Investigating the Start-Up Structures and Their Evolution Within an Under-Expanded Jet Flows
Authors: Feng Dehua , Ferguson Frederick , Gao Yang , Niu Xinru 
Published: February 2024

Abstract
The initialization and evolution of the unsteady flow structures produced by a supersonic under-expanded planar jet are numerically simulated and analyzed. Two sets of engineering tools were used in this study: namely, the Integro-Differential Scheme (IDS) and the Weighted Essentially Non-Oscillatory (WENO) Scheme. The IDS is based on solving the system of Navier-Stokes equations through integration principles, Ref. [1]. Whereas the 5th order WENO-Z with Strong Stability Preserving Runge Kutta based on Finite Volume Method has been conducted Ref. [2–3]. The intent of this study is to understand the evolving nature of the flow phenomena and to identify the mechanisms that are influential in determining the nature of the fully developed flow field. Such understandings are of great engineering importance to mixing and turbulence. As a target of engineering analysis, the under-expanded free jet is perhaps one of the simplest flows. Its flow field physics closely matches the realities of the intended industrial applications, comprising of the many complex unsteady flow phenomena and their interactions, Ref. [4]. During its initial phase, the profile of the emerging jet is primarily dictated by the pressure ratio between the reservoir stagnation conditions and the ambient pressure. However, the genesis and evolution of the under expanded jet is even more interesting, as this developing flow is highly unsteady. In this case, the pressure of the supersonic jet is expected to reach the ambient pressure through a series of oblique shock and expansion waves, and their interactions with the emerging shear layers originating from the nozzle lip. In this analysis, a Mach 1.4 jet steam enters an ambient chamber of equal pressure at a temperature of 1.4 atm and a temperature of 300K. The developing under-expanded jet is modeled using the two sets of CFD tools described earlier, starting with the same initial and boundary conditions. The simulated IDS and Co-WENO results of the unsteady jet streams were analyzed and compared at specified times. This report compares the two simulated solutions and discusses the flow physics revealed by these tools. It was observed that both sets of tools revealed the interactions create within the shear layers instability mechanisms. In both cases, the instability waves grow spatially to create large scale coherent structures that travel downstream. These coherent structures grow as they interact with the surrounding ambient flow field, and with time, they interact with each other, merging to form the larger so-called main vortex. It is of interest to note that the two simulations were not identical, even though they delivered more commonalities and a few less striking differences. No doubt, the flow regimes of interest, the instabilities and the coherent structures are slight functions of the numerical parameters associated with these two schemes. Since at the moment no exact solution exists, the authors of this study will let the interested readers derive which of the two CFD tools best capture the expected flow field physics.