Axisymmetric Field Research Articles

Background-oriented schlieren technique with vector tomography for measurement of axisymmetric pressure fields of laser-induced underwater shock waves

This study aims to overcome the problems that existing background-oriented schlieren (BOS) techniques based on computed tomography (CT-BOS) face when measuring pressure fields of laser-induced underwater shock waves. To do this, it proposes a novel BOS technique based on vector tomography (VT-BOS) of an axisymmetric target. The remarkable feature of the proposed technique is the reconstruction of an axisymmetric vector field with nonzero divergence, such as the field of a laser-induced underwater shock wave. This approach is based on an approximate relation between the projection of the axisymmetric vector field and the reconstructed vector field. For comparison, the pressure fields of underwater shock waves are measured with VT-BOS, CT-BOS, and a needle hydrophone. It is found that VT-BOS is significantly better than CT-BOS in terms of better convergence, less dependence on the spatial resolution of the acquired images, and lower computational cost. The proposed technique can be applied not only to fluid dynamical fields, but also to other axisymmetric targets in other areas, such as electromagnetics and thermodynamics.Graphical abstract

Evaluating Single‐Collector Efficiencies of Colloid Deposition From Lagrangian Simulations: Geometric Models and Particle Release Scenarios

AbstractSingle‐collector efficiency is of paramount importance in colloid filtration theory and widely used to represent the average filtration efficiency of a specific porous medium. In this work we present new formulations (unifying the stochastic and limiting trajectory cases) for efficient evaluation of the single‐collector efficiency with Lagrangian simulations in axisymmetric flow field for two commonly adopted particle‐releasing scenarios: from the envelope boundary (Happel sphere‐in‐cell) and from the upstream projected area (sphere‐in‐cylinder). We introduce an equivalent captured flux and define a capture indicator variable for each particle, to avoid calculation of local capture probability in previous studies. The single‐collector efficiencies obtained with the proposed formulations using particle trajectory simulations in axisymmetric flow field are in excellent agreement with full 3D simulation results, which validates our approach. The results are also compared with the Levich equation and published correlation equations. The differences between the two particle‐releasing scenarios are clarified and their impact on the single‐collector efficiency is quantified. The proposed axisymmetric simulation method can significantly reduce the computational time for obtaining single‐collector efficiency in comparison to 3D modeling approach, and can also be conveniently applied to studying particle transport in other practical scenarios involving axial symmetry, such as constricted tubes, impinging jet, stagnation‐point flow.

Database-wide hazard modelling of the onset of DIII-D tearing modes with field features

The rate of onset (hazard) of tearing modes is modelled probabilistically using statistical learning algorithms. Axisymmetric energy-density equilibrium fields are taken as raw high-dimensional input features which are reduced with principal component analysis. Signal processing of non-axisymmetric magnetics fluctuation array data provides the target information from which to learn. Model selection, visualization and calibration assessment procedures are detailed. The analysis is deployed at large scale across the DIII-D tokamak database. Standard model selection criteria suggest that the energy-density post-processed feature is a better choice for modelling the onset rate compared to the non-processed equilibrium reconstruction solution. Two example applications of the learned rate function are demonstrated: (i) proximity-to-onset discharge monitoring and (ii) database analysis showing an (expected) observational global trend that the general hazard increases as a plasma performance metric increases. An important connection between the hazard function and its use as a conditional probability generator is reviewed in the Appendix.

Quantifying Radiation Belt Electron Loss Processes at L

We present a comprehensive analysis of the processes that lead to quasilinear pitch-angle-scattering loss of electrons from the L<4 region of the Earth's inner magnetosphere during geomagnetically quiet times. We consider scattering via Coulomb collisions, hiss waves, lightning-generated whistler (LGW) waves, waves from ground-based very-low-frequency (VLF) transmitters, and electromagnetic ion cyclotron (EMIC) waves. The amplitude, frequency, and wave normal angle spectra of these waves are parameterized with empirical wave models, which are then used to compute pitch-angle diffusion coefficients. From these coefficients, we estimate the decay timescales, or lifetimes, of 30keV to 4MeV electrons and compare the results with timescales obtained from in-situ observations. We demonstrate good quantitative agreement between the two over most of the L and energy range under investigation. Our analysis suggests that the electron decay timescales are very sensitive to the choice of plasmaspheric density model. At L<2, where our theoretical lifetimes do not agree well with the observations, we show that including Coulomb energy drag (ionization energy loss) in our calculations significantly improves the quantitative agreement with the observed decay timescales. We also use an accurate model of the geomagnetic field to provide an estimate of the effect that the drift-loss cone has on the theoretically calculated electron lifetimes, which are usually obtained using an axisymmetric dipole field.

Numerical simulation of DC casting of large-size rare earth magnesium alloy ingot under low-frequency electromagnetic field

For studying the changes of macro-physical field in the casting process of large-scale rare earth magnesium alloy, through the numerical simulation method, a two-dimensional axisymmetric multi-physical field coupling model was established by using the multi-physical simulation software COMSOL Multiphysics. The changes of temperature field, flow field, Lorentz force, and liquid fraction of large-size rare earth magnesium alloy with diameter of 750 mm under different electromagnetic parameters (magnetic field frequency and current intensity) in steady state of direct-chill (DC) casting were studied. The results reveal that using a magnetic field can reduce the temperature gradient and greatly accelerate the melt flow, the depth of the sump is reduced by about 50 mm. As the current intensity rises, the flow rate in the melt becomes accelerated, the sump depth becomes shallower, while the melt area with a liquid fraction of 0.5 to 0.63 increases. The Lorentz force rises as the magnetic field frequency increases, but the skin depth of the magnetic field decreases from 64.9 to 36.4 mm.

Magnetoconvection in a rotating spherical shell in the presence of a uniform axial magnetic field

ABSTRACT We report simulations of thermal convection and magnetic-field generation in a rapidly-rotating spherical shell, in the presence of a uniform axial magnetic field of variable strength. We consider the effect of the imposed field on the critical parameters (Rayleigh number, azimuthal wavenumber and propagation frequency) for the onset of convection, and on the relative importance of Coriolis, buoyancy and Lorentz forces in the resulting solutions. The imposed field strength must be of order one (corresponding to an Elsasser number of unity) to observe significant modifications of the flow; in this case, all the critical parameters are reduced, an effect that is more pronounced at small Ekman numbers. Beyond onset, we study the variations of the structure and properties of the magnetically-modified convective flows with increasing Rayleigh numbers. In particular, we note the weak relative kinetic helicity, the rapid breakdown of the columnarity, and the enhanced heat transport efficiency of the flows obtained for imposed field strengths of order one. Furthermore, magnetic and thermal winds drive a significant zonal flow in this case, which is not present with no imposed field or with stronger imposed fields. The mechanisms for magnetic field generation (particularly the lengthscales involved in the axisymmetric field production) vary with the strength of the imposed field, with three distinct regimes being observed for weak, order one, and stronger imposed fields. In the last two cases, the induced magnetic field reinforces the imposed field, even exceeding its strength for large Rayleigh numbers, which suggests that magnetically-modified flows might be able to produce large-scale self-sustained magnetic field. These magnetoconvection calculations are relevant to planets orbiting magnetically active hosts, and also help to elucidate the mechanisms for field generation in a strong-field regime.

Visualization of hydrogen jet using deformation of the laser beam profile

Hydrogen has the widest flammable range, the fastest flame propagation speed, and the lowest ignition energy, so its safety needs special attention before the wide application of hydrogen energy. The main objective of this work is to propose a new method to evaluate hydrogen jet pressure by using a Helium–Neon laser through the jet. A mathematical model was proposed, which describes the deformation of the laser beam profile passing through an axisymmetric circular hydrogen jet pressure flow field in detail. This research attempts to apply the expression of density Gaussian distribution, ideal gas equation, and Gladstone Dale equation to disclose the deformation of laser beam profile under different outlet conditions. The experimental uncertainty is about 3 × 10−3. A non-contact optical experimental system is established to visually measure the density gradient distribution of the gas jet. Our findings show that the hydrogen jet can be regarded as a gas-phase lens, and the deformation of the laser beam profile in the horizontal direction increases linearly with jet pressure. Finally, the preliminary results of calculations of the spot area with the theoretical model were presented and compared with the images of the laser beam profile passing through the jet in the experiment. The theoretical model gave similar results and the overall agreement with the experiment was satisfactory. Our technology exhibits high sensitivity in the measurement of hydrogen leakage pressure, providing a theoretical basis for non-contact, non-damaged, high-response, and high-sensitivity detection of hydrogen leakage.

Three-dimensional rapid visualization of flame temperature field via compression and noise reduction of light field imaging

Light field (LF) imaging, as an emerging temperature measurement technique, can simultaneously capture the intensity and direction information of radiation in the combustion flow field and has recently attracted extensive attention. However, the dense sampling of the LF introduces a large amount of redundant information and makes the plenoptic data susceptible to noise pollution, which can significantly affect the performance of 3D temperature field reconstruction. To address this problem, a novel approach, i.e., light field compression and noise reduction (LFCNR), is proposed to extract the main features of the projection matrix and separate the noise-related and signal-related subspaces of the plenoptic data, thus improving the reconstruction accuracy and efficiency. The performance of the proposed LFCNR method and the effect of the hyper-parameters on reconstructed quality are investigated thoroughly. It has been observed that the proposed LFCNR-based method for 3D temperature tomography imaging has higher accuracy, more efficiency, and better anti-noise ability compared to the well-established method. LFCNR can improve the reconstructed temperature accuracy by approximately 20%, and the calculation time is shortened to 10%. Priori smoothing is introduced into the optimization objective to constrain the fluctuation of the retrieval temperature, called LFCNR-PS, which can further improve the reconstructed accuracy of axisymmetric and non-axisymmetric fields about 1.79% and 1.23%. Furthermore, experiments of the LFCNR-based method are carried out to reconstruct the 3D temperature field of ethylene diffusion flames. The reconstructed temperature slices demonstrate that the flame topology can be clearly and rapidly identified at different depths. The efficiency and robustness of the proposed method can be applied to the harsh environment, which will be beneficial to the reliable operation of thermal equipment, the study of turbulent chemical reaction mechanisms, fuel utilization, and the optimization design of the engine combustion chamber.

Bistability in orbital trajectories of a chiral self-propelled particle interacting with an external field.

In this paper, the dynamics of a self-propelled stochastic particle under the influence of an axisymmetric light field is experimentally studied. The particle under consideration has the main characteristic of carrying a light sensor in an eccentric location. For the chosen experimental conditions, the emerging trajectories are orbital, and, more interestingly, they suggest the existence of bistability. A mathematical model incorporating the key experimental components is introduced. By means of numerical simulations and theoretical analysis, it is found that, in addition to the orbiting behavior, the sensor location could produce trapped or diffusive behaviors. Furthermore, the study reveals that stochastic perturbation and the eccentric location of the sensor are responsible for inducing bistability in the orbital trajectories, supporting experimental observations.

Background Oriented Schlieren Technique With Reconstruction Of Three-Dimensional Vector Fields For Pressure Measurement Of Laser Induced Underwater Shock Waves

We propose a novel reconstruction of the three-dimensional vector field (VR) of an axisymmetric target to overcome the problems that existing background-oriented schlieren (BOS) techniques based on reconstruction of three-dimensional scalar field (SR-BOS). This approach is based on an approximate relation between the projection of the axisymmetric vector field and the reconstructed vector field. The remarkable feature of the proposed technique is the reconstruction of an axisymmetric vector field with nonzero divergence, such as the field of a laser-induced underwater shock wave. Reconstruction of 3D vector fields, such as conventional vector tomography, is usually used in the field of electromagnetics with vector fields of zero divergence, and its application to fluid phenomena has been di fficult. We have successfully applied this technique to BOS (VR-BOS) and measured the pressure fields of underwater shock waves. Using the experimental data and previous research data, the superiority of VR-BOS was clarified by comparing the measurement results of SR-BOS and VR-BOS, for example, measurement accuracy, in better convergence, less dependence on the spatial resolution of the acquired images, and lower computational cost. In particular, the fact that the measurement accuracy of VR-BOS is almost independent of resolution is expected to expand the maximum pressure values that can be measured by the BOS technique. We also used synthetic data to investigate the effect of noise on VR-BOS. If the synthetic displacement contains noise, the noise is amplified in the vicinity of the axisymmetry axis in the reconstruction distribution calculated by VT. If the distance from the axisymmetry axis is more than 1/4 of the measurement range, the measurement accuracy of the reconstructed distribution can be sufficiently guaranteed. This proposed technique can be applied fluid dynamical fields, as well as other axisymmetric targets with vector reconstruction fields in other areas, such as electromagnetics and material mechanism.

Meshed axisymmetric flame simulation and temperature reconstruction using light field camera

Axisymmetric flames are widely used in research on flame combustion mechanisms and mass and heat transfer because of their simple structure and applicability to complex reactions and transfer calculations. A new optical diagnostic method named light field camera has been validated as applicable for online detection of the temperature field of an axisymmetric flame. Reconstruction algorithms can be used to estimate the distribution of the flame temperature from the light field images and validated by setting a known distribution of temperature and radiative properties. In the present study, a model of meshed axisymmetric flame light field imaging was put forward. The complicated distribution of temperature and radiative properties were considered in the model after validation using two absorption coefficients arranged at different region. An axisymmetric laminar coflow diffusion ethylene flame was modeled to generate input data. Then, the Lucy–Richardson and nearest neighbor filtering deconvolution algorithms were applied to the refocused light field images for sectional reconstruction of the temperature field. Under the condition of high temperature and soot generated from ethylene flame, the obtained reconstructed temperature was comparable to the input temperature from 1400 K to 2000 K, within the detectable radiative intensity range of the light field camera.

Discretization Analysis of Fluid Mechanical Flow Field Grid

The design basis of the performance of special industrial fluid machinery is to obtain the distribution of air flow parameters through the solution of flow field. In the numerical solution of flow field, the discretization of computational domain grid is the key factor affecting the calculation results. In this paper, the two-dimensional axisymmetric flow field analysis model were adopted. By establishing the software interface and automatic execution script file, the grid discreteness analysis process was established. The Richardson extrapolation method was used to infer the accurate solution of the flow field, and the grid independence and convergence analysis and the grid spacing analysis of the first layer of the wall were carried out. The results showed that the numerical results gradually approached the exact solution with the increase of the total number of grids, but the correlation between the numerical results and the total number of grids decreased in this process; By changing the normal spacing of the first layer of grid on each wall and making mathematical statistical analysis, the sensitive area of grid spacing could be determined. The method established in this paper could significantly improve the overall efficiency of the fluid mechanical mesh discreteness analysis and flow field analysis, and recommended the configuration of the optimal mesh discretization mode for the subsequent simulation calculation, which was conducive to further improve the calculation accuracy and efficiency of the flow field.

Topological and hydrodynamic analyses of solar thermochemical reactors for aerodynamic-aided window protection

ABSTRACT Particles and condensing vapors contribute to the contamination of optical components of solar thermochemical reactors including windows and secondary concentrators and result in severe reactor performance deterioration. We propose an impinging-jet solar reactor in a distinctive topology to enhance aerodynamic-aided window protection. The vector fields on the two-dimensional inner surfaces of the impinging-jet reactor and four conventional reactors are analyzed for the first time using differential topology. The topological analysis demonstrates that the application of an impinging jet in the reactor leads to the prevention of the stagnation point in the vicinity of the window, which is inevitable in any axisymmetric flow field of the conventional reactors. The transient two-dimensional flow fields of all reactors are numerically investigated using the finite volume method to understand the effects of the reactor geometry, aspect ratio, and sweep gas mass flow rate on the window protection performance characterized by the contaminant residence time and peak volumetric concentration near the window. The impinging-jet reactors with aspect ratios of one and two are found to be the most effective designs in aerodynamic-aided window protection among all investigated configurations.

Thermoelastic State of a Piecewise Inhomogeneous Orthotropic Thermosensitive Cylinder

We determine the thermoelastic state caused by a plane axisymmetric temperature field and surface loads in a multilayer hollow orthotropic cylinder with regard for the dependences of physical and mechanical characteristics on the coordinates and temperature. The thermoelasticity problem is reduced to solving systems of integral-algebraic equations for radial displacements. These systems are obtained from the integral representation of the solution of the corresponding problem for an ordinary differential equation with generalized derivatives. In this case, we use the Green function of the elasticity problem for a multilayered orthotropic cylinder with constant physical and mechanical characteristics of its layers. The solutions of the obtained systems are found by the method of successive approximations (restricted to the first approximation). The numerical investigations performed for a three-layer orthotropic cylinder with temperature-dependent physical and mechanical characteristics of layers reveal high accuracy of evaluation of the displacements and stresses.

Waves in the Earth's core. II. Magneto–Coriolis modes

We investigate the normal modes of a rapidly rotating, electrically conducting, inviscid fluid sphere in the presence of a background magnetic field. Neglecting the fast modes that are essentially slightly modified inertial waves, we focus on the slower branch of modes traditionally called magneto–Coriolis (MC) modes. We focus on the magnetostrophic limit, an approximation that neglects the fluid inertia for these modes by setting the magnetic Rossby number E η equal to zero, converting the momentum equation from a prognostic to a diagnostic equation. In contrast to a local analysis and contrary to previous assertions, this inertialess-inviscid double limit is perfectly well behaved and shows that E η → 0 and E η = 0 are essentially identical. With applied axisymmetric background fields, we find the modes are critically damped, with decay rates greater than or equal to the eigenfrequency, in contrast to the local theory. We find evidence for both eastward and westward propagating columnar modes, in contradiction of commonly perceived wisdom. The results bode well for numerical time integrations based on the magnetostrophic approximation, which is highly suited to the core of the Earth and holds the potential for more realistic solutions of the dynamo equations.

Технологические режимы прошивки-калибровки при локальном нагреве

The basic relations for calculating the modes of mold punching a cylindrical hollow billet under viscoplastic conditions are given. The energy calculation method is used in relation to the axisymmetric field of displacement velocities. Theoretical calculations of the work material processing pressure and damage rate are performed.

A new approach for the reconstruction of axisymmetric refractive index fields from background-oriented schlieren measurements

Background-oriented schlieren (BOS) is an optical visualization technique that reconstructs a whole-field flow based on its density gradient. Thanks to the cost-effectiveness of its optical setup and its unlimited field of view, BOS has become an attractive technique for laboratory and large-scale experiments. In BOS, the reconstruction of the refractive index field involves various mathematical calculations, which depend on the flow geometry. In this context, the present study presents a new method for the reconstruction of three-dimensional axisymmetric refractive index fields. The proposed method takes advantage of the bi-sensitivity quality of BOS to gain more accuracy in the reconstructed fields. We demonstrate the method’s precision and robustness against experimental noise throughout a synthetic axisymmetric refraction index field. The application of this new approach is not restricted to the BOS technique but can be extended to several other measurement techniques such as moiré deflectometry, laser speckle photography, and rainbow schlieren.

Zeeman-Doppler imaging of five young solar-type stars

Context. The magnetic activity of the Sun changes with the solar cycle. Similar cycles are found in other stars as well, but their details are not known to a similar degree. Characterising stellar magnetic cycles is important for the understanding of the stellar and solar dynamos that are driving the magnetic activity. Aims. We present spectropolarimetric observations of five young, solar-type stars and compare them to previous observations, with the aim to identify and characterise stellar equivalents of the solar cycle. Methods. We use Zeeman-Doppler imaging (ZDI) to map the surface magnetic field and brightness of our targets. The magnetic field is decomposed into spherical harmonic expansions, from which we report the strengths of the axisymmetric versus non-axisymmetric and poloidal versus toroidal components, and we compare them to the Rossby numbers of the stars. Results. We present five new ZDI maps of young, solar-type stars from December 2017. Of special interest is the case of V1358 Ori, which had gone through a polarity reversal between our observations and earlier ones. A less evident polarity reversal might also have occurred in HD 35296. There is a preference for a more axisymmetric field, and possibly a more toroidal field, for the more active stars with lower Rossby number, but a larger sample should be studied to draw any strong conclusions from this. For most of the individual stars, the amounts of toroidal and poloidal field have stayed on levels similar to those in earlier observations. Conclusions. We find evidence for a magnetic polarity reversal having occurred in V1358 Ori. An interesting target for future observations is χ1 Ori, which may have a short magnetic cycle of a few years. The correlation between the brightness maps and the magnetic field is mostly poor, which could indicate the presence of small-scale magnetic features of different polarities that cancel one another out and are thus not resolved in our maps.

Waves in the Earth’s core. I. Mildly diffusive torsional oscillations

Axisymmetric oscillations of fluid in a rapidly rotating whole sphere immersed in a magnetic field can be supported by the elastic tension of the magnetic field lines. This special class of Alfvén waves is largely geostrophic (invariant along the rotation axis) and describes a set of normal modes that has been extensively studied in the ideal, lossless case, a limit in which regular solutions do not exist when the background magnetic field is axisymmetric. We study the geophysically relevant limit with parameters such that magnetic diffusion plays a realistic role appropriate to the Earth’s core, by choosing a Lundquist numberLuappropriately. We demonstrate for the first time the existence of normal modes in the presence of an axisymmetric background field, and obtain eigenfrequencies and decay rates that lead us to deduce quality factorsQfor these modes for two simple background fields of dipole and quadrupole parity. Two scaling behaviours ofQare seen depending on the background field and normal modes’ frequency, one scaling asLu1/2and another asLu, so that likelyQ&gt;10in the core of the Earth. A one-dimensional theory is presented that is able to capture the frequencies of oscillation quite accurately.

Numerical Solutions of the External Field Effect on the Radial Acceleration in Disk Galaxies

Abstract In modified Newtonian dynamics (MOND)-based theories, the strong equivalence principle is generically broken in an idiosyncratic manner, manifested in the action of an “external field effect” (EFE). The internal dynamics in a self-gravitating system is affected even by a constant external field. In disk galaxies, the EFE can induce warps and modify the rotational speeds. Due to the nonlinearity of MOND, it is difficult to derive analytic expressions of this important effect in a disk. Here we study numerically the EFE in two nonrelativistic Lagrangian theories of MOND: the “Aquadratic–Lagrangian” theory (AQUAL) and “Quasilinear MOND” (QUMOND). For AQUAL, we consider only the axisymmetric field configurations with the external field along the disk axis, or a spherical galaxy with test-particle orbits inclined to the external field. For the more manageable QUMOND, we also calculate the three-dimensional field configurations, with the external field inclined to the disk axis. We investigate in particular to what degree an external field modifies the quasi-flat part of rotation curves. While our QUMOND results agree well with published numerical results in QUMOND, we find that AQUAL predicts weaker EFE than published AQUAL results. However, AQUAL still predicts stronger EFE than QUMOND, which demonstrates current theoretical uncertainties. We also illustrate how the MOND prediction on the rising part of the rotation curve, in the inner parts, depends largely on disk thickness but only weakly on a plausible external field for a fixed galaxy model. Finally, we summarize our results for the outer parts as an improved, approximate analytic expression.