276
Energy & Fuels 1996, 10, 276-283
Mathematical Modeling of Straw Bale Combustion in Cigar Burners Niels Bech* Department of Combustion Research, Risø National Laboratory, DK-4000 Roskilde, Denmark
Lars Wolff I/S VESTKRAFT, Vestkraftkaj 2, DK-6701 Esbjerg, Denmark
Lars Germann Danish Technological Institute, Teknologiparken, DK-8000 A° rhus C, Denmark Received October 2, 1995. Revised Manuscript Received January 16, 1996X
A computer model is presented for the calculation of the steady and nonsteady behavior of straw bales subject to surface combustion in cigar burners. The mathematical formulation is one-dimensional and the flow of gas through the straw bales is described by means of Darcy’s law for flow through a porous medium. The computer model is able to predict flow rate, temperature and composition of gas and straw as function of axial length and time. Calculated results are compared to measurements of temperature and gas composition profiles within the burning straw bales. It is observed that the straw bale temperatures as well as the outlet gas composition are predicted reasonably well. Calculations have been carried out in order to assess the implication of a straw bale feed stop upon combustion in a 3 MW district heating plant fueled with Heston straw bales. The results indicate that serious disturbances may be introduced.
Introduction Heston straw bales are presently used in Denmark as a fuel in small (3-20 MW) district heating plants. The straw bales are burned by surface combustion in so-called cigar burners. Among the challenges facing manufacturers and operators today are (1) a need to reduce construction cost through new plant design; (2) more restrictive emission standards; and (3) a need to increase the power output of the single burner in order to permit combined heat and power production. In order to address such tasks there is a wish among manufacturers as well as operators to gain access to a computer model which is capable of predicting trends in plant behavior as a function of various parameters such as plant geometry and operating conditions. On this background, a computer model, STRAW, has been developed for the calculation of the steady and nonsteady behavior of straw bales subject to surface combustion in cigar burners. The model which is able to predict flow rate, temperature, and composition of gas and straw as function of axial length and time represents one module of a computer program for the calculation of the behavior of small district heating plants based on surface combustion of Heston straw bales. Paralleling the theoretical efforts, experiments have been carried out with the purpose of measuring temperature and concentration profiles within the burning straw bales as well as in the furnace room. The X
Abstract published in Advance ACS Abstracts, February 15, 1996.
0887-0624/96/2510-0276$12.00/0
Figure 1. Surface combustion of straw. Definition of processes and zones.
measurements have been used in the validation of STRAW. The present article describes the mathematical foundation of the model and the experimental work. Calculations have been carried out in order to assess the implication of a straw bale feed stop in a 3 MW district heating plant fueled with Heston straw bales. The results indicate serious disturbances in the performance of the burner. © 1996 American Chemical Society
Straw Bale Combustion in Cigar Burners
Energy & Fuels, Vol. 10, No. 2, 1996 277
Principle of Surface Combustion The principle of surface combustion of straw bales is illustrated in Figure 1 after ref 1. The straw bales are fed from the left at a rate corresponding to the combustion rate in such a way that the burning bale front remains at a fixed position. The figure shows the different process areas. Due to diffusion and subsequent condensation of water vapor, a zone of straw with a water content higher than that of raw straw may appear. As the temperature rises the straw is dried and after that it undergoes pyrolysis. The required heat is transported from the burning surface through thermal conduction and radiation. When the devolatilization of the straw is finished straw char remains. The burning of the char finally results in a layer of ash or slag. Primary air is injected for the combustion at the straw surface, while oxygen for the combustion in the furnace room of the remaining gases is provided by a secondary air stream.
ug ) uh -
p ) RTKgFg/MWg
(7)
Ideal gas law:
Relationships and Constraints.
mg )
∑i mig
(8)
mh )
∑i mih
(9)
Fg ) mg/Φ
(10)
mh 1-Φ
(11)
Cij ) mij/mj
(12)
uig ) ug + ∆uig
(13)
ug )
∂(egug) +
∂t
∂x
) Qg +
∑i
(Γihip
∂t
+ uh
∂eh ∂x
) Qh -
Cpj )
+
∂
( ) ∂Th
Momentum for the gas phase (Darcy’s law):
(15)
∑i Cig/MWi
(16)
∑i CijCpji
(17)
hg ) eg/mg
(18)
hh ) eh/mh
(19)
hg - Cw g hwg + Tref Cpg
(20)
hh + Tref Cph
(21)
Th )
∑i Γihip + ∂x λ*h ∂x
(1) Gundtoft, S. Jysk Teknol. 1989.
Di dCg )ΦCig dx
(2)
i i Sinj hinj )
(14)
MWg ) 1/
Tg )
i (Th - Tref) + ∆hip hip ) Cph
if Γi g 0
(22)
hip ) Cipg(Tg - Tref) + ∆hip
if Γi < 0
(23)
(3)
Energy equation for the straw:
∂eh
∑i miguig/mg i
∆uig
Mass conservation for component i in the straw:
∂eg
(5)
(6)
(1)
Energy equation for the gas phase:
)
uh ) constant
Fh )
Assumptions. The following assumptions are made: 1. The system is one-dimensional in space. 2. The cross-sectional area of the straw bales is constant. 3. The gas is described as an ideal gas. 4. The flow of gas through the straw grid is described by means of Darcy’s law for flow through a porous medium. 5. The velocity of the straw grid is constant in the axial direction (but not in time). 6. The porosity and the permeability of the straw grid depends upon time and the location in the bale. 7. Only water vapor diffusion is considered at the moment. 8. Straw-gas and gas-gas thermal radiation is neglected in the straw bales. Basic Equations. Mass conservation for component i in the gas phase:
∂mih ∂mih + uh ) -Γi - Sih ∂t ∂x
(
Momentum equation for straw:
The Computer Model STRAW
∂mig ∂(miguig) + ) Γi + Sig ∂t ∂x
K dp + g cos ΘFg µg dx
(4)
Qg ) QFg + (1 - ∂)QFh + Qhg
(24)
Qh ) ∂QFh - Qhg
(25)
Qhg ) htc(Th - Tg)A′int/A
(26)
The straw-gas heat transfer coefficient is obtained from the correlation:
278
Energy & Fuels, Vol. 10, No. 2, 1996
Bech et al.
htc ) htc0 + c1Recg2Prcg3
(27)
Reg ) (ug - uh)FglRe/µg
(28)
Prg ) µgCpg/λg
(29)
where
The parameters htc0, c1, c2, c3 and lRe are constants specified through the input. The following constraints apply:
∑i Cij ) 1
(30)
∑i (Sig - Sih) ) Sinj
(31)
(b) The combustible fuel pseudocomponent contains (1) hydrogen, (2) methane, and (3) carbon monoxide also at a fixed a priori specified ratio! These restrictions may be relaxed at a later stage by incorporating a pyrolysis module which yields composition as well as rate of formation of the gas formed by pyrolysis of the straw. The combustion of 1 kg of fuel proceeds as follows: 2 1 kg of fuel + SFU kg of oxidant + (CCO kg of CO2 + v
CO2 2O CH kg of H2O)/CFU + v v f (1 + SFU + (Cv FU 2O CH v )/Cv ) kg of products or a kg of H2O + b kg of CO2 + c kg of N2 (37)
where
(
Evaporation and Condensation of Water. The water evaporation and condensation rates are computed from the following expressions: Evaporation:
(32)
if Th g 0 and else 0
Γw )
-
w mgmax )
Γ )
H2 9CFU
9 CH4 Cv + CFU + FU 4 C
(39)
CO2
b)
(33)
11 CH4 11 CO Cv C + CFU + FU 4 FU 7 C
(40)
v
2 c ) SFUCN OX
if
mw g
g
w mgmax
and else 0 (34)
-1 where kw c ) 0.1 s The maximum possible water content of the gas phase is calculated as function of straw temperature as given in ref 2. Pyrolysis of Straw. The rate of formation of gases from pyrolysis of the straw is computed from an Arrhenius type of expression:
v
(38)
v
-1 C-1. where Aw f ) 100 s Condensation:
w -kw c (mg
)
1 2 /CO OX CFU v H 2O
a)
w Γw ) kw f mh w kw f ) Af (Th - Twsat)
SFU ) a + b -
kvpmvh
kvp ) Avp exp(-TvKp/TKh)
(35) (36)
In the present calculations Avp ) 9000 s-1 and Kpv ) 1 × 106 K. The values of Avp and TvKp have been adjusted so that the devolatilization of the straw takes place between 200 and 600 °C as observed in experiments.3 Combustion of Gas. The gas phase is assumed to consist of up to four pseudocomponents: (1) oxidant; (2) volatiles from the pyrolysis of the straw; (3) water; and (4) combustion products. The oxidant consists of oxygen and nitrogen. In the present version of the code it is further assumed that (a) The volatiles from the pyrolysis of the straw contains (1) carbon dioxide, (2) water, and (3) a combustible fuel pseudocomponent at a fixed a priori specified ratio! (2) Gundtoft, S. In Combustion, theory and practice; (Forbrænding, teori og praksis, in Danish); Bech, N., Dahlin, J., Eds.; Polyteknisk Forening: Copenhagen, 1988; Chapter 6. (3) Kofoed, E.; Pedersen, P. H.; Christensen, O.; Gabriel, S.; Henriksen, U.; Koch, T. “Heat transport in straw” (“Varmetransport i halm”, in Danish); Laboratoriet for Energiteknik, Danish Technical University, July 1991.
(41)
The rate of combustion of the gaseous fuel was computed by means of the eddy breakup model.4
SFU g ) Fg(/k)CRCAClim
(42)
CR ) 4
(43)
CA ) 1
(44)
where
(
Clim ) min Cg,
2 CO CPR g g , SFU 1 + SFU
)
(45)
The ratio of the dissipation of the turbulence kinetic energy, , to the turbulence kinetic energy, k, is an input parameter. The value used in the present calculations is /k ) 1500 s-1. This value represents the turbulence at the straw bale surface. Formation of volatiles (which is negative): FU Svg ) SFU g /Cv
(46)
Formation of oxidant (which is negative): FU SOX g ) SFUSg
(47)
Formation of products from combustion of gaseous fuel: FU FU SPR g ) -Sg (SFU + 1/Cv )
(48)
Heat production from combustion of gaseous fuel: (4) FLOW3D Release 3.2. CFD Department, AEA Industrial Technology, Harwell Laboratory, October 1992.
Straw Bale Combustion in Cigar Burners
QFg ) -SFU g ∆hFg
Energy & Fuels, Vol. 10, No. 2, 1996 279
CO H2 CH4 ∆hFg ) (10.1CFU + 121CFU + 50.1CFU ) × 106 (50)
Combustion of Straw Char. The solid matter which is left after complete pyrolyzation, i.e., the straw char, is assumed to consist of two components: (1) carbon and (2) ash. It is further assumed that the combustion products are (1) carbon dioxide, (2) carbon monoxide, (3) nitrogen, and (4) ash. The ratio of carbon monooxide to carbon dioxide formation rate is described by an Arrhenius expression:
r ) CO/CO2 ) Ar exp(-TKr/TKh)
(64)
where6 Ac ) 497 kg/s/m2 and TKc ) 8540 K. Actually the straw wall thickness is used in eq 62 rather than the straw diameter dh. The formation of oxidant (which is negative) is C SOX hg ) SCSh
(65)
The formation of products from combustion of carbon is C SPR hg ) -Sh (d1 + d2 + e)
(51)
where Ar ) 2500 s-1 and TKr ) 6240 K (see e.g. Field et al.5). Introducing
1+r φ) 1 + r/2
TKm ) 0.5(TKg + TKh)
(49)
(66)
Heat production from combustion of carbon is
QFh ) -SCh ∆hFh
(52)
(
∆hFh ) 32.79
(67)
φ-1 2-φ + 9.21 × 106 φ φ
)
(68)
the carbon burns according to
φC + O2 f 2(φ - 1)CO + (2 - φ)CO2
(53)
The combustion of 1 kg of carbon proceeds as follows:
1 kg of carbon + f kg of ash + Sc kg of oxidant f f kg of ash + d1 kg of CO2 + d2 kg of CO + e kg of N2 (54) where
d1 ) 11(2 - φ)/3φ
(55)
d2 ) 14(φ - 1)/3φ
(56)
2 e ) SCCN OX
(57)
C f ) CASH K /CK
(58)
2 SC ) 8/3φCO OX
(59)
Following Field et al.5 the rate of combustion of the carbon is based on an overall rate constant which is found by combination of the rate constants due to chemical kinetics and bulk diffusion 2 * SCh ) -kCCO g Aint/A
kC )
p 1 1 + k*d k*c
Thermal Radiation. The finite difference grid which constitutes the basis for the discretization of the differential eqs 1-5 is shown in Figure 2. The straw bales enter from the left and burn on the surface N + 1/ to the right. 2 Thermal radiation heat transfer between straw and gas and between the gas in different straw bale cells are neglected. Radiation heat transfer occurs only between straw in different cells and between the burning straw at the exit surface and the combustion chamber. The combustion chamber may be modeled optionally by means of a single gride cell, cell number N + 1, Figure 2. In this case radiative heat transfer is assumed to occur between the burning straw surface and two sources: (1) the combustion chamber walls and (2) the combustion chamber wall flame. If the combustion chamber is not modeled, the burning straw bale surface exchanges heat by means of radiation with the walls of the combustion chamber only. The radiation heat flux between the cells k and k + 1 is obtained from
q′′k+1/2 )
(60) (61)
Ek - Ek+1 1 1 + -1 ek ek+1
(69)
where
E ) σTK4
(70)
σ ) 5.6710 - 8
(71)
5 × 10-12T0.75 Km ) rdh
(62)
) Ac exp(-TKc/TKh)
(63)
The radiation heat flux between the straw bale surface and the flame and walls in the combustion chamber is obtained from
(5) Field, M. A.; Gill, D. W.; Morgan, B. B.; Hawkesley, P. G. W. Combustion of Pulverized Coal; The British Coal Utilization Research Association: Leatherhead, U.K., 1967.
(6) Stopford, P. J.; Marriott, N. Proceedings of the Seminar Harwell Coal Combustion Programme, Harwell Laboratory, U.K., 18 July, 1990, Harwell Laboratory, U.K., 1990.
k*d k*c
280
Energy & Fuels, Vol. 10, No. 2, 1996
Bech et al.
Figure 2. Finite difference grid.
q′′N+1/2 )
γwb (EN - Ew) γfb(En - Ef) + 1 1 1 1 + γwb -1 + γfb -1 ew eN ef eN
(
)
(
)
(72)
where
γfb )
Afb Awb + Afb
(73)
Table 1. Analysis of Barley Straw
γwb ) 1 - γbf
γfw(Ew - Ef) 1 1 + γfb -1 ef ew
(
dry and ash free
(74)
The radiation heat flux between the flame in the combustion chamber and the walls is obtained from
q′′fw )
Figure 3. Experimental setup.
)
(75)
where
γfw ) Afw/Awf
(76)
Boundary and Initial Conditions. The initial steady state is determined by the specification of the following set of parameters: (1) the feed velocity of the straw bales, (2) the inlet gas velocity, (3) the inlet composition of the straw, (4) the inlet composition of the gas, (5) the inlet temperature (assumed equal for gas and straw), (6) the inlet gas pressure, (7) the temperature of the combustion chamber walls, (8) the emissivity of the combustion chamber walls, (9) the temperature of the combustion chamber flame, (10) the emissivity of the combustion chamber flame, (11) the flow rate, diffusion length, and diffusion coefficient of primary air, and (12) the temperature of the primary air. Only the water vapor diffusion is considered in the present version of the code. As a consequence, the depth of penetration of primary air into the straw bale must be specified a priori. The amount of air which diffuses into the bale and which is available for the combustion of gas and straw char is calculated from a turbulence diffusion coefficient which must also be specified. Transients may be imposed by variation of one or more of the above-mentioned parameters determining the initial steady state. Experimental Design and Measurements A test facility for burning straw bales was constructed. It is capable of burning straw packed in small bales of 10-12 kg each by means of surface combustion; i.e., the bale is not torn up but is burnt from one end to the other. By means of probes inside the straw bale, measurements of temperatures and gas compositions during the whole combustion process were performed. This chapter presents a short description of the design of the experiment and the conduction of the measurements. For a more detailed description, reference is made to Wolff.7,8 (7) Wolff, L. A test facility for combustion of straw bales (Forsøgsopstilling til forbrænding af halmballer (‘Pyrolyseforsøg)); Risø-R-721 (DA) Forskningscenter: Risø, Denmark, 1993; in Danish.
water (%) ash (%) volatiles (%) hydrogen (%) carbon (%) nitrogen (%) clorine (%) net calorific value (MJ/kg)
82.1
18.50
as fired 12.1 2.4 70.2 5.4 41.5 0.7 0.2 15.52
Design of Experiment. The purpose was to make the test rig as simple as possible that could include the real conditions in front of a burning straw surface (in a full-size plant). At the same time, it should be easy to connect instruments to the facility. It was decided to make a facility with the shape of a “T”, with the straw being fed perpendicular into a duct where the combustion takes place. See Figure 3. It is possible to burn two bales per experiment. Primary air is injected directly to the straw surface by means of air nozzles. The remaining part of the air, the secondary air, is added in the main duct. Directly in front of the straw surface is an electrically heated zone giving heat flux to the straw, and thereby simulating a combustion chamber with hot walls. To prevent the straw from igniting too early because of the radiation heat, a movable water-cooled plate is placed between the heater and the straw bale surface. The plate can be removed after the main duct has been warmed up. In the present experiments the velocity of the straw bales was 50 mm/min. The total air flow was 113 Nm3/h while the primary air flow varied from 93 to 96 Nm3/h. This corresponds to an excess air ratio of about 1.7. The temperature of the electrical heater was approximately 1000 °C. Conduction of Measurements. Drilled holes were used for placing the temperature and suction probes in the straw bale. In the present experiments the probes were placed about 2/ into the second straw bale. The measuring device would 3 then reach the flame after about 20 min. When the probes were observed sticking 20-50 mm out in the flame, they were drawn back. This was observed through a quartz window in the “cold” end of the combustion chamber. By measuring the temperature and gas composition continuously during the experiment a picture was obtained of the axial variation of these parameters from the interior of the straw bale to the burning surface. The gas was analyzed for O2, CO2, CO, CxHy, and NOx. Fuel Properties. The straw bales burnt during the experiments had the following characteristics: length of straw bale 0.70 m; width of straw bale 0.46 m; height of straw bale 0.39 m; weight 8-10 kg; and porosity 0.93-0.95. The straw which has been burnt in the test facility is barley straw. A fuel analysis is given in Table 1. (8) Wolff, L.; Bech, N. Surface combustion of straw bales, a test facility for pyrolysis investigations. Presented at the 8th European Conference on Biomass for Energy, Environment, Agriculture and Industry, Vienna, 3-5 October, 1994.
Straw Bale Combustion in Cigar Burners
Energy & Fuels, Vol. 10, No. 2, 1996 281
Figure 4. Comparison of measured and calculated thermocouple temperatures. Table 2. Comparison of Measured and Calculated Concentrations in the Gas at the Burning Straw Bale Surface measured calculated
O2
CO2
CO
CxHy
0.04 0.04
0.14 0.15
0.14 0.14
0.015 0.011
The composition of the volatile has been measured by Kofoed et al.:3 methane 5.1%; carbon monoxide 63.0%; carbon dioxide 14.3%; hydrogen 4.5%; and water 13.1%. Other properties of the straw are as follows: heat conductivity 0.32 W/m/C; emissivity of straw 0.9; emissivity of char 0.9; pyrolysis enthalpy 0. J/kg; and density 1188. kg/m3. Concerning the straw heat conductivity, see Wolff.7 The straw density was measured.
Comparison to Measurements Figure 4 shows measured temperatures for the four near-identical experiments that were conducted and analyzed. The calculated temperature (gas-straw average) is shown as well. Measured as well as calculated results indicate that the small variation in bale properties and operating conditions has little influence on the performance of the burner. The main reason for the spread in the measured data shown in Figure 4 is inhomogeneities in the straw bales. Straw bales constitute a very inhomogeneous fuel. The burning straw bale surface is located where the temperature reaches its first maximum around 900 °C (around x ) 230 mm in the figure). It is seen that the rise in straw bale temperature close to the burning surface as well as the temperature at the surface is predicted reasonably well. The measured concentrations at the burning surface shown in Table 2 are averages for the four experiments. It is seen that the gas concentrations of CO2, CO, and CxHy are also predicted reasonably well, although the amount of CxHy is slightly underestimated. The gas composition inside the straw bale close to the burning surface (which is not shown here) is not predicted well enough. This is believed to be due to the fact that the model does not account for turbulent diffusion of gas phase components other than the oxidant. The turbulent diffusion of primary air into the straw bale was adjusted so that the calculated O2 concentration in the exit gas matched the exit value. In other words, the “calculated” value of O2 in Table 2 is specified rather than calculated.
Figure 5. Inlet and exit mass flow rate of straw carbon for straw bale feed stop.
The composition of the gas that enters the furnace room through the burning straw bale surface is a result of several interdependent and complex processes. The quality of the calculated results depends upon the accuracy of the submodels describing these processes. In the present work, standard models used for the description of pulverized-coal combustion have been utilized to describe the combustion of straw. The agreement between measurements and calculations is surprisingly good. But one should have in mind that essentially only one experiment has been predicted. Calculated Feed Stop in Cigar Burner One event which is known to cause problems in terms of a deterioration of the combustion and increased pollution is the stop in the straw bale feed which occurs in some plants in connection with the delivery of a new straw bale. Calculations were carried out in order to assess the implication of a straw bale feed stop in a 3 MW district heating plant fueled with Heston straw bales. The straw bale feed and air injection are interrupted for 60 s and then continued from t ) 75 s at the previous rates. In Figure 5 are shown the inlet and exit mass flow rates of straw carbon WChin and WChex, respectively. The amount fed at the inlet drops to nil after 15 s and increases to the initial rate at 75 s. The exit value is zero initially at the normal operating conditions. This means that all the straw carbon is burned at the straw surface. It is seen, however, that when the feeding starts again at t ) 75 s, the WChex becomes positive for a short period of time (=t s). In other words, unburned straw carbon falls into the combustion chamber when the straw feeding is restarted. The reason is that the temperature at the straw surface drops about 200 °C during the feed stop; cf. Figure 6. Also shown in Figure 6 is the exit straw temperature in the case of a continuous straw bale feed without stop. This situation is modeled by increasing the bale porosity from the nominal value of 0.94 to 0.995 over a distance of 5 cm. It is seen that the resulting disturbance is very benign compared to the feed stop case. Also, no unburnt straw falls into the combustion chamber in case of the continuous straw bale feed. Summary and Conclusions A computer model, STRAW, was developed for the calculation of the steady and nonsteady behavior of
282
Energy & Fuels, Vol. 10, No. 2, 1996
Bech et al. g h ∆h htc htc0 k k* K lRe
Figure 6. Calculated exit straw temperatures with and without straw bale feed stop.
surface combusting straw bales. Model predictions were compared to measurements of temperature and gas composition profiles within the burning straw bales and calculations were carried out in order to assess the implication of a straw bale feed stop in a 3 MW district heating plant fueled with Heston straw bales. Comparisons between calculated and measured results show the following: 1. The rise in straw bale temperature close to the burning surface and the temperature at the surface are predicted reasonably well. 2. The concentrations of CO2, CO, and CxHy in the exit gas are also predicted reasonably well, although the amount of CxHy is slightly underestimated. 3. The gas composition inside the straw bales close to the burning surface is not predicted well enough. This is probably because the model does not account in a proper way for the turbulent diffusion of the gas phase components. It has been shown that an interruption of the feed for 60 s causes violent disturbances in the computed performance of the burner. Unburned straw carbon is pushed into the combustion chamber when the straw feeding is restarted. In order to maintain good burner performance it is essential to avoid this behavior. This can be done by introducing a continuous feeding system which maintains the straw bale feeding rate at the operating value. Glossary a A A* b c c1 c2 c3 C Cp d d1 d2 D e E f
defined in eq 39 cross-sectional area of straw bale (m2) or rate constant (s-1) or (s-1 °C-1) internal area of straw bale per unit axial length (m) defined in eq 40 defined in eq 41 constant in eq 27 (W/m2/s) constant in eq 27 constant in eq 27 mass fraction heat capacity (J/kg/°C) diameter (m) defined in eq 55 defined in eq 56 diffusion coefficient (m2/s) specific energy (J/m3), straw emissivity σTK4 defined in eq 58
ld L m M MW n p Pr q′′ Q r R Re S t T TK u V x
acceleration of gravity (m/s2) enthalpy (J/kg) heat evaluated at phase transition straw-gas or heat evaluation during combustion (J/kg) straw-gas heat transfer coefficient (W/m2/s) straw-gas heat transfer coefficient for ug ) uh (W/ m2/s) reaction rate coefficient (s-1), reaction rate (kg/s/ m2), or turbulence kinetic energy (m2/s2) reaction rate (kg/s/m2/Pa) permeability of straw grid (m2) characteristic length in the gas Reynolds number, Reg, (m) diffusion length of primary air into straw bale (m) length (m) specific mass (kg/m3) weight of straw bale (kg) molecular weight (kg) number of moles per unit volume gas pressure (Pa) Prandtl number heat flux (W/m2) heat production per unit volume (W/m3) ratio of carbon monoxide to carbon dioxide formation rate gas constant (8315 Pa‚m3/K) Reynolds number mass source in gas equations, mass sink in straw equations (kg/m3/s) time (s) temperature (°C) temperature (K) velocity (m/s) volume of straw bale (m3) axial coordinate (m)
Greeks δ ∆ φ Φ Γ λ λ*
σ µ F Θ
fraction of heat developed during combustion of char deposited in the char difference operator disipation of turbulence kinetic energy (m2/s3) or emissivity defined in eq 52 porosity of straw grid transfer of mass from straw grid to the gas phase per unit volume and time (kg/s/m3) thermal conductivity of straw grid (W/m/°C) effective thermal “conductivity” of straw grid which takes into account heat conduction as well as thermal radiation (W/m/°C) Boltzmann constant (5.67 × 10-8 W/m2/K4) dynamic viscosity (kg/m/s) density (kg/m3) angle between x axes and vertical (deg)
Subscripts b c C d f F FU g h hg inj int j k K m
straw bale condensation or chemical kinetics carbon diffusion flashing, evaporation or flame combustion gaseous fuel gas straw grid from straw to gas injection straw grid internal surface phase index grid cell index Kelvin or char average (mean)
Straw Bale Combustion in Cigar Burners max N OX p PR ref sat v w x y z
maximum value number of grid cells and number of last grid cell oxidant pyrolysis, evaporation or condensation products reference saturation gas formed by pyrolysis (volatiles) water or wall coordinate direction coordinate direction coordinate direction
Energy & Fuels, Vol. 10, No. 2, 1996 283 C CH FU i 0 OX PR v w
carbon char combustible part of gas formed by pyrolysis component index reference or dry condition oxidant products pyrolysis gas (volatiles) water
Superscripts
Acknowledgment. This work was supported by Vølund R&D Center, Kolding, Denmark, and The Danish Ministry of Energy.
ASH
EF950192X
ash
