MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets Namespace Reference

Classes
class	InitialValuesLS
class	InitialValuesTemperature
class	SimulationThermoCapillaryTwoDroplets

Functions
	MELTPOOLDG_REGISTER_CASE (MeltPoolCase, SimulationThermoCapillaryTwoDroplets, "thermo_capillary_two_droplets", 1, double)
	MELTPOOLDG_REGISTER_CASE (MeltPoolCase, SimulationThermoCapillaryTwoDroplets, "thermo_capillary_two_droplets", 2, double)
	MELTPOOLDG_REGISTER_CASE (MeltPoolCase, SimulationThermoCapillaryTwoDroplets, "thermo_capillary_two_droplets", 3, double)

Variables
static constexpr double	radius = 0.048
static constexpr double	x_outer = 8. * radius
static constexpr double	z_outer = 16. * radius
static constexpr double	reference_temperature = 0.0
static constexpr double	temperature_gradient = 10.

Detailed Description

This example is derived from

Nas, S., & Tryggvason, G. (2003). Thermocapillary interaction of two bubbles or drops. International Journal of Multiphase Flow, 29(7), 1117-1135. https://doi.org/10.1016/S0301-9322(03)00084-3

and

Balcázar, N., Rigola, J., Castro, J., & Oliva, A. (2016). A level-set model for thermocapillary motion of deformable fluid particles. International Journal of Heat and Fluid Flow, 62, 324-343. https://doi.org/10.1016/j.ijheatfluidflow.2016.09.015

In contrast to the papers' cases the two droplets can coalesce here.

            T2 = fixed
             no slip
       +----------------------------------------+                    -
       |                                        |                    |
       |                                        |                    |
       |                                        |                    |
       |                        -----           |                    |
       |                       --   --          |                    |
       |                      --     --         |                    |
       |                       --   --          |                   16a
       |          -----         -----           |                    |

periodic | – – |-a-| | periodic |

– –
--—

+-------------------------------------—+ - no slip T1 = fixed

|--------------— 8a -----------------—|

droplet radius: a = 0.048 m droplet positions: (2.9a, 4a), (5.1a, 5.8a)

characteristics: Re = 40 Ma = 40 Ca = 0.041666

droplet: rho_i = 250 kg/m³ mu_i = 0.012 N/m²s lambda_i = 1.2e-6 W/m/K cp_i = 5e-5 J/kg/K

ambient fluid: rho_0 = 500 kg/m³ mu_0 = 0.024 N/m²s lambda_0 = 2.4e-6 W/m/K cp_0 = 1e-4 J/kg/K

surface tension coefficient: sigma_0 = 0.023040369 N/m temperature-dependent surface tension coefficient: sigma_T = 0.002 N/m/K

temperature: ∇T = 10 K/m T1 = 0 K T2 = 0 + 16 * a * ∇T = 7.68 K

reference velocity Ur = sigma_T * a * ∇T / mu_0 = 0.04 m/s reference time scale tr = a / Ur = 1.2 s

time step size Δt = 0.1 * min( a / Ur , a^1.5 * ( (rho_0 + rho_i)/(4 * pi * sigma_0) )^0.5 ) = 0.05 s

Function Documentation

MELTPOOLDG_REGISTER_CASE() [1/3]

MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::MELTPOOLDG_REGISTER_CASE	(	MeltPoolCase	,
		SimulationThermoCapillaryTwoDroplets	,
		"thermo_capillary_two_droplets"	,
		1	,
		double
	)

MELTPOOLDG_REGISTER_CASE() [2/3]

MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::MELTPOOLDG_REGISTER_CASE	(	MeltPoolCase	,
		SimulationThermoCapillaryTwoDroplets	,
		"thermo_capillary_two_droplets"	,
		2	,
		double
	)

MELTPOOLDG_REGISTER_CASE() [3/3]

MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::MELTPOOLDG_REGISTER_CASE	(	MeltPoolCase	,
		SimulationThermoCapillaryTwoDroplets	,
		"thermo_capillary_two_droplets"	,
		3	,
		double
	)

Variable Documentation

radius

constexpr double MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::radius = 0.048

staticconstexpr

reference_temperature

constexpr double MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::reference_temperature = 0.0

staticconstexpr

temperature_gradient

constexpr double MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::temperature_gradient = 10.

staticconstexpr

x_outer

constexpr double MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::x_outer = 8. * radius

staticconstexpr

z_outer

constexpr double MeltPoolDG::Simulation::ThermoCapillaryTwoDroplets::z_outer = 16. * radius

staticconstexpr