SBIR Phase I: A Flexion-Based Computational Fluid Dynamics Tool for the Fast Computation of Turbulent Flow over Complex Geometries

小型企业创新研究(SBIR)第一阶段项目的更广泛影响是加快了创新工业设计概念的发展，涉及使用计算流体动力学(CFD)软件的复杂湍流流动。尽管CFD软件在几个行业都有广泛的应用，但该公司对涡流强烈的车身特别感兴趣，例如生物灵感可再生能源提取设备和电动垂直起降(EVTOL)车辆。预计该项目可能导致及时和具有成本效益的能源提取装置设计，而不需要在设计阶段建造和测试原型。该项目还可能增强城市空中机动车辆的安全性和运行范围。拟议的基于云的CFD软件将为初创企业和较小的公司(无需访问高性能计算资源)提供在合理的时间框架内执行CFD分析的能力。提出的新的Navier-Stokes方程的重新表述也将对下一代工程师和科学家的教育产生持久的影响，因为他们更好地了解了新的湍流方程组的优点。这个小型企业创新研究(SBIR)第一阶段项目旨在开发一个快速高保真的计算流体力学(CFD)软件，用于预测大雷诺数(Re)下复杂几何形状的非定常流动分离，而不需要任何启发式湍流建模。该软件将建立在提出者之前的工作基础上，他开发了一种新的基于弯曲的大涡模拟(LES)方法，用于高Re湍流流动。LES方法使用弯曲(涡度旋度)矢量作为Navier-Stokes方程中的主要因变量，以更好地跟踪高再流动中的急剧涡度梯度区。对于未解决的小尺度湍流运动，该方法还使用了高粘性耗散而不是参数化子网格模型。通过将基于弯曲的大涡模拟方法与体表涡面方法相结合，将其扩展到复杂的几何形状。涡面方法能够根据壁面涡度准确地预测壁面上的剪应力，而不需要计算上要求很高的精细网格来解决高再流动中出现的薄边界层。建议的方法代表了一种使用面板方法的新技术，该方法在空气动力学方面有着丰富的历史，为涡流尾流的大型涡流模拟提供边界条件。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The broader impact of this Small Business Innovation Research (SBIR) Phase I project is the acceleration of the development of innovative industrial design concepts involving complex turbulent fluid flow using computational fluid dynamics (CFD) software. Although CFD software has broad applications in several industries, the company’s particular interest is in bodies with strong vortical wakes such as bio-inspired renewable energy extraction devices and electric vertical takeoff/landing (eVTOL) vehicles. It is anticipated that the project may lead to the timely and cost-effective design of energy extraction devices without the need to build and test prototypes during the design phase. The project may also enhance the safety and operating envelope of urban air mobility vehicles. The proposed cloud-based CFD software will provide startups and smaller companies (without access to high-performance computing resources) with the ability to perform CFD analysis in reasonable timeframes. The proposed novel reformulation of the Navier-Stokes equations will also have a lasting impact on the education of the next generation of engineers and scientists as they gain a better understanding of the advantages of the new set of equations for turbulent flows.This Small Business Innovation Research (SBIR) Phase I project seeks to develop a fast high-fidelity computational fluid dynamics (CFD) software for predicting unsteady flow separations over complex geometries at large Reynolds (Re) numbers without any heuristic turbulence modeling. The software will build upon prior work by the proposer who developed a novel flexion-based Large Eddy Simulation (LES) method for high Re turbulent flows. The LES method uses the flexion (vorticity curl) vector as the primary dependent variable in the Navier-Stokes equations to better track sharp vorticity-gradient regions in high Re flows. The method also uses hyperviscous dissipation instead of a parameterized sub-grid model for unresolved small-scale turbulent motions. The flexion-based LES method will be extended to complex geometries by coupling it with a vortex panel method for the body surface. The vortex panel method leads to accurate predictions of the shear stress on wall boundaries from the wall vorticity without the computationally demanding requirement of a fine mesh to resolve the thin boundary layers that occur in high Re flows. The proposed approach represents a new technique of using panel methods, which have a rich history in aerodynamics, to provide boundary conditions for large eddy simulations of the vortical wake.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.