Simulation of evaporation and combustion of droplets 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 (realized for 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 2
Motivation (2) Main aim: simulation of gasification of heavy fuel oils Problem: complexity of considered system Solution: stepwise description (and validation) of singular steps till gasification of liquid fuels More precisely: Primary Breakup Combustion, Gasification discussed here! Secondary Breakup = Evaporation 3
Mathematical Model - Modified Conservation Equations (1) In contrast to standard OpenFOAM R -solver interfoam (VOF) source terms for evaporation and chemical reactions, temperature and species transport equations included Volume-of-fluid equation: Temperature equation: (ρc p T ) t α t + (αu) = Ṡ V,evap + (ρc p UT ) = (λ T )+Ṡq,chem Ṡq,evap 4
Mathematical Model - Modified Conservation Equations (2) Species transport equations e.g. n-heptane: (ρy C7 H 16 ) t + (ρy C7 H 16 U) = (ρd C7 H 16 Y C7 H 16 ) +Ṡm,evap + Ṡm,chem,C 7 H 16 Exemplary source term: volumetric evaporation source Ṡ V,evap = D C 7 H 16 ρ gp Y C7 H 1 Y C7 H 16 ρ 16 ˆnκ λ 1 T ˆnκ l h v ρ l derived from analytics 5
Physics - Evaporation Source Evaporation differential equation described e.g. by [Turns (2000)] considering two different cases dependent on surface temperature T S = T gp = T First case T S < T boil dd 2 dt = 8 ρd AB ρ l ( ) 1 YA, ln 1 Y A,S Second case T S > T boil dd 2 dt = 8 λ ( ) cpgp (T T boil ) ln + 1 ρ l c pgp h v 6
Physics - Fluid Properties Temperature dependent properties calculated using polynomials given by [VDI-Wärmeatlas (2006)] For test cases considered in this work, properties like heat capacities, heat conductivities, densities or evaporation enthalpies fixed for certain temperatures and pressure Mixture of ideal gases Reaction rates according simplified n-heptane combustion mechanism C 7 H 16 + 11 O 2 7 CO 2 + 8 H 2 O calculated using Arrhenius law Further information e.g. on calculating mixture properties or diffusion coefficients can be found in proceedings of ICMF 2010 ([Keller et al. (2010)]) 7
Validation - Analytics Considered case: T < T S Data: d 10 4 m T S = T 363 K Y sat at T S 0.58 ρ l 1000 kg m 3 ρ at Y sat 0.7124 kg m 3 D AB 7.6 10 K 3.1 10 7 m2 s t d 0.032 s 8 m2 s 2D axisymmetric simulation of evaporating water droplet of size d = 100 µm at atmospherical conditions and air temperature below boiling temperature 8
Validation - Analytics: Results (1) 1e-08 8e-09 d 2 analytical ρ =ρ H2 O =0.712kg/m3 d 2 analytical ρ =ρ Air =0.9kg/m 3 d 2 simulation 880 cells ρ const d 2 in m 2 6e-09 4e-09 2e-09 0 0 0.005 0.01 0.015 0.02 0.025 0.03 time in s Figure: Case 1: constant intermediate density ρ at surface 9
Validation - Analytics: Results (2) 1e-08 8e-09 d 2 analytical ρ =ρ H2 O =0.712kg/m3 d 2 analytical ρ =ρ Air =0.9kg/m 3 d 2 simulation 880 cells d 2 simulation 3500 cells d 2 in m 2 6e-09 4e-09 2e-09 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 time in s Figure: Case 2/3: variable density ρ at surface with different mesh sizes 10
Validation - Experiments Experimental data given by [Nomura et al. (1996)] Different inlet temperatures to evaporate n-heptane droplet of size d = 670 µm at atmospherical conditions Inlet velocity U = 0.1 m s Re 3 2D-axisymmetric mesh of size 175000 cells Results: evaporation rate K T exp,nom 471 K 745 K 0.117 mm2 s 0.390 mm2 s K exp,nom K sim,max K sim,mid 0.152 mm2 s 0.129 mm2 s 0.559 mm2 s 0.387 mm2 s err rel,max 0.299 0.43 err rel,mid 0.1026 0.0077 11
Validation - Experiments: Results 1.06 1.04 1.02 d 0 =690µm, T=745K K sim,max =0.559mm 2 /s K sim,mid =0.387mm 2 /s K exp,nom =0.390mm 2 /s 1 0.98 (d/d 0 ) 2 0.96 0.94 0.92 0.9 0.88 0.86 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2 t/d 0 in s/mm 2 Figure: Maximum and intermediate evaporation rates K sim,max and K sim,mid for T N2 = 745 K 12
Demonstration - Chemical Reactions Different test cases to demonstrate simulation of combined evaporation and combustion Simplified properties leading to errors (overshoot of adiabatic flame temperature, heating above critical temperature) Test cases: Case of [Dwyer et al. (2000)] with fixed droplets (p = 20 bar, T 1 = 1000 K, T 2 = 1500 K) In hot air falling droplet (T = 745 K) Coaxial atomizer with air coflow (Tin = 1000 K, p = 20 bar) 13
Demonstration - Chemical Reactions: Some Results (1) Figure: 3D droplet array: iso-surfaces of T. 14
Demonstration - Chemical Reactions: Some Results (2) Figure: 3D droplet array: iso-surfaces of C 7 H 16. 15
Demonstration - Chemical Reactions: Some Results (3) Figure: 3D falling droplet: iso-surface of Y CO2 = 0.01 with contours of T. 16
Demonstration - Chemical Reactions: Some Results (4) Figure: 3D atomizer: iso-surface of Y CO2 = 0.0025 with contours of T. 17
Conclusions Solver for combined atomization, evaporation and combustion (later gasification) implemented With simplified properties validation of analytics possible, experiments suffer temperature dependent properties (right now not completely implemented) First results of simulations due to chemical reactions comprehensible Upcoming tasks: Consideration of temperature dependence where needed (evaporation enthalpy, densities,... ) Inclusion of chemkin library for more complex reaction mechanisms Multicomponent fuel droplets Validation of reaction results 18
Thank You for Your Attention! Questions? 19
Literature Keller, P.; Nikrityuk, P.A.; Meyer, B.; Müller-Hagedorn, M., Numerical Simulation of Evaporating Droplets with Chemical Reactions using a Volume of Fluid Method, 7 th International Conference on Multiphase Flows, 2010 Dwyer, H.A.; Stapf, P.; Maly, R., Unsteady vaporisation and ignition of a three-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-Wärmeatlas, Springer Berlin Heidelberg, 2006 Zhang, H.; Gogos G., Numerical research on a vaporizing fuel droplet in a forced 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, 26 th Symposium (Int.) on Combustion p. 1267-1273, 1996 20