Non-uniform Field Research Articles

Illumination Field Uniformity Correction by Novel Finger Arrays for Lithography Illumination System

In order to correct the integrated nonuniformity of a lithographic illumination field, a high-precision uniformity correction method for an advanced lithographic illumination system is proposed. The method adopts the opaque finger array structure and improves correction ability and accuracy by optimizing the arrangement and structure of the unit without changing the width of each unit. The correction accuracy is expressed as the percentage of the corrected integrated nonuniformity. Through theoretical analysis and simulation, it can be seen that the correction accuracy of a staggered finger array is better than 0.22%. When staggered and layered, the correction accuracy of a finger array is better than 0.14%, which is better than that of a non-layered finger array. When staggered, layered, and chamfered of each unit, the correction accuracy of the finger array structure is better than 0.12%.

Study on the uniform flow in adsorption device with perforated plate distributor

The adsorption device is widely used in the purification of impurity-containing wastewater, which is of great significance. However, the problem of non-uniform distribution of liquid in the packed bed has a large impact on the adsorption process. In the current study, CFD is used to simulate the fluid flow state during the adsorption process based on the physical modelling of the adsorption device, where the packed bed is modelled as a porous medium. By studying the effect of hole distribution, perforation rate, thickness and installation position of the perforated plate on flow uniformity and bed pressure drop, the influencing factors affecting the uniform distribution of fluid and pressure drop are discussed. Results show that changing the hole array did not have a significant effect on the fluid uniformity. When the perforation rate of the distributor is 15–29.4 %, the pressure drop is smaller and the flow distribution uniformity is better. The non-uniformity of flow field decreases first and then increases continuously with the increasing of the thickness. When the thickness of the perforated plate is between 10 and 30 mm, the overall performance is the best. Increasing the distance between the perforated plate and the inlet can reduce the impact strength of high-speed fluid on the perforated plate and improve the flow uniformity and increasing the inlet flow rate of the fluid can improve the uniformity of the flow field within a certain range, but it will increase the fluid flow loss.

Self-Oscillation of a Liquid Crystal Elastomer String-Mass System Under Constant Gradient Temperature

Abstract Recent experiments have found that a fiber-mass system can self-oscillate along the vertical direction under a non-uniform temperature field, which necessitates significant vertical space. To address the challenge in adapting to situations with limited vertical space, the current work introduces a self-oscillating string-mass system, comprising of a mass ball and a thermally responsive liquid crystal elastomer string exposed to a constant gradient temperature. By employing theoretical modeling and numerical simulation, we have identified two motion regimes of the system, namely, the static regime and the self-oscillation regime, and elucidated the mechanism of self-oscillation. Utilizing the analytical method, we derived the expressions for bifurcation point, amplitude, and frequency of the self-oscillation, and investigated the impact of system parameters on these aspects, which were verified by numerical solutions. Compared to a fiber-mass system, the string-mass system has superior stability to deal with small horizontal disturbances, can amplify its amplitude and frequency limited by small thermal deformation of material, and saves a significant amount of vertical space. Given these attributes, such self-oscillating string-mass system presents novel possibilities for designing energy harvesters, active machinery, and soft robots.

Probabilistic fatigue life prediction of notched specimens based on modified stress field intensity method under multiaxial loading

In practical engineering components, due to the existence of non-uniform stress and strain field near the notch, it brings severe challenges to fatigue life prediction when evaluating the integrity of notched components. In this study, a probabilistic fatigue life prediction model for notched specimens was established by coupling the stress field intensity (SFI) method and Weibull distribution. Firstly, the position of the dangerous point is determined by finite element calculation, and the maximum strain energy density plane through the dangerous point is defined as the critical plane. Secondly, from the perspective of 2D features, the traditional SFI method is modified based on the stress distribution on the critical plane, and a new concept of effective stress is proposed to predict the fatigue life of notched specimens by the experimental data of smooth specimens. Finally, a new non-proportional additional hardening factor is established to characterize the influence of material properties and loading path on fatigue life. The experimental data of Q345 low alloy steel and GH4169 nickel base alloy are used to compare and analyze the proposed model. The results show that the predicted life of the proposed model is in good agreement with the experimental life.

Studying the breakdown electric field in uniform and non-uniform air gaps

High voltage is essential in power grids, but it inevitably leads to high electrical stress and the associated risk of electrical discharges. Due to the complexity of the phenomena involved in electrical discharges, there are no analytical formulas for predicting the electric field strength at which they initiate, so experimental data and numerical methods are required for this purpose. According to many sources, electrical discharges can occur in air at normal pressure and temperature when the electric field strength is approximately 3 kV mm−1 or greater. This paper analyzes and discusses this threshold in detail by examining relevant electrode geometries used in high voltage applications from experimental data found in the scientific literature and using 2D finite element analysis simulations. Uniform, quasi-uniform, and non-uniform field gaps are analyzed to help students draw conclusions and gain insight into the nature of gas breakdown and the applicability of the 3 kV mm−1 threshold. The approach proposed in this paper is well suited for a practical session or group project for undergraduate or even graduate courses. Despite the important effects and design implications of electrical discharges on high voltage equipment, apparatus and systems, this topic is often not covered in sufficient detail in regular courses.

Research on tunnel vehicle fire temperature field simulation considering the latent heat of vaporization inside concrete linings

The high temperatures and non-uniform temperature fields caused by fires can lead to the rapid failure of linings, severely affecting tunnel safety. To obtain the temperature distribution of the lining under different fire conditions, simulation research is conducted by CFD technology. First, the fire resistance test of lining is simulated, and a furnace temperature simulation method based on PID control and a lining heat transfer model considering the latent heat of vaporization (LHV) are proposed. Second, the experimentally verified method is applied to a full-scale tunnel model to study the vehicle fire temperature field considering the LHV. The results show that the method based on the PID control can accurately simulate the furnace temperature. By introducing a LHV energy source, the 100 °C temperature plateau within the lining can be effectively simulated to prevent prematurely determining component failure. Compared to traditional methods, the lining-gas heat exchange boundary considering the LHV is more accurate. The temperature rise at the lining surface and rebar is slower, with maximum temperature differences of 80 K and 125 K, respectively. The aim of this research is to provide a complete temperature rise and fall process for the fire protection analysis and design of tunnel linings.

Statistical modeling of equilibrium phase transition in confined fluids

The phase transition of confined fluids in mesoporous materials deviates from that of bulk fluids due to the interactions with the surrounding heterogeneous structure. For example, adsorbed fluids in metal-organic-frameworks (MOFs) have atypical phase characteristics such as capillary condensation and higher-order phase transitions due to a strong heterogeneous field. Considering a many-body problem in the presence of a nonuniform external field, we model the host-guest and guest-guest interactions in MOFs. To solve the three-dimensional Ising model, we use the mean-field theory to approximate the guest-guest interactions and Mayer's f-functions to describe the host-guest interactions in a unit cell. Later, using Hill's theory of nanothermodynamics, we define differential thermodynamic functions to understand the distribution of intensive properties and integral thermodynamic functions to explain the phase transition in confined fluids. The investigation reveals a distinct behavior where fluids confined in larger pores undergo a discontinuous (first-order) phase transition, whereas those confined in smaller pores experience a continuous (higher-order) phase transition. Furthermore, it is observed that the free-energy barrier for low-density adsorbed fluid (LDAF) to high-density adsorbed fluid (HDAF) phase transitions is lower in confined fluids than in bulk fluids resulting in a lower condensation pressure relative to the bulk saturation pressure. Finally, the integral thermodynamic functions are succinctly presented in the form of a phase diagram, marking an initial step toward a more practical approach for understanding the phase behavior of confined fluids. Published by the American Physical Society 2024

Uniform elastic field inside an elliptical inhomogeneity with Neuber’s nonlinear stress–strain law under generalized plane strain deformations

We prove the uniformity of the in-plane and anti-plane elastic field of stresses and strains inside an incompressible nonlinear elastic elliptical inhomogeneity embedded in an infinite linear isotropic elastic matrix subjected to uniform remote in-plane and anti-plane stresses. The elastic material occupying the elliptical inhomogeneity obeys Neuber’s special nonlinear stress-strain law. The original boundary value problem is finally reduced to a single non-linear equation for the constant effective strain within the inhomogeneity, which is rigorously proved to have a unique solution. Once the non-linear equation is solved numerically, we establish the uniform elastic field within the elliptical inhomogeneity and the non-uniform elastic field in the linear elastic matrix.

Assessment of Cavitation Activity by Cavitation Noise in Different Frequency Ranges

The results of testing the spectral-acoustic cavitometer with measurement modes that differ in the frequency ranges of integration of cavitation noise are presented. For each of the H1–H4 modes, the lower integration frequency fmin is 1, 70, 180 and 300 kHz, respectively. The upper frequency is the same for all modes and is fmax = 10 MHz. Piezoelectric waveguide sensors were used as a cavitation noise receivers. The distributions of cavitation activity in non-uniform ultrasonic fields were recorded: in the volume of the ultrasonic bath (f0 = 35 kHz) and in the field of the submersible emitter (f0 = 21 kHz). The frequency range of integration was varied by changing the lower bound. It has been established that a change in the integration range within a fairly wide range does not have a noticeable qualitative effect on the result of measurements of cavitation activity, only a multiple change in the readings occurs. This conclusion was confirmed using sensors that differ in their spectral characteristics.

Free vibration and buckling behavior of porous P-type FGM and S-type FGM circular plates on elastic foundation under non-uniform thermal field

In this paper, in order to satisfied the design and manufacturing requirements of functional materials, an investigation is carried out to study the free vibration and thermal buckling characteristics of porous P- and S-type functionally graded materials (FGM) circular plates in non-uniform thermal fields in the context of first-order shear deformation theory. FGM is formed by gradient changes in metals and ceramics, the thermomechanical properties were characterized by a gradient along the thickness direction of the circular plate by a power-law function containing porosity correction. The differential equations of motion control are derived using the Hamiltonian variational principle, and the dimensionless equations of motion and boundary conditions are solved analytically by the DTM transformation procedure. The problem has been degraded and compared with the results of the existing literature to confirm its validity. In conclusion, the influence of each parameter on the dimensionless natural frequency of the porous FGM circular plate and the influence of relevant parameters on the critical temperature rise are calculated and evaluated. The porosity weakens the overall stiffness and equivalent mass of the structure, and the foundation enhances the stiffness. The DTM calculation iteration speed is fast, and the results are highly consistent. The results can be used to provide model guidance and data support for future studies of porous FGM circular plates as well as follow-up studies.

Mode analysis of spin field of thermal atomic ensembles

The spin dynamics in a thermal atomic vapor cell have been investigated thoroughly over the past decades and have proven to be successful in quantum metrology and memory owing to their long coherent time and manipulation convenience. The existing mean field analysis of spin dynamics among the whole cell is sometimes inaccurate due to the non-uniformity of the ensemble and spatial coupling of multi-physical fields interacting with the ensembles. Here we perform mode analysis onto the quasi-continuous spin field including atomic thermal motion to derive Bloch mode equations and obtain corresponding analytical solutions in diffusion regime. We demonstrate that the widely used mean field dynamics of thermal gas is a particular case in our solution, corresponding to the uniform spatial mode. This mode analysis approach offers a precise method for analyzing the dynamics of the spin ensemble in greater detail from a field perspective, enabling the effective determination of spatially non-uniform multi-physical fields coupling with the spin ensembles, which cannot be accurately analyzed by the mean field method. Furthermore, this work paves the way to address quantum noises and relaxation mechanisms associated with non-uniform fields and inter-atomic interactions, which limit further improvement of ultra-sensitive spin-based sensors.

Symmetry breaking and high-order instability of telephone cord buckles triggered by in-plane gradients of thin films

Buckle delaminations are ubiquitous in natural and artificial systems including tectonic plates, biological tissues, film structures, and two-dimensional materials. Although the formation and manipulation of various buckle delaminations have been extensively investigated in the past few decades, understanding complex buckle delamination patterns is still a challenge. Here we report on the symmetry breaking and high-order instability of telephone cord (TC) buckles triggered by in-plane gradients of thin films, including strain gradient and thickness gradient. Our experimental observations reveal the unique morphological profile of the asymmetric TC buckle due to the strain gradient. Impact of in-plane strain gradient on morphological changes of TC buckles is elucidated by simulations of buckling and delamination of the thin film. Phase diagrams for five buckle delamination morphologies, i.e., symmetric TC buckle, asymmetric TC buckle, symmetric bilateral branched buckle, asymmetric bilateral branched buckle, and unilateral branched buckle with respect to average strain and strain gradient (or thickness gradient) have been numerically established. This work could promote a better understanding of complex buckle delamination patterns with symmetry breaking and high-order instability and controllable fabrication of ordered buckle delamination patterns by regulating in-plane gradients of thin films.

Richtmyer-Meshkov instability when a shock wave encounters with a premixed flame from the burned gas

We present a linear stability analysis of the Richtmyer-Meshkov instability that develops when a shock wave reaches a sinusoidally perturbed premixed flame from behind. In the hydrodynamic regime, when acoustic contributions dominate the flame growth rate, the problem is analytically addressed by the direct integration of the sound wave equations at both sides of the flame, which are bounded by the reflected and transmitted shock waves and the flame front that acts as a contact surface in the hydrodynamic limit. The resolution involves: a hyperbolic change of variables to modify the triangular spatio-temporal domain, a transformation in the Laplace variable, the resolution of the functional equations in the frequency domain, and the final inverse Laplace transform. The latter involves a novel resolution method that is proven beneficial for long-time dynamics. Asymptotic analysis is also carried out to describe the early time and late time hydrodynamic response. The nonuniform flow field resulting from distorted oscillating shocks is characterized by acoustic, rotational, and entropic disturbances, each of which exerts a substantial influence on flame dynamics. These disturbances contribute to the intricate interplay of factors shaping the behavior of the flame in response to the nonuniform flow. In particular, the sensitivity of local flame propagation to temperature disturbances is investigated. This work contributes to a deeper understanding of Richtmyer-Meshkov instability dynamics and offers insights into instability reduction through the modulation of temperature disturbances generated by the transmitted shock.

Characteristics of Penetration Strength and Fracture Features under Nonuniform Stress Field around Borehole Surrounding Rock.

In the process of mining coal energy, the excavation of roadways and drilling causes the formation of a nonuniform stress field around the penetration holes, which will lead to a significant concentration of stress around the penetration hole. It even leads to the destruction of the surrounding rock of the penetration hole, affecting the integrity of the surrounding rock of the penetration hole. It has an effect on the strength of the rock obtained by the borehole penetration methods. Based on Abaqus software, the numerical model of borehole penetration was constructed by embedding cohesion elements between solid elements. After analyzing the simulation results obtained under different stress boundaries and penetration directions, the following findings are obtained. (1) Using the occurrence of cracks in the borehole surrounding rock as the criterion, the rock is categorized into either an elastic stress state or a plastic stress state after applying different stress boundary conditions. (2) When the borehole surrounding rock is in the elastic (plastic) stress state, the penetration strength increases (decreases) with the increase of lateral pressure coefficient. (3) In the elastic stress state, borehole surrounding rock's fracture area and crack penetration depth increase (decrease) with the increase of lateral pressure coefficient when the penetration direction is parallel (perpendicular) to the maximum principal stress. In the plastic stress state, the fracture area increases, while crack penetration depth decreases with higher lateral pressure coefficient.

Error analysis of asymptotic solution of a heavy particle motion equation in fluid flows

For weakly inertial particles subjected to volumetric forces and Stokes drag force in fluid flows, we can solve the simplified particle motion equation using the perturbation method. This method allows us to obtain a recursive formula for the nth-order correction of the asymptotic solution of particle velocity. We verified the error of the asymptotic solution under two typical flow fields: a time-varying uniform flow field with a volumetric force field and a two-dimensional non-uniform cellular flow field. In the former, the relative error of the asymptotic solution of particle velocity and position increases with the Stokes number, and we provided a quantitative analysis of the results. In the latter, we verify and analyze the asymptotic solution from two perspectives: the behavior of a single particle and the collective behaviors of many particles. For asymptotic solutions with maximum velocity and position errors of less than 5%, we select the solution with the lowest order correction and designate it as the optimal asymptotic solution. The order of the optimal asymptotic solution increases with increasing Stokes numbers and motion durations. However, in most cases, for weakly inertial particles [St ∼ O(10−3)], and the time t* ∼ O(10), the first-order asymptotic solution can achieve accuracy, where both St and t* are defined using the flow field characteristic time, Tf = 4π s. The results validate the rationale behind utilizing first-order asymptotic solutions in the fast Eulerian method for turbulent dispersion of weakly inertial particles.

Hydrogen diffusion and precipitation influenced by non-uniformly distributed stress in zirconium alloy with different textures

Hydrogen embrittlement is a crucial factor for the performance and life of zirconium alloys in nuclear industry. During service, the residual stress in the materials induces re-distribution of hydrogen, which further affects the fracture behavior. This study is dedicated to investigating the hydrogen diffusion and precipitation under the meso‑scale non-uniform deformation field. The texture effect of hydrogen behavior was examined by considering three different texture scenarios: grains with c-axis deviating from the tensile direction of random angle, 0°and 90° The cases were termed Random, T000, and T0900 respectively. The crystal plasticity finite element method (CPFEM) was employed to simulate the stress-assisted diffusion of hydrogen atoms in the polycrystalline zirconium alloy. It is determined that the T0900 case gets fewer regions with higher hydrostatic stress gradient, which helps relieve the hydrogen concentration. Compared to the T0900 texture, the interaction between soft and hard grains in the Random and T000 texture conditions results in higher stress gradient and severe hydrogen concentration. Statistical analysis was conducted and the hydrogen concentration in the three textures presents a normal distribution. T0900 gets a relatively lower overall hydrogen concentration while the T000 texture gets severe hydrogen concentration larger than 120 wt.ppm. In Random and T000 textures, hydrogen tends to accumulate at grain interior and boundaries, and continuous hydrogen concentration band forms along adjacent GBs. The T0900 scenario is free of large continuous hydrogen concentration zones, which helps reduces the adverse effects of hydrogen diffusion and precipitation. The findings of the work advance the understanding of the hydrogen behavior affected by stress heterogeneity and texture, which is the basis for the exploration of hydrogen embrittlement.

Novel rotary sliding vane expanders with small eccentricity and guide vane ports: Numerical simulation and structural parameter analysis

Expanders are key equipment in energy storage systems. Traditional sliding vane expanders have many problems, such as severe friction, non-uniform flow fields and limited flow rates. To address these issues, a novel rotating-cylinder sliding vane rotary expander (RC-SVRE) with small eccentricity and guide vane ports is proposed where the rotating-cylinder keeps a distance from the rotor to reduce friction between each other and guiding vanes are added into the intake and exhaust ports to improve flow fields. The friction loss and flow fields are predicted through theoretical analysis and numerical simulations, respectively. Compared with traditional expanders, the friction at sliding vane tips as well as that between the rotor and rotating cylinder of new RC-SVREs can be reduced by more than 98%. Among three optimized port configurations, the scheme #1 with guiding vanes and a 12 mm eccentricity obtains the lowest outlet temperature of 422.35 K and the highest isentropic efficiency of 62.27% because guiding vanes are conducive to intensifying the rotational velocity of working fluid. Among three optimized eccentricities, the scheme #4 with guiding vane and a 9 mm eccentricity obtains the lowest discharge temperature of 418.82 K and the highest flow rate of 2.365×10−2 kg/s. When comprehensively comparing all schemes, scheme #4 performs the most optimal due to the combined effects of port configurations and the smallest eccentricity. This work provides the possibility for designing novel sliding vane rotary expanders.

On the Mechanism of Electromechanical Breakdown of Solids in Strongly Nonuniform Fields in Absence of Ionization and Space Charges

On the Mechanism of Electromechanical Breakdown of Solids in Strongly Nonuniform Fields in Absence of Ionization and Space Charges

Real-time reconstruction of 3D transient non-uniform temperature field for thermal protection system based on machine learning

Reconstructed temperature field will provide critical input for monitoring the aerodynamic heating on the thermal protection system (TPS). In this paper, a novel data-driven method is proposed that allows real-time reconstruction of the 3D transient non-uniform temperature field in a TPS ceramic tile. The measured temperature is obtained by embedding sparse sensors at different layers of the tile. The spatial feature bases and time projection coefficients of the non-uniform temperature fields are extracted using the multi-parameter proper orthogonal decomposition (POD) method. The Fully-connected Long Short-Term Memory (FC-LSTM) networks are used to establish the prediction relationship between the measurements and the full-field temperatures. The problem to estimate the projection coefficients of the spatial feature bases is solved by optimizing the loss function using Adam algorithm. The numerical examples show an approximation error less than 5% and the reconstruction time-consuming less than 1 s in 3D temperature field reconstruction (TFR). The proposed reconstruction method is robust at different measurement noise levels and tested point arrangements.

Influence of cross baffle on heat transfer of nanofluid flow inside circular pipe in existence of electromagnetic field: Computational study

The usage of electromagnetic sources for the improvement of the heat transfer of ferrofluid is an efficient method in heat exchangers. In this article, the effects of the non-uniform electromagnetic field on the thermal characteristics of the nanofluid with 4 % nanoparticles of Fe3O4 streaming inside the pipe with a double cross barrier are extensively investigated. To simulate the nanofluid flow, Computational Fluid Dynamic is applied and a three-dimensional model is chosen to reveal the main effects of the electromagnetic field on the thermal efficiency of the nanofluid flow. The main novelty of this work is related to the application of the cross baffle and non-uniform magnetic field for the heat transfer improvements. The achieved results show that the existence of the electromagnetic field and cross barrier facilitates the production of the vortex inside the pipe. Therefore, the thermal layer diffusion into the stream more efficiently, and the thermal efficiency of nanofluid is improved. The influence of magnetic field intensity also shows that increasing the thermal efficiency is a direct function of magnetic source intensity.