停滞压力对超声速二维塞式喷嘴设计的影响

提出了一种新的计算模型用于研究在出口处存在均匀和平行的气流下,燃烧室的停滞压力对超声速二维塞式喷嘴设计的影响。该模型基于真实气体(Real gas,RG)模型,通过使用Berthelot状态方程,考虑了共体积和分子间的相互作用效应。该模型还考虑了分子振动效应,以评估气体在高温下的行为。停滞压力和停滞温度是模型中的重要参数。在边缘,温度和密度是由2个非线性代数方程的分辨率给出的,这些方程由4个复数函数的积分制定。这是由一个新的、强大的和快速的算法完成的,且其他参数由分析关系决定。喷嘴中的气流扩展是Prandtl Meyer型的。喷嘴轮廓通过将喷嘴边缘的膨胀区离散为几个点来确定。马赫数、流动偏差、压力、温度和密度参数是在反演双变量Prandtl Meyer函数后确定的。计算中提出的函数的积分是由30阶的Gauss Legendre求积获得。由于进口和出口部分的气流是单向的,通过计算临界截面比与理论得到的临界截面比的收敛来进行数值控制并验证结果。在这种情况下,喷嘴的轮廓和流动参数,如喷嘴的质量、长度和推力系数,会自动收敛到精确结果。本文提出的新RG模型是对理想气体(Perfect gas,PG)和高温(High temperature,HT)两种模型的概括。后者可以针对低停滞压力进行设计,并不提供任何关于停滞压力变化的信息。因此,如果后者很高,就有必要通过本文的RG模型来修正PG和HT模型所给出的结果。与其他现有的喷嘴,如最小长度喷嘴(Minimum length nozzle,MLN),相比,塞式喷嘴具有更好的性能和设计参数。将本文RG模型应用到空气气流计算中,可对PG和HT模型的塞式喷嘴的质量、长度和推力系数进行校正。

Supersonic Two-Dimensional Minimum Length Nozzle Design at High Temperature. Application for Air

When the stagnation temperature of a perfect gas increases, the specific heat ratio does not remain constant any more, and start to vary with this temperature. The gas remains perfect, its state equation remains always valid, except it will name in more calorically imperfect gas or gas at High Temperature. The goal of this work is to trace the profiles of the supersonic Minimum Length Nozzle with centered expansion when the stagnation temperature is taken into account, lower than the threshold of dissociation of the molecules and to have for each exit Mach number several nozzles shapes by changing the value of the temperature. The method of characteristics is used with a new form of the Prandtl Meyer function at high temperature. The resolution of the obtained equations is done by the second order of fmite differences method by using the predictor corrector algorithm. A study on the error given by the perfect gas model compared to our model is presented. The comparison is made with a calorically perfect gas for goal to give a limit of application of this model. The application is for the air.