Dpm model - Lecture notes 1-3 PDF

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discrete phase model is used in the ansys fluent ...

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Lappeenranta University of Technol From the SelectedWorks of Kari Myöhänen

2008

Modeling of dispersed phase approach in Fluent Kari Myöhänen

Theory and simulation of dispersed-phase multiph

Modeling of Dispersed by Lagrangian Approach 11 March 2008 Kari Myöhänen [email protected]

Pr e se n t a t ion Ou t lin

• • • • •

Introduction Modeling options and limitations in Flu Model theory Solution strategies Example calculation

I nt r odu ct ion

• The discrete phase model (DPM) in Fluent follows the Eu • The fluid phase (gas or liquid, “continuous phase”) is trea solving the time-averaged Navier-Stokes equations (Eule • The dispersed phase is solved by tracking a number of pa calculated flow field of continuous phase (Lagrangian refe • The particles may be taken to represent solid particles in in gas or bubbles in liquid. • The dispersed phase can exchange momentum, mass an phase.

D iscr e t e Pha se M ode ling Opt io

Fluent provides the following discrete phase modeling optio • Calculation of the particle trajectories using a Lagrangian – Discrete phase inertia – Hydrodynamic drag – Force of gravity – Other forces • pressure gradient, thermophoretic, rotating refere Saffman lift, and user defined forces • Steady state and transient flows. • Turbulent dispersion of particles. • Heating and cooling of the discrete phase. • Vaporization and boiling of liquid droplets. • Combusting particles, including volatile evolution and cha coal combustion. • Optional two-way coupling of the continuous phase flow a • Wall film modeling. • Spray model (droplet collision and breakup).

Lim it a t ions in Flu e n

• Particle-particle interactions are neglected. – Assumption: dispersed phase is sufficiently dilute. – Fluent manual provides a hand rule ”volume fraction u – In general, this limit is far too high and does not fulfil between the momentum response time and collisiona (see lecture notes, session 1). – The DPM model is however often used for dense disp should be taken when interpreting the results. • The steady state DPM model cannot be applied for contin – The particle streams should have well-defined entran – For cases, in which the particles are suspended indef stirred tanks), the unsteady DPM modeling should be • If the dispersed phase model is used with Eulerian-Euleri coupling is defined with the primary phase only. • Several restrictions when using DPM model with other Flu – Limitations with parallel computing, streamwise period models, sliding meshes, etc. See Fluent manual for d

Regim e s of Dispe r sed Tw o- P

fluidparticle

fluidparticle

fluidp

Sommerfeld (2000), based on Elghobashi (

M om en t um Equa t io

The force balance of particle in Lagrangian reference fram movement of the particles. The momentum equation for i-direction:

Acceleration

Drag

Gravity

Addition due to o (force/un

D r a g Coe fficie nt

For smooth spherical particles, Fluent uses equation by Mor

The constants a1, a2 and a3 are determined for different ranges of Re:

For nonspherical particles, the equation by Haider and Leve

Shape factor Surface area of sphere with same volume Actual surface area

Com pa r ison of D r a g Coe fficie n

Coupling

• The discrete phase and the continuous phase can be cou In Fluent, the one-way or two-way coupling are possible t • One-way coupling – The continuous phase affects the discrete phase, but – In Fluent, this is referred as “uncoupled approach”. – The discrete phase is solved once after the continuou solved. • Two-way coupling – Both phases affect each other (exchange of momentu – In Fluent, this is referred as “coupled approach”. – The continuous phase flow field is impacted by the di calculations of the continuous phase and dispersed p alternated until the solution is converged (hopefully). • Three-way coupling – Particle disturbance of the fluid locally affects another particle’s motion, e.g. drafting of a trailing par • Four-way coupling – Particle collisions affect motion of individual particles.

Tw o- W a y Coupling in F

Momentum exchange Drag

Heat exchange (without chemical reactions)

Mass exchange

Othe

Vaporization and pyrolysis

Pa r t icle Type s a n d La w s i Particle type

Description

Requirements

Inert

inert/heating or cooling

Available for all models

Droplet

heating/evaporation/ boiling

Energy equation. Minimum two chemical spec nonpremixed or partially pre combustion model. Gas phase density by ideal l

Combusting

heating; evolution of volatiles/swelling; heterogeneous surface reaction

Energy equation. Minimum three chemical spe the nonpremixed combustion Gas phase density by ideal l

Multicomponent

multicomponent droplets/particles

Energy equation. Min. two chemical species. Use volume weighted mixing define define particle mixture

Law 1: Particle temperature be Law 2: Droplet vaporization. Law 3: Droplet boiling. Law 4: Devolatilization of com Law 5: Surface combustion. Law 6: Volatile fraction of the p Law 7: Multicomponent particl

Temperature

Ex a m ple of La w s App lie d for a D

Different energy and mass transfer equations are a

Tbp

Law 3: Boiling

Tvap

Law 2: Vaporization

Tinjection Law 1: Inert heating before vaporization

M a ss a nd Ene r gy Tr a n sfe r of D Law 1:Inert heating before vaporization Law 6: Volatile fraction consumed Heat transfer Convection

Radiation

Law 2: Vaporization Vapor concentratio

Mass transfer (molar flux of vapor) Diffusion coefficient given by user

Heat transfer Evaporation

Law 3: Boiling Mass transfer without radiation with radiation

Particle temperature is constant. Energy required for vaporization appears as energy sink for gas phase

Pa r t icle - W a ll I nt e r a ct Different particle boundary conditions can be defined for

Escape

Reflect

Trap

For particle reflection, a restitution coefficient e is specifie

Normal comp

Tangential co

Tu r bule n t D ispe r sion of P

In Fluent, the dispersion of particles due to continuous phase turb • a stochastic tracking model (random walk model, eddy interact • a particle cloud model.

In the random walk model, the instantaneous continuous phase v of mean velocity and fluctuating component:

• The fluctuating component varies randomly during a particle tra • Each particle injection is tracked repeatedly in order to generat meaningful sampling.

The cloud model uses statistical methods to trace the turbulent d about a mean trajectory • Mean trajectory is calculated from the ensemble average of the for the particles represented in the cloud. • Distribution of particles inside the cloud is represented by a Ga

Eddy I nt e r a ct ion Mo The stochastic tracking model in Fluent is based on eddy interaction model. The discrete particle is assumed to interact with a succession of eddies. Each eddy is characterized by • a Gaussian distributed random velocity fluctuation u’i • a time scale (life time of eddy) e

• a length scale (size of eddy) Le During interaction, the fluctuating velocity is kept constant. The interaction lasts until time exceeds the eddy lifetime or the eddy crossing Literature presents several theories for determining the above values (see Gra The following presents the equations used in Fluent with k- turbulence mode Fluid Lagrangian integral time

Coefficient CL defined by use

Characteristic life time of eddy

or alternatively random variation

r = uniform random numbe Eddy length scale Le  CL (based on Karema(2008))

k 3/2



Notice: in literature, the length scale a In Fluent, this seems to be: Le  1 e 2

Eddy crossing time

Velocity response

Fluctuating velocity

 = Gaussi (standard n

For k- turbulence model:

I nj e ct ion Set up Particle injections can be defined by various methods: • • • • •

Single: a particle stream is injected from a single point. Group: particle streams are injected along a line. Cone: streams are injected in a hollow conical pattern. Solid cone. Surface: particle streams are injected from a surface (one stream from each cell face). • Atomizer: streams are injected by using various predef atomizer models. • File: injection locations and initial conditions are define in an external file.

For each injection, the following data are defined: • Particle type (inert, droplet, combusting, multicompone • Material (from database) • Initial conditions (particle size, velocity, etc.) • Destination species for reacting particles. • Evaporating material for combusting particles.

D PM Conce n t r a t ion

Fluent can report a ”DPM concentration” in a coupled calculation. T concentration of the discrete phase in a continuous cell.

The mass flow of a particle track is determined based on particle m mass flow at the particle injection and particle mass at current loca The particle mass can change due to evaporation and other phase

The discrete phase concentration inside a cell can be determined f residence time and mass flow.

Inside a cell, the particle stream is tracked with n particle time step residence time of one particle track is the sum of these time steps. The total concentration is summed over all particle tracks. The particle-particle interaction is neglected, thus when multiple particle tracks cross the cell, the calculated concentration can exceed the bulk density of solids or even solid density (volume fraction of solids above 1). These results are not physically sensible but they can show areas, where the particle loading is high and the assumption of dilute flow is not valid.

Solut ion St r a t e gie s: Pa r t icle

• The particle tracks are calculated in steps. The ”step length facto approximately the number of steps per fluid cell. The default valu preferably be higher: 10 – 20. • Increasing the step length factor (i.e. decreasing the step length) heat and mass exchange (e.g. when calculating vaporization). • The ”max. number of steps” limits the number of calculated time large enough so that the particles can travel from entrance to exi • If particles remain suspended in the model (tracking incomplete) solution is questionable and transient tracking should be used in calculations in Fluent can be performed in a number of ways and presentation is focused on steady state calculation.

Solut ion St r a t egie s: Tw o- W a

• The solution of the continuous field without coupling is usually th In most cases, the continuous flow does not have to be fully con the coupling is started, because the particle tracks will have a lar continuous flow. • In a coupled calculation, additional source terms appear in discr equations of continuous phase. During particle tracking, each pa a ”fresh” cell and makes no notice of particles already visited and cell with their source terms. This leads to overprediction of the s bad convergence behaviour with evaporation, combustion and ra – Use solution limits to limit the temperature in the domain. • Increasing the number of trajectories (especially with random wa smooth the particle source terms, which should help convergenc • The discrete phase source terms can be under-relaxed (e.g. 0.5 equations may need to be under-relaxed as well (energy and spe • The number of continuous phase calculations between the trajec calculations can either be small (< 3) or high (>15). In the first ch dispersed and continuous flow are closer coupled and the solutio should slowly convergence. In the second choice, the flows are d the solution of continuous field remains ”better converged” and t more stable. In the latter case, the continuous phase may appea converged, but the discrete phase is not. • If the dispersed phase is not dilute, then convergence is very dif in coupled calculations.

M ode ling Ex a m ple

The model geometry is shown below. Hot air flows in a 200 mm diameter duct. Wet limestone particles are injected from the top of the du (inlet d = 50 mm) at location 500 mm before a 90° bend.

Air inlet: 10 m/s, 270°C, D= 0.2 m Particle inlet: 0.1 kg/s, 0.1 m/s, dp =200 µm, p=2700 kg/m3, H2 O=3

Average volume fraction of solids in the duct:

 dilute, two-way coupling (but only as average)

M e sh

Ga s Prope r t ie s

Solid Pr ope r t ie s ( Lim e s

M ode l Pa r a m e t er s

Solut ion of Cont inu ou s • The continuous phase was first solved without the particles. • The convergence was good.

Un couple d M e a n Pa r t icle

• The mean particle tracks were solved without two-way coupling. • The particle tracks are thus calculated only once after the contin • The following images present particle tracks colored by mass, w

Initia Fully

Un couple d Tur bule nt T

• Random walk model with 50 stochastic tracks (total 2400) was u • Uncoupled solution, ie. one-way coupled calculation of disperse • Turbulence effects are fairly small, but can be noticed in the trac

Initia Fully

Solut ion of Couple d Ca lc

• Two-way coupled solution did not converge well. • Different step length factors, under-relaxation parameters and nu iterations were tried. • In the final calculations, the step length factor was 20 and the nu iterations between dispersed phase calculations was 20. The res convergence.

Couple d Pa r t icle Tr a

• The particle tracks show that some of the particle streams circul reaching the outlet. • The solution of flow is much different from uncoupled solution. • The images do not show all particle tracks.

Initia Fully

Effe ct on Cont inu ou s Flo

• In the coupled calculation, the particle tracks affect the continuou • In this case, the effect is considerable.

D PM Conce n t r a t ion

• The DPM concentration shows the total concentration of dispers • Results indicate that in the bend, the dispersed phase is not dilu • Reaching a converged solution in this case would be impossible » The results should be utilized with cautio

Visu a liza t ion of Resu • Different process variables can be easily visualized: pressure, v concentration of species, turbulence variables, ...

Sum m a r y

• The DPM model in Fluent can be used for studying coupled dilute dispersed flows, including effects of • The basic model is easy to use and physics are cle • The limitations of the DPM model should be carefu analyzing the results. • The model neglects particle-particle interaction, th dispersed phase only. • The one-way coupling is valid for very dilute flow o solution can be much different from the one-way c • The average flow can be dilute, but it can contain r dispersed phase is dense. In these regions, the mo Moreover, the convergence is poor, if the disperse momentum, mass and energy exchange to continu • Despite the limitations, the DPM model can be (an modeling various applications.

Refe r e nce s

• Bakker, A. (2006). Lecture notes, Computational Fluid Dynamics, http://www.bakker.org/dartmouth06/engs150/. • Elghobashi, S. (1994). On predicting particle-laden turbulent flows 329. • Fluent 6.3 Documentation (2008). • Fluent Training Material (2008). http://www.fluentusers.com. • Graham D. I. and James P.W. (1996). Turbulent dispersion of par models. Int. J. Multiphase Flow, 22-1, pp 157-175. • Haider, A. and Levenspiel, O. (1989). Drag Coefficient and Termin Nonspherical Particles.Powder Technology, 58, pp. 63–70. • Jalali, P. (2007). Lecture notes, Theory and simulation of disperse Lappeenranta University of Technology. http://www2.et.lut.fi/ttd/Di • Karema, H. (2008). Discussions with Hannu Karema (Process Flo • Loth, E. (2008). Computational Fluid Dynamics of Bubbles, Drops http://www.ae.uiuc.edu/~loth/CUP/Loth.htm • Morsi, S. and Alexander A. (1972), An investigation of particle traj systems, Journal of Fluid Mechanics 55, pp. 193–208. • Sommerfeld, M. (2000). Theoretical and Experimental Modelling o Series 2000-06, von Karman Institute for Fluid Dynamics. http://www-mvt.iw.uni-halle.de/download.php?id=571340,326,2...