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Mathematical Modelling and Analysis http://mma.vgtu.lt
Volume 24, Issue 4, 507–529, 2019 ISSN: 1392-6292
https://doi.org/10.3846/mma.2019.031 eISSN: 1648-3510
Mathematical Modelling and Experimental
Study of Straw co-Firing with Gas
Inesa Barminab, Harijs Kalisa, Antons Kolmickovsb,
Maksims Marinakia, Liiva Ozolaa, Uldis Strautinsb,
Raimonds Valdmanisband Maija Zakeb
aInstitute of Mathematics and Computer Science of University of Latvia
Raina bulv¯aris 29, R¯ıga LV-1459, Latvija
bInstitute of Physics, University of Latvia
32 Miera Street, Salaspils-1, LV-2169, Latvia
E-mail(corresp.): kalis@lanet.lv
E-mail: inesa.barmina@lu.lv
E-mail: kolmic@lu.lv
E-mail: maksims.marinaki@lu.lv
E-mail: liiva@gmail.com
E-mail: uldis.strautins@lu.lv
E-mail: rww@inbox.lv
E-mail: mzfi@sal.lv
Received September 17, 2018; revised July 2, 2019; accepted July 5, 2019
Abstract. The main goal of the present study is to promote a more effective use
of agriculture residues (straw) as an alternative renewable fuel for cleaner energy
production with reduced greenhouse gas emissions. With the aim to improve the main
combustion characteristics at thermo-chemical conversion of wheat straw, complex
experimental study and mathematical modelling of the processes developing when co-
firing wheat straw pellets with a gaseous fuel were carried out. The effect of co-firing
on the main gasification and combustion characteristics was studied experimentally
by varying the propane supply and additional heat input into the pilot device, along
with the estimation of the effect of co-firing on the thermal decomposition of wheat
straw pellets, on the formation, ignition and combustion of volatiles (CO, H2).
A mathematical model has been developed using the environment of the Matlab
(2D modelling) and MATLAB package ”pdepe”(1D modelling) considering the vari-
ations in supplying heat energy and combustible volatiles (CO, H2) into the bottom
of the combustor. Dominant exothermal chemical reactions were used to evaluate
the effect of co-firing on the main combustion characteristics and composition of the
Copyright c
2019 The Author(s). Published by VGTU Press
This is an Open Access article distributed under the terms of the Creative Commons Attribution
License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribu-
tion, and reproduction in any medium, provided the original author and source are credited.
508 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
products CO2and H2O. The results prove that the additional heat from the propane
flame makes it possible to control the thermal decomposition of straw pellets, the
formation, ignition and combustion of volatiles and the development of combustion
dynamics, thus completing the combustion of biomass and leading to cleaner heat
energy production.
Keywords: reaction-diffusion equations, axisymmetric swirling flow, PDE system, Arrhe-
nius kinetics.
AMS Subject Classification: 35K57; 80A30; 65N06; 65N40; 65N25; 65N35.
1 Introduction
The comprehensive research of swirling flows along with the estimation of their
applicability to stabilize and control fuel combustion was started long ago and
is associated with the studies of Syred, Gupta and Lilley [13], [23], [30]. These
studies provide an analysis of the influence of the swirl level (S) on the swirl
flow dynamics and structure formation in the flame function zone.
Mathematical and physical fundamentals of chemistry, thermodynamics and
fluid mechanics of combustion are given in Law [22] and Powers [26].
In terms of the EU 20/20/20 targets of cleaner energy production [11],
the use of green energy sources, such as harvesting (wood) and agricultural
(straw) residues [3], Barmina et al. [4], Abricka et al. [1], Glithero et al. [12]
has become very important. Due to the rapidly increasing consumption of
harvesting residues, there is a growing demand for wider use of agricultural
residues (wheat or rape straw) for energy production. The use of agricultural
residues as a fuel is more problematic if compare with harvesting residues, and
can decrease energy production per mass of burned fuel, enhance the emission
of polluting CO and NOx along with the enhanced formation of ash, thus
limiting the applicability of straw for clean energy production (Glithero et
al. [12], Vassilev et al. [32]).
In order to eliminate the problems caused by the use of straw for heat
production, fuel mixture combined combustion processes are being developed
providing the co-combustion of straw with solid [25], [31] or gaseous (Brown et
al. [7]) fuel additives.
In the course of the studies of multi-fuel combined gasification/combustion
processes, it has been found [7], [25], that by varying the proportions of the fuels
in the mixture, the composition of emissions, the ash formation, the structure
and deposition on the heating surfaces can be controlled. With this account,
to minimize the negative effects when straw is used as a fuel and to assure the
effective control of the main combustion characteristics and products’ compo-
sition, the present research combines experiment and mathematical modelling
of the processes developing when co-firing straw with a gaseous fuel (propane)
by varying the propane and additional heat energy supply into the device.
In Barmina et al. [3], the formation of flame composition and tempera-
ture profiles downstream the swirling flame flows was studied experimentally.
In Kalis et al. [18], the studies of Choi, Rusak et al. [9], are continued by
conducting a numerical investigation in a cylindrical pipe with an inviscid, ax-
isymmetric, steady swirling flow in a low Mach number approximation. The
Modelling and Experimental Study 509
thermophysical and chemical parameters are assumed constant. The single step
exothermic chemical reaction is modelled by combining a fuel and an oxidant to
produce the product and heat using Arrhenius kinetics. The pressure is omit-
ted from the equations by introducing the stream function and the vorticity.
The swirling flow with axial and azimuthal velocities at the inlet develops. For
a hyperbolic type partial differential equaton (PDE) approximation, upwind
differences in space are used. The approximation in time is implicid, and for
solving the discreate vector problem the ADI Douglas–Rachford method [10] is
used. The results of the calculation show that at the a Lewis number Le ≥1
the increase in axial velocity leads to an increase in maximum temperature of
the reaction (and to a decrease at Le < 1).
A similar experiment in Zake et al. [34], is discussed. In Kalis et al. [19],
a similar numerical experiment with the full Navier–Stokes equations for a
viscous, incompressible axisymmetric swirling flow with the Reynolds number
100 in an axial external uniform magnetic field was performed. The MHD
process is considered in the so-called inductionless approximation. The effect
of gravitation is assumed. The following conclusions are drawn: if gravitation is
concerned an external magnetic field the inlet flow is deflected towards the wall
forming a prominent vortex that blocks the central part of the pipe; since the
conductivity of hot gases, such as air, oxygen, hydrogen is very low, the MHD
mechanism is not effective in practical applications of the gas combustion.
In Barmina et al. [5], experimental studies and mathematical modelling of
the effects of electric and magnetic fields induced by the direct electric current in
a coil electrode at the inlet of the combustor are carried out. The investigation
continues the study of Choi et al. [9] and Kalis et al. [18] in magnetic fields.
The results show the increase of the flow vorticity when increasing the magnetic
field-induced Lorentz force.
In Barmina et al. [6], two exothermic reactions for the combustion of H2
and CO are used for modelling by ANSYS Fluent CFD. The simulations gave
an insight into the combustion process in cases when the proportion of the
volatiles (H2, CO) corresponds to that of the biomass consisting of wood or
wheat straw, or peat, giving the temperature and velocity distributions in the
flame. The maximum flame temperature for the specified ratios 1:1 of the
volume fraction of these chemical substances in the fuel mixture was obtained.
In [2], [14], [15], [17], the applied electric field induces an electric current
between the walls of the combustor and the axially inserted electrode of different
length. The perfect gas model is used to solve the inviscid, axisymmetric,
steady swirling flow with axial and radial velocities and with circulation. The
action of the electric body force results in reduction of the free flame length.
The maximum field effect was achieved with a 10-20% straw mass fraction in
the fuel mixture (peat, wood, coal) [2], [15], [17].
In [16], [20] (Kalis et al.), the combustion process with Arrhenius kinetics
is modelled using simple exothermic chemical reactions and taking into ac-
count the electrodynamic effects due to the action of the Lorentz force on the
combustion process in a cylindrical pipe. A 2D axially symmetric nonstation-
ary physical model for the inviscid (Reynolds number Re =∞), compressible
swirling flow of ideal gas with two components of velocity ur, uz, with circu-
Math. Model. Anal., 24(4):507–529, 2019.
510 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
lation v=ruφ, density ρ, concentration of chemical species, temperature and
electromagnetic force is analyzed. For the discrete approximation of the con-
vective terms, the upwind differences in space are used. The stability for the
finite difference approximation is proved. In [16], to stabilize the calculations
of the MHD equations, the finite Reynolds number (Re=1000) is considered.
Increasing electrodynamic force leads to an increase in maximum velocity and
in temperature of the gas flow.
In this paper, we consider a model taking into account the interplay of 1D
and 2D laminar, axially symmetric compressible swirling flow (Re ≥10000)
with the propane combustion using six different chemical reactions. The value
of the finite Reynolds number Re is used to stabilize the compressible gas
dynamic flow. Modelling laminar flames requires the solution of the coupled
equations of mass, momentum, species balance and energy with detailed ther-
modynamic and transport relations and finite-rate chemistry. These equations
are solved for the density, velocities, species mass fractions, and for the tem-
perature. The obtained numerical and experimental results are compared.
2 Experimental studies
2.1 Experimental device
The processes developing when co-firing propane and wheat straw were stud-
ied using a batch-size pilot setup, which combines a biomass gasifier filled with
wheat straw pellets (1), the water-cooled sections of the combustor (3) and a
propane flame burner (4) with two symmetric nozzles for propane flame injec-
tion into the setup (Figure 1).
The gasifier was filled with straw pellets, the thermal decomposition of
which was initiated and sustained by the propane flame flow. The propane
flame provided an external heat flux input due to the total produced heat
energy varied from 6% up to 42%.
The experimental study involved joint measurements of the wheat straw
weight loss rate, measurements of the concentration of combustible volatiles
entering the combustor, measurements of the axial and tangential flow velocity
components and of the flame temperature, calorimetric measurements of the
heat output from the gasifier and water-cooled sections of the combustor and
of the produced heat energy per mass of burned pellets, and measurements
of the products’ composition (C O2, C O, H2, NOx, ppm), air excess ratio and
combustion efficiency by a gas analyzer Testo 350.
2.2 Experimental results and discussion
The thermo-chemical conversion of straw pellets in the device starts with dry-
ing, heating and thermal decomposition of pellets causing the weight loss of
the pellets which depends on the external heat source provided by the propane
supply into the setup (qprop [l/min]). According to the data of DTG and DTA
analysis, the wheat straw thermal degradation below 630 K can be related to
the development of the endothermic thermal decomposition of hemicelluloses
Modelling and Experimental Study 511
Figure 1. Principal schematic of the
batch size pilot setup for gasification and
co-firing of straw pellets with propane:
1 – gasifier of biomass pellets; 2 – primary
air supply nozzle; 3 – water-cooled
sections; 4 – propane flame injection
nozzles; 5 – secondary air supply nozzle;
6 – orifices for diagnostic tools.
Figure 2. Concentration of CO, H2
formed at the gasifier outlet vesrus the
injection of propane.
with an intensive heat energy consumption from the propane flame flow ac-
companied by the correlating decrease of the produced heat energy inside the
gasifier. A peak value of the wheat straw weight loss rate with a minimum
value of the produced heat energy was observed for a propane supply of about
0.4–0.5 l/min, which corresponds to an average heat power of the propane flame
of 0.65–0.75 kW. The measurements of the flame mix zone composition at the
bottom of the combustor showed that the increase of the weight loss rate at the
thermal decomposition of straw pellets correlated with the enhanced release of
the combustible volatiles CO, H2(Figure 2). In the figure, one can see the peak
value of the volatile mass fraction at the outlet of the gasifier which decreases
when the propane supply into device exceeds 0.5 l/min.
A slight decrease of the axial flow velocity to a minimum value was observed
at a propane supply of about 0.5 l/min, when the endothermic thermal decom-
position of wheat straw pellets resulted in correlating increase to a maximum
value of the weight loss rate of wheat straw pellets and of the mass fraction and
axial mass flow of combustible volatiles. A more pronounced decrease of the
wheat straw weight loss rate and mass flow of volatiles was observed when the
propane supply into the device exceeded 0.5 l/min and the propane flame down-
stream convection restricted the upstream heat/mass transfer and the thermal
decomposition of straw pellets. In Figure 4, one can see the concentration of
CO2versus the injection of propane.
Because of the ignition and flaming combustion of the volatiles entering the
Math. Model. Anal., 24(4):507–529, 2019.
512 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
combustor, the flame temperature and the CO2volume fraction in the products
increase to the peak value (Figure 3).
Figure 3. Effect of the propane supply
on average values of the flame
temperature (a).
Figure 4. Volume fraction of CO2
versus the injection of propane.
The heat output from the setup and the heat energy produced during the
burnout of the volatiles also increase, what allows to suggest that the co-firing
of straw with propane assures the complete combustion of the volatiles. By
analogy with the variations of the wheat straw weight loss rate and formation
of combustible volatiles, the flame temperature and the CO2volume fraction
in the products reach peak values when the propane supply into the device
approaches qprop=0.5 l/min and then they tend to decrease with the further
increase of the propane supply. However, the intensive development of the
endothermic processes at the primary stage of biomass thermo-chemical con-
version (t <1500 s) and the formation of volatiles (CO, H2) (Figures 5–6) affect
the total amount of the produced heat energy, advancing a slight decrease after
the propane supply into the device achieves 0.5 l/min.
3 Mathematical modelling of chemical reactions
For a more throuoght analysis of the processes developing at the combustion
of straw with gas, mathematical modelling and numerical simulation of the
processes were carried out considering three types of second-order exother-
mic irreversible chemical reactions at the chemical conversion of combustible
volatiles in order to assess their influence on the development of the combustion
dynamics.
The mathematical modelling and numerical simulation of the main combus-
tion characteristics were carried out using the experimental data on the mass
fraction of the main reactants at the inlet of the combustor or at the outlet of
the gasifier.
The gasification products H2, C O at the exothermal combustion of biomass
pellets when co-firing wheat straw with propane were investigated. Taking into
Modelling and Experimental Study 513
Figure 5. Effect of the propane supply
on the CO concentration at the bottom of
the combustor.
Figure 6. Effect of the propane supply
on the H2concentration at the bottom of
the combustor.
account the results of the experimental measurements, the average concentra-
tions of H2and CO with propane C3H8were considered in a mathematical
model with three types of exothermic chemical reactions to obtain the final
products H2O, C O2:
1. 2CO +O2→2C O2,2H2+O2→2H2O, 2C3H8+ 3O2→8H2+ 6CO
(three reactions with six species, C3H8is the species of propane);
2. C3H8+ 5O2→3CO2+ 4H2O(one reaction with four species);
3. 2CO +O2→2C O2,2H2+O2→2H2O(two reactions with five species).
The following mass fractions for the species Ck, k = 1, K .
1. K= 6, C1(CO), C2(O2), C3(CO2), C4(H2), C5(H2O), C6(C3H8propane),
2. K= 4, C1(C3H8), C2(O2), C3(CO2), C4(H2O),
3. K= 5, C1(CO), C2(O2), C3(CO2), C4(H2), C5(H2O),
were calculated for the nonlinear parabolic type PDEs. In the physical experi-
ment, the obtained average values of the CO, H2[mol/m3] concentration, such
as the mass fraction of concentration Ck,PK
k=1 Ck= 1, were used in the math-
ematical model at the combustor inlet (the sum of reactants to equal unity, but
that of the products was zero).
Assuming negligible thermal diffusion and equal constant multicomponent
diffusion coefficients, the diffusive mass flux vector of the species is decreased
to −ρD∇Ck,and the species equation for the mass fraction Ckreads as
ρD
Dt Ck=∇ · (ρD∇Ck) + mkΩk,
Math. Model. Anal., 24(4):507–529, 2019.
514 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
where D
Dt is a substantial derivative, D= 5 ·10−5[m2/s] is the constant
molecular diffusivity of the species, mk[g/mol] is the molecular weight of the
k-th species, ρ[kg/m3] is the density of the mixture. The production rate for
the k-th species can be written in the following form [29]:
Ωk=
J
X
j=1 h(ν00
j,k −ν0
j,k)Rj(T)
K
Y
n=1 ρCn
mnν0
jn i, k ∈[1, K ],
where Jis the number of reactions, Rj(T) is the rate constant modified by the
Arrhenius temperature dependence for the forward path of the chemical reac-
tion Rj(T) = A0
jTβjexp(Ej/RT ), A0
jdenotes the reaction-rate pre-exponential
factors, R=8.314 [J/(mol K] is the universal gas constant, ν00
j,k, ν 0
j,k are the cor-
responding stoichiometric coefficients of the k-th species appearing as a prod-
uct and reactant in the j-th reaction, βjis the order for the temperature.
The molecular weight of the species is to be straightforwardly taken from the
periodic table: O2= 32, CO = 28, CO2= 44, H2= 2, H2O= 18, C3H8= 44.
In the equation for the mass fractions of the concentration Ckthe source
term is mkΩk/ρ [1/s].
Under the assumption that the heat capacity does not depend on the tem-
perature T, the specific heat at the constant pressure cp=1000 [J/(kg K)] and
the thermal conductivity λ=0.25 [J/(smK)] are constant, and the only en-
thalpies needed are the enthalpies of the formation hk[kJ/mol] to be deter-
mined from the tables [26] (for H2,cpis approximely 14 [kJ/(kg K)] (Cebeci [8]).
The temperature equation is
ρcp
DT
Dt =∇ · (λ∇T)−
K
X
k=1
hkΩkmk.
In the equation for the temperature, the source term is 1
mρcpPK
k=1 hkmkΩk
[K/s], where m=1
KPK
k=1 mkis the mean molecular weight of the mixture.
The specific enthalpy of the k-th species hkis (Chemkin [27]):
O2= 0, CO =−111, CO2=−394, H2= 0, H2O=−242, C3H8=−105.
4 2D mathematical model
For 2D modelling, an axially symmetric ideal, laminar, compressible swirling
flow in a coaxial cylindrical pipe with the radius r0=0.05 [m], length z0=0.1 [m],
radial and axial components of velocity ur, uz, circulation v=ruϕis consid-
ered using one reaction with propane and oxygen reactants for combustion. In
the governing balance equations, some assumptions are made, i.e. constant
physical properties, negligible soot and flame radiation, laminar flow, and va-
lidity of the ideal gas law. We focus on a configuration in which a steady
low-velocity laminar flame exists in a straight pipe in the base state. The 2D
mathematical model is described by the Navier–Stokes, temperature and four
Modelling and Experimental Study 515
reaction-diffusion dimensionless equations in the cylindrical coordinates (r, z)
and at the time t:
∂ρ
∂t +M(ρ) + ρ1
r
∂(ru)
∂r +∂w
∂x = 0,
∂u
∂t +M(u)−Sv2
r3=−1
ρ
∂p
∂r +Re−1∆u −u
r2,
∂w
∂t +M(w) = −1
ρ
∂p
∂x +Re−1∆w,
∂v
∂t +M(v) = Re−1∆∗v,
∂T
∂t +M(T) = P0
1
ρ∆T +q1ρ5A1C1C5
2exp −δ1
T,
∂C1
∂t +M(C1) = P1∆C1−ρ5A1C1C5
2exp −δ1
T,
∂C2
∂t +M(C2) = P2∆C2−5ρ5A1C1C5
2exp −δ1
Tm2/m1,
∂C3
∂t +M(C3) = P3∆C3+ 3ρ5A1C1C5
2exp −δ1
Tm3/m1,
∂C4
∂t +M(C4) = P4∆C4+ 4ρ5A1C1C5
2exp −δ1
Tm4/m1,
(4.1)
where
∆q =∂2q
∂x2+1
r
∂
∂r (r∂q
∂r ), ∆∗q=∂2q
∂x2+r∂
∂r (1
r
∂q
∂r ), M (q) = w∂ q
∂x +u∂q
∂r .
Following Schlichting [28], in the Navier–Stokes equations in the cylindrical
coordinates for the azimuthal component of velocity uϕ=v
rthe circulation v
is determined and this equation is multiplied by r.
With C1,C2being the mass fractions of the reactants (propane C3H8and
oxygen O2), C3, C4the mass fractions of the products (CO2, H2O), in the
exotermic reaction C3H8+ 5O2→3CO2+ 4H2O,x=z/r0, w =uz/U0, u =
ur/U0, v =ruϕ,qdenotes any of the quantities ρ,u, w, v, T , Ck;Pk=D/(U0r0)
= 0.01, k=1(1)4, P0=λ/(cpρ0r0U0)=0.05, q1=Q1/(cpT0)=5, Q1= (m1h1+
5m2h2−3m3h3−4m4h4)/(m1m), (J/kg) is the heat loss in the reactions, δ1=
E1/(RT0)=48.11 is the scaled activation energy, R=8.314 (J/(mol K) is the
universal gas constant, E1= 1.2·105[J/mol] (Martinez [24], Westley [33]) is the
activation energy, A1=A0
1ρ5
0r0/(U0m5
2) is the scaled pre-exponential factors,
A0
1= 14[m15 /(mol5s)], Re =U0r0ρ0/η=10000 is the Reynolds number, η=
0.5·10−6(kg s/m) is the artificial viscosity. The value of the finite Reynolds
number Re is the stabilization factor to approximate the velocity equations.
The following parameters are also used: P e =r0U0/D,Le =λ/(cpDρ0)
are the Peclet and Lewis numbers, P0=Le
P e , Pk=1
P e , k = 1(1)4, S =V0
U0is
the swirl number. The equations were made dimensionless by scaling all the
lengths to r0=0.05 [m], the meridian velocity to U0=0.1 [m/s], the azimuthal
velocity uϕto V0=0.3 [m/s], the temperature to T0=300 [K], the density to
ρ0= 1[ kg
m3], the pressure to ρ0U2
0.
We introduced the stream function Ψand the vorticity ζto the following
Math. Model. Anal., 24(4):507–529, 2019.
516 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
expressions:
rρw =∂Ψ
∂r , rρu =−∂Ψ
∂x , ζ =∂ u
∂x −∂w
∂r .
Then the following equation for the stream function Ψis derived:
∂Ψ
∂t =∂
∂x ρ−1∂Ψ
∂x +r∂
∂r 1
ρr
∂Ψ
∂r +rζ,
where the equation for numerical simulation is transformed to a non-steady
one. The approach seeks the steady solution as the limit of solutions of the
unsteady equations.
The boundary of the pipe (r=r0) is subject to a heat loss modelled by the
Newtonian cooling in ambient surroundings at a temperature T0and with the
heat transfer coefficient h= 0.1[ J
s m2K].
The dimensionless boundary condition (BCs) are the following:
1) along the axis r= 0 −u=v= 0,∂s
∂r = 0, s =T;ρ;w;Ck, Ψ = 0,
2) at the wall r= 1 −u=v= 0, ∂ T
∂r +Bi(T−1) = 0, ∂s
∂r = 0, s=ρ;
Ck, Ψ =q , α∂ w
∂r + (1 −α)w= 0,
3) at the pipe outlet x=x0=z0
r0−u= 0, ∂s
∂x = 0, s=ρ;Ψ;T;Ck;w;v,
4) at the pipe inlet x= 0 −u= 0, ρ= 1,and w= 1, T= 1, C1=C10 ,
C2=C20,C3=C4=v= 0, Ψ= 0.5r2for r∈[0, r1] and w= 0, T= 1,
Ck= 0, Ψ=q,v= 4(r−r1)(1 −r)/(1 −r1)2for r∈[r1,1] (we have a
uniform jet flow at r < r1and the rotation at r≥r1with the maximum
azimuthal velocity when r= (1 −r1)/2).
Here q=r2
1
2is the dimensionless fluid volume, Bi =h r0
λ=0.1 is the Biot
number, r1= 0.75, x0= 2, α=exp(−1000/Re) is the characteristic parameter
of no-slip conditions for the axial velocity wdepending on Re.
For the invisced laminar flow (large Re), we have the PDE of hyperbolic
type. In this case, for the convective terms M(q), we use the implicit FDS
in time and the upwind diferences in space. The second-order derivatives are
approximed with central differences.
For the stabilization of the calculations, in the first equation of Equa-
tions (4.1), the last terms with density (divergency) with the derivatives ∂(ru)
∂r ,
∂w
∂x are approximated by backward differences, but the terms with the pressure
gradient ∂p
∂r ,∂p
∂z (p=ρT ) are approximated by forward differences [20], [21]. In
this case, we have a fast iteration process.
To solve the discrete problem, the ADI method of Duglas and Rachford [10]
was used in the vector form of nine elements from unknown values in Equa-
tions (4.1). The discrete 2D problem with 40 ×80 uniform grid points and
the time step 0.0008 s was solved. For the stationary solution with the maxi-
mum error 10−7, approximately 5000–7000 time steps were used (the final time
tf=5.1 s).
The boundary conditions for the species C1, C2at the inlet (x=0) are C10 =
0.2,0.6(C3H8), C20 = 1 −C10 (O2) (see Table 1 for tf=10, M w = max(w),
Modelling and Experimental Study 517
MT = max(T), M u = max(u), M C 3 = max(C3), M C 4 = max(C4), dp =
max(p)−min(p), mC2 = min(C2), M ro = max(ρ).
Finally, to prescribe the constant values on the Dirichlet portion of the
boundary x=0, we used the stoichiometric ratio s=0.044
5·0.032 =11
40 and then
solve the system for the mass fractions at stoichiometry:
C1
C2
=11
40,
C1+C2= 1,
which yields C10 =11
51 ≈0.22 and C20 =40
51 ≈0.78. The values of products
C30, C40 are set to zero at this segment of the boundary.
Table 1. Values of Mw, M u, M T, M C3(H2O), M C4(CO2), mC2(O2), dp, M ro versus C10
C10 Mw Mu MT M C 3M C4mC 2dp M ro
0.20 3.26 2.48 1.87 0.49 0.27 0.20 1.67 1.08
0.22 3.26 2.48 1.87 0.49 0.27 0.19 1.67 1.08
0.30 3.21 2.48 1.81 0.45 0.24 0.16 1.65 1.10
0.40 3.10 2.49 1.69 0.37 0.20 0.16 1.59 1.15
0.50 2.94 2.53 1.55 0.27 0.15 0.18 1.50 1.20
0.60 2.42 2.59 1.06 0.03 0.01 0.35 0.90 1.00
The results of the 2D modelling for the propane combustion at the small fi-
nite time (t=5.1 s) show that the maximum values of the products, temperature
and axial velocity are obtained in the combustor with fixed (0.20–0.22) mass
fractions of propane (see Table 1). In this case, the propane mass fraction at
the outlet of the combustor was minimal. The calculation with Re = 107gave
invariable results for these values. In the experimental studies, maxima of the
temperature and of the CO2at the bottom of the combustor at the 0.5 l/min
propane flow at a large time (1000–2000 s) were obtained (see Figures 3–6).
Figures 7–16 illustrate the development of the temperature, axial velocity
and concentrations in time (tf=0.4, 5.1) and in space for C1=C10=0.22,
C2=C20=0.78.
5 1D mathematical model
For mathematical modelling, the 1D distribution of the axial component of
velocity uz, density ρ, mass fraction for different Kspecies and temperature T
has been calculated with the Matlab routine ”pdepe” of the nonlinear parabolic
type PDEs system, depending on the time tand axial coordinate zfor six–nine
unknown functions. The 1D distribution of the axial component of velocity w=
uz/U0,(U0= 0.1m/s), density ρ/ρ0,(ρ0= 1 kg/m3), temperature T /T0,(T0=
300 K) and Kmass fractions Ckat the time t/t0,(t0=1 s), using the axial
coordinate x=z/z0,(z0= 0.1m) for K+3 unknown functions, was obtained.
For the mathematical modelling of the 1D compressible reacting swirling
flow and density, we considered two parabolic type PDEs with ρ, w(u= 0) in
Math. Model. Anal., 24(4):507–529, 2019.
518 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
0 0.5 1 1.5 2
1
1.2
1.4
1.6
1.8
2
T on x,Tmax=1.8681
z/r0
T/T0
r=0.025
r=0.1
r=0.5
r=0.75
r=1
Figure 7. Temperature vs. xwith fixed
rand tf=5.1.
0 0.5 1
1.4
1.6
1.8
2
T on r ,Tmax=1.8681
r/r0
T/T0
x=0.1
x=0.5
x=1
x=1.5
x=2
Figure 8. Temperature vs. rwith fixed
xand tf=5.1.
0 2 4 6
1.5
2
2.5
3
t[s]/5
maxT[K]/300
Figure 9. Maximum temperature vs. t
at tf=5.1.
0 0.1 0.2 0.3 0.4
0
0.05
0.1
0.15
0.2
0.25
t[s]/5
minC1
Figure 10. Minimum concentration of
propane vs. tat tf=0.4.
the following dimensionless form:
∂ρ
∂t +M(ρ) + ρ∂w
∂x =e∂2ρ
∂x2,
∂w
∂t +M(w) = −∂p
ρ∂x +Re−1∂2w
∂x2,
where M(s) = w∂s
∂x , s =ρ, w, Ck,Re=10000 and e= 10−5are the factors
of the artificial viscosity to approximate the velocity and density with upwind
differences in discrete equations.
The BCs at the inlet (x=0) are ρ=w=T= 1. These values are used
as initial conditions at t= 0. At the outlet, zero derivatives conditions are
applied. Numerical results depending on (x, t) are obtained for x∈[0,2], t ∈
[0, tf], tf= 1; 10. At the thermo-chemical conversion of biomass pellets and
their mixtures, maximum values of the temperature max T, axial flow velocity
max wand of the mass fractions of species were obtained.
Modelling and Experimental Study 519
0 0.1 0.2 0.3 0.4
0
0.2
0.4
0.6
0.8
t[s]/5
minC2
Figure 11. Minimum concentration of
O2vs. tat tf=0.4.
0 2 4 6
0
0.05
0.1
0.15
0.2
t[s]/5
minC2
Figure 12. Minimum concentration of
O2vs. tat tf=5.1.
0 2 4 6
0.45
0.5
0.55
0.6
0.65
t[s]/5
maxC3
Figure 13. Maximum concentration of
H2Ovs. tat tf=5.1.
0 2 4 6
0.01
0.02
0.03
0.04
0.05
0.06
t[s]/5
minC1
Figure 14. Minimum concentration of
propane vs. tat tf=5.1.
5.1 First type reaction: 2CO +O2→2CO2,2H2+O2→2H2O,
2C3H8+3O2→8H2+6CO
For the mathematical modelling of the first type reactions, we consider the
following dimensionless equations for six chemical species and for the temper-
ature:
∂T
∂t +M(T) = P0
ρ
∂2T
∂x2+q1ρ2A1Tβ1C2
1C2exp −δ1
T
+q2ρ2A2Tβ2C2C2
4exp −δ2
T+q3ρ4A3Tβ3C3
2C2
6exp −δ3
T,
∂C1
∂t +M(C1) = P1
∂2C1
∂x2−2ρ2A1Tβ1m1/m2C2
1C2exp −δ1
T
+6ρ4A3Tβ3m1/m2C3
2C2
6exp −δ3
T,
∂C2
∂t +M(C2) = P2
∂2C2
∂x2−ρ2A1Tβ1C2
1C2exp −δ1
T
−ρ2A2Tβ2C2C2
4exp −δ2
T−3ρ4A3Tβ3C3
2C2
6exp −δ3
T,
∂C3
∂t +M(C3) = P3
∂2C3
∂x2+ 2ρ2A1Tβ1m3/m2C2
1C2exp −δ1
T,
∂C4
∂t +M(C4) = P4
∂2C4
∂x2−2ρ2A2Tβ2m4/m2C2
4C2exp −δ2
T)
(5.1)
Math. Model. Anal., 24(4):507–529, 2019.
520 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
0 2 4 6
0.26
0.28
0.3
0.32
0.34
0.36
t[s]/5
maxC4
Figure 15. Maximum concentration of
CO2vs. tat tf=5.1.
0
0.4662
0.9324
0.9324
1 1
1
1
1
1.3986
1.3986
1.3986
1.8648
1.8648
1.8648
2.331
2.331
2.331
2.7972
2.7972
2.7972
Levels w ,Maxw = 3.2634,minw=0.0000
z/r0
r/r0
0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
Figure 16. Levels of the axial velocity
at tf=5.1.
+8ρ4A3Tβ3m4/m2C3
2C2
6exp −δ3/T ,
∂C5
∂t +M(C5) = P5
∂2C5
∂x2+ 2ρ2A2Tβ2m5/m2C2C2
4exp −δ2
T,
∂C6
∂t +M(C6) = P6
∂2C6
∂x2−2ρ4A3Tβ3m6/m2C3
2C2
6exp −δ3
T,
where qk=Qk/cpT0), k= 1,2,3; ‘Q1= (2m1h1+m2h2−2m3h3)/(m2m),
Q2= (m2h2+ 2m4h4−2m5h5)/(m2m), Q3= (−6m1h1+ 3m2h2−8m4h4+
2m6h6)/(m2m) are the heat losses for each reaction [J/kg], Pk=Dk/(U0z0) =
0.01, P0=λ/(cpρ0U0z0)=0.05, λ=0.25 [W/(m.K)] is the thermal conductivity,
Dk= 5 ·10−5[m2/s] is the molecular diffusivity of species, δj=Ej/(R T0)
stands for the scaled activation energies, R=8.314 [J/mol K] is the universal
gas constant, A1=A0
1ρ2
0z0/(U0m2
1), β1=β2=β3= 0, A2=A0
2ρ2
0z0/(U0m2
4),
A3=A0
3ρ4
0z0/(U0m2
2m2
6) are the scaled reaction-rate pre-exponential factors,
A0
1= 1500 [m6/mol2s], A0
2= 190 [m6/mol2s], A0
3= 140 [m12/mol4s], E1=
E2=E3=120000 [J/mol] [24].
The BCs for C6, C2at the inlet (x= 0) are C60 ={0.25,0.8}(C3H8),
C20 = 1 −C60(O2) (see Table 2 for tf= 10, C kend =Ck(2, tf), k= 1,3,4,5,6;
C2end = 0(O2). We can also obtain the BCs from the stoichiometric ratio s=
2·0.044
3·0.032 =11
12 and then solve the system for the mass fractions at stoichiometry:
C6
C2
=11
12,
C6+C2= 1,
which gives C20 =12
23 ≈0.52 and C60 =11
23 ≈0.48.
The products C10, C30, C40, C50 are set to zero on this segment of the bound-
ary. These boundary conditions at the inlet were used as initial conditions at
t=0. At the outlet, the zero derivatives conditions were used. The mass fraction
of the reactant O2decreased to zero at t=tf.
The results of 1D modelling for the propane combustion (similar to 2D
modelling) at the finite time (tf= 10 s) demonstrate that maximum values
of the products, temperature, axial velocity are obtained with the 0.25 mass
fractions of propane. The numerical results depending on (x, t) are listed in
Modelling and Experimental Study 521
Table 2: Mw =max(w), M T =max(T), T end =T(2, tf), w end =w(2, tf),
Ckend =Ck(2, tf). For the mass fractions of the combustible volatiles CO , H2,
maximum are obtained at C60 ≥0.7. This is in accord with the results of the
experimental measurements at the outlet of the gasifier (Figure 2) when the
maximum of the concentration CO, H2is obtained at the propane injection
0.5 l/min.
Table 2. Values of Mw, w end, MT , T end, C1end(CO), C3end(CO2), C 4end(H2),
C5end(H2O), C6end(C3H8) versus C60 .
C60 M w wend M T T end C1end C 3end C4end C 5end C6end
0.25 3.57 2.22 10.9 5.10 0.0 0.74 0.00.40 0.0
0.28 3.38 2.20 10.6 4.90 0.01 0.79 0.01 0.38 0.01
0.3 3.69 2.14 10.3 4.59 0.02 0.81 0.01 0.24 0.02
0.35 4.09 2.05 10.1 4.08 0.07 0.79 0.02 0.27 0.04
0.44.14 1.98 9.55 3.76 0.12 0.78 0.03 0.22 0.07
0.5 3.56 1.87 8.11 3.34 0.20 0.68 0.04 0.15 0.17
0.6 3.03 1.76 7.01 3.03 0.28 0.54 0.05 0.09 0.27
0.7 2.83 1.61 5.73 2.76 0.31 0.39 0.05 0.06 0.40
0.8 2.82 1.34 4.56 2.45 0.32 0.24 0.05 0.03 0.55
The time (final time tf=10) and space variations of the temperature and
concentrations at C60=0.4 are displayed in Figures 17–22.
0 0.5 1 1.5 2
0
2
4
6
8
10
T of x,Tend=3.7592
z/z0
T/T0
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 17. Temperature vs. xwith
fixed t.
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
C1 of x c1end=0.1237
z/z0
C1
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.00
Figure 18. CO concentration vs. x
with fixed t.
5.2 Second type reactions: C3H8+5O2→3CO2+4H2O
For the mathematical modelling of this reaction (similar to 2D modelling) for
four chemical species and for the temperature, we use Eqs. (4.1). The BCs
for C1, C2at the inlet (x= 0) are C10 = 0.1,0.7(C3H8), C20 = 1 −C10 (O2)
(see Table 3 with tf= 10). From the other algorithm it follows that C1
C2=
11
40 , C1+C2= 1 or C10 = 0.22, C20 = 0.78.
The maximum values of M T, M w, wend, T end, C O2, H2Owere obtained
(similar to 2D modelling) for C10=0.2 when the propane mass fraction at the
Math. Model. Anal., 24(4):507–529, 2019.
522 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
0 0.5 1 1.5 2
−0.2
0
0.2
0.4
0.6
C2 of x c2end=0.0000
z/z0
C2
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 19. O2concentration vs. x
with fixed t.
0 0.5 1 1.5 2
−0.5
0
0.5
1
1.5
C3 of x c3end=0.7814
z/z0
C3
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 20. CO2concentration vs. x
with fixed t.
0 0.5 1 1.5 2
−0.1
0
0.1
0.2
0.3
C5 of x c5end=0.2223
z/z0
C5
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 21. H2Oconcentration vs. x
with fixed t.
0 0.5 1 1.5 2
−0.1
0
0.1
0.2
0.3
0.4
C6 of x c6end=0.0747
z/z0
C6
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 22. Propane C3H8
concentration vs. xwith fixed t.
outlet x=2, C1end=0.004. For C10=0.1, C1end=0, but the mass fractions of
O2C2end=0.54 (the mass fraction for propane at the inlet was too small).
Figures 23–28 illustrate the development of the temperature, axial velocity
and concentration in time (tf=10) and in space for C1=C10 = 0.4, C2=
C20=0.6.
5.3 Third type reactions: 2CO +O2→2CO2,2H2+O2→2H2O
According to the results of the experimental measurements at the outlet of the
gasifier (Figures 1–2), the average concentrations of H2and CO were used in
the chemical reactions of the mathematical model to obtain the final products
H2O, C O2, where O2is the third reactant in the reactions. Referring to the
experimental data, the average values of C1(CO) and C4(H2) at the inlet of
the combustor depending on the propane injection qprop are the following
(mol
m3=g/m3
g/mol , m(H2) = 2 g
mol , m(CO) = 28 g
mol ):
1*) 0.16 [l/min]-H2= 1.65 [mol/m3], CO = 1.82 [mol/m3];
2*) 0.33 [l/min]-H2= 1.35 [mol/m3], CO = 1.71 [mol/m3];
3*) 0.44 [l/min]-H2= 2.00 [mol/m3], CO = 2.39 [mol/m3];
4*) 0.56 [l/min]-H2= 1.50 [mol/m3], CO = 2.11 [mol/m3];
5*) 0.62 [l/min]-H2= 1.30 [mol/m3], CO = 1.82 [mol/m3].
Modelling and Experimental Study 523
Table 3. Values of Mw, w end, MT , T end, C1end(C3H8), C2end(O2), C 3end(CO2),
C4end(H2O) versus C10.
C10 M w wend M T T end C1end C 2end C3end C 4end
0.1 4.48 1.61 4.78 2.11 0.00 0.54 0.30 0.16
0.26.64 1.97 8.48 3.67 0.01 0.09 0.59 0.32
0.3 6.41 1.93 7.91 3.52 0.12 0.04 0.54 0.30
0.4 5.64 1.87 7.02 3.27 0.25 0.04 0.46 0.25
0.5 4.71 1.81 6.23 3.04 0.37 0.04 0.38 0.21
0.6 4.50 1.73 5.21 2.82 0.50 0.04 0.30 0.16
0.7 2.83 1.61 4.17 2.59 0.63 0.04 0.22 0.12
0 0.5 1 1.5 2
0
2
4
6
8
T of x,Tend=3.2728
z/z0
T/T0
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 23. Temperature vs. xwith
fixed t.
0 5 10
0
2
4
6
8
T of t,Tmax=7.0186
t/t0
T/T0
x=0
x=0.02
x=0.68
x=1.34
x=2.0
Figure 24. Temperature vs. time t
with fixed x.
These values were used in the mathematical model as the concentration
mass fraction Ck, k=1(1)5 for the initial conditions, decreasing thus these val-
ues by about five times. Here C1+C2+C4= 1 (the mass factions of the
reactants) and C3=C5= 0 (the mass factions of the products). To obtain the
temperature and mass fractions of the species, we used the first type reactions
without the propane reaction (with Eqs. 5.1) with A3=0.)
The BCs at the inlet x=0 – C1=C10(CO), C2=C20 (O2), C4=C40(H2) –
depend on five different injections of propane.
The numerical results determined by (x, t) are summarized in Table 4 at
tf=1, C2end = 0(O2).
In Table 4, it is seen that for propane injections qprop 2* and 5*, maximum
values of the temperature, axial velocity and mass fractions of the products
CO2, H2Oare obtained when the mass fraction of O2is maximum at the inlet.
The concentration of the products increases in time. The mass fraction of
the reactants CO, H2in the reactions at a small time moment (t= 0.5 [s])
decreases, and for O2decreases to zero for all propane injections.
For injection 5*, Figures 29–32 show the variation of the temperature and
concentrations of H2, CO in space x∈[0,2] at tf=10. The results of the math-
ematical modelling show that, in accordance with the data of the experimental
study, the maximum values of the flame temperature, axial flow velocity and
mass fractions of the main products (CO2, H2O) at the thermo-chemical con-
Math. Model. Anal., 24(4):507–529, 2019.
524 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
0 0.5 1 1.5 2
0.2
0.25
0.3
0.35
0.4
C1 of x c1end=0.2458
z/z0
C1
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.00
Figure 25. Propane C3H8
concentration vs. xwith fixed t.
0 0.5 1 1.5 2
−0.2
0
0.2
0.4
0.6
C2 of x c2end=0.0392
z/r0
C2
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 26. O2concentration vs. x
with fixed t.
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
0.5
C3 of x c3end=0.4627
z/z0
C3
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 27. CO2concentration vs. x
with fixed t.
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
C4 of x c4end=0.2524
z/z0
C4
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 28. H2Oconcentration vs. x
with fixed t.
version of the biomass pellets and their mixtures were obtained for the fixed
magnitude of the propane flow when co-firing straw with a gas. The results
of the mathematical modelling for the propane combustion give evidence that
the maximum values of the products are obtained for 0.33 and 0.62 l/min of
the propane supply (see Table 4). In the experiments, the maximum of the
temperature and CO2was obtained at 0.5 l/min (Figures 3–4).
In following Table 5 it is seen the comparison values of Tend, obtained in experi-
ment T endexp and in modelling T endmod for 4 series of propane injections qprop
( 1*,2*,4*,5*) (see Figure 34), the errors ∆Ti=T endexpi −T endmodi, δTi=
Pn
i=1 ∆Ti
n−∆Ti, for calculation the error Vk=pPn
i=1(δTi)2/(n(n−1)) =
27.16[K] or 20.3% corresponding to errors ∆Tiaveraging value 133.5[K] (n=4).
Similarly results are obtained for maximum values of temperature TM: Vk=
53.58[K] or 22.1% corresponding to averaging error 242.5[K].
We can see that T Mmod > T Mexp .Using the chemical reaction the flame
temperature by t= 0.2s, x = 0.68(z= 0.068m) rapidly increases to its maxi-
mum value 1149Kand then decreases in the time and space (t= 10s, x = 2.0)
to T end = 570K(see Figure 32 for propane injection 5*).
In following Figures 33–34 we represent the concentration of species CO
in experiment [g/m3] at the inlet and calculated mass fraction at the outlet
and temperature at the outlet T end in experiment and modelling depends on
propane injection qprop [l/min].
Modelling and Experimental Study 525
Table 4. Values of Mw, w end, MT , T end, Ckend, k = 1,3,4,5, tf=10.
Ck1∗2∗3∗4∗5∗
C10(C O) 0.36 0.34 0.44 0.42 0.36
C40(H2) 0.33 0.27 0.32 0.30 0.26
C20(O2) 0.31 0.39 0.24 0.28 0.38
C5end(H2O) 0.26 0.33 0.18 0.21 0.30
C4end(H2) 0.30 0.23 0.29 0.28 0.23
C3end(CO2) 0.22 0.28 0.26 0.27 0.30
C1end(CO) 0.22 0.16 0.28 0.25 0.17
Mw[m/s] 0.44 0.47 0.41 0.44 0.47
wend[m/s] 0.15 0.16 0.15 0.15 0.16
T end[K] 525 570 510 522 570
M T [K] 954 1146 970 939 1149
Table 5. Values of qprop [l/min], T endexp[K], T endmod [K],∆T, δ T, T Mexp, TMmod
qprop T endexp T endmod ∆T δT T Mexp T Mmod
0.16 583 525 58 75.5 783 954
0.33 700 570 130 3.5 797 1140
0.56 698 522 176 −42.5 808 939
0.62 740 570 170 −36.5 824 1149
Differences in curve trends are mainly determined by (in our opinion) the
two main factors – first of all that the difference is in experiment for air predom-
inance. So the CO2concentration in the channel outlet is lower, and the CO
is higher than the stoichiometric combustion process calculations. Secondly, it
is possible that the burning process is not over until the channel exit. This
is essentially confirmed by measurements of the efficiency of the combustion
process, which is relatively low at the channel outlet and does not exceed 80%.
The results of experimental study and mathematical modelling have shown
that the composition and temperature of the products at co-firing straw with
propane is strongly influenced by the propane supply into the device (Figures
33, 34). The enhanced development of the endothermic processes at the thermal
decomposition of straw promotes a correlating increase of the molar fraction of
CO at the outlet of the gasifier (Figure 2) determining a decrease of the tem-
perature at the outlet of the device (Figure 34). Difference between the results
of the experimental study and mathematical modelling is predominately de-
termined by the difference in length of the experimental device (L=z0=0.4 m)
and cylindric pipe (z0= 0.1 m), which is used for the mathematical modelling
of the processes developing at straw co-firing with propane. The local increase
of the molar fraction of CO with correlating decrease of the flow temperature
at this distance (z0=0.1) suggest incomplete combustion of volatiles on the
development of the thermochemical conversion of straw and the flame temper-
ature, as it follows from the results of mathematical modelling (Table 4 and
Math. Model. Anal., 24(4):507–529, 2019.
526 I. Barmina, H. Kalis, A. Kolmickovs, M. Marinaki et al.
0 0.5 1 1.5 2
0.1
0.2
0.3
0.4
0.5
C1 of x c1end=0.1690
z/z0
C1
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.00
Figure 29. Concentration of CO vs. x
with fixed t.
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
C5 of x c5end=0.3047
z/z0
C5
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 30. Concentration of H2Ovs.
xwith fixed t.
0 0.5 1 1.5 2
0
0.1
0.2
0.3
0.4
C3 of x c3end=0.3001
z/z0
C3
t=0.0005
t=0.251
t=1.001
t=3.501
t=10.001
Figure 31. Concentration of CO2vs. x
with fixed t.
0 5 10
1
2
3
4
T of t,Tmax=3.8313
t/t0
T/T0
x=0
x=0.02
x=0.68
x=1.34
x=2.0
Figure 32. Temperature Tvs. twith
fixed x.
Figure 34). Complete combustion of volatiles is observed further downstream
(z0=0.4), when a decrease of the molar fraction of volatiles in the products cor-
relates with an increase of the flame temperature (Figure 3 ) and temperature
at the outlet of the device (Figure 34).
Figure 33. Concentration of species CO in
experiment [g/m3] at the inlet and calculated
mass fraction C1end at the outlet depends on
propane injection qprop [l/min].
Figure 34. Comparision Tend in
experiment and modelling at the outlet
depends on propane injection
qprop[l/min].
Modelling and Experimental Study 527
6 Conclusions
Because of complexity the processes developing during straw co-firing with
propane the comparison of the results of experimental study and mathematical
modelling is rather qualitative, but still to be considered as a productive col-
laboration between the partners. The results of the performed mathematical
modelling have shown that, in accordance with the data of the experimental
study the main flame characteristics (flow velocity, flame temperature and com-
position of the products) are influenced by the variations of the propane supply
into the device responsible for the enhanced thermal decomposition of straw,
the formation, ignition and burnout of combustible volatiles (CO, H2).
The results of 1D and 2D modelling of the processes developing at co-firing
of straw with propane demonstrate that the maximum value of the molar frac-
tion of the products and flame temperature for the stoichiometric combustion
conditions can be achieved during the relatively small time period (t < 10s)
and refer to the mass fraction of propane 0.2–0.25 at the inlet of the combustor.
In the experiments of straw co-firing with propane, which were developing at
the air excess ratio in the flame reaction zone and were lasting up to 2400s,
the propane supply into the device causes a decrease of the molar fraction of
combustible volatiles in the products to the minimum value with correlating
increase of the flame temperature and the CO2volume fraction in the products
up to the peak values, which for the conditions of the air excess supply were
observed at the higher propane supply into the device – 0.5 l/min.
Differences in curve run are mainly determined, in our opinion, by the difference
in length of the reaction zone downstream the experimental device and by the
reduced length of the reaction zone, which is used at mathematical modelling
of straw co-firing.
The results presented above prove that the additional heat supply during
co-firing of straw with propane flame flow makes it possible to control the
thermal decomposition of straw pellets, the formation, ignition and the com-
bustion of volatiles and the development of combustion dynamics, completing
the combustion of biomass and leading to cleaner heat energy production.
Acknowledgements
The authors would like to express their gratitude for the financial support from
the European Regional Funding for a project SAM 1.1.1.1/16/A/004.
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