Numerical Study of Tokamak Equilibrium with Toroidal Flow on EAST

The effect of the toroidal flow on the equilibrium of tokamak plasmas is a sensitive point for high performance plasma and its precise control. In this paper the effect is studied numerically using the EFIT （Equilibrium Fitting） code on EAST （Experimental Advanced Superconducting Tokamak）. Firstly, the numerical calculation exhibits a clear outward shift of pressure contour from the magnetic surfaces in the plasma core and the shift grows with the increase of the toroidal velocity. The peak shift of 8% is observed when the ratio between the plasma velocity and the Alfvdn speed equals to 0.15. Secondly, it is shown that the magnetic surfaces shift outwards from those without flow. With a certain plasma current the safety factor on the magnetic axis decreases as the plasma flow velocity increases. The magnetic shear increases about 10% on the plasma boundary compared with the case without flow.

A General Thermal Equilibrium Discharge Flow Model

Based on isentropic flow and thermal equilibrium assumptions, a model was derived to calculate discharge flow rate, which unified the rules of room temperature water discharge, high temperature and high pressure water discharge, two-phase critical flow, saturated steam and superheated steam critical flow, and gave a method to calculate critical condition. Because of the influence of friction, the entropy is increased in the actual discharge process, and the discharge flow rate in thermal equilibrium condition can be obtained by the original model multiplied by an appropriate correction coefficient. The model calculated results agreed well with the experiment data of long nozzle critical flow.

Grain Composition and Erosive Equilibrium of Debris Flows

Debris flows consist of grains of various sizes ranging from 10^(-6) m ～1 m. Field observations in the Jiangjia Gully (JJG) and other sites throughout China indicate that the grain size distribution of sediment in debris flows can be characterized by an exponential function fit to the cumulative distribution. The exponent value for the function varies by location and may be useful in distinguishing between debris flows from different valleys. For example, minimum values and ranges of the exponent are associated with the high frequency of debris flows in the JJG. Furthermore, the distribution presents piecewise fractality (i.e. scaling laws hold in various ranges of the grain size) and we propose that the fractal structure determines the matrix and that the fractal dimension plays a crucial role in material exchange between a debris flow and the substrate it flows over. Finally, the empirical data support an exponential relation between grain composition and non-dimensional shear stress for the critical state of the channel. Overall we propose a material-determinism approach to studying debris flows which contrasts with the enviro-determinism that has dominated much recent work in this field.

Effect of shear equilibrium flow in Tokamak plasma on resistive wall modes

A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes （RWMs）. The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.

Three-Dimensional Structure of Non-Equilibrium Homogeneous Condensation Flow in a Supersonic Rectangular Nozzle

Numerical simulations have been carried out for a supersonic three-dimensional rectangular arc nozzle, where a secondary flow toward the center of the curvature occurs due to the shape of the nozzle. It is known that secondary flow causes longitudinal vortices to form near the wall of the nozzle corner, making the nozzle outlet flow unstable and induces loss of transport energy. When the working fluid is a condensable gas with relatively large latent heat such as moist air or steam, rapid accelerated expansion in the nozzle causes non-equilibrium condensation due to supersaturation. After the release of latent heat during phase transition, nozzle flow continues expanding at an equilibrium saturation condition. In the absence of foreign particles, e.g. ions or dust particles, condensation nuclei are formed in the gas itself causing non-equilibrium homogeneous condensation. Supersonic nozzle flow properties vary considerably due to the occurrence of condensation phenomenon. The objective of this study is to investigate the effect of non-equilibrium homogeneous condensation on the longitudinal vortices which form in the range close to the corner of rectangular arc nozzle numerically.

Generalization of Solovev's approach to finding equilibrium solutions for axisymmetric plasmas with flow

Solovev's approach of finding equilibrium solutions was found to be extremely useful for generating a library of linear-superposable equilibria for the purpose of shaping studies.This set of solutions was subsequently expanded to include the vacuum solutions of Zheng,Wootton and Solano,resulting in a set of functions{SOLOVEV_ZWS}that were usually used for all toroidally symmetric plasmas,commonly recognized as being able to accommodate any desired plasma shapes(complete-shaping capability).The possibility of extending the Solovev approach to toroidal equilibria with a general plasma flow is examined theoretically.We found that the only meaningful extension is to plasmas with a pure toroidal rotation and with a constant Mach number.We also show that the simplification ansatz made to the current profiles,which was the basis of the Solovev approach,should be applied more systematically to include an internal boundary condition at the magnetic axis;resulting in a modified and more useful set{SOLOVEV_ZWSm}.Explicit expressions of functions in this set are given for equilibria with a quasi-constant current density profile,with a toroidal flow at a constant Mach number and with specific heat capacity 1.The properties of{SOLOVEV_ZWSm}are studied analytically.Numerical examples of achievable equilibria are demonstrated.Although the shaping capability of the set{SOLOVE_ZWSm}is quite extensive,it nevertheless still does not have complete shaping capability,particularly for plasmas with negative curvature points on the plasma boundary such as the doublets or indented bean shaped tokamaks.

Axisymmetric Toroidal Equilibrium with Sheared Toroidal Flows

Problem of the axisymmetric toroidal equilibrium with pure sheared toroidal flow isinvolved. For standard tokamak equilibrium, general approximate solutions are analytically pur-sued for arbitrary current profile and non-circular cross-section. Equilibrium properties includingthe fiow-induced density asymmetry are analyzed.

On transition of type V interaction in double-wedge flow with non-equilibrium effects

The transition between regular reflection （RR） and Mach reflection （MR） of type V shock-shock interaction on a double-wedge geometry with high temperature non-equilibrium effects is investigated by extended shock-polar method and numerical simulation. First, the critical angles of transition from detachment criterion and yon Neumann criterion are determined by the extended shock-polar method considering the non-equilibrium effects. Then wave patterns and the transition process are numerically obtained. Results of the critical transition angles from shock-polar calculation and numerical simulation show evident disagreement, indicating transition mechanism between RR and MR of type V interaction is changed. By comparing with the frozen counterpart, it is also found that non-equilibrium effects lead to a larger critical wedge angle and a larger hysteresis interval.

A probe heat flow value of the East China Sea shelf

Bottom temperature variation (BTV) is a serious problem in determining the thermal gra- dient and heat flow of the sediments in shallow seas. The water depth of the East China Sea shelf is mostly below 150m, and the heat flow measurement is strongly affected by BTV. Following a statistical algorithm, we rechecked the temperature and thermal conductivity data of the cruises KX90-1 and KX91-1, carried out by a cooperation program of China and Japan, and calculate the heat flow in a site without long-term temperature record. The calculated heat flow in the site was 58.6±3.6 mW/m2, being just within the range of the drill heat flow value of East China Sea shelf. The inversed amplitude spectrum of BTV has a peak in frequency of 1/10 per year, and the annual component is also an important part. Comparison with two lakes of Lake Greifensee and Lac Leman (i.e. Lake Geneva), which are in different water depth, revealed that with increasing water depth, the peak of amplitude spectrum moved towards low frequency components. The heat flow values calculated in this paper and from petroleum bore hole in East China Sea shelf are much more close to that in southeast China than in Okinawa Trough.

An Algorithm for Traffic Equilibrium Flow with Capacity Constraints of Arcs

In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on arcs. Using an example, we illustrate the application of the algorithm and show that Beckmann’s formula is a sufficient condition only, not a necessary condition, for traffic equilibrium with capacity constraints of arcs.

Explicit Large Time Stepping with Third-Order Exponential Time Differencing Scheme for Hypersonic Chemical Non-Equilibrium Flow

In this paper, a third-order exponential time differencing scheme, named ETDRK3, was investigated for large time stepping in the computation of hypersonic non-equilibrium flow. The second-order Harten-TVD scheme was used for the spatial discretization. The efficient implementation of the scheme with diagonalization of Jacobin matrix was established and carried out for the semi-cylindrical around flow. Current observations showed that the numerical results were in good agreement with those obtained by the classical explicit three-stage Runge-Kutta scheme (RK3) and implicit LU scheme. Efficiency assessments promised the effectiveness of the ETDRK3 scheme. The rationality of the application of this scheme was proved by its preferable accuracy and efficiency.

DISTRIBUTION OF VIRIOPLANKTON IN THE KUROSHIO CURRENT AND THE ADJACENT AREA IN THE EAST CHINA SEA AS DETERMINED BY FLOW CYTOMETRY

Distribution of one group of marine viral particles along the Kuroshio Current and theadjacent area was investigated in June, 1998 using flow cytometry for the first time. The position of thisgroup of virioplankton in flow cytometry plots coincided with the position of the V-I group reported byMarie et al. （1999）. Abundances of this group of virioplankton in the surface water ranged from 3.4×105 to 2. 3×106 ml-1 in the investigated area. High abundance occurred in the shelf water and low abun-

Research on passenger flow control at metro transfer stations based on real-time flow calculation of streamlines

Purpose – The volume of passenger traffic at metro transfer stations serves as a pivotal metric for theorchestration of crowd flow management. Given the intricacies of crowd dynamics within these stations andthe recurrent instances of substantial passenger influxes, a methodology predicated on stochastic processesand the principle of user equilibrium is introduced to facilitate real-time traffic flow estimation within transferstation streamlines.Design/methodology/approach – The synthesis of stochastic process theory with streamline analysisengenders a probabilistic model of intra-station pedestrian traffic dynamics. Leveraging real-time passengerflow data procured from monitoring systems within the transfer station, a gradient descent optimizationtechnique is employed to minimize the cost function, thereby deducing the dynamic distribution of categorizedpassenger flows. Subsequently, adhering to the tenets of user equilibrium, the Frank–Wolfe algorithm isimplemented to allocate the intra-station categorized passenger flows across various streamlines, ascertainingthe traffic volume for each.Findings – Utilizing the Xiaozhai Station of the Xi’an Metro as a case study, the Anylogic simulation softwareis engaged to emulate the intra-station crowd dynamics, thereby substantiating the efficacy of the proposedpassenger flow estimation model. The derived solutions are instrumental in formulating a crowd controlstrategy for Xiaozhai Station during the peak interval from 17:30 to 18:00 on a designated day, yielding crowdmanagement interventions that offer insights for the orchestration of passenger flow and operationalgovernance within metro stations.Originality/value – The construction of an estimation methodology for the real-time streamline traffic flowaugments the model’s dataset, supplanting estimated values derived from surveys or historical datasets withreal-time computed traffic data, thereby enhancing the precision and immediacy of crowd flow managementwithin metro stations.

A review of the mathematical modeling of equilibrium and nonequilibrium hypersonic flows

This paper systematically reviews the mathematical modeling based on the computational fluid dynamics(CFD)method of equilibrium and nonequilibrium hypersonic flows.First,some physicochemical phenomena in hypersonic flows(e.g.,vibrational energy excitation and chemical reactions)and the flow characteristics at various altitudes(e.g.,thermochemical equilibrium,chemical nonequilibrium,and thermochemical nonequilibrium)are reviewed.Second,the judgment rules of whether the CFD method can be applied to hypersonic flows are summarized for accurate numerical calculations.This study focuses on the related numerical models and calculation processes of the CFD method in a thermochemical equilibrium flow and two nonequilibrium flows.For the thermochemical equilibrium flow,the governing equations,chemical composition calculation methods,and related research on the thermodynamic and transport properties of air are reviewed.For the nonequilibrium flows,the governing equations that include one-,two-,and three-temperature models are reviewed.The one-temperature model is applied to a chemical nonequilibrium flow,whereas the two-and three-temperature models are applied to a thermochemical nonequilibrium flow.The associated calculations and numerical models of the thermodynamic and transport properties,chemical reaction sources,and energy transfers between different energy modes of the three models are presented in detail.Finally,the corresponding numerical models of two special wall boundary conditions commonly used in hypersonic flows(i.e.,slip boundary conditions and catalytic walls)and related research,are reviewed.

A new discovery of The Early Cretaceous Supercritical Hyperpycnal Flow Deposits on Lingshan Island,East China

Objective Understanding the dynamics of sediment gravity flows is of great importance to correctly interpret their related deposits. The discovery of supercritical sediment gravity flows provides some new viewpoints for the explanation of controversial sediment gravity flow deposits. However, the dynamics, formation, evolution processes of supercritical sediment gravity flows and their recognition criteria from their associated deposits are still worldwide controversial. The supercritical hyperpycnal flow deposits recognized in the upper part of Early Cretaceous Lingshandao Formation provide a rare opporttmity to understand their sedimentary characteristics. This work is aimed at documenting the typical sedimentary structures associated with the supercritical hyperpycnal flow, and discussing the vertical stacking and its relationship with flow evolution.

Theoretical investigation of shock stand-off distance for non-equilibrium flows over spheres

We derived a theoretical solution of the shock stand-off distance for a non-equilibrium flow over spheres based on Wen and Hornung＇s solution and Olivier＇s solution. Compared with previous approaches, the main advantage of the present approach is allowing an analytic solution without involving any semi-empirical parameter for the whole non-equilibrium flow regimes. The effects of some important physical quantities therefore can be fully revealed via the analytic solution. By combining the current solution with Ideal Dissociating Gas（IDG） model, we investigate the effects of free stream kinetic energy and free stream dissociation level（which can be very different between different facilities） on the shock stand-off distance.

Self-similarity of spanwise rotational motions’population trends in decelerating open-channel flow

Decelerating open-channel flow is a type of flow that gradually moves forward with decreasing velocity and increasing water depth.Although all flow parameters change along the streamwise direction,previous studies have revealed that these parameters’vertical distributions at different sections can be universally described with a single profile when being nondimensionalised by appropriate scales.This study focuses on the population trends of spanwise rotational motions at various sections along the main flow direction by particle imaging velocimetry(PIV)measurement.The wall-normal population distributions of density,radius,swirling strength,and convection velocity of the prograde and retrograde motions show similar trends in uniform open-channel flows.The dimensionless representation is invariant along the main flow direction.This study’s results indicate the self-similar characteristic of population trends of spanwise rotational motions prevails in decelerating open-channel flow.

AUCTIONING METHOD FOR AIRSPACE CONGESTING RESOURCE ALLOCATION AND GAME EQUILIBRIUM ANALYSIS

The airspace congestion is becoming more and more severe.Although there are traffic flow management（TFM）initiatives based on CDM widely applied,how to reschedule these disrupted flights of different airlines integrating TFM initiatives and allocate the limited airspace resources to these airlines equitably and efficiently is still a problem.The air traffic management（ATM）authority aims to minimizing the systemic costs of congested airspaces.And the airlines are self-interested and profit-oriented.Being incorporated into the collaborative decision making（CDM）process,the airlines can influence the rescheduling decisions to profit themselves.The airlines maybe hide the flight information that is disadvantageous to them,but is necessary to the optimal system decision.To realize the coincidence goal between the ATM authority and airlines for the efficient,and equitable allocation of airspace resources,this paper provides an auction-based market method to solve the congestion airspace problem under the pre-tactic and tactic stage of air traffic flow management.Through a simulation experiment,the rationing results show that the auction method can decrease the total delay costs of flights in the congested airspace compared with both the first schedule first service（FSFS）tactic and the ration by schedule（RBS）tactic.Finally,the analysis results indicate that if reallocate the charges from the auction to the airlines according to the proportion of their disrupted flights,the auction mechanism can allocate the airspace resource in economy equitably and decrease the delay losses of the airlines compared with the results of the FSFS tactic.

Blade bowing effects on radial equilibrium of inlet flow in axial compressor cascades

The circumferentially averaged equation of the inlet flow radial equilibrium in axial compressor was deduced. It indicates that the blade inlet radial pressure gradient is closely related to the radial component of the circumferential fluctuation（CF） source item. Several simplified cascades with/without aerodynamic loading were numerically studied to investigate the effects of blade bowing on the inlet flow radial equilibrium. A data reduction program was conducted to obtain the CF source from three-dimensional（3D） simulation results. Flow parameters at the passage inlet were focused on and each term in the radial equilibrium equation was discussed quantitatively. Results indicate that the inviscid blade force is the inducement of the inlet CF due to geometrical asymmetry. Blade bowing induces variation of the inlet CF, thus changes the radial pressure gradient and leads to flow migration before leading edge（LE） in the cascades. Positive bowing drives the inlet flow to migrate from end walls to mid-span and negative bowing turns it to the reverse direction to build a new equilibrium. In addition, comparative studies indicate that the inlet Mach number and blade loading can efficiently impact the effectiveness of blade bowing on radial equilibrium in compressor design.

A super-network equilibrium optimization method for operation architecture with fuzzy demands

From the view of information flow, a super-network equilibrium optimization model is proposed to compute the solution of the operation architecture which is made up of a perceptive level, a command level and a firepower level. Firstly, the optimized conditions of the perceptive level, command level and firepower level are analyzed respectively based on the demand of information relation,and then the information supply-and-demand equilibrium model of the operation architecture super-network is established. Secondly,a variational inequality transformation(VIT) model for equilibrium optimization of the operation architecture is given. Thirdly, the contraction projection algorithm for solving the operation architecture super-network equilibrium optimization model with fuzzy demands is designed. Finally, numerical examples are given to prove the validity and rationality of the proposed method, and the influence of fuzzy demands on the super-network equilibrium solution of operation architecture is discussed.