基于响应面模型的波瓣混合排气系统近似模型研究

Research on Approximation Model of Lobed Mixing Exhaust System Based on Response Surface Methodology

关键词:  波瓣混合排气系统  波瓣高宽比  多项式响应面模型  波瓣性能参数  波瓣结构参数

Key words:  Lobed mixing exhaust system  Ratio of lobe height to lobe width  Polynomial response surface methodology  Lobe performance parameter  Lobe structure parameter

摘要:

基于Navier-Stokes方程组对涡扇发动机波瓣强迫混合排气系统进行了数值模拟，获得了波瓣尾缘位置内、外涵流通面积与内、外涵入口位置流道截面积相等时，不同波瓣高宽比对波瓣混合排气系统性能参数以及结构参数的影响规律。并以此为基础，采用不同阶数的多项式响应面模型建立了波瓣性能参数随高宽比变化的近似模型。在多项式响应面模型拟合精度方面，相对于二阶、三阶多项式响应面模型，四阶多项式响应面模型能够较好地反映出热混合效率、总压恢复系数、排气系统相对推力、波瓣混合器相对质量随波瓣高宽比的变化规律，其拟合结果与数值仿真结果也相差极小。在波瓣高宽比对混合排气系统性能影响方面，在混合排气系统出口截面处，随着波瓣高宽比的增加，热混合效率在“波浪状”的变化规律中整体呈现出“增大-减小”发展趋势，总压恢复系数则呈现出“缓慢增加-迅速降低-增加-迅速下降”的复杂变化趋势；在排气系统相对推力方面，当高宽比大于3时，虽然相对推力呈现出波浪形的变化趋势，但变化值极小；对于波瓣混合器的相对质量，随着高宽比的增加，波瓣混合器的相对质量逐渐增大。

Abstract:

Numerical simulation based on Navier-Stokes equations was applied to the lobed forced mixing exhaust system of turbofan engine. The effects of ratio of lobe height to lobe width，when area at lobe exit equals to the one at the exhaust entrance，on the performance and structure of lobed mixer were obtained. Based on this，approximation models about change of lobe performance with ratio of lobe height to width were created by polynomial response surface methodology(RSM)with different order of polynomial. In the respect of fitting precision of polynomial response surface methodology，compared with second-order and third-order RSM methods，the forth-order RSM method can well reflect the change of thermal mixing efficiency，total pressure recovery coefficient，relative thrust and lobe relative weight with the ratio of lobe height to width. Moreover，the errors of calculation results between the forth-order RSM method and numerical simulation are very small. In the respect of effects of ratio of lobe height to weight on performance of mixing exhaust system，at the exit of mixing exhaust system，as increasing the ratio of lobe height to width，in general，the thermal mixing efficiency increases at first and then declines in the wavy changing tendency. The total pressure recovery coefficient appears to change like this “slowly increases-sharply declines-augments-quickly reduces”; as for the relative thrust of exhaust system，when ratio of lobe height to width is larger than 3，although it changes like wave，the variation is very small. For the lobe relative weight，it increases with increasing the ratio of lobe height to width.