Modeling the Convection of Entropy Waves in Strongly Non-Parallel Turbulent Flows Using a Linearized Framework

The study investigates two effects, which can lead to a mitigation of entropy waves in a gas turbine combustor: Mean flow shear dispersion and turbulent mixing. Using a transport equation for coherent fluctuations of a passive scalar in combination with a k-ε turbulence model, the advection and turbulent diffusion of entropy waves is modeled. The method is applied to a flow in a duct of rectangular cross section, previously investigated with experimental and numerical means by Weilenmann et al. [1]. We analyze the impact of a steady jet in crossflow (JIC) in the rectangular duct on the mitigation of entropy waves by the mean flow shear dispersion mechanism. First, a comparison to Large Eddy Simulation (LES) results demonstrates the capability of the linearized approach to quantify the decay due to turbulent mixing and mean flow shear dispersion. The results further indicate that the inhomogeneous highly three dimensional flow profile and increased turbulence caused by the JIC significantly mitigates entropy waves due to the enhancement of the mean flow shear dispersion and turbulent mixing in comparison to a base line configuration without the JIC. Second, we investigate in a parameter study the effect of turbulent mixing on the mitigation of the entropy waves. It is shown that the results are highly case dependent. While in some situations an increase in turbulent mixing — as expected — leads to a mitigation of entropy waves, in other situations it may have the opposite effect. We demonstrate that this is the case if turbulent mixing annihilates entropy fluctuations selectively in those regions, which contribute significantly to mean flow shear dispersion.