Bai-Gosman Wall Impingement Model Reference

The Bai-Gosman wall impingement model provides a methodology for modeling the behavior of droplets impacting on a wall. In particular, this model attempts to predict how and when droplets break up or stick to the wall. This model is used with impermeable boundaries (wall, contact, and baffle) as well as with fluid film.

To reflect the stochastic nature of the impingement process, the model uses a random procedure to determine some of the droplet post-impingement quantities. This randomization allows secondary droplets resulting from a primary droplet splash to have a distribution of sizes and velocities. [648], [649], [650]

The Bai-Gosman wall impingement model is applicable only for liquid droplets (single- or multi-component) in the Lagrangian phase. The model can be used with a single-phase gas as the continuous phase or as part of a Volume-of-Fluid (VOF) simulation.

When the Bai-Gosman wall impingement model is used in a VOF simulation, it is possible that the droplet impingement occurs where the droplet is passing through a liquid. As the Bai-Gosman wall impingement model is strictly valid only for droplets in a gas, the impingement is treated as follows:

When impingement in a liquid occurs, the assumed behavior is for the droplet to rebound (using the standard Bai rebound mode).
When impingement in a gas occurs, the droplet behavior is identical to the single-phase gas case.

To determine whether the droplet is in a gas or liquid, Simcenter STAR-CCM+ evaluates the total volume fraction of all of the gas phases in the local cell. When this value is above 0.5, the droplet is determined to be in a gas.


Theory	See Bai-Gosman Wall Impingement.
Provided By	Lagrangian Multiphase > Lagrangian Phases > [phase] > Models > Wall Impingement
Example Node Path	Lagrangian Multiphase > Lagrangian Phases > [phase] > Models > Bai-Gosman Wall Impingement
Requires	Material: one of Gas, Liquid, Multiphase, Multi-Component Gas, Multi-Component Liquid (For Multi-Component Gas or Multi-Component Liquid, or for Multiphase Model: Volume of Fluid (VOF), further models are required to expose the Flow models.) Flow: Coupled or Segregated In Lagrangian Multiphase > Lagrangian Phases > [phase] > Models: Particle Type: Material Particle Particle Spherical: Spherical (selected automatically) Material: Liquid or Multi-Component Liquid
Properties	Key properties are: Wall State. See Bai-Gosman Wall Impingement Properties.
Activates	Model Controls (child nodes)	See Lower and Upper Transition Temperature Properties.
	Materials	Critical Pressure, Critical Temperature, Dynamic Viscosity, Leidenfrost Temperature, Normal Boiling Temperature, Normal Leidenfrost Temperature, Saturation Pressure, Saturation Temperature, Surface Tension. See Materials and Methods.
	Boundary Inputs	`Bai-Gosman`, `Adhere Mode`. See Bai-Gosman Boundary Settings.
	Field Functions	Droplet Dynamic Viscosity, Droplet Leidenfrost Temperature, Droplet Saturation Temperature, Droplet Surface Tension. See Lagrangian Multiphase Field Functions Reference.

Bai-Gosman Wall Impingement Properties

Child Parcels

Number of child parcels to create during a splash/breakup event.

Wall State

This property defines whether an impermeable boundary (other than a Fluid Film boundary) is treated as wet or dry. In the case of a Fluid Film boundary, the wall is treated as wet when the film thickness is larger than zero. See Bai-Gosman Wall Impingement.

Wet

Specifies that the wall is wet; droplet impingement produces different outcomes, depending on Weber number and wall temperature:

At low Weber numbers, droplets adhere, rebound, or spread.
At high Weber numbers, droplets splash, breakup and spread, or break up and rebound.

Dry

Specifies that the wall is dry; droplet impingement produces different outcomes, depending on Weber number and wall temperature:

At low Weber numbers, droplets spread or rebound.
At high Weber numbers, droplets splash, breakup and spread, or break up and rebound.

Leidenfrost effect occurs when the temperature is high enough.

WeT1

Minimum Weber number for breakup

W e_{T 1}

in temperature ranges 2 (Eqn. (3193) and Eqn. (3194)) and 3 (Eqn. (3198) and Eqn. (3199)).

WeT2

Minimum Weber number for breakup and spread

W e_{T 2}

in temperature range 2, see Eqn. (3194) and Eqn. (3195).

Rosin-Rammler Exponent

Exponent in Rosin-Rammler size distribution,

q

in Eqn. (3190).

Cf

Wall friction coefficient for splash-generated droplets, see Eqn. (3191).

Aw

Coefficient governing the onset of the splash regime, see Eqn. (3185).

a0

Coefficient governing the number of splash- generated droplets, see Eqn. (3189).

WeRebound

Minimum Weber number for rebound in range 1. The default value is 2.

WeSpread

Minimum Weber number for spread in range 1. The default value is 20.

Minimum Ejection Angle

Minimum ejection angle from the wall of splash- generated droplets.

Maximum Ejection Angle

Maximum ejection angle from the wall of splash-generated droplets.

Cb

Base coefficient

C_{b}

in Eqn. (3188), applicable in temperature range 1. The default value is 0.2.

Crd

Range coefficient

C_{r d}

for a dry wall in Eqn. (3188), applicable in temperature range 1. The default value is 0.6.

Crw

Range coefficient

C_{r w}

for a wet wall in Eqn. (3188), applicable in temperature range 1. The default value is 0.75.

Setting Cb=0, Crd=Crw=0 simulates droplets spreading with no splashing.

Setting Cb=1, Crd=Crw=0 simulates droplets splashing with no spreading.

Lower and Upper Transition Temperature Properties

The Lower and Upper Transition Temperature nodes are subnodes of the Bai-Gosman Wall Impingement node.

Lower Transition Temperature: Temperature for transition between ranges 1 and 2 ( $T_{12}$ in Eqn. (3179) and Eqn. (3192)). This value is expected to be approximately the boiling temperature of the droplet.
Upper Transition Temperature: Temperature for transition between ranges 2 and 3 ( $T_{23}$ in Eqn. (3192) and Eqn. (3197)). This value is expected to be approximately the Leidenfrost temperature of the droplet.

Materials and Methods

Selecting the Bai-Gosman Wall Impingement model activates the following material properties under Liquid > [liquid] (the default liquid being H2O):

Dynamic Viscosity

The dynamic viscosity of the droplet.

Leidenfrost Temperature

The temperature at which the Leidenfrost effect begins. See Using the Leidenfrost Temperature.


Method	Corresponding Method Node
Habchi	Habchi. Exposes the following terms from Eqn. (169): Critical Temperature $T_{c}$ Normal Boiling Temperature $T_{b}$ Normal Leidenfrost Temperature $T_{L}^{1}$
Lienhard	Lienhard Critical Temperature $T_{c}$ in Eqn. (168)
Speigler	Speigler Critical Temperature $T_{c}$ in Eqn. (167)

Saturation Pressure

The vapor saturation pressure. Available when the Iterative method is selected for Saturation Temperature.


Method	Corresponding Method Node
Antoine Equation	Antoine Equation See Using the Antoine Equation.
Wagner Equation	Wagner Equation See Using the Wagner Equation.

Saturation Temperature

The droplet saturation temperature.


Method	Corresponding Method Node
Iterative This method uses a combination of bisection and a damped Newton's method to extract a saturation temperature corresponding to a given cell pressure from a saturation pressure curve. The iterative method first uses bisection to obtain a good initial guess, iterates a number of times less than or equal to Max Bisection Iterations, then iterates using Newton's method a number of times less than or equal to Max Newton Iterations.	Iterative This node has the following properties: Alpha A damping factor used if Newton's method goes outside the temperature range used in bisection. The default 1. Delta Max The maximum allowed temperature change over an iteration, given as a percentage of the temperature range. The default is 0.3. Convergence Tolerance If successive updates change less than this value, the solution has converged. The default 0.01. Max Newton Iterations The maximum number of iterations of Newton's method. The default is 20. Max Bisection Iterations The maximum number of iterations of bisection. The default is 5. Minimum Temperature The bottom of the temperature range for the bisection method. The default is 273.15 K. Critical Pressure The critical pressure of the vapor. Critical Temperature The critical temperature of the vapor. Saturation Pressure The vapor saturation pressure. See Saturation Pressure.

Surface Tension

The surface tension of the droplet.

Bai-Gosman Boundary Settings

Wall, Baffle, Fluid Film, Phase Impermeable, Contact Interface, or Mapped

Mode: When the Bai-Gosman Wall Impingement model is activated, the Bai-Gosman option becomes available on the Mode node under Lagrangian Phases > [phase] > Boundary Conditions > [boundary] > Physics Conditions. See the Bai-Gosman boundary interaction mode.

Wall, Baffle, Fluid Film, Phase Impermeable, Contact Interface, or Mapped

Adhere Mode

When the Bai-Gosman mode is activated (either directly through the Mode node or when Composite mode is selected), an additional node Adhere Mode appears in the Lagrangian Phases > [phase] > Boundary Conditions > Wall > Physics Conditions. The Adhere Mode allows you to select which specific boundary interaction mode is used when the impingement satisfies the Adhere conditions. The default mode for this condition is Stick.


Mode	Result
Composite	Droplets exhibit a mixture of Escape, Rebound, Stick, and Vaporize.
Escape	Droplet leaves the domain.
Rebound	Droplet rebounds.
Stick	Droplet sticks. This is the default.
Vaporize	Droplet evaporates.