An Actuator Disk Model of Incidence and Deviation for RANS-Based Throughflow Analysis
An Actuator Disk Model of Incidence and Deviation for RANS-Based Throughflow Analysis
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DOI：
10.1115/1.4025155
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发表时间：
2014-02
影响因子：
1.7
通讯作者：
S. Taddei;F. Larocca
中科院分区：
文献类型：
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作者：
S. Taddei;F. Larocca
使用有限体积方案在完整轴流式涡轮机械的子午面中求解带有叶片阻塞和叶片力源项的雷诺平均纳维-斯托克斯 (RANS) 方程。引入可压缩致动器盘 (AD) 方程来修改前缘和后缘（LE 和 TE）处的对流通量的评估。 AD 的行为就像一个紧凑的叶片力，它可以瞬间改变流动而不产生非物理熵。这避免了 LE 不连续性上的非物理入射损失，并允许在 TE 上应用所有所需的偏差。与以前的处理不同，该模型不需要对通流（TF）表面进行手工修改，并且不区分无粘性和粘性子午流，这允许应对通过环空壁边界层的强入射梯度和二次偏差。本文推导了广义叶片力项，其中包括 TF 方程发散形式中 LE 和 TE AD 的贡献，并得出叶片负载、叶片推力、轴扭矩和轴功率的广义定义。在分析入射角为 32 度、偏差为 21 度的线性平板叶栅时，与未建模的数值解相比，所提出的模型将非物理总压损失减少了 105 倍。计算出的质量流量、叶片载荷和叶片推力与理论值非常吻合。完整的 RANS TF 求解器用于分析设计和非设计条件下的四级涡轮机，翼展方向平均倾角分别高达 2 度和 43 度。与传统的流线曲率解决方案相比，具有入射和偏差建模的 RANS 解决方案可以在两种操作条件下对质量流量、轴功率、总压比和绝热效率进行 0.1% 至 0.7% 的准确预测。它还强调了 LE 和 TE 处流角和马赫数的展向分布令人满意的一致性。特别是，有效地预测了二次偏差。没有建模的 RANS 解决方案仅在设计条件下显示出可接受的性能预测，并且不会引入偏差。
Reynolds-averaged Navier-Stokes (RANS) equations with blade blockage and blade force source terms are solved in the meridional plane of complete axial flow turbomachinery using a finite-volume scheme. The equations of the compressible actuator disk (AD) are introduced to modify the evaluation of the convective fluxes at the leading and trailing edges (LEs and TEs). An AD behaves as a compact blade force which instantaneously turns the flow with no production of unphysical entropy. This avoids unphysical incidence loss across the LE discontinuity and allows for application of all of the desired deviation at the TE. Unlike previous treatments, the model needs no handmade modification of the throughflow (TF) surface and does not discriminate between inviscid and viscous meridional flows, which allows for coping with strong incidence gradients through the annulus wall boundary layers and with secondary deviation. This paper derives a generalized blade force term that includes the contribution of the LE and TE ADs in the divergence form of the TF equations and leads to generalized definitions of blade load, blade thrust, shaft torque, and shaft power. In analyzing a linear flat plate cascade with an incidence of 32 deg and a deviation of 21 deg, the proposed model provided a 105 reduction of unphysical total pressure loss compared to the numerical solution with no modeling. The computed mass flow rate, blade load, and blade thrust showed excellent agreement with the theoretical values. The complete RANS TF solver was used to analyze a four-stage turbine in design and off-design conditions with a spanwise-averaged incidence of up to 2 deg and 43 deg, respectively. Compared to a traditional streamline curvature solution, the RANS solution with incidence and deviation modeling provided a 0.1 to 0.7% accurate prediction of mass flow rate, shaft power, total pressure ratio, and adiabatic efficiency in both the operating conditions. It also stressed satisfactory agreement concerning the spanwise distributions of flow angle and Mach number at LEs and TEs. In particular, secondary deviation was effectively predicted. The RANS solution with no modeling showed acceptable performance prediction only in design conditions and could introduce no deviation.