On the dissipation and dispersion of entropy waves in heat transferring channel flows

Abstract

This paper investigates the hydrodynamic and heat transfer effects upon the dissipation and dispersion of entropy waves in non-reactive flows. These waves, as advected density inhomogeneities downstream of unsteady flames, may decay partially or totally before reaching the exit nozzle, where they are converted into sound. Attenuation of entropy waves dominates the significance of the subsequent acoustic noise generation.Yet, the extent of this decay process is currently a matter of contention and the pertinent mechanisms are still largely unexplored. To resolve this issue, a numerical study is carried out by compressible large eddy simulation (LES) of the wave advection in a channel subject to convective and adiabatic thermal boundary conditions. The dispersion, dissipation and spatial correlation of the wave are evaluated by post-processing of the numerical results. This includes application of the classical coherence function as well as development of nonlinear quantitative measures of wave dissipation and dispersion. The analyses reveal that the high frequency components of the entropy wave are always strongly damped. The survival of the low frequency components heavily depends upon the turbulence intensity and thermal boundary conditions of the channel. In general, high turbulence intensities and particularly heat transfer intensify the decay and destruction of the spatial coherence of entropy waves. In some cases, they can even result in the complete annihilation of the wave. The current work can therefore resolve the controversies arising over the previous studies of entropy waves with different thermal boundary conditions.

State prediction of an entropy wave advecting through a turbulent channel flow

“…Further, as the wave spreads out the spectral distribution of the entropy wave becomes limited to the low frequency regions. It has already been shown that low frequency components of the entropy wave can survive turbulent flow much better than those of high frequencies (Fattahi et al 2017). Thus, the contribution of turbulent mixing to the overall diffusion process is progressively hindered as the wave thickens and molecular diffusion becomes the dominant diffusion mechanism.…”

“…This was achieved in a setup with long wavelength entropy waves and an isothermal base flow. However, more recent numerical simulations of heat transferring flows revealed that advective entropy waves in channels could significantly deviate from being one-dimensional fronts (Fattahi et al 2017). Studies on the conversion of entropy waves to sound in turbine stages (Cumpsty & Marble 1977; 2013; Livebardon et al 2016) have supplied their models with realistic entropy waves.…”

“…Further, the one-dimensional treatment of the entropy perturbation implies a SISO (single input, single output) approach to the description of entropy waves (Lieuwen 2012;Dowling & Morgans 2005). However, an experimental (Brear et al 2010) and a recent numerical (Fattahi et al 2017) study have shown that entropy perturbations could become spatially uncorrelated. The threshold frequency at which correlation starts to breakdown, and therefore, the amount of thermal energy that is filtered out by application of an average depends on the thermal boundary conditions and the hydrodynamics of the flow (Fattahi et al 2017).…”

“…However, an experimental (Brear et al 2010) and a recent numerical (Fattahi et al 2017) study have shown that entropy perturbations could become spatially uncorrelated. The threshold frequency at which correlation starts to breakdown, and therefore, the amount of thermal energy that is filtered out by application of an average depends on the thermal boundary conditions and the hydrodynamics of the flow (Fattahi et al 2017). Consequently, it is imperative to model entropy waves as a multi-input-multi-output (MIMO) system.…”

On the dispersion of entropy waves in turbulent flows

“…Eckstein & Sattelmayer 2006;Schulz et al 2019) and with their measurements (Wassmer et al 2017;De Domenico et al 2019). Most of the modelling efforts to date have been about entropy-wave dispersion in fully developed turbulent duct flows (Sattelmayer 2002;Morgans, Goh & Dahan 2013;Morgans & Duran 2016;Giusti et al 2017;Fattahi, Hosseinalipour & Karimi 2017;Christodoulou et al 2020;Hosseinalipour et al 2020), where shear dispersion was identified as the dominant mechanism. There are indeed several mechanisms at play that contribute to the decay of entropy waves (e.g.…”