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

这个小企业创新研究（SBIR）第一阶段项目的更广泛的影响是加速了创新工业设计概念的发展，包括使用计算流体动力学（CFD）软件的复杂湍流。尽管CFD软件在多个行业都有广泛的应用，但该公司特别感兴趣的是具有强涡流尾流的物体，如生物启发的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，而无需在设计阶段建造和测试原型。 该项目还可以提高城市空中交通工具的安全性和运行范围。拟议的基于云的CFD软件将为初创公司和小型公司（无法访问高性能计算资源）提供在合理的时间范围内执行CFD分析的能力。这一新的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，因为他们将更好地理解湍流新方程组的优点。这一小型企业创新研究（SBIR）第一阶段项目旨在开发一种快速的高保真计算流体动力学（CFD）该软件用于预测复杂几何结构在大雷诺数（Re）下的非定常流动分离，无需任何启发式湍流建模。该软件将建立在以前的工作，提出者谁开发了一种新的基于弯曲的大涡模拟（LES）方法的高Re湍流。LES方法使用屈曲（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Re流中的急剧涡度梯度区域。该方法还使用超粘性耗散，而不是一个参数化的子网格模型未解决的小尺度湍流运动。将基于弯曲的LES方法与用于物体表面的涡面元方法耦合，将其扩展到复杂的几何形状。涡面元法可从壁涡量准确预测壁边界上的剪应力，而无需计算要求高的细网格来解决高Re流中出现的薄边界层。所提出的方法代表了一种新的技术，使用面元方法，这在空气动力学中有着丰富的历史，提供边界条件的大涡模拟的旋涡wake.This奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的智力价值和更广泛的影响审查标准。

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.