23.5.2 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  23.3), you choose a particular material as the particle's material. All particle streams of that material will have the same physical properties.

Note that you will not choose a Material for a Massless particle type in the Set Injections Properties dialog box.

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 Create/Edit Materials dialog box when an injection of that type of particle is defined (in the Set Injection Properties or Set Multiple Injection Properties dialog box, as described in Section  23.3). 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.

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.

Note that a discrete-phase material type will not appear in the Material Type list in the Create/Edit Materials dialog boxes 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  23.3).

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 Create/Edit Materials dialog box. The Species dialog box will open, where you will include your Selected Species. The selected species will now be available in the Set Injection Properties dialog box, under the Components tab (Figure  23.5.1).

Figure 23.5.1: 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 Create/Edit Materials dialog box to perform these actions.

Recall that you must define at least one injection (as described in Section  23.3) 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 Create/Edit Materials dialog box vary depending on the particle type (selected in the Set Injection Properties or Set Multiple Injection Properties dialog box, as described in Sections  23.3.15 and 23.3.18) 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  23.5.1- 23.5.4 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 ANSYS FLUENT.

Latent Heat   is the latent heat of vaporization, $h_{\rm fg}$, required for phase change from an evaporating liquid droplet ( this equation in the separate Theory Guide) or for the evolution of volatiles from a combusting particle ( this equation in the separate Theory Guide). 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 ANSYS 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 this equation in the separate Theory Guide , and appears when the thermophoretic force (which is described in this section in the separate Theory Guide) is included in the trajectory calculation (i.e., when the Thermophoretic Force option is enabled in the Discrete Phase Model dialog box). The default is the expression developed by Talbot [ 82] ( 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 ANSYS FLUENT. Until the particle temperature reaches $T_{\rm vap}$, the particle is heated via Law 1, this equation in the separate Theory Guide. 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 ( this equation in the separate Theory Guide) is initiated by ANSYS FLUENT. When a droplet particle reaches the boiling point, ANSYS 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.

For multicomponent particles the boiling point of the components is used only as a reference temperature of the latent heat. Instead, the boiling starts when the sum of the partial component saturation pressures reach the total fluid pressure. The definition of the saturation pressure curve is therefore essential for the boiling of multicomponent particles.

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 ( this equation in the separate Theory Guide), the Peng-Robinson real gas model ( this equation in the separate Theory Guide), or a user-defined function that provides this value.

Critical Temperature   is the temperature $T_{c,i}$ ( this equation in the separate Theory Guide) of the pure component for multicomponent particles when using the Peng-Robinson real gas model for calculating the vapor-particle-equilibrium.

Critical Pressure   is the pressure $p_{c,i}$ ( this equation in the separate Theory Guide) of the pure component for multicomponent particles when using the Peng-Robinson real gas model for calculating the vapor-particle-equilibrium.

Accentric Factor   is the constant $\omega_i$ ( this equation in the separate Theory Guide) of the pure component for multicomponent particles when using the Peng-Robinson real gas model for calculating the vapor-particle-equilibrium.

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

Binary Diffusivity    is the mass diffusion coefficient, $D_{i,m}$, used in the vaporization law, Law 2 ( this equation in the separate Theory Guide). 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 this equation in the separate Theory Guide. (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 ( this equation in the separate Theory Guide). 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, ANSYS 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 this equation in the separate Theory Guide.

Swelling Coefficient    is the coefficient $C_{\rm sw}$ in this equation in the separate Theory Guide , which governs the swelling of the coal particle during the devolatilization law, Law 4 ( this section in the separate Theory Guide). 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, this equation in the separate Theory Guide , 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 ( this equation in the separate Theory Guide).

Heat of Reaction for Burnout   is the heat released by the surface char combustion reaction, Law 5 ( this equation in the separate Theory Guide). 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 $f_h$ ( this equation in the separate Theory Guide), 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, this equation in the separate Theory Guide , 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 this section in the separate Theory Guide) 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 dialog box will appear and you will enter the Pre-exponential Factor, $A_1$, and the Activation Energy, $E$, to be used in this equation in the separate Theory Guide for the computation of the kinetic rate.

When the two competing rates model ( two-competing-rates) is selected, the Two Competing Rates Model dialog box will appear and you will enter, for the First Rate and the Second Rate, the Pre-exponential Factor ( $A_1$ in this equation and $A_2$ in this equation in the separate Theory Guide), Activation Energy ( $E_1$ in this equation and $E_2$ in this equation ), and Weighting Factor ( $\alpha_1$ and $\alpha_2$ in this equation ). The constants you input are used in this equation through  this equation .

When the CPD model ( cpd-model) is selected, the CPD Model dialog box will appear and you will enter the Initial Fraction of Bridges in Coal Lattice ( $p_0$ in this equation in the separate Theory Guide), Initial Fraction of Char Bridges ( $c_0$ in this equation ), Lattice Coordination Number ( $\sigma +1$ in this equation ), Cluster Molecular Weight ( $M_{w,1}$ in this equation ), and Side Chain Molecular Weight ( $M_{w, \delta}$ in this equation ).

Note that the Single Rate Devolatilization Model, Two Competing Rates Model, and CPD Model dialog boxes are modal dialog boxes, 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 this equation in the separate Theory Guide.

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 dialog box will appear and you will enter the Mass Diffusion Limited Rate Constant ( $C_1$ in this equation in the separate Theory Guide), Kinetics Limited Rate Pre-exponential Factor ( $C_2$ in this equation ), and Kinetics Limited Rate Activation Energy ( $E$ in this equation ).

Note that the Kinetics/Diffusion-Limited Combustion Model dialog box is a modal dialog box, 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 dialog box will appear and you will enter the Mass Diffusion Limited Rate Constant ( $C_1$ in this equation in the separate Theory Guide), Kinetics Limited Rate Pre-exponential Factor ( $A_i$ in this equation ), Kinetics Limited Rate Activation Energy ( $E_i$ in this equation ), Char Porosity ( $\theta$ in this equation ), Mean Pore Radius ( $\overline{r}_p$ in this equation ), Specific Internal Surface Area ( $A_g$ in this equation and this equation ), Tortuosity ( $\tau$ in this equation ), and Burning Mode, alpha ( $\alpha$ in this equation ).

Note that the Intrinsic Combustion Model dialog box is a model dialog box, 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. ANSYS FLUENT will display a dialog box informing you that you will need to open the Reactions dialog box, where you can review or modify the particle surface reactions that you specified as described in Section  15.1.1.

If you have not yet defined any particle surface reactions, you must be sure to define them now. See Section  15.3.3 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 Create/Edit Materials dialog box, as these parameters are now computed from the particle surface reactions you defined in the Reactions dialog box.

Note that the multiple surface reactions model is available only if the Particle Surface option for Reactions is enabled in the Species Model dialog box. See Section  15.3.1 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 dialog box, 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 ( this equation , this equation , this equation , this equation , and this equation in the separate Theory Guide) 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 dialog box. Recommended values of particle emissivity are 1.0 for coal particles and 0.5 for ash [ 45].

Particle Scattering Factor   is the scattering factor, $f_p$, due to particles in the P-1 or discrete ordinates radiation model ( this equation in the separate Theory Guide). Note that you must enable particle effects in the radiation model, using the Particle Radiation Interaction option in the Discrete Phase Model dialog box. The recommended value of $f_p$ for coal combustion modeling is 0.9 [ 45]. 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 dialog box (atomizers) and/or Discrete Phase Model dialog box (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. More information about user-defined functions can be found in the separate UDF Manual.

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. More information about user-defined functions can be found in the separate UDF Manual.