Direct Numerical and Large-eddy Simulation of Supersonic Transverse Jets Using a Novel Numerical Method

PI计划使用直接数值和大涡模拟来研究高速横流中的横向射流，并与现有的实验数据进行比较。提出的研究目标是在低雷诺数下开发高保真的直接Navier-Stokes （DNS）数据库，并在实验雷诺数下开发超音速横流中横向射流的大涡模拟（LES）能力。具体的研究将涉及该流的渗透、夹带和混合特性，并利用这一具有挑战性的问题作为测试平台，开发一种新的数值方法。模拟使用了一种新颖的数值方法和由PI小组开发的非结构化网格的子网格模型。该算法保证了鲁棒性和精度，没有数值损耗。对控制方程进行了尺度调整，保证了在低马赫数极限下，离散方程解析化为不可压缩方程。推导了在高度倾斜的非结构化网格上精确的离散算子，并在校正步骤中采用了冲击捕获方案。该子网格模型求解了一个无可调系数的子网格动能演化方程。如果成功，这种数值方法将对超出本工作范围的广泛问题产生重大影响。高速横向射流是实现超燃冲压发动机内部持续燃烧的核心，代表了航空推进的下一个前沿。高速横向射流的另一个重要应用是再入条件下的推力矢量控制。从模拟中得到的物理理解将有助于开发实际的缩放定律，而非结构化LES方法将允许对这些系统进行实际预测和设计。该研究还寻求将紊流混合的知识扩展到高速。在影响喷气轨迹、穿透和混合等基本问题上缺乏共识。本研究将由一名博士生和一名本科生进行。这名本科生将从明尼苏达超级计算机研究所的暑期实习项目中挑选，该项目吸引了来自全国各地的学生。PI还将参与超级计算机研究所的另一个扩展项目，该项目涉及双子城地区的高中生。建议的工作将成为PI的教学材料的一部分，以及面向广大受众的演示文稿和文章。

CBET - 0828162 Mahesh, Krishnan The PI plans use of direct numerical and large-eddy simulation to study transverse jets in high-speed cross flow and compare to existing experimental data. The objectives of the proposed research are to develop a high-fidelity Direct Navier-Stokes (DNS) database at low Reynolds numbers, and Large-Eddy Simulation (LES) capability at experimental Reynolds numbers for transverse jets in supersonic cross flow. Specific studies will concern penetration, entrainment and mixing characteristics of this flow and developing a novel numerical methodology using this challenging problem as a testbed. The simulations use a novel numerical method and subgrid model developed by the PI's group for unstructured grids. The algorithm ensures robustness and accuracy without numerical dissipation. It rescales the governing equations and ensures that the discrete equations analytically reduce to the incompressible equations in the limit of low Mach number. Discrete operators are derived to be accurate on highly skewed unstructured grids and a shock-capturing scheme is applied in a corrector step. The subgrid model solves an evolution equation for the subgrid kinetic energy with no adjustable coefficients. If successful, this numerical methodology will have significant impact on a wide class of problems beyond the scope of this work. High-speed transverse jets are central to enabling sustained combustion inside scramjet engines which represent the next frontier in aviation propulsion. Another important application of high-speed transverse jets is thrust vector control under re-entry conditions. The physical understanding developed from the simulations will help develop practical scaling laws, while the unstructured LES methodology will allow actual prediction and design of these systems. The study also seeks to expand knowledge of turbulent mixing to high speeds. There is a lack of consensus on fundamental issues such as what affects jet trajectories, penetration and mixing. This study will be performed by one PhD student and one undergraduate student. The undergraduate student will be chosen from the Minnesota Supercomputing Institute's summer internship program which draws students from across the country. The PI will also participate in another outreach program of the Super-computing Institute involving high school students from the Twin Cities area. The proposed work will form part of the PI's teaching material, and presentations and articles intended for a broad audience.