Particle-size distribution model wherein random samples are drawn from the doubly-truncated two-parameter Rosin-Rammler (Weibull) probability density function: More...

Inheritance diagram for RosinRammler:

[legend]

Collaboration diagram for RosinRammler:

[legend]

Public Member Functions
	TypeName ("RosinRammler")

	RosinRammler (const dictionary &dict, Random &rndGen)

	RosinRammler (const RosinRammler &p)

virtual autoPtr< distributionModel >	clone () const

void	operator= (const RosinRammler &)=delete

virtual	~RosinRammler ()=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 doubly-truncated two-parameter Rosin-Rammler (Weibull) probability density function:

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

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:

$\infty > B > A > 0$
$x \in [B,A]$
$\lambda > 0$

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

$x = \lambda \left( q_{min} - \ln (1 - u r) \right)^{1/n}$

with

$r = 1 - \exp(-q_{max} + q_{min})$

$q_{min} = \left(\frac{A}{\lambda}\right)^n$

$q_{max} = \left(\frac{B}{\lambda}\right)^n$

where $ u $ is sample drawn from the uniform probability density function on the unit interval $ (0, 1) $ .

Reference:

    Doubly-truncated two-parameter Weibull distribution and its moments (tag:C):
        Crénin, F. (2015).
        Truncated Weibull Distribution Functions and Moments.
        SSRN 2690255.
        DOI:10.2139/ssrn.2690255

Usage

Minimal example by using constant/<CloudProperties>:

subModels
{
    injectionModels
    {
        <name>
        {
            ...

            sizeDistribution
            {
                type        RosinRammler;
                RosinRammlerDistribution
                {
                    lambda      <scaleParameterValue>;
                    n           <shapeParameterValue>;
                    minValue    <minValue>;
                    maxValue    <maxValue>;
                }
            }
        }
    }
}

where the entries mean:

Property	Description	Type	Reqd	Deflt
`type`	Type name: RosinRammler	word	yes	-
`RosinRammlerDistribution`	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	-