Modeling of a charcoal cook stove

Energy Vol. 13, No. 11, pp. 813-821, 1988 Printed in Great Britain. All rights reserved

MODELING

0360-5442/88 $3.00+0.00 Copyright @ 1988 Pergamon Press plc

OF A CHARCOAL

COOK STOVE

P. KHUMMONGKOL,~. WIBULSWAS,and S. C. BHAITACHARYA Asian Institute of Technology,

P.O. Box 2754, Bangkok,

Thailand

(Received 31 March 1988)

model for simulating a charcoal cook stove is proposed. We develop mass and energy balances and evaluate these in terms of variations of temperature in the The model is used to predict the combustion zone with time during combustion. combustion rate of charcoal. For semi-empirical use, a correlation has been established between air velocity and temperature. The pressure drop across the charcoal bed was found to be negligibly small. The model yields results in good agreement with experimental values. The charcoal-combustion rate is an exponential function of time. Abstract-A

INTRODUCTION

causes of rapid deforestation occurring in many developing countries has been the excessive use of firewood and charcoal for cooking purposes. For example, Thailand’s consumption of wood and charcoal for cooking is about 40 x lo6 m3 of solid wood annually.’ To prevent continuation of this disastrous trend, a number of designs for highly efficient stoves have been proposed. Improvements of stove designs are normally achieved by trial and error, which are both time-consuming and inefficient. For this reason, we have developed a dynamic stove model. The theoretical analysis of various modes of heat transfer related to the stove geometry is presented, The proposed cook-stove model is then verified by comparison with experiments. One of the principal

MODELING

OF A CHARCOAL

STOVE

The stove is the Thai bucket stove with cylindrical shape. The configuration of this bucket is illustrated in Fig. 1. The stove can be divided into two zones: ash and combustion zones. The stove has a uniform wall thickness. At the bottom, there is an air-inlet to allow fresh air to be drawn in by convection. The grate, which supports charcoal fuel, is located at the center of the stove. There are four gaps at the top between the stove and the pot. These gaps are areas from which the flue gas leaves the combustion chamber during operation. stove

Kinetics of combustion

Chemical reactions occurring in the combustion zone produce the heat input to the overall system. Generally, the rate of combustion r_,,b can be expressed as* -rcomb=k'CO,,

(1)

where k’ is the overall mass-transfer coefficient when diffusion through a gas film controls the reaction rate. It is a function of diffusivity and the radius of the unreacted core when diffusion through ash is rate-controlling. It is kinetically controlled when the reaction rate depends only on the intrinsic rate and the available surface area of the charcoal particle. In general, k’ is the combined effect of these three resistances. For this investigation, the mass-transfer resistance through the ash layer will be ignored since the ash content of charcoal is only about l-2% by weight. In this case, l/k’ = l/k, + Ilk,.

(2)

The mass-transfer coefficient of oxygen k, may be estimated from the Nusselt No. for stagnant diffusion around a sphere,3*4 viz. Nu = 2.0 + 0.6Sc1’3Re”2 EGY

13:11-c

813

814

P. KHUMMONGKOL et al

exhaust

combustion

chamber

Oreo

chorcool

grate stove wall

osh

chamber

oir

Inlet ore0

Fig. 1. A charcoal cook stove configuration.

or

(k&W/b,

= 2.0 + 0.6(~pI~p~p)1’3(D,u,p~/~~)“2.

Sundaresan and Amundson’ gave a detailed analysis of char combustion in a fluid&d bed. They assumed the concentrations of carbon monoxide, methane, and hydrogen to be zero. The rate constant k, in this model is a function of temperature, carbon weight and core. conversion. Parker and Hotte16 obtain the rate constant experimentally in the simpler form k, = 7.84 x 1011fiexp(-44,000

where T is the temperature

in the combustion

cal/RT),

chamber.

Mass and energy balances within the combustion chamber Mass balance. It is assumed that each charcoal particle is a sphere with diameter 0, and density pC, Assuming that n pieces of such charcoal are used in the stove, the total mass of the fuel will be

MC= (n/6)n,p,Dz. Therefore, the combustion expressed as

(3)

rate in terms of weight loss of charcoal

per unit

time

= 12xD&(-r,,,,).

-dMJdt

can

be

(4)

The

rate of combustion is found to depend both on the temperature and the oxygen concentration. The oxygen concentration may be obtained by using an equation describing the mass balance for oxygen in the combustion chamber. This formulation generally requires knowledge of stoichiometry, which varies with the type of fuel but is known for charcoal. The consumption rate of oxygen in the combustion chamber is =

mg,inWO*,in-mg,outWO*,out

32nD$,(

-rCOmb).

(5)

The mass-flow rate of air into the stove is WZg,in in Eq. (5) and can be expressed as mg.in

=

Pam&g,inAin-

It is well established that natural convection occurs as the result of the decrease in fluid density, which is a consequence of the increase of temperature. This fact implies that the velocity of the fluid depends on the temperature difference. For natural convection on a vertical hot plate, it has been found7 that the velocity of gas along the plate is proportional to the difference between the temperatures of the bulk fluid and the plate raised to the power l/4. If the difference also changes. geometry of the system changes, the power of the temperature Therefore, the air velocity at the stove inlet can be described as z+

= a(T - Tam,Jb = a(AT)b.

The constants a and b were determined

experimentally.

(6)

The mass flow rate of air in Eq. (5) can

then be estimated from mg,in

=

Pan&g.iAin-

(7)

815

Modeling of a charcoal cook stove

Similarly, mg,out = mg,in + dM,fdt.

(8)

Energy balance The energy balance in the stove chamber

involves the heat generated by combustion and heat losses to the surroundings. The enthalpy carried in with the inflow air at room temperature is very small and may be considered to be negligible. The heat-loss terms consist of the enthalpy flowing out with the flue gas, heat radiation, heat accumulation in the stove material, and heat conduction through the stove wall. Once the combustion rate is known, the rate of heat generated in the StOVe qComb iS qm,,,b = H,( -dMcldf).

(9)

For a charcoal stove, the heat is radiated from the charcoal bed upward to the pot and downward to the ash compartment. The governing equations for radiative heat transfer are’ q’p = (Jt/4)q,F,,(

T4 - T;)

qra = (JG/4)~,h@h~g,(T4

(10)

- TZ,).

(11)

Heat transfer by convection is due to fluid motion. Convection in the stoves is mostly natural, except when the stove operator fans the stove manually or electrically. Hence, the rates of enthalpy flow in and out have the form

4 conv,in 9 COI1”,0”1

= =

mg,i&.in3 mg,out

(12)

(13)

H g,out.

The heats of conduction and accumulation are considered simultaneously by using Fourier’s law to estimate the heat flux through the stove wall and the heat stored in the wall during cooking. The equation governing the energy balance in the wall is

auat = ff(aWa2),

(14)

where T is the temperature at any point x in the wall and at any time t. Equation solved with the following initial and boundary conditions: at t s 0,

(14) can be

T = Tamto

at x = 0,

T=T,,

at x = d,

-k,(dT/dX)

(15)

t>O;

(16) = h(T - Tam,,).

(17)

The solution of Eq. (14) with the initial and boundary condition given in Eqs. (15)-(17) is obtained by separation of variables. This procedure yields the solution in the form of an infinite series of some functions. Application of this solution is tedious. We can also estimate the solution by other methods. One of the methods is the method of weighted residuals.’ The estimated heat fluxes and the energy accumulated in the wall derived by the method of weighted residuals are

4

k(T - T,,,)/(dfi), t s l/12, 1 ‘cc = (2kld)(T - T,,b)eXp[-8(1+ B)(r - l/12)/(3 0,

qcond=

( h(T

+ B)],

(18)

t > l/12;

?JG l/12, -

T,,,)/(l

+ B){l

- exp[-8(1+

B)(z - l/12)/(3

+ I?)]},

z> l/12.

(19)

Applying Eq. (9) to Eqs. (13), (18) and (19), the energy balance in the stove chamber can be written as dE/dt = 4conv,in-I-qcomb - qrp - Qra - qconv.out - qacc - qcond, (20) where E = M&,0

- i%,b).

(21)

816

P. KHU~M~NGKOL Table 1. Characteristic

parameters used for the stove model.

Parameter

Prqerties

eta1

CNmtity

of Air

C?,a, 'cJb?.K

0.959+1.524c10-4Tc2,038x10-8~

%'

6 3x10-10T1.823 .

2, m's

k , !cJ/m.s.X Li

2 .627xlO-6+8 .383~10-~~1 .847~10-~%~

P , kq/m.s g

4.278x10-6+5.054x10-8~-1.284x10-%2

pg, kg/m3

1.817eq~(-1.578x10-~~)

Hg' wJ%i

0.959T+0.762x10-4?+0.679x10-8T3

Prcperties of the Stow CF s, WM.K

0.88

k s, kJ/m.s.K

1.3x1o-3

OS,

1.45x103

,

Wh3

A

m2

0.0156

gap' 2

A ,m gr A. Inlet

0.0132 2 m

0.0084

Dgrh,m

0.015

Dgr, m

0.27

Ds, m

0.30 75

"sh xgar m

0.08

xql

O.l.2

m

Properties of Cbrcoal Cp c' w%.K ,

1.26

n,

100

pieces

DC' Mb3

780.0

H+

2.6~10~

m/kg

Pate CorstJnts kg' m/s

!2.0+0.6(~&6~)

ks, w's

7.84xlO11@

1'3(Dc~qp~q)1/2:

(6pCy)

e..(-44,000 cal/rrrf

Equation (20) is a differential equation with temperature-dependent variables and the stove and fuel configurations as parameters. Table 1 shows the parameters used in the mathematical modeling of the charcoal stove. The initial conditions of the model are: combustion chamber temperature = Tgr= 400.0 K, stove wall thickness = d = 0.03 m, charcoal diameter = 0, = 0.03 m, charcoal weight = MC= 1.0 kg, mass fraction of oxygen = woz = 0.23. With these initial conditions, Eq. (20) was solved numerically by using the improved Eulier method.” The increment for the time interval was chosen to be 1 s. The flow diagram is given in Fig. 2 and

c Compute E from T,r

+ Compute

H.

YOI...L,

Compute

interchange

Rc.

Pr.

factor:

Nu,

Fe.,

h.

B

F~v

I

c Do mass balance tor the first iteration: Compute dkk/dt. Xc.

,

Dc

1

DC

1

I Compute heat Qc..~, Qr,, Qr., Qs....,. QC.....ll, Q..s, Q,..4 I 30 energy balance and make the first estimation of E according to the Improved Euler Method I Compute

Compute heat Qc.~,, Qrr. Qr.. Qe ..a Qc*mv.emt, Q.r.. Qt..4

.

1 Do energy

balance and make the second estimation oC E according to the Improved Euler Method

1 T. r

Compute

t

-

T. r

1 t+intcrval 1

Fig. 2. A flow diagram used for simulation of the cook-stove model.

I.

?

P. KHUMMONGKOL~~~~

818

shows details. The dynamic performance of the stove was studied to determine the temperature variation in the combustion chamber and the weight loss of charcoal with time.

EXPERIMENTAL

STUDIES

The first part of the experiment was carried out to determine the relation of air velocity to temperature in the combustion chamber and the pressure drop across the charcoal bed. The second part of the experimental work dealt with the rate of combustion of charcoal and the temperature variation within the combustion chamber. The stove prototype used in the experiments was made of fire clay and manufactured by a local stove factory in Thailand. Its configuration is shown in Fig. 1. Air velocity -temperature

relation

A series of tests was performed using an electric heater to heat up the combustion zone. An electric heater was used instead of combusting charcoal fuel to obtain better control of the steady stove temperature. For each test, the temperature was set equal to a constant value starting at 400 K and increasing to 1000 K, with increments of 100 K. When the temperature at each setting had reached a steady state, the air velocity was recorded by using a hot-wire anemometer. Pressure drop across the grate

During the tests for the determination of the air-velocity-temperature correlation, the pressure drop across the grate was measured by means of a micromanometer with a precision of 0.01 mm HzO. Pieces of fire clay cut into a charcoal-like shape were placed in the combustion chamber in order to simulate the effect of charcoal resistance to the flow of the inlet air. Temperature variation in the stove ignition of charcoal

The experimental charcoals were of the mangrove type and commercially sold in long stalks. These charcoals were cut approximately to a spherical shape with diameter of 3 cm, as was assumed in the theoretical computation. To initiate combustion, a few pieces of red-glowing charcoal were placed on the center of the grate. Charcoal was then added up to a total of 1 kg. The temperatures at various positions were immediately recorded by a micrologger connected to a tape recorder, starting from time zero and then in 2 min intervals. It required approx. 100 min for complete combustion of 1 kg of charcoal. For the next batch run, the stove had to be cooled down to room temperature in order to avoid effects from heat accumulation in the stove material. Combustion rate of charcoal

Under the experimental conditions, the stove was placed on top of an electronic balance with a scale ranging from 0 to 30.0 kg, as shown by a 6-digit LED display. The change in charcoal weight was recorded every 2 min.

RESULTS

AND

DISCUSSIONS

Air velocity

The effect of temperature difference on air velocity is shown in Fig. 3, which shows that an approximately linear relation applies between the logarithm of air velocity and the temperature difference. Using a curve-fitting program in BASIC, the general equation obtained is Ug,in= 0.0488(AT)“.234. This equation is useful for evaluating the oxygen concentration and the quantity of sensible heat of the inflow and outflow streams. The pressure drop across the charcoal bed as a function of time is shown in Fig. 4. The drop is small and varies nearly linearly with time. The average value ranges from 0.02 to 0.08 mm of water.

819

Modeling of a charcoal cook stove

-12

- I .4

0 0 0 0

0

-1.6

0

80

00

00

0 0

00 OO

00 0 0

0

00 0

0 0

0

0

a3

0

0 0

00 0

-2.2

0 0

-2.4

0

.

I 3.6

. 4

4.4

.

. 48

Fig. 3. Air velocity vs temperature

-

-

I

52

5.6

6

6.4

6.8

difference correlation in a charcoal cook stove

Stove modeling Figure 5 shows comparisons between variations of predicted temperatures in the combustion chamber and experimental values. Figure 6 shows the weight loss of charcoal with time. In the modeling, the initial temperaure 7”r.i in the combustion chamber was assumed to start at 400 K in order to create the required heat input by combustion into the system. In the experiments, the measured combustion-chamber temperature started from room temperature and required about 40 s to reach 400 K (see the dashed line in Fig. 5). During this period, the weight loss of charcoal was about 0.01 kg (see the dashed line in Fig. 6). Since the heating value of charcoal was 2.6 x lo4 kJ/kg, the initial energy input into the system before the temperature reached 400 K was approx. 260 kJ or only 1% of the total energy released by cornbusting 1 kg of charcoal. This small energy input hardly affected the actual rise of temperature in the combustion zone. Comparison between variations of predicted temperatures in the combustion chamber and experimental values is shown in Fig. 5. The agreement is good for the temperature range from 300 to 1200 K during the first 500s. After this time, the predicted

0000000000

0.02

0

1000

3000

2000 Time

(t),

4000

s

Fig. 4. The pressure drop is shown as a function of time in the charcoal cook stove.

820

P. KHUMMONGKOL et al 1600 ,

y

1200

F

600

400 0

1000

Time (11,

Fig. 5. Variation of temperature

3000

2000

s

with time; both theoretical line) data are shown.

(solid line) and experimental

(dashed

values fall slightly above the experimental data. The deviation is probably caused by components other than carbon present in the charcoal (e.g., volatile matter, moisture, and ash), while the model has been developed for pure carbon, which has a higher heat of However, these effects are not combustion than the charcoal used in the experiments. dominant since the inpurity contents of charcoal are small. The weight loss of charcoal with time is shown in Fig. 6. The result shows good agreement between theoretical predictions and experiments. Small deviations during the first 300s are caused by the slow initial start-up of charcoal combustion, since all of the individual charcoal particles are not ignited at once. However, after 300s the charcoal particles are all ignited rapidly and are involved in the highly exothermic reactions. The result is rapid consumption of charcoal, which further increases the combustion rate and the weight-loss rate of the charcoal. For times >2500 s, the combustion rate of charcoal appears to decrease; ultimately, the charcoal weight approaches a constant value, which reflects the ash content in the charcoal used. IO

0

I 0

1000

2000 Time

3000

4000

(t),s

Pig. 6. Weighted loss of charcoal with time; both theoretical line) data are shown.

(solid line) and experimental

(dashed

Modeling of a charcoal cook stove From

the

experimental

821

data, the weight loss of charcoal as a function of time is determined

to be

MC = exp(-5.6 Differentiating

this equation,

the combustion

-dMJdt

X 10e4 t).

rate of charcoal in the stove is obtained as

= 5.6 x 10e4 exp(-5.6

x 10e4 t).

CONCLUSIONS The derived relation

between air velocity and combustion-chamber temperature is sufficiently accurate for use in this model study. The predictions of temperature variations with time in the combustion chamber show good agreement with the experimental data. The consumption rate of charcoal is also well predicted by the model. The methodology used by us for the predictions should be applicable to other types of cook stoves. REFERENCES 1. A. Chomcham, P. Khummongkol, and B. Srisom, “Improved Biomass Cooking Stove for Household Ministry of Science, Use,” p. 33, report submitted to the National Energy Administration, Technology and Energy, Bangkok (1984). 2. 0. Levenspiel, Chemical Reaction Engineering, 2nd edn., p. 373, Wiley, New York, NY (1972). 3. W. E. Ranz and W. R. Marshall, Chem. Engng Prog. 48,173 (1952). 4. S. V. Sotirchos, B. Srinivas, and N. R. Amundson, Rev. Chem. Engng 2, 181 (1984). 5. S. Sundaresan and N. R. Amundson, Chem. Engng Sci. 34,359 (1979). 6. A. L. Parker and H. C. Hottel, Znd. Engng Chem. 28, 1334 (1936). 7. E. Schmidt and W. Beckmann, Tech. Mech. Thermodynam. 1,341,391 (1930). 8. W. H. McAdams, Heat Transmission, p. 72, McGraw-Hill Series in Chemical Engineering, New York, NY (1954). 9. B. A. Finlayson, The Method of Weighted Residuals and Variational Principles with Application in Fluid Mechanics, Heat and Mass Transfer, Academic Press, New York, NY (1972). 10. A. C. Bajpai, L. R. Mustoe, and D. Walker, Engineering Mathematics, pp. 521-522, Wiley, London (1974). NOMENCLATURE

A B C c, f: E F H H, h k k’ M m iill

02 Z? Re r SC T t u W X

Y

= = = = = = = =

Area Biot No. = hd/k Concentration Isobaric specific heat Diameter Wall thickness Energy Interchange factor for opposed parallel disks = Enthalpy = Heating value = Heat-transfer coefficient = Thermal conductivity = Rate constant = Mass = Mass-flow rate = Number = Nusselt No. = kDyf 6 = Oxygen = Heat rate = Ideal gas law constant = Reynolds No. = Dup/u = Rate = Schmidt No. = u/p8 = Temperature = Time = Average velocity = Mass fraction of oxygen = Distance = Mole fraction

EGY13:11-D

: CL P u t

= = = = =

Thermal diffusivity = k/PC, Mass diffusivity Viscosity Density Stefan-Boltzmann constant = 5.6 x lo-” kJ/m’s.K“ = Dimensionless time = at/d’

Subscripts act af amb C comb cond conv g ga gap gh gP gr in out P ra rp S

= = = = = = = = = = = = = = = = = = =

Accumulation Ash-floor area Ambient Charcoal Combustion Conduction Convection Gas Grate to ash floor Gap or exhaust area Grate hole Grate to pot base Grate Inlet Outlet Pot Radiation from grate to ash floor Radiation from grate to pot base Stove