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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