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Binary collision of CMAS droplets—Part II: Unequal-sized droplets

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Abstract

The analysis presented in Part I of this study on the binary collision of equal molten calcium–magnesium–alumino–silicate (CMAS) droplets is extended to investigate the flow and interfacial dynamics of unequal CMAS droplet collision. Numerical investigations of head-on, off-center, and grazing collisions of two CMAS droplets of size 1 and 2 mm are conducted at pressure and temperature of 20 atm and 1548 K, respectively, that are representative of a gas-turbine combustor. At these conditions, the physical properties of CMAS are density, ρCMAS = 2690 kg/m3, surface tension between CMAS/air, σCMAS = 0.40 N/m, and viscosity, μCMAS = 11.0 N-s/m2. The primary difference between the CMAS and a fictitious fluid with viscosity 1/10 of CMAS was higher deformation for the lower viscosity case, leading to stretching and subsequent breakup of the liquid structure. These mechanisms are supported by the time evolution of surface, kinetic, and viscous dissipation energies.

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Acknowledgments

The authors gratefully acknowledge the Advanced Computing Center at the University of Cincinnati, and the DoD High Performance Computing Modernization Program (HPCMP) subproject number, ARLAP44862H70 for the computational resources. Luis Bravo was supported by the US Army Research Laboratory 6.1 basic research program in propulsion sciences.

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Authors and Affiliations

  1. Department of Aerospace Engineering, University of Cincinnati, Cincinnati, OH, 45221-0070, USA

    Himakar Ganti & Prashant Khare

  2. Vehicle Technology Directorate, Army Research Laboratory, Aberdeen Proving Ground, MD, 21005, USA

    Luis Bravo

Authors
  1. Himakar Ganti
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  2. Prashant Khare
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  3. Luis Bravo
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Corresponding author

Correspondence to Prashant Khare.

Appendix A: Computational Challenges, Model Validation, and Grid-Sensitivity Analysis

Appendix A: Computational Challenges, Model Validation, and Grid-Sensitivity Analysis

Irrespective of the numerical method, the challenges accompanying the numerical simulation of incompressible two-phase systems increase dramatically, as the density ratio increases [1, 2 ]. The time integration scheme used in the current approach involves a classical time-splitting projection method, which requires the solution of the Poisson equation to obtain the pressure field:

$$\nabla \cdot \left[{\displaystyle{{\Delta t} \over {\rho_{n + {1 \over 2}}}}\nabla p_{n + {1 \over 2}}} \right] = \nabla \cdot u_\ast.$$
((15))

Equation (A1) is solved using a standard multigrid V-cycle methodology, and for large density and viscosity ratios, its solution suffers from slow convergence rates. One of the ways to overcome this issue is by using high grid resolution to resolve the steep density and viscosity gradients at the interface to ensure consistency in the momentum equation. Another method of speeding up the convergence rate is to spatially filter the interface during reconstruction. Even though the current methodology performs very well for the current configuration of droplet interaction at high viscosity and density ratios, the convergence can seriously degrade, depending on the problem and interface topology [3 ], in comparison with other methods [4]. Therefore, for all the cases conducted as a part of this research effort, including the validation study described in the next section, we have used both the aforementioned strategies to ensure accuracy: high grid resolution and spatially filtering (at least once) to ensure numerical accuracy and adequate resolution of the gas–liquid interface.

As a first step, grid-sensitivity analysis which is conducted to ensure appropriate grid resolution is used to resolve the physics under consideration. The canonical configuration of equal CMAS droplets colliding head-on (B = 0.0) is selected for the grid-sensitivity study. Figure A1 shows a comparison of the liquid morphology for four different refinement levels described below

  1. (i)

    level 6 at liquid/gas interface, level 5 for the droplet interior, and level 3 for the rest of the domain—L6

  2. (ii)

    level 7 at liquid/gas interface, level 6 for the droplet interior, and level 3 for the rest of the domain—L7

  3. (iii)

    level 8 at liquid/gas interface, level 7 for the droplet interior, and level 4 for the rest of the domain—L8

  4. (iv)

    level 9 at liquid/gas interface, level 8 for the droplet interior, and level 5 for the rest of the domain—L9

Figure A1:
figure 11

Grid-sensitivity study based on levels 6, 7, 8, and 9. The figure on the right shows an overlay of the liquid interface for these levels.

Full size image

As seen clearly, L6 is unable to refine the interface sufficiently. While L7 resolves the interface better, to ensure that the gas film when the droplets come closer to each other is resolved, L8 and L9 were investigated, which show almost identical results for interface deformation and evolution as well as the gas film. Therefore, for this study, L8 was selected as the grid resolution. While for high Weber number droplet collision, such as the current study, bouncing is not expected to be an outcome, in addition to gradient and value-based refinements, distance-based refinement is employed to ensure that the gas film is resolved accurately.

Next, model validation is conducted by simulating the experiments conducted by Qian and Law [5 ]. It should be noted that since no study in the past has investigated CMAS droplet collision, we have to resort to using data on tetradecane droplet collision for validation purposes. We chose a case that incorporates merging, retracting, and formation of satellite droplets to ensure that our framework can accurately model different aspects of the droplet collision phenomena. In this experiment, conducted at a pressure of 1 atm and 300 K, two droplets of diameter 336 μm with 2.48 m/s collide. The density and viscosity of air at these conditions are 1.18 kg/m3 and 1.79 × 10−4 N-s/m2, respectively. The density, viscosity, and surface tension of tetradecane are 785.88 kg/m3, 2.21× 10−3 N-s/m2, and 0.02656 N/m. Figure A2 shows the time evolution of events that take place, as these droplets collide. The left side shows the experimental measurements and the right side shows results from the current simulation, showing excellent comparison. All flow features, including droplet coalescence, ligament formation and elongation, subsequent separation by pinching, and satellite droplet formation, are accurately captured.

Figure A2:
figure 12

Time evolution of liquid interface when two tetradecane droplets collide at an impact factor, B = 0.06. (a) Experimental images of Qian and Law [5] shown on the left and (b) results from current simulations.

Full size image

Details of grid-sensitivity and experimental validation can be found in the previous article for Binary Collision of CMAS Droplet–Part I: Equal Sized Droplets [6 ].

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Ganti, H., Khare, P. & Bravo, L. Binary collision of CMAS droplets—Part II: Unequal-sized droplets. Journal of Materials Research 35, 2275–2287 (2020). https://doi.org/10.1557/jmr.2020.153

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