Question about 2D spray problem

[Soobin120596]

Hello everyone!
I’m curious about how droplets are treated in 2D simulations in Pele. Does the solver still maintain a grid in the z-direction in such cases?

[d-montgomery]

The spray droplet equations are included in the PelePhysics documentation. These are shared by PeleLMeX and PeleC, which is why they are not documented here. There is no need for a grid in the z-direction for 2D simulations with spray. This PR #521 demonstrates single droplet evaporation in 2D.

[Soobin120596]

I truly appreciate your response. However, given the inherently three-dimensional nature of the droplet, how is the size handled in the unsimulated dimension (i.e., the z-direction)? Is it set to a unit length of 1 m in LM, while in PELEC it is assumed to be 1 cm instead?

[d-montgomery]

Droplets are assumed to be spherically symmetric so the size is tracked via its diameter, which is related to the mass and density of the droplet.

[Soobin120596]

I would like to calculate the equivalence ratio of a droplet/air mixture. The droplet mass can be computed using m = rho \times \frac{4}{3} \pi r^3 , but how should the O2 mass be determined? In my 2D simulation, the dimensional units for mass are kg/m, which lacks the distance of a direction. For the unsimulated direction (e.g., z), is it can be think to a unit length of 1 m of gas in LM, while in PELEC it is assumed to be 1 cm instead?

[d-montgomery]

This is a classic case of how 2D simulations of 3D things can be weird. @baperry2 and I have been discussing this and found an error in the gas phase source terms from the evaporating spray. Currently the source terms in 2D are per unit area, but mathematically they need to be per unit volume. The question then becomes what is that volume?

While we could set dz = dx and assume a narrow domain in the z-direction, this ignores the effect of Stefan flow in the z-direction, which dominates the flow field in quiescent flow cases. We're going to be looking into this more, but please let us know if you have ideas!

[d-montgomery]

PR #581 in PelePhysics addresses the issue of dimensionality by assuming a narrow width in the z-direction such that $L_z = \Delta x$.

[Soobin120596]

Thanks for thoughtfully considering my question！