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Combustion and direct energy conversion inside a micro-combustor
Accepted Manuscript Title: Combustion and direct energy conversion inside a micro-combustor Author: Yafeng Lei, Wei Chen, Jiang Lei PII: DOI: Reference:
S1359-4311(16)30116-8 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.162 ATE 7725
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
18-9-2015 31-1-2016
Please cite this article as: Yafeng Lei, Wei Chen, Jiang Lei, Combustion and direct energy conversion inside a micro-combustor, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.162. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Combustion and Direct Energy Conversion inside a Micro-Combustor Yafeng Lei1, Wei Chen2, Jiang Lei3 1
General Electrical Company, Houston 77041, Texas, USA
6 7 8 9 10
2
3
School of Aerospace, Xi’an Jiaotong University, Xi’an, Shanxi, 710049, China
11
2
Author Correspondence:
12
Professor: Wei Chen
13
China University of Mining and Technology
14
Xuzhou, Jiangsu 221008, China
15 16 17 18 19 20 21 22 23 24 25
[email protected]
26
Abstract
27
Electrical energy can be generated by employing a micro-thermophotovoltaic (TPV) cell
28
which absorbs thermal radiation from combustion taking place in a micro-combustor. The
29
stability of combustion in a micro-combustor is essential for operating a micro-power system
30
using hydrogen and hydrocarbon fuels as energy source. To understand the mechanism of
School of Electric power Engineering, China University of Mining and Technology, Xuzhou 221008, China
Highlights
The flammability range of micro-combustor was broadened with heat recirculation The quenching diameter decreased with heat recirculation compared to without recirculation The surface areas to volume ratio was the most important parameter affecting the energy conversion efficiency The maximum conversion efficiency (3.15%) was achieved with 1 mm inner diameter
1
Page 1 of 28
31
sustaining combustion within the quenching distance of fuel, this study proposed an annular
32
micro combustion tube with recirculation of exhaust heat. To explore the feasibility of
33
combustion in the micro annular tube, the parameters influencing the combustion namely,
34
quenching diameter, and flammability were studied through numerical simulation. The results
35
indicated that combustion could be realized in micro- combustor using heat recirculation.
36
Following results were obtained from simulation. The quenching diameter reduced from 1.3
37
mm to 0.9 mm for heat recirculation at equivalence ratio of 1; the lean flammability was
38
2.5%-5% lower than that of without heat recirculation for quenching diameters between 2
39
mm to 5 mm. The overall energy conversion efficiency varied at different inner diameters. A
40
maximum efficiency of 3.15% was achieved at an inner diameter of 1 mm. The studies
41
indicated that heat recirculation is an effective strategy to maintain combustion and to
42
improve combustion limits in micro-scale system
43 44
Keywords: Micro-combustor; Equivalence ratio; Flammability, Quenching diameter;
45
Quenching cross sectional area; Energy conversion efficiency
46 47 48
Nomenclature C
Tube perimeter (m)
d
Tube diameter (mm)
49
D
Diffusion coefficient (m2/s)
E
Total energy (kJ)
50
hc
Lower heating value (kJ/kmole)
hH
51
L
Tube length (mm)
T
52
Tout
Gas temperature in counter flow (K)
53
w F
Chemical reaction rate (kmole/m3∙s)
u
2
Heat transfer coefficient (kW/m2∙K) Gas temperature (K) Velocity (m/s) Dynamic viscosity (Pa∙s)
Page 2 of 28
54
Kinematic viscosity (m2/s)
55
cP
Specific heat (kJ/kg∙K)
56
Thermal conductivity (kW/m∙K)
Efficiency
Fluid density (kg/m3)
Equivalence ratio
57
LFL
Lean flammability limit
MEMS Micro-electromechanical system
58
MIT
Massachusetts Institute of Technology
TPV
59
TE
Thermoelectric
Thermophotovoltaic
60 61
1. Introduction
62
The micro-electromechanical systems (MEMS) experienced growing interest during the
63
past few years. The combustion of hydrogen or hydrocarbon fuels such as methane in MEMS
64
to produce electrical power has several advantages over the batteries because of high specific
65
energy of liquid fuels. The specific energy of liquid hydrocarbons is 35 to 300 times higher
66
than that of batteries built on latest technology [1]. For example, the specific energy of
67
methane is 50 MJ/kg whereas for an alkaline battery it is only 0.6 MJ/kg [1]. Thus, the direct
68
conversion from chemical to electrical energy even at 10% efficiency is attractive.
69
The hydrocarbon fuel based MEMS were found promising for application in micro
70
combustion. The MIT gas turbine laboratory developed MEMS based on gas turbine power
71
generator with an approximate total volume of 300 mm3 to produce 10~20 W of electric
72
power [2]. At the Combustion laboratories of UC Berkeley, research was conducted to
73
develop a liquid hydrocarbon fueled internal combustion rotary engine on millimeter scale [3].
74
A centimeter magnitude thermoelectric (TE) power generator integrated with plat-flame
75
micro combustor system was developed by Jiang et al. [4]. The maximum power output
3
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76
reached was 2 W, and the maximum overall chemical-electrical energy conversion efficiency
77
was 1.25% [4]. In addition to electric power generation, a micro-combustor was employed to
78
recirculate heat to produce hydrogen from ammonia [5]. Also, a thin-film-coated combustor
79
and a packed-bed combustor were designed and fabricated to operate as a heat source for a
80
methanol micro-reformer [6].
81
Even though the micro-power systems hold promise, the primary issue in them is
82
obtaining sustainable combustion in a micro-combustor. As the combustor size decreases, the
83
surface area to volume ratio increases. Because of the high surface area to volume ratio for
84
micro-combustor, there is a high amount of heat loss (proportional to area) compared to heat
85
energy generated (proportional to volume). Thus, the quenching and flammability problems
86
are more critical in a micro-scale combustor. On the other hand, the high surface area to
87
volume ratio characteristic of the micro combustor is most suitable for TPV systems. The
88
TPV system consists of three main parts: a heat source (combustor), a selective emitter, and a
89
photovoltaic array. The photovoltaic array converts the heat radiation absorbed from
90
combustion to electricity. Thus s smaller system will have higher energy conversion
91
efficiency due to its relatively larger surface area to volume ratio as long as the combustion is
92
sustainable. To maintain an optimal balance between the sustainable combustion and
93
maximum heat output is the main issue for micro TPV system.
94
The above concern necessitates innovative schemes to improve the performance of
95
micro-combustor. Several energy management methods including external heating,
96
backward-facing step, catalyzed combustion, and heat recirculation were employed to
97
improve the combustion in the MEMS[7]. The gas flow rates, equivalence ratio, and wall
4
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98
material are the main parameters which affect the combustion characteristics and heat loss in
99
a micro-combustor. Li et al. found that maximum heat was released when equivalence ratio
100
was slightly greater than one (and stainless steel wall resulted in more heat loss than ceramic
101
wall) [8]. Leach et al. investigated the effect of structural heat exchange and heat loss on the
102
power density and flame stability in order to optimize the design of silicon micro-combustors
103
[9]. Moreover, the geometry of combustor also has an important role in the flame stability.
104
Zhong et al. conducted experiments on micro Swiss-roll combustors with premixed CH4/air
105
mixture [10]. The combustion stability in the central regions of the combustors was enhanced
106
and the extinction limits of methane/air mixtures were significantly extended [10]. Li et al.
107
used backward-facing step in the combustor to effectively stabilize the flame position [11].
108
Fan et al. found that a triangular and semicircular bluff bodies significantly increased blow-
109
off limit of hydrogen/air flame in a planar micro-combustor [12]. Yang et al. investigated the
110
effect of wall thickness on the performance of three micro-cylindrical SiC combustors and
111
found that wall thickness of 0.4 mm gave maximum power output from micro-
112
thermophotovoltaic power generator [13].
113
Li et al. used porous medium in a 1 mm planar micro-combustor to enhance the flame
114
stability which included flame flashback, blow-off, and heat transfer [7]. Recently, catalysts
115
were employed to improve the combustion and heat transfer in a micro-combustor. Wang et
116
al. found that catalyst can effectively inhibit extinction and actively promote air-hydrogen
117
lean mixture reaction in the combustor [14]. In order to improve the efficiency and
118
performance of mico-combustors, the exhaust gas was recirculated to heat the outer wall of
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119
the micro-combustor and the incoming cold reactants. As result, the mean wall temperature,
120
total radiation energy emitted and useful radiation energy were improved [15].
121
In addition to experimental studies, extensive numerical simulations were developed by
122
various investigators to evaluate the combustion and heat transfer performance of the micro-
123
combustor. The flame stability in different numerical models was studied at different
124
Reynolds and swirl numbers for MEMS [16, 17]. Fanaee et al. used a two-dimensional model
125
to investigate the effects of reaction zone thickness, maximum temperature and quenching
126
distance on combustion phenomenon in micro-combustors under catalytic and non-catalytic
127
conditions and obtained acceptable agreement between the analytical and experimental data
128
[18]. Pan et al. investigated the effects of porous media, hydrogen to oxygen equivalence ratio,
129
porosity and fuel mixture flow rates on the performance of the micro-combustor [19]. Li et al.
130
found that in 1D cylindrical micro-combustor model hydrogen was superior to methane and
131
propane as a fuel owing to its higher flame temperature and lower flame thickness. [20]. Tang
132
et al. conducted studies on premixed hydrogen/air combustion in 3D model of a micro planar
133
combustor and found enhancement in heat transfer and increase in mean temperature of the
134
radiation wall by inserting plates in the micro-combustor chamber [21].
135
The effect of cross-sectional geometry on the ignition/extinction behavior of catalytic micro-
136
combustors using CFD models was studied by Benedetto [22]. He found that square cross-
137
section channel was more resistant to extinction compared to circular channel [22]. Moreover,
138
heat recirculation from the post-flame to the pre-flame in a micro combustor improved the
139
flame stabilization and enhanced burning rate on a 2D mode [23].
6
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140
The objective of this work is to develop a one-dimensional numerical model using
141
FORTRAN code to explore the feasibility of CH4/air combustion in a micro-combustor
142
(straight tube combustor with heat recirculation) and investigate on its application to TPV
143
power system. The effect of heat recirculation of a micro-scale counter flow combustor on the
144
lean flammability, quenching diameter, and overall energy conversion efficiency were
145
investigated in this study.
146 147 148
2. Numerical Modeling and Its Formulation 2.1 Physical Model of the Micro-combustor
149
Figure 1 illustrates the physical model of the micro combustor used in this study. It
150
includes a combustion tube made of carbon steel with inner diameter varying from 1 mm to 3
151
mm and a concentric outer tube of same material which served as a counter flow heat
152
exchanger. The incoming cold mixture in the inner tube was preheated by the hot combustion
153
gases in the outer tube resulting in reduction of the chemical reaction time and helping
154
complete combustion. For a micro-size combustor, the reduced diffusion time resulting from
155
small size has a crucial effect on making the concentration distributions uniform near the
156
flame in the combustor. In addition, the laminar flow prevented rapid mixing between fuel
157
and air due to the low mass and heat transfer coefficients in the combustor. Therefore, a
158
premixed combustion instead of diffusion combustion was assumed in this study. The flame
159
propagation in the current model is two-dimensional in nature. However, if interest is limited
160
to micro-scale burners with tube diameter and wall thickness much smaller than the tube
161
length, the problem could be simplified to one-dimensional. This study assumed one
162
dimensional laminar plug flow in the model.
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163
The baseline micro-combustor configuration consisted of two annular tubes with an inner
164
tube of 3 mm in diameter and 30 mm in length and an outer tube of 4.2 mm in diameter and
165
30 mm in length. Cold premixed fuel mixture which passes through inner tube will be ignited
166
by hot gases in outer tube. In the mean time the heat radiation from high temperature outer
167
tube wall will reach TPV system and be converted to electricity.
168
2.2 Heat Transfer:
169 170
The Nusselt number Nu for the inner tube was determined by using the following empirical correlation for constant wall temperature [24] Nu
h in n e r d i k
171
4 .3 6 4 B i 1 0 .2 6 8 2 B i
(1)
172
In the above relationship, hinner is the convective heat transfer coefficient, di is the diameter of
173
inner tube, k is the thermal conductivity of the fluid, and Bi is the Biot number of the micro-
174
tube. The dimensionless Bi characterizes the heat transfer resistance "inside" a solid body and
175
it was defined as: Bi
176
h Lc
(2)
k
177
Where LC is characteristic length, which is commonly defined as the volume of the
178
body． This empirical correlation is applicable to the forced convection laminar flow in
179
circular duct. The Biot number is 0.006 for steel tube of dimensions shown in Figure 1.
180
Figure 2 shows the heat transfer model for the micro-combustor proposed. The convective
181
heat transfer coefficient at the outer surface of inner tube is denoted as houter,i. Heat is
182
dissipated via radiation from the outer surface of outer tube with heat transfer coefficient
183
houter,o. The Bi number
in
equation１is close to zero as the micro-combustor is small
8
Page 8 of 28
184
enough. This corresponds to a heat transfer coefficient of 111 W/m2.k [24]. For outer tube
185
section with associated hydraulic diameter dh （the different between outer diameter do and
186
inner diameter di）, the outer surface Nu is 5.38 and the inner surface Nu is 4.602 for limited
187
wall condition and Nu is 4.364 for the inner tube[25]. The estimation of heat transfer
188
coefficient is very coarse in the current model. In practice, the heat transfer coefficient can be
189
enhanced for rough and grooved wall. In this model, to be simple, it was assumed a constant
190
convective heat transfer coefficient for both inner and outer tubes (e.g., hH.outerr,o=
191
hH.inner,o=hH.inner,i=111 w/m2.K).
192 193 194 195
2.3 Combustion Methane consumption rate during combustion can be expressed by Eq.(3) [26]: w F A T P n
m
exp(
E
a
)[C H 4 ] [O 2 ]
RT
b
(3)
196
Where a=0.3, b=1.3, n=0, and m=0; A is the pre-exponential factor which is dimensionless
197
and equals to 1.3x109 here. P is pressure, E is activation energy and E=202,408 kJ/kmole, R is
198
universal gas constant, and
199
kmol/m3 , respectively.
200
Fuel and oxygen mass conservation equations were established as follow:
201
[C H 4 ]
u
and
[O 2 ]
2
dyF
D
d yF
dx
202
u
dyO dx
are concentration of CH4 and O2 with the unit of
dx
w F
2
(4)
2
2
D
d yO dx
2
2
w O
2
9
(5)
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203
In the above relationships, is the gas density, u is the velocity, D is diffusion coefficient,
204
and yF is fuel mass fraction and yO2 is the oxygen mass fraction in air-fuel mixture.
205
At the entrance to the combustor, where x=0, yF=yF.0, yO2=yO2.0, and T=T0.
206
The Eqs. (4) and (5) can be combined and written in terms of Schvab-Zeldovich variable as
207
shown by Eq.(6): u
d 2
D
dx
208 209
d
dx
2
(6)
In the above relationship,
o2 F
yF
210 o 2
yo
2
o2
2 k m o le O 2 k m o le C H
211
and
212
Based on the assumptions listed above, the fluid flow field was divided into a finite number
213
of small control volumes as illustrated in Figure 3. The first law of thermodynamics as shown
214
by Eq.(7) was applied to each control volume:
215
dE dt
4
Q W m i h to t , i m e h to t , e
Q
(7)
Where, E is the total energy of the fuel,
217
inlet and outlet mass flow rate, respectively, and
218
enthalpy of formation, and
219
fueled with diesel and natural gas was conducted by Gümüş et al[27].
h
is heat transfer rate,
W
216
h to t h f h
is work,
mi
and
is the total enthalpy,
mi
hf
are
is
is thermal enthalpy. Similar energy analysis for a CI engine
10
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220
The equations (8) and (9) express the combined combustion and heat transfer processes in the
221
inner and outer tubes respectively: u c p Ai
222 223 224 225 226
u c p Ao
dT dx
dT dx
2
Ai
d T dx
2
h H C i ( T g , o T ) w F h c A i
(8)
2
Ao
d T dx
2
h H C i ( T g , i T ) h H , o u te r , o C o ( T w ,1 T ) w F h c A o
(9)
The Eq. (10) can be obtained by combining the equations (4) and (8). u
227
d
d 2
D
dx
dx
2
hH C i hc Ai
(T g , o T )
(10)
228
Where T is the temperature, cp is the specific heat of gas species, Ai cross area of the inner
229
tube, Ao is the cross area of outer tube, and
h
t F
ht hc
yF
where
ht c pT
230
The Eq. (9) was used to determine the temperatures of gas and outer surface of the wall which
231
served as a selective emitter. For a photovoltaic array made of low band gap material such as
232
GaSb (gallium antimony), the efficiency of heat radiation to electrical energy transfer was
233
determined by Planck’s radiation law.
234
2.4 TPV System Modeling
235
Figure 4 illustrates a typical TPV system using a combustion heat radiation source. The
236
micro-TPV
system
consists
of
two
main
237
thermophotovoltaic convertor. Fuels combust in the micro-combustor and electricity will be
238
generated through photovoltaic cells by absorbing heat radiation from combustor. To
239
determine the spectrum emissivity, the wall temperatures along the outer surface of outer tube
240
need to be calculated. The black body hemispherical spectral emissive power is given by
241
Planck’s radiation law as shown by Eq.(11) [28].
11
components:
micro-combustor
and
Page 11 of 28
E b
242
C 1 e
5
C 2 /( T )
1
W/m3
(11)
243
Where λ is the wavelength, C
244
The range of spectrum from which a photon can be converted into electricity depends on the
245
type of TPV cells. In this study, GaSb cells were used as photovoltaic converter for which the
246
band gap was 0.72 eV. This implies that only photons emitted from a heat radiation source
247
with a wavelength smaller than 1.7 μm can generate electricity from the GaSb cells.
248 249 250
3. Results and Discussion
251
velocity and heat transfer coefficient on combustion performance in a micro-combustor were
252
studied. To better understand the effect of heat recirculation, the quenching diameters and
253
lean limits for combustion were compared with and without heat recirculation. The base case
254
conditions and sensitivity analysis parameters for this study are given in appendix A.
255
3.1 Quenching Diameter
256
3.1.1 Effect of Equivalence Ratio on Quenching Diameter
257
In this study, the equivalence ratio was defined as:
258
1
3 .7 4 2 1 0
16
W m
2
,C
2
2
1 .4 3 8 8 1 0 m K
In this investigation, the influence of equivalence ratio, inner diameter, fuel inlet
ER
s to ic h io m e tr ic a ir m o le s p e r m o le e m p itic a l fu e l a c tu a l a ir m o le s p e r m o le e m p itic a l fu e l
A F s to ic h i A F a c tu a l
F A a c tu a l F A s to ic h i
(12)
259
Figure 5 shows the variation of quenching diameter with respect to equivalence ratio (ER) for
260
CH4/air mixture with and without heat recirculation for the base case conditions. The model
261
without heat circulation is just a straight tube that has the same diameter as the inner tube of
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262
the model with heat circulation. With heat recirculation, the quenching diameter decreased,
263
especially at low values of equivalence ratio, which means that heat recirculation can help
264
combustion to sustain in micro-combustor at smaller scale. When the combustor scales down,
265
the surface area to volume ratio increases and the circulating heat compensates for part of the
266
heat lost to the environment resulting in the combustion to sustain inside the inner tube. The
267
stoichiometric calculations of premixed CH4/air combustion indicated that the diameter can
268
be as small as 0.9 mm for a combustor with heat recirculation whereas the minimum
269
diameter was 1.3 mm for combustor without heat recirculation.
270 271
3.1.2 Effect of Mixture Inlet Velocity on Quenching Diameter
272
The fundamental time constraint can be quantified in terms of a homogeneous
273
Damkohler number, which is the ratio of the residence time and characteristic chemical
274
reaction time [29] as shown by Eq. (13):
275
D ah
r e s id e n c e
(13)
c h e m ic a l
276
To maintain stable combustion inside the tube, more fuel residence time than chemical
277
reaction time is necessary to have the Damkohler number greater than 1. The residence time
278
τresidence is defined as:
279 280 281 282
r e s id e n c e
L
(14)
v
Where L is the length of the combustor and v is the gas velocity. For a micro-combustion tube, the residence time is very small due to relatively high flow velocity and short tube length. The chemical reaction time has an inverse relationship with
13
Page 13 of 28
283
combustion temperature. In the current model, the heat transfer from outer tube to inner tube
284
increased reactants temperature and hence decreased chemical reaction time. Higher fuel inlet
285
velocity would increase power output, but a very high inlet velocity requires a larger tube
286
diameter to sustain combustion inside the tube. Figure 6 illustrates the relationship between
287
air/fuel inlet velocity and quenching diameter with heat circulation.. With heat recirculation,
288
the mixture could be burnt in micro combustor at mean flow velocities four to six times
289
higher than the stoichiometric laminar burn velocity (.40~.50 m/s). From Figure 6, for
290
velocities less than 2m/s, increasing velocity would increase fuel consumption rate and lead
291
to a decreased quenching diameter. For velocities higher than 2 m/s, the flame advanced
292
towards the end of inner tube due to the decreased residence time. This caused reduction of
293
chemical energy release, and hence required a larger quenching diameter to sustain the
294
combustion. The high velocity extinction limit was certainly caused by insufficient residence
295
time rather than the chemical reaction completion time.
296
At a fixed tube diameter, either extremely high or low Reynolds number (e.g., inlet velocity)
297
would lead to quenching. This is due to the fact that the mixture at low Reynolds number has
298
less amount of heat energy to sustain the combustion, and mixture at high Reynolds number
299
leads to insufficient residence time compared to the time required to complete the combustion
300
reactions. The calculations show that the Reynolds number as low as 53 can sustain
301
combustion with heat recirculation at tube diameter of 2 mm and the energy input of 10 W.
302
For a fixed tube of diameter of 3 mm, the maximum heat input is 70 W and corresponding
303
Reynolds number is 930.
304
3.2 Lean Flammability Limit
14
Page 14 of 28
305
When the equivalence ratio decreased from base case value of 0.83 to a value called lean
306
flammability limit (LFL), the flame failed from being stabilized. It is reasonable to expect
307
that the limits of flammability would be widened if preheating of inlet mixture by heat
308
recirculation is available. Figure 7 shows the lean flammability of micro combustor with and
309
without heat recirculation at different inner tube diameters and with inlet air/fuel mixture
310
velocity of 1 m/s. Both LFL for cases with and without heat circulation decreased along with
311
increased diameter. The LFL with heat circulation was 2.5%-5% lower than that of without
312
heat circulation for tube diameters between 2 mm and 5 mm. It indicates that heat
313
recirculation can enhance combustion at lower equivalence ratio. Similar results were
314
reported by Veeraragavan et al. [23]. Heat recirculation was found as the governing
315
parameter in enhancing the flame temperature and speed [23].
316
3.3 Overall Energy Conversion Efficiency
317
3.3.1 The Effect of Heat Transfer Coefficient
318
For tmicro-combustion-TVP system, the conversion of thermal energy into electrical
319
energy is obtained through the thermophotovoltaic cells which cover the outer surface of
320
micro-combustor to absorb heat radiation. The overall energy conversion efficiency is defined
321
as following:
322 323
con
e le c tr ic ity g e n e r a te d
(15)
c h e m ic a l e n e r g y in p u t
324
The effect of heat transfer coefficient on conversion efficient has been studied. Figure 8
325
illustrates the variation of overall energy conversion efficiency ηcon with respect to heat
326
transfer coefficient for base case combustion with heat recirculation. Higher heat transfer
15
Page 15 of 28
327
coefficients would enhance heat recirculation which resulted in higher energy conversion
328
efficiency. In addition, a broader flame flammability and smaller quenching diameter were
329
obtained by increasing the heat transfer coefficient which can be simply realized through
330
grooved or rough surface of tube.
331
3.3.2 The Effect of Inner Tube Diameter
332
The effect of inner tube diameter on overall energy conversion efficiency has also been
333
studied. Figure 9 shows efficiency at various diameters for stoichiometric mixture at inlet
334
velocity of 1m/s with heat circulation. It is not surprised to see that for diameters less than 1.5
335
mm or greater than 3 mm, the efficiency dropped at larger diameter due to lower surface area
336
to volume ratio at larger diameter. However, for diameters located in between 1.5 mm and 3
337
mm, the efficiency increased with increased diameter. In a micro-combustor system, both
338
wall temperature and surface area to volume ratio would influence the heat radiation and
339
hence the overall energy conversion efficiency. For diameters less than 1.5 mm, wall
340
temperature increased with increased diameter as shown in Figure 9 but surface area to
341
volume ratio decreases and dominates heat radiation. This caused efficiency to decrease.
342
When diameter increases from 1.5 mm to 3 mm, the increased wall temperature dominated
343
the heat radiation which caused efficiency to increase. As diameter continued to increase, the
344
wall temperature increase slowed down. For this situation, the surface area to volume ratio
345
dominated heat radiation again and efficiency dropped. The influence of surface area to
346
volume ratio on conversion efficiency observed by numerical simulation is yet to be validated
347
by experiments. Generally, MEMS are suffering from high surface area to volume ratio
16
Page 16 of 28
348
which leads to high heat loss to wall of combustor and flame quenching. However, this
349
feature is advantageous for direct energy conversion MEMS.
350
4. Conclusions:
351
In this study, a theoretical model was developed to simulate the combustion of CH4/air
352
fuel mixture in a micro-combustor with and without heat recirculation. The energy
353
conversion efficiency of the micro-combustor-TPV system was evaluated. Following are the
354
conclusion from this study:
355
1.
356
by reducing the heat losses from the system. A flame could be established in the micro-
357
combustor even at a small Reynolds number (Re=53) and energy input of around 10 W with
358
heat recirculation and inner tube diameter of 2 mm. For a fixed inner tube diameter of 3 mm,
359
the maximum heat input can be up to 70 W without flame blow off.
360
2.
361
with heat recirculation, the flammability range was broadened compared to that of without
362
heat recirculation. Also, the lean limit of flammability in air was 2.55%-5% lower than that of
363
without heat recirculation. With heat recirculation, the combustion can sustain at mean flow
364
velocities four to six times the stoichiometric laminar combustion velocity.
365
3.
366
combustor without heat recirculation. The quenching diameter can be as low as 0.9 mm with
367
an equivalence ratio of 1. In addition, the higher heat transfer coefficient between gas and
368
wall improved the energy conversion efficiency.
Combustion in a micro scale combustor with inner tube diameter of 3 mm was achieved
The flammability range decreased with decreasing diameter of combustor. However,
The quenching diameter of combustor with heat recirculation was smaller than that of the
17
Page 17 of 28
369
4.
370
the most important parameters affecting the overall energy conversion efficiency. The
371
maximum conversion efficiency (3.15%) was achieved for case with 1 mm inner diameter.
372 373 374
Acknowledgement:
375
for the Central University- 2015Q NA11”.
376 377
5. Reference
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combustors with conjugate heat transfer," Combustion and Flame, vol. 158, pp. 2178–
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2187, 2011.
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W. M. Rohsenow, Handbook of Heat Transfer: 3rd (Third) edition: New York, McGraw-Hill Companies, 1998.
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K. Annamalai and I. K. Puri, "Combustion science and Engineering " vol. Taylor& Francis Group, 2007.
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Micro Thermophotovoltaic Power
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458 459 460
22
Page 22 of 28
461
Appendix A
462 463 464 465
Base case conditions and sensitivity study This study started for a base case with parameters listed in Table 1. Table 1: Base case data Diameter of inner tube,
di
3
mm
Diameter of outer tube,
do
4.2
mm
30
mm
1
m/s
Tube length,
L
Inlet fuel mixture velocity,V0
u
Equivalence ratio
0.83
Emissivity of outer tube
0.93
Effective wavelength (GaSb)
< 1.7
m
466 467
In addition to the base case, sensitivity studies with different combustor configurations and
468
fuel properties as shown in Table 2 were also performed.
469 470
Table 2: Parametric studies Inlet velocity, u Equivalence ratio, Inner diameter, d i Heat transfer coefficient, h H
m/s mm W/m2K
0.5~3 0.4~1.2 0.5~ 5 50~200
471 472 473
23
Page 23 of 28
inflow outflow
4.2 mm
3mm
outflow
30 mm
474 475 476
Figure 1． Baseline micro-combustor in the theoretical model (carbon steel)
477 478 479
Figure 2． Heat Transfer Model for Micro-combustor
480
24
Page 24 of 28
481
482 483
Figure 3．Energy conservation in a control volume inside the inner tube
484 485
486 487 488
Figure 4 . Micro-TPV system [30]
489
25
Page 25 of 28
490 Equivalence ratio vs quenching diameter with heat recirculation
without heat recirculation
3
Quenching diameter (mm)
2.5 2 1.5 1 0.5
0 0
491 492 493 494 495
0.2
0.4
0.6 0.8 Equivalence ratio
1
1.2
1.4
Figure 5. CH4/air quenching diameter at different equivalence ratios
1.1
Quenching diameter (mm)
1 0.9 0.8 0.7 0.6
0.5 0.4
0
0.5
1
1.5
2
2.5
3
Velocity (m/s)
496 497 498
Figure 6. Variation of quenching diameter Vs inlet velocity with heat circulation
26
Page 26 of 28
Flammability limit(% of fuel by volume)
499
9.5
lean limit with heat circulation
9
lean limit without heat circulation
8.5 8 7.5 7 0
500 501 502 503
1
2
3 Diameter (mm)
4
5
6
Figure 7. Lean limit of flammability in air (% of fuel by volume)
Efficiency %
3
2
1
0
504 505 506 507 508
0
50
100 150 200 Heat transfer coefficient(W/m2K)
250
Figure 8. Effect of heat transfer coefficient on overall energy conversion efficiency with heat circulation
27
con
Page 27 of 28
509
1200
0.03
1000
Tw
0.025
Overall efficiency
800 0.02 600 0.015
overall
400 0.01 200
0.005 0
510 511 512 513 514
Wall temperature (K)
0.035
0
2
4
6
8
10
12
0
Diameter (mm)
Figure 9.Variation of energy conversion efficiency Vs inner tube diameter with heat circulation
28
Page 28 of 28
S1359-4311(16)30116-8 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.162 ATE 7725
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
18-9-2015 31-1-2016
Please cite this article as: Yafeng Lei, Wei Chen, Jiang Lei, Combustion and direct energy conversion inside a micro-combustor, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.162. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1 2 3 4 5
Combustion and Direct Energy Conversion inside a Micro-Combustor Yafeng Lei1, Wei Chen2, Jiang Lei3 1
General Electrical Company, Houston 77041, Texas, USA
6 7 8 9 10
2
3
School of Aerospace, Xi’an Jiaotong University, Xi’an, Shanxi, 710049, China
11
2
Author Correspondence:
12
Professor: Wei Chen
13
China University of Mining and Technology
14
Xuzhou, Jiangsu 221008, China
15 16 17 18 19 20 21 22 23 24 25
[email protected]
26
Abstract
27
Electrical energy can be generated by employing a micro-thermophotovoltaic (TPV) cell
28
which absorbs thermal radiation from combustion taking place in a micro-combustor. The
29
stability of combustion in a micro-combustor is essential for operating a micro-power system
30
using hydrogen and hydrocarbon fuels as energy source. To understand the mechanism of
School of Electric power Engineering, China University of Mining and Technology, Xuzhou 221008, China
Highlights
The flammability range of micro-combustor was broadened with heat recirculation The quenching diameter decreased with heat recirculation compared to without recirculation The surface areas to volume ratio was the most important parameter affecting the energy conversion efficiency The maximum conversion efficiency (3.15%) was achieved with 1 mm inner diameter
1
Page 1 of 28
31
sustaining combustion within the quenching distance of fuel, this study proposed an annular
32
micro combustion tube with recirculation of exhaust heat. To explore the feasibility of
33
combustion in the micro annular tube, the parameters influencing the combustion namely,
34
quenching diameter, and flammability were studied through numerical simulation. The results
35
indicated that combustion could be realized in micro- combustor using heat recirculation.
36
Following results were obtained from simulation. The quenching diameter reduced from 1.3
37
mm to 0.9 mm for heat recirculation at equivalence ratio of 1; the lean flammability was
38
2.5%-5% lower than that of without heat recirculation for quenching diameters between 2
39
mm to 5 mm. The overall energy conversion efficiency varied at different inner diameters. A
40
maximum efficiency of 3.15% was achieved at an inner diameter of 1 mm. The studies
41
indicated that heat recirculation is an effective strategy to maintain combustion and to
42
improve combustion limits in micro-scale system
43 44
Keywords: Micro-combustor; Equivalence ratio; Flammability, Quenching diameter;
45
Quenching cross sectional area; Energy conversion efficiency
46 47 48
Nomenclature C
Tube perimeter (m)
d
Tube diameter (mm)
49
D
Diffusion coefficient (m2/s)
E
Total energy (kJ)
50
hc
Lower heating value (kJ/kmole)
hH
51
L
Tube length (mm)
T
52
Tout
Gas temperature in counter flow (K)
53
w F
Chemical reaction rate (kmole/m3∙s)
u
2
Heat transfer coefficient (kW/m2∙K) Gas temperature (K) Velocity (m/s) Dynamic viscosity (Pa∙s)
Page 2 of 28
54
Kinematic viscosity (m2/s)
55
cP
Specific heat (kJ/kg∙K)
56
Thermal conductivity (kW/m∙K)
Efficiency
Fluid density (kg/m3)
Equivalence ratio
57
LFL
Lean flammability limit
MEMS Micro-electromechanical system
58
MIT
Massachusetts Institute of Technology
TPV
59
TE
Thermoelectric
Thermophotovoltaic
60 61
1. Introduction
62
The micro-electromechanical systems (MEMS) experienced growing interest during the
63
past few years. The combustion of hydrogen or hydrocarbon fuels such as methane in MEMS
64
to produce electrical power has several advantages over the batteries because of high specific
65
energy of liquid fuels. The specific energy of liquid hydrocarbons is 35 to 300 times higher
66
than that of batteries built on latest technology [1]. For example, the specific energy of
67
methane is 50 MJ/kg whereas for an alkaline battery it is only 0.6 MJ/kg [1]. Thus, the direct
68
conversion from chemical to electrical energy even at 10% efficiency is attractive.
69
The hydrocarbon fuel based MEMS were found promising for application in micro
70
combustion. The MIT gas turbine laboratory developed MEMS based on gas turbine power
71
generator with an approximate total volume of 300 mm3 to produce 10~20 W of electric
72
power [2]. At the Combustion laboratories of UC Berkeley, research was conducted to
73
develop a liquid hydrocarbon fueled internal combustion rotary engine on millimeter scale [3].
74
A centimeter magnitude thermoelectric (TE) power generator integrated with plat-flame
75
micro combustor system was developed by Jiang et al. [4]. The maximum power output
3
Page 3 of 28
76
reached was 2 W, and the maximum overall chemical-electrical energy conversion efficiency
77
was 1.25% [4]. In addition to electric power generation, a micro-combustor was employed to
78
recirculate heat to produce hydrogen from ammonia [5]. Also, a thin-film-coated combustor
79
and a packed-bed combustor were designed and fabricated to operate as a heat source for a
80
methanol micro-reformer [6].
81
Even though the micro-power systems hold promise, the primary issue in them is
82
obtaining sustainable combustion in a micro-combustor. As the combustor size decreases, the
83
surface area to volume ratio increases. Because of the high surface area to volume ratio for
84
micro-combustor, there is a high amount of heat loss (proportional to area) compared to heat
85
energy generated (proportional to volume). Thus, the quenching and flammability problems
86
are more critical in a micro-scale combustor. On the other hand, the high surface area to
87
volume ratio characteristic of the micro combustor is most suitable for TPV systems. The
88
TPV system consists of three main parts: a heat source (combustor), a selective emitter, and a
89
photovoltaic array. The photovoltaic array converts the heat radiation absorbed from
90
combustion to electricity. Thus s smaller system will have higher energy conversion
91
efficiency due to its relatively larger surface area to volume ratio as long as the combustion is
92
sustainable. To maintain an optimal balance between the sustainable combustion and
93
maximum heat output is the main issue for micro TPV system.
94
The above concern necessitates innovative schemes to improve the performance of
95
micro-combustor. Several energy management methods including external heating,
96
backward-facing step, catalyzed combustion, and heat recirculation were employed to
97
improve the combustion in the MEMS[7]. The gas flow rates, equivalence ratio, and wall
4
Page 4 of 28
98
material are the main parameters which affect the combustion characteristics and heat loss in
99
a micro-combustor. Li et al. found that maximum heat was released when equivalence ratio
100
was slightly greater than one (and stainless steel wall resulted in more heat loss than ceramic
101
wall) [8]. Leach et al. investigated the effect of structural heat exchange and heat loss on the
102
power density and flame stability in order to optimize the design of silicon micro-combustors
103
[9]. Moreover, the geometry of combustor also has an important role in the flame stability.
104
Zhong et al. conducted experiments on micro Swiss-roll combustors with premixed CH4/air
105
mixture [10]. The combustion stability in the central regions of the combustors was enhanced
106
and the extinction limits of methane/air mixtures were significantly extended [10]. Li et al.
107
used backward-facing step in the combustor to effectively stabilize the flame position [11].
108
Fan et al. found that a triangular and semicircular bluff bodies significantly increased blow-
109
off limit of hydrogen/air flame in a planar micro-combustor [12]. Yang et al. investigated the
110
effect of wall thickness on the performance of three micro-cylindrical SiC combustors and
111
found that wall thickness of 0.4 mm gave maximum power output from micro-
112
thermophotovoltaic power generator [13].
113
Li et al. used porous medium in a 1 mm planar micro-combustor to enhance the flame
114
stability which included flame flashback, blow-off, and heat transfer [7]. Recently, catalysts
115
were employed to improve the combustion and heat transfer in a micro-combustor. Wang et
116
al. found that catalyst can effectively inhibit extinction and actively promote air-hydrogen
117
lean mixture reaction in the combustor [14]. In order to improve the efficiency and
118
performance of mico-combustors, the exhaust gas was recirculated to heat the outer wall of
5
Page 5 of 28
119
the micro-combustor and the incoming cold reactants. As result, the mean wall temperature,
120
total radiation energy emitted and useful radiation energy were improved [15].
121
In addition to experimental studies, extensive numerical simulations were developed by
122
various investigators to evaluate the combustion and heat transfer performance of the micro-
123
combustor. The flame stability in different numerical models was studied at different
124
Reynolds and swirl numbers for MEMS [16, 17]. Fanaee et al. used a two-dimensional model
125
to investigate the effects of reaction zone thickness, maximum temperature and quenching
126
distance on combustion phenomenon in micro-combustors under catalytic and non-catalytic
127
conditions and obtained acceptable agreement between the analytical and experimental data
128
[18]. Pan et al. investigated the effects of porous media, hydrogen to oxygen equivalence ratio,
129
porosity and fuel mixture flow rates on the performance of the micro-combustor [19]. Li et al.
130
found that in 1D cylindrical micro-combustor model hydrogen was superior to methane and
131
propane as a fuel owing to its higher flame temperature and lower flame thickness. [20]. Tang
132
et al. conducted studies on premixed hydrogen/air combustion in 3D model of a micro planar
133
combustor and found enhancement in heat transfer and increase in mean temperature of the
134
radiation wall by inserting plates in the micro-combustor chamber [21].
135
The effect of cross-sectional geometry on the ignition/extinction behavior of catalytic micro-
136
combustors using CFD models was studied by Benedetto [22]. He found that square cross-
137
section channel was more resistant to extinction compared to circular channel [22]. Moreover,
138
heat recirculation from the post-flame to the pre-flame in a micro combustor improved the
139
flame stabilization and enhanced burning rate on a 2D mode [23].
6
Page 6 of 28
140
The objective of this work is to develop a one-dimensional numerical model using
141
FORTRAN code to explore the feasibility of CH4/air combustion in a micro-combustor
142
(straight tube combustor with heat recirculation) and investigate on its application to TPV
143
power system. The effect of heat recirculation of a micro-scale counter flow combustor on the
144
lean flammability, quenching diameter, and overall energy conversion efficiency were
145
investigated in this study.
146 147 148
2. Numerical Modeling and Its Formulation 2.1 Physical Model of the Micro-combustor
149
Figure 1 illustrates the physical model of the micro combustor used in this study. It
150
includes a combustion tube made of carbon steel with inner diameter varying from 1 mm to 3
151
mm and a concentric outer tube of same material which served as a counter flow heat
152
exchanger. The incoming cold mixture in the inner tube was preheated by the hot combustion
153
gases in the outer tube resulting in reduction of the chemical reaction time and helping
154
complete combustion. For a micro-size combustor, the reduced diffusion time resulting from
155
small size has a crucial effect on making the concentration distributions uniform near the
156
flame in the combustor. In addition, the laminar flow prevented rapid mixing between fuel
157
and air due to the low mass and heat transfer coefficients in the combustor. Therefore, a
158
premixed combustion instead of diffusion combustion was assumed in this study. The flame
159
propagation in the current model is two-dimensional in nature. However, if interest is limited
160
to micro-scale burners with tube diameter and wall thickness much smaller than the tube
161
length, the problem could be simplified to one-dimensional. This study assumed one
162
dimensional laminar plug flow in the model.
7
Page 7 of 28
163
The baseline micro-combustor configuration consisted of two annular tubes with an inner
164
tube of 3 mm in diameter and 30 mm in length and an outer tube of 4.2 mm in diameter and
165
30 mm in length. Cold premixed fuel mixture which passes through inner tube will be ignited
166
by hot gases in outer tube. In the mean time the heat radiation from high temperature outer
167
tube wall will reach TPV system and be converted to electricity.
168
2.2 Heat Transfer:
169 170
The Nusselt number Nu for the inner tube was determined by using the following empirical correlation for constant wall temperature [24] Nu
h in n e r d i k
171
4 .3 6 4 B i 1 0 .2 6 8 2 B i
(1)
172
In the above relationship, hinner is the convective heat transfer coefficient, di is the diameter of
173
inner tube, k is the thermal conductivity of the fluid, and Bi is the Biot number of the micro-
174
tube. The dimensionless Bi characterizes the heat transfer resistance "inside" a solid body and
175
it was defined as: Bi
176
h Lc
(2)
k
177
Where LC is characteristic length, which is commonly defined as the volume of the
178
body． This empirical correlation is applicable to the forced convection laminar flow in
179
circular duct. The Biot number is 0.006 for steel tube of dimensions shown in Figure 1.
180
Figure 2 shows the heat transfer model for the micro-combustor proposed. The convective
181
heat transfer coefficient at the outer surface of inner tube is denoted as houter,i. Heat is
182
dissipated via radiation from the outer surface of outer tube with heat transfer coefficient
183
houter,o. The Bi number
in
equation１is close to zero as the micro-combustor is small
8
Page 8 of 28
184
enough. This corresponds to a heat transfer coefficient of 111 W/m2.k [24]. For outer tube
185
section with associated hydraulic diameter dh （the different between outer diameter do and
186
inner diameter di）, the outer surface Nu is 5.38 and the inner surface Nu is 4.602 for limited
187
wall condition and Nu is 4.364 for the inner tube[25]. The estimation of heat transfer
188
coefficient is very coarse in the current model. In practice, the heat transfer coefficient can be
189
enhanced for rough and grooved wall. In this model, to be simple, it was assumed a constant
190
convective heat transfer coefficient for both inner and outer tubes (e.g., hH.outerr,o=
191
hH.inner,o=hH.inner,i=111 w/m2.K).
192 193 194 195
2.3 Combustion Methane consumption rate during combustion can be expressed by Eq.(3) [26]: w F A T P n
m
exp(
E
a
)[C H 4 ] [O 2 ]
RT
b
(3)
196
Where a=0.3, b=1.3, n=0, and m=0; A is the pre-exponential factor which is dimensionless
197
and equals to 1.3x109 here. P is pressure, E is activation energy and E=202,408 kJ/kmole, R is
198
universal gas constant, and
199
kmol/m3 , respectively.
200
Fuel and oxygen mass conservation equations were established as follow:
201
[C H 4 ]
u
and
[O 2 ]
2
dyF
D
d yF
dx
202
u
dyO dx
are concentration of CH4 and O2 with the unit of
dx
w F
2
(4)
2
2
D
d yO dx
2
2
w O
2
9
(5)
Page 9 of 28
203
In the above relationships, is the gas density, u is the velocity, D is diffusion coefficient,
204
and yF is fuel mass fraction and yO2 is the oxygen mass fraction in air-fuel mixture.
205
At the entrance to the combustor, where x=0, yF=yF.0, yO2=yO2.0, and T=T0.
206
The Eqs. (4) and (5) can be combined and written in terms of Schvab-Zeldovich variable as
207
shown by Eq.(6): u
d 2
D
dx
208 209
d
dx
2
(6)
In the above relationship,
o2 F
yF
210 o 2
yo
2
o2
2 k m o le O 2 k m o le C H
211
and
212
Based on the assumptions listed above, the fluid flow field was divided into a finite number
213
of small control volumes as illustrated in Figure 3. The first law of thermodynamics as shown
214
by Eq.(7) was applied to each control volume:
215
dE dt
4
Q W m i h to t , i m e h to t , e
Q
(7)
Where, E is the total energy of the fuel,
217
inlet and outlet mass flow rate, respectively, and
218
enthalpy of formation, and
219
fueled with diesel and natural gas was conducted by Gümüş et al[27].
h
is heat transfer rate,
W
216
h to t h f h
is work,
mi
and
is the total enthalpy,
mi
hf
are
is
is thermal enthalpy. Similar energy analysis for a CI engine
10
Page 10 of 28
220
The equations (8) and (9) express the combined combustion and heat transfer processes in the
221
inner and outer tubes respectively: u c p Ai
222 223 224 225 226
u c p Ao
dT dx
dT dx
2
Ai
d T dx
2
h H C i ( T g , o T ) w F h c A i
(8)
2
Ao
d T dx
2
h H C i ( T g , i T ) h H , o u te r , o C o ( T w ,1 T ) w F h c A o
(9)
The Eq. (10) can be obtained by combining the equations (4) and (8). u
227
d
d 2
D
dx
dx
2
hH C i hc Ai
(T g , o T )
(10)
228
Where T is the temperature, cp is the specific heat of gas species, Ai cross area of the inner
229
tube, Ao is the cross area of outer tube, and
h
t F
ht hc
yF
where
ht c pT
230
The Eq. (9) was used to determine the temperatures of gas and outer surface of the wall which
231
served as a selective emitter. For a photovoltaic array made of low band gap material such as
232
GaSb (gallium antimony), the efficiency of heat radiation to electrical energy transfer was
233
determined by Planck’s radiation law.
234
2.4 TPV System Modeling
235
Figure 4 illustrates a typical TPV system using a combustion heat radiation source. The
236
micro-TPV
system
consists
of
two
main
237
thermophotovoltaic convertor. Fuels combust in the micro-combustor and electricity will be
238
generated through photovoltaic cells by absorbing heat radiation from combustor. To
239
determine the spectrum emissivity, the wall temperatures along the outer surface of outer tube
240
need to be calculated. The black body hemispherical spectral emissive power is given by
241
Planck’s radiation law as shown by Eq.(11) [28].
11
components:
micro-combustor
and
Page 11 of 28
E b
242
C 1 e
5
C 2 /( T )
1
W/m3
(11)
243
Where λ is the wavelength, C
244
The range of spectrum from which a photon can be converted into electricity depends on the
245
type of TPV cells. In this study, GaSb cells were used as photovoltaic converter for which the
246
band gap was 0.72 eV. This implies that only photons emitted from a heat radiation source
247
with a wavelength smaller than 1.7 μm can generate electricity from the GaSb cells.
248 249 250
3. Results and Discussion
251
velocity and heat transfer coefficient on combustion performance in a micro-combustor were
252
studied. To better understand the effect of heat recirculation, the quenching diameters and
253
lean limits for combustion were compared with and without heat recirculation. The base case
254
conditions and sensitivity analysis parameters for this study are given in appendix A.
255
3.1 Quenching Diameter
256
3.1.1 Effect of Equivalence Ratio on Quenching Diameter
257
In this study, the equivalence ratio was defined as:
258
1
3 .7 4 2 1 0
16
W m
2
,C
2
2
1 .4 3 8 8 1 0 m K
In this investigation, the influence of equivalence ratio, inner diameter, fuel inlet
ER
s to ic h io m e tr ic a ir m o le s p e r m o le e m p itic a l fu e l a c tu a l a ir m o le s p e r m o le e m p itic a l fu e l
A F s to ic h i A F a c tu a l
F A a c tu a l F A s to ic h i
(12)
259
Figure 5 shows the variation of quenching diameter with respect to equivalence ratio (ER) for
260
CH4/air mixture with and without heat recirculation for the base case conditions. The model
261
without heat circulation is just a straight tube that has the same diameter as the inner tube of
12
Page 12 of 28
262
the model with heat circulation. With heat recirculation, the quenching diameter decreased,
263
especially at low values of equivalence ratio, which means that heat recirculation can help
264
combustion to sustain in micro-combustor at smaller scale. When the combustor scales down,
265
the surface area to volume ratio increases and the circulating heat compensates for part of the
266
heat lost to the environment resulting in the combustion to sustain inside the inner tube. The
267
stoichiometric calculations of premixed CH4/air combustion indicated that the diameter can
268
be as small as 0.9 mm for a combustor with heat recirculation whereas the minimum
269
diameter was 1.3 mm for combustor without heat recirculation.
270 271
3.1.2 Effect of Mixture Inlet Velocity on Quenching Diameter
272
The fundamental time constraint can be quantified in terms of a homogeneous
273
Damkohler number, which is the ratio of the residence time and characteristic chemical
274
reaction time [29] as shown by Eq. (13):
275
D ah
r e s id e n c e
(13)
c h e m ic a l
276
To maintain stable combustion inside the tube, more fuel residence time than chemical
277
reaction time is necessary to have the Damkohler number greater than 1. The residence time
278
τresidence is defined as:
279 280 281 282
r e s id e n c e
L
(14)
v
Where L is the length of the combustor and v is the gas velocity. For a micro-combustion tube, the residence time is very small due to relatively high flow velocity and short tube length. The chemical reaction time has an inverse relationship with
13
Page 13 of 28
283
combustion temperature. In the current model, the heat transfer from outer tube to inner tube
284
increased reactants temperature and hence decreased chemical reaction time. Higher fuel inlet
285
velocity would increase power output, but a very high inlet velocity requires a larger tube
286
diameter to sustain combustion inside the tube. Figure 6 illustrates the relationship between
287
air/fuel inlet velocity and quenching diameter with heat circulation.. With heat recirculation,
288
the mixture could be burnt in micro combustor at mean flow velocities four to six times
289
higher than the stoichiometric laminar burn velocity (.40~.50 m/s). From Figure 6, for
290
velocities less than 2m/s, increasing velocity would increase fuel consumption rate and lead
291
to a decreased quenching diameter. For velocities higher than 2 m/s, the flame advanced
292
towards the end of inner tube due to the decreased residence time. This caused reduction of
293
chemical energy release, and hence required a larger quenching diameter to sustain the
294
combustion. The high velocity extinction limit was certainly caused by insufficient residence
295
time rather than the chemical reaction completion time.
296
At a fixed tube diameter, either extremely high or low Reynolds number (e.g., inlet velocity)
297
would lead to quenching. This is due to the fact that the mixture at low Reynolds number has
298
less amount of heat energy to sustain the combustion, and mixture at high Reynolds number
299
leads to insufficient residence time compared to the time required to complete the combustion
300
reactions. The calculations show that the Reynolds number as low as 53 can sustain
301
combustion with heat recirculation at tube diameter of 2 mm and the energy input of 10 W.
302
For a fixed tube of diameter of 3 mm, the maximum heat input is 70 W and corresponding
303
Reynolds number is 930.
304
3.2 Lean Flammability Limit
14
Page 14 of 28
305
When the equivalence ratio decreased from base case value of 0.83 to a value called lean
306
flammability limit (LFL), the flame failed from being stabilized. It is reasonable to expect
307
that the limits of flammability would be widened if preheating of inlet mixture by heat
308
recirculation is available. Figure 7 shows the lean flammability of micro combustor with and
309
without heat recirculation at different inner tube diameters and with inlet air/fuel mixture
310
velocity of 1 m/s. Both LFL for cases with and without heat circulation decreased along with
311
increased diameter. The LFL with heat circulation was 2.5%-5% lower than that of without
312
heat circulation for tube diameters between 2 mm and 5 mm. It indicates that heat
313
recirculation can enhance combustion at lower equivalence ratio. Similar results were
314
reported by Veeraragavan et al. [23]. Heat recirculation was found as the governing
315
parameter in enhancing the flame temperature and speed [23].
316
3.3 Overall Energy Conversion Efficiency
317
3.3.1 The Effect of Heat Transfer Coefficient
318
For tmicro-combustion-TVP system, the conversion of thermal energy into electrical
319
energy is obtained through the thermophotovoltaic cells which cover the outer surface of
320
micro-combustor to absorb heat radiation. The overall energy conversion efficiency is defined
321
as following:
322 323
con
e le c tr ic ity g e n e r a te d
(15)
c h e m ic a l e n e r g y in p u t
324
The effect of heat transfer coefficient on conversion efficient has been studied. Figure 8
325
illustrates the variation of overall energy conversion efficiency ηcon with respect to heat
326
transfer coefficient for base case combustion with heat recirculation. Higher heat transfer
15
Page 15 of 28
327
coefficients would enhance heat recirculation which resulted in higher energy conversion
328
efficiency. In addition, a broader flame flammability and smaller quenching diameter were
329
obtained by increasing the heat transfer coefficient which can be simply realized through
330
grooved or rough surface of tube.
331
3.3.2 The Effect of Inner Tube Diameter
332
The effect of inner tube diameter on overall energy conversion efficiency has also been
333
studied. Figure 9 shows efficiency at various diameters for stoichiometric mixture at inlet
334
velocity of 1m/s with heat circulation. It is not surprised to see that for diameters less than 1.5
335
mm or greater than 3 mm, the efficiency dropped at larger diameter due to lower surface area
336
to volume ratio at larger diameter. However, for diameters located in between 1.5 mm and 3
337
mm, the efficiency increased with increased diameter. In a micro-combustor system, both
338
wall temperature and surface area to volume ratio would influence the heat radiation and
339
hence the overall energy conversion efficiency. For diameters less than 1.5 mm, wall
340
temperature increased with increased diameter as shown in Figure 9 but surface area to
341
volume ratio decreases and dominates heat radiation. This caused efficiency to decrease.
342
When diameter increases from 1.5 mm to 3 mm, the increased wall temperature dominated
343
the heat radiation which caused efficiency to increase. As diameter continued to increase, the
344
wall temperature increase slowed down. For this situation, the surface area to volume ratio
345
dominated heat radiation again and efficiency dropped. The influence of surface area to
346
volume ratio on conversion efficiency observed by numerical simulation is yet to be validated
347
by experiments. Generally, MEMS are suffering from high surface area to volume ratio
16
Page 16 of 28
348
which leads to high heat loss to wall of combustor and flame quenching. However, this
349
feature is advantageous for direct energy conversion MEMS.
350
4. Conclusions:
351
In this study, a theoretical model was developed to simulate the combustion of CH4/air
352
fuel mixture in a micro-combustor with and without heat recirculation. The energy
353
conversion efficiency of the micro-combustor-TPV system was evaluated. Following are the
354
conclusion from this study:
355
1.
356
by reducing the heat losses from the system. A flame could be established in the micro-
357
combustor even at a small Reynolds number (Re=53) and energy input of around 10 W with
358
heat recirculation and inner tube diameter of 2 mm. For a fixed inner tube diameter of 3 mm,
359
the maximum heat input can be up to 70 W without flame blow off.
360
2.
361
with heat recirculation, the flammability range was broadened compared to that of without
362
heat recirculation. Also, the lean limit of flammability in air was 2.55%-5% lower than that of
363
without heat recirculation. With heat recirculation, the combustion can sustain at mean flow
364
velocities four to six times the stoichiometric laminar combustion velocity.
365
3.
366
combustor without heat recirculation. The quenching diameter can be as low as 0.9 mm with
367
an equivalence ratio of 1. In addition, the higher heat transfer coefficient between gas and
368
wall improved the energy conversion efficiency.
Combustion in a micro scale combustor with inner tube diameter of 3 mm was achieved
The flammability range decreased with decreasing diameter of combustor. However,
The quenching diameter of combustor with heat recirculation was smaller than that of the
17
Page 17 of 28
369
4.
370
the most important parameters affecting the overall energy conversion efficiency. The
371
maximum conversion efficiency (3.15%) was achieved for case with 1 mm inner diameter.
372 373 374
Acknowledgement:
375
for the Central University- 2015Q NA11”.
376 377
5. Reference
378
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458 459 460
22
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461
Appendix A
462 463 464 465
Base case conditions and sensitivity study This study started for a base case with parameters listed in Table 1. Table 1: Base case data Diameter of inner tube,
di
3
mm
Diameter of outer tube,
do
4.2
mm
30
mm
1
m/s
Tube length,
L
Inlet fuel mixture velocity,V0
u
Equivalence ratio
0.83
Emissivity of outer tube
0.93
Effective wavelength (GaSb)
< 1.7
m
466 467
In addition to the base case, sensitivity studies with different combustor configurations and
468
fuel properties as shown in Table 2 were also performed.
469 470
Table 2: Parametric studies Inlet velocity, u Equivalence ratio, Inner diameter, d i Heat transfer coefficient, h H
m/s mm W/m2K
0.5~3 0.4~1.2 0.5~ 5 50~200
471 472 473
23
Page 23 of 28
inflow outflow
4.2 mm
3mm
outflow
30 mm
474 475 476
Figure 1． Baseline micro-combustor in the theoretical model (carbon steel)
477 478 479
Figure 2． Heat Transfer Model for Micro-combustor
480
24
Page 24 of 28
481
482 483
Figure 3．Energy conservation in a control volume inside the inner tube
484 485
486 487 488
Figure 4 . Micro-TPV system [30]
489
25
Page 25 of 28
490 Equivalence ratio vs quenching diameter with heat recirculation
without heat recirculation
3
Quenching diameter (mm)
2.5 2 1.5 1 0.5
0 0
491 492 493 494 495
0.2
0.4
0.6 0.8 Equivalence ratio
1
1.2
1.4
Figure 5. CH4/air quenching diameter at different equivalence ratios
1.1
Quenching diameter (mm)
1 0.9 0.8 0.7 0.6
0.5 0.4
0
0.5
1
1.5
2
2.5
3
Velocity (m/s)
496 497 498
Figure 6. Variation of quenching diameter Vs inlet velocity with heat circulation
26
Page 26 of 28
Flammability limit(% of fuel by volume)
499
9.5
lean limit with heat circulation
9
lean limit without heat circulation
8.5 8 7.5 7 0
500 501 502 503
1
2
3 Diameter (mm)
4
5
6
Figure 7. Lean limit of flammability in air (% of fuel by volume)
Efficiency %
3
2
1
0
504 505 506 507 508
0
50
100 150 200 Heat transfer coefficient(W/m2K)
250
Figure 8. Effect of heat transfer coefficient on overall energy conversion efficiency with heat circulation
27
con
Page 27 of 28
509
1200
0.03
1000
Tw
0.025
Overall efficiency
800 0.02 600 0.015
overall
400 0.01 200
0.005 0
510 511 512 513 514
Wall temperature (K)
0.035
0
2
4
6
8
10
12
0
Diameter (mm)
Figure 9.Variation of energy conversion efficiency Vs inner tube diameter with heat circulation
28
Page 28 of 28