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...
Public Member Functions | |
| TypeName ("massRosinRammler") | |
| Runtime type information. More... | |
| massRosinRammler (const dictionary &dict, Random &rndGen) | |
| Construct from components. More... | |
| massRosinRammler (const massRosinRammler &p) | |
| Copy construct. More... | |
| virtual autoPtr< distributionModel > | clone () const |
| Construct and return a clone. More... | |
| void | operator= (const massRosinRammler &)=delete |
| No copy assignment. More... | |
| virtual | ~massRosinRammler ()=default |
| Destructor. More... | |
| virtual scalar | sample () const |
| Sample the distribution. More... | |
| virtual scalar | meanValue () const |
| Return the theoretical mean of the distribution. More... | |
 Public Member Functions inherited from distributionModel | |
| TypeName ("distributionModel") | |
| Runtime type information. More... | |
| declareRunTimeSelectionTable (autoPtr, distributionModel, dictionary,(const dictionary &dict, Random &rndGen),(dict, rndGen)) | |
| Declare runtime constructor selection table. More... | |
| distributionModel (const word &name, const dictionary &dict, Random &rndGen) | |
| Construct from dictionary. More... | |
| distributionModel (const distributionModel &p) | |
| Copy construct. More... | |
| virtual | ~distributionModel ()=default |
| Destructor. More... | |
| virtual scalar | minValue () const |
| Return the minimum of the distribution. More... | |
| virtual scalar | maxValue () const |
| Return the maximum of the distribution. More... | |
Additional Inherited Members | |
| Static Public Member Functions inherited from distributionModel | |
| static autoPtr< distributionModel > | New (const dictionary &dict, Random &rndGen) |
| Selector. More... | |
| Protected Member Functions inherited from distributionModel | |
| virtual void | check () const |
| Check that the distribution model is valid. More... | |
| Protected Attributes inherited from distributionModel | |
| const dictionary | distributionModelDict_ |
| Coefficients dictionary. More... | |
| Random & | rndGen_ |
| Reference to the random number generator. More... | |
| scalar | minValue_ |
| Minimum of the distribution. More... | |
| scalar | maxValue_ |
| Maximum of the distribution. More... | |
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 |
| \( n \) | = | Shape parameter |
| \( x \) | = | Sample |
| \( A \) | = | Minimum of the distribution |
| \( B \) | = | Maximum of the distribution |
Constraints:
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.2004.07.006constant/<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 | - |
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).Definition at line 249 of file massRosinRammler.H.
| massRosinRammler | ( | const dictionary & | dict, |
| Random & | rndGen | ||
| ) |
Construct from components.
Definition at line 47 of file massRosinRammler.C.
Referenced by massRosinRammler::clone().
| massRosinRammler | ( | const massRosinRammler & | p | ) |
Copy construct.
Definition at line 70 of file massRosinRammler.C.
|
virtualdefault |
Destructor.
| TypeName | ( | "massRosinRammler" | ) |
Runtime type information.
|
inlinevirtual |
Construct and return a clone.
Implements distributionModel.
Definition at line 277 of file massRosinRammler.H.
References massRosinRammler::massRosinRammler().
|
delete |
No copy assignment.
|
virtual |
Sample the distribution.
Implements distributionModel.
Definition at line 82 of file massRosinRammler.C.
References Foam::Math::incGamma_P(), Foam::Math::invIncGamma(), distributionModel::maxValue_, distributionModel::minValue_, Random::position(), Foam::pow(), distributionModel::rndGen_, and x.
|
virtual |
Return the theoretical mean of the distribution.
Implements distributionModel.
Definition at line 102 of file massRosinRammler.C.
1.8.17