Закономерность зажигания и выхода на режим горения метановоздушной смеси в щелевой горелке c внутренней вставкой
Крайнов А. Ю., Моисеева К. М., Порязов В. А.
Томский государственный университет, 634050, Россия, Томск, пр. Ленина, 36
[email protected]
The mechanism of the ignition and the combustion mode establishment
of the methane-air mixture in the slot burner with inert partition
Krainov A. Yu., Moiseeva K. M., Poryazov V. A.
Tomsk State University, 634050, Russia, Tomsk, Lenina St, 36
[email protected]
Keywords: Methane-air mixture, slot burner, establishment state mode, heat and mass transfer,
ignition.
Abstract. A one-dimensional numerical model of the combustion of the 6% methane-air mixture in
the slot burner with inert internal partition and adiabatic outer walls was developed including the
effect of temperature-depended gas, heat transfer and one-step chemical reaction. The case of the
mixture ignition by the hot internal partition was considered for a multiple values of the initial
temperature of the partition. The influence of the initial temperature of the partition and the gas
flow velocity on the combustion mode of the methane-air mixture in the slot burner was defined.
Intorduction
The problem of development of effective portable devices for combustion is one of the main
objectives of a modern small-scale power generator. It can explains the for industry tendency
miniaturization of batteries and to searching for alternative energy sources. The gas combustion
stability in a micro burner depends on by several factors.
At first, the heat loses has essential impact on the stability of combustion. One of the methods of
the reduction of heat losses and maintenance of steady combustion is development of perspective
constructional decisions. As specific design features of a burner can be used an additional heat
transfer agent [1 - 2], heating of a part of a burner surface [3], a change of a device form [4 - 9]. The
gas combustion in the devises with recovery of heat was considered at [4 – 9]. Among devices with
recovery of heat are Swiss-roll burners, counter flow burners and U – shape canals [6]. Energy
efficiency of combustion in these burners is based on heating of cold gas mixture by products of
reaction or the mixture flow in the parallel channel. The heating is carried out due to heat exchange
through the partition or internal wall of a burner. Burners with the heat recovery allow one to
maintain the steady combustion of lean gas mixtures [5, 8], or gas combustion in narrow channels
and slots [9].
At second, the initial conditions also can have essential impact on stability of gas mixtures
combustion [2]. The different modes of combustion are possible independents on the reference
temperature of gas or burner walls. These modes can be differing on quantitative and qualitative
behavior. The reference temperature of internal partition or outer walls has an influence on the
established stable mode of combustion if the gas mixture combustion was initiated by preheated
internal inert nozzle [2] or burner outlet walls [8].
In our previously paper [9] the influence of initial conditions on the established stable
combustion mode was not considered. So, in this paper the problem of 6% methane-air mixture
combustion in the slot burner with an inert internal partition is investigated on the base of
mathematical model from [9]. The main purpose of the research is to determine the area of hightemperature stable state mode independence of the initial temperature of inert partition and the
value of the gas feeding.
Formulation of the problem
The cold methane-air mixture feeds in the slot burner with an inert internal partition (fig. 1). The
internal partition is the thin metal plate separated upper and bottom parts of the slot burner (part II,
fig. 1b). The entrance temperature of the mixture is Tv, the velocity of feeding is uv, the
concentration of combustible component is av. The mixture comes into the burner from the side
x = 0, (part I, fig. 1b). On the side x = L mixture changes the flow direction. The gas flows out on
the side x = 2L, (part III, fig. 1b). It is supposes the internal partition was uniformly preheated to
initial inert partition temperature T1v. The outer walls are adiabatic. The reaction mixture exchanges
heat with internal partition according to the Newton law with a heat transfer coefficient .
Coefficients of diffusion D and heat conductivity λ depend on temperature [9 – 10].
Fig. 1. A model of the slot burner (а); a scheme of a burner (b): I – input channel,
II – internal nozzle, III – output channel
To simplify the mathematical formulation of the problem, it is assumed that there are no radial
components of the heat flux and reactant concentrations. The consumption of the reaction mixture
in the burner is set constant, G = ρu = const. The chemical process proceeds according to the
Arrhenius law. The pressure in a burner is constant. Under these assumptions, the mathematical
formulation of the problem has the form:
The energy equation for the reaction mixture:
T
T
  T  
 E 
 cu
 
  T1,S  T   Qak 0 exp  
, 0  x  2 L,
t
x x  x  h
 RT 
T x, t , x  L,
T1,S x, t    1
T1 2 L  x, t , x  L.
с
(1)
The energy equation for the internal partition:
T1
 2T1 

с11
 1 2  T1  T x, t   T1  T 2 L  x, t  , 0  x  L .
t
h1
h1
x
(2)
The mass balance equation for the combustible component:

a
a  
a 
 E
 u
  D    a k 0 exp  
t
x x 
x 
 RT
The perfect gas law:

, 0 x2 L.

(3)
p

RT  const .

(4)
The continuity equation:
  u 

 0.
t
x
(5)
The boundary conditions:
T x,0  Tv
ax,0  av , T1 x,0  T1v , x,0 
T 2 L, t 
 0,
x
a2 L, t 
a0, t   av ,
 0,
x
T1 0, t  T1 L, t 

 0,
x
x
p
0, t  
, u 0, t   uv .
RT 0, t 
p
, u x,0  u v .
RT x,0
T 0, t   Tv ,
(6)
(7)
(8)
(9)
(10)
Where: t is the time; х – the axial coordinate; T – the temperature; a – the methane mass
concentration in a mixture; ρ – the density; p – the pressure; с – the heat capacity; u – the mixture
flow velocity; D – the diffusion coefficient; λ – the heat conduction coefficient;  - the heat transfer
coefficient; R – the universal gas constant; E – the activation energy; Q – the reaction heat; h – the
wide of the internal cross section of the slot burner; μ – the gas molar mass; L – the length of the
internal partition. The subscribes 1, v correspond to the parameters of the inert internal partition and
input parameters, respectively.
The variable a defines the quantity of methane mass concentration in the mixtures. The relation
between the mass and volume methane concentration in the mixture is defined from the equation:
avol   CH 4
. Where avol – the percent methane by volume of the mixture,
a
100  avol    air  avol   CH 4
μ𝐶𝐻4 – the methane molar mass, μair– the air molar mass. The dependence of heat conductivity and
s
diffusion coefficients on temperature are described by relationships: D  Dst  st T Tv  ,
s
   st T Tv  [10]. The subscribe st corresponds the value of parameters for T = 300 К. The heat
transfer coefficient in the equations (1) – (2) is defined from the relationship    Nu h . Where
Nu is the Nusselt number and it is defined for the case of the mixture flow in the slot formed by two
concurrent planes [12].
0.33

h Re Pr
 h Re Pr 
 1000,
0.979 
 ,
x
x




h Re Pr  100

h Re Pr
x
, 100 
 1000,
Nu  3.78  Nu*  3.78
900
x



h Re Pr
3.78,
 100.
x

(11)
Where Re is the Reynolds number, Re  u h  ; Pr is the Prandtl number; Pr  c  ; s is
the power in the relationships for definition heat conductivity and diffusion coefficients; η is the air
dynamic viscosity; Nu* is the value of the Nusselt number corresponding to the value
h Re Pr  x  1000 . Local values of the Nusselt number are defined by relationship (11). This
relationship considers influence of establishment of a mixture flow at the entrance of a burner on
the heat exchange coefficient between gas and a partition [12].
Calculation results and analysis
Problem (1)–(10) was solved numerically using the sweep method [13]. The calculations were
performed with an implicit difference scheme with a four-point stencil. Approximation convergence
was tested on successively refining meshes, and computation parameters were chosen such that the
error of the calculations was not more than 3%. The calculations were performed for a methane-air
mixture with the following set of kinetic and thermophysical properties: Q = 55.7 MJ/kg,
E =0.239 MJ/mol [14], c = 1065 J/(kg·K), s = 2/3, λst = 0.025 J/(m·K·s), p = 0.10132 MPa,
R = 8.31 J/(mol·K), ρst = 1.179 kg/m3, Dst = 1.992·10-5 m2/s, η = 2·10-5 Pa·s, μ = 28·10-3 kg/mol,
Tv = 300 K, av = 0.035, k0 = 2.1·1010 s-1. Geometric properties of the slot burner are: the wide of the
internal cross section of the slot burner h = 6·10-3 m, the thickness of the nozzle h1 = 2·10-3 m, the
total length of the burner – 2L = 0.1 m. Thermophysical properties of a burner walls material, which
correspond to heat-resisting steel, are c1 = 687 J/(kg·K), λ1 = 30 J/(m·K·s), ρ1 = 7500 kg/m3. The
initial temperature of the internal partition T1v and the mixture flow velocity in the entrance part of
the burner uv are changed in the wide ranges. Results of calculations are shown in fig. 2.
Fig. 2. Regions of possible combustion modes of a methane–air mixture in a slot burner.
I – region of a failure of ignition, II – region of ignition
The curve in the Fig. 2 corresponded the value of the maximum of the mixture flow velocity in
the entrance of the burner uv for which the high-temperature stable state mode establishes. The parts
I and II correspond to the mode without ignition and the one with ignition, respectively. Previously
[9], the maximum initial temperature in the slot burner was 1700 К. It has been shown that the
maximum velocity of the mixture flow in the burner inlet is uv = 0.33 м/с. The failure of
combustion takes place for the values of uv less than 0.33 м/с. The results from [9] agreement with
the results given above. According to this study findings for the burner geometry set, the minimum
temperature of T1v at which it is possible to initiate and maintain stable combustion of methane-air
mixture, is equal to T1v = 1120 К. At smaller values of T1v the gas mixture quickly cools the internal
partition to smaller temperatures. The reaction mixture did not manage to be ignited during the gas
flow through the slot burner.
Conclusions
The numerical analysis of the 6% methane-air mixture combustion in a slot burner with an inert
internal partition was carried out. A region of the high-temperature stable state combustion mode
was defined. It was shown that the initial temperature of the internal partition and the mixture flow
velocity at the inlet part of the burner had an effect on the combustion modes.
This study (research grant No 8.1.70.2015) was supported by The Tomsk State University
Academic D.I. Mendeleev Fund Program in 2015.
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