雷诺数指数与雷诺数比的关系分析与应用
Analysis and application of relationship between Reynolds number index and Reynolds number ratio
倪明 1魏佐君 1赵晨彦 1任光明 1甘晓华1
作者信息
- 1. 南方科技大学工学院力学与航空航天工程系,广东深圳 518055
- 折叠
摘要
雷诺数指数(RNI)与雷诺数比(RNR)作为常用的雷诺数相关问题重要无量纲数广泛地用于航空发动机研发过程中,然而前者多用于工程研制阶段,后者多用于研究初期阶段,两者长期处于应用层级割裂状态.为了厘清RNI与RNR之间的关系,首先用Π定理和无量纲数代数推导两种方法推导出了 RNI,结果揭示了 RNI的物理含义为考虑马赫数修正的RNR,代表了雷诺数强相似性原理;RNR仅基于表速相似,代表了雷诺数弱相似性原理.其次,比较了雷诺数指数与雷诺数比之间的关系,在两者的相对差仅为温度的函数,在工况温度比处于0.94～1.06的范围时,RNI与RNR两者相差±3％以内,认为两者可以互换;因为工况间温度比差距过大目前以RNR为自变量的雷诺数修正公式在实际使用中误差过大的原因之一.最后,给出了一种基于RNI为1.0、保证雷诺数强相似性的冷热态工作点模化方法,作为RNI的应用范例,并给出了两组冷热态换算结果,计算得到冷热态工况的Π函数是一致的,因此可以认为冷热态模化满足相似性原理.分析并解释了 RNI与RNR的关系,可作为航空发动机研制各阶段中雷诺数相关问题无量纲参数选取的依据.
Abstract
The Reynolds number index(RNI)and Reynolds number ratio(RNR)are commonly used as important dimensionless numbers for Reynolds number related problems in the development of aero-engine.However,the former is mostly used in the engineering development stage and the latter mostly used in the early stage of research,and the two have long been in a fragmented state at the application level.In order to clarify the relationship between RNI and RNR,RNI was firstly derived from two perspectives:Π theorem and algebraic derivation of dimensionless numbers,whose physical meaning was RNR considering Mach number correction,which represented the Reynolds number strong similarity principle.Secondly,the relationship between RNI and RNR was compared,in which the relative difference between these two was only a function of temperature;and when the difference between RNI and RNR was within the working temperature ratio range of 0.94-1.06,the difference between RNI and RNR was within±3％and these two were considered interchangeable;given the temperature ratio gap between working conditions was too large,this was one of the reasons why the current Reynolds number correction formula with RNR as the independent variable had too much errors in practice.Finally,the operation point at cold and hot states based on RNI of 1.0 was given as one of the applications of RNI,which guaranteed the strong Reynolds number similarity;and the results of two sets of cold and hot state conversions were given,and the Π functions of cold and hot state conditions were calculated to be consistent,and the cold and hot state modelling was considered to satisfy the similarity principle.The relationship between RNI and RNR explained and analyzed herein can be used as a basis for selection of dimensionless parameters for Reynolds number related problems in all stages of aero-engine development.
关键词
雷诺数指数/雷诺数比/相似性/模化/冷热态模化Key words
Reynolds number index/Reynolds number ratio/similarity/modalization/cold and hot states modalization引用本文复制引用
基金项目
深圳市基础研究重点项目(JCYJ20200109141403840)
国家自然科学基金青年科学基金(52106045)
出版年
2024
NETL
NSTL
万方数据