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22.14.2 Setting Discrete-Phase Physical Properties



The Concept of Discrete-Phase Materials


When you create a particle injection and define the initial conditions for the discrete phase (as described in Section  22.12), you choose a particular material as the particle's material. All particle streams of that material will have the same physical properties.

Discrete-phase materials are divided into four categories, corresponding to the four types of particles available. These material types are inert-particle, droplet-particle, combusting-particle, and multicomponent-particle. Each material type will be added to the Material Type list in the Materials panel when an injection of that type of particle is defined (in the Set Injection Properties or Set Multiple Injection Properties panel, as described in Section  22.12). The first time you create an injection of each particle type, you will be able to choose a material from the database, and this will become the default material for that type of particle. That is, if you create another injection of the same type of particle, your selected material will be used for that injection as well. You may choose to modify the predefined properties for your selected particle material, if you want (as described in Section  8.1.2). If you need only one set of properties for each type of particle, you need not define any new materials; you can simply use the same material for all particles.

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If you do not find the material you want in the database, you can select a material that is close to the one you wish to use, and then modify the properties and give the material a new name, as described in Section  8.1.2.

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Note that a discrete-phase material type will not appear in the Material Type list in the Materials panel until you have defined an injection of that type of particles. This means, for example, that you cannot define or modify any combusting-particle materials until you have defined a combusting particle injection (as described in Section  22.12).

For a particle-mixture material type, you will need to select the species in your mixture. To do this, click the Edit... button next to Mixture Species in the Materials panel. The Species panel will open, where you will include your Selected Species. The selected species will now be available in the Set Injection Properties panel, under the Components tab.

Defining Additional Discrete-Phase Materials

In many cases, a single set of physical properties (density, heat capacity, etc.) is appropriate for each type of discrete phase particle considered in a given model. Sometimes, however, a single model may contain two different types of inert, droplet, combusting particles, or multicomponent particles (e.g., heavy particles and gaseous bubbles or two different types of evaporating liquid droplets). In such cases, it is necessary to assign a different set of properties to the two (or more) different types of particles. This is easily accomplished by defining two or more inert, droplet, or combusting particle materials and using the appropriate one for each particle injection.

You can define additional discrete-phase materials either by copying them from the database or by creating them from scratch. See Section  8.1.2 for instructions on using the Materials panel to perform these actions.

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Recall that you must define at least one injection (as described in Section  22.12) containing particles of a certain type before you will be able to define additional materials for that particle type.



Description of the Properties


The properties that appear in the Materials panel vary depending on the particle type (selected in the Set Injection Properties or Set Multiple Injection Properties panel, as described in Sections  22.12.4 and 22.12.7) and the physical models you are using in conjunction with the discrete-phase model.

Below, all properties you may need to define for a discrete-phase material are listed. See Tables  22.14.1- 22.14.4 to see which properties are defined for each type of particle.

Density   is the density of the particulate phase in units of mass per unit volume of the discrete phase. This density is the mass density and not the volumetric density. Since certain particles may swell during the trajectory calculations, your input is actually an "initial'' density.

Cp   is the specific heat, $c_p$, of the particle. The specific heat may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of Cp. See Section  8.2 for details about temperature-dependent properties. For multicomponent particles, it can be calculated as a mass-weighted value of the specific heat of the droplet component.

Thermal Conductivity   is the thermal conductivity of the particle. This input is specified in units of W/m-K in SI units or Btu/ft-h- $^\circ$F in British units and is treated as a constant by FLUENT.

Latent Heat   is the latent heat of vaporization, $h_{\rm fg}$, required for phase change from an evaporating liquid droplet (Equation  22.9-25) or for the evolution of volatiles from a combusting particle (Equation  22.9-66). This input is supplied in units of J/kg in SI units or of Btu/lb $_m$ in British units and is treated as a constant by FLUENT. For the droplet particle, the latent heat value at the boiling point temperature should be used.

Thermophoretic Coefficient   is the coefficient $D_{T,p}$ in Equation  22.2-14, and appears when the thermophoretic force (which is described in Section  22.2.1) is included in the trajectory calculation (i.e., when the Thermophoretic Force option is enabled in the Discrete Phase Model panel). The default is the expression developed by Talbot [ 367] ( talbot-diffusion-coeff) and requires no input from you. You can also define the thermophoretic coefficient as a function of temperature by selecting one of the function types from the drop-down list to the right of Thermophoretic Coefficient. See Section  8.2 for details about temperature-dependent properties.

Vaporization Temperature    is the temperature, $T_{\rm vap}$, at which the calculation of vaporization from a liquid droplet or devolatilization from a combusting particle is initiated by FLUENT. Until the particle temperature reaches $T_{\rm vap}$, the particle is heated via Law 1, Equation  22.9-11. This temperature input represents a modeling decision rather than any physical characteristic of the discrete phase.

Boiling Point   is the temperature, $T_{\rm bp}$, at which the calculation of the boiling rate equation ( 22.9-28) is initiated by FLUENT. When a droplet particle reaches the boiling point, FLUENT applies Law 3 and assumes that the droplet temperature is constant at $T_{\rm bp}$. The boiling point denotes the temperature at which the particle law transitions from the vaporization law to the boiling law.

Volatile Component Fraction   ( $f_{v0}$) is the fraction of a droplet particle that may vaporize via Laws 2 and/or 3 (Section  22.9.2). For combusting particles, it is the fraction of volatiles that may be evolved via Law 4 (Section  22.9.2).

Binary Diffusivity    is the mass diffusion coefficient, $D_{i,m}$, used in the vaporization law, Law 2 (Equation  22.9-23). This input is also used to define the mass diffusion of the oxidizing species to the surface of a combusting particle, $D_{i,m}$, as given in Equation  22.9-73. (Note that the diffusion coefficient inputs that you supply for the continuous phase are not used for the discrete phase.)

Saturation Vapor Pressure   is the saturated vapor pressure, $p_{\rm sat}$, defined as a function of temperature, which is used in the vaporization law, Law 2 (Equation  22.9-21). The saturated vapor pressure may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of its name. (See Section  8.2 for details about temperature-dependent properties.) In the case of unrealistic inputs, FLUENT restricts the range of $P_{\rm sat}$ to between 0.0 and the operating pressure. Correct input of a realistic vapor pressure curve is essential for accurate results from the vaporization model.

Heat of Pyrolysis   is the heat of the instantaneous pyrolysis reaction , $h_{\rm pyrol}$, that the evaporating/boiling species may undergo when released to the continuous phase. This input represents the conversion of the evaporating species to lighter components during the evaporation process. The heat of pyrolysis should be input as a positive number for exothermic reaction and as a negative number for endothermic reaction. The default value of zero implies that the heat of pyrolysis is not considered. This input is used in Equation  22.9-2.

Swelling Coefficient    is the coefficient $C_{\rm sw}$ in Equation  22.9-65, which governs the swelling of the coal particle during the devolatilization law, Law 4 (Section  22.9.2). A swelling coefficient of unity (the default) implies that the coal particle stays at constant diameter during the devolatilization process.

Burnout Stoichiometric Ratio    is the stoichiometric requirement, $S_b$, for the burnout reaction, Equation  22.9-72, in terms of mass of oxidant per mass of char in the particle.

Combustible Fraction    is the mass fraction of char, $f_{\rm comb}$, in the coal particle, i.e., the fraction of the initial combusting particle that will react in the surface reaction, Law 5 (Equation  22.9-71).

Heat of Reaction for Burnout   is the heat released by the surface char combustion reaction, Law 5 (Equation  22.9-72). This parameter is input in terms of heat release (e.g., Joules) per unit mass of char consumed in the surface reaction.

React. Heat Fraction Absorbed by Solid   is the parameter $f_h$ (Equation  22.9-86), which controls the distribution of the heat of reaction between the particle and the continuous phase. The default value of zero implies that the entire heat of reaction is released to the continuous phase.

Devolatilization Model    defines which version of the devolatilization model, Law 4, is being used. If you want to use the default constant rate devolatilization model, Equation  22.9-34, retain the selection of constant in the drop-down list to the right of Devolatilization Model and input the rate constant $A_0$ in the field below the list.

You can activate one of the optional devolatilization models (the single kinetic rate, two kinetic rates, or CPD model, as described in Section  22.9.2) by choosing single rate, two-competing-rates, or cpd-model in the drop-down list.

When the single kinetic rate model ( single-rate) is selected, the Single Rate Devolatilization Model panel will appear and you will enter the Pre-exponential Factor, $A_1$, and the Activation Energy, $E$, to be used in Equation  22.9-36 for the computation of the kinetic rate.

When the two competing rates model ( two-competing-rates) is selected, the Two Competing Rates Model panel will appear and you will enter, for the First Rate and the Second Rate, the Pre-exponential Factor ( $A_1$ in Equation  22.9-38 and $A_2$ in Equation  22.9-39), Activation Energy ( $E_1$ in Equation  22.9-38 and $E_2$ in Equation  22.9-39), and Weighting Factor ( $\alpha_1$ and $\alpha_2$ in Equation  22.9-40). The constants you input are used in Equations  22.9-38 through  22.9-40.

When the CPD model ( cpd-model) is selected, the CPD Model panel will appear and you will enter the Initial Fraction of Bridges in Coal Lattice ( $p_0$ in Equation  22.9-51), Initial Fraction of Char Bridges ( $c_0$ in Equation  22.9-50), Lattice Coordination Number ( $\sigma +1$ in Equation  22.9-62), Cluster Molecular Weight ( $M_{w,1}$ in Equation  22.9-62), and Side Chain Molecular Weight ( $M_{w, \delta}$ in Equation  22.9-61).

Note that the Single Rate Devolatilization Model, Two Competing Rates Model, and CPD Model panels are modal panels, which means that you must tend to them immediately before continuing the property definitions.

Combustion Model   defines which version of the surface char combustion law (Law 5) is being used. If you want to use the default diffusion-limited rate model, retain the selection of diffusion-limited in the drop-down list to the right of Combustion Model. No additional inputs are necessary, because the binary diffusivity defined above will be used in Equation  22.9-73.

To use the kinetics/diffusion-limited rate model for the surface combustion model, select kinetics/diffusion-limited in the drop-down list. The Kinetics/Diffusion-Limited Combustion Model panel will appear and you will enter the Mass Diffusion Limited Rate Constant ( $C_1$ in Equation  22.9-74), Kinetics Limited Rate Pre-exponential Factor ( $C_2$ in Equation  22.9-75), and Kinetics Limited Rate Activation Energy ( $E$ in Equation  22.9-75).

Note that the Kinetics/Diffusion-Limited Combustion Model panel is a modal panel, which means that you must tend to it immediately before continuing the property definitions.

To use the intrinsic model for the surface combustion model, select intrinsic-model in the drop-down list. The Intrinsic Combustion Model panel will appear and you will enter the Mass Diffusion Limited Rate Constant ( $C_1$ in Equation  22.9-74), Kinetics Limited Rate Pre-exponential Factor ( $A_i$ in Equation  22.9-84), Kinetics Limited Rate Activation Energy ( $E_i$ in Equation  22.9-84), Char Porosity ( $\theta$ in Equation  22.9-81), Mean Pore Radius ( $\overline{r}_p$ in Equation  22.9-83), Specific Internal Surface Area ( $A_g$ in Equations  22.9-78 and 22.9-80), Tortuosity ( $\tau$ in Equation  22.9-81), and Burning Mode, alpha ( $\alpha$ in Equation  22.9-85).

Note that the Intrinsic Combustion Model panel is a model panel, which means that you must tend to it immediately before continuing the property definitions.

To use the multiple surface reactions model, select multiple-surface-reactions in the drop-down list. FLUENT will display a dialog box informing you that you will need to open the Reactions panel, where you can review or modify the particle surface reactions that you specified as described in Section  14.1.2.

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If you have not yet defined any particle surface reactions, you must be sure to define them now. See Section  14.3.3 for more information about using the multiple surface reactions model.

You will notice that the Burnout Stoichiometric Ratio and Heat of Reaction for Burnout are no longer available in the Materials panel, as these parameters are now computed from the particle surface reactions you defined in the Reactions panel.

Note that the multiple surface reactions model is available only if the Particle Surface option for Reactions is enabled in the Species Model panel. See Section  14.3.2 for details.

When the effect of particles on radiation is enabled (for the P-1 or discrete ordinates radiation model only) in the Discrete Phase Model panel, you will need to define the following additional parameters:

Particle Emissivity   is the emissivity of particles in your model, $\epsilon_p$, used to compute radiation heat transfer to the particles (Equations  22.9-11, 22.9-25, 22.9-31, 22.9-66, and 22.9-86) when the P-1 or discrete ordinates radiation model is active. Note that you must enable radiation to particles, using the Particle Radiation Interaction option in the Discrete Phase Model panel. Recommended values of particle emissivity are 1.0 for coal particles and 0.5 for ash [ 220].

Particle Scattering Factor   is the scattering factor, $f_p$, due to particles in the P-1 or discrete ordinates radiation model (Equation  13.3-13). Note that you must enable particle effects in the radiation model, using the Particle Radiation Interaction option in the Discrete Phase Model panel. The recommended value of $f_p$ for coal combustion modeling is 0.9 [ 220]. Note that if the effect of particles on radiation is enabled, scattering in the continuous phase will be ignored in the radiation model.

When an atomizer injection model and/or the droplet breakup or collision model is enabled in the Set Injection Properties panel (atomizers) and/or Discrete Phase Model panel (droplet breakup/collision), you will need to define the following additional parameters:

Viscosity   is the droplet viscosity, $\mu_l$. The viscosity may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of Viscosity. See Section  8.2 for details about temperature-dependent properties. You also have the option of implementing a user-defined function to model the droplet viscosity. See the separate UDF Manual for information about user-defined functions.

Droplet Surface Tension   is the droplet surface tension, $\sigma$. The surface tension may be defined as a function of temperature by selecting one of the function types from the drop-down list to the right of Droplet Surface Tension. See Section  8.2 for details about temperature-dependent properties. You also have the option of implementing a user-defined function to model the droplet surface tension. See the separate UDF Manual for information about user-defined functions.

Vapor-Particle-Equilibrium   is the selected approach for the calculation of the vapor concentration of the components at the surface. This can be Raoult's law (Equation  22.3-4), or a user-defined function that provides this value.


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