liquidtransport/evaporation command

Purpose

Command

Warning

GPU support for this command has not been tested and may not work as expected.

Syntax

liquidtransport/evaporation keyword value

With the following keyword argument pairs:

Keywords	Description
transport	bool (`yes` or `no`) determining if liquid can be transferred between particles upon contact default: `yes`
liquid_species_name	name of the species of the composition that can undergo evaporation ; units: [-]
variable_properties	list of properties that are changed due to evaporation or spray->particle mass transfer, available properties are `mass` and `size` (default: `{}`)
evaporation_model	selector for the evaporation model. Available options: `simple`, `boil`, `Gunn` default: `simple`
liquid_density (deprecated -> use `liquid_species_name`)	scalar value setting the liquid density ; units: [mass/volume units]

Examples

liquidtransport/evaporation transport no liquid_species_name liquid variable_properties {mass,size}

Description

This command solves for the evolution of liquid for each particle. Every time step, the liquid content of each particle is updated based on the sum of liquid fluxes with other particles and additional sources.

This command internally creates four properties instances, that store the following variables:

`surfaceLiquidContent`	liquid content of a particle	volume % of solid (core+pore) volume
`liquidFlux`	liquid flux of a particle, as computed by a liquid bridge model	volume % of solid (core+pore) volume / time
`liquidSource`	liquid source via surface films, as computed by a liquid bridge model	volume % of solid (core+pore) volume / time
`evaporatedMassAccumulated`	liquid mass evaporated during a CFD coupling interval	mass

The per-particle variable surfaceLiquidContent is defined as the volume of liquid carried by the particle divided by the volume of the solid particle. There is no upper boundary for the liquid content; neither the particle radius nor its thermal capacity change with liquid content.

Liquid transport between particles, denoted by the variable liquidFlux, occurs only if transport = yes and a liquid bridge model has been defined, e.g. cohesion easo/capillary_viscous or cohesion washino/capillary_viscous.

In order to use this fix, the initial liquid content of each particle must be defined as follows:

global_scalar id surfaceLiquidContentInitial value <value>

In case the evaporation model is activated, the following additional properties must be defined for all materials

latentHeat
tempEvaporate
liquidHeatCapacity

Please note that when inserting particles with liquid content, the massflow rate of the insertion command only accounts for the mass of the dry material. For inserting the correct amount of material please scale the massflow rate down by the mass of the defined liquid film.

Evaporation models

The evaporation_model allows for the following choices:

simple: Evaporation only occurs if the particle reaches the evaporation temperature. At or above the evaporation temperature all excess and incoming heat is used to evaporate liquid. This also means that a particle does not increase its temperature during an ongoing evaporation processs.

This approach is similar to the one taken in fix_heat_gran_melting. The property evaporatedMassAccumulated can be communicated to CFD and used there by the LaEuScalarMass model as source term in the CFD.

boil: The liquid content may evaporate already below the evaporation temperature. At each time step, the evaporation mass rate is computed according to the Stefan–Fuchs equation based on the vapour saturation density at the particle’s surface $\rho_\mathrm{s}$ (set by the surface_fluid_density keyword), on the particle’s cross-section area $A$ , on the particle’s diameter $d_p$ , on the Sherwood number $\mathit{Sh}$ , on the diffusion coefficient $D$ , and on the vapour concentrations at the particle’s surface $X_\mathrm{s}$ and far away $X_\infty$ :

$\dot{m} = \rho_\mathrm{s} A \frac{\mathit{Sh} D}{d_p} \ln(1 + \frac{X_\mathrm{s} - X_\infty}{1 - X_\mathrm{s}})$

where the Sherwood number is defined according to Frössling as:

$\mathit{Sh} = 2 + 0.6 \sqrt{\mathit{Re}} \mathit{Sc}^{2/3}$

The Reynolds $\mathit{Re}$ and Schmidt $\mathit{Sc}$ numbers are defined as:

$\mathit{Re} = \frac{d_p u}{\nu} \mathit{Sc} = \frac{\nu}{D}$

where $\nu$ is the kinematic viscosity of the environmental fluid, $u$ is the relative velocity between particle and fluid. The diffusion coefficient $D$ is defined as:

$D = \frac{2.381065}{p_f} \left( \frac{T_p}{273.15} \right)^{1.81}$

where $p_f$ is the pressure of the environmental fluid and $T_p$ is the particle temperature.

This evaporation model requires the following additional keywords:

Keywords	Description
fluid_viscosity	scalar value setting the kinematic viscosity of the environmental fluid default: `1.5e-5`; units: [length^2/time]
fluid_pressure	scalar value setting the pressure of the environmental fluid if not obtained from the CFD simulation default: `101325`; units: [force/length^2]
surface_fluid_density	scalar value setting the vapour saturation density at the particle’s surface default: `1`; units: [mass/length^3]

Note

If running in a coupled simulation data for the local pressure and the vapour concentration are received from the CFD. On the CFD side the transferVapour forceModel is required to match the communication requirements.

Note

The surface_fluid_density in reality is not constant, as the vapour saturation density of a certain substance depends on the temperature of the vapour. For example, the saturation density of water vapour in air is 0.005 kg/m3 at 0 °C, 0.03 kg/m3 at 30 °C, and 0.13 kg/m3 at 60 °C. The Gunn model automatically calculates the vapour saturation density.

Gunn: The liquid content may evaporate already below the evaporation temperature. At each time step, the evaporation mass rate is computed according to the Stefan–Fuchs equation based on the vapour saturation density at the particle’s surface $\rho_\mathrm{s}$ , on the particle’s cross-section area $A$ , on the particle’s diameter $d_p$ , on the Sherwood number $\mathit{Sh}$ , on the diffusion coefficient $D$ , and on the vapour concentrations at the particle’s surface $X_\mathrm{s}$ and far away $X_\infty$ .

$\dot{m} = \rho_\mathrm{s} A \frac{\mathit{Sh} D}{d_p} \ln(1 + \frac{X_\mathrm{s} - X_\infty}{1 - X_\mathrm{s}})$

where the Sherwood number is defined according to the empirical Gunn correlation:

$\mathit{Sh} = (7 - 10 \phi + 5 \phi^2) (1 + 0.7 \mathit{Re}^{0.2} \mathit{Sc}^{1/3}) + (1.33 - 2.4 \phi + 1.2 \phi^2 \mathit{Re}^{0.7} \mathit{Sc}^{1/3})$

where $\phi$ is the local fluid volume fraction, $\mathit{Re}$ and $\mathit{Sc}$ are the Reynolds and Schmidt numbers respectively.

$\mathit{Re} = \frac{d_p u}{\nu} \mathit{Sc} = \frac{\nu}{D}$

where $\nu$ is the kinematic viscosity of the environmental fluid, $u$ is the relative velocity between particle and fluid. The diffusion coefficient $D$ is defined as:

$D = \frac{2.381065}{p_f} \left( \frac{T_p}{273.15} \right)^{1.81}$

where $p_f$ is the pressure of the environmental fluid and $T_p$ is the particle temperature. The vapour saturation density at the particle’s surface $\rho_\mathrm{s}$ is calculated according to the following formula:

$\rho_\mathrm{s} = \frac{M_\mathrm{M}}{R} \frac{p_\mathrm{Sat}}{T_p}$

where $M_\mathrm{M}$ is the molar mass of the evaporating liquid, $p_\mathrm{Sat}$ is the saturation pressure of the vapour, and $T_f$ is the temperature of the environmental fluid.

This model requires the following additional keywords:

Keywords	Description
fluid_viscosity	scalar value setting the kinematic viscosity of the environmental fluid default: `1.5e-5`; units: [length^2/time]
fluid_pressure	scalar value setting the pressure of the environmental fluid if not obtained from the CFD simulation default: `101325`; units: [force/length^2]
fluid_temperature	scalar value setting the fluid temperature if not obtained from the CFD simulation default: `303`; units: [temperature]
liquid_molar_mass	scalar value setting the molar mass of the evaporating liquid default: `0.01801528`; units: [mass/mole]

Note

If running in a coupled simulation, data for the local temperature, pressure, and the vapour concentration are received from the CFD. On the CFD side the transferVapour forceModel is required to match the communication requirements. Further note, that for this model combination the flags transferTemperature true; and transferVoidfraction true; should be activated in couplingProperties/transferVapourProps.

If this model is used in a pure DEM case, the voidfraction $\phi$ is set to unity and the following options can be used to set the other parameters globally:

fluid_viscosity: the fluid (kinematic) viscosity (default: 1.5e-5)
fluid_pressure : the fluid pressure (default: 101325)
fluid_temperature: the fluid temperature (default: 303)
liquid_molar_mass: the evaporating liquids molar mass (default: 0.01801528)

Also note that fluid_temperature is not set from a temperature field provided by an eventually present fix temperature/fluid/field command.

If using at least one droplet_solid custom material, liquidtransport/evaporation command tracks the volume of solid volume deleted due to the droplet_solid being dried up completely. The deleted solid volume of every droplet_solid material stored as an additional quantity accessible via <fix_id>.total_deleted_solid_<material_id>.

Output info

This gran model stores a couple of per-particle properties, for access by various output commands.

You can access the property surfaceLiquidContent by f_surfaceLiquidContent (units % of solid particle volume), liquidFlux (units % of solid particle volume/time) by accessing f_liquidFlux and liquidSource (units % of solid particle volume/time) by accessing f_liquidSource. The latter can be used to manually set a surface liquid source via the set command.

Currently, there is a restriction that these properties can only be accessed after a run 0 command.

Restart, fix_modify, run start/stop:

The all of the quantities used by this fix are written to binary restart files so simulations can continue properly. None of the fix_modify options are relevant to this fix.

No parameter of this fix can be used with the start/stop keywords of the run command.

Restrictions

liquid_density is a deprecated input for defining the density the surface film. Please use the new composition_properties framework.

Literature

[1] Gunn, D. J. Transfer of heat or mass to particles in fixed and fluidised beds. Int. J. Heat Mass Transfer 1978, 21 (4), 467−476

[2] Frössling, F, Über die Verdunstung Fallender Tropfen. Gerlands Beitr. Geophys. 1938, 52, 107−216