Density Gradient Field Research Articles

Electronic Force Density Fields: Insights into Partial Bonds, Transition States, and Chemical Structure Evolution.

This paper presents the quantum-topological binding approach, in which the electrostatic and total static force density fields, Fes(r) and , together with the electron density gradient field ∇ρ(r), are simultaneously analyzed to elucidate the chemical structure of transition states and the nature of interatomic interactions for semibroken semiformed partial chemical bonds. The approach attributes the discrepancies between the force fields and Fes(r) to the nonclassical electron-electron interaction effects. The internuclear gap between the zero-flux boundaries of Fes(r) and ∇ρ(r) indicates the interatomic charge transfer phenomenon (ICT) that occurs upon the formation of a system from free atoms. Concomitantly, the mismatch of the zero-flux surfaces defined in and ∇ρ(r) can be interpreted as a phenomenon of the electron-transfer-induced quantum chemical response (QCR), which originates from the electron exchange correlation. Our study permits the assertion of parallels between partial bonds and noncovalent interactions, as both typically exhibit incomplete QCRs, indicating the partial electron sharing of the transferred density. The changes in atomic and pseudoatomic charges are employed to describe the evolution of the chemical structure upon the substitution reaction. It is observed that the acquired difference in the actual atomic electronegativity causes polarization upon the heterolytic breaking of virtually nonpolar bonds. It is further proposed that the proximity of closely related stationary states along the reaction path on a potential energy hypersurface implies their similarity in the manifestation of the ICT and sympathetic QCR. Furthermore, the involvement of an electron pair in a partial bond facilitates its delocalization through the attraction by the static forces and Fes(r) to a neighboring nucleus and through the smearing by the Pauli kinetic force FP(r).

Plant-Denoising-Net (PDN): A plant point cloud denoising network based on density gradient field learning

Effective point cloud denoising is critical in 3D plant phenotyping applications, which reduces interference in subsequent algorithms and improves the accuracy of plant phenotypes measurement. Deep learning-based point cloud denoising algorithms have shown excellent denoising performance on simple CAD models. However, these algorithms suffer from issues including over-smoothing or shrinkage and low efficiency when applied on density uneven, incomplete, various types of noise and complex plant point clouds. We proposed a plant point cloud denoising network (PDN) based on point cloud density gradient field learning, which can effectively address the challenges posed by plant point clouds. PDN consists of three main modules: point density feature (PDF) exception module, umbrella operator feature (UOF) computation module, and point density gradient (DG) estimation module. The performance of PDN was evaluated in experiments using point clouds of multiple plant species with noise of different types. Under different levels of Gaussian noise, our method achieved a relative performance improvement of 7.6%-19.3% compared to the state-of-the-art baseline methods, reaching state-of-the-art denoising performance. For noise of different types, the majority of our denoising results outperformed the baseline methods. In addition, our method was 0.5 and 8.6 times faster than the baseline methods when processing point clouds with low and high noise level, respectively. The good robustness, generalization, and computational efficacy of PDN are expected to facilitate the acquisition of high-precision 3D point clouds for various plant species, enhance the versatility of 3D phenotyping methods, improve the accuracy of the measurement of structural phenotypes, and increase the throughput of data processing, therefore facilitate the development of modern breeding research. The source code and the datasets used in this study is available on GitHub at https://github.com/suetme/PDN-plant-denoising-net.

Carbon Dioxide Electroreduction and Formic Acid Oxidation by Formal Nickel(I) Complexes of Di-isopropylphenyl Bis-iminoacenaphthene.

Processing CO2 into value-added chemicals and fuels stands as one of the most crucial tasks in addressing the global challenge of the greenhouse effect. In this study, we focused on the complex (dpp-bian)NiBr2 (where dpp-bian is di-isopropylphenyl bis-iminoacenaphthene) as a precatalyst for the electrochemical reduction of CO2 into CH4 as the sole product. Cyclic voltammetry results indicate that the realization of a catalytically effective pattern requires the three-electron reduction of (dpp-bian)NiBr2. The chemically reduced complexes [K(THF)6]+[(dpp-bian)Ni(COD)]- and [K(THF)6]+[(dpp-bian)2Ni]- were synthesized and structurally characterized. Analyzing the data from the electron paramagnetic resonance study of the complexes in solutions, along with quantum-chemical calculations, reveals that the spin density is predominantly localized at their metal centers. The superposition of trajectory maps of the electron density gradient vector field and the electrostatic force density field per electron, as well as the atomic charges, discloses that, within the first coordination sphere, the interatomic charge transfer occurs from the metal atom to the ligand atoms and that the complex anions can thus be formally described by the general formulae (dpp-bian)2-Ni+(COD) and (dpp-bian)2 -Ni+. It was also shown that the reduced nickel complexes can be oxidized by formic acid; resulting from this reaction, the two-electron and two-proton addition product dpp-bian-2H is formed.

Experimental investigation of transonic buffeting, frequency lock-in and their dependence on structural characteristics

Transonic buffet is a phenomenon that appears in compressible flow around an airfoil and plays a substantial role in the limitation of the flight envelope of commercial aircraft. If the structural natural frequencies of the wing are similar to the buffet frequency, the oscillation of the compression shock, fluid, and structure may interact (transonic buffeting) and lead to strong loads and potential structural failure. Numerical research has shown that structural parameters can have a significant effect on the onset point of shock oscillations as well as on the typology of the fluid–structure interaction, which presented classical structural excitation, modal veering, or frequency lock-in.The aim of this research is a systematic experimental investigation to examine the structural effects and the lock-in phenomenon. It provides a partial validation of the numerical results available in the literature. A lightweight, elastically-suspended wing model (OAT15A profile) was tested in the Trisonic Wind Tunnel Munich. Optical measurement techniques were deployed to non-intrusively observe the flow-induced density gradient field (background-oriented Schlieren) and the structural deformation and displacement of the wing (digital image correlation). Mass ratios varied from 282 to 322 and the half-chord-based, reduced natural pitch frequency ranged from 0.169 to 0.280. The experimental results confirm the existence of frequency lock-in, an interaction dominated by the structural mode that presents high but limited pitch amplitudes for natural pitch frequencies above the natural buffet frequency. The effects of mass ratio and natural pitch frequency on the interaction are discussed. A substantial effect of the mass ratio on the onset of buffeting and the resulting pitch amplitude for frequency lock-in was discovered.

Towards Density Measurements In A Supersonic Turbulent Boundary Layer

Quantitative mean density measurements using calibrated schlieren technique are demonstrated in a Mach 2 compressible turbulent boundary layer. A calibration procedure, where schlieren and particle image velocimetry measurements are conducted on a symmetric double wedge model, is utilised. By assuming that the shock and expansion fan generated by the double wedge model can be idealised, the density gradient field is calculated based on the measured velocity field. Thus, based on the calibration data, a linear relation from schlieren intensity to density gradient is constructed. Moreover, to resolve a large range of density gradients expected within the boundary layer, schlieren measurements with five different knife edge positions are performed and the results are stitched together. The combined density gradient and the integrated density profiles showed good agreement with the literature, and therefore the current technique may provide a promising avenue to measure the mean density fields in compressible boundary layer flows.

A novel compressible enstrophy transport equation-based analysis of instability during Magnus–Robins effects for high rotation rates

The effects of compressibility on the instability of a two-dimensional flow past a rotating cylinder executing high rotation rates are investigated, in detail, using a novel analysis based on the compressible enstrophy transport equation (CETE). Accurate analysis of the instability necessitates the generation of high fidelity numerical solutions, and this is achieved by employing optimized numerical methods that enable high accuracy direct numerical simulation of compressible flows. To study the effects of compressibility induced by rotation alone, a low free stream Mach number and two high rotation rates are considered, as compared to that reported in the literature. Results demonstrate single-sided vortex shedding, the presence of significant compressibility in the flow field confirmed by local Mach number, and temperature and density gradient fields with transient formation of supersonic pockets noted for the higher rotation speed cases. The temporal instability is studied by analyzing the relative contributions of different terms in the CETE to the growth of enstrophy. As per the authors' knowledge, this is the first such research effort demonstrating an application of the CETE for instabilities. Analysis shows that viscous diffusion is the dominant mechanism in creating the flow instability with a secondary role played by the baroclinic mechanism.

Cosmological constraints from the density gradient weighted correlation function

ABSTRACT The mark weighted correlation function (MCF) W(s, μ) is a computationally efficient statistical measure which can probe clustering information beyond that of the conventional two-point statistics. In this work, we extend the traditional mark weighted statistics using powers of the density field gradient |∇ρ/ρ|α as the weight, and use the angular dependence of the scale-averaged MCFs to constrain cosmological parameters. The analysis shows that the gradient-based weighting scheme is statistically more powerful than the density-based weighting scheme, while combining the two schemes together is more powerful than separately using either of them. Utilizing the density-weighted or the gradient-weighted MCFs with α = 0.5, 1, we can strengthen the constraint on Ωm by factors of 2 or 4, respectively, compared with the standard two-point correlation function, while simultaneously using the MCFs of the two weighting schemes together can be 1.25 times more statistically powerful than using the gradient weighting scheme alone. The mark weighted statistics may play an important role in cosmological analysis of future large-scale surveys. Many issues, including the possibility of using other types of weights, the influence of the bias on this statistics, and the usage of MCFs in the tomographic Alcock–Paczynski method, are worth further investigations.

Inhomogeneous behavior of supercritical hydrocarbon fuel flow in a regenerative cooling channel for a scramjet engine

Supercritical hydrocarbon fuel is employed to simultaneously cool associated combustors and to recover heat. Aiming to improve the thermal performance of the regenerative cooling channels in an advanced aircraft, the flow behavior, vortex structures, and transport characteristics of supercritical n-decane are investigated using an LES model. The flow patterns are identified by several common buoyancy criteria, and oscillation effects are observed in strongly mixed flows. Using temperature and density gradient fields, distinct inhomogeneity shows that the thermal oscillations aggravate the further occurrence of uneven performance. Furthermore, the positive helicity gradually increases with the accumulation of buoyancy force. The notably strong vorticity mainly concentrates near the heated wall, while a narrow section appears in the turbulent region, which indicates that the variable vorticity behavior contributes to the transport properties.

Large-eddy simulation of methane direct injection using the full injector geometry

Understanding the mixing process of under-expanded gaseous-fuel jets from an outward opening injector is essential for developing Direct Injection (DI) internal combustion engines. This paper presents a Large-Eddy Simulation (LES) study of the DI of methane into a Constant Volume Chamber (CVC), considering the full, internal geometry of a prototype injector. Four cases at conditions relevant to Compressed Natural Gas (CNG) DI engines are investigated, with methane as a surrogate for CNG. A new post-processing method permits the 3D LES field to be projected into a 2D density gradient field that can be compared to a schlieren image. The LES results are then validated against high-speed, schlieren imaging experiments, demonstrating that the simulations are able to reproduce experimental trends. Three main regions of the external flow are observed: a recirculation zone just downstream of the injector tip, a stagnation zone and a far-mixing zone. The location of the stagnation zone increases as the CVC pressure decreases, consistent with a theory presented in the literature. The modelling of the full internal geometry of the injector leads to a determination of the injector pressure losses. Once the pressure loss within the injector is considered, a short version of the injector can reasonably represent the full injector for prediction of the external flow.

Ionospheric disturbance caused by artificial plasma clouds under different release conditions

The generation and evolution of artificial plasma clouds is a complicated process that is strongly dependent on the background environment and release conditions. In this paper, based on a three-dimensional two-species fluid model, the evolution characteristics of artificial plasma clouds under various release conditions were analyzed numerically. In particular, the effect of ionospheric density gradient and ambient horizontal wind field was taken into account in our simulation. The results show that an asymmetric plasma cloud structure occurs in the vertical direction when a nonuniform ionosphere is assumed. The density, volume, and expansion velocity of the artificial plasma cloud vary with the release altitude, mass, and initial ionization rate. The initial release velocity can change the cloud's movement and overall distribution. With an initial velocity perpendicular to the magnetic field, an O+ density cavity and two bumps exist. When there is an initial velocity parallel to the magnetic field, the generated plasma cloud is bulb-shaped, and only one O+ density cavity and one density bump are created. Compared to the cesium case, barium clouds expand more rapidly. Moreover, Cs+ clouds have a higher density than Ba+ clouds, and the snowplow effect of Cs+ is also stronger.

Uncertainty-based weighted least squares density integration for background-oriented schlieren

We propose an improved density integration methodology for Background Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. The method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge show a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

We theoretically analyze the effect of density/refractive-index gradients on the measurement precision of Volumetric Particle Tracking Velocimetry (V-PTV) and Background Oriented Schlieren (BOS) experiments by deriving the Cramer-Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a particle or dot viewed through a medium containing density gradients that includes the effect of various experimental parameters such as the particle depth, viewing direction and f-number. Using the model we show that non-linearities in the density gradient field lead to blurring of the particle/dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is a function of the ratio of the dot diameters and dot intensities. We term this parameter the Amplification Ratio (AR), and we propose a methodology for estimating the position uncertainties in tracking-based BOS measurements. The theoretical predictions of the particle/dot position estimation variance from the CRLB are compared to ray tracing simulations with good agreement. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where we show that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position error on density and refractive-index gradient induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

Optical Measurements on Thermal Convection Processes inside Thermal Energy Storages during Stand-By Periods

Thermal energy storages (TES) are increasingly important for storing energy from renewable energy sources. TES that work with liquid storage materials are used in their most efficient way by stratifying the storage fluid by its thermal density gradient. Mixing of the stratification layers during stand-by periods decreases the thermal efficiency of the TES. Tank sidewalls, unlike the often poorly heat-conducting storage fluids, promote a heat flux from the hot to the cold layer and lead to thermal convection. In this experimental study planar particle image velocimetry (PIV) measurements and background-oriented schlieren (BOS) temperature measurements are performed in a model experiment of a TES to characterise the influence of the thermal convection on the stratification and thus the storage efficiency. The PIV results show two vertical, counter-directed wall jets that approach in the thermocline between the stratification layers. The wall jet in the hot part of the thermal stratification shows compared to the wall jet in the cold region strong fluctuations in the vertical velocity, that promote mixing of the two layers. The BOS measurements have proven that the technique is capable of measuring temperature fields in thermally stratified storage tanks. The density gradient field as an intermediate result during the evaluation of the temperature field can be used to indicate convective structures that are in good agreement to the measured velocity fields.

On the application of non-standard rainbow schlieren technique upon supersonic jets

A quantitative rainbow schlieren study was conducted on an over-expanded jet at nozzle pressure ratio of 2.8, based on two different schlieren set-ups: the standard z-type and a single-mirror schlieren set-up. The technique used a single, weak focal-length lens placed in the field of view of the system to provide the calibration information required for the extraction of the quantitative data. In the case of the single-mirror set-up, the calibration image required further post-processing procedures to take into account the double refraction experienced by the light. Density gradients were calculated using Abel transform and compared to validated reference data. Results indicate that the single-mirror set-up is able to improve prediction of the density gradient field as compared to the standard z-type schlieren, due to its inherent property of higher sensitivity. The study has shown that the single-mirror set-up performs on average better than the standard z-type system, yielding an overall averaged error of ± 20%, with localized values as low as ± 5% where the shock cell structure is clearly defined, with respect to the validated reference data. At the same time, both systems perform poorly in regions where the flow structure displays poor image contrast.

Mobile visualization of density fields using smartphone background-oriented schlieren

The conventional background-oriented schlieren (BOS) technique is an image-based technique that can calculate the density field in fluids using two static images [i.e., an undistorted background image (reference image) and a distorted background image due to the density change in fluids (target image)]. This paper proposes the smartphone BOS (SBOS) technique, which offers the measurement of the density gradient using the high-speed imaging feature of the smartphone being carried with a moving observer. The conventional BOS with a fixed camera visualizes the density gradient by comparing the reference image and the target image. In contrast, SBOS can obtain the time difference of the density gradient field. A reference image in SBOS is a target one at a previous time step. The movement of the smartphone is canceled using a registration technique for image accurate alignment. Three demonstrations are conducted to perform SBOS. First, in a static situation, the density field of heated air by a gas burner is visualized by comparing between SBOS and conventional BOS. Second, the local displacement of density field and the error displacement is estimated quantitatively when the smartphone is moving. Third, SBOS using an embossed wallpaper to visualize the density field is performed in the mobile condition. These achievements suggest that SBOS is an effective system to visualize the density field using only the smartphone, and is expected to be a useful tool such as a preliminary experiment in the laboratory and a teaching tool for general smartphone users.

Mitigation of under-expanded supersonic jet noise through stepped nozzles

An experimental investigation into noise reduction of supersonic jets through nozzle trailing-edge modifications was conducted, whereby far-field acoustic measurements were captured for two different stepped nozzles under two distinct under-expanded conditions. When compared to a baseline nozzle, results show that stepped nozzles lead to significant noise reductions at certain polar and azimuthal angles. In particular, a maximum noise reduction of 6 dB is observed for the longest stepped nozzle at a nozzle-pressure-ratio of 4 and 0° azimuthal angle. Spectral analysis shows that the noise reduction is mainly due to reduction in broadband shock associated noise and elimination of jet screech phenomenon. Abrupt changes in nozzle lip lengths of the stepped nozzles appear to disrupt acoustic feedback loop, thus resulting in screech cessation. Qualitative schlieren imaging and quantitative schlieren measurements were subsequently performed to correlate the shock structures and density gradient fields with the resulting noise components. Unlike those produced by the baseline nozzle, shock structures generated by the stepped nozzles are highly irregular and the jet plumes undergo discernible deflections. Lastly, the reduction in broadband shock associated noise is related to the lower shock strengths, as demonstrated by the density gradient profiles.

PIV/BOS synthetic image generation in variable density environments for error analysis and experiment design

We present an image generation methodology based on ray tracing that can be used to render realistic images of particle image velocimetry (PIV) and background oriented schlieren (BOS) experiments in the presence of density/refractive index gradients. This methodology enables the simulation of aero-thermodynamics experiments for experiment design, error, and uncertainty analysis. Images are generated by emanating light rays from the particles or dot pattern, and propagating them through the density gradient field and the optical elements, up to the camera sensor. The rendered images are realistic, and can replicate the features of a given experimental setup, like optical aberrations and perspective effects, which can be deliberately introduced for error analysis. We demonstrate this methodology by simulating a BOS experiment with a known density field obtained from direct numerical simulations of homogeneous buoyancy driven turbulence, and comparing the light ray displacements from ray tracing to results from BOS theory. The light ray displacements show good agreement with the reference data. This methodology provides a framework for further development of simulation tools for use in experiment design and development of image analysis tools for PIV and BOS applications. An implementation of the proposed methodology in a Python-CUDA program is made available as an open source software for researchers.

Background Oriented Schlieren (BOS) imaging of condensation from humid air on wettability-engineered surfaces

Condensation of water vapor in presence of non-condensable gas is observed in several engineering applications ranging from power generation to water harvesting. Non-intrusive optical diagnostics of the thermal and vapor concentration boundary layers on a condensing surface can offer a veritable means of predicting the condensation heat transfer coefficient (CHTC), but the literature in this field is far from being well-developed. Here we perform a Schlieren imaging-based mapping of the thermogravitational density boundary layer during condensation from humid air on vertical surfaces of three different wettability, i.e., superhydrophilic, hydrophilic (control) and superhydrophobic. A lens-free, Background Oriented Schlieren (BOS) technique is used to cross-correlate the refraction of light and quantify the density gradient fields near the condenser plates for three different humidity ratios (13.5, 15.5 and 17.5 g/kg dry air) at a constant degree of subcooling (19.5 °C). CHTC measurement from condensate collection data is used to validate the non-intrusive data. The mean refraction angle and the mean density gradient near the plate are found to scale linearly with the CHTC and the condensate mass flux, respectively. The study clearly shows the potential of BOS technique in predicting the condensation heat transfer rates from humid air.

Solving the enigma of weak fluorine contacts in the solid state: a periodic DFT study of fluorinated organic crystals.

The nature and strength of weak interactions with organic fluorine in the solid state are revealed by periodic density functional theory (periodic DFT) calculations coupled with experimental data on the structure and sublimation thermodynamics of crystalline organofluorine compounds. To minimize other intermolecular interactions, several sets of crystals of perfluorinated and partially fluorinated organic molecules are considered. This allows us to establish the theoretical levels providing an adequate description of the metric and electron-density parameters of the C–F⋯F–C interactions and the sublimation enthalpy of crystalline perfluorinated compounds. A detailed comparison of the C–F⋯F–C and C–H⋯F–C interactions is performed using the relaxed molecular geometry in the studied crystals. The change in the crystalline packing of aromatic compounds during their partial fluorination points to the structure-directing role of C–H⋯F–C interactions due to the dominant electrostatic contribution to these contacts. C–H⋯F–C and C–H⋯O interactions are found to be identical in nature and comparable in energy. The factors that determine the contribution of these interactions to the crystal packing are revealed. The reliability of the results is confirmed by considering the superposition of the electrostatic potential and electron density gradient fields in the area of the investigated intermolecular interactions.

Plenoptic background oriented schlieren imaging

The combination of the background oriented schlieren (BOS) technique with the unique imaging capabilities of a plenoptic camera, termed plenoptic BOS, is introduced as a new addition to the family of schlieren techniques. Compared to conventional single camera BOS, plenoptic BOS is capable of sampling multiple lines-of-sight simultaneously. Displacements from each line-of-sight are collectively used to build a four-dimensional displacement field, which is a vector function structured similarly to the original light field captured in a raw plenoptic image. The displacement field is used to render focused BOS images, which qualitatively are narrow depth of field slices of the density gradient field. Unlike focused schlieren methods that require manually changing the focal plane during data collection, plenoptic BOS synthetically changes the focal plane position during post-processing, such that all focal planes are captured in a single snapshot. Through two different experiments, this work demonstrates that plenoptic BOS is capable of isolating narrow depth of field features, qualitatively inferring depth, and quantitatively estimating the location of disturbances in 3D space. Such results motivate future work to transition this single-camera technique towards quantitative reconstructions of 3D density fields.