is developed to analyze probabilistic solution of nonlinear vibration energy harvesters (VEHs) in this paper. First, traditional energy harvesters are briefly introduced, and their nondimensional governing and moment equations are given. These moment equations can be solved through the Runge–Kutta and Gaussian closure method. Then, the path integration method is extended to three-dimensional situation, solving the probability density function (PDF) of VEH. Three illustrative examples are considered to evaluate the effectiveness of this method. The effectiveness of nonlinearity of traditional monostable VEH is studied. The bistable VEH is further studied too. At the same time, equivalent linearization method (EQL) and Monte Carlo simulation (MCS) are employed. The results indicate that three-dimensional path integration method can give satisfactory results for the global PDF, especially when solving bistable VEH problems. The results of this method have better consistency with the simulation results than those of EQL. In addition, different degrees of hardening and softening behaviors of PDFs occur when the magnitude of nonlinearity coefficient increases or the bistable VEH is considered.

Research on Laser Ablation Technology in the Material Interaction of Two-dimensional Axisymmetric Ablation Model

In order to explore the mechanism of interaction between nanosecond pulsed intense laser and material, the paper established a two-dimensional numerical model, using finite difference method to numerically simulate the temperature field of nanosecond laser pulse ablation of metal aluminium. By comparing different pulse widths, the temperature field caused by the laser under the spot and energy evolves with time. It is found that the temperature in the early stage of the pulse rises faster than in the later stage. The isotherm diagram shows that the centre temperature rises fastest, the ablation profile is similar to the shape of the laser beam, and the ablation depth reaches 1 -5μm. The longer the pulse width, the narrower and deeper the ablation, the larger the spot, the wider and the shallower the ablation. The calculation results show that, compared to the uniform distribution, when the laser has a Gaussian distribution, the target aluminium centre can be obtained the higher the temperature rise, the more prone to ablation and the shorter the melting time of aluminium. The model established in this paper can be easily extended to three-dimensional situations.

Vertical measurable displacement approach for altitude accuracy improvement in 3D visible light positioning

Visible light positioning (VLP) techniques using light-emitting diodes (LEDs) are mostly based on the assumption that the height of the receiver is fixed and not intended to be measured. We evaluate the received signal strength (RSS)-based positioning with changed receiver altitude in both two-dimensional (2D) and three-dimensional (3D) situations, taking into account of non-line-of-sight (NLOS) channel with first reflection. Simulation results show that, the positioning accuracy deteriorates with the increase of the receiver altitude. To alleviate such problems and locate the target more accurately, we proposed a simple and convenient method by intentionally changing receiver altitude with direct measurable displacement. By employing the proposed approach, the resultant altitude error can be limited within ∼34 cm.

Development of thermal model for the determination of SLM process parameters

In this study, a mathematical model is developed for determining the process parameters used in the manufacturing process of powder materials with selective laser melting method. Although the studies carried out to date cover detailed modeling studies including three-dimensional and time-dependent situations, obtaining quite different approaches from experimental results has led to the idea that a change should be made in the construction of the mathematical problem. Therefore, different from other studies and for the first time, the Eigen-function expansion method was used in the analytical solution of the selective laser melting thermal model. The developed mathematical model includes the steady-state solution with the appropriate boundary conditions of the 2-D non-homogeneous heat equation. The mathematical model was first solved analytically with the Eigen-function expansion method, and the function obtained as a result of the solution was introduced into the MATLAB software. The parametric study was performed numerically over laser power, laser spot size and powder bed thickness. With the developed model, the solution was converged in 30 s and 11.5% more accurate with respect to experimental results were obtained in width, 29% in depth and 3% in temperature as compared to other analytical models exist in the literature.

On the Problem of Describing Holomorphically Homogeneous Real Hypersurfaces of Four-Dimensional Complex Spaces

We discuss two fragments of a large problem that extends the author’s recently completed similar studies in the space $$\mathbb C^3$$ to the next dimension. One of the fragments is related to the local description of nonspherical holomorphically homogeneous strictly pseudoconvex hypersurfaces in $$\mathbb C^4$$ with stabilizers of submaximal dimension. Using the Moser normal form technique and the properties of subgroups of the unitary group $$\mathrm U(3)$$ , we show that up to holomorphic equivalence there exist only two such surfaces. Both of them are natural generalizations of known homogeneous hypersurfaces in the space $$\mathbb C^3$$ . In the second part of the paper, we consider a technique of holomorphic realization in $$\mathbb C^4$$ of abstract seven-dimensional Lie algebras that correspond, in particular, to homogeneous hypersurfaces with trivial stabilizer. Some sufficient conditions for the Lie algebras are obtained under which the orbits of all realizations of such algebras are Levi degenerate. The schemes of studying holomorphically homogeneous hypersurfaces that were used in the two-dimensional (E. Cartan) and three-dimensional (Doubrov, Medvedev, and The; Fels and Kaup; Beloshapka and Kossovskiy; Loboda) situations and resulted in full descriptions of such hypersurfaces turn out to be quite efficient in the case of greater dimension of the ambient space as well.