Shear layer instability and acoustic interaction in solid propellant rocket motors

Segmentation of solid propellant rocket motors has been demonstrated to be a source of unpredicted and undesirable pressure and thrust oscillations. Surface discontinuities are the primary cause of these vortex-shedding-driven oscillations, which result from a strong coupling between the shear layer instability and the acoustic motion in the chamber. The analysis of an axisymmetric geometry corresponding to a {1\over 15} subscale P230 motor of the Ariane 5 rocket is numerically computed. With a suitable mesh for the viscosity value studied, the aeroacoustics in the chamber is fully described. A coupling between the hydrodynamic instability and the organ-pipe acoustic mode is clearly demonstrated. The mechanism for frequency selection is discussed. © 1997 John Wiley & Sons, Ltd.     

Scattered-light photoelastic stress analysis of a solid-propellant rocket motor

Scattered-light photoelasticity, a nondestructive technique, is used to determine the stress distribution in a three-dimensional, solid-propellant rocket motor. The model is a case-bonded solid propellant with a stargrain internal boundary. Stresses are induced by internal pressure. The pressure load simulates part of the stresses developed in firing a rocket. The model material is polyurethane rubber which is similar to the binder material in actual rockets. The model construction and data analysis are discussed in detail, and the results are presented in graphical form.     

平板湍流边界层的声辐射

基于平板湍流边界层的壁压起伏波数—频率谱 ,给出了一种湍流边界层声辐射的估算方法 ,并对光滑平板湍流边界层和平板表面粗糙度引起的湍流边界层声辐射进行了分析。结果表明 :湍流边界层声辐射是一种四极子声辐射 ,且其辐射声能集中于平板表面粗糙度引起的湍流边界层声辐射 ;光滑平板湍流边界层的声辐射也不可忽略。     

Numerical modeling of the processes within the combustion chamber of a solid propellant rocket engine during the stabilization of the design operation mode

Comprehensive numerical modeling of the processes occurring in the combustion chamber of a solid propellant rocket engine during the stabilization of the design operation mode is performed. The self-consistent problem considered includes nonstationary operation of an ignition device, warmup and ignition of a solid propellant charge followed by its nonstationary burning, nonstationary threephase homogeneous-heterogeneous flow of the combustion products in the combustion chamber, in the nozzle, and behind the engine nozzle unit, engine depressurization, and nozzle unit plug blowing-out. The results of the calculations are presented.     

Analysis of self-sustained oscillation sources in segmented flows

The analysis of self-sustained oscillations in segmented flow generated through porous walls has been carried out over a wide range of velocity levels; in fact, we studied a cold gas flow induced by injection through different wall injecting blocks. We have attempted in this study to analyse the potential unstable development occurring in solid propellant rocket motors. We lay emphasis upon the phenomenon of wall vortex shedding insofar as it conduces to acoustic mode resonance in the whole chamber, within whose confines impingement of such structures generates a source of noise. It is on account of segmented flow that the thin shear layer develops and that the aforementioned vortex shedding comes to induce aero-acoustic coupling. Subsequent experimental results highlight a link in such flows between these two noise sources - they also allow one to observe a pronounced form of selectivity in the energy transfer, i.e. in longitudinal acoustic mode amplification, which has an attested effect upon all of the pressure oscillations in the chamber.     

喷嘴结构对液氧煤油火箭发动机高频燃烧不稳定性的影响

为了筛选高压补燃循环液氧煤油火箭发动机的喷嘴,在喷注单元低压高频燃烧不稳定性模拟实验系统上开展实验,研究了喷嘴结构对燃烧稳定性边界的影响。实验使用气态空气与氧气的混合物作为氧化剂,加热的煤油蒸汽作为燃料;喷嘴为全尺寸气液同轴直流离心式喷嘴,模拟燃烧室与真实燃烧室的固有声学频率相等。根据测量模拟燃烧室内的脉动压力区分大幅振荡、小幅振荡和稳定工作。研究结果表明,喷嘴长度、缩进室长度和入口节流嘴直径对高频燃烧不稳定性裕量有很大影响,并存在相对最佳值。     

激波作用下含缺陷固体火箭装药的流固耦合数值模拟

采用弱耦合方法对激波作用下固体火箭发动机含缺陷药柱的流固耦合相互作用进行数值模拟。其中非定常流场采用基于任意拉格朗日-欧拉坐标系下的二维可压缩Euler方程进行描述,并采用格心格式的有限体积方法对方程进行离散求解;对激波冲击作用下含装药裂纹的固体位移场采用时域间断Galerkin扩展有限元法进行数值模拟,并对裂纹尖端动态应力强度因子进行计算。结果表明:激波在固体火箭发动机内装药裂缝传播过程中具有反射、绕射等现象,表现出高度非定常非线性的特点;同时流固耦合相互作用使得裂纹尖端位移场以及应力强度因子表现出振荡效应。     

考虑自然对流的某固体火箭发动机慢速烤燃特性数值分析

针对某高氯酸铵/端羟基聚丁二烯(AP/HTPB)推进剂固体火箭发动机,采用两步总包反应描述AP/HTPB 的烤燃过程,建立了考虑发动机空腔自然对流的二维轴对称烤燃模型,对加热速率分别为 3.6、7.2 和10.8 K/h 时火箭发动机的慢速烤燃行为进行了数值预测,研究了该火箭发动机的热安全性问题。结果表明,固体火箭发动机空腔内的自然对流对 AP/HTPB 推进剂的着火温度、着火延迟期和着火位置有一定影响,在热安全性精确分析中不可忽略。3种加热速率下,AP/HTPB 推进剂的最初着火位置均出现在药柱肩部的环形区域内,3种加热速率对应的着火延迟期、着火温度及着火时壳体温度分别为30.71、20.06、18.68 h,526.52、528.10、530.64 K,和479.56、496.82、508.77 K。随着加热速率的增大,烤燃响应区域向推进剂与绝热层交界处移动,着火位置的二维截面由椭圆形变为半椭圆形。     

AERODYNAMICALLY GENERATED ACOUSTIC RESONANCE IN A PIPE WITH ANNULAR FLOW RESTRICTORS

An experimental study of the coupling between fluid dynamic instabilities and an acoustic field is performed for the case of a pipe with annular flow restrictors, representing a segmented solid propellant booster. As long as the distance between the restrictors remains smaller than the length of the flow recovery region behind the upstream restrictor, the fluid flow can amplify the acoustic pereturbations at the frequencies of the acoustic modes, leading to strong resonance for specific flow velocity ranges. A physical explanation is proposed, linking the amplification of the acoustic perturbation to the phase and frequency of vortex shedding from the restrictors. An approximate semi-empirical correlation is developed for the critical Strouhal number of the phenomenon as a function of the restrictor size and other problem parameters.     

Large-eddy simulation of wing tip vortex in the near field

Large-eddy simulation with filtered-structure-function subgrid model and implicit large-eddy simulation (ILES without explicit subgrid model) using high-order accuracy and high resolution compact scheme have been performed on the tip vortex shedding from a rectangular half-wing with a NACA 0012 airfoil section and a rounded wing tip. The formation of the tip vortex and its initial development in the boundary layer and the near field wake are investigated and analysed in detail. The physics, why the tip vortex, which is originally turbulent in the boundary layer, is re-laminarised and becomes stable and laminar rapidly after shedding in the near field, is revealed by this simulation. The computation also shows the widely used second-order subgrid model is not consistent to six-order compact scheme and would degenerate the six-order LES results to second-order. Therefore, high-order schemes, grid refinement and six-order subgrid models are critical to LES approaches.     

Vortex-shedding from single and tandem cylinders in the presence of applied sound

A single cylinder and two tandem cylinder configurations with longitudinal pitch ratios L/D=1.75 and 2.5 were rigidly mounted in an open circuit wind tunnel and a standing acoustic pressure wave was imposed so that the acoustic particle velocity was normal to both the cylinder axis and the mean flow velocity. The effect of sound on the vortex-shedding was investigated for various amplitudes by means of pressure taps on the cylinders and wake hot-wire probes. These tests show that applied sound can entrain and shift the natural vortex-shedding frequency to the frequency of excitation and produce nonlinearities in the wake. The lock-in envelope for the tandem cylinders is considerably larger than for the single cylinder. The lock-in range for the smaller tandem cylinder spacing was broader still than either the single cylinder, or the L/D=2.5 tandem cylinder case. The pressure and hot-wire measurements show for the single cylinder, and tandem cylinder configuration with pitch ratio L/D=2.5, that there was a phase jump near the coincidence of the vortex-shedding frequency and the excitation frequency, while there was no jump for the pitch ratio of 1.75. As well, the applied sound field was also noted to induce vortex-shedding in the gap for the L/D=2.5 case, while no vortex-shedding was noted for the smaller pitch ratio.     

Numerical simulation of flow‐induced noise using LES/SAS and Lighthill's acoustic analogy

We present a finite element (FE) formulation of Lighthill's acoustic analogy for the hybrid computation of noise generated by turbulent flows. In the present approach, the flow field is computed using large eddy simulation and scale adaptive simulation turbulence models. The acoustic propagation is obtained by solving the variational formulation of Lighthill's acoustic analogy with the FE method. In order to preserve the acoustic energy, we compute the inhomogeneous part of Lighthill's wave equation by applying the FE formulation on the fine flow grid. The resulting acoustic nodal loads are then conservatively interpolated to the coarser acoustic grid. Subsequently, the radiated acoustic field can be solved in both time and frequency domains. In the latter case, an enhanced perfectly matched layer technique is employed, allowing one to truncate the computational domain in the acoustic near field, without compromising the numerical solution. Our hybrid approach is validated by comparing the numerical results of the acoustic field induced by a corotating vortex pair with the corresponding analytical solution. To demonstrate the applicability of our scheme, we present full 3D numerical results for the computed acoustic field generated by the turbulent flow around square cylinder geometries. The sound pressure levels obtained compare well with measured values. Copyright © 2009 John Wiley & Sons, Ltd.     

Vibroacoustic responses of a heavy fluid loaded cylindrical shell excited by a turbulent boundary layer

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.     

Analysis of energy transfers of a sheared flow generated by wall injection

 We propose in this work to characterize the unsteady behavior of a flow generated by wall injection and encountering an obstacle. This sutdy concerns the prediction of the stability of segmented solid propellant rocket motors. The simulation of such a system is studied in cold flow, which makes it possible to analyze the basic phenomena and the energy transfer mechanisms of the flow. The results obtained allow the identification of the vortex structures by visualization inside a shear layer created at the top of an obstacle. The analysis of the pressure field shows that the dynamic parameters (mass flow rate or flow velocity) generate a phenomenon of selective excitation and of longitudinal acoustic modes amplification, which is accompanied by an energy transfer between modes. Received: 30 October 1997 / Accepted: 8 June 1998     

Acoustic field in a borehole within fluid formations with a horizontal interface

The acoustic field in a cylindrical borehole embedded in a horizontally layered infinite medium is studied. The modes in each layer are found to consist of continuous as well as discrete ones, the orthogonality and completeness of which are proven. The relevant weights associated with the two kinds of modes are determined by solving a set of integral equations deduced from the boundary conditions at the layer interface. This technique is not limited to low frequencies, but applies well to frequencies prevailing in typical logging environment. Reflection, transmission and coupling coefficients of different modes are evaluated. The numerical results are verified by comparison with the method of real axis integration (RAI) and the hybrid mehtod proposed by Tsang [“Transient acoustic waves in a fluid-filled borehole with a horizontal bed boundary separating two solid formations”, J. Acoust. Soc. Am. 81, 844–853 (1987)]. The scaled laboratory experiments are carried out and the corresponding results are presented for comparison with the numerical computation.     

Noise radiated by a non-isothermal,temporal mixing layer. Part I: Direct computation and prediction using compressible DNS

Direct numerical simulations (DNSs) are performed in order to study acoustic emissions generated during the transition of isothermal and non-isothermal mixing layers. The sound from temporally evolving mixing layers is computed directly using DNS for a computational domain, which includes both aerodynamic and acoustic fields. Good precision of the computed acoustic field is ensured by using a numerical code based on high-order finite difference schemes of quasi-spectral accuracy. Two- and three-dimensional simulations of mixing layers are performed for various Mach numbers and temperature ratios. For each case, the acoustic radiation of the mixing layer transition is investigated. Comparisons illustrate the importance of the combined effects of temperature and Mach number on the acoustic intensity. Qualitative agreement with existing experimental observations for hot jet flows is observed. It is also found that the appearance of three-dimensional motion leads to a substantial reduction of sound emissions. In the second part of this study, DNS data are used to perform acoustic analogy predictions. Excellent agreement between direct computations and predictions is obtained in all cases. Analysis of the source terms yields a new interpretation of temperature and Mach number effects, based on the predominance of one term over the other.     

Unsteady turbulent flow of a gas suspension in a channel under conditions of injection and forced pressure oscillations

A turbulent flow of a suspension of solid particles in a gas is considered. The suspension is located in a channel with permeable walls (the pressure at the left end face of the channel follows a sinusoidal law). The flow considered here reflects the principal features of the flow in the combustion chamber of a solid-propellant rocket motor. The unsteady flow of the gas suspension is described by using the Eulerian-Lagrangian approach. A stochastic variant of the discrete-trajectory approach is used for modeling the particle motion. The influence of the condensed phase on the turbulence characteristics and acoustic oscillations of the parameters of the working medium in the channel in the case of injection is discussed. The calculated results are compared with data obtained in a physical experiment.     

A large-scale matched index of refraction flow facility for LDA studies around complex geometries

Useage of laser-Doppler anemometry (LDA) requires optical access to the flow field of interest. This has not always proved easy, as in the case of complex geometries or very near-wall boundary layer measurements. One solution is to employ a solid material and fluid with the same refractive index. In this case, there is no optical interference of the solid with the LDA. Although this technique is not new, previous studies have been limited to small flow apparatus and relatively unpleasant fluids. A large-scale flow tunnel has now been constructed, permitting matched index of refraction LDA measurements in difficult geometries, higher Reynolds numbers, and increased spatial resolution in the measurements. This paper describes the facility and fluid flow quality, and presents some preliminary results for very near-wall measurements of a transitional boundary layer behind a roughness element. Received: 13 March 2000/Accepted: 30 July 2000     

Implicit schemes with large time step for non‐linear equations: application to river flow hydraulics

In this work, first‐order upwind implicit schemes are considered. The traditional tridiagonal scheme is rewritten as a sum of two bidiagonal schemes in order to produce a simpler method better suited for unsteady transcritical flows. On the other hand, the origin of the instabilities associated to the use of upwind implicit methods for shock propagations is identified and a new stability condition for non‐linear problems is proposed. This modification produces a robust, simple and accurate upwind semi‐explicit scheme suitable for discontinuous flows with high Courant–Friedrichs–Lewy (CFL) numbers. The discretization at the boundaries is based on the condition of global mass conservation thus enabling a fully conservative solution for all kind of boundary conditions. The performance of the proposed technique will be shown in the solution of the inviscid Burgers' equation, in an ideal dambreak test case, in some steady open channel flow test cases with analytical solution and in a realistic flood routing problem, where stable and accurate solutions will be presented using CFL values up to 100. Copyright © 2004 John Wiley & Sons, Ltd.     

射流元件控制通道流动的三维数值模拟

针对一种射流元件控制通道的复杂结构 ,采用分块对接技术和网格“融合”技术生成计算网格 ,并运用五步显式格式的 Runge-Kutta法和多重网格法对含全 N-S方程、RNG k-ε湍流模型和两层分区壁面模型的流动模型进行数值求解。通过对控制通道内部流动的数值模拟和流场特性分析 ,提出了改进方案