Calculation and prediction of divertor detachment via impurity seeding by using one-dimensional model

Achieving the detachment of divertor can help to alleviate excessive heat load and sputtering problems on the target plates,thereby extending the lifetime of divertor components for fusion devices.In order to provide a fast but relatively reliable prediction of plasma parameters along the flux tube for future device design,a one-dimensional(1D)modeling code for the operating point of impurity seeded detached divertor is developed based on Python language,which is a fluid model based on previous work(Plasma Phys.Control.Fusion 58045013(2016)).The experimental observation of the onset of divertor detachment by neon(Ne)and argon(Ar)seeding in EAST is well reproduced by using the 1D modeling code.The comparison between the 1D modeling and two-dimensional(2D)simulation by the SOLPS-ITER code for CFETR detachment operation with Ne and Ar seeding also shows that they are in good agreement.We also predict the radiative power loss and corresponding impurity concentration requirement for achieving divertor detachment via different impurity seeding under high heating power conditions in EAST and CFETR phase II by using the 1D model.Based on the predictions,the optimized parameter space for divertor detachment operation on EAST and CFETR is also determined.Such a simple but reliable 1D model can provide a reasonable parameter input for a detailed and accurate analysis by 2D or three-dimensional(3D)modeling tools through rapid parameter scanning.

Updated Lagrangian Particle Hydrodynamics (ULPH)Modeling of Natural Convection Problems

Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.

Asymptotic Behavior of the Solutions to the One-Dimensional Nonisentropic Hydrodynamic Model for Semiconductors

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.

Research on Hydrodynamics Model Test for Deepsea Open-Framed Remotely Operated Vehicle

This paper presents the features of newly designed hydrodynamics test for the scaled model of 4500 m deepsea open-framed remotely operated vehicle （ROV）, which is being researched and developed by Shanghai Jiao Tong University. Accurate hydrodynamics coefficients measurement and spatial modeling of ROV are significant for the maneuverability and control algorithm. The scaled model of ROV was constructed by 1：1.6. Hydrodynamics coefficients were measured through VPMM and LAHPMM towing test. And dynamics model was derived as a set of equations, describing nonlinear and coupled 5-DOF spatial motions. Rotation control motion was simulated to verify spatial model proposed. Research and application of hydrodynamics coefficients are expected to enable ROV to overcome uncertainty and disturbances of deepsea environment, and accomplish some more challengeable and practical missions.

Numerical simulation and experimental study of the hydrodynamics of a modeled reef located within a current

The hydrodynamic forces and flow field of artificial reef models in steady flow were numerically investigated using the RNG κ-ε turbulent model. The numerical simulation results are consistent with results observed by experimental means. A comparative study indicates that the corresponding errors of forces between calculated values and values observed in the experiment vary in the range of2.3%-11.2% and that the corresponding errors of velocities vary in the range of 1.3%-15.8%. The flow field numerical results show that upstream and vortices exist when the current passes over and through the surface of the reef model. This study suggests that the numerical simulation method can be applied to predict the forces and flow field associated with artificial reefs.

Numerical Investigation of Penetration in Ceramic/Aluminum Targets Using Smoothed Particle Hydrodynamics Method and Presenting a Modified Analytical Model

Radius of ceramic cone can largely contribute into final solution of analytic models of penetration into ceramic/metal targets.In the present research,a modified model based on radius of ceramic cone was presented for ceramic/aluminum targets.In order to investigate and evaluate accuracy of the presented analytic model,obtained results were compared against the results of the Florence’s analytic model and also against numerical modeling results.The phenomenon of impact onto ceramic/aluminum composites were modeled using smoothed particle hydrodynamics(SPH)implemented utilizing ABAQUS Software.Results indicated that,with increasing initial velocity and ceramic thickness and decreasing support layer thickness,the radius of ceramic cone decreases;this ends up increasing residual velocity of the projectile and penetration time and extending the area across which the pressure is distributed.These findings indicate enhanced levels of target energy absorption and the required energy for bending and tensioning the target.As such,it can be observed that,at the same thickness and areal density,the ceramic target has its efficiency enhanced with increasing ceramic thickness and decreasing the support layer thickness.Finally,the results revealed that the associated data with SPH confirm the modified analytic model at higher accuracy than the Florence’s analytic model.

A Vertical Two-Dimensional Model to Simulate TidalHydrodynamics in A Branched Estuary

A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The governing equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are governed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations, tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.

GLOBAL SOLUTIONS TO A HYDRODYNAMIC MODEL FOR SEMICONDUCTORS WITH VELOCITY RELAXATION

In this paper,we apply the method given in the paper“Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors”(Mathematische Annalen,2022,382:1031–1046)to study the Cauchy problem for a one dimensional inhomogeneous hydrodynamic model of two-carrier types for semiconductors with the velocity relaxation.

Numerical analysis of submarine landslides using a smoothed particle hydrodynamics depth integral model

Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Currently, commercial calculation programs such as BING have limitations in simulating underwater soil movements. All of these processes can be consistently simulated through a smoothed particle hydrodynamics（SPH） depth integrated model. The basis of the model is a control equation that was developed to take into account the effects of soil consolidation and erosion. In this work, the frictional rheological mode has been used to perform a simulation study of submarine landslides. Time-history curves of the sliding body＇s velocity, height,and length under various conditions of water depth, slope gradient, contact friction coefficient, and erosion rate are compared; the maximum sliding distance and velocity are calculated; and patterns of variation are discussed.The findings of this study can provide a reference for disaster warnings and pipeline route selection.

Numerical Study on the Effect of Gap Diffraction on the Hydrodynamic Performance of A Floating Breakwater

Two-dimensional(2D)flume experiments are useful in investigating the performances of floating breakwaters(FBs),including hydrodynamic performances,motion responses,and mooring forces.Designing a reasonable gap between the flume wall and the FBs is a critical step in 2D flume tests.However,research on the effect of the gap on the accuracy of 2D FB experimental results is scarce.To address this issue,a numerical wave tank is developed using CFD to estimate the wave-FB interaction of a moored dual-cylindrical FB,and the results are compared to experimental data from a previously published work.There is good agreement between them,indicating that the numerical model is sufficiently accurate.The numerical model is then applied to explore the effect of gap diffraction on the performance of FBs in2D experiments.It was discovered that the nondimensional gap length L_(Gap)/W_(Pool)should be smaller than 7.5%to ensure that the relative error of the transmission coefficient is smaller than 3%.The influence of the gap is also related to the entering wave properties,such as the wave height and period.

A study on the numerical prediction method for the vertical thermal structure in the Bohai Sea and the Huanghai Sea-I.One-dimensional numerical prediction model

In this paper, on the basis of the heat conduction equation without consideration of the advection and turbulence effects, one-dimensional model for describing surface sea temperature ( T1), bottom sea temperature ( Tt ) and the thickness of the upper homogeneous layer ( h ) is developed in terms of the dimensionless temperature θT and depth η and self-simulation function θT - f(η) of vertical temperature profile by means of historical temperature data.The results of trial prediction with our one-dimensional model on T, Th, h , the thickness and gradient of thermocline are satisfactory to some extent.

Reconstructing the upper ocean thermal profiles using one-dimensional numerical model

The observation data for 5 d at a station in the South China Sea is presented. After brief anMysis of the wind speed, air temperature from the ship-borne meteorological instruments and temperature and salinity profiles from the CTD （conductivity, temperature, depth recorder） data, the authors find that the CTD casts are too sparse for us to understand the diurnal evolution of the thermal structure in the upper ocean. A one-dimensional （1D） numericM code based on Mellor-Yamada turbulence closure model is used to reconstruct the upper ocean thermal structure, utilizing the atmospheric forcing data from ship-borne weather station. The simulation results show good agreement with the observational data; the significance of breaking waves is also briefly discussed. The evolution of turbulence kinetic energy （TKE） and the contribution from shear production and buoy- ancy production are discussed respectively. Finally, several possible factors which might influence the numerical results are briefly analyzed.

Research on the Application of the Radiative Transfer Model Based on Deep Neural Network in One-dimensional Variational Algorithm

As a typical physical retrieval algorithm for retrieving atmospheric parameters,one-dimensional variational(1 DVAR)algorithm is widely used in various climate and meteorological communities and enjoys an important position in the field of microwave remote sensing.Among algorithm parameters affecting the performance of the 1 DVAR algorithm,the accuracy of the microwave radiative transfer model for calculating the simulated brightness temperature is the fundamental constraint on the retrieval accuracies of the 1 DVAR algorithm for retrieving atmospheric parameters.In this study,a deep neural network(DNN)is used to describe the nonlinear relationship between atmospheric parameters and satellite-based microwave radiometer observations,and a DNN-based radiative transfer model is developed and applied to the 1 DVAR algorithm to carry out retrieval experiments of the atmospheric temperature and humidity profiles.The retrieval results of the temperature and humidity profiles from the Microwave Humidity and Temperature Sounder(MWHTS)onboard the Feng-Yun-3(FY-3)satellite show that the DNN-based radiative transfer model can obtain higher accuracy for simulating MWHTS observations than that of the operational radiative transfer model RTTOV,and also enables the 1 DVAR algorithm to obtain higher retrieval accuracies of the temperature and humidity profiles.In this study,the DNN-based radiative transfer model applied to the 1 DVAR algorithm can fundamentally improve the retrieval accuracies of atmospheric parameters,which may provide important reference for various applied studies in atmospheric sciences.

Mathematical Modeling of the Hydrodynamics of an EGSB Reactor

Generally, in the literature, the hydrodynamic behavior of an EGSB （expanded granular sludge bed） reactor is considered as a complete mix reactor. Few works study in detail the flow of such reactors. The aim of this work was to study, in detail, the hydrodynamics of an EGSB reactor and to propose a mathematical model to describe its flow. A 3.04 L reactor was used with HRT （hydraulic retention time） of 12 h, affluent flowrate of 4 mL·min^-1, and the recirculation flow rate was changed to study three different upflow velocities in the tube （6, 8 and 10 m·h^-1. The pulse input method was used, with the use of blue dextran as tracer. In order to consider the dimensional differences between the tube and the separator, the reactor was divided into two regions （tube and separator）. Initially, a model with two tubular reactors with dispersion in series was proposed and the Peclet number was adjusted for the two regions. It was observed that the region of the tube shows the behavior of a tubular reactor with high dispersion, whereas the region of the separator shows the behavior of a complete mix reactor. In order to simplify the equation, and by knowing that the concentration profile along the reactor was almost constant, a model of two CSTRs （continuous stirred tank reactors） was proposed in series and the number of reactors （N） was set. The best combination was five CSTRs, three in the tube region and two in the separator region. The presented models were equivalent and can be used to describe the hydrodynamic behavior of the EGSB reactor.

Simulation of the Influence of Ion-Produced NO_X and HO_X Radicals on the Antarctic Ozone Depletion with a One-Dimensional Model

A one -dimensional time-dependent photochemical model is used to simulate the influence of ion-produced NOx and HOx radicals on the Antarctic ozone depletion in polar night and polar spring at a latitude of 73 degrees south.Vertical transport and nitrogen-oxygen (NOx). hydrogen-oxygen (HOx) production by ionic reactions have been introduced into the model.NOx and HOx produced by precipitating ions are transported into the lower stratosphere by vertical motion and have some effects in the development of the Antarctic ozone depletion.From winter through spring the calculated ozone column decreases to 269.4 DU. However, this value is significantly higher than the total ozone observed at several Antarctic ozone stations.

3D Numerical Modeling of Hydrodynamics in the Dubai Coastal Zone

A three dimensional hydrodynamic was developed for the Dubai coastal zone including the Dubai Creek. The model is based on DHI （Danish Hydraulic Institute＇s） MIKE 3 HD （FM） modeling software. The model was subjected to extensive calibration making use of recorded water levels, currents, water temperature and salinity. A high level of accuracy in calibration was achieved as indicated by the computed statistical error parameters at all recording stations. The model results combined with field recording of water levels were used to ascertain tidal wave propagation pattern in the Dubai coastal zone and in and out of the Dubai creek. This model will be a very useful tool in assessing impacts of planned connection of artificial waterways to the Dubai Creek.

Entanglement in the Quantum Phase Transition of the Half-Integer Spin One-Dimensional Heisenberg Model

We use the Bethe’s ansatz method to study the entanglement of spinons in the quantum phase transition of half integer spin one-dimensional magnetic chains known as quantum wires. We calculate the entanglement in the limit of the number of particles . We obtain an abrupt change in the entanglement next the quantum phase transition point of the anisotropy parameter ?from the gapped phase ?to gapless phase .