针对叶轮机流场分析的不同Spalart-Allmaras湍流模型评价

Evaluation of Different Spalart-Allmaras Turbulence Models for Turbomachinery Flow Field Analysis

关键词:  叶轮机  湍流模型  边界层  流场分析  分离  数值模拟

Key words:  Turbomachine  Turbulence model  Boundary layer  Flow field analysis  Separation  Numerical simulation

摘要:

Spalart-Allmaras（SA）湍流模型在Reynolds-Average Navier-Stokes（RANS）方程求解中得到了广泛的应用。针对叶轮机数值模拟，国内外学者提出了很多修正的SA模型，但它们之间的对比少有研究。为此，综述了原始的SA（SA-standard），SA-neg，SA-Helicity，SA-Ning及SA-R五种不同SA湍流模型。针对NASA Rotor 67和NASA Rotor 37，考察这五种湍流模型对数值计算稳定性的影响及对叶轮机内部流动细节捕捉的能力。研究表明：SA-standard和SA-neg湍流模型计算结果几乎相同；相比于SA-standard湍流模型，SA-Ning湍流模型计算的压比、效率和堵塞流量均较大；SA-R湍流模型模拟的激波/边界层干涉更严重，分离区域更大，计算的压比小，模型修正效果不理想；SA-Helicity湍流模型不仅能极大地提高计算的压比和流量范围，而且能提高计算的稳定性和失速工况下的计算准确性，但计算的堵塞流量和效率较小。

Abstract:

Spalart-Allmaras （SA） turbulence model has been widely used in solving the Reynolds-Averaged Navier-Stokes （RANS） equations. To simulate the flow fields within turbomachines， many variants of SA turbulence models have been proposed， but the comparison between them is rarely conducted. The SA-standard， SA-neg， SA-Helicity， SA-Ning and SA-R turbulence models are reviewed. By taking NASA rotor 67 and NASA rotor 37 as the test vehicles， the influence on the numerical stability and the capability of the five turbulence models to capture the flow details within turbomachines are investigated. It is shown that the results from both SA-standard and SA-neg turbulence models are almost the same. Compared with the SA-standard turbulence model， the SA-Ning turbulence model predicts higher pressure ratio， efficiency and choked mass flow rate. The shock-wave/boundary-layer interaction is over-predicted by the SA-R turbulence model and thus the size of separation is larger， the pressure ratio of the compressors calculated by this model is lower， the modification is not satisfactory. The SA-Helicity turbulence model can improve not only the pressure ratio and the range of mass flow rate but also the numerical stability and solution accuracy at a near stall condition. Nevertheless it underestimates the choked mass flow rate and efficiency.