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22.12.1 Injection Types

You will define the initial conditions for a particle/droplet stream by creating an "injection'' and assigning properties to it. FLUENT provides 11 types of injections:

For each nonatomizer injection type, you will specify each of the initial conditions listed in Section  22.12, the type of particle that possesses these initial conditions, and any other relevant parameters for the particle type chosen.

You should create a single injection when you want to specify a single value for each of the initial conditions (Figure  22.12.1). Create a group injection (Figure  22.12.2) when you want to define a range for one or more of the initial conditions (e.g., a range of diameters or a range of initial positions). To define hollow spray cone injections in 3D problems, create a cone injection (Figure  22.12.3). To release particles from a surface (either a zone surface or a surface you have defined using the items in the Surface menu), you will create a surface injection. (If you create a surface injection, a particle stream will be released from each facet of the surface. You can use the Bounded and Sample Points options in the Plane Surface panel to create injections from a rectangular grid of particles in 3D (see Section  27.6 for details).

Figure 22.12.1: Particle Injection Defining a Single Particle Stream
figure

Figure 22.12.2: Particle Injection Defining an Initial Spatial Distribution of the Particle Streams
figure

Figure 22.12.3: Particle Injection Defining an Initial Spray Distribution of the Particle Velocity
figure

Particle initial conditions (position, velocity, diameter, temperature, and mass flow rate) can also be read from an external file if none of the injection types listed above can be used to describe your injection distribution. The file has the following form:

(( x y z u v w diameter temperature mass-flow) name )

with all of the parameters in SI units. All the parentheses are required, but the name is optional.

The inputs for setting injections are described in detail in Section  22.12.4.



Point Properties for Single Injections


For a single injection, you will define the following initial conditions for the particle stream under the Point Properties heading (in the Set Injection Properties panel):



Point Properties for Group Injections


For group injections, you will define the properties described in Section  22.12.1 for single injections for the First Point and Last Point in the group. That is, you will define a range of values, $\phi_1$ through $\phi_N$, for each initial condition $\phi$ by setting values for $\phi_1$ and $\phi_N$. FLUENT assigns a value of $\phi$ to the $i$th injection in the group using a linear variation between the first and last values for $\phi$:


 \phi_i = \phi_1 + \frac{\phi_N - \phi_1}{N-1} (i-1) (22.12-2)

Thus, for example, if your group consists of 5 particle streams and you define a range for the initial $x$ location from 0.2 to 0.6 meters, the initial $x$ location of each stream is as follows:

figure   

In general, you should supply a range for only one of the initial conditions in a given group--leaving all other conditions fixed while a single condition varies among the stream numbers of the group. Otherwise you may find, for example, that your simultaneous inputs of a spatial distribution and a size distribution have placed the small droplets at the beginning of the spatial range and the large droplets at the end of the spatial range.

Note that you can use a different method for defining the size distribution of the particles, as discussed below.

Using the Rosin-Rammler Diameter Distribution Method

By default, you will define the size distribution of particles by inputting a diameter for the first and last points and using the linear equation ( 22.12-2) to vary the diameter of each particle stream in the group. When you want a different mass flow rate for each particle/droplet size, however, the linear variation may not yield the distribution you need. Your particle size distribution may be defined most easily by fitting the size distribution data to the Rosin-Rammler equation. In this approach, the complete range of particle sizes is divided into a set of discrete size ranges, each to be defined by a single stream that is part of the group. Assume, for example, that the particle size data obeys the following distribution:


Diameter Range ( $\mu$m) Mass Fraction in Range
0-70
70-100
100-120
120-150
150-180
180-200
0.05
0.10
0.35
0.30
0.15
0.05

The Rosin-Rammler distribution function is based on the assumption that an exponential relationship exists between the droplet diameter, $d$, and the mass fraction of droplets with diameter greater than $d$, $Y_d$:


 Y_d = e^{-(d/\overline{d})^n} (22.12-3)

FLUENT refers to the quantity $\overline{d}$ in Equation  22.12-3 as the Mean Diameter and to $n$ as the Spread Parameter. These parameters are input by you (in the Set Injection Properties panel under the First Point heading) to define the Rosin-Rammler size distribution. To solve for these parameters, you must fit your particle size data to the Rosin-Rammler exponential equation. To determine these inputs, first recast the given droplet size data in terms of the Rosin-Rammler format. For the example data provided above, this yields the following pairs of $d$ and $Y_d$:


Diameter, $d$ ( $\mu$m) Mass Fraction with
Diameter Greater than $d$, $Y_d$
70
100
120
150
180
200
0.95
0.85
0.50
0.20
0.05
(0.00)

A plot of $Y_d$ vs. $d$ is shown in Figure  22.12.4.

Figure 22.12.4: Example of Cumulative Size Distribution of Particles
figure

Next, derive values of $\overline{d}$ and $n$ such that the data in Figure  22.12.4 fit Equation  22.12-3. The value for $\overline{d}$ is obtained by noting that this is the value of $d$ at which $Y_d = e^{-1} \approx 0.368$. From Figure  22.12.4, you can estimate that this occurs for $d \approx 131$ $\mu$m. The numerical value for $n$ is given by


n = \frac{\ln (-\ln Y_d)}{\ln \left (d/\overline{d} \right)}

By substituting the given data pairs for $Y_d$ and $d/\overline{d}$ into this equation, you can obtain values for $n$ and find an average. Doing so yields an average value of $n$ = 4.52 for the example data above. The resulting Rosin-Rammler curve fit is compared to the example data in Figure  22.12.5. You can input values for $\overline{d}$ and $n$, as well as the diameter range of the data and the total mass flow rate for the combined individual size ranges, using the Set Injection Properties panel.

This technique of fitting the Rosin-Rammler curve to spray data is used when reporting the Rosin-Rammler diameter and spread parameter in the discrete phase summary panel in Section  22.16.8.

Figure 22.12.5: Rosin-Rammler Curve Fit for the Example Particle Size Data
figure

A second Rosin-Rammler distribution is also available based on the natural logarithm of the particle diameter. If in your case, the smaller-diameter particles in a Rosin-Rammler distribution have higher mass flows in comparison with the larger-diameter particles, you may want better resolution of the smaller-diameter particle streams, or "bins''. You can therefore choose to have the diameter increments in the Rosin-Rammler distribution done uniformly by $\ln d$.

In the standard Rosin-Rammler distribution, a particle injection may have a diameter range of 1 to 200 $\mu$m. In the logarithmic Rosin-Rammler distribution, the same diameter range would be converted to a range of $\ln 1$ to $\ln 200$, or about 0 to 5.3. In this way, the mass flow in one bin would be less-heavily skewed as compared to the other bins.

When a Rosin-Rammler size distribution is being defined for the group of streams, you should define (in addition to the initial velocity, position, and temperature) the following parameters, which appear under the heading for the First Point:

The Stochastic Rosin-Rammler Diameter Distribution Method

For atomizer injections, a Rosin-Rammler distribution is assumed for the particles exiting the injector. In order to decrease the number of particles necessary to accurately describe the distribution, the diameter distribution function is randomly sampled for each instance where new particles are introduced into the domain.

The Rosin-Rammler distribution can be written as

 1-Y = \exp \left[ -\left( \frac{D}{\bar{d}} \right)^n \right] (22.12-4)

where $Y$ is the mass fraction smaller than a given diameter $D$, $\bar{d}$ is the Rosin-Rammler diameter and $n$ is the Rosin-Rammler exponent. This expression can be inverted by taking logs of both sides and rearranging,
 D = \bar{d} \left( -\ln(1-Y) \right)^{1/n}. (22.12-5)

Given a mass fraction $Y$ along with parameters $\bar{d}$ and $n$, this function will explicitly provide a diameter, $D$. Diameters for the atomizer injectors described in Section  22.12.1 are obtained by uniformly sampling $Y$ in equation 22.12-5.



Point Properties for Cone Injections


In 3D problems, you can define a hollow or solid cone of particle streams using the cone or solid-cone injection type, respectively. For both types of cone injections, the inputs are as follows:

The distribution of the particle streams for the solid cone injection is random, as seen in Figure  22.12.3. Furthermore, duplicating this injection may not necessarily result in the same distribution, at the same location.

figure   

For transient calculations, the spatial distribution of streams at the initial injection location is recalculated at each time step. Sampling different possible trajectories allows a more accurate representation of a solid cone using fewer computational parcels. For steady state calculations, the trajectories are initialized one time and kept the same for subsequent DPM iterations. The trajectories are recalculated when a change in the injection panel occurs or when a case and data file are saved. If the residuals and solution change when a small change is made to the injection or when a case and data file are saved, it may mean that there are not enough trajectories being used to represent the solid cone with sufficient accuracy.

Note that you may want to define multiple spray cones emanating from the same initial location in order to specify a size known distribution of the spray or to include a known range of cone angles.



Point Properties for Surface Injections


For surface injections, you will define all the properties described in Section  22.12.1 for single injections except for the initial position of the particle streams. The initial positions of the particles will be the location of the data points on the specified surface(s). Note that you will set the Total Flow Rate of all particles released from the surface (required for coupled calculations only). If you want, you can scale the individual mass flow rates of the particles by the ratio of the area of the face they are released from to the total area of the surface. To scale the mass flow rates, select the Scale Flow Rate By Face Area option under Point Properties.

Note that many surfaces have nonuniform distributions of points. If you want to generate a uniform spatial distribution of particle streams released from a surface in 3D, you can create a bounded plane surface with a uniform distribution using the Plane Surface panel, as described in Section  27.6. In 2D, you can create a rake using the Line/Rake Surface panel, as described in Section  27.5.

In addition to the option of scaling the flow rate by the face area, the normal direction of a face can be used for the injection direction. To use the face normal direction for the injection direction, select the Inject Using Normal Direction option under Point Properties (Figure  22.12.9). Once this option is selected, you only need to specify the velocity magnitude of the injection, not the individual components of the velocity magnitude.

figure   

Note also that only surface injections from boundary surfaces will be moved with the grid when a sliding mesh or a moving or deforming mesh is being used.

A nonuniform size distribution can be used for surface injections, as described below.

Using the Rosin-Rammler Diameter Distribution Method

The Rosin-Rammler size distributions described in Section  22.12.1 for group injections is also available for surface injections. If you select one of the Rosin-Rammler distributions, you will need to specify the following parameters under Point Properties, in addition to the initial velocity, temperature, and total flow rate:

FLUENT will inject streams of particles from each face on the surface, with diameters defined by the Rosin-Rammler distribution function. The total number of injection streams tracked for the surface injection will be equal to the number of diameters in each distribution ( Number of Diameters) multiplied by the number of faces on the surface.



Point Properties for Plain-Orifice Atomizer Injections


For a plain-orifice atomizer injection, you will define the following initial conditions under Point Properties:

See Section  22.8.1 for details about how these inputs are used.



Point Properties for Pressure-Swirl Atomizer Injections


For a pressure-swirl atomizer injection, you will specify some of the same properties as for a plain-orifice atomizer. In addition to the position, axis (if 3D), temperature, mass flow rate, duration of injection (if unsteady), injector inner diameter, and azimuthal angles (if relevant) described in Section  22.12.1, you will need to specify the following parameters under Point Properties:

See Section  22.8.2 for details about how these inputs are used.



Point Properties for Air-Blast/Air-Assist Atomizer Injections


For an air-blast/air-assist atomizer, you will specify some of the same properties as for a plain-orifice atomizer. In addition to the position, axis (if 3D), temperature, mass flow rate, duration of injection (if unsteady), injector inner diameter, and azimuthal angles (if relevant) described in Section  22.12.1, you will need to specify the following parameters under Point Properties:

See Section  22.8.3 for details about how these inputs are used.



Point Properties for Flat-Fan Atomizer Injections


The flat-fan atomizer model is available only for 3D models. For this type of injection, you will define the following initial conditions under Point Properties:

See Section  22.8.4 for details about how these inputs are used.



Point Properties for Effervescent Atomizer Injections


For an effervescent atomizer injection, you will specify some of the same properties as for a plain-orifice atomizer. In addition to the position, axis (if 3D), temperature, mass flow rate (including both flashing and nonflashing components), duration of injection (if unsteady), vapor pressure, injector inner diameter, and azimuthal angles (if relevant) described in Section  22.12.1, you will need to specify the following parameters under Point Properties:

See Section  22.8.5 for details about how these inputs are used.


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