Non-uniform Density Distribution Research Articles

Radiofrequency Diagnostic of the Decaying Plasma in the “Gigantic” Coaxial Line at the Large Plasma Device

At the large-scale Krot facility (Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences), a new device was developed for laboratory simulations of the effects of the interaction of ultrawideband electromagnetic pulses with the partially ionized atmosphere and ionosphere: the “gigantic” coaxial line with a length of 10 m and diameter of 1.4 m that is filled by the decaying plasma of the inductive discharge. Two radiofrequency methods of wave diagnostics used in the device are described, the cutoff method and the wave interferometer, which can be used to determine the electron density of the plasma in the line in a wide range of values, Ne = 107–1011 cm–3. The measurement results are compared with the values obtained by the contact diagnostic, a probe with a microwave resonator. The interferometric method is implemented taking into account the nonuniform distribution of plasma density both along and across the transmission line, which, in the working range of pulsed and continuous diagnostic signals, is an oversized waveguide. The specific features of application and the limitations of the contact (probe) and contactless (wave) methods of diagnostics are discussed, taking into account the nonuniform plasma distribution in the coaxial line and the specific features of its construction.

Effects of Contact Loss at Electrolyte/Negative Electrode Interface on Current Density Distribution in Solid-State Batteries

Cyclic volume changes and non-uniform electrodeposition/stripping, among other cycling-induced chemo-mechanical degradation of lithium metal and lithium-alloy solid state batteries, lead to contact loss between the anode and the solid electrolyte separator. Operando experiments have shown accelerated short-circuiting behavior due to contact loss in “anode-free” solid-state batteries. Simulations have shown the relationship between active area fraction and the ratio of effective conductivities in regular-shape active area configurations. Through modeling experiments using imputed active contact area of lithium-metal negative electrode batteries, we quantify the effects of this contact loss. Specifically, we (1) quantify the interfacial resistance due to this contact loss, (2) show non-uniform local current density distribution such that evaluation of what area fraction has current exceeding critical current densities is possible, and (3) show non-uniform reaction distribution at the positive electrode. This work sheds light on the tradeoffs in the design of solid state batteries within the context of contact loss.

AA5754 aluminium alloy springback reduction by post forming electro plastic effect (PFEPE)

Post Forming Electro Plastic Effect (PFEPE) has been proposed as a promising technology for mitigating forming forces and addressing springback challenges in the metal forming industry. However, several research gaps remain unaddressed for the industrialization of this technology. Firstly, there is a lack of experimental validation regarding the impact of stress reduction on springback. Secondly, the potential effect of the skin-effect on the current metrics of stress reduction needs to be evaluated. Additionally, a post-forming electrically assisted elastoplastic material model is necessary for further technology development in stamping processes. This study tackles these challenges by utilizing AA5754H22 as a reference material and integrating a comprehensive experimental campaign with finite element numerical models and empirical material model developments. Our findings confirm that PFEPE facilitates a significant reduction in springback, achieving approximately a 100% reduction. Although the skin-effect introduces non-uniform current flux density distribution, its impact at the macroscopic level is negligible for the studied thin samples. While the numerical results of springback fails to accurately replicate experimental results, the developed material model aligns well with experimental trends.

Design of Lithium Metal Anode and Other High-Capacity Alloy Anodes Solid-State Batteries in Context of Contact Loss between Anode and Solid Electrolyte Separator

Cyclic volume changes and non-uniform electrodeposition/stripping, among other cycling-induced chemo-mechanical degradation of lithium metal and lithium-alloy solid state batteries, lead to contact loss between the anode and the solid electrolyte separator[1, 2]. In-operando experiments have shown ac-celerated short-circuiting behavior due to contact loss in “anode-free” solid-state batteries[2]. Simulations reveal the relationship between active area fraction and the ratio of effective conductivities in made-up active area configurations[3]. Through modeling experiments using imputed active con-tact area of lithium-metal anode batteries, we quantify the effects of this contact loss in terms of accelerated chemo-mechanical degradation and de-creased rate capability. Specifically, we (1) quantify the interfacial resistance due to this contact loss, (2) show non-uniform local current density distribution such that local current densities could exceed lithium filament growth critical current densities, (3) show uniaxial stress inhomogeneity due to non-uniform reaction at the anode/separator interface, and (4) show non-uniform reaction distribution at the positive electrode.Besides allowing for the optimization of designs to minimize contact loss, our work sheds light on tradeoffs in the design of solid electrolyte separators.

Exploring an Electrochemical Batch Reactor for Nutrient Recovery from Wastewater: Continuum Modeling Analysis of Hydrodynamics and Tertiary Current Distribution

Advancing electrochemical reactors for nutrient recovery from wastewater requires an integration of continuum modeling alongside experimental investigations to appropriately capture transport effects on electrode performance. This continuum modeling approach facilitates the comprehensive evaluation and optimization of electrochemical reactor performance, especially with respect to intricate phenomena that may be challenging to observe solely through experimentation. The optimization process not only enhances the efficacy of existing batch reactors but also lays the foundation for designing and scaling up continuous electrochemical reactors for nutrient recovery [1].A key transport phenomenon in electrochemistry is hydrodynamics because flow dynamics around electrodes dictate mass transport magnitude and uniformity, thereby impacting current distribution, efficiency, and electrolytic energy consumption during electrolysis. Achieving homogeneous velocity fields while avoiding undesirable flow features is essential to prevent non-uniform potential and current density distributions along the electrodes, mitigating side reactions and ensuring the overall efficacy of the electrochemical processes [2].In this study, a two-dimensional model of an electrochemical batch reactor was developed using COMSOL Multiphysics software to investigate reactor hydrodynamics, electrochemical reactions, and mass transfer of species. Employing the finite element method, the model incorporated the k-epsilon turbulence model for hydrodynamics simulation, widely used in literature for simulating fluid flow and mixing behavior [3]. Electrochemical reactions at the cathode (oxygen reduction) were modeled using the Butler-Volmer equation, while the Tafel equation was applied at the anode (hydrogen evolution). Boundary conditions were a grounded counter electrode (anode) and a potential of -1.1 vs Ag/AgCl(sat.) applied to the working electrode (cathode). Fick's second law diffusion-convective equation was employed to model the mass transfer of species, including hydroxide and oxygen.Preliminary findings indicate that while impellers contribute to turbulence and affect local conditions around electrodes, the impact on the backside of the modeled electrodes is relatively weak (Figure 1). This observation may adversely influence mass transfer rates and electrochemical reactions, underscoring the significance of integrating these results with electrochemical reactions for a comprehensive understanding of reactor behavior. Additional results will be presented at the meeting.

Foam density mapping via THz imaging

Plastic foams, near-ubiquitous in everyday life and industry, show properties that depend primarily on density. Density measurement, although straightforward in principle, is not always easy. As such, while several methods are available, plastic foam industry is not yet supported with a standard technique that effectively enables to control density maps. To overcome this issue, this paper proposes Terahertz (THz) time-of-flight imaging using normal reflection measurements as a fast, relatively cheap, contactless, non-destructive and non-dangerous way to map plastic foam density, based on the expected relationship between density and refractive index. The approach is demonstrated in the case of polypropylene foams. First, the relationship between the estimated effective refractive index and the polypropylene foam density is derived by characterizing a set of carefully crafted samples having uniform density in the range 70–900 kg/m3. The obtained calibration curve subtends a linear relationship between the density and the refractive index in the range of interest. This relationship is validated against a set of test samples, whose estimated average densities are consistent with the nominal ones, with an absolute error lower than 10 kg/m3 and a percentage error on the estimate of 5%. Exploiting the calibration curve, it is possible to build quantitative images depicting the spatial distribution of the sample density. THz images are able to reveal the non-uniform density distribution of some samples, which cannot be appreciated from visual inspection. Finally, the complex spatial density pattern of a graded foam sample is characterized and quantitatively compared with the density map obtained via X-ray microscopy. The comparison confirms that the proposed THz approach successfully determines the density pattern with an accuracy and a spatial scale variability compliant with those commonly required for plastic foam density estimate.

Doppler Tomography of the Circumstellar Disk of the Be Star κ Draconis

κ Draconis is a binary system with a classical Be star as the primary component. Its emission-line spectrum consists of hydrogen lines, notably the Hα line with peak intensity ratio (V/R) variations phase-locked with the orbital period P = 61.55 days. Among binaries demonstrating the Be phenomenon, κ Dra stands out as one of a few systems with a discernible mass of its secondary component. Based on more than 200 spectra obtained in 2014–2023, we verified the physical parameters and constructed the mass function. We used part of these data obtained in 2014–2021 to investigate regions in the circumstellar disk of the primary component that emit the Hα line using the Doppler tomography method. The results show that the disk has a non-uniform density distribution with a prominent enhancement at Vy ≈ 99 km s−1 and Vx≈−6 km s−1 that corresponds to a cloud-like source of the double-peaked Hα line profile. We argue that this enhancement’s motion is responsible for the periodic variations in the Hα V/R ratio, which is synchronised in orbital phase with the radial velocity (RV) of absorption lines from the atmosphere of the primary component.

A density correction method for radioactive waste drum based on SRGS technology

The segmented ringed gamma scanning (SRGS) technique represents an advancement in segmented gamma scanning (SGS) technology used for detecting the density of radioactive waste drums, offering enhanced measurement accuracy. However, significant occur errors in the reconstruction of matrix densities due to the non-uniform distribution of density in radioactive waste and the conical beam emitted from the transmission source collimator. This paper proposes a density correction method based on dichotomy to address this issue. The efficacy of this method was verified through both simulations and experiments on a sample containing five different materials, utilizing 137Cs and 60Co for transmission and emission measurements, respectively. The experimental results demonstrate that the errors in the corrected matrix densities are reduced, falling within a margin of 16.8%. Additionally, the corrected reconstruction error of the activity is approximately 25% of the uncorrected results.

A magnetic reconnection model for the hot explosion with both ultraviolet and Hα wing emissions

Context. Ellerman bombs (EBs) with significant Hα wing emissions and ultraviolet bursts (UV bursts) with strong Si IV emissions are two kinds of small transient brightening events that occur in the low solar atmosphere. The statistical observational results indicate that about 20% of the UV bursts connect with EBs. While some promising models exist for the formation mechanism of colder EBs in conjunction with UV bursts, the topic remains an area of ongoing research and investigation. Aim. We numerically investigated the magnetic reconnection process between the emerging arch magnetic field and the lower atmospheric background magnetic field. We aim to find out if the hot UV emissions and much colder Hα wing emissions can both appear in the same reconnection process and how they are located in the reconnection region. Methods. The open-source code NIRVANA was applied to perform the 2.5D magnetohydrodynamic (MHD) simulation. We developed the related sub-codes to include the more realistic radiative cooling process for the photosphere and chromosphere and the time-dependent ionization degree of hydrogen. The initial background magnetic field is 600 G, and the emerged magnetic field in the solar atmosphere is of the same magnitude, meaning that it results in a low- β magnetic reconnection environment. We also used the radiative transfer code RH1.5D to synthesize the Si IV and Hα spectral line profiles based on the MHD simulation results. Results. Magnetic reconnection between emerged and background magnetic fields creates a thin, curved current sheet, which then leads to the formation of plasmoid instability and the nonuniform density distributions. Initially, the temperature is below 8000 K. As the current sheet becomes more vertical, denser plasmas are drained by gravity, and hotter plasmas above 20 000 K appear in regions with lower plasma density. The mix of hot tenuous and much cooler dense plasmas in the turbulent reconnection region can appear at about the same height, or even in the same plasmoid. Through the reconnection region, the synthesized Si IV emission intensity can reach above 106 erg s−1 sr−1 cm−2 Å−1 and the spectral line profile can be wider than 100 km s−1, the synthesized Hα line profile also show the similar characteristics of a typical EB. The turbulent current sheet is always in a dense plasma environment with an optical depth larger than 6.5 × 10−5 due to the emerged magnetic field pushing high-density plasmas upward. Conclusions. Our simulation results indicate that the cold EB and hot UV burst can both appear in the same reconnection process in the low chromosphere, the EB can either appear several minutes earlier than the UV burst, or they can simultaneously appear at the similar altitude in a turbulent reconnection region below the middle chromosphere.

Influence of the Skin and Proximity Effects on the Thermal Field in Flat and Trefoil Three-Phase Systems with Round Conductors

The passage of current generates heat and increases the temperature of electrical components, which affects the environment, support insulators and contacts. Knowledge of the temperature allows for the determination of important operational parameters. Time-varying currents result in a nonuniform current density distribution due to the skin and proximity effects. As a result, temperature and energy losses are increased compared to the uniform DC current density case. In this paper, these effects are considered for three-phase systems with round conductors in flat and trefoil arrangements. In the first step, the analytical expressions for current distributions are determined and used to construct the heat source density. Then, a suitable Green’s function, which allows for obtaining temperature distribution in analytical form, is used to evaluate temperature at any point throughout the conductors. The temperature differences throughout individual wires are usually negligible, whereas noticeable differences can be observed between the wires. The impact of various parameters is examined, and an approximate closed formula is derived to assess the influence of the skin and proximity effects. When the skin depth is not smaller than the wire radius, the skin effect enlarges the temperature increase by around 2% compared to the DC case. As for the proximity effect, the additional increase can be neglected if the distance is above around 10 wire radii, but for closely spaced wires, it can reach up to around 17%, depending on the arrangement and the distance between the wires. Such an additional increase may result in exceeding the permissible temperatures, which damages particular components of the system; therefore, it is important to take it into account at the design stage.

The heat transfer mechanism coupling pyrolysis and flow of hydrocarbon fuel in heated tube under supercritical pressure

The coupling mechanism between pyrolysis and fluid flow of endothermic hydrocarbon fuels plays a crucial role in the design of regenerative cooling systems for advanced aircraft. In this work, the convective heat transfer for HF-1 with pyrolysis including 18 species and 24 reactions is numerically investigated in a horizontal circle tube under supercritical pressure (5 MPa). The results show that the mechanism of small molecule products on different heat transfer phenomena varies. In the inlet heat transfer deterioration region, small molecule products exacerbate the non-uniform radial distribution of fluid density and dynamic viscosity. At the outlet position, it significantly enhances the physical heat sink of the mixture with its high thermal conductivity and specific heat capacity. Additionally, the aromatic hydrocarbons significantly contribute to non-uniformities in thermal conductivity and specific heat capacity due to the low specific heat capacity and thermal conductivity in inlet HTD region. When the radial non-uniformity coefficient of fuel conversion keeps between −0.1 and 0, the pyrolysis of the fuel enhances heat transfer, remarkably.

Numerical investigation of parameter distributions in high-temperature PEMFCs under various cooling surface temperature gradients

Non-uniform current density distribution can lead to localized hotspots, resulting in shortened lifespans of fuel cells. The temperature distributions on the bipolar plate cooling surface significantly influence various parameters within a fuel cell. This study develops a mathematical model for a high-temperature proton exchange membrane fuel cell (HT-PEMFC) to simulate its operation in four different directions of temperature gradient on the cooling surface. The distributions of membrane temperature, proton conductivity, oxygen concentration, activation loss, and current density were obtained to clarify the interaction mechanism between cooling surface temperature and these parameters in fuel cell. The results show that the membrane temperature and proton conductivity increase and the oxygen concentrations decrease with increasing cooling surface temperature. A lower temperature in the catalyst layer regions leads to a decrease in the current density. In particular, when the cooling surface temperature distribution is characterized by a temperature decrease in the upstream area with a high reactant concentration and an increase in the downstream area with a low reactant concentration, the fuel cell has an excellent current density uniformity, which reaches 92.61 % at a voltage of 0.6 V and a cooling surface temperature difference of 10 K.

High-frequency loss modeling of nanocrystalline core considering nonuniform distribution of flux density

Nanocrystalline core is widely used in the design process of high-frequency transformers and inductors due to the attractive magnetic properties of nanocrystalline material. However, the flux density distribution is nonuniform in the core because the reluctance is closely related to its geometric shape. The nonuniformity of flux density distribution may cause huge calculation errors of core losses. In this paper, Finite Element Method (FEM) is used to justify taking into account nonuniform distribution of flux density during the process of core loss calculation. An improved loss separation equation considering nonuniform distribution of flux density is proposed, and the improved equation is verified through calculating and analyzing the losses of nanocrystalline cores with different wound thicknesses. Compared with the traditional loss separation equation, the accuracy is improved, and the average error of improved equation is confined in 10%.

The effect of small perturbation on dynamics of absorptive LiBr–water solution

In a binary solution of lithium bromide–water, even a small disturbance in the initial homogeneous mass fraction at the absorbing interface has profound effects on the entire system dynamics. This perturbation of absorption disrupts the equilibrium, leading to the formation of surface tension gradients and subsequently, Marangoni flows. While these flows are relatively weak, they result in a non-uniform distribution of density within the bulk, initiating buoyant convection. We investigate complexities of the Marangoni, solutal, and buoyant convection caused by localized disruptions in uniform absorption, all in the absence of any surfactants. We have conducted numerical simulations to explore fluid dynamics and heat and mass transfer, revealing three different regimes. Initially, shortly after disturbance, variations in mass fraction and flow within the cell are primarily governed by the Marangoni force. After a finite period, the emergence of buoyant convection leads to the strong growth of velocity and significant changes in temperature and mass fraction. Finally, the destabilization of the boundary layer becomes so significant that the emission of plumes is observed. At later times, the parallel existence of two types of patterns takes on a spatially fixed form. The central part, occupied by bands (visible on space-time maps), exhibits minimal changes in time, while a periodic structure is established near the wall. This behavior can be characterized as a relaxation–oscillation mode of instability.

Hybrid simulation of instabilities in capacitively coupled RF CF4/Ar plasmas driven by a dual frequency source

Instabilities in capacitively coupled Ar/CF4 plasma discharges driven by dual frequency sources are investigated using a one-dimensional fluid/electron Monte Carlo hybrid model. Periodic oscillations of the electron density and temperature on the timescale of multiple low frequency (LF) periods are observed. As the electron density increases, an intense oscillation of the electron temperature within each high frequency (HF) period is initiated. This causes a fluctuation of the electron density and results in a discharge instability. This phenomenon is consistent with the discharge behavior observed in scenarios with single-frequency (SF) sources, as reported by Dong et al (2022 Plasma Sources Sci. Technol. 31 025006). However, unlike the SF case, plasma parameters such as the electron density, electric field, electron power absorption and ionization rate exhibit not only periodic fluctuations but also a spatial asymmetry under the influence of the dual-frequency source. This spatial asymmetry leads to a non-uniform distribution of the electron density between the electrodes, which is related to a spatially asymmetric electric field, electron heating, and ionization around a region of minimum electron density (inside the bulk). This region of minimum electron density is shifted back and forth through the entire plasma bulk from one electrode to the other within multiple LF period. The above phenomena are related to superposition effect between the instabilities and the dual-frequency source. Moreover, the time averaged electric field influences the spatio-temporal evolution of ion fluxes. The ion fluxes at the electrodes, which play an important role in etching processes, are affected by both the high and LF components of the driving voltage waveform as well as the observed instabilities. As the HF increases, the electronegativity and electron temperature are reduced and the electron density increases, resulting in a gradual disappearance of the instabilities.

An extended Hasegawa–Mima equation for nonlinear drift wave turbulence in general magnetic configurations

We propose an extended Hasegawa–Mima equation describing the evolution of nonlinear drift wave turbulence in general magnetic configurations. Such HMGM equation can be derived within the kinetic framework of guiding center motion or from a two-fluid model of an ion-electron plasma by application of a drift wave turbulence ordering that does not involve conditions on spatial derivatives of magnetic field and plasma density. The HMGM equation is therefore appropriate to describe the evolution of drift wave turbulence in strongly inhomogeneous magnetized plasmas, such as magnetospheric and stellarator plasmas, involving complex magnetic field geometries and non-uniform plasma density distributions. We find conservation laws (mass, energy, and generalized enstrophy) of the HMGM equation, study its algebraic (Hamiltonian) structure, and prove a nonlinear stability criterion for steady solutions through the energy-Casimir method. We then apply these results to describe drift waves and infer the existence of stable toroidal zonal flows with radial shear in dipole magnetic fields.

Molecular dynamics investigation of shale oil occurrence and adsorption in nanopores: Unveiling wettability and influencing factors

Shale oil, an unconventional petroleum resource, has gained significant attention in the industry. Understanding how shale oils exist in nanopores is crucial for unraveling their flow mechanisms and production prediction. The molecular dynamics simulations are conducted to explore oil occurrence and adsorption in various mineral nanopores, and the wettability and influencing factors. This study reveals a non-uniform fluid density distribution within nanopores, decreasing from the solid wall to the center. Distinct differences are observed between adsorbed and free-state oil phases. The effects of temperature, pressure, mineral type, and pore size effects on wettability, adsorption layer thickness, and molecule proportion are studied. Adsorption energy is calculated using physicochemical methods. Findings show temperature and mineral properties primarily influence shale oil wettability, with less impact from pressure. Adsorption capacity and layer thickness are affected by temperature, mineral type, and size. Octane distribution in nanopores is non-uniform, with a 1.5–1.75 nm layer on non-polar mineral walls and 0.67–1.35 nm on polar minerals. A positive correlation exists between shale oil adsorption on mineral nanopores, layer thickness, and adsorption energy. This study enhances our understanding of oil behavior in nanopores of shale oil reservoirs.

An investigation of the effects of porosity and N-defects of 2D CxNy membranes on the wettability behavior and separation capability of water and oil mixtures

In this study, three different structures of two dimentional (2D) CxNy were investigated experimentally and theoretically to determine their wettability behavior and separation capability based on their porosity, surface defect structure, and surface energy. The C3N, C1N1, and graphitic-C3N4 (g-C3N4) were synthesized and coated on stainless steel mesh. Wettability characteristics of the C3N, C1N1, and g-C3N4-coated mesh showed hydrophobic/oleophilic, hydrophilic/ underwater super-oleophobic, and super-hydrophilic/underwater super-oleophobic, respectively. The experimental results showed that the best performance of C3N with the highest surface area was obsereved in oil removal and the best performance of g-C3N4 with the highest pyridinic-N/pyrrolic-N XPS peak-area ratio was observed in water removal. Since electrostatic interaction plays an important role in water-removing state, increasing the number of pyridinic-N increases the electrostatic potential of water with the surface during water removal. Based on surface energy calculations, the highest dispersed surface energy is found in C3N, whereas the strongest polar component is found in g-C3N4, confirming their hydrophobic and hydrophilic wettability, respectively. Density functional theory investigations confirmed the higher hydrophilicity of g-C3N4 due to its non-uniform electron density distribution. The adsorption energies of water and decalin molecules are proportional to the amounts of charge transfer between porous substrates and adsorbents.

Energy and Mass Matching Characteristics of the Heat-Absorbing Side of the Ammonia Energy Storage System under Nonuniform Energy Flow Density.

Ammonia thermochemical energy storage is based on a reversible reaction and realizes energy storage and utilization by absorbing and releasing heat. Under different energy flow densities, the efficiency of an ammonia reactor composed of multiple ammonia reaction tubes is different. Based on the coupling model of light, heat, and chemical energy of an ammonia decomposition reaction system, taking a 20 MW solar thermal power plant as the research object, this paper proposes a new model of ammonia energy storage system, which places the ammonia decomposition side in a low-pressure environment and the ammonia synthesis side in a high-pressure environment. The effects of different inlet temperatures, inlet flow rates, flow distribution, and energy flow density distribution on the ammonia energy storage system were studied. The results show that the increase of inlet temperature and the decrease of inlet flow rate are beneficial to the improvement of thermal efficiency and exergy efficiency of the system to a certain extent, but when the inlet temperature increases or the inlet flow rate decreases to a certain extent, the efficiency of the system will decline. Under the condition of nonuniform energy flow density and nonuniform inlet flow distribution, more ideal system thermal efficiency and exergy efficiency can be obtained.

Modelling of ultrasonic vibration-assisted forming considering the distribution of ultrasonic field with structure deformation

Ultrasonic vibration-assisted (UVA) forming is typically used to promote the forming quality of complex structures due to the acoustic-plastic effect. Ultrasonic vibration (UV) is always applied via the contact of tools with the structure surface; thus a distribution of ultrasonic field exists owing to the propagation and attenuation of ultrasonic waves, which may vary with structural deformation. This makes the prediction and control of ultrasonic effect extremely difficult in achieving high forming quality. To develop a new coupling model considering the interaction between ultrasonic field and deformation field, UVA tensile experiments of superalloy sheet were performed first. The experimental results demonstrated that UV had a local effect on the tensile specimen, resulting in non-uniform distribution of temperature, strain and dislocation density. During the modelling, the intensity of ultrasonic field was quantified by acoustic energy density, which can be calculated using vibration velocity. A dislocation-based constitutive relation was also established, in which ultrasonic-related functions were introduced to reflect the effect of ultrasonic field on structural deformation. Then, a sequential coupling modelling method was proposed. Through the cyclic calculation of ultrasonic field and deformation field, the simulation of UVA forming considering the distribution of ultrasonic field with structure deformation was realised. With the coupling model, the non-uniform distribution of deformation accompanied by a non-uniform ultrasonic field during UVA forming was revealed. When applied to a complex W-bending process, the targeted softening effect on the W-bending specimen was precisely predicted. The coupling model is expected to lay a foundation for the optimisation and control of the UVA forming process.