See also the GENTRA workshop

- Introduction
- User Interface
- Modelling Features
- When to Use GENTRA
- GENTRA Equations in General
- The GENTRA Particle Equations
- The Stochastic Turbulence Model
- The Overall Solution Algorithm
- Solution of the Particle Equations
- Implementation in PHOENICS
- Activation in PHOENICS
- Main Limitations
- Sources of Further Information
- References

GENTRA is an 'add-on' for PHOENICS. The name GENTRA stands for GENeral TRAcker.

GENTRA tracks particles moving through a flow field, taking into account the effects of fluid velocity, temperature, turbulence etc. The effect of the particles on the continuous phase is also considered.

Whilst IPSA solves the equations for both phases in the same Eulerian frame of reference, using the concept of interpenetrating continua, GENTRA solves the dispersed phase equations using Lagrangian methods.

PHOENICS solves the equations governing the behaviour of the continuous phase in the normal manner. GENTRA integrates the particle equations in a Lagrangian frame, to give particle trajectories, and properties along the tracks.

The two sets of equations are linked by inter-phase transfer sources.

Pre-processing

- Three complementary user interfaces (menu, command language and FORTRAN)
- The VR-Editor supports GENTRA
- Full on-line help in the menu
- Library of examples and test cases

Post-processing

- Particle trajectory files for VR-Viewer and PHOTON, which display the path of the particles through the domain
- History files for Autoplot, which record the evolution of particle properties with time.

All three types of coordinate systems are supported.

Steady and transient operation.

Six types of particles available:

- Tracers (lazy particles) which just follow the gas flow field.
- Beams (stubborn particles) which follow straight lines.
- Isothermal particles which exchange momentum but not heat with the gas.
- Heat exchanging particles.
- Melting/solidifying particles with internal phase change.
- Vaporising droplets.

Automatic detection of internal walls and blockages with options for:

- Particle bouncing with user-specified restitution coefficient.
- Particle adhesion to the wall.
- Withdrawal of the particle.
- Flash vaporisation of a droplet.

Optional stochastic particle dispersion model for turbulent flow.

Compatibility with PHOENICS conjugate heat transfer option.

Although IPSA or ASM will simulate flows with particles or droplets, GENTRA is to be preferred if:

- Detailed information on particle trajectories is required.
- A large number of particle sizes, temperatures or densities has to be considered simultaneously.
- Numerical diffusion of the particulate phases is to be completely eliminated.

However, if particle loadings are high, so that particle-particle interactions are important, GENTRA cannot be used without modification.

The equations of the continuous phase take the standard PHOENICS form:

d(rf)/dt + div[(r

uf) - G_{f}.grad(f)] = S_{f}+ S_{p}(1)

where Sp is the source representing interaction with the dispersed phases.

These equations are solved by PHOENICS in the usual way.

The particle equations can be written in the form:

d(f

_{p})/dt = A . (f_{c}- f_{p}) + B (2)

where f_{c} is the continuous phase value, f_{p} is the particulate phase value and A and B represent
the rest of the equation.

The equations are linked by S_{p} in eqn (1), and f_{c}
in eqn (2).

In the following, p stands for particle, c for continuous phase.

The particle trajectory equation takes the form:

d(

x)/dt =_{p}U_{p}

The particle momentum equation takes the form:

m

_{p}d(U)/dt = D_{p}_{p}(U-_{c}U) + m_{p}_{p}bg- V_{p}grad(p)

where D_{p} is the drag function, m_{p} is the particle mass, b is the buoyancy parameter, V_{p} is the particle volume and p is the continuous-phase pressure.

The particle temperature equation takes the form:

Cp

_{p}. m_{p}.d(T_{p})/dt = h.t.c (T_{c}- T_{p}) + L . d(m_{p})/dt + ...

Since these ordinary differential equations are simple in form, their integration is straightforward if the continuous phase field is known.

The effect of turbulence on the particles is simulated by a stochastic model in which particles are assumed to be deflected by the eddies they cross.

The defection effect is achieved by employing instantaneous values U for continuous-phase velocities in the particle equations of motion:

U

_{c}= U_{c}+ U_{c}'

The fluctuating velocity field U_{c}' is obtained by sampling, for each
component, a normal distribution with a mean of 0.0 and a standard deviation of (2/3k)^{1/2},
where k is the local value of the turbulent kinetic energy.

The time interval over which the particle interacts with the randomly-sampled velocity field is taken as the minimum of:

- the lifetime of the local eddy, t
_{e}=L_{e}/|U_{c}'|; and - the particle transit time, t
_{r}= L_{e}/|U - U_{p}|.

where the eddy size L_{e}=(C_{m}C_{d})^{3/4}
k^{3/2}/e and (C_{m}C_{d})=0.09.

The gas and particle equations are solved separately, using well-known mathematical techniques.

However, because the gas and particle equations are linked, the solution procedure has to iterate between both algorithms, in the following manner:

- Solve the gas phase without particles - perhaps for many sweeps.
- Integrate the particle equations using the current gas field, and compute the inter-phase sources.
- Solve the gas phase again, including the new particle sources.
- Repeat steps 2 and 3 until both sets of equations have converged.

The numerical integration of the particle equations takes place according to the following sequence:

- The Lagrangian time-step is calculated;
- The particle is moved;
- The particle properties (velocities, temperatures etc.) at the new position are calculated;
- The interphase source terms are calculated.

An overview of each of these steps will now be given.

The Lagrangian time step is estimated by GENTRA, based on a user-set fraction of the minimum cell-crossing time. This in turn is based on the minimum cell size, and the maximum particle velocity component.

The particle is not allowed to jump more than one cell per time step. At boundaries or blockages, the particle is placed on the cell boundary by reducing the time step.

The new particle location, x_{n}, is obtained by integrating the particle
position equation as:

x

_{n}= x_{0}+ U_{0p}dt

where x_{0} and U_{0p} are the location and velocity vector at the
start of the Lagrangian time step.

The integration is always performed in a Cartesian coordinate system.

At the new particle location, the new values of local fluid properties are obtained, and then the particle equations are integrated analytically.

For velocity components in Cartesian and polar grids, the value at the particle location is obtained by interpolation from the neighbouring nodes. For all other variables, and velocity resolutes in BFC grids, the cell centre value is used.

As particles traverse each cell, exchange of heat, mass and momentum may occur. For example, a particle traveling faster than the surrounding fluid will be decelerated, and will in turn accelerate the fluid.

Sources expressing these interchanges are computed once the particle equations have been integrated. They are stored, and will be used the next time PHOENICS solves the gas phase equations.

Pre-processing for GENTRA is carried out in the VR-Editor main menu.

GENTRA itself is attached to PHOENICS as a GROUND station, parts of which are not supplied in source. It is divided into four main sections:

- GENTRA which is called from GREX, and contains the flow control. Users are not normally expected to modify this;
- GENIUS, called from GENTRA. This is a blank user-routine for replacing or supplementing built-in physical laws;
- GPROPS, also called from GENTRA. It allows users to add in their own property laws for the particles; and
- GENLIB, the object library of the tracking module, PSICEL. This is not supplied in source.

The first step is to generate the Q1 for the gas phase. This can be done in any convenient way - loading a case from the library, running one of the input menus, or just editing.

The GENTRA menu can then be entered from the 'Models' panel of the VR-Editor Main menu.

The GENTRA menu can then be used to configure the GENTRA solver, select particle types, identify inlets and outlets, set output controls and so on.

Inlet and outlet objects act as particle exits by default. They can be made impervious to particles if required.

The menu sets GENTR=T, to trigger the call in GREX.

On exit, the GENTRA menu inserts PIL statements into the Q1. These can be edited by the user, or changed by further menu sessions.

The PIL generated by GENTRA menu includes STOREs for the interphase sources, and PATCH to apply the sources.

In addition to the menu settings, the initial positions, velocities, diameters and densities of the particles must be set. This data can be edited into Q1 itself, or can be held in a separate file.

The particle inlet data consists of a table of numbers, in the order:

x,y,z coordinate, u,v,w cartesian velocity component, diameter, density, mass flow rate

In polar coordinates, the data takes the form:

q,r,z coordinate, v,u,w cartesian velocity component, diameter, density, mass flow rate

Each particle will have its own separate line of data, defining its starting condition.

Each particle actually represents a 'parcel' of particles moving along the same path. The total mass flow of disperse phase has to be divided amongst the tracks.

A small number of tracks, each carrying a large fraction of the total mass will be computationally efficient, but will almost certainly give a poor representation of the true flow.

A large number of tracks, each carrying a small fraction of the total mass will be computationally expensive, but will give much better solutions, especially if the stochastic dispersion model is activated.

Once data set-up is complete, the EARTH run is started as normal. If GENTRA is available, it is configured into the 'public' EARTH, so nothing special need be done.

GENTRA writes information about the progress of each track to the VDU.

At the end of the run, GENTRA will write out whatever data files have been requested in the menu.

Particle trajectory files are in the format of PHOTON geometry files. They can be displayed in PHOTON with the command: GEOMETRY READ; file_name. The file GENUSE is written by EARTH - it contains GEOMETRY READ commands for all the requested tracks. It can be used as PHOTON 'use' file.

The tracks can be displayed in the VR-Viewer by using the GENUSE file as a macro.

The filenames are made up of an identifying character set in menu and a five-digit track number - eg T00001.

The particle history files are in the format of Autoplot table files.

The data for up to 20 tracks can be saved in this way. The data for ALL tracks is always written to the file GHIS. The VR-Viewer can read all the tracks at once if GHIS is given as the name of the macro file.

In BFC cases, cyclic boundaries must be physically coincident.

Particle-particle interactions such as collision or coalescence are not considered.

Although GENTRA can calculate and display the volume fraction occupied by the particles, it is not taken into account by the gas phase.

Turbulence modulation - the damping of gas phase turbulence due to the presence of particles - is not considered.

GENTRA cannot perform simulations on multi-block meshes, or meshes with fine-grid embedding.

A detailed account of GENTRA is provided in TR211 - The GENTRA User Guide, available from CHAM on request.

A library of test cases and examples is available, either through the Library option of the top menu under 'Gentra library', or in command mode through SEELIB(G).

The main reference for the methodology of GENTRA is:

Crowe CT, Sharma MP, Stock DE 1977 "The Particle-Source-In-Cell Model for Gas-Droplet Flows." ASME J. fluids Eng., pp 325 - 332

The main reference for the turbulence stochastic model is:

Gosman AD, Ioannides E 1981 "Aspects of computer simulation of liquid-fuelled combustors", AIAA-81-0323, AIAA 19th Aerospace Sciences Meeting, St. Louis, Missouri, USA.

Other references include:

Moffat J, Pericleous K 1989 "The modelling of two-phase flows using the general purpose particle tracking program GENTRA." Proceedings of the 3rd PHOENICS User Conference - Dubrovnik. PHOENICS Journal of Computational Fluid Dynamics and Its Applications Vol 2, No 1, pp 21-40 1989. Published by CHAM

Fueyo N, Hamill I, Zhang Q, Adair D, 1997 "The GENTRA User Guide." CHAM/TR211