Direct Numerical Simulations of Boundary Layer Stability for Non-ideal Fluids

Abstract

The process in which a smooth laminar flow transits to a chaotic to a chaotic, turbulent state, is a topic of particular interest in the sectors of energy technology and aerodynamics. To study the different paths that can be followed during the transition process, various tools and methods have been developed. A preliminary investigation of the response of a laminar flow to an internal or external disturbance can be performed by applying Linear Stability Theory principles. In the recent years, the Direct Numerical Simulations of flows offer a more insightful method to study the transition process, since the flow fields are numerically solved using high computational power. Previous research has primarily focused on the stability and transition of Ideal Gas flows, with little attention to the effects of a highly Non-Ideal behaviour. The present work aims to develop a DNS code that can be used to investigate the stability of compressible boundary layers in the vicinity of theWidom Line. For the initialization of a DNS, a two dimensional base flow profile is required. For the calculation of the base flow, a self-similar solution is obtained, using a MATLAB script that has been developed for the purpose of this study. The DNS code is developed in FORTRAN. An inviscid characteristic wave analysis is utilized for the implementation of the boundary conditions, along with numerical sponges to avoid reflections. To trigger the instabilities, periodic suction and blowing is incorporated. For the simulations of non-ideal fluids, a thermodynamic table interpolation tool is incorporated. For the validation of the results obtained by the DNS code, an in-house MATLAB script is used to for the calculation of the growth rate and fluctuation amplitude profiles using LST. Initially, the FORTRAN code is used on ideal-gas simulations, to investigate how different computational parameters will affect the flow field. The parameters are related to mesh resolution, boundary conditions and numerical sponges. To investigate the stability of non-ideal fluids, cases of different free-stream temperatures and Eckert numbers are simulated. The free-stream temperature is altered to control the non-ideal gas effects, whereas the Eckert number is used to control the compressibility effects. In general, the flow is stabilized as non-ideal gas and compressibility effects become more prominent. However, a second unstable mode is observed in the case where the temperature profile crosses the pseudo-critical point. This second mode has a higher growth rate of instabilities, compared to the first mode. All the results are validated using the LST predicted profiles.