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基于喷流拟序结构预测的SGS模型比较研究

COMPARISON OF SUB-GRID-SCALE MODELS BASED ON PREDICTION OF COHERENT STRUCTURES IN PLANE TURBULENT JETS

  • 摘要: 拟序结构是湍流机理研究的重要对象, 而亚网格尺度(sub-grid scale, SGS)模型的准确性是高精度大涡模拟的关键, 对正确预测湍流拟序结构有重要影响. 本文对马赫数0.9的可压缩喷流开展大涡模拟, 使用4阶空间截差和3阶时间截差的高精度有限差分算法, 亚网格尺度模型分别采用了Smagorinsky模型(Smagorinsky model, SM)、拟序结构动能模型(CKM)、选择多尺度模型(selective mixed-scale model, SMSM)、局部动态Smagorinsky模型(localized dynamic Smagorinsky model, LDSM)和拟序结构模型(coherent-structure Smagorinsky model, CSM)以及对平均耗散、瞬时涡结构、脉动速度POD主导模态的分析表明, u'的主导模态呈带状, 在下游分岔或破碎, 呈现出多尺度特征, v'的主导模态则呈流向排列的肋状, 矢量\left( u', v' \right)的模态在肋的两端呈环流模式, 表征流动卷吸, w'的主导模态呈流向排布的脊状, 表征流场受展向拉伸的模式. 脉动速度的POD模态对亚网格尺度耗散敏感, 其中CKM模型预测的峰值耗散区对应u'模态的低谷区, 因而预测的环流模式不明显; SM模型则未能预测出w'的脊状模态. SMSM, CSM和LDSM模型均较好地反映了湍流中涡结构的多尺度特性, 揭示了流动卷吸、脊状的展向拉伸等流动模式, 其中CSM模型的计算效率较高.

     

    Abstract: A compressible plane jet at Mach 0.9 is numerically studied by large-eddy simulation. The governing equations are discretized by fourth-order spatial and third-order temporal schemes. Five sub-grid-scale (SGS) models, namely, the standard Smagorinsky model (SM), the coherent structure kinetic model (CKM) and the selective mixed-scale model (SMSM), the localized dynamic Smagorinsky model (LDSM), and the coherent-structure Smagorinsky model (CSM), are employed for closure of the sub-grid scale (SGS) terms, respectively, and compared. Proper orthogonal decomposition (POD) method is applied to extract the leading modes of the fluctuating velocity components, i.e., u' in the streamwise, v' in the lateral and w' in the spanwise. The averaged flow fields, dissipation, the instantaneous vortical structures and the coherent structures represented by the leading POD modes, are compared. The leading POD modes of u' are two longitudinal stripes with fracted contours in the turbulent region, representing the multi-scaled flow and the decay of fluctuation strength. The leading modes of v' are a row of ribs with the lateral size growing along the streamwise, while the modes of \left( u', v' \right) are in a circular flow pattern around the ends of the ribs. The circular pattern penetrates both the jet flow and the peripheral flow, representing the flow entrainment. The leading modes of w' are a train of ridges along streamwise. Their positive and negative values represent the spanwise stretching pattern of the coherent structures. In comparison of these five SGS models, the instantaneous multi-scale vortical flow is not effectively predicted by the SM and the CKM, as the small vortical scale is smeared. The POD modes are found to be sensitive to the sub-grid dissipation, since the valley regions of the mode of u' coincide with the peak dissipation regions predicted by the CKM. The circular flow pattern is also not clearly predicted by the CKM. Neither the ridge pattern of the mode of w' is predicted by the SM. On the other hand, the multi-scales turbulent flow and the flow patterns of POD modes are well predicted by the CSM, the SMSM, and the LDSM, in which the CSM is computationally more efficient.

     

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