Bai-ONERA Wall Impingement Model Reference

The Bai-ONERA Wall Impingement model is a further development of the Bai-Gosman model, adding smoother transitions between impingement outcomes across transition temperatures.

The original ONERA model, described in [693], was developed for a smooth and dry wall. Modifications made to it in the Bai-ONERA model are designed to:

Allow for the effect of a rough or wet wall.
Achieve a smooth transition to recover the Bai-Gosman model for situations where the wall temperature is lower than the droplet saturation temperature.

When the Bai-ONERA wall impingement model is used in a VOF region, it is possible that the droplet impingement occurs where the droplet is passing through a liquid. As the Bai-ONERA 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-ONERA Wall Impingement.
Provided By	Lagrangian Multiphase > Lagrangian Phases > [phase] > Models > Wall Impingement
Example Node Path	Lagrangian Multiphase > Lagrangian Phases > [phase] > Models > Bai-ONERA 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-ONERA 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-ONERA`, `Adhere Mode`. See Bai-ONERA Boundary Settings.
	Field Functions	Droplet Dynamic Viscosity, Droplet Leidenfrost Temperature, Droplet Saturation Temperature, Droplet Surface Tension. See Lagrangian Multiphase Field Functions Reference.

Bai-ONERA Wall Impingement Properties

The Rosin-Rammler exponent $q$ , the wall friction coefficient $c_{f}$ , the onset coefficient $A_{w}$ , and the splash number coefficient $a_{0}$ are used just as they are in the Bai-Gosman treatment.

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. For a Fluid Film boundary, the wall is treated as wet when the film thickness is larger than zero.

At low K numbers, droplets spread or rebound.
At high K numbers, droplets splash, spread, or rebound.

Leidenfrost effect occurs when the temperature is high enough. See Bai-ONERA Wall Impingement.

Wet: Specifies that the wall is wet; droplet impingement produces different outcomes, depending on K number (see Eqn. (3201)) and wall temperature. The transition point between rebound and spreading depends on the Laplace number of the droplet. See Wet Wall in Bai-ONERA Wall Impingement.
Dry: Specifies that the wall is dry; droplet impingement produces different outcomes, depending on K number (see Eqn. (3201)) and wall temperature. The transition point between splashing and spreading depends on wall roughness. See Dry Wall in Bai-ONERA Wall Impingement.

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). The default value is 0.2.

Crd

Range coefficient

C_{r d}

for a dry wall in Eqn. (3188). The default value is 0.6.

Crw

Range coefficient

C_{r w}

for a wet wall in Eqn. (3188). The default value is 0.75.

K1

Model constant

K_{1}

. See Regime Transition Criteria in Bai-ONERA Wall Impingement.

Gamma

The exponent

γ

in Eqn. (3203), describing the transition between spreading and splashing in the temperature range between the saturation point and the Leidenfrost point.

Smrf

Splash Mass Ratio Exponent, the exponent

n

in Eqn. (3205), describing the splash ratio between the saturation point and the Leidenfrost point.

Lower and Upper Transition Temperature Properties

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

Lower Transition Temperature: Temperature for transition between ranges 1 and 2 ( $T_{12}$ in Bai-ONERA Wall Impingement). 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 Bai-ONERA Wall Impingement). This value is expected to be approximately the Leidenfrost temperature of the droplet.

Materials and Methods

Selecting the Bai-ONERA 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-ONERA Boundary Settings

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

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

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

Adhere Mode

When the Bai-ONERA 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.