基于Gauss羽流模型低阶预估旋流燃烧室中守恒标量的空间分布  

Low⁃Order Predictions of Spatial Distributions of Conserved Scalars in Swirl Combustors Based on the Gaussian Plume Function

作　　者：吴子恒 张弛[1] 张世红 王柏森[1] WU Ziheng;ZHANG Chi;ZHANG Shihong;WANG Bosen(National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics,Research Institude of Aero-Engine,Beihang University,Beijing 102206,P.R.China)

机构地区：[1]北京航空航天大学航空发动机研究院航空发动机气动热力国家级重点实验室,北京102206

出　　处：《应用数学和力学》2023年第9期1070-1086,共17页Applied Mathematics and Mechanics

基　　金：国家科技重大专项(J2019-III-0014-0057)。

摘　　要：混合分数是表征燃料-空气混合的守恒标量,是湍流燃烧建模的关键参考标量.其空间分布通常通过三维数值模拟获得,然而对于几何形状复杂的燃烧器,三维数值模拟耗时长、成本高,导致燃烧器迭代设计过程效率低.该研究发展了基于Gauss羽流(Gaussian plume)模型的低阶模型来计算旋流燃烧室中的混合分数场,以加速燃料-空气混合策略的评估和参数化设计过程.相比传统的构型,新推导的Gauss羽流模型包含了径向对流的影响和针对旋流来流的修正.进一步发展了镜像反射模型来模拟壁面-羽流的相互作用,并引入相关修正来确保质量守恒.将新推导的Gauss羽流模型应用于甲烷旋流燃烧室混合分数场的低阶预测.基于数值收敛的三维数值模拟生成的数据库,首先采用最小二乘法对模型参数进行优化,然后在宽范围条件下验证了模型的预测精度.该研究不仅为旋流燃烧器内混合分数的快速预测提供了一种新方法,而且为Gauss羽流模型的进一步发展和应用提供了实例.The mixture fraction is a conserved scalar characterizing the fuel⁃air mixing.As a key reference sca⁃lar for turbulent combustion modelling,its spatial distribution is usually obtained through 3D numerical simula⁃tion,which are,however,time⁃consuming and costly for combustors with complex geometries.To overcome such low efficiency in the iterative designing process,a low⁃order model was developed based on the Gaussian plume function to compute the mixture fraction field in the swirl combustor to accelerate the evaluation of the fuel⁃air mixing strategy and the parameterized design process.Compared with the conventional formulation,the derived new Gaussian plume function includes the effects of convection and corrections due to swirl flows.A mirror image reflection model was further developed to simulate the wall⁃plume interactions,together with the relevant corrections to ensure mass conservation.This newly derived Gaussian plume model was applied to the low⁃older prediction of the mixture fraction field in a methane swirl combustor.Based on the database genera⁃ted through 3D numerical simulations,the model parameters were optimized with the least square method first.The prediction accuracy under broad working conditions was demonstrated.This study not only provides a no⁃vel approach for quick predictions of mixture fractions in swirl combustors,but also sets an instance for further development and application of the Gaussian plume model.

关 键 词：混合分数 Gauss羽流模型 低阶预估 旋流燃烧室 

分 类 号：V231.2[航空宇航科学与技术—航空宇航推进理论与工程]