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...

Inheritance diagram for massRosinRammler:

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Collaboration diagram for massRosinRammler:

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Public Member Functions
	TypeName ("massRosinRammler")

	massRosinRammler (const dictionary &dict, Random &rndGen)

	massRosinRammler (const massRosinRammler &p)

virtual autoPtr< distributionModel >	clone () const

void	operator= (const massRosinRammler &)=delete

virtual	~massRosinRammler ()=default

virtual scalar	sample () const

virtual scalar	meanValue () const

Public Member Functions inherited from distributionModel
	TypeName ("distributionModel")

	declareRunTimeSelectionTable (autoPtr, distributionModel, dictionary,(const dictionary &dict, Random &rndGen),(dict, rndGen))

	distributionModel (const word &name, const dictionary &dict, Random &rndGen)

	distributionModel (const distributionModel &p)

virtual	~distributionModel ()=default

virtual scalar	minValue () const

virtual scalar	maxValue () const

Additional Inherited Members
Static Public Member Functions inherited from distributionModel
static autoPtr< distributionModel >	New (const dictionary &dict, Random &rndGen)

Protected Member Functions inherited from distributionModel
virtual void	check () const

Protected Attributes inherited from distributionModel
const dictionary	distributionModelDict_

Random &	rndGen_

scalar	minValue_

scalar	maxValue_

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 $x^3$ difference between the size distribution probability density function of individual particles and modeled parcels of particles, $f_{parcels}(D) = x^3 f_{particles}(D)$ , because the submodel parameter, $ PPP $ (number of particles per parcel) is based on a fixed mass per parcel which weights the droplet distribution by a factor proportional to $ 1/x^3 $ (i.e. $PPP = \dot{m}_{total} \Delta_{t_{inj(per-parcel)}} / {m}_{particle}$ )." (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.