Assessment of turbulence modeling for gas flow in two-dimensional convergent–divergent rocket nozzle

In the present study, the turbulent gas flow dynamics in a two-dimensional convergent–divergent rocket nozzle is numerically predicted and the associated physical phenomena are investigated for various operating conditions. The nozzle is assumed to have impermeable and adiabatic walls with a flow straightener in the upstream side and is connected to a plenum surrounding the nozzle geometry and extended in the downstream direction. In this integrated component model, the inlet flow is assumed a two-dimensional, steady, compressible, turbulent and subsonic. The physics based mathematical model of the considered flow consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The system of the governing equations with turbulent effects is solved numerically using different turbulence models to demonstrate their numerical accuracy in predicting the characteristics of turbulent gas flow in such complex geometry. The performance of the different turbulence models adopted has been assessed by comparing the obtained results of the static wall pressure and the shock position with the available experimental and numerical data. The dimensionless shear stress at the nozzle wall and the separation point are also computed and the flow field is illustrated. The various implemented turbulence models have shown different behavior of the turbulent characteristics. However, the shear-stress transport (SST) k–ω model exhibits the best overall agreement with the experimental measurements. In general, the proposed numerical procedure applied in the present paper shows good capability in predicting the physical phenomena and the flow characteristics encountered in such kinds of complex turbulent flow.     

Exact solution of a boundary value problem describing the uniform cylindrical or spherical piston motion

In this paper, we construct the exact solution for fluid motion caused by the uniform expansion of a cylindrical or spherical piston into still air. Following Lighthill [1], we introduce velocity potential into the analysis and seek a similarity form of the solution. We find both numerical and analytic solutions of the second order nonlinear differential equation, with the boundary conditions at the shock and at the piston. The results obtained from the analytic solutions justify numerical solution and the approximate solution of Lighthill [1]. We find that although the approximate solution of Lighthill [1] gives remarkably good numerical results, the analytic form of that solution is not mathematically satisfactory. We also find that in case of spherical piston motion Lighthill’s [1] solution differs significantly from that of our analytic and numerical solutions. We use Pade′ approximation to extend the radius of convergence of the series solution. We also carry out some local analysis at the boundary to obtain some singular solutions.     

Frequency lock-in phenomenon for oscillating airfoils in buffeting flows

Navier-Stokes based computer simulations are conducted to determine the aerodynamic flow field response that is observed for a NACA0012 airfoil that undergoes prescribed harmonic oscillation in transonic buffeting flows, and also in pre-buffet flow conditions. Shock buffet is the term for the self-sustained shock oscillations that are observed for certain combinations of Mach number and steady mean flow angle of attack even in the absence of structural motion. The shock buffet frequencies are typically on the order of the elastic structural frequencies, and therefore may be a contributor to transonic aeroelastic response phenomena, including limit-cycle oscillations. Numerical simulations indicate that the pre-shock-buffet flow natural frequency increases with mean angle of attack, while the flow damping decreases and approaches zero at the onset of buffet. Airfoil harmonic heave motions are prescribed to study the interaction between the flow fields induced by the shock buffet and airfoil motion, respectively. At pre-shock-buffet conditions the flow response is predominantly at the airfoil motion frequency, with some smaller response at multiplies of this frequency. At shock buffet conditions, a key effect of prescribed airfoil motions on the buffeting flow is to create the possibility of a lock-in phenomenon, in which the shock buffet frequency is synchronized to the prescribed airfoil motion frequency for certain combinations of airfoil motion frequencies and amplitudes. Aerodynamic gain-phase models for the lock-in region, as well as for the pre-shock-buffet conditions are suggested, and also a possible relationship between the lock-in mechanism and limit-cycle oscillation is discussed.     

一类一维的辐射流体力学方程组激波的存在性

该文主要讨论一维空间中一类辐射流体力学方程组的激波. 由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题. 首先通过变量代换, 将其自由边界转换为固定边界, 然后研究关于此非线性方程组的一个初边值问题解的存在唯一性. 为此先构造了此问题的一个近似解, 然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列. 通过一系列估计与紧性理论得到此近似解序列的收敛性, 其极限即为原辐射热力学方程组的一个激波.     

基于方向信息测度的图像边缘检测

边缘检测是图像处理中—个重要的研究课题．针对传统图像边缘检测算法对噪声敏感的问题,本文在分析图像像素灰度信息的基础上,建立了—个改进的确定方向信息测度的方法,并利用震动滤波对边缘检测图像进行增强,该方法在滤除噪声的同时,能有效地保留图像的基本目标信息,正确提取图像的边缘．     

Asymptotic behavior of solutions for the 1-D isentropic Navier–Stokes–Korteweg equations with free boundary

In this paper, we consider the problem with a gas–gas free boundary for the one dimensional isentropic compressible Navier–Stokes–Korteweg system. For shock wave, asymptotic profile of the problem is shown to be a shifted viscous shock profile, which is suitably away from the boundary, and prove that if the initial data around the shifted viscous shock profile and its strength are sufficiently small, then the problem has a unique global strong solution, which tends to the shifted viscous shock profile as time goes to infinity. Also, we show the asymptotic stability toward rarefaction wave without the smallness on the strength if the initial data around the rarefaction wave are sufficiently small.     

A driver gas detection device for shock tunnels

A device has been produced which can detect the contamination of the test gas by the driver gas in a reflected shock tunnel. This device monitors the static pressure in a converging duct. The duct is designed to choke at a predetermined contamination level due to the change in the specific heat ratio produced by the contaminants. Experimental results are given for a freestream enthalpy of nominally 6 MJ/kg.     

Vibrational temperature measurements in a shock layer using laser induced predissociation fluorescence

Single shot spatially and spectrally resolved laser induced predissociation fluorescence measurements in a shock layer around a cylinder in a pulsed supersonic free stream are presented. Fluoresence signals were produced using the tuned output of an argon fluoride excimer laser to excite a mixture of rovibrational transitions in molecular oxygen. The signals produced along a line inside the shock layer were focussed onto a two dimensional detector coupled to a spectrometer, thus allowing spectral and spatial resolution of the fluoresence. In this way, it was possible to detect two fluoresence signals from two different transitions simultaneously, allowing the determination of vibrational temperatures without the need for calibration. To minimize problems associated with low signal to noise ratios, background subtraction and spatial averaging was required.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Supercritical flow in manholes with a bend extension

 Bend manholes of sewers with 45° deflection angles are considered. Previous results are reconsidered by introducing the so-called bend extension. It is demonstrated that the discharge capacity of the 45°- and the 90°-bend manholes is identical if the bend extension, a U-shaped straight downstream portion, is added to the 45° manhole. In addition, the effect of the bend cover is analyzed as a general means to suppress shock waves. Both bend extensions and bend covers may be added to existing structures that convey discharge close to or over the design discharge. The hydraulics of bend manholes are analyzed in detail, including the wave profiles along the inner and the outer bend walls, the complete free surface, the recirculation zone, the pressure distributions on the walls and flow in the downstream sewer. Received: 12 March 2001 / Accepted: 10 August 2001     

Transonic viscous-inviscid interaction by a finite element method

A method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.