simulation of evaporation and combustion of droplets...
TRANSCRIPT
Simulation of evaporation and combustion ofdroplets using a VOF method
P. Keller, P.A. Nikrityuk, B. Meyer
June 23, 2010
Motivation Mathematics Physics Validation & Test Cases Conclusions
Motivation (1) - HP POX Test Plant
System specifications
I Operating pressure: up to 100 bar (realizedfor partial oxidation of liquids and gases)
I Performance: up to 5 MW
I Startup: Oct 2003
Research Topics
I Reactor and process modelling
I Catalyst test program
I Trace components at high pressures
I Atomization behaviour of liquid feeds
Figure: Outline of the entrained-flow HP POX reactor and main feed and product flows by
courtesy of Lurgi GmbH
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Motivation (2)
⇓
I Main aim: simulation of gasification of heavy fueloils
I Problem: complexity of considered system
I Solution: stepwise description (and validation) ofsingular steps till gasification of liquid fuels
I More precisely:
Primary Breakup Combustion, Gasification
⇓ discussed ⇑ here!
Secondary Breakup =⇒ Evaporation
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Mathematical Model - Modified Conservation Equations (1)
I In contrast to standard OpenFOAMr-solver interFoam (VOF)source terms for evaporation and chemical reactions,temperature and species transport equations included
I Volume-of-fluid equation:
∂α
∂t+∇ · (αU) = −SV ,evap
I Temperature equation:
∂(ρcpT )
∂t+∇ · (ρcpUT ) = ∇ · (λ∇T )+Sq,chem − Sq,evap
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Mathematical Model - Modified Conservation Equations (2)
I Species transport equations e.g. n-heptane:
∂(ρYC7H16)
∂t+∇ · (ρYC7H16U) = ∇ · (ρDC7H16∇YC7H16)
+Sm,evap + Sm,chem,C7H16
I Exemplary source term: volumetric evaporation source
SV ,evap =DC7H16
1− YC7H16
ρgp
ρl∇YC7H16 · nκ−
λ
∆hv
1
ρl∇T · nκ
⇒ derived from analytics
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Physics - Evaporation Source
I Evaporation differential equation described e.g. by[Turns (2000)] considering two different cases dependent onsurface temperature TS = Tgp = T∞
I First case TS < Tboil
dd2
dt= −8ρDAB
ρlln
(1− YA,∞1− YA,S
)I Second case TS > Tboil
dd2
dt= − 8λ
ρlcpgp
ln
(cpgp (T∞ − Tboil)
∆hv+ 1
)
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Physics - Fluid Properties
I Temperature dependent properties calculated usingpolynomials given by [VDI-Warmeatlas (2006)]
I For test cases considered in this work, properties like heatcapacities, heat conductivities, densities or evaporationenthalpies fixed for certain temperatures and pressure
I Mixture of ideal gases
I Reaction rates according simplified n-heptane combustionmechanism
C7H16 + 11 O2 −→ 7 CO2 + 8 H2O
calculated using Arrhenius law
I Further information e.g. on calculating mixture properties ordiffusion coefficients can be found in proceedings of ICMF2010 ([Keller et al. (2010)])
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Validation - Analytics
I Considered case: T < TS
I Data:
d 10−4 m TS = T∞ 363 K
Ysat at TS 0.58 ρl 1000 kgm3
ρ at Ysat 0.7124 kgm3 DAB 7.6 · 10−8 m2
s
K 3.1 · 10−7 m2
s td 0.032 s
I 2D axisymmetric simulation of evaporating water droplet ofsize d = 100µm at atmospherical conditions and airtemperature below boiling temperature
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Validation - Analytics: Results (1)
0
2e-09
4e-09
6e-09
8e-09
1e-08
0 0.005 0.01 0.015 0.02 0.025 0.03
d2 in
m2
time in s
d2 analytical ρ = ρH2O=0.712kg/m
3
d2 analytical ρ = ρAir=0.9kg/m
3
d2 simulation 880 cells ρ const
Figure: Case 1: constant intermediate density ρ at surface
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Validation - Analytics: Results (2)
0
2e-09
4e-09
6e-09
8e-09
1e-08
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
d2 in
m2
time in s
d2 analytical ρ = ρH2O=0.712kg/m
3
d2 analytical ρ = ρAir=0.9kg/m
3
d2 simulation 880 cells
d2 simulation 3500 cells
Figure: Case 2/3: variable density ρ at surface with different mesh sizes
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Validation - Experiments
I Experimental data given by [Nomura et al. (1996)]
I Different inlet temperatures to evaporate n-heptane droplet ofsize d = 670µm at atmospherical conditions
I Inlet velocity U = 0.1ms ⇒ Re ≈ 3
I 2D-axisymmetric mesh of size ≈ 175000 cells
I Results: evaporation rate K
Texp,Nom 471 K 745 K
Kexp,Nom 0.117 mm2
s 0.390 mm2
s
Ksim,max 0.152 mm2
s 0.559 mm2
s
Ksim,mid 0.129 mm2
s 0.387 mm2
serrrel,max 0.299 0.43errrel,mid 0.1026 −0.0077
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Validation - Experiments: Results
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
(d/d
0)2
t/d02 in s/mm
2
d0=690µm, T=745K
Ksim,max=0.559mm2/s
Ksim,mid=0.387mm2/s
Kexp,Nom=0.390mm2/s
Figure: Maximum and intermediate evaporation rates Ksim,max andKsim,mid for TN2 = 745 K
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Demonstration - Chemical Reactions
I Different test cases to demonstrate simulation of combinedevaporation and combustion
I Simplified properties leading to errors (overshoot of adiabaticflame temperature, heating above critical temperature)
I Test cases:I Case of [Dwyer et al. (2000)] with fixed droplets (p = 20 bar ,
T1 = 1000 K , T2 = 1500 K )I In hot air falling droplet (T = 745 K )I Coaxial atomizer with air coflow (Tin = 1000 K , p = 20 bar)
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Demonstration - Chemical Reactions: Some Results (1)
Figure: 3D droplet array: iso-surfaces of T .
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Demonstration - Chemical Reactions: Some Results (2)
Figure: 3D droplet array: iso-surfaces of C7H16.
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Demonstration - Chemical Reactions: Some Results (3)
Figure: 3D falling droplet: iso-surface of YCO2 = 0.01 with contours of T .
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Demonstration - Chemical Reactions: Some Results (4)
Figure: 3D atomizer: iso-surface of YCO2 = 0.0025 with contours of T .
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Conclusions
I Solver for combined atomization, evaporation and combustion(later gasification) implemented
I With simplified properties validation of analytics possible,experiments suffer temperature dependent properties (rightnow not completely implemented)
I First results of simulations due to chemical reactionscomprehensible
I Upcoming tasks:I Consideration of temperature dependence where needed
(evaporation enthalpy, densities, . . . )I Inclusion of chemkin library for more complex reaction
mechanismsI Multicomponent fuel dropletsI Validation of reaction results
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Motivation Mathematics Physics Validation & Test Cases Conclusions
Thank Youfor Your Attention!
Questions?
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Motivation Mathematics Physics Validation & Test Cases Conclusions
LiteratureKeller, P.; Nikrityuk, P.A.; Meyer, B.; Muller-Hagedorn, M., ”NumericalSimulation of Evaporating Droplets with Chemical Reactions using a Volume ofFluid Method”, 7th International Conference on Multiphase Flows, 2010
Dwyer, H.A.; Stapf, P.; Maly, R., ”Unsteady vaporisation and ignition of athree-dimensional droplet array”, Combustion and Flame 121, p. 181-194, 2000
Turns, S.R., ”An Introduction to Combustion - Concepts and Applications”,McGraw-Hill Higher Education, 2000
VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen,”VDI-Warmeatlas”, Springer Berlin Heidelberg, 2006
Zhang, H.; Gogos G., ”Numerical research on a vaporizing fuel droplet in aforced convective environment”, International Journal of Multiphase Flow 30 p.181-198, 2004
Nomura, H.; Ujiie, Y.; Rath, H. J.; Sato, J.; Kono, M., ”Experimental study on
high pressure droplet evaporation using microgravity conditions”, 26th
Symposium (Int.) on Combustion p. 1267-1273, 1996
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