UNICAMP GENERAL PARTICLE TRACKING ALGORITHM

Sources of Information : • Phoenics Lecture: GENTRA• Workshop: GENTRA• GENTRA user guide: (html) or (PDF)

UNICAMP

Coupling of the Interfacial Force to the Continuous Phase

UNICAMP Introduction

• The Gentra algorithm applies to low concentration (one way coupling) and, at most, two way coupling.

• This section describes a simple one-way coupling where the solids concentration is too low that it does not interfere to the continuous fluid flow field.

UNICAMP Simple Theory

• The Technical Report 211 brings, in detail, all theoretical content of particle tracking including its implementation on the CFD routine.

• For a fully account one must go to TR 211.

• The following slides brings, in a concise form, a simple theory for isothermal particles.

UNICAMP Simple Theory

• The particle velocity equation stems from Newton’s 2nd law:

EXTERNAL FORCES

pp p D p p p

PRESSUREBUOYANCYDRAG

dU 1 C U U U U g Pdt 2

UNICAMP Particle Acceleration

• The particle acceleration is better written as:

• and the vector equation can be represented in a general form as:

pp

p p p

BA

p pD p

p

dU D 1 D U Eg P Udt

A1D C U U ; E2

pp

dUA BU

dt

UNICAMP Particle Velocity

• Notice that vector A and the scalar B are known from the continuous phase flow when one follows the particle (Lagrangian concept).

• The equation above has an analytical solution for Up which, expressed as function of the time step becomes:

pp

dUA t B t U

dt

B t B t

p p

A tU t t 1 e U t e

B t

UNICAMP Particle Trajectory

• The particle trajectory and its time history are determined integrating the particle velocity at each time step.

t t

pt

S U dt

UNICAMP Particle Trajectory

• The particle trajectory and its time history are determined integrating the particle velocity at each time step.

t t

pt

S U dt

UNICAMP Particle Initial Conditions

• To get the particle’s velocity and position is necessary to declare:–the (X,Y,Z) particle position– the (U,V,W) particle initial velocity, –the particle size and density and finally, –the particle mass flow rate / frequency delivered by the emission point.

• Notice that for that particular point the these particle features can not change in time.

•This information is transmitted to phoenics in a separate file, usually embedded inside q1 file (it will seen shortly).

UNICAMP The Particle Frequency

• Every particle emission spot delivers particles at a constant mass flow rate (kg/s). These particles parcels will describe the particle trajectory as shown on the figure bellow

• The particle frequency, , for each particle’s parcels is evaluated by the ratio

Mass Flow RateParticle Mass

UNICAMP The Particle Concentration

n

k k kk 1

CELL

tC

k – parcel of particles Vk – volume of particle on parcel k k – particle freq. of parcel k tk – residence time of parcel k in the cellVcell – is the cell volume

• The volumetric concentration of particles, C, within a specific grid volume VG is defined by the ratio between the volume of particles within the cell by the volume of the cell:

UNICAMP The Particle Momentum Source

• It is the law of action and reaction. If the continuous fluid acts on the particle accelerating or decelerating therefore a force with the same magnitude but opposite direction will act on the continuous phase.

•The source of momentum Smom (N/m3) which appears on the continuous phase momentum eq. is equal to the rate of change of particle momentum as each particle parcel traverses a cell

n t t t3 3mom k p p p p p p

k 1

S U d U d6

k – parcel of particles k – particle freq. of parcel k Uk – particle vel. of parcel k within the cell

UNICAMP MAIN LIMITATIONS

•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.

• In polar coordinates RINNER has to be zero. Annular domains still can be built setting REINNER=0 and blocking cells.

UNICAMP

WORKSHOP - GENTRAFlow of solid particles over a backward facing step

•This workshop shows the user how to set up a simple case which simulates the 2d turbulent flow of solid particles over a backward facing step.

•Air, laden with solid particles, enters a 2d plane channel with a velocity of 13 m/s. The total channel width is 0.1143m and the length of the channel is 0.762m. The step is 0.1524m long by 0.0381m high. Turbulence is represented by means of the standard k-e model with equilibrium wall functions.

• Load single phase flow Q1, case 300. Change for 500 iterations and turn-off ASCII output. Run case for reference .

0.15

0.04

0.76

0.11

UNICAMP The work shop

•Go to Help/POLIS/Tutorials/Multi-phase Flow/Gentra. Open CHAM’s workshop.

• At Menu/Model/Lagrangian Particle Tracking – ACTIVATE model.

UNICAMP The work shop 1)Particle Type

• Select the Isothermal particles.

UNICAMP The work shop 1) Isothermal Particle Settings

•Drag Coefficient, Buoyancy, Pressure & Stochastic Model Isothermal particles.

UNICAMP workshop 2) Boundary Conditions for Particles

UNICAMP workshop 2) Boundary Conditions for Particles INLET

• An inlet-data file has to be written with the particles properties.

•It can be done externally or inside the Q1 file.

UNICAMP

• Inlet data file sample to the workshop (isothermal particles). Start typing after the 3rd column.

• MASSFLO means mass flow rate kg/s

workshop 2) Boundary Conditions for Particles INLET

UNICAMP workshop 2) Boundary Conditions for Particles OUTLET

• The inlet and outlet patches have names starting with GX, do not forget the change the names.

UNICAMP

• For time definitions see section 2.8, page 25 of TR211.

workshop 3) Numerical Controls

UNICAMP workshop 4) I/O

UNICAMP

• MONX, MONY,MONZ are the external forces acting on the particles and its negative value are the source terms acting on the continous phase flow.

• GHIS has the history of the particle or the displacement of the particle as a function of time

• Files h001, h002 etc are the history files for each track• Files t001, t002 etc are the trajectory files for each track

workshop 4) Output variables

UNICAMP

•The particle trajectories are displayed in VR Viewer by using the MACRO file written by EARTH. Click on 'Macro' and then enter 'GHIS' as the name of the macro file to run. Click 'OK' to close the dialog and plot the particle paths will be displayed automatically on the screen.

•HISTORY READfilename m n     filename is the name of the history file. All tracks are read unless;                     if m is present, it is the track to be read                     if n is present, all tracks in the range m-n are read

workshop 5) Visualizing particles trajectories

UNICAMP Flow Simulation (1)

•Buoyancy OFF•Pressure Gradient OFF•Stochastic Model OFF• Particle size and density 10 μm & 1500 kg/m3• Mass flow rate 5e-05 kg/s

UNICAMP Flow Simulation (2)

•Buoyancy OFF•Pressure Gradient OFF•Stochastic Model ON• Particle size and density 10 μm & 1500 kg/m3

UNICAMP Flow Simulation (3)

•Buoyancy ON•Pressure Gradient ON•Stochastic Model ON• Particle size and density 10 μm & 1500 kg/m3

UNICAMP Flow Simulation (4)

•Buoyancy ON•Pressure Gradient ON•Stochastic Model ON• Particle size and density 100 μm & 1500 kg/m3

UNICAMP

END