Compressible Flow and Transonic Shock in a Diverging Nozzle

The paper is devoted to the study of compressible flows and transonic shocks in diverging nozzles in the framework of the full compressible Euler system. Consider a nozzle having a shape as a diverging truncated sector with generic opening angle: if the upstream flow at the entrance is supersonic and is near to an axial symmetric flow, and if all parameters of the upstream flow and the receiver pressure at the exit are suitably assigned, then a transonic shock appears in the nozzle. To determine the transonic shock and the flow in the nozzle leads to a free boundary value problem for a nonlinear partial differential equation. We prove that the receiver pressure can uniquely determine the location of the transonic shock, as well as the flow behind the shock. Such a conclusion was conjectured by Courant and Friedrichs, and is confirmed theoretically in this paper for the divergent nozzles. The main advantage of this paper compared with the previous studies on this subject is that the section of the nozzle is allowed to vary substantially, while the transonic shock is not assumed to pass a fixed point. The situation coincides with the requirement in Courant-Friedrichs’ conjecture. To describe the compressible flow we use the full Euler system, which is purely hyperbolic in the supersonic region and is elliptic-hyperbolic in the subsonic region. Solving the free boundary value problem of an elliptic-hyperbolic problem forms the main part of this paper. In our demonstration some new approaches, including the introduction of a pseudo-free boundary problem and the corresponding relaxation, design of a delicate double iteration scheme, are developed to overcome the difficulties caused by the divergence of the nozzle.     

自发凝结流动数值模拟方法及其在Laval喷管中的应用

本文对存在自发凝结的湿蒸汽两相流动建立了完全欧拉坐标系统下的数理模型。采用考虑了真实流体性质的 LU-SGS-GE隐式时间推进算法和改良型高精度、高分辨率MuSCL TVD差分格式求解存在自发凝结的汽液两相流动控制方程组。文中水及水蒸汽性质数据全部取自IAPWS-IF97国际标准公式。对某Laval缩放喷管内的湿蒸汽自发凝结流动的数值模拟结果表明,本文所采用的数理模型及计算方法是有效和可靠的。     

用PIV技术测量跨音压气机转子内流的激波结构

在跨音压气机试验台上进行了用ＰＩＶ技术测量内流激波结构的试验研究。乙二醇微小液滴成功地被用作示踪粒子；自行设计制造的激光潜望镜成功地将双脉冲激光器发出的激光束导入机匣。用数字ＰＩＶ技术测量到的跨音压气机叶片流道内的二维瞬态绝对速度场分布被转化为相对速度分布，发现的激波结构测量结果与静压分布测量结果进行了比较，得到了比较满意的符合。本文讨论了目前试验装置和测量系统所存在的问题，提出了进一步工作的要求．     

Characteristics of a magnetogasdynamic diffuser under different modes of electric current switching

This paper elaborates upon a previous investigation into the influence of external electric and magnetic fields on a flow through a supersonic diffuser. The aim of the present study is to correlate a change in the configuration of a shock wave emerging near the diffuser inlet at magnetohydrodynamic interaction with the amount of force and energy actions and with total pressure losses. For this purpose, the main parameters of the shock wave structure and the total pressure are measured at the diffuser outlet when the flow is subjected to magnetic and electric fields of various strengths at different routes of current passage. In the experiments, a shock tube with a supersonic nozzle is employed. The shock tube forms a flow behind the shock wave reflecting from the end of the tube, which terminates in the nozzle. The diffuser is located directly downstream of the nozzle. The investigation is carried out in xenon. The flow is subjected to external fields at the inlet of the diffuser. The shock wave structure is visualized by frame sweeping of Schlieren patterns of the flow. The total pressure is measured with a piezoelectric transducer located at the end of the channel. The results obtained make it possible to optimize the action on the flow in terms of power consumption and total pressure losses for a given design of the diffuser.     

Transonic flow control by means of local energy deposition

Experimental data for the feasibility of transonic flow control by means of energy deposition are generalized. Energy supplied to the immediate vicinity of a body in stream before a compression shock is found to result in the nonlinear interaction of introduced disturbances with the shock and the surface in zones extended along the surface. A new, explosive gasdynamic mechanism behind the shift of the compression shock is discovered. It is shown that the nonlinear character of the interaction may considerably decrease the wave resistance of, e.g., transonic airfoils. It is found that energy supply from without stabilizes a transonic flow about an airfoil—the effect similar to the Khristianovich stabilization effect. The dependence of the energy deposition optimal frequency on the energy source parameters and Mach number of the incoming flow at which the resistance drops to the greatest extent is obtained. The influence of the real thermodynamic properties and viscosity of air is studied.     

离心压气机内激波/叶排相互作用

对根部存在疲劳裂纹的某跨音离心级进行了非定常流场数值研究,其中着重关注运动激波／叶排相互作用物理图画及其影响。研究表明:离心压气机中运动激波／叶排相互作用仍然服从一般激波／固壁相交行为规则;叶轮／扩压器间距小以及叶轮尾迹相对较宽造成扩压器内激波剧烈变化;扩压器前伸波深入叶轮通道深度由激波强度及扩压器前缘附近叶表形状决定;扩压器前伸波与叶轮尾缘相互作用可能是本叶轮根部尾缘发生高周疲劳的原因。     

跨音压气机转子叶尖流场试验与分析

本文利用高频响动态压力测试技术测量了某跨音压气机转子叶尖间隙流场,其中包括对跨音转子叶尖漏流和激波／漏流干扰的细致流场特征．测试结果表明激波在机匣壁面处受漏流干扰的影响相当大,这一干扰分别来自于前缘漏流涡的干扰和叶尖第二次漏流对通道激波的直接冲击干扰,使激波结构呈“S”形.在低背压高攻角条件下,转子存在十分明显的尾涡．     

蒸汽喷射制冷系统中喷射器内特殊流动现象的研究

本文通过求解二维N-S方程来模拟蒸汽喷射器内复杂的流动混合过程,模拟时使用了蒸汽的真实物性公式。与理想气体假设不同,真实物性的带入,真实地反映了蒸汽经缩放喷嘴时,温度递减,喷嘴出口后温度场波动变化的特征．模拟时,通过对节点焓值的计算,得出了喷射器内发生相变的蒸汽的百分含量,实现了相变现象的定量分析。在激波捕捉方面,验证了喷射器内喷嘴出口后,膨胀波(压缩波)经混合层反复折射、转化、衰减的过程,以及在扩压室入口会产生斜激波的理论预测。     

对运动斜激波绕射波纹壁面的研究

使用计算流体动力学的方法,对经典的运动激波绕射现象做数值模拟,研究了一类复杂激波反射问题一入射的运动斜激波绕射现象.给出一组运动斜激波绕射波纹壁面的非定常过程的模拟结果。计算结果显示出由运动斜激波绕射诱导的多波干扰产生的复杂流场结构。     

On Transonic Shocks in a Nozzle with Variable End Pressures

In the book, Courant and Friedrichs (Supersonic Flow and Shock Waves. New York: Interscience Publishers, 1948) described the following transonic shock phenomena in a de Laval nozzle: Given the appropriately large receiver pressure p _r , if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes p _r . When the end pressure p _r varies and lies in an appropriate scope, in general, it is expected that a curved transonic shock is still formed in a nozzle. In this paper, we solve this problem for the two-dimensional steady Euler system with a variable exit pressure in a nozzle whose divergent part is an angular sector. Both existence and uniqueness are established. Supported by the National Natural Science Foundation of China (No.10571082) and the National Basic Research Programm of China (No.2006CB805902). Supported in part by Zheng Ge Ru Foundation, and Hong Kong RGC Earmarked Research Grants CUHK4028/04P, CUHK4040/06P and RGC Central Allocation Grant CA05/06.SC01.     

Numerical flow visualization of a Single Expansion Ramp Nozzle with hypersonic external flow

Numerical simulation of scramjet asymmetric nozzle flow is carried out to visualize and investigate the effects of interaction between engine exhaust and hypersonic external flow. The Single Expansion Ramp Nozzle (SERN) configuration studied here consists of flat ramp and a cowl with different combinations of ramp angle and cowl geometry. UsingPARAS 3D, simulations are performed for a free stream Mach number of 6.5 that constitutes the external flow around the vehicle. Appropriate specific heats ratio has been simulated for the jet and free stream flow. External shock wave due to jet plume interaction with free stream flow, the internal barrel shock wave and the shear layer emanating from the cowl trailing edge and sidewalls are well captured. Wall static pressure distribution on the nozzle ramp for different nozzle expansion angles has been computed for both with and without side fence. Axial thrust and normal force have been evaluated by integrating the wall static pressure. Effect of cowl length variation and side fence on the SERN performance has also been studied and found to be quite significant. Based on this study, an optimum ramp angle at which the SERN generates maximum axial thrust is obtained. SERN angle of 20° was found to be optimum when the flight axis coincides with nozzle axis.     

Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil

A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoil in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic “tone bursts” by a supercritical airfoil section.     

应用GAO-YONG可压缩湍流模式数值模拟RAE2822翼型绕流

应用Gao-Yong可压缩湍流模式,数值模拟RAE2822二维翼型在两种不同来流情况下的跨音速粘性绕流问题.湍流模式的对流项用ROE格式离散,扩散项用中心差分格式离散,空间离散后的控制方程用多步Runge-Kutta显式时间推进格式求解.计算结果预测了翼型表面的压力系数的分布、平均速度剖面、激波的位置、马赫数等值线等情况.同时,对翼型表面激波与边界层相互干扰以及转捩问题进行分析计算,结果表明,Gao-Yong可压缩湍流模式结合适当的数值方法能够成功地模拟翼型跨音速粘性流动.最后,基于Gao-Yong可压缩湍流模式各项异性湍流粘性的机理,初步提出一种预测转捩起始位置的方法.     

Global solutions to the compressible Euler equations with geometrical structure

We prove the existence of global solutions to the Euler equations of compressible isentropic gas dynamics with geometrical structure, including transonic nozzle flow and spherically symmetric flow. Due to the presence of the geometrical source terms, the existence results themselves are new, especially as they pertain to radial flow in an unbounded region, , and to transonic nozzle flow. Arbitrary data withL bounds are allowed in these results. A shock capturing numerical scheme is introduced to compute such flows and to construct approximate solutions. The convergence and consistency of the approximate solutions generated from this scheme to the global solutions are proved with the aid of a compensated compactness framework.     

平面叶栅中的湿蒸汽两相结流动数值模拟

对存在自发凝结的湿蒸汽两相流动建立了完全欧拉坐标系下的数值模型.考虑水蒸汽与理想气体的偏差,引入维里型状态方程对模型作了进一步完善.对平面叶栅中的两相凝结流动进行了数值模拟,计算结果与实验值比较表明本文计算模型正确,可以扩展到三维复杂两相凝结流场的计算.     

自由旋涡气动窗口全流场的数值模拟

建立自由旋涡气动窗口全流场仿真模型,对大密封压比气动窗口的全流场展开数值研究,得到自由旋涡气动窗口的流场结构,发现大密封压比气动窗口形成的自由旋涡射流在光束输出通道内无明显的波系结构.根据模拟结果对自由旋涡气动窗口的性能进行优化,对自由旋涡喷管上壁面型线进行二次粘性修正.优化自由旋涡射流场后,激光器输出光束通道内压力分布稳定上升;增加扩压器外端壁吹气1.19MPa、内端壁吹气1.68MPa时,自由旋涡射流总能提高,气动窗口密封压力从37.5torr降低至6torr.该研究结果对自由旋涡气动窗口技术的发展具有参考意义.     

Effect of nose shape on the shock standoff distance at nearsonic flows

This paper describes a numerical solution of the bow shock shape ahead of some blunt and sharp axisymmetric noses containing sphere, blunt cone, and sharp cone at steady transonic flow in the Mach number range of 1.01 to 1.2. For validating the results, one sphere and three blunt cones are modeled, and their shock standoff distance is compared with other experimental and numerical studies. The flow over other noses with similar geometric parameters is then solved and compared with each other. In this study, the Reynolds-averaged Navier—Stokes equations are solved using the Spalart—Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for some blunt and sharp noses at low supersonic free flight speed. The shock standoff distance is determined from the Mach number curve on the symmetry line. The present numerical simulations reach down to M8=1.01 a range where it is almost very difficult to set in experimental studies. The shock wave locations were found to agree well with previous numerical and experimental studies. Our results are closer to the experimental results compared to other numerical studies. In addition, the results for shock standoff distances over paraboloids in these speed ranges have not been previously published as far as we know.     

Nonlinear stability and instability of transonic flows through a nozzle

We study transonic flows along a nozzle based on a one-dimensional model. It is shown that flows along the expanding portion of the nozzle are stable. On the other hand, flows with standing shock waves along a contracting duct are dynamically unstable. This was conjectured by the author based on the study of noninteracting wave patterns. The author had shown earlier that supersonic and subsonic flows along a duct with various cross sections are stable. Basic to our analysis are estimates showing that shock waves tend to decelerate along an expanding duct and accelerate along a contracting duct.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. This material is based upon work supported by the National Science Foundation under Grant No. MCS 7802202 and by the Sloan Foundation     

Control of spray spot in cold spray technology. Part 1. Gas dynamic aspects

This paper presents a study of supersonic jets formed by approaches that are new for cold spray technique: the main flow is swirled, the nozzles with permeable profiles and with exit slots on the supersonic section are engineered. The flow swirling achieved in the nozzle prechamber retains downstream to substrate surface. The system of vortices created within the permeable nozzles changes the shock wave features of the overexpanded jet and the geometry of the bow shock wave ahead of the substrate surface. These new features of flow may affect particle motion and particlesubstrate interaction under the conditions of cold spray process; this offers tools for obtaining the necessary shape of a spray spot.     

Investigation of magnetohydrodymamic interaction in a supersonic air flow at <Emphasis Type="Italic">M</Emphasis> = 8

The influence of magnetohydrodynamic interaction localized before a model on the position of a shock wave attached to a wedge is experimentally and numerically investigated. The investigation is carried out in an air flow with a Mach number of 8. It is shown that, for a hydromagnetic interaction parameter on the order of 0.1, the slope angle of the shock wave can be increased by 10°. Experiments are conducted for the case when the flow is ionized by an electron beam or by a pulsed electric discharge. Good agreement between experimental and numerical results is obtained for both ways of ionization if the Joule heating of the gas is insignificant. The conclusion is drawn that the way of providing a nonequilibrium conductivity of the flow has a minor effect on the position of the oblique shock wave near the wedge with the hydromagnetic interaction parameter being the same.