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Prediction of a three rectangular jet turbulent mixing and diffusion flame
COMBUSTION
AND FLAME
195
61: 195-198 (1985)
BRIEF’ COMMUNICATION Prediction of a Three Rectangular Jet Turbulent Mixing and Diffusion Flame C. BERTRAND Centre de Recherches sur la Chimie de la Combustion et des Hautes Temperatures, CNRS, Orleans, France
and F. C. LOCKWOOD and P. STOLAKIS Mechanical Engineering Department, Imperial College of Science and Technology, London S W7 ZBX, England
Velocity and temperature data in the 3 stream reacting turbulent jet issuing from the rectangular burner of Fig. 1, and submerged in a slow (0.07 m/s) moving stream of nitrogen, have been obtained by Bertrand and coworkers [ 1, 21. Velocity data are also reported for the case of no reaction. The experimental conditions are cited in Table 1. Predictions of the flow have been obtained using a parabolic version [3] of the TEACH code. The physical modeling comprises the k-e turbulence model with standard values for the constants and in particular with C,, set to 1.44, the plane jet value [4]; a one step fast irreversible reaction; the use of two mixture fractions (one for the oxidant bearing stream and one for the fuel bearing stream, ignoring fluctuations of that for the oxidant stream) to describe the three stream mixing [5]; and a beta probability density function for the fuel stream mixture fraction. The variable specific heats are calculated from relations recommended in [6]. Thermal radiation effects are ignored. The numerical treatment is two-dimensional and planar so the predictions will not be valid far Copyright @ 1985 by The Combustion Institute Published by Elscvier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
from the burner. The parabolic solution treatment cannot accommodate the small zones of recirculation downstream of the burner walls. So (i) the Or stream was widened by the thickness of its bounding walls while maintaining the experimental mass flow rate, and (ii) the burner geometry was assumed to be symmetrical about a plane located at the midthickness of the 02/N2 duct. With respect of (ii) reference to Table 1 reveals that the momenta of the CH4/N2 and 02 streams are small enough to make this assumption reasonable. The initial conditions for the main oxidant jet (02/N2) were considered to be those appropriate to a fully developed turbulent flow between two parallel plates. The fuel jet was considered to be laminar because of its relatively low Reynolds number (2: 1000) and its entry velocity profile was assumed to have a parabolic shape. A sensitivity study on the effect of the initial conditions was not performed since it was felt that the chosen ones constituted the most reasonable specification that could be made. Figure 2a compares the measured and predicted streamwise velocity profiles for the inert
OolO-2180/85/$03.30
196
C. BERTRAND ET AL.
Fig.
1. Illustration
of the burner.
jet 50 mm above the burner. Two predicted curves are shown: one for the “standard” value for the turbulence model constant C, of 0.09, and the other for the value of 0.17 determined in the experiment [2]. There is little to choose between these two predicted results. Figure 2b shows similar comparisons at an elevation of 100 mm above the burner. Here the improvement in calculations when using a value of 0.17 for C, is rather apparent. The “standard” value of C, is based on data from flows in which the production and dissipation of turbulence energy are in approximate balance. However, in weak shear flows, of which the present flow because of its low velocities is an example, the rate of production of turbulence energy can be significantly lower than its dissipation rate, implying higher C,, values [4]. Figures 3a and 3b compare the square root of the measured streamwise normal stress with the square root of the calculated turbulence energy for the inert jet at 50 and 100 mm above the burner. The comparisons are fairly satisfactory. This is especially so if at the higher 100 mm elevation we are justified in anticipating that the relation (G)1’2 = 0.97k112 [7] for the fully developed inert jet is also applicable here. Finally Fig. 4 compares the measured and predicted mean temperatures at 50 mm above the burner for the reacting jet. The near field region where the present approach is valid is shorter for the buoyancy influenced reacting
THREE RECTANGULAR 15
.;lEj
x= 50 m
u
/ ----EXPERIMENTS
(In/S)
197
JET DIFFUSION FLAME
(1,2)
-_-
CPLCULATIONS,C,=0.09
___-
CALCULATIONS,C,=0.17
----EXPERIMENTAL
(u~)~, cl,21
10 -
5-
Y(mn)
0
5
10
10
Y(nm
Fig.
Fig. 2(a) 15 ,
,
3(a)
1 x= 100 m
u Cm/s)
0
5
----
EXPERIMENTS (1.2) CALCULATIONS, C,=O.O9
---
-CALCULATIONS,
C.=O.17 2.0 /
.'
_*--
t /’
1.0
5
10 Y(lllll)
0
Fig. 2(b) Fig. 2. Profiles of mean streamwise mm, (b) x = 100 mm (inert jet).
./----.
.y
I’
.'
/*
1.
/--------____
\ I__.-.-_ 1 I
(b)
AXIS OF .-
o.o. Y(mll)
\.
10
5
02/N2 JET i
0
Fig. 3(b) velocity
at (a) x = 50
flow. The predictions shown are for the experimentally determined C, of 0.11, but the predictions for the value of 0.09 are very little different. The comparisons all exhibit a somewhat underpredicted spreading rate. The most likely cause is the fast entrainment of the low velocity CHJ
Fig. 3. Profiles of the mean streamwise normal stress and the calculated turbulence energy at (a) x = 50 mm, (b) x = 100 mm (inert jet).
N2 and O2 streams by the principal Oz/Nz stream due to the artificial elimination of the splitter wall recirculation zones. So in Fig. 2a the velocity “excess” in the tail of the measured profile is already at this station absent from the predicted profiles. Similarly in Fig. 4 the faster predicted entrainment has absorbed the temperature ex-
198
C. BERTRAND ET AL. 1
T (OC) 1600_
I
x= 50 mm
I
----
EXPEIUMENTS (1,2)
---
CALCULATIONS,
stream were all in excess of 400 for the inert flow and 85 for the reacting one [2]. Low Reynolds number effects are important only for ReT less than about 10, and so to the extent that the 02/N2 stream is the dominant one the use of the conventional k-e turbulence model without low Re number modifications is justified.
C,=O.ll
1200-
800-
I' _.c /H'
400-
REFERENCES C
1' 01
1
Y(mll)
Fig. 4. Profiles (reacting jet).
15
1.
I
I
I
10
5
0
of mean temperature
at x = 50 mm
cess revealed by the measurements. The overall conformity between the predictions and data may be judged as fair. Last, it is well to mention that the measured turbulent Reynolds numbers ReT = k2/vc, where v is the laminar kinematic viscosity, along the centerline of the 02/N*
2. 3.
Bertrand, C., Hamon, F., Sarh, B., and Gokalp, I., 20th Symp. (Znt.) on Combustion, 1984. Bertrand, C., CNRS-CRCCHT, Orleans, France, 1981. Stolakis, P., Ph.D. Thesis, University of London, 1984. Rodi, W., Report SFB 80/T/127, University of Karlsruhe, Germany, 1978. Lockwood, F. C., and Salooja, A. P., Cornbust. Flume 41:217-219 (1981). Tribus, M., Thermostatics and Thermodynamics, Van Nostrand, London, 1961. Launder, B. E., J. Fluid Mech. 569-581 (1975).
Received 14 July 1984; revised 5 December 1984
AND FLAME
195
61: 195-198 (1985)
BRIEF’ COMMUNICATION Prediction of a Three Rectangular Jet Turbulent Mixing and Diffusion Flame C. BERTRAND Centre de Recherches sur la Chimie de la Combustion et des Hautes Temperatures, CNRS, Orleans, France
and F. C. LOCKWOOD and P. STOLAKIS Mechanical Engineering Department, Imperial College of Science and Technology, London S W7 ZBX, England
Velocity and temperature data in the 3 stream reacting turbulent jet issuing from the rectangular burner of Fig. 1, and submerged in a slow (0.07 m/s) moving stream of nitrogen, have been obtained by Bertrand and coworkers [ 1, 21. Velocity data are also reported for the case of no reaction. The experimental conditions are cited in Table 1. Predictions of the flow have been obtained using a parabolic version [3] of the TEACH code. The physical modeling comprises the k-e turbulence model with standard values for the constants and in particular with C,, set to 1.44, the plane jet value [4]; a one step fast irreversible reaction; the use of two mixture fractions (one for the oxidant bearing stream and one for the fuel bearing stream, ignoring fluctuations of that for the oxidant stream) to describe the three stream mixing [5]; and a beta probability density function for the fuel stream mixture fraction. The variable specific heats are calculated from relations recommended in [6]. Thermal radiation effects are ignored. The numerical treatment is two-dimensional and planar so the predictions will not be valid far Copyright @ 1985 by The Combustion Institute Published by Elscvier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
from the burner. The parabolic solution treatment cannot accommodate the small zones of recirculation downstream of the burner walls. So (i) the Or stream was widened by the thickness of its bounding walls while maintaining the experimental mass flow rate, and (ii) the burner geometry was assumed to be symmetrical about a plane located at the midthickness of the 02/N2 duct. With respect of (ii) reference to Table 1 reveals that the momenta of the CH4/N2 and 02 streams are small enough to make this assumption reasonable. The initial conditions for the main oxidant jet (02/N2) were considered to be those appropriate to a fully developed turbulent flow between two parallel plates. The fuel jet was considered to be laminar because of its relatively low Reynolds number (2: 1000) and its entry velocity profile was assumed to have a parabolic shape. A sensitivity study on the effect of the initial conditions was not performed since it was felt that the chosen ones constituted the most reasonable specification that could be made. Figure 2a compares the measured and predicted streamwise velocity profiles for the inert
OolO-2180/85/$03.30
196
C. BERTRAND ET AL.
Fig.
1. Illustration
of the burner.
jet 50 mm above the burner. Two predicted curves are shown: one for the “standard” value for the turbulence model constant C, of 0.09, and the other for the value of 0.17 determined in the experiment [2]. There is little to choose between these two predicted results. Figure 2b shows similar comparisons at an elevation of 100 mm above the burner. Here the improvement in calculations when using a value of 0.17 for C, is rather apparent. The “standard” value of C, is based on data from flows in which the production and dissipation of turbulence energy are in approximate balance. However, in weak shear flows, of which the present flow because of its low velocities is an example, the rate of production of turbulence energy can be significantly lower than its dissipation rate, implying higher C,, values [4]. Figures 3a and 3b compare the square root of the measured streamwise normal stress with the square root of the calculated turbulence energy for the inert jet at 50 and 100 mm above the burner. The comparisons are fairly satisfactory. This is especially so if at the higher 100 mm elevation we are justified in anticipating that the relation (G)1’2 = 0.97k112 [7] for the fully developed inert jet is also applicable here. Finally Fig. 4 compares the measured and predicted mean temperatures at 50 mm above the burner for the reacting jet. The near field region where the present approach is valid is shorter for the buoyancy influenced reacting
THREE RECTANGULAR 15
.;lEj
x= 50 m
u
/ ----EXPERIMENTS
(In/S)
197
JET DIFFUSION FLAME
(1,2)
-_-
CPLCULATIONS,C,=0.09
___-
CALCULATIONS,C,=0.17
----EXPERIMENTAL
(u~)~, cl,21
10 -
5-
Y(mn)
0
5
10
10
Y(nm
Fig.
Fig. 2(a) 15 ,
,
3(a)
1 x= 100 m
u Cm/s)
0
5
----
EXPERIMENTS (1.2) CALCULATIONS, C,=O.O9
---
-CALCULATIONS,
C.=O.17 2.0 /
.'
_*--
t /’
1.0
5
10 Y(lllll)
0
Fig. 2(b) Fig. 2. Profiles of mean streamwise mm, (b) x = 100 mm (inert jet).
./----.
.y
I’
.'
/*
1.
/--------____
\ I__.-.-_ 1 I
(b)
AXIS OF .-
o.o. Y(mll)
\.
10
5
02/N2 JET i
0
Fig. 3(b) velocity
at (a) x = 50
flow. The predictions shown are for the experimentally determined C, of 0.11, but the predictions for the value of 0.09 are very little different. The comparisons all exhibit a somewhat underpredicted spreading rate. The most likely cause is the fast entrainment of the low velocity CHJ
Fig. 3. Profiles of the mean streamwise normal stress and the calculated turbulence energy at (a) x = 50 mm, (b) x = 100 mm (inert jet).
N2 and O2 streams by the principal Oz/Nz stream due to the artificial elimination of the splitter wall recirculation zones. So in Fig. 2a the velocity “excess” in the tail of the measured profile is already at this station absent from the predicted profiles. Similarly in Fig. 4 the faster predicted entrainment has absorbed the temperature ex-
198
C. BERTRAND ET AL. 1
T (OC) 1600_
I
x= 50 mm
I
----
EXPEIUMENTS (1,2)
---
CALCULATIONS,
stream were all in excess of 400 for the inert flow and 85 for the reacting one [2]. Low Reynolds number effects are important only for ReT less than about 10, and so to the extent that the 02/N2 stream is the dominant one the use of the conventional k-e turbulence model without low Re number modifications is justified.
C,=O.ll
1200-
800-
I' _.c /H'
400-
REFERENCES C
1' 01
1
Y(mll)
Fig. 4. Profiles (reacting jet).
15
1.
I
I
I
10
5
0
of mean temperature
at x = 50 mm
cess revealed by the measurements. The overall conformity between the predictions and data may be judged as fair. Last, it is well to mention that the measured turbulent Reynolds numbers ReT = k2/vc, where v is the laminar kinematic viscosity, along the centerline of the 02/N*
2. 3.
Bertrand, C., Hamon, F., Sarh, B., and Gokalp, I., 20th Symp. (Znt.) on Combustion, 1984. Bertrand, C., CNRS-CRCCHT, Orleans, France, 1981. Stolakis, P., Ph.D. Thesis, University of London, 1984. Rodi, W., Report SFB 80/T/127, University of Karlsruhe, Germany, 1978. Lockwood, F. C., and Salooja, A. P., Cornbust. Flume 41:217-219 (1981). Tribus, M., Thermostatics and Thermodynamics, Van Nostrand, London, 1961. Launder, B. E., J. Fluid Mech. 569-581 (1975).
Received 14 July 1984; revised 5 December 1984