A CFD Study of the Combustion Stability inside a Micro-tube Combustor
C. B. Oh, B. I. Choi, Y. S. Han and M. B. Kim
171 Jang-Dong, Yuseong-Gu, Daejeon, 305-343, South Korea
Tel +82-42-868-7929, Fax +82-42-868-7355, E-mail cboh@kimm.re.kr
Energy Systems Research Center, Korea Institute of Machinery and Materials
Abstract
A computational fluid dynamic (CFD) study was performed to investigate the flame structure, stability and dynamic behavior of a
premixed flame exposed to the wall heat loss. A 3-step global reaction mechanism was adopted in this study. Simulations were
performed for two tube combustors with inner diameters (di) of 1 mm and 4 mm. The material of the tube combustor was assumed to
be a silicon nitride. The heat loss from the outer tube wall was controlled by adjusting the amount of convective and radiative heat
loss. A conical premixed flame could be stabilized inside a tube of di=4 mm. The flame stability inside a tube of di=4 mm combustor
was not much sensitive to the amount of heat loss. In case of a tube of di=1 mm, an oscillating flame was observed in low heat loss
condition and a flame could not be sustained in realistic heat loss condition.
Keywords : Micro-tube, Flame quenching, Flame stability, Heat loss effect, Computational fluid dynamics.
1 INTRODUCTION
2.1 Governing Equations
One of key issues for the integration technology of the
microelectro-mechanical system (MEMS) is the development
of micro power generation source. Because the advance of
battery technology is approaching limitations, the development
of new, micro power generation system is essential. Many
feasibility studies that focused on using a micro combustor as a
new power generating system of MEMS have been performed
during last decade [1].
A two-dimensional (2D) computational simulation code was
developed to investigate the time-dependent, axisymmetric,
premixed CH4-air flames inside a micro-tube combustor. The
geometry and the heat transfer mechanism of the tube
combustor are shown in Fig. 1. To reasonably investigate the
stabilizing mechanism of the premixed flame inside a tube, the
conduction in the solid wall and the heat transfer from the gas
phase to the wall surface were incorporated in the present
simulation code. The governing equations to be solved are
written in the following forms:
A micro-tube has the major features, related to the combustion
and the heat transfer, which many other micro-scale
combustion devices may have. Furthermore, the combustion
characteristics and the heat loss mechanisms inside a microtube combustor are very similar to those of the channel-type
combustors which have been widely used as an elementary
component of micro power generation system. Thus, an
examination of the micro-tube combustor may give useful
information on the fundamental combustion characteristics of
power MEMS based on a micro-combustion.
∂ρ
+ ∇ ⋅ ( ρu) = 0
∂t
∂ ( ρu)
+ ∇ ⋅ ( ρuu) = −∇p1
∂t
(1)
2
⎡
⎤
+ ∇ ⋅ µ ⎢(∇u) + (∇u)T − (∇ ⋅ u) I ⎥
3
⎣
⎦
To date, experimental methods for the micro-scale combustion
have not been established firmly and computational approaches
are believed to be a useful tool to investigate the phenomenon
occurs in a micro-scale combustor.
∂ ( ρYi )
+ ∇ ⋅ ( ρuYi ) =
∂t
∇ ⋅ ( ρDim ∇Yi ) + Wiω& i , (i = 1, 2, ⋅ ⋅ ⋅, N )
Thus, in this study, unsteady simulations were performed to
investigate the detailed, unsteady flame stabilization and heat
loss mechanisms. For simplicity, a finite, global reaction model,
which can consider the chemical reaction of CH4-air premixed
flame, was adopted in this study.
ρc p ⎜
(2)
(3)
⎞
⎛ ∂T
+ u ⋅ ∇T ⎟ = ∇ ⋅ ( λ ∇ T )
t
∂
⎠
⎝
N
−
∑
i =1
2 SIMULATION METHODS
136
N
Wi hi0ω& i + ρ
∑ (c
i =1
pi Dim ∇Yi
)
⋅ ∇T + q& r
(4)
Table 1. Dimensions of combustor and simulation domain and
grid system for the simulation.
Fig. 1 Schematic of micro-tube combustor and heat loss
mechanism from combustor.
⎛ ∂T ⎞
ρ wc pw ⎜⎜ w ⎟⎟ = ∇ ⋅ (λw∇Tw )
⎝ ∂t ⎠
N
p0 = ρR0T
⎛ Yi ⎞
∑ ⎜⎜⎝ W ⎟⎟⎠
i =1
Inner diameter (di)
Wall thickness (Lt)
Simulation Domain
(x × r)
Grid Number
(Non-uniform grids)
Combustor 1
1mm
0.4mm
Combustor 2
4mm
1.6mm
10mm × 0.9mm
25mm × 3.6mm
180 × 18
(8 for the wall)
210 × 71
(20 for the wall)
Minimum grid spacing
in x and r direction
0.03mm
0.04mm
heat transfer coefficient and the emissivity in the following
equation (7).
q w, o = h(Tw − T∞ ) + εσ (Tw4 − T∞4 )
(7)
where, T∞ is the ambient temperature, which is fixed to 298
K. In the simulations, unless otherwise given, the convective
heat transfer coefficient is fixed to 20 W/m2K, which is similar
to the value obtained in micro combustor experiment [5].
(5)
(6)
i
where, p0 and p1 represent the thermodynamic and
hydrodynamic pressures, respectively; u is the velocity vector;
T is the gas temperature; Tw is the solid wall temperature; ρ is
the gas density; ρw is the solid wall density; R0 is the universal
gas constant; cpw is the specific heat of solid wall; and Yi, hio,
ω& i , and cpi are the mass fraction, heat of formation, production
rate, and specific heat of species i, respectively. In addition, Dim,
are the the mixture-averaged diffusion coefficients; λ and λw
denote the thermal conductivity of gas and solid wall,
respectively. The Soret and the Dufour effects and the
gravitational force are neglected in this study. In the governing
equations, the thermodynamic and transport properties are
calculated using the CHEMKIN-II [2] and the TRANFIT [3]
packages, respectively.
2.3 Reaction Mechanism
Considering the simulation cost for the parametric study, a 3step global reaction mechanism [6] is used to predict the
chemical reaction of CH4-air premixed flame. 6 species, CH4,
CO2, CO, H2O, O2, and N2, are considered in the reaction
mechanism:
CH 4 + 1.5O2 → CO + 2 H 2O
(8)
CO + 0.5O2 → CO2
(9)
CO2 → CO + 0.5O2
(10)
In preliminary test, the reaction mechanism was validated by
the comparison with the laminar burning velocity using the
PREMIX code [7] in the range of Φ =0.6~1.0.
3 RESULTS AND DISCUSSION
2.2 Simulation Scheme and Boundary Conditions
A predictor-corrector scheme is used for time integration of the
governing equations. An efficient algebraic relaxation for the
velocity-pressure correction is performed using the HSMAC
method. The detailed numerical scheme can be found in
elsewhere [4].
Fig. 2 shows the steady-state distributions of the heat release
rate (HRR) and the flame temperature for the case of di=4 mm
combustor. The upper half part of the combustor inside denotes
the HRR and the other lower half part denotes the flame
temperature. The solid wall temperature is also plotted in the
figure. The coefficients related to the heat loss condition on the
outer solid wall are h=20 W/m2K and ε =0.9. If the solid wall
is not heated up by an external heat sources, a premixed flame
cannot be stabilized inside a tube combustor. Thus, the solid
wall temperature was assumed to 1,300 K initially so that the
premixed flame was well stabilized inside the tube combustor.
This implies that the heating to the solid wall at initial ignition
stage is essential to stabilize a premixed flame inside a tube.
Fig. 2 shows a typical, conical, premixed flame shape stabilized
inside a tube. Although not shown here, it was identified that
the premixed flame shapes and stabilities inside a tube
combustor of di=4 mm are not much sensitive to the heat loss
condition where ε is in the range of 0~0.9. The emissivity of
silicon nitride, which is combustor material in this work, was
known as 0.8~0.9 [8]. Thus, above result implies that in
Simulations are performed for the tube combustors with inner
diameters (di) of 4 and 1 mm. Each combustor wall thickness
(Lt) is determined so that Lt/di should be 0.4. The combustor
material is assumed as a silicon nitride (Si3N4) because its
melting point is very high. The dimensions of each combustor
and grid system are described in Table. 1.
The reactant is CH4-air mixture with an equivalence ratio ( Φ )
of 1.0. The inflow velocity is fixed to 0.5 m/s for each
simulation. The first-order extrapolation is used as an outflow
boundary condition and the no-slip condition is enforced on the
inner solid wall of the combustor. No-mass flux condition for
the species equations is given at all wall boundaries. The heat
flux incoming into the inner solid wall is set to be the same as
the outgoing heat flux from the gas phase. The heat loss from
the outer solid wall is adjusted by controlling the convective
137
976
1267
1558
1849
2140
3.9E+09
5.5E+09
7.2E+09
8.9E+09
1.1E+10
T1D
2400
1.0E+010
2100
2
1
3
4
5
6
Temperature (K)
3
r (mm)
2
1
0
6.0E+009
1200
300
0
0.0
x (mm)
10
932
651
1213
1775
1494
2
1
5
-0.5
2
4
x (mm)
6.0
6
8.0
x (mm)
10.0
12.0
14.0
1.6E+010
T1D
1.4E+010
2100
6
0
0
4.0
2400
Temperature (K)
3 2 1
0.5
4
0.0E+000
2.0
2700
2056
HRR
3
(J/m s) 5.5E+08 2.2E+09 3.9E+09 5.5E+09 7.2E+09 8.9E+09 1.1E+10
3
2.0E+009
Tube (2D)
Flat (1D)
Fig. 4 Heat release rate and flame temperature at the
centerline and inner wall temperature for the case
of di=4mm tube combustor (h=20 W/m2K, ε =0.9).
Tw (K) 1 : 820, 2 : 812, 3 : 797, 4 : 781, 5 : 766, 6 : 751
370
4.0E+009
HRR
15
Fig. 2 Heat release rate, flame temperature and wall temperature for the case of di=4mm tube combustor (h=20 W/m2K,
ε =0.9).
T (K)
Tw, inner
900
-2
5
8.0E+009
1500
600
0
r (mm)
1800
-1
-3
Heat loss ef f ect
T
Heat Release Rate, HRR (J/m3s)
1.2E+010
2700
686
2.2E+09
395
8
1.2E+010
Heat loss ef f ect
T
1800
1.0E+010
1500
8.0E+009
Tw, inner
1200
900
6.0E+009
HRR
Tube (2D)
Flat (1D)
Tw (K) 1 : 1538, 2 : 1535, 3 : 1532, 4 : 1528, 5 : 1526, 6 : 1521
4.0E+009
600
Fig. 3 Heat release rate, flame temperature and wall temperature for the case of di=1mm tube combustor (h=2 W/m2K,
ε =0).
300
0.0
2.0E+009
1.0
2.0
3.0
4.0
5.0
x (mm)
6.0
7.0
Heat Release Rate, HRR (J/m3s)
T (K)
HRR
3
(J/m s) 5.5E+08
0.0E+000
8.0
Fig. 5 Heat release rate and flame temperature at the
centerline and inner wall temperature for the case
of di=1mm tube combustor (h=2 W/m2K, ε =0).
realistic heat loss condition, a CH4-air premixed flame can be
sufficiently stabilized inside a tube combustor di=4 mm.
Fig. 3 shows the HRR and the flame temperature for the case of
di=1 mm combustor. In this case, the emissivity was fixed to 0
since a stable flame could not exist inside a tube for the range
of ε >0. In this figure, the coefficients related to the heat loss
condition on the outer solid wall are h=2 W/m2K and ε =0. In
this case, the flame shape is flat and the high-temperature
region, located immediate downstream of the flame surface, is
very narrow although the premixed flame can be stabilized
inside the tube. Through parametric studies where the heat loss
condition was varied, an oscillating premixed flame was
observed in slightly larger heat loss condition (h=20 W/m2K
and ε =0) than that of Fig. 3. However, it was also found that
in realistic heat loss condition, a CH4-air premixed flame
cannot be stabilized inside a tube combustor of di=1 mm since
no flame can be observed at ε >0.
temperature decrease is much steeper than the case of di=4 mm
as increasing axial distance. For wall temperature, it can be
seen that the wall temperature in a combustor of di=1 mm is
much higher than the case of di=4 mm. The high wall
temperature in the upstream region near tube inlet is attributed
to the heat conduction through the combustor solid wall from
the downstream, hot product gas. The high temperature region
of solid wall near the inlet contributes to the stabilizing of the
premixed flame. Thus, it can be noted that the heat conduction
through the combustor solid wall should be essentially
considered in simulating the premixed flame stability inside a
tube combustor.
Fig. 6 shows the temporal variation of the maximum
temperature at the centerline for the oscillating case of di= 1mm.
A premixed flame is stabilized initially near the tube inlet when
the inflowing mixture was ignited. The initial solid wall
temperature is high in comparison with real wall temperature
under a normal operating condition because the solid wall was
initially heated up to 1,300 K. However, the solid wall
temperature gradually decreases as the heat loss condition on
the outer combustor wall approaches a normal condition
determined by the balance between the chemical heat
generation and the heat loss from the combustor. The stabilized
premixed flame suddenly starts to oscillate back and forth when
the amount of heat loss exceeds a certain critical value. At
initial stage of oscillation, the amplitude of temperature is small
and the oscillating frequency is high (~ 1 kHz). However, the
amplitude of temperature gradually increases and the frequency
decreases after this, and the oscillating premixed flame reaches
a quasi-steady-state condition where the amplitude and
frequency are nearly constant. The result of Fig. 6 shows the
temperature variation in the quasi-steady-state condition. At
Figs. 4 and 5 show the HRR and temperature profiles at the
centerline of tube combustors of di=4 and 1 mm. The HRR and
temperature profiles obtained from 1D simulation are also
plotted. The 1D simulation results represent a flat premixed
flame which is not affected by a heat loss. Thus, the difference
between the 2D and 1D results implies the heat loss effects on
the flame structure. The coordinate of 1D result was adjusted so
that the peak HRR location of 1D flame coincided with that of
2D tube flame. In Fig. 4, the HRR profile and the value of peak
temperature of 2D tube flame of di=4 mm are very similar to
those of 1D flat flame. However, the temperature of 2D tube
flame decreases due to heat loss effects as increasing axial
distance while 1D flat flame keeps its temperature nearly
constant. These heat loss effects are more significant in a
combustor of di=1 mm because the ratio of the surface area to
the volume of combustor increases as decreasing the inner
diameter of tube combustor. The peak temperature of 2D tube
flame is lower than that of 1D flame and the trend of the
138
Tw (K)
3000
1210
HRR
(J/m3s) 6.0E+08
1218
1226
1234
1246
1.1E+10
2.2E+10
3.3E+10
4.3E+10
2800
0.5
r (mm)
2600
2400
(a)
0
-0.5
2200
0
2
2000
1800
4
x (mm)
6
8
0.5
r (mm)
Max. Temperature at the Centerline (K)
3200
1600
(b)
0
-0.5
1400
1200
0
1000
0.700 0.705 0.710 0.715 0.720 0.725 0.730 0.735 0.740
2
4
x (mm)
6
8
r (mm)
0.5
Time (s)
(c)
0
-0.5
Fig. 6 Temporal variation in the maximum temperature
at the centerline of di=1mm tube combustor (h=20W/m2K,
ε=0).
0
2
4
x (mm)
6
8
r (mm)
0.5
(d)
0
-0.5
this condition, the frequency is around 350 Hz and the
maximum and the minimum temperatures are 1,250 K and
2,920 K, respectively.
0
2
4
x (mm)
6
8
r (mm)
0.5
Fig. 7 shows the sequential HRR distribution of periodically
oscillating premixed flame and the solid wall temperature. As
described earlier, a premixed flame is extinguished when the
amount of heat loss exceeds a certain critical value. The
unburned reactant mixture flows downstream by the convection
and re-ignited near the hot solid wall. This ignited premixed
flame propagates rapidly upstream and is extinguished again
near the tube inlet because the cold reactants are introduced
into the flame front. The periodic behavior of the premixed
flame inside a tube combustor is attributed to these sequential
phenomena. Although not shown here, this periodically
oscillating flame behavior could be well understood using the
plot of the sequential temperature distribution inside a tube
combustor.
(e)
0
-0.5
0
2
4
x (mm)
6
8
Fig. 7 Oscillating heat release rate and wall temperature of
di=1mm tube combustor (h=20 W/m2K, ε=0). (a)0 ms, (b)
0.15 ms, (c)0.4 ms, (d)0.6 ms, (e) 0.8 ms.
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Miller, J. A., 1986, “A Fortran Computer Code Package for the
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The flame stability inside a tube combustor depends on fuel
type, material and geometry of combustor, and combustion
condition, such as equivalence ratio and velocity etc. As future
works, CFD and experimental studies considering above
parameters will be performed to obtain basic information
needed in the design of a micro-combustor.
4 CONCLUSIONS
A computational fluid dynamic study, which considers a finite
chemistry and the conduction in a solid wall, was performed to
investigate the fundamentals of combustion stability inside a
micro-tube combustor.
The result showed that a conical premixed flame could be
stabilized inside a tube of di=4 mm. The flame stability and the
flame structure inside a tube of di=4 mm were not much
sensitive to the amount of heat loss from the combustor. In case
of a tube of di=1 mm, a premixed flame could be stabilized
only in very low heat loss condition (h=2 W/m2K and ε =0),
and an oscillating flame was observed in low heat loss
condition (h=20 W/m2K and ε =0) and a flame could not be
sustained in realistic heat loss condition of ε >0. As the
diameter of tube combustor decreases, special adiabatic
treatments are needed to stabilized a CH4-air premixed flame
inside a micro-tube combustor.
139