1. A Correlation for Flame Length of Oxygen-
Assisted, Swirled, Coal and Biomass Flames
David Ashworth, John Tobiasson, Dale Tree
Bhupesh Dhungel
Air Liquide, USA
Clearwater Clean Coal Conference
June 7th, 2016
1

2. Introduction
• Biomass has been investigated for use in coal-fired power plants as a CO2-
neutral fuel
• Longer biomass flames become an issue in fixed volume boilers designed
to burnout coal
• The effects of oxygen enrichment and swirl on biomass flames were
explored
• Trends in NOx formation and burnout associated with flame length are
apparent as burner geometry, swirl, and O2 flow rates change
• A model to predict such trends could aid in the design of optimal burner
geometries
• Efforts have been made to model flame length for gaseous flames
• An initial, low-fidelity mathematical model for solid fuel flames with curve-fit
constants was created
2

3. Experimental Setup
Burner Flow Reactor (BFR) 2.4 m length
0.75 m diameter
150 kWth
3

4. Background - Visual Model
Enlarged View
1
2 2
3 3
1 – Center flow (Oxygen Enrichment)
4
2 – Primary flow (Solid Fuel in Air)
3 – Secondary flow (Air and Oxygen)

5. Background - Volatiles Flame
Determine axial location where fuel and
air mix to a stoichiometric composition
𝐶𝑠
𝐿 𝑓
5
𝑐 𝑠 =
𝑚 𝑓𝑢𝑒𝑙
𝑚 𝑜𝑥 𝑠

6. Background - Flame Length Model
𝑐 𝑠 =
𝑚 𝑓𝑢𝑒𝑙
𝑚 𝑜𝑥 𝑠
=
𝜌 𝑚𝑖𝑥 𝑉𝑝
𝜋
4
𝑑 𝑝
2
− 𝑑 𝑐
2
∗ 𝑌𝑓𝑢𝑒𝑙,𝑝
𝑌𝑂2,𝑠𝑒𝑐 𝜌𝑠𝑒𝑐 𝑉𝑝 − 𝑉𝑠𝑒𝑐 𝜋𝑑 𝑝 𝐿 𝑓 𝑐1 + 𝜌𝑠𝑒𝑐 𝑈 𝑅𝑍 𝜋𝑏𝐿 𝑓 𝑐2 + 𝑚 𝑂2,𝑐 + 𝑚 𝑂2,𝑝
𝑈 𝑅𝑍 =
0.2 ∗ 𝑆 ∗ 𝑉𝑠𝑒𝑐
0.2 + 𝑆
Recirculation term including
swirl and velocity
Mixing due to
Recirculation
Mixing due to shearing
between streams
𝑑 𝑐
𝑑 𝑝
𝑏
𝐿 𝑓
𝑚 = 𝜌𝑉𝐴
6

7. Background - Flame Length Model
𝐿 𝑓 =
𝑚 𝑓𝑢𝑒𝑙
𝑐 𝑠
− 𝑚 𝑂2,𝑝 − 𝑚 𝑂2,𝑐
𝜌 𝑉𝑝 − 𝑉𝑠𝑒𝑐 𝑑 𝑝 𝜋𝑐1 + 𝜌𝑠𝑒𝑐 𝜋𝑏𝑈 𝑅𝑍 𝑐2 𝑌𝑂2,𝑠𝑒𝑐
Factor out Lf (flame length) and rearrange terms
7
Total Fuel
Empirical Constants

8. Objectives
1. Refine the flame length model by:
– Using volatiles fraction from ASTM Proximate Analysis
– Predicting empirical constants
2. Compare modeled results to experimental data
8

9. Straw Medium Fine Switchgrass PRB Coal
Wood Wood
0.7381 0.7906 0.7642 0.6778 0.3376
Results - Volatiles Fraction
For total fuel mass flow:
• Correlation is good for biomass
• Coal data is more horizontally oriented
9
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5
TheoreticalCalculatedLength(m)
Visual Length (m)
Med. Wood
Fine Wood
Straw
Coal
Switchgrass

10. 0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5
TheoreticalCalculatedLength(m)
Visual Length (m)
Med. Wood
Fine Wood
Straw
Switchgrass
Coal
Results - Volatiles Fraction
10
For volatiles mass flow:
• Scatter increases slightly for all fuels
• Coal data correlates better
Straw Medium Fine Switchgrass PRB Coal
Wood Wood
0.7381 0.7906 0.7642 0.6778 0.3376

11. Results - Empirical Constants
11
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
0.0040
0 100 200 300 400 500
C1Value
Mean Particle Size (μm)
Fuel c1 c2
Coal 0.00000 0.02156
Fine Wood 0.00000 0.04915
Straw 0.00000 0.02675
Med Wood 0.00352 0.02823
Switchgrass 0.00326 0.02362
y = -3E-05x + 0.0374
R² = 0.141
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0 100 200 300 400 500
C2Value
Mean Particle Size (μm)
𝐿 𝑓 =
𝑚 𝑓𝑢𝑒𝑙
𝑐 𝑠
− 𝑚 𝑂2,𝑝 − 𝑚 𝑂2,𝑐
𝜌 𝑉𝑝 − 𝑉𝑠𝑒𝑐 𝑑 𝑝 𝜋𝑐1 + 𝜌𝑠𝑒𝑐 𝜋𝑏𝑈 𝑅𝑍 𝑐2 𝑌𝑂2,𝑠𝑒𝑐

12. Results - Empirical Constants
12
𝐿 𝑓 =
𝑚 𝑓𝑢𝑒𝑙
𝑐 𝑠
− 𝑚 𝑂2,𝑝 − 𝑚 𝑂2,𝑐
𝜌 𝑉𝑝 − 𝑉𝑠𝑒𝑐 𝑑 𝑝 𝜋𝑐1 + 𝜌𝑠𝑒𝑐 𝜋𝑏𝑈 𝑅𝑍 𝑐2 𝑌𝑂2,𝑠𝑒𝑐
-0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
0.0040
0 100 200 300 400 500
C1Value
Mean Particle Size (μm)
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
0.0040
0 100 200 300 400 500
C1Value
Mean Particle Size (μm)
𝑐1 =
0.1854
𝐷 − 443
− 7.147 ∗ 10−4

13. Results - Empirical Constants
13
𝐿 𝑓 =
𝑚 𝑓𝑢𝑒𝑙
𝑐 𝑠
− 𝑚 𝑂2,𝑝 − 𝑚 𝑂2,𝑐
𝜌 𝑉𝑝 − 𝑉𝑠𝑒𝑐 𝑑 𝑝 𝜋𝑐1 + 𝜌𝑠𝑒𝑐 𝜋𝑏𝑈 𝑅𝑍 𝑐2 𝑌𝑂2,𝑠𝑒𝑐
𝑐2 = (−9.677 ∗ 10−5
𝐷 + 7.482 ∗ 10−2
) ∗ 𝑓𝑣
y = -3E-05x + 0.0374
R² = 0.141
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0 100 200 300 400 500
C2Value
Mean Particle Size (μm)
y = -0.0000968x + 0.0748245
R² = 0.9582012
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 100 200 300 400 500
C2/VolatilesFraction
Mean Particle Size (μm)

14. Results - Refined Model
14
𝐿 𝑓 =
𝑚 𝑓𝑢𝑒𝑙 ∗ 𝑓𝑣
𝑐 𝑠
− 𝑚 𝑂2,𝑝 − 𝑚 𝑂2,𝑐
𝜌 𝑉𝑝 − 𝑉𝑠𝑒𝑐 𝑑 𝑝 𝜋𝑐1 + 𝜌𝑠𝑒𝑐 𝜋𝑏𝑈 𝑅𝑍 𝑐2 𝑌𝑂2,𝑠𝑒𝑐
𝑐1 =
0.1854
𝐷 − 443
− 7.147 ∗ 10−4
𝑐2 = (−9.677 ∗ 10−5
𝐷 + 7.482 ∗ 10−2
) ∗ 𝑓𝑣

15. Results - Comparison
15
• Overall scatter has increased but not within a specific fuel
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5
TheoreticalCalculatedLength(m)
Visual Length (m)
Med. Wood
Fine Wood
Straw
Switchgrass
Coal

16. Conclusions
• A model has been created which predicts volatiles flame
length for solid fuel as a function of burner geometry, flow
rates, and fuel properties
• Two constants which were previously determined empirically
were found to be predicted well by particle size and volatiles
fraction making the model fully predictive
• The model enables an understanding of how the following
parameters impact flame length:
– Volatiles fraction
– Oxygen addition, location and flow rates
– Swirl
– Primary and secondary velocities
– Burner diameters
– Particle Size
16

17. Thank You
Questions
17

18. Results
18
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5
TheoreticalCalculatedLength(m)
Visual Length (m)
Med. Wood
Fine Wood
Straw
Coal
Switchgrass
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5
TheoreticalCalculatedLength(m)
Visual Length (m)
Med. Wood
Fine Wood
Straw
Switchgrass
Coal
Initial Final

19. CO Mapping
19
Coal Wood
• Visual and CO flame lengths follow similar trends