有壁面质量注入通道流体动力学典型问题分析
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摘要
鉴于有壁面注入通道空间流动在发汗冷却、多孔介质通道空间流动、固体火箭发动机燃烧室流动、内弹道设计、燃烧及稳定性研究中的重要性,本论文主要针对典型的带壁面注入通道空间流动进行了系统研究,研究考虑了不同头部注入模式的壁面注入通道、考虑壁面退移的轴对称壁面注入通道、有颗粒相注入的两相流通道、具有小倾斜角度的二维壁面注入通道及旋转情况下的带壁面注入通道流,主要工作及其结论如下：
(1)给出了任意头部注入情况下Taylor-Culick流的分析解并进行了数值研究,分别通过无粘、层流和湍流数值解验证了分析解的准确性及应用范围；
(2)对具有壁面退移的带壁面质量注入通道内流场进行研究,通过运用空间相似与时间相似原理简化N-S方程,基于解析方法以及运用摄动法求解高阶微分方程,然后采用CFD方法通过动网格技术对该问题进行数值模拟。分析比较不同的燃面无量纲减退率a及燃气注入雷诺数R下,通道的速度场、压力场及剪应力分布。对于高燃速推进剂,即α/R较大时,时间相关性必须考虑,不考虑燃面退移的准稳态计算将低估ur,△pr。
(3)对二维两相流通道内的流动规律进行了分析研究。首先采用Lagrange方法,基于摄动法获得了小Stokes数情况下通道两相流的分析解。然后应用Euler方法,获得了通道两相流的自相似解,应用4阶R-K方法求解出相似函数、速度及密度分布,给出了不同Stokes数情况下两相流规律。
(4)对具有倾斜燃面的有质量注入通道内流场进行了研究。结果表明,燃面倾斜角a与平直燃面长度L对燃烧室内流场具有很重要的影响,用平直燃面代替倾斜燃面,不仅会高估压降,而且会影响流场的其它参数,这种影响在加长燃烧室或大燃面倾斜角发动机中表现的尤为突出。
(5)对带壁面注入的旋转通道(具有柱形装药旋转固体火箭发动机通道)内流场进行了研究。首先通过解析方法求解简化后的欧拉方程,获得了无粘情况下的旋转通道解析解,在此基础上,运用渐进展开匹配法求解引入粘性修正的切向动量方程,并获得解析解,切向速度分布解具有组合涡特征。分析了涡核半径与注入雷诺数及旋转转数的关系。同时考虑了可压缩修正条件下的组合涡规律。然后采用CFD对柱形装药旋转固体火箭发动机通道进行数值模拟。分析比较不同转速下的速度分布、涡核尺度、燃烧室的分区特征及旋转情况下的封头端面的二次涡效应,进而为旋转对发动机封头烧蚀研究给出了理论依据。
Since the channel flows such as transpiration cooling, porous medium with mass injection and bulk gas flow of porous chamber in solid rocket motors (RSM) etc., are characterized by wall mass injection, especially for interior ballastics of RSM, hydrodynamic and combustion instability. The study is focus on typical channel spatial flow with mass injection, which includes the Taylor-Culick flow with arbitrary headwall injection, axisymmetric chamber gas flow with regression walls, two-phase channel flow with particles injection, planar channel flow with tapered wall and mean flow of spinning channel with wall mass injection (especially for RSM). The main conclusions are as follows:
(1) Analytical and numerical studies on the Taylor-Culick flow with arbitrary headwall injection are performed and numerical validation of the analytical solutions is in consideration of inviscid, laminar and turbulent flow.
(2) Analytical and numerical solutions of axisymmetric chamber gas flow with regression walls are compared. A high order ordinary differtial equation, Reduced N-S equations by spatial similarity andt emporal similarity, is analytically solved with perturbation method. Numerical simulation is based on laminar flow with dynamic mesh techinique to deal with regressing wall. The velocity fields, pressure fields and shear stress distributions are mainly studied for different rates of wall regression a and injection Reynolds number R. The fact that numerical results are well in agreement with the analytical solutions gains confidence in the analytical approximation.
(3) Analytical study on the gas-particle two phase mean flow with particles injection is performed with Lagrange method and Euler method respectively. The perturbation approximate solution for small Stokes number with Lagrange method is gained. The self-similarity solution of particle phase flow field is derived and the similarity functions and profiles of velocity and density for different Stokes Number are solved with fourth order R-K method.
(4) The channel mean flow with tapered sidewalls is studied with both analytical method and numerical method. The results indicate that the influence of taper angle of sidewalls a and the length of straight sidewalls L is important, the numerical results are well in agreement with the analytical solutions. The pressure drop may be over-estimated only in consideration of straight sidewalls and its influence on other parameters is so on, especially for SRM with the longer chamber and larger tapered combustion surface.
(5) The analytic and numerical studies on spinning channel mean flow with porous wall injection is accomplished. The analytical inviscid solutions of spinning mean flow are based on the reduced Euler equations and viscous core corrections to swirl driven mean flow with wall injection is based on tangential momentum equation with the second order viscous terms. Pursuant to conventional asymptotic matching theory, a complete solution is arrived by a separate expansion (the sum of inner and outer expansions), which is cheraterized by The Rankine vortex (sum of free votex and forced vortex) The viscous core radius versus injection velocity with swirl speed is analysed, meanwhile, in consideration of compressibility corrections. Numerical simulation is performed with CFD to study the channel mean flow of a spinning SRM with inner burning cylindrical circle grain. The velocity profiles, viscous core size, segment characteristics of flow in the chamber and secondary vortex near the headwall vernus swirl speed are analysed in details. It provides theoretical basis for the study on the erosion of headwall closure in spinning SRM.
(1)给出了任意头部注入情况下Taylor-Culick流的分析解并进行了数值研究,分别通过无粘、层流和湍流数值解验证了分析解的准确性及应用范围；
(2)对具有壁面退移的带壁面质量注入通道内流场进行研究,通过运用空间相似与时间相似原理简化N-S方程,基于解析方法以及运用摄动法求解高阶微分方程,然后采用CFD方法通过动网格技术对该问题进行数值模拟。分析比较不同的燃面无量纲减退率a及燃气注入雷诺数R下,通道的速度场、压力场及剪应力分布。对于高燃速推进剂,即α/R较大时,时间相关性必须考虑,不考虑燃面退移的准稳态计算将低估ur,△pr。
(3)对二维两相流通道内的流动规律进行了分析研究。首先采用Lagrange方法,基于摄动法获得了小Stokes数情况下通道两相流的分析解。然后应用Euler方法,获得了通道两相流的自相似解,应用4阶R-K方法求解出相似函数、速度及密度分布,给出了不同Stokes数情况下两相流规律。
(4)对具有倾斜燃面的有质量注入通道内流场进行了研究。结果表明,燃面倾斜角a与平直燃面长度L对燃烧室内流场具有很重要的影响,用平直燃面代替倾斜燃面,不仅会高估压降,而且会影响流场的其它参数,这种影响在加长燃烧室或大燃面倾斜角发动机中表现的尤为突出。
(5)对带壁面注入的旋转通道(具有柱形装药旋转固体火箭发动机通道)内流场进行了研究。首先通过解析方法求解简化后的欧拉方程,获得了无粘情况下的旋转通道解析解,在此基础上,运用渐进展开匹配法求解引入粘性修正的切向动量方程,并获得解析解,切向速度分布解具有组合涡特征。分析了涡核半径与注入雷诺数及旋转转数的关系。同时考虑了可压缩修正条件下的组合涡规律。然后采用CFD对柱形装药旋转固体火箭发动机通道进行数值模拟。分析比较不同转速下的速度分布、涡核尺度、燃烧室的分区特征及旋转情况下的封头端面的二次涡效应,进而为旋转对发动机封头烧蚀研究给出了理论依据。
Since the channel flows such as transpiration cooling, porous medium with mass injection and bulk gas flow of porous chamber in solid rocket motors (RSM) etc., are characterized by wall mass injection, especially for interior ballastics of RSM, hydrodynamic and combustion instability. The study is focus on typical channel spatial flow with mass injection, which includes the Taylor-Culick flow with arbitrary headwall injection, axisymmetric chamber gas flow with regression walls, two-phase channel flow with particles injection, planar channel flow with tapered wall and mean flow of spinning channel with wall mass injection (especially for RSM). The main conclusions are as follows:
(1) Analytical and numerical studies on the Taylor-Culick flow with arbitrary headwall injection are performed and numerical validation of the analytical solutions is in consideration of inviscid, laminar and turbulent flow.
(2) Analytical and numerical solutions of axisymmetric chamber gas flow with regression walls are compared. A high order ordinary differtial equation, Reduced N-S equations by spatial similarity andt emporal similarity, is analytically solved with perturbation method. Numerical simulation is based on laminar flow with dynamic mesh techinique to deal with regressing wall. The velocity fields, pressure fields and shear stress distributions are mainly studied for different rates of wall regression a and injection Reynolds number R. The fact that numerical results are well in agreement with the analytical solutions gains confidence in the analytical approximation.
(3) Analytical study on the gas-particle two phase mean flow with particles injection is performed with Lagrange method and Euler method respectively. The perturbation approximate solution for small Stokes number with Lagrange method is gained. The self-similarity solution of particle phase flow field is derived and the similarity functions and profiles of velocity and density for different Stokes Number are solved with fourth order R-K method.
(4) The channel mean flow with tapered sidewalls is studied with both analytical method and numerical method. The results indicate that the influence of taper angle of sidewalls a and the length of straight sidewalls L is important, the numerical results are well in agreement with the analytical solutions. The pressure drop may be over-estimated only in consideration of straight sidewalls and its influence on other parameters is so on, especially for SRM with the longer chamber and larger tapered combustion surface.
(5) The analytic and numerical studies on spinning channel mean flow with porous wall injection is accomplished. The analytical inviscid solutions of spinning mean flow are based on the reduced Euler equations and viscous core corrections to swirl driven mean flow with wall injection is based on tangential momentum equation with the second order viscous terms. Pursuant to conventional asymptotic matching theory, a complete solution is arrived by a separate expansion (the sum of inner and outer expansions), which is cheraterized by The Rankine vortex (sum of free votex and forced vortex) The viscous core radius versus injection velocity with swirl speed is analysed, meanwhile, in consideration of compressibility corrections. Numerical simulation is performed with CFD to study the channel mean flow of a spinning SRM with inner burning cylindrical circle grain. The velocity profiles, viscous core size, segment characteristics of flow in the chamber and secondary vortex near the headwall vernus swirl speed are analysed in details. It provides theoretical basis for the study on the erosion of headwall closure in spinning SRM.
引文
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