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How to model 1 phase STEFAN problem - Explicit FREE boundary condition

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Old   July 28, 2019, 04:33
Default How to model 1 phase STEFAN problem - Explicit FREE boundary condition
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Kumaresh
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Dear Foamers, Help me out here. Attachment gives clear overview. Hereby explaining the gist of my problem. In my work, boiling is considered as a point sink of moisture calculated based on mass and energy balances.

(i) I would like to know as how to implement the Stefan condition (Rankine-Hugoniot condition) based on heat balance (Equ: 10) for moisture in OpenFOAM?
Quote:
Mass balance (r) = rho * alpha * (dx/dt) [kg/m2.s]
Heat balance (-K dT/dx) = (r) * latent heat [W/m2]
The calculated mass and heat balances are explicitly substituted in energy equation as a source term. (only heat is convected, no velocity and pressure terms here)
ENERGY EQU: rho*Cp*(delT/delt) = del/delx[K*delT/delx ] + r_gas*c_gas*delT/delx + rho*delQ/delT (W/m3)

(ii)
The interface (boiling plane) is located based on sign changes technique as xb- & xb+ where, xb = position of boiling plane. Should I need to adopt level set method ? I'm confused here.

REF - Clear details here in this MANUSCRIPT ~ https://sci-hub.tw/https://doi.org/1...361(83)90225-9 Kindly share some advisable methodology in OpenFOAM. Thank you Foamers !!
Attached Images
File Type: jpg ATTACHMENT_1_Boiling.jpg (110.9 KB, 39 views)
File Type: png ATTACHMENT_2_Convection.png (153.7 KB, 24 views)
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Old   July 29, 2019, 01:16
Default Temperature jump based on heat balance
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Some additional info:
The heat balance equation mentioned above serve as Rankine-Hugoniot ‘‘shock’’ condition which indicates ‘‘interface jump’’ condition expressing energy conservation. At T = 100 ==> the energy undergoes a jump of magnitude based on heat balance term. Figure attached ==> shows how jump occurs during phase transition.

~ No separate transport equations for phase change phenomenon.

Phenomenon ==> when the wet coal is heated up, initially a part of heat is needed for the phase change of the water: so should consider this in the energy equation of the pyrolisis model maybe as additional source term - (r*Cp*delT/Delx) - r= rate of evaporation calculated based on mass balance (based on temperature only) stated above.

Someone throw light upon this problem please. Some guiding steps in OpenFOAM..?? Thank you !!
Attached Images
File Type: png Phase Changes.png (79.0 KB, 15 views)
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Old   July 30, 2019, 01:56
Default Energy balance across the liquid-gas interface
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Quote:
interface
{ type compressible::turbulentTemperature CoupledBaffleMixed;
value uniform 293;
neighbourFieldName T;
K solidThermo;
KName none; }
Using the above interface condition, the temperature supplied from the wall is converted into heat flux. With this heat flux, how the energy balance across the liquid-gas interface can be established ?
Quote:
Heat balance (-K dT/dx) = (r) * latent heat [W/m2]
Attached Images
File Type: jpg Schematic model wit explanations.JPG (148.6 KB, 17 views)
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Old   July 30, 2019, 21:51
Default Evaporation condition for liquid-vapor interface
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(i) As seen in the attached image, inside the chamber the energy equation follows, which contains the source term for evaporation as "TEMPERATURE CONVECTION" - there is no velocity and pressure in my case.
(ii) Near the interface [location (2)], by default I have prescribed the condition as "compressible::turbulenttemperatureCoupledBaffleMix ed".
But I require "EVAPORATION INTERFACE CONDITION"
Quote:
@T=100 [w(moisture content)->at high (-) temperature side =0]
@mass balance (calculated at -> low (+) temperature side)
@then heat balance is formulated at the INTERFACE
REF - Clear details here in this MANUSCRIPT ~ http://sci-hub.tw/https://doi.org/10...361(83)90225-9
Please read my above conditions and correct me if I understood something wrong.
PS: The interface (boiling plane) is located based on sign changes technique as xb- & xb+ where, xb = position of boiling plane. What technique should I need to adopt here? I'm confused here.

On the whole, I am in need of evaporation boundary condition at the interface.

Although I gone through many cases related to this study, unfortunately I'm out of ideas as how to overcome this problem. I would real appreciate if anyone could give me a hint where to look at or point me about the implementation in OpenFOAM.

Thank you Foamers.
Attached Images
File Type: jpg B.C for evaporation.JPG (157.2 KB, 26 views)
File Type: png curve for boiling - Merrick.png (38.2 KB, 13 views)
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