(389e) Identification of Effective Mass Transport Models in Falling Film Flows

During recent decades, practical inverse-problem approaches, which rely on practically available measurements for the estimation of unknown physical quantities, have attained enormous research interest because of their practical significance and academic value. They are considered more efficient and economical when the direct measurement is not practical due to environmental obstacles or high experimental cost and have a wide range of applications across different engineering disciplines, particularly in the field of heat and mass transfer.

In this work, we focus on an interesting but hard-to-solve large-scale inverse problem arising in a gravity-driven falling film process for the identification of the effective diffusion coefficients. It is well known that the heat and mass transfer in laminar-wavy film flows can be significantly enhanced. Due to the dynamic and complex structure of the film, its detailed experimental and numerical analysis is complicated. The understanding of the transport phenomena is limited and comprehensive transport models are still not available.

In general, the direct numerical simulation of mass transfer inside the film requires the simultaneous solution of the two-phase Navier-Stokes equations in the gas and liquid phases. However, according to current simulation studies, the numerical simulation of the coupled momentum and mass transport equations is computationally infeasible due to its multiphase nature and the dynamic, unstable gas-liquid interface. Hence, the use of reduced models is considered as a practical alternative to balance the accurate description of the transport phenomena in falling films and the computational demand.

As a first step towards this research aim, we consider a reduced one-phase flow model of the liquid phase instead of the two-phase flow model of the liquid and gas phase. The film height of the wavy film, which is a function of time and space, is then approximated based on the long-wave theory. We employ a two-equation expansion of the film thickness and the volume flow rate in the film, which has been shown to accurately describe surface waviness in thin films for a wide range of flow regimes [1]. With the obtained velocity field, the 3D unsteady convection-diffusion problems are solved by DROPS [2, 3] to obtain the dynamic concentration profiles. Among the various stabilization techniques for FEM, the streamline upwind Petrov-Galerkin (SUPG) method [4] has been applied. This leads to a significant decrease in computational effort for convection dominated problems. The time-dependent computational domain is handled by an Arbitrary Lagrangian-Eulerian (ALE) approach [5, 6, 7].

Based on the aforementioned computational strategy, we have conducted a series of forward simulations with respect to different Reynolds number for a few gas-liquid pairs. The obtained results have been used to validate the proposed film model. The evaluated Sherwood numbers using the proposed model show good agreement with published experimental data [8, 9, 10]. Based on the validated forward simulation model, an incremental identification approach [11], is being set up to solve the aforementioned inverse problem. In our next step, the model identification procedure will be applied to real experimental data obtained by high-resolution concentration measurements of oxygen being physically absorbed into an aqueous film via a planar laser-induced luminescence (pLIL) measurement technique.

REFERENCES
[1] R. R. Mudunuri, V. Balakotaiah, Solitary waves on thin falling films in the very low forcing frequency limit, AIChE Journal, 52(12), 2006, 3995–4003.
[2] DROPS package. http://www.igpm.rwth-aachen.de/DROPS/.
[3] S. Groß, A. Reusken, Numerical Methods for Two-phase Incompressible Flows, vol. 40 of Springer Series in Computational Mathematics. Springer, 2011.
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[10] C. D. Park, T. Nosoko, Three-Dimensional Wave Dynamics on a Falling Film and Associated Mass Transfer, AIChE Journal, 49(11), 2003, 2715–2727.
[11] M. Karalashvili, S. Groß, A. Mhamdi, A. Reusken, W. Marquardt, Incremental identification of transport coefficients in convection-diffusion systems, SIAM J. Sci. Comput., 30, 3249-3269, 2008.