Accurately predicting unsteady wakes and vortex-dominated flows is essential to a wide range of engineering applications, including aircraft, rotorcraft, shipboard operations, bio-inspired unsteady flight and propulsion, wind turbines, and urban flows. While current CFD software can model the complete flow field and wake system, the computational costs incurred in high Reynolds number unsteady turbulent flow simulations often remain prohibitive for routine engineering use, particularly for applications involving moving components. Prior work has demonstrated that by adopting a vorticity-velocity formulation in a grid-based off-body flow solver (VorTran-M and VorTran-M2) one can lower these costs by several orders of magnitude when compared to conventional approaches. This paper describes the extensions made to VorTran-M2 to support turbulent flows, and associated benchmarking activity to assess its performance for problems involving strong stretching and diffusion processes, whose competing contributions to the vorticity field are core drivers of turbulent flow evolution. Predictions are presented for: (i) the Kida-Pelz problem whose inviscid form is of mathematical interest due to its apparent formation of singular flow in finite time; and (ii) the Taylor Green vortex arrangement, which has been extensively studied as a fundamental simulation challenge in the turbulence modeling community. The results are used to evaluate the overall predictive ability and performance of two sub-grid scale models incorporated into VorTran-M2. Results indicate that the computational cost savings seen previously for inviscid and convection dominated problems extend to turbulent flow simulations supporting the viability of VorTran-M2 as a low cost means for accurately modeling far-field and background flows, particularly when long duration vorticity evolution is of interest.

准确预测不稳定的尾流和涡流占主导地位的流量对于广泛的工程应用至关重要，包括飞机，旋翼飞机，船上作业，受生物启发的不稳定飞行和推进，风力涡轮机以及城市流量。尽管当前的CFD软件可以对完整的流场和尾流系统进行建模，但雷诺数高的非恒定湍流模拟所引起的计算成本对于常规工程应用（尤其是涉及移动部件的应用）通常仍然是不利的。先前的工作表明，通过在基于网格的体外流量求解器（VorTran-M和VorTran-M2）中采用涡度-速度公式，与传统方法相比，可以将这些成本降低几个数量级。本文介绍了对VorTran-M2进行的扩展，以支持湍流，以及相关的基准测试活动，以评估其在涉及强拉伸和扩散过程的问题上的性能，这些问题对涡度场的竞争贡献是湍流发展的核心驱动力。提出以下预测：（i）由于在有限时间内明显地形成奇异流动，因此其无粘性形式具有数学意义的Kida-Pelz问题；（ii）泰勒格林涡旋装置，在湍流建模领域已被广泛研究为基本的模拟挑战。结果用于评估合并到VorTran-M2中的两个子网格规模模型的总体预测能力和性能。