Modeling of Spray/Acoustic Interactions with Lagrangian and Polydisperse Euler-Euler Approaches
by Javier Achury and Wolfgang Polifke
Background and Motivation
Combustors operating with spray flames are particularly susceptible to develop thermo-acoustic instabilities. Such phenomenon is produced by a feedback coupling between fluctuations in heat release and acoustic fields. Heat release fluctuations are associated to unsteady fuel evaporation and perturbations either in the field or in the fuel/air ratio. Depending on many factors, an acoustic wave can cause droplets clustering and modulation of the droplet size distribution (DSD), leading to fluctuating rates of evaporation. This means that a perturbed field of equivalence ratio, and subsequently of heat release, can be directly linked to the acoustics and one possible mechanism of instability in spray flames could be inferred. Spray clustering and periodic modulation of the DSD have been shown experimentally by imposing an acoustic standing wave on non-evaporating and evaporating sprays[1].
An acoustic field can also cause relative motion, sorting and agglomeration of suspended particles. This phenomenon, called acoustic agglomeration, has many potential uses in air pollution control [2], since acoustics fields can enhance the capacity of filtering devices to capture particulate material.
The spray response to an acoustic field and the mechanisms for droplet population clustering, modulation of the DSD and agglomeration due to acoustics are investigated in this project by means of CFD models.
Modeling
A spray is a two-phase flow which consists of one disperse phase (droplets) and one continuous phase (air). Modeling of its disperse regime can be based on one of two frameworks, the Euler-Euler (EE) or the Euler-Lagrange (EL). While in the EL approach, the droplet population dynamics is determined by solving the equation of motion for each particle, in the EE the disperse phase is described as a "continuous" fluid, whose properties are derived from statistical average of the droplet population. Although the EE approach has advantages regarding the computational costs, requires complex models to account for polydispersity.
At the Professur für Thermofluiddynamik a model, based on the moments of the particle size distribution function f(D), has been developed to account for polydispersity[3]. The moments of order k are given by M(k)=∫0∞Dkf(D)dD, where D is the particle diameter. Convection of the moments with their respective moment transport velocities captures the development of the particle population through motion and evaporation. Closure is obtained by using a presumed shape function for f(D), which bases the PMoM (Presumed density function Method of Moments). In both frameworks, EE and EL, the acoustics is intrinsically resolved in the continuous phase, which is valid for disperse sprays.
Fig. 1: Simulation of the liquid volume fraction fields of the non-evaporative spray with EE-PMoM (Left) and EL (Right).
Results
The PMoM solver for the spray is being validated against the experimental results of Gurubaran[1]. The spray structure (without acoustic excitation) can be seen in Fig. 1 (Left). A Lagrangian case for this spray is also simulated, Fig. 1 (Right).
An acoustic standing wave has been generated to interact with the spray. Periodic modulations of the DSD and the spray velocity are observed. Perturbations of the spray shape can also be detected.
Fundamental mechanisms that enhance acoustic agglomeration have also been studied for a simplified configuration with EL and EE-PMoM simulations. The formation of a particle number density wave is demonstrated (Fig. 2) and the ability of the PMoM to capture accurately those interactions is being assessed. The dynamics and parametric stability of a single particle response in an standing wave field was also theoretically investigated. Further steps include the computational modeling for the evaporative spray, attempting to close the description of one possible mechanism of instability in spray flames.
Fig. 2: Formation of a particle number density wave in a polydisperse population of particles due to an axial acoustic standing wave.
Acknowledgments
This project is funded by the Administrative Department of Science, Technology and Innovation - COLCIENCIAS (Republic of Colombia), whose support is gratefully acknowledged.
References
[1] Kumara Gurubaran, R. and Sujith, R. ”An Experimental Investigation of Non-Evaporative Sprays in Axial Acoustic Fields”. 46th AIAA Aerospace Sciences Meeting, 2008.
[2] J. Gallego-Juarez, E. Riera-Franco, T. Hoffman, J. Galvez-Moraleda. "Application of acoustic agglomeration to reduce fine particle emissions from coal combustion plants". Environmental Science Technology. 33(1999) 3843–3849.
[3] Dems, P., Carneiro, J. V. and Polifke, W. LES Simulation of a Polydisperse, Evaporating, Spray Jet with a Presumed Function Method of Moments”. Proceedings of the 12th ICLASS, 2012.