Farahani, Hamed Farmahini

Jomaas, Grunde

Rangwala, Ali S.

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Apr 10, 2018Theoretical Analysis on Marangoni-driven Cavity Formation in Ice during In-situBurning of Oil Spills in Ice-infested Waters -Paper Number IN43D-0096Farahani, Hamed Farmahini ; Jomaas, Grunde; Rangwala, Ali S.Publication date:2017Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Farahani, H. F., Jomaas, G., & Rangwala, A. S. (2017). Theoretical Analysis on Marangoni-driven CavityFormation in Ice during In-situ Burning of Oil Spills in Ice-infested Waters -Paper Number IN43D-0096. Postersession presented at 2017 AGU Fall Meeting, New Orleans, United States.Hamed F. Farahani a, Grunde Jomaas b,c, Ali S. Rangwala aa Department of Fire Protection Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA  E-mail: ffarahani.hamed@gmail.comb Department of Civil Engineering, Technical University of Denmark (DTU), 2800 Kgs. Lyngby, Denmarkc BRE Centre for Fire Safety Engineering, University of Edinburgh, Edinburgh, EH9 3FG, United KingdomTheoretical Analysis on Marangoni-driven Cavity Formation in Ice during In-situ Burning of Oil Spills in Ice-infested Waters - Paper Number IN43D-0096Motivation Cleanup of oil spills in the ArcticLateral Cavity ProblemAcknowledgementThis study was funded by Danish Council for Independent Research (Grant DDF – 1335-00282).Conclusions1- The analysis considered the different physical aspects of the lateral cavity problem including the heat feedback from the flame to fuel surface, the convective transfer toward the ice, and the melting energy continuity of the ice wall. 2- The scaling of this problem has provided a predictive tool to estimate the intrusion length of lateral cavity problem which will be useful in evaluating the success of ISB operation.  References1- H. Farmahini Farahani, G. Jomaas, A. S. Rangwala, Effects of convective motion in n-octane pool fires in an ice cavity, Combustion and Flame 162 (12) (2015) 4643-4648.2- H. Farmahini Farahani, W. U. R. Alva, A. S. Rangwala, G. Jomaas, Convection-driven melting in an n-octane pool fire bounded by an ice wall, Combustion and Flame 179  (2017)  219-227.3- H. Farmahini Farahani, G. Jomaas, A. S. Rangwala, A study on burning behavior and convective flows in Methanol pool fires bound by ice, International Oil Spill Conference Proceedings 2017 (1), 1983-1998.4- Y. Fu, H. Farmahini Farahani, G. Jomaas, A. S. Rangwala, Parametric study on cavity formation during in-situ burning of oils in ice, International Oil Spill Conference Proceedings 2017, No. 1, p. 2017293Figure 1. Different oil-in-ice situations Figure 3. Cavity formation and the mechanisms that are involved. The available experimental data showing the intrusion length of oil in different studies were collected. The scaling correlation was adjusted to experimental data using least square regression method.In situ burning as an effective and practical method for cleanupFigure 2. Burning of oil in pack ice. 2- convective transfer(Marangoni)𝒒𝒙3- melting by conduction1- flame feedbackTo develop a scaling model of the ice melting that occurs during in-situ burning.Objectives of the Study𝑻𝑪x, uy, v𝑻𝑯𝒖𝑳(𝒕)1-  𝑞"𝑥 = 𝜒 𝜌∞𝐶𝑝∞ 𝑇∞𝑔 𝑇𝑓 − 𝑇∞12𝐷  1 22-𝜕𝑢𝜕𝑥+𝜕𝑣𝜕𝑦= 0𝜕3𝑢𝜕𝑦3− 𝑔𝛽𝜕𝑇𝜕𝑥= 0𝑢𝜕𝑇𝜕𝑥+ 𝑣𝜕𝑇𝜕𝑦= 𝛼𝛻2𝑇B.C. : 𝜇𝜕𝑢𝜕𝑦= −𝜎𝑇𝜕𝑇𝜕𝑥3-𝜌𝑖𝑐𝑒𝐿𝑚,𝑖𝑐𝑒′𝑈𝜕𝑦𝜕𝑥= 𝑘(𝜕𝑇𝜕𝑦𝑦=−𝛿𝑢𝛿2~𝑣𝛿1𝑢𝛿13~ 𝑔𝛽∆𝑇𝛿2𝑢∆𝑇𝛿2, 𝑣∆𝑇𝛿1~𝛼∆𝑇𝛿12And𝑢𝛿1~−𝜎𝑇𝜇∆𝑇𝛿2𝑘∆𝑇 𝛿 1~𝜌𝑖𝑐𝑒𝐿𝑚,𝑖𝑐𝑒′𝑈𝛿 1 𝛿 2𝑻𝑪𝑇𝐻 − 𝑇𝐶 = ∆𝑇 = 𝑞"𝑥𝑑𝑘Figure 4. Examples of lateral cavity formation a) n-octane burning in a 10 cm square tray with an ice wall on the side , b) ANS crude oil burning in an ice channel of 60 by 16 cm, c) ANS crude oil burning in a 100 cm square. 𝐿~−𝜎𝑇𝜇𝛼 2 3  𝑞"𝑥𝑑𝑘 5 3𝑘𝑡𝜌𝑖𝑐𝑒𝐿𝑚,𝑖𝑐𝑒′1𝛿2 1 3𝐿𝛿2~ 𝑀𝑎23(𝑆𝑡𝑒. 𝐹𝑜)where 𝑀𝑎 =−𝜎𝑇∆𝑇𝛿2𝜇𝛼, 𝑆𝑡𝑒 =𝐶𝑝∆𝑇𝐿𝑚,𝑖𝑐𝑒′ , and 𝐹𝑜 =𝛼𝑖𝑐𝑒𝑡𝛿22are the dimensionless numbers associated with theice melting problem.Order of magnitude scaling Cavity intrusion lengthAssumptions1- Flame feedback may be quantified with pool firediameter as shown in Equation 1.2- Coordinate system is attached to the tip of the meltingfront which advances to the right with velocity U = L/t.3- Intrusion layer is slender with thickness of 𝛿<<L.4- Liquid is assumed Newtonian with constant propertiesand a simplified form of momentum equations.5- Marangoni is assumed to be the driving force of liquidtherefore the boundary condition on the top surface ofthe liquid layer is considered for scaling. 5- Energyconservation for the melting interface may be written byEquation 3.𝑳~ 𝟎. 𝟒𝟓−𝝈𝑻𝝁𝜶𝟎.𝟏𝟒𝒅  𝒒"𝒙𝒌𝟏.𝟏𝟖𝒌𝒊𝒄𝒆𝒕𝝆𝒊𝒄𝒆𝑳𝒎,𝒊𝒄𝒆𝟎.𝟖𝟒𝟏𝜹𝟐 𝟏 𝟑Scaling with Order of MagnitudeAssessment of ScalingIn dimensionless form:Final Correlation:Figure 5. Comparison of the scaling analysis with experimental data.00.050.10.150.20.250.30 0.05 0.1 0.15 0.2 0.25 0.3Theoretical intrusion length (m)Experimental intrusion length (m)ModelFarahani et. al []Farahani et. al []van Gelderen et. al []Bellino et. al []Shi et. al []Shi et. al []20% error40% errorR^2= 0.91

Theoretical Analysis on Marangoni-driven Cavity Formation in Ice during In-situ Burning of Oil Spills in Ice-infested Waters -Paper Number IN43D-0096

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Theoretical Analysis on Marangoni-driven Cavity Formation in Ice during In-situ Burning of Oil Spills in Ice-infested Waters -Paper Number IN43D-0096

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