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1. A Dual Scale Approach to Modeling Sub-Filter Shear-Induced Instabilities with a Vortex Sheet Method

   Goodrich, A.; Herrmann, M. (May 2021, ILASS-Americas 31st Annual Conference on Liquid Atomization and Spray Systems)

   null (Ed.)

   A method to predict sub-filter shear-induced velocities on a liquid-gas phase interface for use in a dual scale LES model is presented. The method reconstructs the sub-filter velocity field in the vicinity of the interface by introducing a vortex sheet at the interface. The vortex sheet is transported by an unsplit geometric volume and surface area advection scheme with a Piecewise Linear Interface Construction (PLIC) representation of the material interface. At each step and desired location the shear-induced velocities can be calculated by integrating the vortex sheet and other relevant quantities over the liquid-gas interface with the sub-grid velocity reconstruction limited to a small number of cells near the phase interface. The vortex sheet method is tested and compared against prior literature. 

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2. Verification of a Dual Scale Model for Sub-Filter Shear-Induced Velocities with a Vortex Sheet Method

   Goodrich, A.; Herrmann, M. (May 2022, Proceedings of the 32nd Annual Conference on Liquid Atomization and Spray Systems)

   A method to predict sub-filter shear-induced velocities on a liquid-gas phase interface for use in a dual scale LES model is presented and compared against prior work on Vortex Sheet methods. The method reconstructs the sub-filter velocity field in the vicinity of the interface by employing a vortex sheet at the interface location. The vortex sheet is transported by an unsplit geometric volume and surface area advection scheme with a Piecewise Linear Interface Construction (PLIC) representation of the material interface. At each step, the vorticity field is constructed by evaluating a volume integral of the vortex sheet and a numerical spreading parameter near the liquid-gas interface. A Poisson equation can then be constructed and solved for the vector potential; the self-induced velocities due to the vortex sheet are subsequently evaluated from the vector potential. The described vortex sheet method is tested and compared against prior literature. 

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3. A Dual Scale Approach to Modeling Sub-Filter Velocities due to Shear-Induced Instabilities

   Goodrich, A.; Herrmann, M. (May 2020, ILASS-Americas 31st Annual Conference on Liquid Atomization and Spray Systems)

   null (Ed.)

   A method to compute sub-filter velocities due to shear induced instabilities on a liquid-gas interface for use in a dual scale LES-DNS model is presented. The method reconstructs the sub-filter velocity field as the sum of a prescribed base velocity profile and a perturbation velocity field determined by the Orr-Sommerfeld equations. The base velocity profile is approximated as an error function appropriately scaled with flow parameters, and the perturbation velocity field is computed by solving the Orr-Sommerfeld equations with appropriate boundary and interface conditions. The perturbation velocities of the Orr-Sommerfeld equations are expanded into Chebyshev polynomials to create a linear eigenvalue problem as outlined by Schmid and Henningson (2001). Finally the eigenvalue problem is solved using a standard linear algebra package and used to evaluate the perturbation velocities. The Chebyshev method is tested under a variety of flow parameters and initial interface disturbances. Results are presented and compared against prior literature and asymptotic solutions. 

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4. The vortex-entrainment sheet in an inviscid fluid: theory and separation at a sharp edge

   https://doi.org/10.1017/jfm.2019.134  

   DeVoria, A. C.; Mohseni, K. (May 2019, Journal of Fluid Mechanics)

   In this paper a model for viscous boundary and shear layers in three dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the layer are represented by a two-dimensional surface having its own internal tangential flow. Namely, the sheet has a mass density per-unit-area making it dynamically distinct from the surrounding outer fluid and allowing the sheet to support a pressure jump. The mechanism of entrainment is represented by a discontinuity in the normal component of the velocity across the sheet. The velocity field induced by the vortex-entrainment sheet is given by a generalized Birkhoff–Rott equation with a complex sheet strength. The model was applied to the case of separation at a sharp edge. No supplementary Kutta condition in the form of a singularity removal is required as the flow remains bounded through an appropriate balance of normal momentum with the pressure jump across the sheet. A pressure jump at the edge results in the generation of new vorticity. The shedding angle is dictated by the normal impulse of the intrinsic flow inside the bound sheets as they merge to form the free sheet. When there is zero entrainment everywhere the model reduces to the conventional vortex sheet with no mass. Consequently, the pressure jump must be zero and the shedding angle must be tangential so that the sheet simply convects off the wedge face. Lastly, the vortex-entrainment sheet model is demonstrated on several example problems. 

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5. Impact of inlet gas turbulence on the formation, development and breakup of interfacial waves in a two-phase mixing layer

   https://doi.org/10.1017/jfm.2021.481  

   Jiang, D.; Ling, Y. (August 2021, Journal of Fluid Mechanics)

   Understanding the development and breakup of interfacial waves in a two-phase mixing layer between the gas and liquid streams is paramount to atomization. Due to the velocity difference between the two streams, the shear on the interface triggers a longitudinal instability, which develops to interfacial waves that propagate downstream. As the interfacial waves grow spatially, transverse modulations arise, turning the interfacial waves from quasi-two-dimensional to fully three-dimensional. The inlet gas turbulence intensity has a strong impact on the interfacial instability. Therefore, parametric direct numerical simulations are performed in the present study to systematically investigate the effect of the inlet gas turbulence on the formation, development and breakup of the interfacial waves. The open-source multiphase flow solver, PARIS, is used for the simulations and the mass–momentum consistent volume-of-fluid method is used to capture the sharp gas–liquid interfaces. Two computational domain widths are considered and the wide domain will allow a detailed study of the transverse development of the interfacial waves. The dominant frequency and spatial growth rate of the longitudinal instability are found to increase with the inlet gas turbulence intensity. The dominant transverse wavenumber, determined by the Rayleigh–Taylor instability, scales with the longitudinal frequency, so it also increases with the inlet gas turbulence intensity. The holes formed in the liquid sheet are important to the disintegration of the interfacial waves. The hole formation is influenced by the inlet gas turbulence. As a result, the sheet breakup dynamics and the statistics of the droplets formed also change accordingly. 

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