Particle-size distribution model wherein random samples are drawn from the two-parameter Rosin-Rammler (Weibull) probability density function corrected to take into account varying number of particles per parcels for fixed-mass parcels. More...

#include <massRosinRammler.H>

Inheritance diagram for massRosinRammler:

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Collaboration diagram for massRosinRammler:

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Public Member Functions
	TypeName ("massRosinRammler")
	Runtime type information.
	massRosinRammler (const dictionary &dict, Random &rndGen)
	Construct from components.
	massRosinRammler (const massRosinRammler &p)
	Copy construct.
virtual autoPtr< distributionModel >	clone () const
	Construct and return a clone.
void	operator= (const massRosinRammler &)=delete
	No copy assignment.
virtual	~massRosinRammler ()=default
	Destructor.
virtual scalar	sample () const
	Sample the distribution.
virtual scalar	meanValue () const
	Return the theoretical mean of the distribution.
Public Member Functions inherited from distributionModel
	TypeName ("distributionModel")
	Runtime type information.
	declareRunTimeSelectionTable (autoPtr, distributionModel, dictionary,(const dictionary &dict, Random &rndGen),(dict, rndGen))
	Declare runtime constructor selection table.
	distributionModel (const word &name, const dictionary &dict, Random &rndGen)
	Construct from dictionary.
	distributionModel (const distributionModel &p)
	Copy construct.
virtual	~distributionModel ()=default
	Destructor.
virtual scalar	minValue () const
	Return the minimum of the distribution.
virtual scalar	maxValue () const
	Return the maximum of the distribution.

Additional Inherited Members
Static Public Member Functions inherited from distributionModel
static autoPtr< distributionModel >	New (const dictionary &dict, Random &rndGen)
	Selector.
Protected Member Functions inherited from distributionModel
virtual void	check () const
	Check that the distribution model is valid.
Protected Attributes inherited from distributionModel
const dictionary	distributionModelDict_
	Coefficients dictionary.
Random &	rndGen_
	Reference to the random number generator.
scalar	minValue_
	Minimum of the distribution.
scalar	maxValue_
	Maximum of the distribution.

Detailed Description

Particle-size distribution model wherein random samples are drawn from the two-parameter Rosin-Rammler (Weibull) probability density function corrected to take into account varying number of particles per parcels for fixed-mass parcels.

"There is a factor of \_form#520 difference between the size distribution probability density function of individual particles and modeled parcels of particles, \_form#521, because the submodel parameter, \_form#522 (number of particles per parcel) is based on a fixed mass per parcel which weights the droplet distribution by a factor proportional to \_form#523 (i.e. \iline 34 \_form#524@_fakenl)." (YHD:p. 1374-1375).

massRosinRammler should be preferred over RosinRammler when parcelBasisType is based on mass:

    parcelBasisType mass;

The doubly-truncated mass-corrected Rosin-Rammler probability density function:

$\‍[ f(x; \lambda, n, A, B) = x^3 \frac{n}{\lambda} \left( \frac{x}{\lambda} \right)^{n-1} \frac{ \exp\{ -(\frac{x}{\lambda})^n \} } { \exp\{ -(\frac{A}{\lambda})^n \} - \exp\{ -(\frac{B}{\lambda})^n \} } \‍]$

where

$f(x; \lambda, n, A, B)$	=	Rosin-Rammler probability density function
$\lambda$	=	Scale parameter
	=	Shape parameter
	=	Sample
	=	Minimum of the distribution
	=	Maximum of the distribution

Constraints:

$\lambda > 0$

Random samples are generated by the inverse transform sampling technique by using the quantile function of the doubly-truncated two-parameter mass-corrected Rosin-Rammler (Weibull) probability density function:

$\‍[ d = \lambda \, Q(a, u)^{1/n} \‍]$

with

$\‍[ a = \frac{3}{n} + 1 \‍]$

where $ Q(z_1, z_2) $ is the inverse of regularised lower incomplete gamma function, and $ u $ is a sample drawn from the uniform probability density function on the interval $ (x, y) $ :

$\‍[ x = \gamma \left( a, \frac{A}{\lambda}^n \right) \‍]$

$\‍[ y = \gamma \left( a, \frac{B}{\lambda}^n \right) \‍]$

where $\gamma(z_1, z_2)$ is the lower incomplete gamma function.

Reference:

        Standard model (tag:YHD):
            Yoon, S. S., Hewson, J. C., DesJardin, P. E.,
            Glaze, D. J., Black, A. R., & Skaggs, R. R. (2004).
            Numerical modeling and experimental measurements of a high speed
            solid-cone water spray for use in fire suppression applications.
            International Journal of Multiphase Flow, 30(11), 1369-1388.
            DOI:10.1016/j.ijmultiphaseflow.2004.07.006

Usage

Minimal example by using constant/<CloudProperties>:

subModels
{
    injectionModels
    {
        <name>
        {
            ...
            parcelBasisType  mass;
            ...

            sizeDistribution
            {
                type        massRosinRammler;
                massRosinRammlerDistribution
                {
                    lambda      <scaleParameterValue>;
                    n           <shapeParameterValue>;
                    minValue    <minValue>;
                    maxValue    <maxValue>;
                }
            }
        }
    }
}

where the entries mean:

Property	Description	Type	Reqd	Deflt
`type`	Type name: massRosinRammler	word	yes	-
`massRosinRammlerDistribution`	Distribution settings	dict	yes	-
`lambda`	Scale parameter	scalar	yes	-
`n`	Shape parameter	scalar	yes	-
`minValue`	Minimum of the distribution	scalar	yes	-
`maxValue`	Maximum of the distribution	scalar	yes	-

Note

In the current context, lambda (or d) is called "characteristic droplet size", and n "empirical dimensionless constant to specify the distribution width, sometimes referred to as the dispersion coefficient." (YHD:p. 1374).

Source files

Definition at line 245 of file massRosinRammler.H.