Interfacial area concentration is defined as the interfacial area between two phases per unit mixture volume. This is an important parameter for predicting mass, momentum and energy transfers through the interface between the phases. When using the Mixture multiphase model with non-granular secondary phases, you can have Ansys Fluent compute the interfacial area in one of following ways:
use a transport equation for interfacial area concentration as further described in Transport Equation Based Models. This allows for a distribution of bubble diameters and coalescence/breakage effects.
use an algebraic relationship between a specified bubble diameter and the interfacial area density. For more information, see Algebraic Models.
The key difference between the transport equation based interfacial area concentration (IAC) models (Transport Equation Based Models) and algebraic models (Algebraic Models) is that the algebraic models assume the interface to be spherical, whereas the IAC models can predict the interface area concentration directly through the solution of a transport equation
In two-fluid flow systems, one discrete (particles) and one continuous, the size and its distribution of the discrete phase or particles can change rapidly due to growth (mass transfer between phases), expansion due to pressure changes, coalescence, breakage and/or nucleation mechanisms. The Population Balance model (see Population Balance Model ) ideally captures this phenomenon, but is computationally expensive since several transport equations need to be solved using moment methods, or more if the discrete method is used. The interfacial area concentration model uses a single transport equation per secondary phase and is specific to bubbly flows in liquid at this stage.
The transport equation for the interfacial area concentration can be written as
 | (14–147) |
where 
is the interfacial area concentration
(m2/m3), and 
is the gas volume fraction. The first two terms on the right hand side of
Equation 14–147 are of gas bubble expansion due to compressibility
and mass transfer (phase change). 
is the mass transfer rate into the gas phase per unit mixture volume
(kg/m3/s). 
and 
are the coalescence sink terms due to random collision and wake entrainment,
respectively. 
is the breakage source term due to turbulent impact.
Two sets of models, the Hibiki-Ishii model [244] and the Ishii-Kim model [306], [272], exist for those source and sink terms for the interfacial area concentration, which are based on the works of Ishii et al. [244], [306]. According to their study, the mechanisms of interactions can be summarized in five categories:
Coalescence due to random collision driven by turbulence.
Breakage due to the impact of turbulent eddies.
Coalescence due to wake entrainment.
Shearing-off of small bubbles from large cap bubbles.
Breakage of large cap bubbles due to flow instability on the bubble surface.
In Ansys Fluent, only the first three effects will be considered.
 | (14–148) |
where 
, 
and 
are the frequency of particle/bubble collision, the efficiency of coalescence
from the collision, and the number of particles per unit mixture volume, respectively. The
averaged size of the particle/bubble 
is assumed to be calculated as:
 | (14–149) |
and
 | (14–150) |
 | (14–151) |
where 
, 
and 
are the frequency of collision between particles/bubbles and turbulent eddies
of the primary phase, the efficiency of breakage from the impact, and the number of turbulent
eddies per unit mixture volume, respectively. In Equation 14–151,
 | (14–152) |
The experimental adjustable coefficients are given as follows:
; 
; 
; 
.
Note that based on experimental data, Ansys Fluent uses a different value for 
than that proposed by Hibiki and Ishii [244]. If you
want to modify this value for your case, contact Ansys Technical Support for information on
how to customize your settings.
The shape factor 
is given as 6 and 
as 
for spherical particles/bubbles. There is no model for 
in the Hibiki-Ishii formulation.
 | (14–153) |
 | (14–154) |
 | (14–155) |
where the mean bubble fluctuating velocity, 
, is given by 
. The bubble terminal velocity, 
, is a function of the bubble diameter and local time-averaged void
fraction.
 | (14–156) |
 | (14–157) |
 | (14–158) |
where 
is the molecular viscosity of the fluid phase, 
is the gravitational acceleration and 
is the interfacial tension. In this model, when the Weber number,
, is less than the critical Weber number, 
, the breakage rate equals zero, that is, 
. The coefficients used are given as follows [272]:
|
| |
|
| |
|
| |
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| |
|
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Important: Currently, this model is only suitable for two-phase flow regimes, one phase being gas and another liquid, that is, bubbly column applications. However, you can always use UDFs to include your own interfacial area concentration models, which can apply to other flow regimes.
See the Fluent Customization Manual for details.
The volumetric interfacial area is an important quantity that appears in the calculation of the interphase exchange forces like momentum, mass, and heat transfer. In Ansys Fluent, the Hibiki and Ishii model ([244]) and the Ishii and Kim model (Hibiki-Ishii Model) have been implemented In the context of bubbly flows with bulk mass transfer. An extension to these two models exists. This will include heterogeneous mass transfer effects on wall based on the work done by Yao and Morel [722] for nucleate boiling applications. The volumetric interfacial area transport Equation 14–147 contains a nucleation term and models for coalescence and breakup. Yao and Morel [722] modeled the coalescence term as follows:
 | (14–159) |
where 
and 
are the free traveling time and the interaction time for coalescence,
is the bubble number density, 
is the coalescence efficiency and the factor one-half has been included to
avoid double counting on the same events between bubble pairs. The final expression for the
above equation is
 | (14–160) |
where 
is the critical Weber number and the coefficients have the values
, 
, 
, 
is the Weber number, 
is the dissipation obtained from the k-epsilon turbulence model,
is a modification factor defined as 
and 
is the packing limit. Regarding Equation 14–147,
the coalescence sink terms due to random collision and wake entrainment are as follows:
 | (14–161) |
The breakage term, as modeled by Yao and Morel [722], is
 | (14–162) |
where 
and 
are the free traveling time and the interaction time for breakage and
is the breakage efficiency. The final expression for the above equation is of
the form
 | (14–163) |
Here, the coefficients have the values 
and 
Regarding Equation 14–147, the 
breakage source term due to turbulent impact is of the form
 | (14–164) |
When including source terms due to bubble nucleation at the heated wall a new term should be added to Equation 14–147. This is of the form
 | (14–165) |
where 
is the diameter of the nucleation bubble, 
is the nucleation site density, and 
is the frequency of the bubble. These parameters can be connected to the
boiling models described in Wall Boiling Models. The bubble departure
frequency is given by Equation 14–514, the nucleate site density by Equation 14–515, and the bubble departure diameter by Equation 14–518,
Equation 14–519, or Equation 14–520.
To learn how to apply this model, refer to Defining the Interfacial Area Concentration via the Transport Equation in the User's Guide.
The algebraic models are derived from the surface area to volume ratio, 
, for a spherical bubble or droplet:
 | (14–166) |
where 
is the bubble or droplet diameter. Although the algebraic models are derived
based on the assumption that the bubble or droplet has a spherical shape, the unit of the
interfacial area density 
is the same as that of in the transported equation based models. When using the Mixture multiphase
model with non-granular secondary phases, you can have Ansys Fluent compute the interfacial area in
one of the following ways:
Symmetric model (default)
The symmetric model treats both phases
and 
symmetrically. Phases 
and 
can be continuous or dispersed. The interphase area density is calculated
as:
(14–167)
where
and 
are the volume fraction of the phase 
and phase 
, respectively, and 
is the characteristic length scale computed as follows:Particle model
For a dispersed phase,
, with volume fraction, 
, the particle model estimates the interfacial area density, 
as 
(14–170)
Gradient model
The Gradient model differs from the Symmetric model in that it introduces the gradient at the phase interface as the interfacial length scale. This model is typically used for free surface problems. Two versions of the Gradient model are available in Ansys Fluent:
Pure gradient model
If there is a free surface between the continuous phase
and dispersed phase 
, then the interfacial area density is computed as:
(14–171)
For dispersed-dispersed systems with more than two phases, the interfacial area density for phases
and 
is expressed as:
(14–172)
Gradient-Symmetric model
The Gradient-Symmetric model computes the interfacial area density based on the free surface position as follows. If
< specified limit (default 1e-6), then the interfacial area density is
computed using the Symmetric model Equation 14–167. Otherwise, the
interfacial area density is set to zero.
User-Defined
See
DEFINE_EXCHANGE_PROPERTYin the Fluent Customization Manual.
