THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW

We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

一维多介质可压缩Euler方程的高精度RKDG有限元方法

采用RKDG有限元方法、Level Set方法和改进的带“Isentropic”修正的Ghost Fluid方法模拟了一维多介质可压缩Euler方程,其中Euler方程、Level Set方程和重新初始化方程都采用了三阶精度的RKDG有限元方法进行离散,并对一维两种介质可压缩流体进行了数值实验,得到了较高分辨率的计算结果.

Level Set方法和多介质可压缩流

多介质可压缩流问题计算的关键是如何精确的捕获不同时刻物质界面的位置,从而将多介质问题分解成多个单介质问题去处理。Level Set方法的优点是不用显示的追踪物质界面,而用距离函数就能精确定位界面。同时,用Level Set方法追踪界面运动易于处理界面拓扑结构的变化、易于处理大变形问题。本文成功地将Level Set方法应用在二维多介质可压缩流计算。

应用改进虚拟流方法计算多介质可压缩流动

原始的虚拟流(GFM)方法在处理强激波与物质界面作用时遇到了困难,计算结果不准确.本文采用改进虚拟流方法(MGFM)对多介质可压缩流体进行了数值模拟,采用二阶TVD-WAF格式结合HLLC求解器求解Euler方程得到流场参数分布,应用五阶WENO求解level set方程捕捉物质界面.在此基础上分别计算了一维和二维数值算例.结果表明,该方法在能精确捕捉到物质界面的同时可以计算较强激波情况下的流场,并且可以捕获激波、物质界面和各类间断的相互作用.

Arguing on Entropic and Enthalpic First-Order Phase Transitions in Strongly Interacting Matter

The pattern of isentropes in the vicinity of a first-order phase transition is proposed as a key for a sub-classification. While the confinement-deconfinement transition, conjectured to set in beyond a critical end point in the QCD phase diagram, is often related to an entropic transition and the apparently settled gas-liquid transition in nuclear matter is an enthalphic transition, the conceivable local isentropes w.r.t. “incoming” or “outgoing” serve as another useful guide for discussing possible implications, both in the presumed hydrodynamical expansion stage of heavy-ion collisions and the core-collapse of supernova explosions. Examples, such as the quark-meson model and two-phase models, are shown to distinguish concisely the different transitions.

高超声速进气道起动问题的理论判据新认识

为了判断进气道起动马赫数,基于Kantrowitz起动判据,联系激波关系式和流量连续方程得到一系列等值线,将等值线推广到有入射激波和低马赫数溢流的情况。结果表明这些等值线具有以下特性:等值线连接进气道的内收缩比和总收缩比;等值线是等总压恢复线和等流量线;等值线可由Isentropic曲线方程乘于进气道内收缩段自起动时总压恢复的倒数得到;存在入射激波的起动等值线在设计状态等值线的右侧;有低马赫数溢流的起动等值线在设计状态等值线的左侧;等值线提供了一种联系Kantrowitz和Isentropic曲线的方法。根据以上特性,将等值线应用于高超声速进气道起动问题,并通过实例应用文中的理论判据评估无粘条件下混压式多楔二元进气道来流起动马赫数理论值,与CFD结果吻合较好,误差小于2%,初步探索了理论快速估算进气道起动马赫数的可行性。

From concept to reality-A review to the primary test stand and its preliminary application in high energy density physics

Pulsed power technology,whereas the electrical energy stored in a relative long period is released in much shorter timescale,is an efficient method to create high energy density physics(HEDP)conditions in laboratory.Around the beginning of this century,China Academy of Engineering Physics(CAEP)began to build some experimental facilities for HEDP investigations,among which the Primary Test Stand(PTS),a multi-module pulsed power facility with a nominal current of 10 MA and a current rising time~90 ns,is an important achievement on the roadmap of the electro-magnetically driven inertial confinement fusion(ICF)researches.PTS is the first pulsed power facility beyond 10 TW in China.Therefore,all the technologies have to be demonstrated,and all the engineering issues have to be overcome.In this article,the research outline,key technologies and the preliminary HEDP experiments are reviewed.Prospects on HEDP research on PTS and pulsed power development for the next step are also discussed.

POINTWISE ESTIMATE OF SOLUTIONS OF ISENTROPIC NMIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSION

This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and the generalized Huygan's principle is exhibited. The approch of the paper is based on the detailed analysis of the Green function of Iinearized system. This is used to study the coupling of nonlinear diffesion waves.

GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.

TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.

GLOBAL L~∞ SOLUTIONS TO SYSTEM OF ISENTROPIC GAS DYNAMICS IN A DIVERGENT NOZZLE WITH FRICTION

In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.

An Isentropic Mass Circulation View on the Extreme Cold Events in the 2020/21 Winter

Three extreme cold events successively occurred across East Asia and North America in the 2020/21 winter.This study investigates the underlying mechanisms of these record-breaking persistent cold events from the isentropic mass circulation(IMC)perspective.Results show that the midlatitude cold surface temperature anomalies always co-occurred with the high-latitude warm anomalies,and this was closely related to the strengthening of the low-level equatorward cold air branch of the IMC,particularly along the climatological cold air routes over East Asia and North America.Specifically,the two cold surges over East Asia in early winter were results of intensification of cold air transport there,influenced by the Arctic sea ice loss in autumn.The weakened cold air transport over North America associated with warmer northeastern Pacific sea surface temperatures(SSTs)explained the concurrent anomalous warmth there.This enhanced a wavenumber-1 pattern and upward wave propagation,inducing a simultaneous and long-lasting stronger poleward warm air branch(WB)of the IMC in the stratosphere and hence a displacement-type Stratospheric Sudden Warming(SSW)event on 4 January.The WB-induced increase in the air mass transported into the polar stratosphere was followed by intensification of the equatorward cold branch,hence promoting the occurrence of two extreme cold events respectively over East Asia in the beginning of January and over North America in February.Results do not yield a robust direct linkage from La Niña to the SSW event,IMC changes,and cold events,though the extratropical warm SSTs are found to contribute to the February cold surge in North America.

Characteristics of compressible flow of supercritical kerosene

In this paper, compressible flow of aviation kerosene at supercritical conditions has been studied both numerically and experimentally. The thermophysical properties of supercritical kerosene are calculated using a 10- species surrogate based on the principle of extended corresponding states （ECS）. Isentropic acceleration of supercritical kerosene to subsonic and supersonic speeds has been analyzed numerically. It has been found that the isentropic relationships of supercritical kerosene are significantly dif- ferent from those of ideal gases, A two-stage fuel heating and delivery system is used to heat the kerosene up to a tem- perature of 820 K and pressure of 5.5 MPa with a maximum mass flow rate of 100 g/s. The characteristics of supercritical kerosene flows in a converging-diverging nozzle （Laval nozzle） have been studied experimentally. The results show that stable supersonic flows of kerosene could be established in the temperature range of 730 K-820 K and the measurements in the wall pressure agree with the numerical calculation.

CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅰ)

A compactness frame of the Lax-Friedrichs scheme for the equations of gas dynamics is obtained by using some embedding theorems and an analysis of the difference scheme and the weak entropy.

GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM

In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method. In particular, the entropy solutions are uniformly bounded independent of time.

Is the Isentropic Surface Always Impermeable to the Potential Vorticity Substance?

The impermeability of isentropic surfaces by the potential vorticity substance （PVS） has often been used to help understand the generation of potential vorticity in the presence of diabatic heating and friction. In this study, we examined singularities of isentropic surfaces that may develop in the presence of diabatic heating and the fictitious movements of the isentropic surfaces that are involved in deriving the PVS impermeability theorem. Our results show that such singularities could occur in the upper troposphere as a result of intense convective-scale motion, at the cloud top due to radiative cooling, or within the well-mixed boundary layer. These locally ill-defined conditions allow PVS to penetrate across an isentropic surface. We conclude that the PVS impermeability theorem is generally valid for the stably stratified atmosphere in the absence of diabatic heating.

A SUPPLEMENT TO THE PAPERS CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅱ)-(Ⅲ)

In the papers (Ⅱ)—(Ⅲ), we studied the global existence of the solutions for the isentropic equation of gas dynamics

STUDY ON VARIATION OF SETTING AND STOPPING PRESSURES OF SAFETY VALVE WITH STRUCTURAL MODIFICATION

The possibility of pressure control with the structural change of a safety valve is investigated Safety valve is commonly used as safety devices for numerous applications which include boilers,ships,industrial plants,and piping Setting and stopping pressures of a safety valve, p set and p sto ,are traditionally adjusted with a fine tuning of seat ring and valve ring heights, h sr and h vr However, it is not easy to achieve the proper setting and stopping pressures of a safety valve in practice The depth of inside and outside grooves in a valve, d i and d o are modified and their effects on setting and stopping pressures of a safety vlave are tested The most appropriate values appear 1 0 mm in d i and 0 5～1 0 mm in d o,respectively The valve ring height, h vr ,shows that the best results can be achieved at 2 3 mm for setting pressures of 0 1～0 4 MPa and 1 0 mm for setting pressures of 0 5～1 0 MPa The stopping pressures increases with the increase of seat ring height, h sr , upto certain h sr value and then becomes independent to the seat ring height This implies that there exists the optimum h sr ,which provides the largest flow rate and the proper stopping pressure Stopping pressures of a safety valve are adjusted with the seat ring and valve ring heights This study,however,demonstrated that the modification of value grooves also changes setting and stopping pressures of a safety valve Therefore,the proper selection in dimensions of the inside and outside grooves should be considered for the safety valve design

Analyses on the Ionization Instability of Non-Equilibrium Seeded Plasma in an MHD Generator

Recently,closed cycle magnetohydrodynamic power generation system research has been focused on improving the isentropic efficiency and the enthalpy extraction ratio.By reducing the cross-section area ratio of the disk magnetohydrodynamic generator,it is believed that a high isentropic efficiency can be achieved with the same enthalpy extraction.In this study,the result relating to a plasma state which takes into account the ionization instability of non-equilibrium seeded plasma is added to the theoretical prediction of the relationship between enthalpy extraction and isentropic efficiency.As a result,the electron temperature which reaches the seed complete ionization state without the growth of ionization instability can be realized at a relatively high seed fraction condition.However,the upper limit of the power generation performance is suggested to remain lower than the value expected in the low seed fraction condition.It is also suggested that a higher power generation performance may be obtained by implementing the electron temperature range which reaches the seed complete ionization state at a low seed fraction.

The Development and Initial Tests of an Atmospheric Model Based on a Vertical Coordinate with a Smooth Transition from Terrain Following to Isentropic Coordinates

An atmospheric model (η model) is developed by modifying the UW θ-σ hybrid model. In the η model, the vertical coordinate transforms smoothly from terrain following to isentropic coordinates. The model is developed to capitalize on the inherent advantage of numerical modeling in isentropic coordinates and to eliminate the interface between the sigma planetary boundary layer and isentropic free atmosphere present in the UW θ-σ model. This formulation provides the potential for the data assimilation and the application of higher order schemes. This paper describes the structure of the η model and presents results from initial numerical experiments. The first experiment tests the capability of the η model for simulating the baroclinic development process. In the 48-hr numerical weather forecast experiment, the η model produces reasonable precipitation and synoptic fields at all levels which are similar to those from the UW θ-σ model. The second and third experiments test the capability of the η model for conserving 1) the joint distribution of isentropic potential vorticity (IPV) and proxy ozone and 2) equivalent potential temperature under frictionless and isentropic conditions. These experiments show that distributions of IPV and proxy ozone in the pure isentropic domain and the distributions of prognostic and diagnostic equivalent potential temperture in the model domain remain highly correlated to day 10.