The Physically Relevant Parameter Space of the Nukiyama‐Tanasawa distribution function

Paloposki, Tuomas

doi:10.1002/ppsc.19910080152

Cited by 9 publications

(14 citation statements)

References 8 publications

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“…The enthusiastic aspect of the diameter distribution given by Equation 27 is that it is a form of the Nukiyama-Tanasawa distribution which is another well-known empirical drop-diameter distribution [1,9,17]. Li and Tankin [15] In their second contribution, Li and Tankin [16] extended the previous work to derive a joint drop diameter-velocity distribution.…”

Section: Application Of Mef To Determine Liquid Spray Drop-size Distrmentioning

confidence: 99%

“…Dumouchel [40] demonstrated that it is identical to the empirical Nukiyama-Tanasawa distribution, which is an empirical distribution often used in the literature to represent liquid spray drop-diameter distribution. Paloposki [17] identified the permissible range of the parameters q and  of the Nukiyama-Tanasawa distribution in order to allow any drop-diameter distribution type (number-based, length-based, surface based and volume-based) to be physically representative. This permissible range defines two regions in the (q, ) space, namely: constraint ensures the existence of a minimum diameter.…”

Section: G(d) = Cte Equation 59 Is Identical To Cousin Et Al's Somentioning

confidence: 99%

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The Maximum Entropy Formalism and the Prediction of Liquid Spray Drop-Size Distribution

Dumouchel

2009

Entropy

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Abstract:The efficiency of any application involving a liquid spray is known to be highly dependent on the spray characteristics, and mainly, on the drop-diameter distribution. There is therefore a crucial need of models allowing the prediction of this distribution. However, atomization processes are partially known and so far a universal model is not available. For almost thirty years, models based on the Maximum Entropy Formalism have been proposed to fulfill this task. This paper presents a review of these models emphasizing their similarities and differences, and discusses expectations of the use of this formalism to model spray drop-size distribution.

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Section: Application Of Mef To Determine Liquid Spray Drop-size Distrmentioning

confidence: 99%

Section: G(d) = Cte Equation 59 Is Identical To Cousin Et Al's Somentioning

confidence: 99%

The Maximum Entropy Formalism and the Prediction of Liquid Spray Drop-Size Distribution

Dumouchel

2009

Entropy

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“…Ahmadi and Sellens [9] simplified this approach and showed that the number-based drop-size distribution could be derived on the basis of the mass conservation, the surface energy conservation and the partition constraints, three constraints equivalent to the definition of the mean diameters D 30 , D 20 and D -10 , respectively. All of these studies carried out by Sellens [22] conclude that it is possible to describe a drop-size distribution with only three moments, or mean diameters: D -10 , D 30 and D 32 (D 32 being a combination of D 20 and D 30 ). Another consequence of the absence of information relating to the production of the small drops is that, whatever the type of distribution, the smallest drop diameter is always equal to zero (e.g., see Figure 1).…”

Section: S àKmentioning

confidence: 99%

A New Formulation of the Maximum Entropy Formalism to Model Liquid Spray Drop-Size Distribution

Dumouchel

2006

Part. Part. Syst. Charact.

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Considering the differences and disagreements involving the previous application of the Maximum Entropy Formalism to modeling the drop-size distribution of liquid sprays, a new formulation is suggested. The constraints introduced in this formulation are based on characteristic features common to any liquid atomization process, i. e., the production of large and small drops is always limited. These limitations are a consequence of the action of both destabilizing and stabilizing forces such as aerodynamic and surface tension forces, respectively. The solution resulting from this approach, which makes use of statistical mechanics, is a three-parameter Generalized Gamma Distribution, which can treat any type of distribution. It is shown that this solution is identical to a Nukiyama-Tanasawa distribution that should no longer be regarded as an empirical distribution. Although this new formulation clearly answers the question concerning the amount of information required to describe a spray drop-size distribution, it raises the problem of the mathematical form to be given to this information, and is discussed here.

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“…Comparison of Equations and shows that the Weibull density function w ( x ) is indeed identical to the R‐R volume density distribution d V /d x . For the sake of completeness, it is mentioned that the R‐R distribution is a special case of the Nukiyama‐Tanasawa distribution …”

Section: Properties Of the Rosin‐rammler Distributionmentioning

confidence: 99%

“…For the sake of completeness, it is mentioned that the R-R distribution is a special case of the Nukiyama-Tanasawa distribution. [31][32][33]…”

Section: Relationship Of Rosin-rammler and Weibull Distributionsmentioning

confidence: 99%

Mean Particle Diameters. Part VII. The Rosin‐Rammler Size Distribution: Physical and Mathematical Properties and Relationships to Moment‐Ratio Defined Mean Particle Diameters

Alderliesten

2013

Part & Part Syst Charact

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The Rosin‐Rammler particle size distribution is used for a broad range of applications. Physical and statistical properties of the Rosin‐Rammler distribution and its parameters were investigated to evaluate their suitability in the particulate area. The Rosin‐Rammler volume density distribution is identical to the Weibull density distribution describing material failure and fatigue phenomena. The physical meaning of the Rosin‐Rammler location parameter depends on the value of its spread parameter. This makes the location parameter physically uninterpretable and less suitable for development of physical models. The distribution can still be used for, e.g., production control purposes. Rosin‐Rammler distributions with spread parameter values less than three cannot exist. They can at most give a rough description of size distributions within the measured particle size range. They should not be expected to describe correctly the quantity of small particles outside the measured size range. Their parameters are unsuitable for model development aiming at estimating parameters explaining/predicting physical product or process parameters. Two data sets were used for validation. Mean particle diameters (Moment‐Ratio notation) and the Rosin‐Rammler parameters are mathematically related, but the relationship is not valid for mean parameter values of a set of size distributions. It is not possible to predict a type of mean particle diameter showing a behavior close to that of the Rosin‐Rammler location parameter. For both data sets, the quality of the relationship of physical product property with proper mean particle diameter type is better than that with the Rosin Rammler location parameter. For process control applications a replacement of the Rosin‐Rammler location parameter by a mean particle diameter (Moment‐Ratio) should be considered. The type of mean particle diameter to be chosen depends on the values of the Rosin‐Rammler spread parameter occurring in the process. Two steps in the migration path are identified.

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The Physically Relevant Parameter Space of the Nukiyama‐Tanasawa distribution function

Abstract: The range of the parameters of the Nukiyama-Tanasawa of the physically relevant parameter space.

Cited by 9 publications

References 8 publications

The Maximum Entropy Formalism and the Prediction of Liquid Spray Drop-Size Distribution

The Maximum Entropy Formalism and the Prediction of Liquid Spray Drop-Size Distribution

A New Formulation of the Maximum Entropy Formalism to Model Liquid Spray Drop-Size Distribution

Mean Particle Diameters. Part VII. The Rosin‐Rammler Size Distribution: Physical and Mathematical Properties and Relationships to Moment‐Ratio Defined Mean Particle Diameters

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