One of the most critical weaknesses of the Euler-Euler approach for gas-liquid flows is the limited validity range of the closure laws (such as drag, lift, wall lubrication, turbulent dispersion, and turbulent interaction). The fluid particle size range of the closure relations is highly restricted by experimental data on one hand and the computational complexity of DNS simulations on the other hand. Interfacial closures for large gaseous particles, such as churn-like or Taylor bubbles, are not easy to obtain due to the instability of the interface of the large bubbles rising without interference from the small bubbles. Conventional Eulerian approaches cannot be used for predictions of transitional flows in industrial applications where separated and dispersed flow structures appear simultaneously.
The GENeralized TwO Phase flow (GENTOP) method bypasses these limitations by resolving the
largest fluid structures for which no closure laws exist. In essence, the GENTOP concept extends
the population balance equation (PBE) method known as the inhomogeneous discrete method (iDM) by
introducing a potentially continuous secondary phase. In the GENTOP method, the last velocity
group defined within the iDM represents all gas structures that are larger than an equivalent
spherical bubble diameter 
.
The GENTOP method is a multi-field two-fluid approach where the flow is represented by a
continuous primary phase (
), one or several polydispersed secondary phases (
), and a GENTOP phase (
). The term “polydispersed” refers to a wide range of size
distribution. The GENTOP phase can behave as either continuous or dispersed depending on the
phase volume fraction and critical bubble diameter. The dispersed phases are modeled using the
iDM, which can deal with different size groups and associated velocity fields. With the iDM,
various interfacial closures can be used depending on the expected size of the dispersed fields
(for example, this is useful when both negative and positive lift coefficients are expected
depending on the bubble size and deformability based on the Eötvös number, which
determines whether the bubble moves towards the wall or the bulk of a pipe). In addition, the iDM
uses appropriate models to consider transfer between different size groups due to coalescence and
breakup within the polydispersed fields.
The GENTOP approach was originally introduced by the Helmholzt-Zentrum Dresden-Rossendorf (HZDR) and has been further improved, extended, and extensively validated as reported in [232], [233], [456], [454], [452], and [453].
The GENTOP method can model flows with bubbles smaller than the grid size and track the interface of larger continuous gaseous structures (such as churn, Taylor bubbles, and even transition to annular gas core) while accounting for mass transfer between the dispersed and the continuous gas fields.
Within the GENTOP framework, the simulation initially uses the Euler-Euler model
to predict the flow behavior. Once the maximum diameter of the largest fluid
structures 
is reached, the simulation switches to the GENTOP method.
The key aspects of the GENTOP method are described in the following sections:
To resolve the large fluid structures, the GENTOP model detects a potential gas-liquid
interface. A blending function 
is used to identify the local interfacial structure. The free surface region
is defined using the volume fraction gradient of the GENTOP phase 
. The interface between the GENTOP phase and the primary phase is characterized
by a variation of the volume fraction of 
from 0 to 1 over 
grid cells of the size 
. This leads to a critical value 
which gives a definition of the interface. The free-surface detection function
is then defined as:
 | (14–482) |
where 
= 100.
The clustering force is an additional interfacial force that works exclusively between the GENTOP phase and the primary phase. It provides a smooth transition from the dispersed to continuous morphology within the GENTOP phase using an aggregative effect over the volume fraction of the continuous gas phase. While the Eulerian approach produces smearing of the volume fraction by numerical diffusion, the clustering force also stabilizes the interface without the need to use interface sharpening schemes.
The clustering force is included in the interfacial momentum transfer and is proportional to the gradient of the volume fraction of the primary phase:
 | (14–483) |
where
= clustering force in the primary phase |
= contribution from the GENTOP phase to the clustering
force |
= clustering coefficient, which by default is equal to
1 |
= range of applicability of the clustering
force |
= primary phase density |
= gradient of the volume fraction of the primary
phase |
When the critical bubble size 
specified for the GENTOP phase is reached, the clustering force
begins to slowly increase creating regions of the continuous volume fraction by
inducing aggregation of the GENTOP phase volume fraction until the formation of the
continuous structures is completed. The clustering force is not present in the
continuous structures and acts only outside of the interface agglomerating the gas
when the GENTOP phase is in a dispersed state. Once the GENTOP phase reaches the
critical gradient of the volume fraction, the clustering force decreases and
disappears when a full interface is established.
The Ansys Fluent GENTOP model uses a modified version of the original blending function proposed in [452]. This modified function is based on a more physical approach to determining the regions where the clustering force should be activated.
The surface tension model creates a physical transition between the dispersed and continuous structures. This is achieved by decreasing the effect of the clustering force and including the surface tension effects as soon as the interface is detected, thus allowing deformability of the interface. The surface tension and contact angle are calculated as described in Surface Tension and Adhesion for the Eulerian Multiphase Model. In the GENTOP model, the surface tension acts only between the GENTOP and primary phase pairs.
To accurately model interfacial transfer between the dispersed and continuous morphologies
of the GENTOP phase depending on the corresponding volume fraction, the GENTOP method detects
the local GENTOP phase morphologies using a concept similar to that of the AIAD model ([135]). (For details, see section Algebraic Interfacial Area Density (AIAD)
Model in the Ansys Fluent Theory Guide.) The transition parameters between the closure models are
defined in terms of the GENTOP formulation for the interfacial area density and drag and
non-drag forces. The blending function for the interfacial transfers 
is defined as [452]:
 | (14–484) |
Then, the interfacial transfer for the interfacial area density, drag, and non-drag forces can be defined as:
 | (14–485) |
 | (14–486) |
 | (14–487) |
where 
, 
, and 
are the drag coefficients for the GENTOP phase, dispersed part of the GENTOP
phase, and continuous part of the GENTOP phase, respectively; 
, 
, and 
are interfacial area densities for the GENTOP phase, dispersed part of the
GENTOP phase, and continuous part of the GENTOP phase, respectively; and 
and 
are the non-drag forces for the GENTOP and continuous phases, respectively.
The non-drag forces become zero when the GENTOP phase becomes continuous.
During the calculation, low fractions of the dispersed secondary phases may arise in a region of the continuous GENTOP phase (for example, inside a churn or slug bubble). To prevent such unphysical occurrences, upon reaching the critical void fraction gradient, the GENTOP model uses a special coalescence method for complete mass transfer in the area within a fully formed interface instead of the methods for modeling aggregation due to the averaged coalescence used in the Euler-Euler approach. When certain conditions are met, the complete coalescence method converts all the remaining dispersed secondary phases within a specific grid cell into the continuous GENTOP phase. The complete coalescence method is disabled at the gas-liquid interface to allow typical coalescence and breakup at these locations.