STABILITY OF TRANSONIC SHOCKS TO THE EULER-POISSON SYSTEM WITH VARYING BACKGROUND CHARGES

This paper is devoted to studying the stability of transonic shock solutions to the Euler-Poisson system in a one-dimensional nozzle of finite length.The background charge in the Poisson equation is a piecewise constant function.The structural stability of the steady transonic shock solution is obtained by the monotonicity argument.Furthermore,this transonic shock is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.One of the crucial ingredients of the analysis is to establish the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions.

REVIEW OF THE GREEN＇S FUNCTION METHOD FOR STEADY ＆UNSTEADY，SUBSONIC，TRANSONIC ＆SUPERSONIC AERODYNAMICS AROUND COMPLEX CONFIGURATIONS

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Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

基于SubSonic和Nhibernate框架的在线购书系统设计与实现

为营造客户与销售商之间互动和谐的购物环境,设计了一个基于SubSonic+Nhibernate的ASP.NET架构的在线购书系统。论述了基于.NET技术的开源框架SubSonic和Nhibernate的技术特点,提出了系统的总体架构图,分析了系统的主要实现方法,最后介绍了系统的关键技术。

Transonic Rudder Buzz on Tailless Flying Wing UAV

Transonic rudder buzz responses based on the computational fluid dynamics or computational structural dynamics(CFD/CSD)loosely method are analyzed for a tailless flying wing unmanned aerial vehicle(UAV).The Reynolds-averaged Navier-Stokes(RANS)equations and finite element methods based on the detailed aerodynamic and structural model are established,in which the aerodynamic dynamic meshes adopt the unstructured dynamic meshes based on the combination of spring-based smoothing and local remeshing methods,and the lower-upper symmetric-Gauss-Seidel(LU-SGS)iteration and Harten-Lax-van Leer-Einfeldt-Wada(HLLEW)space discrete methods based on the shear stress transport(SST)turbulence model are used to calculate the aerodynamic force.The constraints of the rudder motions are fixed at the end of structural model of the flying wing UAV,and the structural geometric nonlinearities are also considered in the flying wing UAV with a high aspect ratio.The interfaces between structural and aerodynamic models are built with an exact match surface where load transferring is performed based on 3Dinterpolation.The flying wing UAV transonic buzz responses based on the aerodynamic structural coupling method are studied,and the rudder buzz responses and aileron,elevator and flap vibration responses caused by rudder motion are also investigated.The effects of attack,height,rotating angular frequency and Mach number under transonic conditions on the flying wing UAV rudder buzz responses are discussed.The results can be regarded as a reference for the flying wing UAV engineering vibration analysis.

AN INVISCID MODEL FOR THE BASE PRESSURE OF TRANSONIC TURBINE CASCADE

An inviscid base pressure model for transonic turbine blade has been presented. It has been shown that for a given back pressure the base pressure at the trailing edge, and the profile loss of a turbine blade are fixed according to the model and the base pressure can be calculated with the help of an inviscid numerical scheme. A parameteric study on the model shows that a blade profile with positive curvature downstream of the throat is advantageous for generating less loss, whilst the worst situation is when the exit flow reaches the sonic condition.

Numerical simulation and analysis of aerodynamic drag on a subsonic train in evacuated tube transportation

The aerodynamic drag on a train running in an evacuated tube varies with tube air pressure, train speed and shape, as well as blockage ratio. This paper uses numerical simulations to study the effects of different factors on the aerodynamic drag of a train running at subsonic speed in an evacuated tube. Firstly, we present the assumption of a steady state, two dimensional, incompressible viscous flow with lubricity wall conditions. Subsequently, based on the Navier-Stokes equation and the k-c turbulent models, we calculate the aerodynamic drag imposed on the column train with a 3-meter diameter running under different pressure and blockage ratio conditions in an evacuated tube transporta- tion （ETT） system. The simulation is performed with FLUENT 6.3 software package. An analyses of the simulation re- sults suggest that the blockage ratio for ETT should be in the range of 0.25-0.7, and the tube internal diameter in the range of 2-4 m, with the feasible vacuum pressure in the range of 1-10 000 Pa for the future subsonic ETT trains.

ON SUBSONIC AND SUBSONIC-SONIC FLOWS IN THE INFINITY LONG NOZZLE WITH GENERAL CONSERVATIVES FORCE

In this article, we study irrotational subsonic and subsonic-sonic flows with gen- eral conservative forces in the infinity long nozzle. For the subsonic case, the varified Bernoulli law leads a modified cut-off system. Because of the local average estimate, conservative forces do not need any decay condition. Afterwards, the subsonic-sonic limit solutions are constructed by taking the extract subsonic solutions as the approximate sequences.

ANISOTROPIC MULTISTAGE FINITE ELEMENT METHOD FOR TWO DIMENSIONAL VISCOUS TRANSONIC FLOW IN TURBOMACHINERY

A new method based on the anisotropic tensor force finite element and Taylor-Galerkin finite element is presented in the present paper.Its application to two-dimensional viscous transonic flow in turbomachinery improves the conver- gence rate and stability of calculation,and the results obtained agree well with the experimental measurements.

Numerical simulation of the dimensional transformation of atomization in a supersonic aerodynamic atomization dust-removing nozzle based on transonic speed compressible flow

To simulate the transonic atomization jet process in Laval nozzles,to test the law of droplet atomization and distribution,to find a method of supersonic atomization for dust-removing nozzles,and to improve nozzle efficiency,the finite element method has been used in this study based on the COMSOL computational fluid dynamics module.The study results showed that the process cannot be realized alone under the two-dimensional axisymmetric,three-dimensional and three-dimensional symmetric models,but it can be calculated with the transformation dimension method,which uses the parameter equations generated from the two-dimensional axisymmetric flow field data of the three-dimensional model.The visualization of this complex process,which is difficult to measure and analyze experimentally,was realized in this study.The physical process,macro phenomena and particle distribution of supersonic atomization are analyzed in combination with this simulation.The rationality of the simulation was verified by experiments.A new method for the study of the atomization process and the exploration of its mechanism in a compressible transonic speed flow field based on the Laval nozzle has been provided,and a numerical platform for the study of supersonic atomization dust removal has been established.

Numerical investigation of transonic flow over deformable airfoil with plunging motion

In this article, the transonic inviscid flow over a deformable airfoil with plunging motion is studied numerically. A finite volume method based on the Roe scheme developed in a generalized coordinate is used along with an arbitrary Lagrangian-Eulerian method and a dynamic mesh algorithm to track the instantaneous position of the airfoil. The effects of different governing parameters such as the phase angle, the deformation amplitude, the initial angle of attack, the flapping frequency, and the Mach number on the unsteady flow field and aerodynamic coefficients are investigated in detail. The results show that maneuverability of the airfoil under various flow conditions is improved by the deformation. In addition, as the oscillation frequency of the airfoil increases, its aerodynamic performance is significantly improved.

Numerical Study on Transonic Flow with Local Occurrence of Non-Equilibrium Condensation

Characteristics of transonic flow over an airfoil are determined by a shock wave standing on the suction surface. In this case, the shock wave/boundary layer interaction becomes complex because an adverse pressure gradient is imposed by the shock wave on the boundary layer. Several types of passive control techniques have been applied to shock wave/boundary layer interaction in the transonic flow. Furthermore, possibilities for the control of flow fields due to non-equilibrium condensation have been shown so far and in this flow field, non-equilibrium condensation occurs across the passage of the nozzle and it causes the total pressure loss in the flow field. However, local occurrence of non-equilibrium condensation in the flow field may change the characteristics of total pressure loss compared with that by non-equilibrium condensation across the passage of flow field and there are few for researches of locally occurred non-equilibrium condensation in a transonic flow field. The purpose of this study is to clarify the effect of locally occurred non-equilibrium condensation on the shock strength and total pressure loss on a transonic internal flow field with circular bump. As a result, it was found that shock strength in case with local occurrence of non-equilibrium condensation is reduced compared with that of no condensation. Further, the amount of increase in the total pressure loss in case with local occurrence of non-equilibrium condensation was also reduced compared with that by non-equilibrium condensation across the passage of flow field.

Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow

Turbo-machineries,as key components,have wide applications in civil,aerospace,and mechanical engineering.By calculating natural frequencies and dynamical deformations,we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies.In this paper,the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed.The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations,including the centrifugal force and the aerodynamic force.In view of the first-order shear deformation theory and von-K′arm′an nonlinear geometric relationship,the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle.The second-order ordinary differential equations are acquired by the Galerkin approach.With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance,the averaged equation is derived by the asymptotic perturbation methodology.Bifurcation diagrams,phase portraits,waveforms,and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.

Flow Diagnosis and Optimization Based on Vorticity Dynamics for Transonic Compressor/Fan Rotor

This paper presents two optimized rotors. The first rotor is as part of a 3-blade row optimization (IGV-rotor-stator) of a high-pressure compressor. It is based on modifying blade angles and advanced control of curvature of the airfoil camber line. The effects of these advanced blade techniques on the performance of the transonic 1.5-stage compressor were calculated using a 3D Navier-Stokes solver combined with a vortex/vorticity dynamics diagnosis method. The first optimized rotor produces a 3-blade row efficiency improvement over the baseline of 1.45% while also improving stall margin. The throttling range of the compressor is expanded largely because the shock in the rotor tip area is further downstream than that in the baseline case at the operating point. Additionally, optimizing the 3-blade row block while only adjusting the rotor geometry ensures good matching of flow angles allowing the compressor to have more range. The flow diagnostics of the rotor blade based on vortex/vorticity dynamics indicate that the boundary-layer separation behind the shock is verified by on-wall signatures of vorticity and skin-friction vector lines. In addition, azimuthal vorticity and boundary vorticity flux (BVF) are shown to be two vital flow parameters of compressor aerodynamic performance that directly relate to the improved performance of the optimized transonic compressor blade. A second rotor-only optimization is also presented for a 2.9 pressure ratio transonic fan. The objective function is the axial moment based on the BVF. An 88.5% efficiency rotor is produced.

TRANSONIC SHOCK SOLUTIONS TO THE EULER SYSTEM IN DIVERGENT-CONVERGENT NOZZLES

In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range.In addition,we establish the monotonicity between the location of the transonic shock and the pressure downstream.

STABILIZATION EFFECT OF FRICTIONS FOR TRANSONIC SHOCKS IN STEADY COMPRESSIBLE EULER FLOWS PASSING THREE-DIMENSIONAL DUCTS

Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.

Symmetries and Group-Invariant Solutions for Transonic Pressure-Gradient Equations

Lie symmetry group method is applied to study the transonic pressure-gradient equations in two-dimensionalspace.Its symmetry groups and corresponding optimal systems are determined,and several classes of irrotational groupinvariantsolutions associated to the symmetries are obtained and special case of one-dimensional rarefaction wave isfound.

Transonic Airfoil Design and Optimization for an Unmanned Air Vehicle Concept

Design,optimization and analysis of a new energy efficient 16%thick transonic airfoil were completed for a notional air vehicle concept.The airfoil specifications included a range of Reynolds number per foot from 1.7 million to 2.5 million and Mach number from 0.4 to 0.8.Shape optimization in geometry and inverse design modules of the airfoil analysis program MSES were used to design a new 16%thick reference airfoil.The performance of the reference airfoil was then optimized with an objective of minimizing drag coefficient for 7 design points with conflicting requirements in Reynolds and Mach number by using the MSES/LINDOP optimizer.The optimization results in an upward shift of drag bucket in the direction of higher lift coefficient.Both surface pressure distribution and Mach contour plots show that supersonic compression waves on airfoil surface are terminated at Mach 0.78 with a normal shock wave and associated flow separation,which causes not only a decrease of the maximum suction pressure,but also a decrease in lift and increase in drag coefficient.The new optimized airfoil shows robust performance when operating within the specified design constraints.

Numerical Calculation of Supercavitating Flows over the Disk Cavitator of a Subsonic Underwater Projectile

为了在 supercavitating 上处理可压缩的液体的效果，溢出射弹的亚声的磁盘 cavitator，一个有限的卷方法基于理想的可压缩的潜在的理论被提出。由使用连续性方程和 Tait 状态方程以及 Riabouchinsky 闭合模型，一个反的问题答案为 supercavitating 流动被介绍。根据 supercavity 的表面上的刺不进的条件，为 supercavity 形状的一个新反复的方法被设计在 supercavity 形状上处理压缩的可能性的效果，压力拖系数和密度地。由这个方法，低成穴数字能被计算。计算结果与试验性的数据和实验公式同意很好。以亚声的条件，液体压缩的可能性将使 supercavity 成为长度和半径增加。supercavity 扩展，但是留下球状体。supercavity 的第一 1/3 部分上的效果不是明显的。成穴数字或马赫数字增加的射弹增加的 drag 系数。与马赫数字增加，压缩的可能性是越来越重要的。根据 supercavitating 流动的精确计算被担心，压缩的可能性必须被考虑。