Investigation of dense gas effects on transition to turbulence over a flat plate boundary layer

Abstract

Laminar-turbulent transition (LTT) is the process through which smooth laminar flow transits into chaotic turbulent flow. Investigation of the paths taken to transit into turbulence is a front-runner among other methods followed to characterise turbulent flows. This is of particular importance in aerospace and energy industries for the design of wings and gas turbines. Early research used Linear Stability Theory (LST) to analyse the stability of the flow; with the increase in computational power, Direct Numerical Simulation (DNS) has been developed to solve the flow field entirely. Most of the research on LTT has been centered on ideal fluids with limited focus on the effects of high temperature. The impact of other strong non-ideal effects on LTT such as dense gas effects have not been investigated. This work aims to study the effects of dense gas on LTT for boundary layer flows of toluene over a flat plate.Flows over a flat plate boundary layer are investigated in 3 stages. First, the base flow is solved for ideal air and non-ideal toluene for 6 different Eckert numbers (Ec). Second, the base flow is provided as an input to solve the eigenvalues of the stability equations for both fluids and each Ec using an in-house MATLAB code. The unstable eigenmode is identified and tracked. The growth rates and phase velocities are calculated and compared between ideal air and toluene. Third, DNS simulations are performed using a FORTRAN code, to solve the governing equations of compressible flows for different Ec. The simulations are performed on a pre-processed base flow solution, subjected to 2D sinusoidal perturbations forced into the computation domain at the wall. A no-slip and adiabatic wall boundary conditions are applied to the flat plate with a sponge region at the outlet and the top of the computation domain. The growth rates and phase velocities of these perturbations are calculated and validated with the predictions made by LST. Finally, a perturbation energy budget analysis is conducted to study the nature of the unique results obtained.The LST results show that as Ec number increases, all flows over a flat plate become more stable. For toluene flows, the stabilising effect of increasing Ec is more pronounced and all flows with Ec > 0.15 are stable and have no modal instabilities. The results from the DNS simulations validate these predictions from LST and match perfectly in growing conditions, but deviate from one another in stable conditions. The deviation in results are hypothesised to be the contribution of multiple decaying modes to stable behaviour of the flow. Furthermore, perturbation energy budget analysis showed that for Ec = 0.05 and 0.10, the spatial growth of perturbations are positive due to a positive production term and negative for Ec = 0.15, with a negative production term. The negative production term is attributed to the negative integral of the perturbation profile.