Coal Combustion Simulation In Fluent

Tutorial 12. Using the Non-Premixed Combustion Model

Introduction: A pulverized coal combustion simulation involves modeling a continuous gas phase flow field and its interaction with a discrete phase of coal particles. The coal particles, traveling through the gas, will devolatilize and undergo char combustion, creating a source of fuel for reaction in the gas phase. Reaction can be modeled using either the species transport model or the non-premixed combustion model. In this tutorial you will model a simplified coal combustion furnace using the non-premixed combustion model for the reaction chemistry. In this tutorial you will learn how to: • Prepare a PDF table for a pulverized coal fuel using the prePDF preprocessor • Define FLUENT inputs for non-premixed combustion chemistry modeling • Define a discrete second phase of coal particles • Solve a simulation involving reacting discrete phase coal particles The non-premixed combustion model uses a modeling approach that solves transport equations for one or two conserved scalars, the mixture fractions. Multiple chemical species, including radicals and intermediate species, may be included in the problem definition and their concentrations will be derived from the predicted mixture fraction distribution. Property data for the species are accessed through a chemical database and turbulence-chemistry interaction is modeled using a Beta or double-delta probability density function (PDF). See the User’s Guide for more detail on the non-premixed combustion modeling approach.

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Prerequisites: This tutorial assumes that you are familiar with the menu structure in FLUENT, and that you have solved Tutorial 1 or its equivalent. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The coal combustion system considered in this tutorial is a simple 10 m by 1 m two-dimensional duct depicted in Figure 12.1. Only half of the domain width is modeled because of symmetry. The inlet of the 2D duct is split into two streams. A high-speed stream near the center of the duct enters at 50 m/s and spans 0.125 m. The other stream enters at 15 m/s and spans 0.375 m. Both streams are air at 1500 K. Coal particles enter the furnace near the center of the high-speed stream with a mass flow rate of 0.1 kg/s (total flow rate in the furnace is 0.2 kg/s). The duct wall has a constant temperature of 1200 K. The Reynolds number based on the inlet dimension and the average inlet velocity is about 100,000. Thus, the flow is turbulent. Details regarding the coal composition and size distribution are included in Step 5: Models: Continuous (Gas) Phase and Step 8: Materials: Discrete Phase.

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T = 1200 K w

Air: 15 m/s, 1500 K

0.5 m Coal Injection: 0.1 kg/s 0.125 m

Air: 50 m/s, 1500 K Symmetry Plane 10 m

Figure 12.1: 2D Furnace with Pulverized Coal Combustion

Preparation for prePDF 1. Start prePDF. When you use the non-premixed combustion model, you prepare a PDF file with the preprocessor, prePDF. The PDF file contains information that relates species concentrations and temperatures to the mixture fraction values, and is used by FLUENT to obtain these scalars during the solution procedure.

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Step 1: Define the Preliminary Adiabatic System in prePDF 1. Define the prePDF model type. You can define either a single fuel stream, or a fuel stream plus a secondary stream. Enabling a secondary stream allows you to keep track of two mixture fractions. For coal combustion, this would allow you to track volatile matter (the secondary stream) separately from the char (fuel stream). In this tutorial, we will not follow this approach. Instead, we will model coal using a single mixture fraction. Setup −→Case...

(a) Under Heat transfer options, keep the default setting of Adiabatic. The coal combustor studied in this tutorial is a non-adiabatic system, with heat transfer at the combustor wall and heat 12-4

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transfer to the coal particles from the gas. Therefore, a nonadiabatic combustion system must be considered in prePDF. Because non-adiabatic calculations are more time-consuming than those for adiabatic systems, you will start the prePDF setup by considering the results of an adiabatic system. By computing the PDF/equilibrium chemistry results for the adiabatic system, you will determine appropriate system parameters that will make the non-adiabatic calculation more efficient. Specifically, the adiabatic calculation will provide information on the peak (adiabatic) flame temperature, the stoichiometric mixture fraction, and the importance of individual components to the chemical system. This process of beginning with an adiabatic system calculation should be followed in all PDF calculations that ultimately require a non-adiabatic model. (b) Under Chemistry models, keep the default setting of Equilibrium Chemistry. In most PDF-based simulations, the Equilibrium Chemistry option is recommended. The Stoichiometric Reaction (mixed is burned) option requires less computation but is generally less accurate. The Laminar Flamelets option offers the ability to include aerodynamic strain induced non-equilibrium effects, such as super-equilibrium radical concentration and sub-equilibrium temperatures. This can be important for NOx prediction, but is excluded here. (c) Keep the default setting of the PDF models. The Beta PDF integration is always recommended because it is more accurate than the Delta PDF approach. (d) Under Empirically Defined Streams, enable the Fuel stream option. This will allow you to define the fuel stream using the empirical input option. The empirical input option allows you to define the composition in terms of atom fractions of H, C, N, and O, along with the lower heating value and heat capacity

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of the fuel. This is a useful option when the ultimate analysis and heating value of the coal are known. (e) Click Apply and close the panel.

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2. Define the chemical species in the system. The choice of which species to include depends on the fuel type and combustion system. Guidelines on this selection are provided in the FLUENT User’s Guide. Here, you will assume that the equilibrium system consists of 13 species: C, C(s), CH4 , CO, CO2 , H, H2 , H2 O, N, N2 , O, O2 , and OH. C, H, O, and N are included because the fuel stream will be defined in terms of these atom fractions, using the “empirical” input method. !

You should include both C and C(S) in the system when the empirical input option is used.

Setup −→ Species −→Define...

(a) Set the Maximum # of Species to 13. Use the up and down arrows to set the maximum number of species, or enter the number in the text field followed by <ENTER>. (b) Select the top species in the Defined Species list (initially labeled UNDEFINED).

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(c) In the Database Species drop-down list, use the slider bar to scroll the list, and select C. The Defined Species list now shows C as the first entry. (d) Select the next species in the Defined Species list (or increment the Species # counter to 2). (e) In the Database Species drop-down list, use the slider bar to scroll the list, and select the next species (C(S)). (f) Repeat steps (d) and (e) until all 13 species are defined. (g) Click Apply and then close the panel. Note: In other combustion systems, you might want to include additional chemical species, but you should not add slow chemical species like NOx . 3. Determine the fuel composition inputs. The fuel considered here is known, from proximate analysis, to consist of 28% volatiles, 64% char, and 8% ash. You will use this information, along with the ultimate analysis given below, to define the coal composition in prePDF. The fuel stream composition (char and volatiles) is derived as follows. Begin by converting the proximate data to a dry-ash-free basis: Proximate Analysis Volatiles Char (C(s)) Ash

Wt % (dry) 28 64 8

Wt % (DAF) 30.4 69.6 -

The ultimate analysis, for the dry-ash-free coal, is known to be: Element C H O N S 12-8

Wt % (DAF) 89.3 5.0 3.4 1.5 0.8

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For modeling simplicity, the sulfur content of the coal can be combined into the nitrogen mass fraction, to yield: Element C H O N S

Wt % (DAF) 89.3 5.0 3.4 2.3 -

We can combine the proximate and ultimate analysis data to yield the following elemental composition of the volatile stream: Element C H O N Total

Wt % 89.3 5.0 3.4 2.3

Moles 7.44 5 0.21 0.16 12.81

Mole Fraction 0.581 0.390 0.016 0.013

You will enter the mole fractions in the final column, above, in order to define the fuel composition. prePDF will use this information, along with the coal heating value, to define the species present in the fuel. The lower heating value of coal (DAF) is known to be: • LCVcoal,DAF = 35.3 MJ/kg The specific heat and density of the coal are known to be 1000 J/kgK and 1 kg/m3 respectively.

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4. Enter the fuel and oxidizer compositions. Setup −→ Species −→Composition... (a) Enable the input of the oxidizer stream composition. The oxidizer (air) consists of 21% O2 and 79% N2 by volume.

i. Under Stream, select Oxidiser. ii. Under Specify Composition In, retain the default selection of Mole Fractions. iii. Select O2 in the Defined Species list and enter 0.21 in the Species Fraction field. 12-10

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iv. Select N2 in the Defined Species list and enter 0.79 in the Species Fraction field. (b) Enable the input of the fuel stream composition. Note: Because the empirical input option is enabled for the fuel stream, you will be prompted to enter atom mole fractions for C, H, O, and N, along with the heating value and heat capacity of the coal.

i. Under Stream, select Fuel. ii. Under Specify Composition In, retain the default selection of Mole Fractions.

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iii. Select C in the Defined Species list and enter 0.581 in the Atom Fraction field. iv. Select H in the Defined Species list and enter 0.390 in the Atom Fraction field. v. Select N in the Defined Species list and enter 0.016 in the Atom Fraction field. vi. Select O in the Defined Species list and enter 0.013 in the Atom Fraction field. vii. Enter 3.53e7 J/kg for the Lower Caloric Value and 1000 J/kg-K for the Specific Heat. viii. Click Apply and close the panel. 5. Define the density of the solid carbon. Here, a value of 1300 kg/m3 is assumed. Setup −→ Species −→Density...

(a) Select C(S) in the Defined Species list. (b) Set the Density to 1300. (c) Click Apply and close the panel.

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Note: prePDF will use this information during computation of the mixture density for the fuel. You should enter the density of solid char. This input will differ from the coal density defined in FLUENT, which is the apparent density of the ashcontaining coal particles. 6. Define the system operating conditions. The system pressure and inlet stream temperatures are required for the equilibrium chemistry calculation. The fuel stream inlet temperature for coal combustion should be the temperature at the onset of devolatilization. The oxidizer inlet temperature should correspond to the air inlet temperature. In this tutorial, the coal devolatilization temperature will be set to 400 K and the air inlet temperature is 1500 K. The system pressure is one atmosphere. Setup −→Operating Conditions...

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(a) Enter 400 K and 1500 K as the Fuel and Oxidiser inlet temperatures. (b) Click Apply and close the panel.

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Step 2: Compute and Review the Adiabatic System prePDF Look-Up Tables 1. Accept the default PDF solution parameters. Setup −→Solution Parameters...

The look-up table calculation performed by prePDF will result in a table of values for species mole fractions and temperature at a set of discrete mixture fraction values. You control the number and distribution of these discrete points using the Solution Parameters panel. You can also set the Fuel Rich Flamability Limit in this panel. The Fuel Rich Flamability Limit allows you to perform a “partial equilibrium” calculation, suspending equilibrium calculations when the mixture fraction exceeds the specified rich limit. This increases the efficiency of the PDF calculation, allowing you to bypass the complex equilibrium calculations in the fuel-rich region, and is more physically realistic than the assumption of full equilibrium. For empirically defined streams, the rich limit is always 1.0 and cannot be altered.

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(a) Keep the default setting for Automatic Distribution. This feature allows you to improve the prePDF prediction by optimizing the distribution of the discrete mixture fraction values, clustering them around the peak temperature value. If you choose not to use the Automatic Distribution, you should set the distribution center point on the rich side of the stoichiometric scale mixture fraction. (b) Click Apply and close the panel. 2. Save your inputs (coal ad.inp). File −→ Write −→Input... 3. Calculate the adiabatic system chemistry. Calculate −→PDF Table During the calculation, prePDF first retrieves thermodynamic data from the database. Then the time-averaged values of temperature, composition, and density at the discrete mixture-fraction/mixturefraction-variance points (21 points as defined in the Solution Parameters panel) are calculated. The result will be a set of tables containing time-averaged values of species mole fractions, density, and temperature at each discrete value of these two parameters. prePDF reports the progress of the look-up table construction in the console window. When the calculations are complete, prePDF will warn you that equilibrium calculations have been performed for the fuel inlet. You can simply acknowledge this warning, as the equilibrium conditions predicted do not impact your modeling inputs unless the fuel stream is representing a gaseous fuel inlet.

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4. Save the adiabatic PDF file (coal ad.pdf). File −→ Write −→PDF... (a) Under File Type, select Write Formatted File. When you write a PDF file, prePDF will save a binary file by default. If you are planning to use the PDF file on the same machine, you can save the file using the default Write Binary File option. However, if you are planning to use the PDF file on a different machine, you should save an ASCII (formatted) file from prePDF. Note that ASCII files take up more disk space than binary files. (b) Under Solver, select FLUENT 6. (c) Enter coal ad.pdf as the Pdf File name. (d) Click OK to write the file. 5. Examine the temperature/mixture-fraction relationship in the adiabatic system. The results of the adiabatic calculation provide insight into the system description that will be used for the non-adiabatic calculation. Display −→PDF Table...

(a) Select TEMPERATURE from the Plot Variable list and then click Display to generate the table (Figure 12.2).

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The temperature display shows how the time-averaged system temperature varies with the mean mixture fraction and its variance. The temperature/mixture-fraction relationship shows that the peak flame temperature is about 2750 K at fuel stoichiometric mixture fractions of approximately 0.1. The relatively high flame temperature is a result of the high pre-heat in the combustion air. Note: The adiabatic flame temperature predicted by the adiabatic system calculation will be used to select the maximum temperature in the non-adiabatic system calculation.

2.8E+03

2.4E+03 T E M P E R A T U R E

2.0E+03

2.50E-01 2.00E-01

1.6E+03 1.50E-01 SCALED-F-VARIANCE

K

1.00E-01

1.2E+03 5.00E-02

7.6E+02

0.00E+00 0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F-MEAN

PDF TABLE - CHEMICAL EQUILIBRIUM MEAN FLAME TEMPERATURE

prePDF V4.00

Fluent Inc.

Figure 12.2: Time-Averaged Temperature: Adiabatic prePDF Calculation

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Step 3: Create and Compute the Non-Adiabatic prePDF System Creating a non-adiabatic PDF system description requires that you do the following: • Redefine the system as non-adiabatic. • Set the peak system temperature (based on the adiabatic result of 2750 K). After these modifications, you will recompute the system chemistry and save a non-adiabatic PDF file for use in FLUENT.

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1. Define the prePDF model type as non-adiabatic. Setup −→Case...

(a) Select Non-Adiabatic under Heat transfer options and click Apply.

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2. Set the system temperature limits. Minimum and maximum temperatures in the system are required when the PDF calculation is non-adiabatic. The minimum temperature should be a few degrees lower than the lowest boundary condition temperature (e.g., the inlet temperature or wall temperature). In coal combustion systems, the minimum system temperature should also be set below the temperature at which the volatiles begin to evolve from the coal. Here, the vaporization temperature at which devolatilization begins will be set to 400 K. Thus, the minimum system temperature is set to 298 K (the default). The maximum temperature should be at least 100 K higher than the peak flame temperature found in the preliminary adiabatic calculation. Here, the maximum temperature will be taken as 3000 K, well above the peak adiabatic system temperature of 2750 K. Setup −→Operating Conditions...

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(a) Enter 298 for Min. Temperature and 3000 for Max. Temperature. (b) Click Apply and close the panel. 3. Save the non-adiabatic system inputs (coal.inp). File −→ Write −→Input... 4. Compute the non-adiabatic PDF look-up tables. Calculate −→PDF Table The non-adiabatic prePDF calculation requires much more computation than the adiabatic calculation. prePDF begins by accessing the thermodynamic data from the database. Next, the enthalpy 12-22

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field is initialized and the enthalpy grid adjusted to account for inlet conditions and solution parameters. Time-averaged values of temperature, composition, and density at the discrete mixturefraction/mixture-fraction-variance/enthalpy points (21 points, as defined in the Solution Parameters panel) are then calculated. The result will be a set of tables containing time-averaged values of species mole fractions, density, and temperature at each discrete value of these three parameters. When the calculations are complete, prePDF will warn you that equilibrium calculations have been performed for the fuel inlet. As noted above, you can simply acknowledge this warning, which has no impact on your inputs when you are modeling coal or liquid fuels.

5. Write the PDF output file (coal.pdf). File −→ Write −→PDF... (a) Under File Type, select Write Formatted File. (b) Select FLUENT 6 under Solver. (c) Enter coal.pdf as the Pdf File name. (d) Click OK to write the file.

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6. Review one slice of the 3D look-up table prepared by prePDF. Display −→Nonadiabatic Table...

(a) Select TEMPERATURE from the Plot Variable drop-down list and click Display (Figure 12.3). Note: Review of the 3D look-up tables is accomplished on a sliceby-slice basis. By default, the slice selected is that corresponding to the adiabatic enthalpy values. This display should look very similar to the look-up table created during the adiabatic calculation. You can select other slices of constant enthalpy for display, as well.

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2.8E+03

2.4E+03 T E M P E R A T U R E

2.0E+03

2.50E-01 2.00E-01

1.6E+03 1.50E-01 SCALED-F-VARIANCE

K

1.00E-01

1.2E+03 5.00E-02

7.6E+02

0.00E+00 0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F-MEAN

MEAN ENTHALPY SLICE NUMBER 23

prePDF V4.00

MEAN FLAME TEMPERATURE FROM 3D-PDF-TABLE

Fluent Inc.

Figure 12.3: Non-Adiabatic Temperature Look-Up Table on the Slice Corresponding to Adiabatic Enthalpy

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7. Examine the species/mixture-fraction relationship in the non-adiabatic system. Display −→Nonadiabatic Table...

(a) Select SPECIES from the Plot Variable drop-down list. The Species Selection panel will open automatically. (b) In the Species Selection panel, select C(S) in the Species dropdown list and click OK.

(c) Click Display in the Nonadiabatic-Table panel to generate the table (Figure 12.4). 8. Follow the steps above to plot the instantaneous mole fractions for CO (Figure 12.5).

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7.6E-01

6.1E-01 M O L E F R A C T I O N

4.6E-01

2.50E-01 2.00E-01

3.1E-01 1.50E-01 SCALED-F-VARIANCE 1.00E-01

1.5E-01 5.00E-02

0.0E+00

0.00E+00 0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F-MEAN

MEAN ENTHALPY SLICE NUMBER 23 SPECIES C(S)

prePDF V4.00

FROM 3D-PDF-TABLE

Fluent Inc.

Figure 12.4: Time-Averaged C(S) Mole Fractions: prePDF Calculation

Non-Adiabatic

3.1E-01

2.4E-01 M O L E F R A C T I O N

1.8E-01

2.50E-01 2.00E-01

1.2E-01 1.50E-01 SCALED-F-VARIANCE 1.00E-01

6.1E-02 5.00E-02

0.0E+00

0.00E+00 0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

F-MEAN

MEAN ENTHALPY SLICE NUMBER 23 SPECIES CO

FROM 3D-PDF-TABLE

prePDF V4.00

Fluent Inc.

Figure 12.5: Time-Averaged CO Mole Fractions: Non-Adiabatic prePDF Calculation

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9. Exit from prePDF. File −→Exit

Preparation for FLUENT Calculation With the PDF file creation completed, you are ready to use the nonpremixed combustion model in FLUENT to predict the combusting flow in the coal furnace. 1. Copy the file coal/coal.msh from the FLUENT documentation CD to your working directory (as described in Tutorial 1). The mesh file coal.msh is a quadrilateral mesh describing the system geometry shown in Figure 12.1. 2. Start the 2D version of FLUENT.

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Step 4: Grid 1. Read the 2D mesh file, coal.msh. File −→ Read −→Case... The FLUENT console window reports that the mesh contains 1357 quadrilateral cells. 2. Check the grid. Grid −→Check The grid check should not report any errors or negative volumes. 3. Display the grid (Figure 12.6). Display −→Grid... Due to the grid resolution and the size of the domain, you may find it more useful to display just the outline, or to zoom in on various portions of the grid display. Note: You can use the mouse probe button (right button, by default) to find out the boundary zone labels. As annotated in Figure 12.7, the upstream boundary contains two velocity inlets (for the low-speed and high-speed air streams), the downstream boundary is a pressure outlet, the top boundary is a wall, and the bottom boundary is a symmetry plane.

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Grid

Aug 28, 2001 FLUENT 6.0 (2d, segregated, lam)

Figure 12.6: 2D Coal Furnace Mesh Outline Display

wall-7

velocity-inlet-2

velocity-inlet-8

symmetry-5

Grid

Aug 28, 2001 FLUENT 6.0 (2d, segregated, lam)

Figure 12.7: Mesh Display with Annotated Boundary Types

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Step 5: Models: Continuous (Gas) Phase 1. Accept the default segregated solver. The non-premixed combustion model is available only with the segregated solver. Define −→ Models −→Solver...

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2. Turn on the standard k- turbulence model. Define −→ Models −→Viscous...

Note: As indicated in the problem description, the Reynolds number of the flow is about 105 . Thus, the flow is turbulent and the high-Re k- model is suitable.

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3. Turn on the non-premixed combustion model. Define −→ Models −→Species... (a) Select Non-Premixed Combustion under Model. The panel will expand to show the related inputs.

When you click OK, FLUENT will open the Select File dialog box, requesting input of the PDF file to be used in the simulation. (b) In the Select File dialog box, select and read the non-adiabatic PDF file (coal.pdf). FLUENT reports in the console window that it is reading the nonadiabatic PDF file containing 13 species. It also reports that a new material, called pdf-mixture, has been created. This mixture contains the 13 species that you defined in prePDF and their thermodynamic properties. FLUENT will present an Information dialog box telling you that available material properties have changed. You will be setting properties later, so you can simply click OK in the dialog box to acknowledge this information. Note: FLUENT will automatically activate solution of the energy equation when it reads the non-adiabatic PDF file, so you do not need to visit the Energy panel to enable heat transfer.

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4. Turn on radiation by selecting the P1 radiation model. Define −→ Models −→Radiation...

The P-1 model is one of the radiation models that can account for the exchange of radiation between gas and particulates. After you click OK, FLUENT will present an Information dialog box telling you that available material properties have changed. You will be setting properties later, so you can simply click OK in the dialog box to acknowledge this information.

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Step 6: Models: Discrete Phase The flow of pulverized coal particles will be modeled by FLUENT using the discrete phase model. This model predicts the trajectories of individual coal particles, each representing a continuous stream (or mass flow) of coal. Heat, momentum, and mass transfer between the coal and the gas will be included by alternately computing the discrete phase trajectories and the gas phase continuum equations. 1. Enable the discrete phase coupling to the continuous phase flow prediction. Define −→ Models −→Discrete Phase... (a) Under Interaction, turn on the Interaction with Continuous Phase option. This option enables coupling, in which the discrete phase trajectories (along with heat and mass transfer to the particles) are allowed to impact the gas phase equations. If you leave this option turned off, you can track particles but they will have no impact on the continuous phase flow.

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(b) Set the coupling parameter, the Number of Continuous Phase Iterations per DPM Iteration, to 20. You should use higher values of this parameter in problems that include a high particle mass loading or a larger grid size. Less frequent trajectory updates can be beneficial in such problems, in order to converge the gas phase equations more com12-36

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pletely prior to repeating the trajectory calculation. (c) Under Tracking Parameters, set the Max. Number of Steps to 10000. The limit on the number of trajectory time steps is used to abort trajectories of particles that are trapped in the domain (e.g., in a recirculation). (d) Retain the default Length Scale of 0.01 m. The Length Scale controls the time step size used for integration of the discrete phase trajectories. The value of 0.01 m used here implies that roughly 1000 time steps will be used to compute trajectories along the 10 m length of the domain. (e) Under Options, turn on Particle Radiation Interaction.

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2. Create the discrete phase coal injections. The flow of the pulverized coal is defined by the initial conditions that describe the coal as it enters the gas. FLUENT will use these initial conditions as the starting point for its time integration of the particle equations of motion (the trajectory calculations). Here, the total mass flow rate of coal (in the half-width of the duct) is 0.1 kg/s (per unit meter depth). The particles will be assumed to obey a Rosin-Rammler size distribution between 70 and 200 micron diameter. Other initial conditions (velocity, temperature, position) are detailed below along with the appropriate input procedures. Define −→ Injections...

(a) Click the Create button in the Injections panel. This will open the Set Injection Properties panel where you will define the initial conditions defining the flow of coal particles.

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In the Set Injection Properties panel you will define the initial conditions of the flow of coal particles. The particle stream will be defined as a group of 10 distinct initial conditions, all identical except for diameter, which will obey the RosinRammler size distribution law. (b) Select group in the Injection Type drop-down list.

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(c) Set the Number of Particle Streams to 10. These inputs tell FLUENT to represent the range of specified initial conditions by 10 discrete particle streams, each with its own set of discrete initial conditions. Here, this will result in 10 discrete particle diameters, as the diameter will be varied within the injection group. (d) Select Combusting under Particle Type. By selecting Combusting you are activating the submodels for coal devolatilization and char burnout. Similarly, selecting Droplet would enable the submodels for droplet evaporation and boiling. (e) Select coal-mv in the Material drop-down list. The Material list contains the combusting particle materials in the FLUENT database. You can select an appropriate coal from this list and then review or modify its properties in the Materials panel (see Step 8: Materials: Discrete Phase). (f) Select rosin-rammler in the Diameter Distribution drop-down list. The coal particles have a nonuniform size distribution with diameters ranging from 70 µm to 200 µm. The size distribution fits the Rosin-Rammler equation, with a mean diameter of 134 µm and a spread parameter of 4.52. (g) Select o2 (the default) in the Oxidizing Species drop-down list.

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(h) Specify the range of initial conditions under Point Properties starting with the following inputs for First Point: • X-Position: 0.001 m • Y-Position: 0.03124 m • X-Velocity: 10 m/s • Y-Velocity: 5 m/s • Temperature = 300 K • Total Flow Rate: 0.1 kg/s • Min. Diameter: 70e-6 m • Max. Diameter: 200e-6 m • Mean Diameter: 134e-6 m • Spread Parameter: 4.52 (i) Under Last Point, specify identical inputs for position, velocity, and temperature. (j) Define the turbulent dispersion. i. Click on Turbulent Dispersion. The panel will change to show the related inputs.

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ii. Under Stochastic Tracking, turn on Stochastic Model. Stochastic tracks model the effect of turbulence in the gas phase on the particle trajectories. Including stochastic tracking is important in coal combustion simulations, to simulate realistic particle dispersion. iii. Set the Number of Tries to 10.

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Note: The new injection (named injection-0, by default) now appears in the Injections panel.

This panel can be used to copy and delete injection definitions. You can also select an existing injection and list the initial conditions of particle streams defined by that injection in the console window. The listing for the injection-0 group will show 10 particle streams, each with a unique diameter between the specified minimum and maximum value, obtained from the Rosin-Rammler distribution, and a unique mass flow rate.

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Step 7: Materials: Continuous Phase All thermodynamic data including density, specific heat, and formation enthalpies are extracted from the prePDF chemical database when the non-premixed combustion model is used. These properties are transferred to FLUENT as the pdf-mixture material, for which only transport properties, such as viscosity and thermal conductivity, need to be defined. Define −→Materials...

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1. Set Thermal Conductivity to 0.025 (constant). 2. Set Viscosity to 2e-5 (constant). 3. Select wsggm-cell-based in the drop-down list for the Absorption Coefficient. This specifies a composition-dependent absorption coefficient, using the weighted-sum-of-gray-gases model. See the User’s Guide for details. 4. Click the Change/Create button. Note: You can click on the View... button next to Mixture Species to view the species included in the pdf-mixture material. These are the species included during the system chemistry setup in prePDF. Note that the Density and Cp laws cannot be altered: these properties are stored in the non-premixed combustion look-up tables. prePDF uses the gas law to compute the mixture density and a mass-weighted mixing law to compute the mixture cp . Although it is possible for you to alter the properties of the individual species, you should not do so when the non-premixed combustion model is used. This would create an inconsistency with the look-up table created in prePDF.

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Step 8: Materials: Discrete Phase Define −→Materials...

1. Select combusting-particle from the Material Type list. The combusting-particle material type appears because you have activated combusting particles using the Set Injection Properties panel. Other discrete phase material types (droplets, inert particles) will appear in this list if you have created injections of those types. 2. Keep the current selection (coal-mv) in the Combusting Particle Materials list.

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This is the combusting particle material type that you selected from the list of database options in the Set Injection Properties panel. Additional combusting particle materials can be copied from the property database, if desired. You can click the Database... button in order to view the combusting-particle materials that are available. Here, you will simply modify the property settings for the selected material, coal-mv. 3. Set the following constant property values for the coal-mv material: Density Cp Thermal Conductivity Latent Heat Vaporization Temperature Volatile Component Fraction (%) Binary Diffusivity Particle Emissivity Particle Scattering Factor Swelling Coefficient Burnout Stoichiometric Ratio Combustible Fraction (%)

1300 kg/m3 1000 J/kg-K 0.0454 w/m-k 0 400 K 28 5e-4 m2/s 0.9 0.6 2 2.67 64

FLUENT uses these inputs as follows: • Density impacts the particle inertia and body forces (when the gravitational acceleration is non-zero). • Cp determines the heat required to change the particle temperature. • Latent Heat is the heat required to vaporize the volatiles. This can usually be set to zero when the non-premixed combustion model is used for coal combustion. If the volatile composition has been selected in order to preserve the heating value of the fuel, the latent heat has been effectively included. (You would, however, use a non-zero latent heat if water content had been included in the volatile definition as vapor phase H2 O.)

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• Vaporization Temperature is the temperature at which the coal devolatilization begins. It should be set equal to the fuel inlet temperature used in prePDF. • Volatile Component Fraction determines the mass of each coal particle that is devolatilized. • Binary Diffusivity is the diffusivity of oxidant to the particle surface and is used in the diffusion-limited char burnout rate. • Particle Emissivity is the emissivity of the particles. It is used to compute radiation heat transfer to the particles. • Particle Scattering Factor is the scattering factor due to particles. • Swelling Coefficient determines the change in diameter during coal devolatilization. A swelling coefficient of 2 implies that the particle size will double as the volatile fraction is released. • Burnout Stoichiometric Ratio is used in the calculation of the diffusion-controlled burnout rate. Otherwise, this parameter has no impact when the non-premixed combustion model is used. When finite-rate chemistry is used instead, the stoichiometric ratio defines the mass of oxidant required per mass of char. The default value represents oxidation of C(s) to CO2 . • Combustible Fraction is the mass fraction of char in the coal particle. It determines the mass of each coal particle that is consumed by the char burnout submodel. !

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The settings for the Vaporization Temperature, Combustible Fraction, and Volatile Component Fraction inputs should all be consistent with your prePDF inputs. (See Step 1: Define the Preliminary Adiabatic System in prePDF.)

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4. Select the Single Rate Devolatilization Model for Devolatilization Model. (a) Select the single-rate option in the Devolatilization Model dropdown list. This opens the Single Rate Devolatilization Model panel.

(b) Accept the default devolatilization model parameters. 5. Select kinetics/diffusion-limited for the Combustion Model. (a) Select the kinetic/diffusion-limited option in the Combustion Model drop-down list. This opens the Kinetics/Diffusion Limited Combustion Model panel.

(b) Accept the default values. 6. Click Change/Create and then close the Materials panel.

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Step 9: Boundary Conditions Define −→Boundary Conditions... Hint: You can click your mouse probe button (the right button, by default) on the desired boundary zone in the graphics display window. FLUENT will then select that zone in the Boundary Conditions panel. 1. Set the following conditions for the velocity-inlet-2 zone (the lowspeed inlet boundary). Note: Turbulence parameters are defined here based on intensity and hydraulic diameter. The relatively large turbulence intensity of 10% may be typical for combustion air flows. The hydraulic diameter has been set to twice the height of the 2D inlet stream. For the non-premixed combustion calculation, you need to define the inlet Mean Mixture Fraction and Mixture Fraction Variance. For coal combustion, all fuel comes from the discrete phase and thus the gas phase inlets have zero mixture fraction. Therefore, you can accept the zero default settings.

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2. Set the following conditions for the velocity-inlet-8 zone (the highspeed inlet boundary).

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3. Set the following conditions for the pressure-outlet-6 zone (the exit boundary).

The exit gauge pressure of zero simply defines the system pressure at the exit to be the operating pressure. The backflow conditions for scalars (temperature, mixture fraction, turbulence parameters) will be used only if flow is entrained into the domain through the exit. It is a good idea to use reasonable values in case flow reversal occurs at the exit at some point during the solution process.

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4. Set conditions for the wall-7 zone (the furnace wall). The furnace wall will be treated as an isothermal boundary with a temperature of 1200 K.

(a) Under Thermal Conditions, select Temperature. (b) Enter 1200 in the Temperature field. Note: The default boundary condition for particles that hit the wall is reflect, as shown under DPM. Alternate treatments can be selected, using the BC Type list, for particles that hit the wall.

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Step 10: Solution 1. Set the P1 under-relaxation factor to 1. Solve −→ Controls −→Solution... 2. Initialize the flow field using conditions at velocity-inlet-2. Solve −→ Initialize −→Initialize...

(a) Select velocity-inlet-2 in the Compute From list. (b) Click the Init button to initialize the flow field, and then close the panel. !

The Apply button does not initialize the flow field data. You must use the Init button. (Apply simply allows you to store your initialization parameters for later use.)

Note: Here, with very high pre-heat of the oxidizer stream, you can start the combustion calculation from the inlet-based initialization. In general, you may need to start your coal combustion calculations by patching a high-temperature region and

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performing a discrete phase trajectory calculation. This provides the initial volatile and char release required to initiate combustion. The Solve/Initialize/Patch... menu item and the solve/dpm-update text command can be used to perform this initialization. 3. Enable the display of residuals during the solution process. Solve −→ Monitors −→Residual... 4. Save the case file (coal.cas). File −→ Write −→Case... 5. Begin the calculation by requesting 400 iterations. Solve −→Iterate...

Note: The default convergence criteria will be met in about 170 iterations. 6. Save the converged flow data (coal.dat). File −→ Write −→Data...

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Step 11: Postprocessing 1. Display the predicted temperature field (Figure 12.8). Display −→Contours...

The peak temperature in the system is about 2260 K. Hint: Use the Views panel (Display/Views...) to mirror the display about the symmetry plane.

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2.26e+03 2.16e+03 2.05e+03 1.94e+03 1.84e+03 1.73e+03 1.63e+03 1.52e+03 1.41e+03 1.31e+03 1.20e+03

Contours of Static Temperature (k)

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.8: Temperature Contours

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2. Display the Mean Mixture Fraction distribution (Figure 12.9). Display −→Contours...

The mixture-fraction distribution shows where the char and volatiles released from the coal exist in the gas phase.

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3.72e-02 3.35e-02 2.98e-02 2.61e-02 2.23e-02 1.86e-02 1.49e-02 1.12e-02 7.45e-03 3.72e-03 0.00e+00

Contours of Mean Mixture Fraction

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.9: Mixture-Fraction Distribution

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3. Display the devolatilization rate (Figure 12.10). Display −→Contours...

(a) Select Discrete Phase Model... and DPM Evaporation/Devolatilization in the drop-down lists under Contours Of. 4. Display the char burnout rate (Figure 12.11) by selecting DPM Burnout from the lower drop-down list. Note: The display of devolatilization rate shows that volatiles are released after the coal travels about one eighth of the furnace length. (The onset of devolatilization occurs when the coal temperature reaches the specified value of 400 K.) The char burnout occurs following complete devolatilization. Figure 12.11 shows that burnout is complete at about three-quarters of the furnace.

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2.95e-03 2.66e-03 2.36e-03 2.07e-03 1.77e-03 1.48e-03 1.18e-03 8.86e-04 5.90e-04 2.95e-04 0.00e+00

Contours of DPM Evaporation/Devolatilization (kg/s)

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.10: Devolatilization Rate

4.42e-04 3.97e-04 3.53e-04 3.09e-04 2.65e-04 2.21e-04 1.77e-04 1.32e-04 8.83e-05 4.42e-05 0.00e+00

Contours of DPM Burnout (kg/s)

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.11: Char Burnout Rate

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5. Display the particle trajectory of one particle stream (Figure 12.12). Display −→Particle Tracks...

(a) Select injection-0 in the Release From Injections list. (b) Select Particle Residence Time in the Color By drop-down list. (c) Turn on Track Single Particle Stream and set the Stream ID to 5. (d) Click Display.

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3.63e-01 3.27e-01 2.90e-01 2.54e-01 2.18e-01 1.81e-01 1.45e-01 1.09e-01 7.26e-02 3.63e-02 0.00e+00

Particle Traces Colored by Particle Residence Time (s)

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.12: Trajectories of Particle Stream 5 Colored by Particle Residence Time

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6. Display the oxygen distribution (Figure 12.13). Display −→Contours...

Note: Although transport equations are solved only for the mixture fraction and its variance, you can still display the predicted chemical species concentrations. These are predicted by the PDF equilibrium chemistry model. 7. Select other species and display their mass fraction distributions (e.g., Figures 12.14–12.16).

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2.33e-01 2.22e-01 2.11e-01 2.00e-01 1.89e-01 1.78e-01 1.67e-01 1.56e-01 1.45e-01 1.34e-01 1.23e-01

Contours of Mass fraction of o2

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.13: O2 Distribution 1.19e-01 1.07e-01 9.54e-02 8.35e-02 7.15e-02 5.96e-02 4.77e-02 3.58e-02 2.38e-02 1.19e-02 0.00e+00

Contours of Mass fraction of co2

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.14: CO2 Distribution

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1.60e-02 1.44e-02 1.28e-02 1.12e-02 9.62e-03 8.02e-03 6.42e-03 4.81e-03 3.21e-03 1.60e-03 0.00e+00

Contours of Mass fraction of h2o

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.15: H2 O Distribution 6.99e-03 6.29e-03 5.59e-03 4.89e-03 4.19e-03 3.49e-03 2.79e-03 2.10e-03 1.40e-03 6.99e-04 0.00e+00

Contours of Mass fraction of co

Sep 10, 2001 FLUENT 6.0 (2d, segregated, pdf13, ske)

Figure 12.16: CO Distribution

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Step 12: Energy Balances and Particle Reporting FLUENT can provide many useful reports, including overall energy accounting and detailed information regarding heat and mass transfer from the discrete phase. Here, you will examine these reports. 1. Compute the fluxes of heat through the domain boundaries. Report −→Fluxes...

(a) Select Total Heat Transfer Rate under Options. (b) Under Boundaries, select the pressure-outlet-6, velocity-inlet-2, velocity-inlet-8, and wall-7 zones. (c) Click Compute. Note: Positive flux reports indicate heat addition to the domain. Negative values indicate heat leaving the domain. In reacting flows, the heat report uses total enthalpy (sensible heat plus

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heat of formation of the chemical species). Here, the net “imbalance” of total enthalpy (about 14 KW) represents the total enthalpy addition from the discrete phase. 2. Compute the volume sources of heat transferred between the gas and discrete particle phase. Report −→Volume Integrals...

(a) Select Sum under Options. (b) Select Discrete Phase Model... and DPM Enthalpy Source in the drop-down lists under Field Variable. (c) Select fluid-1 under Cell Zones. (d) Click Compute. The total enthalpy transfer to the discrete phase from the gas is about -13.2 KW, as expected based on the boundary flux report above. This represents the total enthalpy addition from the discrete phase to the gas during the devolatilization and char combustion processes.

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3. Obtain a summary report on the particle trajectories. The discrete phase model summary report provides detailed information about the particle residence time, heat and mass transfer between the continuous and discrete phases, and (for combusting particles) char conversion and volatile yield. Display −→Particle Tracks... (a) Select Summary under Report Type. (b) Select injection-0. (c) Click Track. FLUENT will report the summary in the console window. (You can write the report to a file by selecting File under Report to. (d) Review the summary printed in the console window:

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DPM Iteration .... number tracked = 100, escaped = 0, aborted = 0, trapped = 0, evaporated = 0, incomp Fate

Number

---Incomplete

-----100

Elapsed Time (s) Inj Min Max Avg Std Dev ---------- ---------- ---------- ---------- ------2.398e-01 4.653e-01 3.096e-01 4.818e-02 inj

(*)- Mass Transfer Summary -(*) Fate ---Incomplete

Mass Flow (kg/s) Initial Final Change ---------- ---------- ---------1.000e-01 8.005e-03 -9.200e-02 (*)- Energy Transfer Summary -(*)

Fate ---Incomplete

Heat Content (W) Initial Final Change ---------- ---------- ----------3.712e+03 9.532e+03 1.324e+04 (*)- Combusting Particles -(*)

Fate ---Incomplete

Volatile Content (kg/s) Initial Final %Conv ---------- ---------- ------2.800e-02 0.000e+00 100.00

Char Content (kg/s) Initial Final %Con ---------- ---------- -----6.400e-02 5.351e-06 99.9

Done.

The report shows that the average residence time of the coal particles is about 0.33 seconds. Volatiles are completely released within the domain and the char conversion is 100% . Extra: You can obtain a detailed report of the particle position, velocity, diameter, and temperature along the trajectories of individual particles. This type of detailed track reporting can be useful if you are trying to understand unusual or important details in the discrete model behavior. To generate the report, visit the Particle Tracks panel. Select Step By Step under Report Type, and File under Report to. Enable the Track Single Particle Stream option, and set the Stream ID to the desired particle stream. Clicking Track will bring

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up the Select File dialog box, where you will enter the name of the file to be written. This file can then be viewed with a text editor.

Summary: Coal combustion modeling involves the prediction of volatile evolution and char burnout from the pulverized coal along with simulation of the combustion chemistry occuring in the gas phase. In this tutorial you learned how to use the non-premixed combustion model to represent the gas phase combustion chemistry. In this approach the fuel composition was defined in prePDF and the fuel was assumed to react according to the equilibrium system data. This equilibrium chemistry model can be applied to other turbulent, diffusion-reaction systems. Note that you can also model coal combustion using the finite-rate chemistry model. You also learned how to set up and solve a problem involving a discrete phase of combusting particles. You created discrete phase injections, activated coupling to the gas phase, and defined the discrete phase material properties. These procedures can be used to set up other simulations involving reacting or inert particles.

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