Investigating the Unsteady Fluid Physics within Jet Flows

In the nineteen sixties, the Aerospace Industry started using Computational Fluid Dynamics (CFD) as an important engineering tool in their design processes. Over time, and with both, improvements in High-Performance Computing (HPC) technologies, and improvements in numerical techniques, CFD became a tool of significant value to the engineer. The benefits derived from computational predictive techniques has created a demand in the CFD community for detailed physics capturing capabilities. Designers are craving greater specificity and with even greater details within flow fields. Most recently, capturing the origination of eddies, the growth of these eddies and the interactions among these eddies are of significant interest to the CFD community. In most cases, the growth and interactions of eddies lead to full blown turbulence. Nevertheless, the ultimate goal of all CFD techniques is to always attain consistently high degrees of accurate in all fluid physics simulations in any regime of fluid flow as governed by the Navier-Stokes equations. High fidelity tools, such as, Direct numerical simulations (DNS) and unsteady Reynolds average Navier-Stokes (URANS) use either superfine grid-sizes and/or complex turbulence models or filters in efforts to capture the details associated with fluid flows. In combination with these methods, very high-ordered numerical methods, such as, the weighted essentially non-oscillatory (WENO) schemes and others are employed. However, these schemes are not only cumbersome to execute but equally expensive to execute. Often times, the results of these high ordered schemes, especially when applied to hyperbolic partial differential equations in space and time, do not adequately capture the complete life cycles of the eddies. In unsteady flows, the complex building blocks for the flow development are often times eroded due either to dispersion and/or dissipation errors. The under-expanded jet flow which is typically generated by rocket engines is an example of an unsteady, ever developing flow filed, which is rich in fluid physics that will challenge all CFD simulation schemes. Moreover, the under-expanded flow field features consist of the main vortex pair, the vortex-induced shock waves, shock-vortex interactions, and Kelvin-Helmholtz type-structures, their evolution and their interactions until the flow transforms into a fully developed turbulent profile. The Integro-Differential Scheme (IDS) is used to evaluate this unsteady flow field and its solution is compared to that on a HOM. This investigation focuses on the formation of eddies and their interactions. The IDS numerical study not only revealed the existing of the Kelvin-Helmholtz instability structures, their evolutions, and their interactions, but its overall results closely mimic the simulated results of its LES counterpart.