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

CBET-0828162，Mahesh，Krishnan，The 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。这项研究的目的是建立一个低雷诺数下的高保真直接N-S数据库和实验雷诺数下的超音速横向射流大涡模拟(LES)能力。具体的研究将涉及这种流动的渗透、卷吸和混合特性，并以这一具有挑战性的问题为试验台开发一种新的数值方法。模拟使用了一种新的数值方法和PI小组为非结构网格开发的子网格模型。该算法在不耗散数值的前提下，保证了算法的稳健性和准确性。它对控制方程进行了重新标度，保证了离散方程在低马赫数极限下解析化为不可压缩方程。离散算子在高度倾斜的非结构网格上是精确的，并在校正步骤中应用了激波捕捉格式。亚格子模型求解一个无可调系数的亚格子动能演化方程。如果成功，这种数值方法将对超出这项工作范围的广泛类别的问题产生重大影响。高速横向喷流是实现超燃冲压发动机持续燃烧的核心，而超燃冲压发动机代表着航空推进的下一个前沿。高速横向喷流的另一个重要应用是再入条件下的推力矢量控制。从模拟中发展出来的物理理解将有助于制定实际的标度律，而非结构大涡模拟方法将允许实际预测和设计这些系统。这项研究还试图将湍流混合的知识扩展到高速。在基本问题上缺乏共识，例如什么影响喷流轨迹、穿透和混合。这项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学院的暑期实习项目中挑选出来，该项目吸引了全国各地的学生。PI还将参加超级计算学院的另一个外展项目，该项目涉及来自双子城地区的高中生。拟议的工作将成为国际和平协会教材的一部分，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.