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combustor with high-velocity jets
COMBUSTION AN D FLAME 99:669-678 (1994)
669
Gas-Particle Flows and Coal Combustion in a Burner/Combustor with High-Velocity Jets L. X. ZHOU*, W. Y. LIN, W. W. LUO and X. Q. HUANG Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China Coflowing high-velocity jets have been used in a burner/combustor to stabilize a coal flame, instead of swirlers or baffles, for burning low-grade coals. The LDV measurements and three-dimensional numerical simulation of gas-particle flows in these combustors show a large and strong reverse-flow zone induced by the high-velocity jets, high particle concentrations in the reverse-fow zone, high velocity slip between two phases and also high mixing rates due to high turbulence, favorable to ignition and coal-flame stabilization. The three-dimensional numerical simulation of coal combustion indicates the important role of the central reverse-flow zone in volatile ignition and combustion. Numerical modeling has been used for seeking optimal geometrical sizes and flow parameters for practical combustors by creating a strong gas recirculation zone to stabilize the combustion of anthracite in tangentially fired furnaces without supporting oil and without slagging. In fact. the total amount of oil saved is about 10000 tons/yr for a 410 T / h boiler.
NOMENCLATURE B preexponential factor c constant; specific heat d diameter E activation energy G production term g gravitational acceleration h enthalpy k turbulent kinetic energy m mass n number density p pressure q heat flux Q heating effect Re Reynolds number R universal gas constant r radial coordinate S source term T temperature t time u, v, w velocity w reaction rate x coordinate Y mass fraction
Greek Symbols F
E
O/
/3 v
P o-
0 TT
turbulent kinetic energy dissipation rate; emissivity dynamic viscosity fraction of contribution stoichiometric coefficient kinematic viscosity density Prandtl number; Stefan-Boltzmann constant generalized dependent variables azimuthal coordinate particle relaxation time fluctuation time
Subscripts c e F h i, j ox p T t, w
raw coal effective fuel char coordinate directions oxygen particle turbulent volatile moisture, surface
transport coefficient INTRODUCTION
* Corresponding author. Presented at the Twenty-Fifth Symposium (International) on Combustion, Irvine, California, 31 July-5 August 1994. Copyright © 1994 by The Combustion Institute Published by Elsevier Science Inc.
To save the oil consumed in ignition and flame stabilization when burning coal, anthracite or 0010-2180/94/$7.00
670
L. X. Z H O U ET AL.
other low-grade coals a combustor with coflowing high-velocity jets was developed several years ago and now serves as the main coal burner in tangentially fired furnaces. The principle of this burner/combustor is shown in Fig. la. Two holes are opened on the backward facing step of the combustor (either on one side or on two sides from the central inlet) for introducing coflowing high-velocity jets. The velocity in the jets ( > 200 m/s) is almost ten times that of the primary-air stream (nearly 20 m/s), whereas the mass flow rate of the jet is less than one tenth that of the primary-air. These coflowing high-velocity jets can induce large and strong reverse flows and make coal particles enter the reverse-flow zone, giving a fuel concentration distribution to match the flow field, which cannot be realized by swirlers or baffles. After many-years of application, three designs of these combustors were developed, including a combustor with tangentially introduced high-velocity jets (Fig. lb) and a two-channel combustor with coflowing highvelocity jets (Fig. lc). The latter one shown in Fig. 1 has not only the advantage described above, but also the ability to avoid slagging on the wall. In order to understand the mechanism of gas-particle flows and coal combustion in these combustors and to formulate optimal design, laser Doppler velocimetry (LDV) measurements and numerical simulation have been carried out. Some preliminary results of earlier studies on three-dimensional single-phase flows and two-dimensional coal combustion have been reported [1]. In this paper further results,
mainly measurements and modeling of threedimensional gas-particle flows and three-dimensional coal combustion, are presented. These results reveal more clearly the physical features of both the actual flow and combustion processes; modeling studies are then applied to the combustor design, seeking optimal geometrical sizes and flow parameters. Finally, the application of newly developed combustors is reported. MEASUREMENTS IN COLD
GAS-PARTICLE FLOWS The experimental set-up for measuring cold, turbulent, recirculating, gas-particle flows in a model combustor is shown in Fig. 2. It consists of blowers and air compressors for supplying the primary air and high-velocity jets, a SKQ4C electromagnetically vibrating powder feeder for supplying 60 t~m alumina particles with material density of 2900 k g / m 3 and a mass flow rate of 60 g/min. The test section is made of Plexiglas. The geometrical configuration is that shown in Fig. la. The geometrical sizes and inlet flow parameters are: L = 400 mm, D = 100mm, d = 2 4 m m , d j = 1 mm, h = 6 7 mm, u 1 = 15 m/s, and u 2 = 2 6 5 m/s. The ratio of mass flow rates in the high-velocity jets to the primary air is 6.1%. The inlet solid-gas mass loading is 0.12. Both single-phase (pure gas-phase) and gas-particle, two-phase, timeaveraged, velocity, and RMS fluctuation velocity are measured using a DISA-55 two-dimensional two-color, three-beam, laser Doppler
C
Fig. 1. Burners/combustors with highvelocity jets.
A B U R N E R COMBUSTOR WITH HIGH-VELOCITY JETS
Fig. 2. Experimental setup.
velocimeter with a counter signal processor. The LDV works in a forward scattering mode to increase the signal to noise ratio (> 5). Measurements in the recirculation zone with very low velocity and high turbulence are made by selecting appropriately the frequency shift and adjusting the frequency filter, keeping the sample acquisition time greater than the maximum turbulent fluctuation time. The particle mass flux is measured using a sampling probe of 3 mm i.d. The sampled powder is collected by a small cyclone separator with a vacuum cleaner as an induced draft fan. NUMERICAL SIMULATION OF THREE-DIMENSIONAL TURBULENT RECIRCULATING GAS-PARTICLE FLOWS AND THREE-DIMENSIONAL
COAL COMBUSTION In simulating turbulent reacting gas-particle flows, instead of the widely used trajectory models [2, 3] and multicontinuum models [4] a continuum-trajectory (CT) or Lagrangian-Eulerian (LE) model of the reacting particle phase [5] is used to account for both particle dispersion due to turbulence and any particle history effects due to moisture evaporation, devolatilization, char combustion, or heat transfer from a particle to the gas. The idea of the C T / L E model is to compute the particle velocity, the particle turbulence intensity and the particle concentration distribution by using a continuum description of particle's mass, momentum, and turbulent kinetic energy conservation equations in Eulerian coordinates. Also, the particle's temperature and any mass changes
671
due to moisture evaporation, devolatilization, char combustion and particle heat transfer are calculated using a trajectory description for the ordinary differential equations in Lagrangian coordinates. For closure models, since the oncoming flow is nonswirling, the conventional k-E model is assumed for the gas-phase turbulence. In the continuum description of the particle phase, how to simulate the particle turbulent fluctuation (particle diffusion or dispersion) is of vital importance. The classical Hinze-Tchen's particle-tracking-fluid (or fluid-shaking-particle) theory gives a simple algebraic m o d e l (Ap model), which leads to smaller particle fluctuations than gas fluctuations everywhere for all cases; this is not in agreement with the experimental results. A more advanced model is the transport equation model for particle's turbulent kinetic energy (kp model) [6], which is used in this paper. To simulate gas-phase combustion, previously the EBU (Eddy-Break-Up)-Arrhenius model was used. Subsequently, it has been found that the E B U - A r model actually results in almost no effect of finite-rate kinetics on the timeaveraged reaction rate; this sometimes leads to unchangeable plots of flame length versus the fuel-air ratio, which is not in agreement with the experimental facts. Therefore, a secondorder moment closure model [7] is used in order to account for both the effect of turbulence and the effect of finite-rate kinetics on the time-averaged reaction rate. Considering that gas radiation has only a minor effect on gas recirculation and volatile ignition in smallsize combustors/stabilizers with high gas velocity, only particle radiation is taken into account. The basic conservation equations for the gas and particle phases for three-dimensional, turbulent, recirculating, reacting, gasparticle flows in cylindrical coordinates based on the closure models described above can be expressed in the following generalized form: 3
3
O
-~x( PU~) + r cgr(rpt'q~) + -7~( pwq~) - ox L T x + 0----0 r
+ -;-2;IrL + S~
(1)
672
L . X . ZHOU ET AL.
0
0
~X(tlpUp~Pp) + r S-----r(npVp%)
Gkp = npt,p
OUpi OVpj t OUpi Oxj + ~ ] Oxj '
0
pp = c~pkpZ/ep
+ roo(npWpq~p)
2 zr = dpps/(18g) , Zrp = Tr(l + Rep2/3/6)-' ,
d (F Oq~P] + _ _ rF~p__ Ox ~ ¢p Ox ] r Or 8 ( O¢p] +S¢p, +r~-r~o r~p o o 1
Rep = Ivi - Vpildp//~ ,, (2)
where q~ and q~p denote generalized variables, expressing 1, u, v, w, k, e, Y~, h and 1, Up, Vp, Wp, kp, respectively, I'~ and F~p stand for transport coefficients, expressing 0, /ze/~r~ and npl~p/O'p, respectively, and S~ and S¢p are source terms. For gas-phase continuity, momentum, turbulent kinetic energy and its dissipation rate, species and enthalpy equations, S¢ is, respectively,
S = -nprhp; - - - -
OXi
+
Pgi
+
C)Xj I~e OXi ]
ep = -2(rnp + rhprr)/(mpT ~) X[(cp
k~p - k p )
u i - U p i O'p Pp t)nP] Ox i
The time-averaged reaction rate in the species conservation equations for the second-order moment closure model is
ws = BpzYFYoxexp(E/RT) [
__Y~Y°x E ( T ' Y ~ T'Y'x) × 1 + Y¢Yo~ + RT TYr + TYo~
- -
2~RT]
(3)
~ T ] ]"
+ npmp(Vpi - V,)/Zrp + vsS; G k - pc; e(clG k - c 2 p e ) / k ; -- Ws + asS; npQp + hS.
The correlations in Eq. 3 are determined by the following generalized expression: qb'~' = CR(k3/~ 2)
For particle-phase continuity, momentum and turbulent kinetic energy equations, S~ expresses
o¢ o~o [ 06 o~ × ____ + __m
Ox Ox
aq,
)
Or Or + r 2 30 -~ ' (4)
Sp = nprhp; npmpg i + - npVp OXj
+ npmp(V i
-- U p i ) / / T r p
3X i ]
+
Gkp -- rlp ~p where
mp = m w + m L, + mh,
tze = tx + IZT,
Gk
l)iSp;
where 4, and ~0 denote YF, Yox or T, and c R is an empirical constant, taken as 0.01. Particle temperature and mass change are determined by the trajectory calculations, using the following ordinary differential equations and algebraic expressions, accounting for simultaneous moisture evaporation, devolatilization and char combustion by using a one-equation pyrolysis model and a diffusion-kinetic char combustion model with a single global surface reaction
0 Ui ]J~T c~Xj
tzr = c g p k 2 / ¢ ,
0 Uj ) C9Ui OXi Oxj
m w = ~dpNU Dp In x [1 + (Yww - YwD/(1 - Yw~)],
Yww = Bwexp(-E/RTe),
A BURNER COMBUSTOR WITH HIGH-VELOCITY JETS
m c aB,,exp( - E J R T p ) ,
673
consists of about 9000 FORTRAN-4 statements. The CPU time for the coal combustion case in a SUN-3 work station is about 50 h, and for the case of cold gas-particle flows in a ELXSI computer is about 40 min.
rh c = - m cB,,exp(-E,,/RTp), ~ h h = rrdpNU Dp In
>[1 + (Yox~ - Y o x w ) / ( f l + Yoxw)] RESULTS AND DISCUSSION
= rrdpNu Dp In[1 + cp(T - Tp)/qw]
Figures 3 and 4 show predicted boundaries of gas reverse-flow zones for cases 1 and 2 (Table 1), as well as their comparison with the measured results. Both predictions and measurements give the same general features of the reverse flows: in the x - r plane of 0 = 0° (the plane containing two jet holes) a strong reverse flow zone in the near-axis region is induced by the high-velocity jets, whereas in the plane of 0 = 90° a large reverse-flow zone combining the central and the near-wall reverse-flow zones is formed. The predicted and the measured locations and sizes of these reverse-flow zones are in qualitative agreement, although there probably is quantitative disagreement due to the error in LDV measurements (nearly 20%-30% owing to low signal/noise ratio in some regions) and the shortcomings of the isotropic k-e turbulence model. Predicted cold gas-particle flow fields for case 3 using the k - e - k p model, as well as its comparison with LDV measurements, are shown in Figs. 5-7. Predicted and measured gas and particle velocities have the same features (Fig. 5). There is a very large velocity slip between gas and particle phases, in particular in the central-reverse flow zone, where the particle velocity is much larger than the gas velocity, and particles keep their forward motion. There is an obvious discrepancy between predictions and measurements due to the deficiency of the isotropic kp model and k - e model and the error in LDV measurements. Predicted particle mass flux
= rrdp2~BYox ~ 19e x p ( - E / R T v ) , ~rdp3
drp
- - - ~ p ~ c ~ dt
=
7rdp2o.,(T4 Tp4) (5)
- ~hq~ + rhhQ ~, where d dt
--
=
o Up Ox - -
+Up
o -~r
+
o wp r ~0
The boundary conditions of Eqs. 1 and 2 are taken as those used in other two-fluid models of gas-particle flows. Some empirical relations of the shear stress, gas velocity and gas turbulent kinetic energy are taken for the near wall grid nodes. The differential equations are discretized into finite difference equations. Then FDE's are solved by using the SIMPLE algorithm [8]. The solution procedure is called LEAGAP-3, in which there are three kinds of iterations: iterations in the gas and particle phases; iterations between gas-phase and particle-phase Eulerian predictions; iterations between trajectory predictions and gas-phase predictions. The criterion of convergence is the residual mass source for gas phase (< 10 - 3 ) and particle phase ( < 10-2). The predictions are for the combustor shown in Fig. la; the geometrical sizes and inlet-flow parameters are given in Table 1. The results of proximate analysis of the coal used in these predictions are shown in Table 2. The computer code
TABLE 1 Parameters Used in Predictions Case
Process
L (mm)
d(mm)
dj (mm)
h (ram)
D (ram)
tq ( m / s )
u 2 (m/s)
Gp/Q4
1 2 3 4 5
Single-phase flows Single-phase flows Cold gas-particle flows Pure gas combustion Coal combustion
650 400 400 400 400
40 24 24 24 24
2 1 1 1 1
90 72 67 67 80
186 102 100 100 100
15 14.4 15 15 2
243 165 260 265 40
0 0 0.2 0 0.2
674
L . X . ZHOU ET AL. TABLE 2
Analysis of Coal Used Volatile (%) Fixed Carbon (%) Ash (%) Moisture (%) 25.4
44.2
28.9
1.5
profiles (Fig. 6) are in good agreement with those measured by the sampling probe. The maximum concentration of particles is located on the axis and a large amount of particles enter the central reverse-flow zone. The mass flux profiles become nearly uniform within a short axial distance due to strong mixing caused by high turbulence of both two phases, indicated by predictions and measurements (Fig. 7). Hence, the cold, single-phase and two-phase flow field studies point out the most important features of the proposed combustor: largesize/area and strong reverse flows; high particle concentrations in reverse-flow or low-velocity zones; high velocity slip and high mixing-rate due to high turbulence. All these features are favorable for ignition and coal-flame stabilization. Predicted gas velocity vectors during coal combustion for case 5 (Fig. 8) show that the "hot" flow field and cold flow field are similar in their main features, but in the case of coal combustion, the size of the reverse-flow zone (dashed line) is reduced, compared with that of cold flow (solid line). Figure 9 gives the predicted gas temperature map during coal combustion, indicating that ignition takes place
0 =0o
{a)
265rrt/s
-
14.4m/s 0
I 0. I
I 0.4 (m)
o
o.I
-
0.2
0.3
0.4 (m)
o
o I
0 2 - -
Pred.
0.3 ¢
~
(m) Exp.
Fig. 3. Single-phase reverse-flow boundaries.
0.4
f 0
243m/s 0=0 °
(a)
I 100
200
300
400
500
400
500
650
(ram)
0
100
200
300 (ram)
650
0~90 °
0 ..~
lSm ~s.
0
lOO
"~
. ~1
200
\\ '
300
400
.
I 500
650
(ram) Pred .
.
.
.
Exp.
Fig. 4. Single-phase reverse-flow boundaries.
right at the stagnation point of the central reverse-flow zone. The predicted volatile concentration map (Fig. 10) implies that volatiles already complete their combustion at x = 300 mm, where the reverse flow disappears. The predictions for coal combustion indicate the important role of the central reverse-flow zone in ignition and coal-flame stabilization (i.e., volatile combustion) for the combustor with coflowing high-velocity jets. APPLICATION The numerical simulation has been applied in designing combustors with optimal geometrical sizes (such as d/d, h/D), inlet flow parameters (such as Ul/U2) and fuel/air ratios for a given coal type to create a strong recirculation zone for flame stabilization. On the basis of this optimal design, practical combustors with coflowing high-velocity jets have been developed and applied to tangentially fired, boiler furnaces with steam outputs of 35, 75, 130, 220, 410, and 670 T / h , burning bituminous coal, lean coal (or low-volatile bituminous coals), lignite or anthracite. The effect is most obvious when burning anthracite. The proximate analysis of the anthracite burnt in a 410 T / h , tangentially fired boiler furnace in Fujian Prov., PRC is shown in Table 3. The furnace operation results are given in Table 4. Obviously, the combustor with coflowing high-velocity jets can
A BURNER
COMBUSTOR
---
WITH
HIGH-VELOCITY
JETS
675
4m/s
.
.:.., "
.:+'+f
54)
"" .......
,
,
"+---A,,
-!- . . . . . . .
,
,
<,
7
++',
10
IrlO
220
29qI
x(mm) {--Gas Prediction ( k - ~ -k=,) ......
....
E
i
n
÷ i * Particle
n
• m 2)
.
.
.
.
.
.
.
.
.
.
[ [ A
'-" ¢
~
-*-----
5,0
i
i
Fig. 5. Axial velocity profiles of cold gas particle flows.
Gas reverse flow zone (measured)
0.5kg/(s
50
{ - G-a s . LDV measu.
Particle
i
i
i
-
;
•
.
.
.
.
.
PpUl
-
~
0 -0
•
220
L~90
xlmm) Pred. ( k - ~ - k .
-~
)
i
•
100
I(~
J
eo
Fig. 6. Particle mass flux of cold gas particle flows.
Exp.
6%
I()
I00
220
290
x(mm) { Prediction (k e - k p )
Gas
l''" Gas LDV m e a s u . t ~ - + + Particle
....
Particle
.....
Gas r e v e r s e - f l o w zone (measured)
Fig. 7. Turbulence intensity of cold gas particle flows.
676
L . X . Z H O U ET AL.
4O
i 3°F 10
.
_
(,.~.j, -
,
0
Y k, -
-~",. 2
]
"
I00
-.')
L~
,
.(--. -
I}
.
.
. -
.
.
.
.
.
-L__
.
.
.
-
°
400
.
"-, -
"~.
.
~
lot)
-
"'--.
.
.
.~
_
300
.
.
x x.
"
"";,
200 xlmm) (al 0 = 0 "~
, ~:~.~'
"
,
-
200 x(mml
.
.
,-,
°
300
400
(b) 8 = 4 5 ° - - -- - -
Gas reverse
flow boundary
(ioothermal flow)
. . . .
Gas reverse
flow boundary
(coal c o m b u s t i o n )
40
g2o
O0
F i g . 8. G a s
1 4 0 0 _
flow
field during
coal
combustion.
i
_= 5o0
....
0
I O0
__'200 tmm) 0=0
(a)
[ O0
~7oo -
300
40(1
30(I
400
°
200 (ram)
Fig. 9. G a s t e m p e r a t u r e
map during coal com-
bustion.
(b) 0 = 4 5 ~
0.005
20
,o[ "- ~x... t o
I oo
200 tmm)
la) 40
0.005
0.005 400
°
~x\
3010
o
0=0
300
~
It)~)
~,
20O
(ram) (b) 0 = 4 5 °
3(~q)
41)t)
Fig. 10. V o l a t i l e coal combustion.
concentration
map
during
A B U R N E R COMBUSTOR WITH HIGH-VELOCITY JETS TABLE 3 Proximate Analysis of Anthracite V(%)
C(%)
A(%)
W(%)
Heating Value (kJ/kg)
2.39
75.33
21.5
0.78
22847
TABLE 4 Furnace Operation Results
Temperature inside the furnace (K) Combustion efficiency Coal-flame stabilization Slagging
With high-velocity Jets
No Jets
1780
1780
87 Without oil burners No
85 With four oil burners No
achieve stable combustion of anthracite in tangentially fired furnaces with a higher combustion efficiency, without any supporting oil. In addition, there is no slagging in the combustor. It has been estimated that for only one 410 T / h boiler the total amount of oil saved is 104 Tons/year, so the saving of money by using coal to replace oil in such an innovative burner/combustor is considerable. CONCLUSIONS 1. The coflowing high-velocity jets can induce large and strong reverse flows, and also create high coal concentrations in the reverseflow zone, a large velocity slip between the two phases, and high mixing rates due to turbulence. All this is favorable to ignition and coal-flame stabilization. 2. The central reverse-flow zone plays a major role in volatile ignition and combustion; hence it is of vital importance for stabilizing a coal flame.
677
3. The newly developed coal combustor with coflowing high-velocity jets can achieve stable anthracite combustion in tangentially fired furnaces with a higher combustion efficiency, without any supporting oil or slagging. 4. The numerical simulations and LDV measurements point out clearly the general features of the three-dimensional gas-particle, flows and coal combustion processes, and also serve as a tool for designing a burner/ combustor.
This study was sponsored by the National Natural Science Foundation of China under the Key Project 9587003-14. The research results have won the Scientific and Technical Awards of State Education Commission, PRC in 1991. REFERENCES 1. Zhou, L. X., Lin, W. Y., Zhang, J., and Wang, Z. L., Twenty-First Symposium (International), The Combustion Institute, Pittsburgh, 1986, pp. 257-264. 2. Smoot, L. D., and Smith, P. J., Coal Combustion and Gasification, Plenum, New York, 1985. 3. Shuen, J. S., Solomon, A. S. P., Zhang, Q. F, and Faeth, G. M., Structure of particle-laden jets: Measurements and predictions, AIAA 22nd Aerospace Science Meeting, Nevada, 1984. 4. Soo, S. L., Muhiphase Fluid Dynamics, Science Press (Beijing) and Gower Technical (USA), 1990. 5. Zhou, L. X., and Zhang, J., Tenth International Conference on Numerical Methods in Fluid Dynamics, Springer-Verlag, 1986, pp. 705-709. 6. Zhou, L. X., and Huang, X. Q., Science in China, A.33, n.l (1989). 7. Zhou, L. X., Theory and Numerical Modeling of Turbulent Gas-Panicle Flows and Combustion, Science Press (China) and CRC Press (USA), 1993. 8. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, 1980. Received 13 April 1994; revised 19 May 1994
COMMENTS L. Douglas Smoot, Young University, USA. 1. Was the high velocity, coflowing burner originally conceived through modeling calculations or used subsequently to explain experimental observations? 2. You reported 87% burnout of
coal in the burner. Is the balance of the carbon consumed subsequently in the furnace?
Author's Reply. 1. The burner was originally developed experimentally, but subsequently
678 numerical modeling was used to give the optimal geometrical configuration and sizes for creating the strongest recirculation. 2. 87% burnout of coal is reached not in the burner but in the furnace; however, the volatiles can completely combust in the burner, so the burner serves only as a good flame stabilizer.
L . X . Z H O U ET AL.
F. Liu, Queen's University, Canada. 1. How do you calculate the dissipation rate for turbulent kinetic energy of the particle? 2. Can you apply your second-order moment method for modeling turbulent combustion with relatively detailed chemical kinetics?
Author's Reply. 1. It is calculated by the term Peter Jansohn, ABB Corporate Research, Switzerland. Have you also looked into the effect of varying the spacing of the high velocity air jets from the central coal jet? If so, what was the optimum distance in terms of coal jet diameters? Did you also test arrangements (e.g., multiple coaxial jets) other than just two high velocity jets on the top and bottom? Please comment on their effectiveness compared to the two-jet standard configuration.
expressing the effect of gas turbulent kinetic energy on the particles' turbulent kinetic energy through the drag force. 2. Recently, Prof. C. Q. Liu (University of Colorado at Denver) has successfully used this model to simulate turbulent diffusion flames with detailed chemical kinetics for methane/air combustion with nearly 300 reactions and 50 species.
Bo Yang, University of California, San Diego, USA. Which chemical model did you use? Did it influence the results of your calculations?
Author's Reply. For the combustion of the Author's Reply. We have studied the effect of spacing the high velocity jets, and found that the optimal h / d is in the range of 0.67-0.8. As for the arrangement, it seems that two jets are good enough for inducing strong recirculation.
volatiles and CO we used global reactions, each with second-order, Arrhenius kinetics. For char combustion we used a first-order reaction. We have not tested the effect of different chemical kinetics.
669
Gas-Particle Flows and Coal Combustion in a Burner/Combustor with High-Velocity Jets L. X. ZHOU*, W. Y. LIN, W. W. LUO and X. Q. HUANG Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China Coflowing high-velocity jets have been used in a burner/combustor to stabilize a coal flame, instead of swirlers or baffles, for burning low-grade coals. The LDV measurements and three-dimensional numerical simulation of gas-particle flows in these combustors show a large and strong reverse-flow zone induced by the high-velocity jets, high particle concentrations in the reverse-fow zone, high velocity slip between two phases and also high mixing rates due to high turbulence, favorable to ignition and coal-flame stabilization. The three-dimensional numerical simulation of coal combustion indicates the important role of the central reverse-flow zone in volatile ignition and combustion. Numerical modeling has been used for seeking optimal geometrical sizes and flow parameters for practical combustors by creating a strong gas recirculation zone to stabilize the combustion of anthracite in tangentially fired furnaces without supporting oil and without slagging. In fact. the total amount of oil saved is about 10000 tons/yr for a 410 T / h boiler.
NOMENCLATURE B preexponential factor c constant; specific heat d diameter E activation energy G production term g gravitational acceleration h enthalpy k turbulent kinetic energy m mass n number density p pressure q heat flux Q heating effect Re Reynolds number R universal gas constant r radial coordinate S source term T temperature t time u, v, w velocity w reaction rate x coordinate Y mass fraction
Greek Symbols F
E
O/
/3 v
P o-
0 TT
turbulent kinetic energy dissipation rate; emissivity dynamic viscosity fraction of contribution stoichiometric coefficient kinematic viscosity density Prandtl number; Stefan-Boltzmann constant generalized dependent variables azimuthal coordinate particle relaxation time fluctuation time
Subscripts c e F h i, j ox p T t, w
raw coal effective fuel char coordinate directions oxygen particle turbulent volatile moisture, surface
transport coefficient INTRODUCTION
* Corresponding author. Presented at the Twenty-Fifth Symposium (International) on Combustion, Irvine, California, 31 July-5 August 1994. Copyright © 1994 by The Combustion Institute Published by Elsevier Science Inc.
To save the oil consumed in ignition and flame stabilization when burning coal, anthracite or 0010-2180/94/$7.00
670
L. X. Z H O U ET AL.
other low-grade coals a combustor with coflowing high-velocity jets was developed several years ago and now serves as the main coal burner in tangentially fired furnaces. The principle of this burner/combustor is shown in Fig. la. Two holes are opened on the backward facing step of the combustor (either on one side or on two sides from the central inlet) for introducing coflowing high-velocity jets. The velocity in the jets ( > 200 m/s) is almost ten times that of the primary-air stream (nearly 20 m/s), whereas the mass flow rate of the jet is less than one tenth that of the primary-air. These coflowing high-velocity jets can induce large and strong reverse flows and make coal particles enter the reverse-flow zone, giving a fuel concentration distribution to match the flow field, which cannot be realized by swirlers or baffles. After many-years of application, three designs of these combustors were developed, including a combustor with tangentially introduced high-velocity jets (Fig. lb) and a two-channel combustor with coflowing highvelocity jets (Fig. lc). The latter one shown in Fig. 1 has not only the advantage described above, but also the ability to avoid slagging on the wall. In order to understand the mechanism of gas-particle flows and coal combustion in these combustors and to formulate optimal design, laser Doppler velocimetry (LDV) measurements and numerical simulation have been carried out. Some preliminary results of earlier studies on three-dimensional single-phase flows and two-dimensional coal combustion have been reported [1]. In this paper further results,
mainly measurements and modeling of threedimensional gas-particle flows and three-dimensional coal combustion, are presented. These results reveal more clearly the physical features of both the actual flow and combustion processes; modeling studies are then applied to the combustor design, seeking optimal geometrical sizes and flow parameters. Finally, the application of newly developed combustors is reported. MEASUREMENTS IN COLD
GAS-PARTICLE FLOWS The experimental set-up for measuring cold, turbulent, recirculating, gas-particle flows in a model combustor is shown in Fig. 2. It consists of blowers and air compressors for supplying the primary air and high-velocity jets, a SKQ4C electromagnetically vibrating powder feeder for supplying 60 t~m alumina particles with material density of 2900 k g / m 3 and a mass flow rate of 60 g/min. The test section is made of Plexiglas. The geometrical configuration is that shown in Fig. la. The geometrical sizes and inlet flow parameters are: L = 400 mm, D = 100mm, d = 2 4 m m , d j = 1 mm, h = 6 7 mm, u 1 = 15 m/s, and u 2 = 2 6 5 m/s. The ratio of mass flow rates in the high-velocity jets to the primary air is 6.1%. The inlet solid-gas mass loading is 0.12. Both single-phase (pure gas-phase) and gas-particle, two-phase, timeaveraged, velocity, and RMS fluctuation velocity are measured using a DISA-55 two-dimensional two-color, three-beam, laser Doppler
C
Fig. 1. Burners/combustors with highvelocity jets.
A B U R N E R COMBUSTOR WITH HIGH-VELOCITY JETS
Fig. 2. Experimental setup.
velocimeter with a counter signal processor. The LDV works in a forward scattering mode to increase the signal to noise ratio (> 5). Measurements in the recirculation zone with very low velocity and high turbulence are made by selecting appropriately the frequency shift and adjusting the frequency filter, keeping the sample acquisition time greater than the maximum turbulent fluctuation time. The particle mass flux is measured using a sampling probe of 3 mm i.d. The sampled powder is collected by a small cyclone separator with a vacuum cleaner as an induced draft fan. NUMERICAL SIMULATION OF THREE-DIMENSIONAL TURBULENT RECIRCULATING GAS-PARTICLE FLOWS AND THREE-DIMENSIONAL
COAL COMBUSTION In simulating turbulent reacting gas-particle flows, instead of the widely used trajectory models [2, 3] and multicontinuum models [4] a continuum-trajectory (CT) or Lagrangian-Eulerian (LE) model of the reacting particle phase [5] is used to account for both particle dispersion due to turbulence and any particle history effects due to moisture evaporation, devolatilization, char combustion, or heat transfer from a particle to the gas. The idea of the C T / L E model is to compute the particle velocity, the particle turbulence intensity and the particle concentration distribution by using a continuum description of particle's mass, momentum, and turbulent kinetic energy conservation equations in Eulerian coordinates. Also, the particle's temperature and any mass changes
671
due to moisture evaporation, devolatilization, char combustion and particle heat transfer are calculated using a trajectory description for the ordinary differential equations in Lagrangian coordinates. For closure models, since the oncoming flow is nonswirling, the conventional k-E model is assumed for the gas-phase turbulence. In the continuum description of the particle phase, how to simulate the particle turbulent fluctuation (particle diffusion or dispersion) is of vital importance. The classical Hinze-Tchen's particle-tracking-fluid (or fluid-shaking-particle) theory gives a simple algebraic m o d e l (Ap model), which leads to smaller particle fluctuations than gas fluctuations everywhere for all cases; this is not in agreement with the experimental results. A more advanced model is the transport equation model for particle's turbulent kinetic energy (kp model) [6], which is used in this paper. To simulate gas-phase combustion, previously the EBU (Eddy-Break-Up)-Arrhenius model was used. Subsequently, it has been found that the E B U - A r model actually results in almost no effect of finite-rate kinetics on the timeaveraged reaction rate; this sometimes leads to unchangeable plots of flame length versus the fuel-air ratio, which is not in agreement with the experimental facts. Therefore, a secondorder moment closure model [7] is used in order to account for both the effect of turbulence and the effect of finite-rate kinetics on the time-averaged reaction rate. Considering that gas radiation has only a minor effect on gas recirculation and volatile ignition in smallsize combustors/stabilizers with high gas velocity, only particle radiation is taken into account. The basic conservation equations for the gas and particle phases for three-dimensional, turbulent, recirculating, reacting, gasparticle flows in cylindrical coordinates based on the closure models described above can be expressed in the following generalized form: 3
3
O
-~x( PU~) + r cgr(rpt'q~) + -7~( pwq~) - ox L T x + 0----0 r
+ -;-2;IrL + S~
(1)
672
L . X . ZHOU ET AL.
0
0
~X(tlpUp~Pp) + r S-----r(npVp%)
Gkp = npt,p
OUpi OVpj t OUpi Oxj + ~ ] Oxj '
0
pp = c~pkpZ/ep
+ roo(npWpq~p)
2 zr = dpps/(18g) , Zrp = Tr(l + Rep2/3/6)-' ,
d (F Oq~P] + _ _ rF~p__ Ox ~ ¢p Ox ] r Or 8 ( O¢p] +S¢p, +r~-r~o r~p o o 1
Rep = Ivi - Vpildp//~ ,, (2)
where q~ and q~p denote generalized variables, expressing 1, u, v, w, k, e, Y~, h and 1, Up, Vp, Wp, kp, respectively, I'~ and F~p stand for transport coefficients, expressing 0, /ze/~r~ and npl~p/O'p, respectively, and S~ and S¢p are source terms. For gas-phase continuity, momentum, turbulent kinetic energy and its dissipation rate, species and enthalpy equations, S¢ is, respectively,
S = -nprhp; - - - -
OXi
+
Pgi
+
C)Xj I~e OXi ]
ep = -2(rnp + rhprr)/(mpT ~) X[(cp
k~p - k p )
u i - U p i O'p Pp t)nP] Ox i
The time-averaged reaction rate in the species conservation equations for the second-order moment closure model is
ws = BpzYFYoxexp(E/RT) [
__Y~Y°x E ( T ' Y ~ T'Y'x) × 1 + Y¢Yo~ + RT TYr + TYo~
- -
2~RT]
(3)
~ T ] ]"
+ npmp(Vpi - V,)/Zrp + vsS; G k - pc; e(clG k - c 2 p e ) / k ; -- Ws + asS; npQp + hS.
The correlations in Eq. 3 are determined by the following generalized expression: qb'~' = CR(k3/~ 2)
For particle-phase continuity, momentum and turbulent kinetic energy equations, S~ expresses
o¢ o~o [ 06 o~ × ____ + __m
Ox Ox
aq,
)
Or Or + r 2 30 -~ ' (4)
Sp = nprhp; npmpg i + - npVp OXj
+ npmp(V i
-- U p i ) / / T r p
3X i ]
+
Gkp -- rlp ~p where
mp = m w + m L, + mh,
tze = tx + IZT,
Gk
l)iSp;
where 4, and ~0 denote YF, Yox or T, and c R is an empirical constant, taken as 0.01. Particle temperature and mass change are determined by the trajectory calculations, using the following ordinary differential equations and algebraic expressions, accounting for simultaneous moisture evaporation, devolatilization and char combustion by using a one-equation pyrolysis model and a diffusion-kinetic char combustion model with a single global surface reaction
0 Ui ]J~T c~Xj
tzr = c g p k 2 / ¢ ,
0 Uj ) C9Ui OXi Oxj
m w = ~dpNU Dp In x [1 + (Yww - YwD/(1 - Yw~)],
Yww = Bwexp(-E/RTe),
A BURNER COMBUSTOR WITH HIGH-VELOCITY JETS
m c aB,,exp( - E J R T p ) ,
673
consists of about 9000 FORTRAN-4 statements. The CPU time for the coal combustion case in a SUN-3 work station is about 50 h, and for the case of cold gas-particle flows in a ELXSI computer is about 40 min.
rh c = - m cB,,exp(-E,,/RTp), ~ h h = rrdpNU Dp In
>[1 + (Yox~ - Y o x w ) / ( f l + Yoxw)] RESULTS AND DISCUSSION
= rrdpNu Dp In[1 + cp(T - Tp)/qw]
Figures 3 and 4 show predicted boundaries of gas reverse-flow zones for cases 1 and 2 (Table 1), as well as their comparison with the measured results. Both predictions and measurements give the same general features of the reverse flows: in the x - r plane of 0 = 0° (the plane containing two jet holes) a strong reverse flow zone in the near-axis region is induced by the high-velocity jets, whereas in the plane of 0 = 90° a large reverse-flow zone combining the central and the near-wall reverse-flow zones is formed. The predicted and the measured locations and sizes of these reverse-flow zones are in qualitative agreement, although there probably is quantitative disagreement due to the error in LDV measurements (nearly 20%-30% owing to low signal/noise ratio in some regions) and the shortcomings of the isotropic k-e turbulence model. Predicted cold gas-particle flow fields for case 3 using the k - e - k p model, as well as its comparison with LDV measurements, are shown in Figs. 5-7. Predicted and measured gas and particle velocities have the same features (Fig. 5). There is a very large velocity slip between gas and particle phases, in particular in the central-reverse flow zone, where the particle velocity is much larger than the gas velocity, and particles keep their forward motion. There is an obvious discrepancy between predictions and measurements due to the deficiency of the isotropic kp model and k - e model and the error in LDV measurements. Predicted particle mass flux
= rrdp2~BYox ~ 19e x p ( - E / R T v ) , ~rdp3
drp
- - - ~ p ~ c ~ dt
=
7rdp2o.,(T4 Tp4) (5)
- ~hq~ + rhhQ ~, where d dt
--
=
o Up Ox - -
+Up
o -~r
+
o wp r ~0
The boundary conditions of Eqs. 1 and 2 are taken as those used in other two-fluid models of gas-particle flows. Some empirical relations of the shear stress, gas velocity and gas turbulent kinetic energy are taken for the near wall grid nodes. The differential equations are discretized into finite difference equations. Then FDE's are solved by using the SIMPLE algorithm [8]. The solution procedure is called LEAGAP-3, in which there are three kinds of iterations: iterations in the gas and particle phases; iterations between gas-phase and particle-phase Eulerian predictions; iterations between trajectory predictions and gas-phase predictions. The criterion of convergence is the residual mass source for gas phase (< 10 - 3 ) and particle phase ( < 10-2). The predictions are for the combustor shown in Fig. la; the geometrical sizes and inlet-flow parameters are given in Table 1. The results of proximate analysis of the coal used in these predictions are shown in Table 2. The computer code
TABLE 1 Parameters Used in Predictions Case
Process
L (mm)
d(mm)
dj (mm)
h (ram)
D (ram)
tq ( m / s )
u 2 (m/s)
Gp/Q4
1 2 3 4 5
Single-phase flows Single-phase flows Cold gas-particle flows Pure gas combustion Coal combustion
650 400 400 400 400
40 24 24 24 24
2 1 1 1 1
90 72 67 67 80
186 102 100 100 100
15 14.4 15 15 2
243 165 260 265 40
0 0 0.2 0 0.2
674
L . X . ZHOU ET AL. TABLE 2
Analysis of Coal Used Volatile (%) Fixed Carbon (%) Ash (%) Moisture (%) 25.4
44.2
28.9
1.5
profiles (Fig. 6) are in good agreement with those measured by the sampling probe. The maximum concentration of particles is located on the axis and a large amount of particles enter the central reverse-flow zone. The mass flux profiles become nearly uniform within a short axial distance due to strong mixing caused by high turbulence of both two phases, indicated by predictions and measurements (Fig. 7). Hence, the cold, single-phase and two-phase flow field studies point out the most important features of the proposed combustor: largesize/area and strong reverse flows; high particle concentrations in reverse-flow or low-velocity zones; high velocity slip and high mixing-rate due to high turbulence. All these features are favorable for ignition and coal-flame stabilization. Predicted gas velocity vectors during coal combustion for case 5 (Fig. 8) show that the "hot" flow field and cold flow field are similar in their main features, but in the case of coal combustion, the size of the reverse-flow zone (dashed line) is reduced, compared with that of cold flow (solid line). Figure 9 gives the predicted gas temperature map during coal combustion, indicating that ignition takes place
0 =0o
{a)
265rrt/s
-
14.4m/s 0
I 0. I
I 0.4 (m)
o
o.I
-
0.2
0.3
0.4 (m)
o
o I
0 2 - -
Pred.
0.3 ¢
~
(m) Exp.
Fig. 3. Single-phase reverse-flow boundaries.
0.4
f 0
243m/s 0=0 °
(a)
I 100
200
300
400
500
400
500
650
(ram)
0
100
200
300 (ram)
650
0~90 °
0 ..~
lSm ~s.
0
lOO
"~
. ~1
200
\\ '
300
400
.
I 500
650
(ram) Pred .
.
.
.
Exp.
Fig. 4. Single-phase reverse-flow boundaries.
right at the stagnation point of the central reverse-flow zone. The predicted volatile concentration map (Fig. 10) implies that volatiles already complete their combustion at x = 300 mm, where the reverse flow disappears. The predictions for coal combustion indicate the important role of the central reverse-flow zone in ignition and coal-flame stabilization (i.e., volatile combustion) for the combustor with coflowing high-velocity jets. APPLICATION The numerical simulation has been applied in designing combustors with optimal geometrical sizes (such as d/d, h/D), inlet flow parameters (such as Ul/U2) and fuel/air ratios for a given coal type to create a strong recirculation zone for flame stabilization. On the basis of this optimal design, practical combustors with coflowing high-velocity jets have been developed and applied to tangentially fired, boiler furnaces with steam outputs of 35, 75, 130, 220, 410, and 670 T / h , burning bituminous coal, lean coal (or low-volatile bituminous coals), lignite or anthracite. The effect is most obvious when burning anthracite. The proximate analysis of the anthracite burnt in a 410 T / h , tangentially fired boiler furnace in Fujian Prov., PRC is shown in Table 3. The furnace operation results are given in Table 4. Obviously, the combustor with coflowing high-velocity jets can
A BURNER
COMBUSTOR
---
WITH
HIGH-VELOCITY
JETS
675
4m/s
.
.:.., "
.:+'+f
54)
"" .......
,
,
"+---A,,
-!- . . . . . . .
,
,
<,
7
++',
10
IrlO
220
29qI
x(mm) {--Gas Prediction ( k - ~ -k=,) ......
....
E
i
n
÷ i * Particle
n
• m 2)
.
.
.
.
.
.
.
.
.
.
[ [ A
'-" ¢
~
-*-----
5,0
i
i
Fig. 5. Axial velocity profiles of cold gas particle flows.
Gas reverse flow zone (measured)
0.5kg/(s
50
{ - G-a s . LDV measu.
Particle
i
i
i
-
;
•
.
.
.
.
.
PpUl
-
~
0 -0
•
220
L~90
xlmm) Pred. ( k - ~ - k .
-~
)
i
•
100
I(~
J
eo
Fig. 6. Particle mass flux of cold gas particle flows.
Exp.
6%
I()
I00
220
290
x(mm) { Prediction (k e - k p )
Gas
l''" Gas LDV m e a s u . t ~ - + + Particle
....
Particle
.....
Gas r e v e r s e - f l o w zone (measured)
Fig. 7. Turbulence intensity of cold gas particle flows.
676
L . X . Z H O U ET AL.
4O
i 3°F 10
.
_
(,.~.j, -
,
0
Y k, -
-~",. 2
]
"
I00
-.')
L~
,
.(--. -
I}
.
.
. -
.
.
.
.
.
-L__
.
.
.
-
°
400
.
"-, -
"~.
.
~
lot)
-
"'--.
.
.
.~
_
300
.
.
x x.
"
"";,
200 xlmm) (al 0 = 0 "~
, ~:~.~'
"
,
-
200 x(mml
.
.
,-,
°
300
400
(b) 8 = 4 5 ° - - -- - -
Gas reverse
flow boundary
(ioothermal flow)
. . . .
Gas reverse
flow boundary
(coal c o m b u s t i o n )
40
g2o
O0
F i g . 8. G a s
1 4 0 0 _
flow
field during
coal
combustion.
i
_= 5o0
....
0
I O0
__'200 tmm) 0=0
(a)
[ O0
~7oo -
300
40(1
30(I
400
°
200 (ram)
Fig. 9. G a s t e m p e r a t u r e
map during coal com-
bustion.
(b) 0 = 4 5 ~
0.005
20
,o[ "- ~x... t o
I oo
200 tmm)
la) 40
0.005
0.005 400
°
~x\
3010
o
0=0
300
~
It)~)
~,
20O
(ram) (b) 0 = 4 5 °
3(~q)
41)t)
Fig. 10. V o l a t i l e coal combustion.
concentration
map
during
A B U R N E R COMBUSTOR WITH HIGH-VELOCITY JETS TABLE 3 Proximate Analysis of Anthracite V(%)
C(%)
A(%)
W(%)
Heating Value (kJ/kg)
2.39
75.33
21.5
0.78
22847
TABLE 4 Furnace Operation Results
Temperature inside the furnace (K) Combustion efficiency Coal-flame stabilization Slagging
With high-velocity Jets
No Jets
1780
1780
87 Without oil burners No
85 With four oil burners No
achieve stable combustion of anthracite in tangentially fired furnaces with a higher combustion efficiency, without any supporting oil. In addition, there is no slagging in the combustor. It has been estimated that for only one 410 T / h boiler the total amount of oil saved is 104 Tons/year, so the saving of money by using coal to replace oil in such an innovative burner/combustor is considerable. CONCLUSIONS 1. The coflowing high-velocity jets can induce large and strong reverse flows, and also create high coal concentrations in the reverseflow zone, a large velocity slip between the two phases, and high mixing rates due to turbulence. All this is favorable to ignition and coal-flame stabilization. 2. The central reverse-flow zone plays a major role in volatile ignition and combustion; hence it is of vital importance for stabilizing a coal flame.
677
3. The newly developed coal combustor with coflowing high-velocity jets can achieve stable anthracite combustion in tangentially fired furnaces with a higher combustion efficiency, without any supporting oil or slagging. 4. The numerical simulations and LDV measurements point out clearly the general features of the three-dimensional gas-particle, flows and coal combustion processes, and also serve as a tool for designing a burner/ combustor.
This study was sponsored by the National Natural Science Foundation of China under the Key Project 9587003-14. The research results have won the Scientific and Technical Awards of State Education Commission, PRC in 1991. REFERENCES 1. Zhou, L. X., Lin, W. Y., Zhang, J., and Wang, Z. L., Twenty-First Symposium (International), The Combustion Institute, Pittsburgh, 1986, pp. 257-264. 2. Smoot, L. D., and Smith, P. J., Coal Combustion and Gasification, Plenum, New York, 1985. 3. Shuen, J. S., Solomon, A. S. P., Zhang, Q. F, and Faeth, G. M., Structure of particle-laden jets: Measurements and predictions, AIAA 22nd Aerospace Science Meeting, Nevada, 1984. 4. Soo, S. L., Muhiphase Fluid Dynamics, Science Press (Beijing) and Gower Technical (USA), 1990. 5. Zhou, L. X., and Zhang, J., Tenth International Conference on Numerical Methods in Fluid Dynamics, Springer-Verlag, 1986, pp. 705-709. 6. Zhou, L. X., and Huang, X. Q., Science in China, A.33, n.l (1989). 7. Zhou, L. X., Theory and Numerical Modeling of Turbulent Gas-Panicle Flows and Combustion, Science Press (China) and CRC Press (USA), 1993. 8. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, 1980. Received 13 April 1994; revised 19 May 1994
COMMENTS L. Douglas Smoot, Young University, USA. 1. Was the high velocity, coflowing burner originally conceived through modeling calculations or used subsequently to explain experimental observations? 2. You reported 87% burnout of
coal in the burner. Is the balance of the carbon consumed subsequently in the furnace?
Author's Reply. 1. The burner was originally developed experimentally, but subsequently
678 numerical modeling was used to give the optimal geometrical configuration and sizes for creating the strongest recirculation. 2. 87% burnout of coal is reached not in the burner but in the furnace; however, the volatiles can completely combust in the burner, so the burner serves only as a good flame stabilizer.
L . X . Z H O U ET AL.
F. Liu, Queen's University, Canada. 1. How do you calculate the dissipation rate for turbulent kinetic energy of the particle? 2. Can you apply your second-order moment method for modeling turbulent combustion with relatively detailed chemical kinetics?
Author's Reply. 1. It is calculated by the term Peter Jansohn, ABB Corporate Research, Switzerland. Have you also looked into the effect of varying the spacing of the high velocity air jets from the central coal jet? If so, what was the optimum distance in terms of coal jet diameters? Did you also test arrangements (e.g., multiple coaxial jets) other than just two high velocity jets on the top and bottom? Please comment on their effectiveness compared to the two-jet standard configuration.
expressing the effect of gas turbulent kinetic energy on the particles' turbulent kinetic energy through the drag force. 2. Recently, Prof. C. Q. Liu (University of Colorado at Denver) has successfully used this model to simulate turbulent diffusion flames with detailed chemical kinetics for methane/air combustion with nearly 300 reactions and 50 species.
Bo Yang, University of California, San Diego, USA. Which chemical model did you use? Did it influence the results of your calculations?
Author's Reply. For the combustion of the Author's Reply. We have studied the effect of spacing the high velocity jets, and found that the optimal h / d is in the range of 0.67-0.8. As for the arrangement, it seems that two jets are good enough for inducing strong recirculation.
volatiles and CO we used global reactions, each with second-order, Arrhenius kinetics. For char combustion we used a first-order reaction. We have not tested the effect of different chemical kinetics.