Vol. 4, No. 4 April 2013 ISSN Journal of Emerging Trends in Computing and Information Sciences CIS Journal. All rights reserved.

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1 Numeric Simulation of an Ethanol/Air Spray Flame Based on Parallel Calculation 1 Dong-mei Zhao 2 Tao Liu 1 2 School of Computer Science and Technology Southwest University of Science and Technology Mian Yang SiChuan China ABSTRACT In this paper an open source field operation and manipulation software Open FOAM is adopted to simulate a turbulent spray flame experiment given by University of California Berkeley in 2007 along with KHRT breakup model evaporation model k ε two-equation turbulent model reflect model and one-step chemical reaction of ethanol and oxygen. To accelerate the whole process parallel calculation is adopted to complete the simulation. By comparing the experimental and simulating data of liquid temperature and mist temperature it can be found that simulation agrees with experimental data well KHRT breakup model can describe the breakup process well and spray combustion can be explained with evaporation model and turbulent model as might be valuable to the designing simulating and assessment of combustion chamber of engine. Keywords: KHRT breakup model; evaporation model; spray flame; parallel calculation 1. INTRODUCTION At present liquid fuels occupy a large portion of modern energy supply compared to both gaseous and solid fuels it s easy and convenience to transport and store liquid fuels. In 2004 liquid fuels covered 34.3% of the world s total energy consumption [1]. Liquid fuels are used widely in automotive and aircraft engines liquidfueled rockets and liquid-fueled furnaces so the flame of liquid fuels should be studied very carefully to reduce the NOx emission and to improve the thermal efficiency. In general after liquid fuels are injected into the combustion chamber as a spray evaporation and mixing with air occurs then an ignitable mixture is formed and combustion happens. So the size and distribution of liquid droplet are crucial for the combustion efficiency stability and pollutant emission [2]. The whole process of spray combustion is complicated turbulence chemical reaction collision breakup and evaporation may happen at the same time and they affect each other deeply. It still needs lots of works to describe spray flame accurately. Because of the complicated coupling of turbulence atomization and chemical reactions of spray flame and the cost of experiment numeric simulation plays an important role in the designing of combustion chamber for its low cost and low time consumption [3]. For now DNS (Direct Numerical Simulation) LES(Large eddy simulation) and RANS(Reynolds Average Navier- Stoke) are the three methods for numeric simulation [4-5]. RANS is adopted in this paper. To accelerate the whole simulation process parallel calculation is adopted. The whole mesh is divided into different sub-meshes and then different sub-meshes are transported to different nodes with parallel calculation the whole process of simulation can be accelerated sharply. 2. GOVERNING MODELS 2.1 Breakup Model In this paper Kelvin-Helmholtz-Rayleigh-Taylor (KHRT) is adopted as droplet breakup model which is the most widely used breakup model along with TAB model [6]. KHRT model includes two breakups KH breakup is mainly caused by the velocity difference between gas and liquid and RT breakup is caused by the growth of droplet surface caused by the accelerated velocity on the dropletgas interface KH Breakup Model During the period of KH breakup the wave growth rate Λ and the wave length Ω are determined by formula (1) and (2) respectively (... ) ( )(.. ).. (.. ) (.. ). (1) (2) Where Oh is liquid Ohnesorge number h. / ; We is liquid Weber number / ; Re is Reynolds number / ; Ta is Taylor number h ; is gaseous Weber number /. Breakup time is assumed to be determined by and r as formula (3) and (4). (3). (4) Where is a model constant 0.61 is a model constant too. 417

2 2.1.2 RT Breakup Model When the amplitude of RT unsteady wave is larger than thickness of droplet breakup occurs the process is determined by and as following. ( ) ( ). (5) is velocity compressible turbulent dissipation rate of inflation on the total effect. Turbulence energy k and dissipation rate ε are determined as formula (13) and (14) respectively. ( + + ) (13) ( + ) (6) 2 ( ) Where determines whether droplets can turn into smaller droplets and the size of new droplets. 2.2 Evaporation Model Time-to-live of droplet is the key to evaporation model the mass of droplet determines the time-to-live [6]. According to the researches of Crowe C. Somerfield M [7] the mass of droplet can be determined as formula (8). h h (1 + (8) ) Where Sherwood number Sh can be determined by Ranz-Marshall (or Frössling) [8] as formula (9). h (9) (7) And time-to-live can be calculated as formula (10). ( ) (10).. (14) Where and are the velocity of xyz directions l is the character length a constant Turbulent viscosity coefficient is determined as formula (15). (15) 2.4 Chemical Reaction One-step irreversible chemical reaction of ethanol and oxygen is given as following. C 2 H 5 OH + 3O 2 > 2CO 2 + 3H 2 O Droplet collision model and heat conduction model are involved too. 3. SPRAY FLAME EXPERIMENT The target of the context is to simulate a turbulent spray flame experiment given by University of California Berkeley in 2007 [2] to figure out whether KHRT model is appropriate for this kind of nozzle. The setup of the spray flame burner is shown in figure Turbulent Model Because of the complexity of turbulence it s hard to describe the phenomenon accurately. For now twoequation turbulent model is popular especially since the two-equation turbulent model is set up the model is used widely [9]. The governing equations are listed as following [10] (11) + + ( + ) (12) Fig 1: Setup of experiment of turbulent spray flame Where is the turbulence energy caused by average velocity gradient; is the turbulence energy caused by buoyant effect; As shown in figure 1 the nozzle has a diameter of 10 mm and produces a hollow-cone spray. It is fixed about 80 mm above the center of a multi-hole plate that generates a homogeneous air co-flow. A stable flame is obtained by preheating the ethanol to 45 at the nozzle exit. The resulting flame has two flame zones. The inner 418

3 flame is located 1 mm above the nozzle exit while the outer flame position depends on the fuel pressure and is located 5 15 mm above the nozzle. The fuel pressure is varied between 1.4 and 2.6 bar. The resulting liquid flow rate is varied between 0.39 and 0.54 g/s. The air co-flow velocity is set between 0 and 0.64 m/s [2]. 4. CALCULATING CONDITIONS AND MESH Calculating condition is given in table 1. Table 1: Calculating conditions or I/O performance. Because the low difference of time consumption of 4 8 and 16 nodes 4 nodes are adopted in this simulation and the total time consumption is about 28 hours. 6. SIMULATING RESULTS After parallel calculation done we can get the stable combustion status of 0.5 second the distribution of droplets is shown in figure 4. Item Pressure at nozzle Fuel flux Co-flow velocity Step Value 2.0Mpa 0.45g/s 0.32m/s 5eE-6s 3-D mesh is adopted in this context which contains about cells as shown in figure 2. Fig 4: Droplet breakup status of inner flame After primary and second breakup the distribution and size of droplets in the inner flame zone is good. Fuel is mixed with air very well at the upper zone and then combustion occurs. The comparisons of gas temperature between experimental and simulating data are shown in figure 5 and figure 6. Fig 2: Mesh 5. PARALLEL CALCULATION To accelerate the simulation parallel calculation is used with MPI. The main idea is to divide the whole mesh into different sub-meshes then give different submeshes to different nodes to accelerate the whole process. For example time consumption of one job with different nodes is shown in figure 3. Time consumption(s) Time consumption per step 1 Node 2 Nodes 4 Nodes 8 Nodes 16 Nodes Fig 3: Comparison of time consumption per step With the increment of nodes time consumption decreases nonlinearly because the way of inner-connection Fig 5: Gas temperature 6MM above nozzle Fig 6: Gas temperature 10MM above nozzle As shown in figure 5 and figure 6 the trend of gas temperature of simulating data agrees with that of experimental data well which means KHRT model can describe the spray flame and the atomization quiet well. But simulating gas temperature is higher than 419

4 experimental data one-step chemical reaction and combustion model may cause the difference between experimental and simulating data. The comparisons of liquid temperature between experimental and simulating data are shown in figure 7 and figure 8. ii. temperature the multi-step reversible chemical reactions may improve it but the calculation time consumption increases sharply. Lower setup of initial temperature of simulation cause lower gas temperature than experimental data. iii. Parallel calculation can accelerate the whole simulating process sharply especially those simulations with complicated multi-step reversible chemical reactions and complicated mesh. ACKNOWLEDGEMENT This work is supported by the Youth Fund Project Southwest University of Science and Technology(11zx3116). Fig 7: Liquid temperature 10MM above nozzle REFERENCES [1] H.-W. Ge I. Dűwel H. Kronemayer. et al. Laserbased experimental and Monte Carlo PDF numerical investigation of an ethanol/air spray flame[j]. Combustion Science and Technology : [2] Duwel I Ge H.W. Experimental and numerical characterization of a turbulent spray flame[c] proceeding of the combustion institute 31: Fig 8: Liquid temperature 20MM above nozzle As shown in figure 7 and figure 8 the difference of liquid temperature between experimental and simulating data is lower than that of gas temperature which means before smaller droplets are formed no combustion occurs so the liquid temperature stays in about 350K. The simulation assumes that liquid temperature is 300K which may cause the difference between experimental and simulating data. Anyway we can see that KHRT model can describe the breakup process very well and simulating data of liquid temperature agrees with that of experimental data. 7. CONCLUSIONS Some conclusions can be drawn as following. a. KHRT model can describe the breakup and atomization process of ethanol/air spray flame well the fuel can turn into droplets and the simulating distribution and size of droplets are good an Ethanol/Air mixture can be formed and then combustion occurs the temperature field of gas and liquid agree with experimental data. b. The simulating temperature is high than experimental temperature data the reasons may be listed as following: i. One-step irreversible chemical reaction of ethanol and oxygen may cause higher [3] YAN Ying-wen ZHAO Jian-xing ZHANG Jingzhou et al. Large eddy simulation of turbulent spray combustion in an annular combustor[j]. Journal of Aerospace Power Vol. 21 No. 5: [4] R. Hilbert F. Tap H. El-Rabii et al. Impact of detailed chemistry and transport on turbulent combustion simulations[j]. Progress in Energy and Combustion Science[J] : [5] YAN Ying-wen ZHAO Jian-xing ZHANG Jing- Zhou et al. Large-eddy Simulation of Turbulent Reacting Flows in the Combustor by Threedimensional Body-fitted Grid[J]. Journal of Propulsion Technology (3) PP: [6] Fabian Peng Kärrholm. Numerical Modeling of Diesel Spray Injection Turbulence Interaction and Combustion[D]. Department of Applied Mechanics Chalmers University of Technology.2008: [7] Crowe C. Somerfield M. Tsuji Y. Multiphase flows with droplets and particles[m]. CRC Press LLC [8] Nordin N. Complex chemistry modeling of diesel spray combustion[d]. Dept. of Thermo and Fluid Dynamics Chalmers University of Technology Goteborg

5 [9] ZHOU L X. Dynamics of Multiphase Turbulent Reacting Fluid Flows[M]. National Defense Industry Press. 2002: [10] SUN Zhao-guo LIU Zhi-qin LIU Tao et al. Research and implementation of numerical simulation of turbulent combustion[j]. Computer Engineering and Design Vol33: AUTHOR PROFILES Dong-mei Zhao received her M.S. degree in computation application from University of Science and Technology of China P.R. China in Currently she is working as lecturer at Southwest University of Science and Technology. Her research interests include distributed parallel calculation and numeric simulation. Tao Liu received his M.S. degree in mechanical engineering from National University of Science and Technology in His main research interests are numeric simulation and high performance calculation. 421