International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
Numerical Simulation of Wood –Volatiles &
Air Combustion in Differentially Heated
Diffuser Tube under Free Convection
Gopal Kumar Deshmukh1, Rajesh Gupta 2
1
Post Graduate Student, Department of Mechanical Engineering, M.A.N.I.T, Bhopal, India 462051
Associate Professor, Department of Mechanical Engineering, M.A.N.I.T, Bhopal, India 462051
2
Abstract- Simulation of combustion phenomenon in a
vertical diffuser in the presence of buoyancy-induced
airflow and radial fuel inflow is presented. This
combustion problem is similar to the combustion of
pyrolysis gases in an annular vertical diffuser which is
widely used in rural areas for cooking. The analysis of
the problem is complicated owing to the coupling
amongst natural convection flow, heat transfer and
combustion. A simple finite reaction rate model for a
single component fuel is presented for the combustion
process. Then, the fuel is taken to be a mixture of
combustible gases and an Arrhenius-type single step
reaction is assumed between each of the combustible
gases and oxygen. In each stage of modelling,
temperature and species profiles are generated for
various tube wall temperatures and fuel inflow rates.
Results indicate that the maximum flame temperature is
located close to the radial diffuser. The flame tends to
move away from the wall with higher volatiles flow rate
and higher wall temperatures also. It was also seen that
maximum flame temperature increases with increase in
tube wall temperature and power input, maximum
flame temperature region spread in radial diffuser.
the pan placed above the conical tube. Scientific
investigation of such combustor is difficult because
of the coupled phenomena of natural convection
flow, heat transfer, and flaming combustion. In this
work a certain radial flow rate of combustible
volatiles has been prescribed from the inner surface
of a vertical tube. In the present work, the
combustion phenomenon of fuel gas in a buoyancyinduced airflow in a vertical tube is modeled under
the assumptions of a finite reaction rate. The volatile
flow rate and the inner wall temperature were
parametrically varied over a restricted range for
studying their effects on combustion.
Keywords: wood-volatiles, vertical diffuser, natural
convection, mixture fraction formulation.
1.
INTRODUCTION
Research and development of cook stoves and
vertical combustors have been receiving its due share
of attention at least in the developing world where a
large chunk of the population still resides below a
standard of living. This part of the population
generally resorts to the use of wood, wood volatiles
or any other bio mass fuel available easily for its
cooking needs. The issue of stove or combustor is
therefore quite sensitive and has direct implications
on the socio-economic developments of the poorest
of the poor human beings. A general layout of
vertical diffuser combustor has shown in figure 1. A
combustion zone is sustained in the central passage
by a buoyancy-induced upward flow of air and a
radial inflow of combustible volatile gases from the
vertical combustor. The hot flue gases transfer heat to
ISSN: 2231-5381
Fig. 1 vertical diffuser combustor
2.
MATHEMATICAL FORMULATION
A typical vertical diffuser is shown in figure 1. The
simulation becomes relatively simplified and well
defined if the vertical portion of the hole considered.
The phenomena involved in the combustion process
in vertical diffuser are
(1) Natural convection flow and heat transfer
(buoyancy induced flow )
http://www.ijettjournal.org
Page 2751
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
(2) Combustion
Axial Momentum Equation:
Natural convection flow methodology from existing
model is adopted for the present work uniform fuel
rate is assumed from the wall and taken as input to
replace pyrolysis model. Present work mainly
concentrates on combustion modeling. The fuel
mixture is taken as CH4, C2H6, CO, H2, CO2, and
H2O from pyrolysis of wood. Composition of
volatiles for CH4, C2H6, CO, H2, CO2, and H2O are
taken as 0.0489, 0.10756, 0.4756, 0.0187, 0.249 &
0.1 respectively.
Assuming one step reaction, four single step reactions
are possible for this mixture.
1.
2.
3.
4.



The vertical hole is used in the diffuser. The
assumption has been made to make the
model axi-symmetric.
The viscous dissipation is negligible
The flow will be Turbulent and K & 
models are used.
Process assumed to be Steady state.
Governing Equations for Reactions




Conservation of mass
Conservation of momentum
Conservation of species (CH4, C2H6, CO2,
H2, CO, and H2O)
Conservation of energy
Mass Conservation Equation:
ˆrVˆ
ˆVˆ

1 
r
z

 0
rˆ
rˆ
zˆ

(1)
Energy Equation:

     
Tˆ
Tˆ 1 1  ˆ Tˆ 1  ˆ Tˆ 
C p Vˆr Vˆz 
rˆk

rˆk
Qgen (4)
rˆ
zˆ Pr rˆ  r̂ e  rˆ rˆ  rˆ e zˆ
Species Equation:
The combustion model consists of
conservation of species equations. The fuel mixture
contains species namely CH4, C2H6, CO2, H2, CO,
H2O and O2, N2.
These species are assumed to undergo a
finite rate, single-step irreversible reaction kinetics.
ˆ
ˆ
1

1 1  ˆ Yi  ˆ Yi
ˆ rˆVˆrYˆi  ˆVˆzYˆi 
ˆrˆD  ˆD
ˆ
rˆ rˆ
zˆ
Le Pr rˆ  rˆ
 rˆ  zˆ
 zˆ i (5)

 

Radial Momentum Equation:
2
Vˆ 2 1 
Vˆ
1 ˆ rˆVˆr ˆ VˆrVˆz  pˆ
41 

   ˆ Vˆr Da 
rˆˆ r 
rˆˆ z
rˆ rˆ
zˆ
 rˆ
3 rˆ  rˆ  rˆ 3 rˆ  rˆ  zˆ

Vˆ 4 ˆ
21 
2 ˆ Vˆr
rˆˆ r  Vˆr2 
3 rˆ  rˆ  rˆ 3 rˆ
3 rˆ  rˆ
2 ˆ Vˆz  Vˆz  Vˆr

 ˆ
 ˆ
3 rˆ  zˆ  ẑ  rˆ  zˆ  zˆ
ISSN: 2231-5381
(2)

    
Le and D refer to the Lewis number and
diffusion coefficient respectively while Y i and i
represent mass fraction and the rate of generation or
depletion of the ith species respectively. The rate of
generation or depletion non-dimensional i for each
individual species mentioned above can be expressed
in terms of Arrhenius equation.
3.
   
 
  
     
2  1 rˆVˆr 1  Vˆz 1  Vˆr (3)
ˆ

rˆˆ

rˆˆ
3  zˆ rˆ rˆ rˆ  r̂  rˆ rˆ  rˆ  zˆ
The symbols Gr, Pr and Da indicate the Grashof
number, Prandtl number and Darcy numbers
respectively. Qgen refers to the source term
representing volumetric heat generation during
combustion. The species equation, which will be
presented in the latter section, is coupled to the
energy equation through these source terms.
CH4 + 2O2 ――› CO2 + 2H2O
C2H6 + 3.5 O2 ――› 2 CO2 + 3H2O
CO + 0.5 O2 ――› CO2
H2+ 0.5 O2 ――› H2O
Assumptions of the proposed model

 
2
1 ˆ rˆVˆrVˆz ˆ Vˆz
 pˆ
4  Vˆz

   ˆ Gr  ˆVˆz Da 
ˆ
rˆ rˆ
zˆ
 ẑ
3  ẑ  zˆ
BOUNDARY CONDITIONS
At the fuel inlet:
At fuel inlet the stagnation pressure is taken
equal to the ambient pressure at the same elevation.
Then, neglecting the viscous losses due to
acceleration of the fluid from surroundings to the
stove inlet. Further, the fluid is considered entering
the stove radially thus; axial velocity at the fuel inlet
is taken to be zero. Then, continuity equation dictates
the normal gradient of axial velocity is also zero. The
http://www.ijettjournal.org
Page 2752
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
temperature at the stove inlet can be assumed to the
ambient temperature,
ˆVˆz
1
pˆ   ˆVˆz2 , Vˆz 0,
0,
2
z

 0 for 0 rˆ 1, zˆ 0
(6)
At the axis of symmetry:
Due to assumed axi-symmetry of the flow,
computations may be carried out for only one axisymmetric plane of the domain as shown in figure 1.
Symmetry, then, dictates the radial velocity, normal
gradients of the axial-velocity and the temperature
respectively to be zero,
Vˆr 0,

ˆVˆz
r
0,
Tˆ
0 for rˆ 0, 0 zˆ  sˆ  Hˆ
r̂
(7)
( p0  0 gz) r12
0 02

, Vˆz  0,
ˆ Vˆr
rˆ
 0,
Tˆ
0
rˆ
(8)
At solid walls:
Ceramic liner is a solid wall boundary at all
locations other than the primary and secondary air
slots. At solid walls, the no slip boundary condition
would apply, i.e., both radial and axial velocities are
zero. For temperature, the convective boundary
condition is imposed,
Tˆ
Vˆr 0, Vˆz 0, k̂  qˆ w  NuTˆ for r rmax (z), 0 zˆ  Hˆ
rˆ

(9)
At the air inlets:
The air can be assumed to enter in the
combustor axial direction and stagnation pressure is
taken equal to the ambient pressure. The temperature
at port can be taken as the ambient temperature. Air
will flow due to free convection.
ˆVˆr
1 2
pˆ   ˆVˆr , Vˆr  0,
 0, Tˆ  0
2
rˆ
ISSN: 2231-5381
Equation for Property Variation:
The fluid properties such as viscosity and
thermal conductivity are assumed to be varying
according to the Sutherland’s relation as follows
 




3 1 Sˆ
194.44 ˆ 110.56
ˆ Tˆ 2
, Sˆk 
, S 
T0
T0
  Sˆ
3 1 Sˆ
kˆ Tˆ 2 k ,
  Sˆk
(11)
The variation of specific heat in terms of temperature
is expressed by a cubic polynomial as:
3
2
Cˆ p  0.1291Tˆ  0.3408Tˆ  0.0691Tˆ  0.9987
At the stoves exit:
The exhaust gases leaving the combustion
chamber can be treated as a jet entering a still
medium i.e. static pressure is equal to the local
ambient pressure. Also, assuming that the flow leaves
the exit radially, consequently, axial velocity is zero.
Thus, boundary conditions at the exit can be written
as;
pˆ 

(10)
where T̂ 
T
; T is in Kelvin.
1000
4 SOLUTION PROCEDURE
A finite volume method was employed to discretise
the governing equations. The SIMPLER algorithm,
Steady state, & K-  Turbulence model were used.
The discretised sets of algebraic equations were
solved by Ansys–fluent 13.0. To predict the effect
near the wall clearly, uniform grids are selected in
such a way that more number of grid points are near
the wall.
5 RESULTS AND DISCUSSION
The variation in Wall temperature and power input
gives different combustion temperature. The species,
temperature profiles and contours are generated of
800 K, 900K, and 1000K for 0.5KW, 1.0KW & 1.2
KW for each case. The temperature profile in the
domain shows that maximum temperature region
away from wall. This region corresponds to the flame
location. This also matches with maximum velocity
region. Maximum combustion temperature obtained
is 1263 K. The maximum combustion temperatures
shown in the table 1.1 for various cases.
http://www.ijettjournal.org
Page 2753
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
Figure a, b, & c shows temperature profile for
0.5KW, 1KW, &1.2KW respectively. The effect of
wall temperature and power on combustion
temperature is studied by varying power between 0.5
KW to 1.2 KW and wall temperatures between 800 to
1000 K. the simulations results show in figures (I-IX)
that with increase in wall temperature, by keeping
same power shows increase in combustion
temperature. It is clear that with increase in wall
temperature flame region is increasing and flame is
moving away from the wall and spread in radial
diffuser.
Similar effects are obtained with increase of power
with constant wall temperature. It is clearly indicates
increase in maximum combustion temperature with
increase in power and increase in wall temperature.
The contours below show to temperature variation in
vertical combustor. The contours arranged in the
manner of case id according to Table 1.1.
TABLE 1.1
Case
ID
Wall
Temperature
(K)
Power
1
P1T1
800
0.5 KW
1190
2
P2T1
800
1 KW
1200
3
P3T1
800
1.2 KW
1206
4
P1T2
900
0.5 KW
1219
5
P2T2
900
1 KW
1230
6
P3T2
900
1.2 KW
1232
7
P1T3
1000
0.5 KW
1249
8
P2T3
1000
1 KW
1262
9
P3T3
1000
1.2 KW
1263
Fig. (II)
Fig. (I)
ISSN: 2231-5381
Maximum
Combustion
Temperature
(K)
S.
N
.
http://www.ijettjournal.org
Page 2754
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
Fig. (III)
Fig. (VI)
Fig. (IV)
Fig. (VII)
Fig. (V)
Fig. (VIII)
ISSN: 2231-5381
http://www.ijettjournal.org
Page 2755
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
Fig. (b)
Fig. (IX)
Fig. (c)
Fig. (a)
6 CONCLUSIONS
Maximum flame temperature region tends to
move in radial diffuser.
In present work, the results of the combustion
simulation are summarized as follows:
(1) The velocity, species profiles and
temperature profiles are predicted by the
present combustion model. Results indicate
movement of the flame away from the wall
for higher volatiles flow rates and higher
wall temperatures.
(2) The region of maximum combustion
temperature also corresponds the zone where
the velocities are maximum.
(3) In general, maximum temperature in the
flame region tends to increase with increase
in wall temperature as well as power input.
ISSN: 2231-5381
ACKNOLEDGEMENT
I would like to express my deepest sense of gratitude
and sincere thanks to my highly respected and
esteemed guide Dr. RAJESH GUPTA (Associate
Professor), Department of Mechanical Engineering,
MANIT, Bhopal, for suggesting the subject of the
work and providing constant support, great advice
and supervision during the work of this thesis, which
appointed him as a backbone of this work. His
cooperation and timely suggestions have been
unparalleled stimuli for me to travel eventually
towards the completion of this thesis.
http://www.ijettjournal.org
Page 2756
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
REFRENCES
1.
S. Kohli & M.R. Ravi, Biomass stove: A Review, Journal of
Solar Energy Society of India, 6 (1996): 101-145.
2.
S. Bhandari, S. Gopi, A.W. Date, Investigation of CTARA
wood burning stove: Part I. experimental investigation,
Sadhana, 13(4) (1988): 271-293.
3.
S. Kohli, Buoyancy induced flow and heat transfer in
biomass stoves, PhD thesis, Indian Institute of Science,
Bangalore.
4.
S. Karthikeyan, Development of a combustion model for a
sawdust stove, M.Tech thesis, Department of Mechanical
Engineering, IIT-Delhi, (2000):12-24.
5.
G. Kaur, Modelling of carbon monoxide emissions in sawdust
stove, M.Tech thesis, Department of Mechanical
Engineering, IIT-Delhi, (2000):
6.
A.F. Roberts, Problems associated with theoretical analysis
of burning wood, Combustion Flames, 14(1971): 261.
7.
R. Gupta, Heat transfer & Fluid flow modeling of a single
pan wood stove, PhD thesis Department of Applied
Mechanics MANIT Bhopal (2010): 4312-5088.
ISSN: 2231-5381
http://www.ijettjournal.org
Page 2757