Sprinkler Spray Modelling

Centre for Fire and Explosion StudiesCentre for Fire and Explosion Studies

SPRINKLER SPRAY MODELLING

Hamed Aghajani

Supervisors:Prof. Jennifer Wen and Dr. Siaka Dembele

CFES, Kingston University, London   

3rd FM Global Open Source CFD Fire Modeling Workshop, Norwood MA

May 9-10

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Outline

• Objectives

• Modelling Approach

• Preliminary studies and results

• Conclusion

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Objectives

Sheppard, D. T. Spray characteristics of fire sprinklers. PhD Dissertation, Evanston, IL: North-western University, 2002.

Studying Available Modeling Approaches for Sprinklers and Understand their Limitations

Develop a Model to Study Droplets Transport and Interaction with Fire

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Modelling Approaches

• Deterministic Atomization ModelInitial

Sprinkler Condition

Sheet Breakup

Droplet size, location, Velocity

Ligament Breakup

Marshall, A. W., and M. Di Marzo. Process Safety and Environmental Protection 82 (2004): 97–104.

Film Formation

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Modelling Approaches

Film Formation

Sheet Breakup

𝜌𝐿h(𝜕 𝑓𝜕𝑡 )2

+𝜇h𝑛2(𝜕 𝑓𝜕𝑡 )− 2𝜌𝜎𝑈 2 −2𝜎𝑛2=0 𝒇= 𝝆𝑼 𝟐 𝒕√𝟐𝒉𝝆 𝑳𝝈

h𝑏𝑢=h𝑑𝑟𝑑𝑟 𝑏𝑢

𝑟𝑏𝑢=𝑟 𝑑+𝑈 𝑠h𝑒𝑒𝑡 𝑡𝑏𝑢

𝑼 𝒔𝒉𝒆𝒆𝒕 𝒕𝒃𝒖𝟑 +𝒓 𝒅 𝒕𝒃𝒖

𝟐 −𝒉𝒅𝒓 𝒅( 𝒇 √𝟐𝝆𝑳𝝈

𝝆𝑼 𝒔𝒉𝒆𝒆𝒕𝟐 )

𝟐

=𝟎

Sheet Tracking

h𝑑=𝐶2×(𝜈𝐿

𝑄 )0 .25 𝑟 𝑑

94 +𝑙

94

𝑟𝑑

h𝑑=𝑟0

2𝑟 𝑑

+𝐶1×( 7𝜈𝐿

𝑈 0)

0 .2

𝑟𝑑0 . 8

Presently derived equation

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Modelling Approaches

Ligament Formation

𝑉 𝑙𝑖𝑔=𝜋𝑟 𝑙𝑖𝑔2 [2𝜋 (𝑟 𝑏𝑢+𝑟 𝑙𝑖𝑔) ]

𝑉 𝑙𝑖𝑔=𝜋 h𝑏𝑢[(𝑟𝑏𝑢+ 𝜆2 )2

−𝑟 𝑏𝑢2 ]

𝝅𝟒𝑻

𝒅𝒍𝒊𝒈𝟑 + 𝝅

𝟐𝒉𝒃𝒖

𝒓 𝒃𝒖𝒅𝒍𝒊𝒈𝟐 −[(𝒓 𝒃𝒖+

𝝀𝟐 )

𝟐

−𝒓𝒃𝒖𝟐 ]=𝟎

Drop Formation

𝑛𝑐𝑟𝑖𝑡 𝑙𝑖𝑔𝑑𝑙𝑖𝑔=[ 12+ 3𝜇

2√𝜌𝐿𝜎𝑑𝑙𝑖𝑔]− 0 .5

43𝜋𝑟 𝐷𝑟𝑜𝑝

3 =𝜋 𝑟 𝑙𝑖𝑔2 𝜆𝑐𝑟𝑖𝑡𝑙𝑖𝑔

𝒅𝑫𝒓𝒐𝒑❑ =𝟑√ 𝟑𝝅

𝒏𝒄𝒓𝒊𝒕𝒍𝒊𝒈

𝒅𝒍𝒊𝒈𝟐

Deterministic approach predicts a single droplet characteristic

Presently derived conservation equation

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Modelling Approaches• Stochastic Modeling

Critical Breakup Amplitude (

Sheet Breakup Wavelength (

Ligament Breakup Wavelength (

Stochastic Model

Wu, Di, Delphine Guillemin, and Andre W Marshall. "A modeling basis for predicting the initial sprinkler spray." Fire Safety Journal 42 (2007): 283-294.

Droplet Size

Initial Location

Existing model is mainly for simple deflectors

Do not account for actual sprinkler configurations (Pendant, Upright)[There is no model for fluctuation intensity]

Normal distribution have been utilized for all 3 parameters.0.1 < I < 0.3

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Ibrahim, E A., and McKinney, T R., Proceedings of the Institution of Mechanical Engineers 220 (2006): 203-214.

Preliminary Studies and Results

Alternative Sheet Tracking Model

𝜕𝜕𝜉 (𝜌 𝑓 𝑢𝑓 𝛿 )=0Mass

Momentum 𝜌 𝑓 𝑢𝑓

𝜕𝑢𝑓

𝜕𝜉−𝜌 𝑓 𝑢 𝑓𝑤 𝑓

sin 𝜃𝑟

=𝑆𝜉+𝜌 𝑓 𝑔cos𝜃

𝜌 𝑓 𝑢𝑓 𝑢𝑓

𝜕𝑢𝑓

𝜕 𝜉−𝜌 𝑓𝑤 𝑓 𝑤 𝑓

cos𝜃𝑟

=−𝜕𝑝 𝑓

𝜕𝜂−𝜌 𝑓 𝑔sin 𝜃

Geometry𝑑𝑟𝑑 𝜉

=sin𝜃

𝑑𝑧𝑑𝜉

=cos𝜃

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Preliminary Studies and Results

Implementation thoroughly satisfies the original paper

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Preliminary Studies and Results

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K=2

K=3

K=4

K=5

Preliminary Studies and Results

Wu, Di, Delphine Guillemin, and Andre W Marshall. "A modeling basis for predicting the initial sprinkler spray." Fire Safety Journal 42 (2007): 283-294.

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2/11min2.3

,25

psigalK

mmDdef

)3.0,1.0(

50,50,1000

randIII

pnm

dropligf

Preliminary Studies and Results

Ren, Ning. “Analysis of the Initial Spray from Canonical Fire Suppression Nozzles”, Master Thesis, Maryland: University of Maryland, College Park, 2007.

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Preliminary Studies and Results

Dundas, P., FMRC serial no. 18792 RC73-T-40

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Preliminary Studies and Results

Normalized radial displacement Vs. Normalized Vertical displacement

AT 300K

P = 10 psi

P = 20 psi

P = 30 psi

P = 50 psi

P= 70 psi

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Normalized Velocity Vs. Normalized Vertical displacement

AT 300K

Preliminary Studies and Results

P = 10 psi

P = 20 psi

P = 30 psi

P = 50 psi

P= 70 psi

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Preliminary Studies and ResultsLiquid sheet deflection Vs. Normalized Vertical displacement

AT 300K

P = 10 psi

P = 20 psi

P = 30 psi

P = 50 psi

P= 70 psi

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Formerly introduced atomization models implemented as a frame tool for further investigations and improvements

Verification of the model against published research has been conducted Normally distributed stochastic parameters droplet size predicts droplet sizes in

range of , which are in range of published experimental work.

FURTHUR STUDIES Effect of surrounding air on spray parameters Explore the effects of some physical sprinkler parameters as boss and tine/space. Studying the interaction of different spray pattern with fire

Conclusion and Future Work

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Thank you.

Comments and Questions?