@TechReport{PereiraFach:2020:ShFlFo,
author = "Pereira, Lucas Soares and Fachini Filho, Fernando",
title = "Shvab-Zel’dovich and Flamelet formulations applied on quasi-steady
droplet combustion with soot formation and radiative heat
transfer",
institution = "Instituto Nacional de Pesquisas Espaciais",
year = "2020",
type = "RPQ",
address = "S{\~a}o Jos{\'e} dos Campos",
note = "{Bolsa PIBIC/INPE/CNPq.}",
keywords = "droplet combustion, Shvab-Zel’dovich, soot formation,
combust{\~a}o de got{\'{\i}}cula, Shvab-Zel’dovich,
forma{\c{c}}{\~a}o de fuligem.",
abstract = "The present work studies theoretically the quasi-steady combustion
of an isolated droplet with the formation of soot. For this, an
analysis was made on the conservation equations to determine the
characteristic spatial and temporal scales of the problem, which
were used for the nondimensionalization of those equation. The
problem has spherical symmetry, which allows for a one-dimensional
analysis of the problem. The quasi-steady combustion regime is
justified by the fact that the thermal inertia of the gas phase
close to the droplet is much less than that of the liquid phase,
so the environment adapts thermically much faster than the
droplet. The boiling temperature is considered for the whole
droplet, i.e., all heat transferred to the droplet is used for the
phase change (vaporization). It was admitted that the chemical
process occurs at the Burke-Schumann limit, thus the reaction rate
is infinitely fast which leads to infinitely thin flame. To solve
the system of governing differential equations, the
Shvab-Zeldovich formulation was used, which eliminates the
dependence of the chemical reaction term, which is non-linear.
Therefore, the mass fraction of species and the temperature field
are described by the mixture fraction, Z, and excess enthalpy, H,
equations. The boundary conditions were imposed at the surface of
the droplet and in a region far from it. To describe the formation
of soot in the problem, a simplified mathematical model was
adopted. The resulting system of second order differential
equations allow to be integrated analytically once, and the final
system of first order differential equations is integrated
numerically. The next step will be to implement a computational
code to solve the numerical integration, in addition to
implementing the heat transfer by radiation. RESUMO: O presente
trabalho estuda teoricamente a combust{\~a}o quase est{\'a}vel
de uma got{\'{\i}}cula isolada com a forma{\c{c}}{\~a}o de
fuligem. Para isso, foi feita uma an{\'a}lise das
equa{\c{c}}{\~o}es de conserva{\c{c}}{\~a}o para determinar as
escalas espaciais e temporais caracter{\'{\i}}sticas do
problema, as quais foram utilizadas para a
adimensionaliza{\c{c}}{\~a}o dessas equa{\c{c}}{\~o}es. O
problema tem simetria esf{\'e}rica, o que permite uma
an{\'a}lise unidimensional. O regime de combust{\~a}o quase
est{\'a}vel {\'e} justificado pelo fato de que a in{\'e}rcia
t{\'e}rmica da fase gasosa pr{\'o}xima {\`a} got{\'{\i}}cula
{\'e} muito menor que a da fase l{\'{\i}}quida, de modo que o
ambiente se adapta muito mais rapidamente que a got{\'{\i}}cula.
A temperatura de ebuli{\c{c}}{\~a}o foi considerada para toda a
got{\'{\i}}cula, isto {\'e}, todo o calor transferido para ela
{\'e} usado para a mudan{\c{c}}a de fase
(vaporiza{\c{c}}{\~a}o). Foi admitido que o processo
qu{\'{\i}}mico ocorre no limite de Burke-Schumann, portanto a
taxa de rea{\c{c}}{\~a}o {\'e} infinitamente r{\'a}pida, o que
leva a chamas infinitamente finas. Para resolver o sistema de
equa{\c{c}}{\~o}es diferenciais governantes, foi utilizada a
formula{\c{c}}{\~a}o de Shvab-Zeldovich, que elimina a
depend{\^e}ncia do termo de rea{\c{c}}{\~a}o qu{\'{\i}}mica,
que n{\~a}o {\'e} linear. Portanto, a fra{\c{c}}{\~a}o de
massa das esp{\'e}cies e o campo de temperatura s{\~a}o
descritos pelas equa{\c{c}}{\~o}es da fra{\c{c}}{\~a}o da
mistura, Z, e de excesso de entalpia, H. As condi{\c{c}}{\~o}es
de contorno foram impostas na superf{\'{\i}}cie da
got{\'{\i}}cula e em uma regi{\~a}o distante da mesma. Para
descrever a forma{\c{c}}{\~a}o de fuligem no problema, foi
adotado um modelo matem{\'a}tico simplificado. O sistema
resultante de equa{\c{c}}{\~o}es diferenciais de segunda ordem
permite uma integra{\c{c}}{\~a}o anal{\'{\i}}tica, e o sistema
final de equa{\c{c}}{\~o}es diferenciais de primeira ordem
{\'e} integrado numericamente. O pr{\'o}ximo passo ser{\'a}
implementar um c{\'o}digo computacional para resolver a
integra{\c{c}}{\~a}o num{\'e}rica, al{\'e}m de implementar a
transfer{\^e}ncia de calor por radia{\c{c}}{\~a}o.",
affiliation = "{Universidade Federal de Itajub{\'a} (UNIFEI)} and {Instituto
Nacional de Pesquisas Espaciais (INPE)}",
language = "en",
pages = "29",
ibi = "8JMKD3MGP3W34R/443HEF5",
url = "http://urlib.net/ibi/8JMKD3MGP3W34R/443HEF5",
targetfile = "PIBIC - Lucas Soares Pereira - Relat{\'o}rio Final....pdf",
urlaccessdate = "23 abr. 2024"
}