Diffusion Jet Flame Models Using Open Source Code CFD Software

Transcription

1 Kasetsart J. (Nat. Sc.) 49 : (2015) Dffuson Jet Flame Models Usng Open Source Code CFD Software Chart Suvanjumrat * and Panya Aroonjarattham ABSTRACT Open-source code software (OpenFOAM) based on computatonal flud dynamcs (CFD) was mplemented and appled to smulate the dffuson of a jet flame. The large eddy smulaton (LES) of the turbulence combuston model was wrtten usng the C++ language. The mxture fracton approach, an nfntely-fast chemstry assumpton and radatve heat transfer were combned wth ths LES model. The fnte volume method was performed to solve and smulate dffuson jet flame models under varyng methane flow rates and envronmental pressures. The results of the jet flame smulaton comprsng the percentage of maxmum burnng temperature, the heat release rate and oxygen from the oxygen fracton were defned to be the flame shape for valdaton wth experments. It was found that the flame length measured usng the heat release rate from the results of smulatons had the best agreement wth the experments. An average error of less than 5.84% was obtaned by a comparson between the developed CFD model and the experment when the CFD flame length was depcted by the heat release rate. Keywords: dffuson, jet flame, model, open source code, computatonal flud dynamcs (CFD) INTRODUCTION A dffuson jet flame usually conssts of gaseous fuel whch s ejected from a ppe, tube or an orfce nto an oxdzng envronment such as ar. The dffuson jet flame s nown as the nonpremxed flame arsng from fuel and ar whch are ntally separated untl combuston whch s controlled by the dffuson and turbulence that occurs (McAllster et al., 2011; Hu et al., 2013). A further understandng of jet flames s very mportant n the combuston analyss and desgn of burners. Smulaton of jet flames s a potental methodology to represent the flame structure whch can avod expensve cost assocated wth the apparatus n experments. The computatonal flud dynamcs (CFD) modelng technque s wdely used to model jet flames and s governed by basc transport equatons for the flud flow and heat transfer wth addtonal models for the combuston chemstry, radatve heat transfer and other mportant sub-processes (Versteeg and Malalasera, 2007). Flame modelng has been successfully performed usng commercal software such as ANSYS (Wang and Tare, 2011; Oh et al., 2014), FLOW-3D (Martnez et al., 2013) and CHEMKIN (Wang et al., 2010) whch have a lcense cost and are not open source software (OSS) (Ferrars and Wen, 2007; Ln et al., 2009; Severno et al., 2013). The OpenFOAM software s OSS and s based on CFD codes usng the C++ language under a GNU general publc lcense wth open access for mplementaton and development, and provdes a flexble framewor whch combnes tools for solvng CFD problems (OpenFOAM, 2009). The developed codes n OSS Department of Mechancal Engneerng, Faculty of Engneerng, Mahdol Unversty, Nahon Pathom 73170, Thaland. * Correspondng author, e-mal: chart.suv@mahdol.ac.th Receved date : 17/08/14 Accepted date : 11/05/15

2 466 Kasetsart J. (Nat. Sc.) 49(3) can be used wth confdence to analyze combuston and to desgn burners after mplementaton and n valdaton wth the results of experments. Many researchers have developed flame shapes from dffuson jet flame experments. The experment of Zeng et al., (2013) was selected to obtan the flame lengths to compare wth the results of the developed CFD code n ths research. The comparson wll nform the accuracy of the developed CFD codes whch are used to mprove combuston and burners for future wor. MATERIALS AND METHODS Mathematcal model The large eddy smulaton (LES) governng equatons of dffuson jet flames are the fltered conservaton equatons for mass, momentum, speces and energy (Equatons 1 4): ρ + ρu = 0 (1) t ρu j + ρuu j = ρ + t j u ρ ( µ µ ) + ρu t j j 2 3 ρ u δ j + ρg (2) ρy + ρ = µ + uy t Y ρ D + ω t x x Sc x (3) ρh + ρuh = + µ ρ + Dp t h + t Dt c P p r u + τ j + Q C Q R (4) j where ρ s the mxture densty, u s the velocty n drecton, p s pressure, u t s the turbulence vscosty, δ j s the Kronecer delta, Y s the mass fracton of speces, D s the mass dffusvty of speces, h s an enthalpy, c p s the specfc heat capacty and P r s the turbulence Prandtl number. The bar and tlde sgnfy a tme-averaged value and a Favre-average value, respectvely. The turbulence vscosty can be descrbed wrtes by Equaton 5: µ = ρc (5) t The Favre-average netc energy,, n Equaton 5 can be determned by Equaton 6: ρ + ρu = t 2 u + µ S S t : ρ u Cε ρ (6) j 3 j where C and C ε are constants, S s the fltered stran rate and S c s the turbulence Schmdt number. The mxture fracton,, s gven by Equaton 7: 0 F O O sy Y + Y Z = 0 0 sy + Y F O + t µ µ S c scp ( Q T T ) Y + Y = scp Q T T 0 ( O) Y 0 O 0 0 O O O (7) where Y F s the fuel mass fracton, Y O s the oxdant mass fracton, Y O 0 and Y F 0 are the oxdant and the fuel mass fracton n the pure oxdant stream, respectvely. The mxture fracton s rearranged n the conservaton equaton form and wrtten as Equaton 8: ρ Z + ρuz = µ + t Z ρ D t x x S c (8) The nfntely-fast chemstry assumpton s used to assume that fuel and oxdzer cannot mx. The lnear pecewse functon relates the mass fracton of fuel and oxdzer as shown n Equaton 9: 0 Z YF ( Z)= 0; YO( Z)= YO 1 (9) Zst f Z Z st, and as shown n Equaton 10:

3 Kasetsart J. (Nat. Sc.) 49(3) 467 Z YF ( Z)= Y 0 O 1 ; YO ( Z)= 0 (10) Zst f Z Z st, where Z st s the mxture fracton at the stochometrc mxture. The temperature of the mass fracton for nfntely-fast chemstry n the lnear pecewse form s wrtten as Equaton 11: 0 0 QY F T( Z)= Z TF + C + P ( ) f Z < Z st, and as Equaton 12: 1 O 1 Z T (11) Z QYF T( Z)= ZTF + ( Z) TO + Zst Zst C (12) 1 P f Z > Z st. A thermal radaton model s employed n the flame model to compute the radatve heat loss, wrtten by Equatons 13 and 14: ( ) 4 QR = P( 4πIb IdΩ )= P 4σT G (13) M Mθ m ( l ) = 1l= 1 m m G = Id( θ, ) I θ, 2snθ θ sn 2 m l θ m m l (14) where P s the Planc mean absorpton coeffcent, I s the radaton ntensty, I b s the blac body radaton ntensty and σ s the Stefan-Boltzmann constant. The fuel consumpton rate s modeled by Equaton 15 whch s related to the heat release rate of combuston as wrtten by Equaton 16. ω Q ρ = tc c O Y Y mn F, (15) s = ω h (16) C C Implementaton of jet flame models Zeng et al., (2013) performed experments usng a vacuum ar pump to control the pressure from 50 to 100 Pa nsde a cabn whch had a wdth of 2 m, a length of 3 m and a heght of 2 m. The round burner had an ext dameter of 3 mm and was nstalled n the cabn to supply 99.9 % purty methane from 5.95 to mg.s -1. In the current research, the CFD model was mplemented by defnng a cylndrcal doman wth a dameter of 0.25 m and a heght of 0.4 m correspondng to the space above the burner as the CFD doman for smulatng the dffuson jet flame as llustrated n Fgure 1. The CFD doman comprsed a base, a Top surface 0.25 m Cylndrcal surface 0.40 m CH 4 Base surface Burner orfce dameter 3 mm CFD doman Gas-nlet surface Fgure 1 Collectng space over a gas burner nsde a cabn for the computatonal flud dynamcs (CFD) doman.

4 468 Kasetsart J. (Nat. Sc.) 49(3) top, a cylndrcal surface and a gas-nlet surface wth a dameter equal to the burner dameter. All surfaces of the CFD doman except the gas-nlet surface were appled usng an open boundary condton. Hexahedral cells were defned to dvde the CFD doman. The governng equaton was dscretzed through nodes at the center of the cells usng the fnte volume method (FVM). There were 95,100 hexahedral cells whch correlated to the ndependent grd as llustrated by the cell or grd structure of the CFD doman n Fgure 2. Fne cells whch had a maxmum length less than 0.35 mm were confned n the flame zone to descrbe n good detal the flames as shown by the secton vews n Fgure 2b. An ntal temperature of 285 K nsde the cabn was defned nsde the grd structure for all smulated cases. The constant mass flow rates of the gaseous methane consstng of 5.95, 11.90, and mg.s -1 were appled at the gas-nlet surface of the CFD doman for each smulaton. The pressures nsde the grd structure were specfed as 50, 60, 70, 80, 90 and 100 Pa for each mass flow rate of gas. In total, 24 CFD cases were mplemented and performed usng the governng equaton and boundares whch were developed usng the C++ language for CFD codes n the OpenFOAM software (OpenFOAM, 2009). The combnaton algorthm between the SIMPLE (sem-mplct method for pressure lned equatons) and PISO (pressure mplct wth splttng of operator) algorthms s the PIMPLE algorthm n the OpenFOAM software whch was appled to solve the velocty-energy-pressure couplng n the CFD cases. The PIMPLE algorthm converged wth fve PISO loops and three SIMPLE loops. RESULTS AND DISCUSSION Smulaton of the dffuson jet flame produced estmates of the burnng temperature, mass fracton and heat release rate among others. It was not possble to measure the length of the jet flames drectly usng these CFD results. Thus t was necessary to nterpret and provde the specfcatons of flame shapes and the measurement of flame lengths for the CFD results. Fgure 2 Grd structure of the computatonal flud dynamcs (CFD) doman: (a)three-dmensonal vew; and (b) Secton vew.

5 Kasetsart J. (Nat. Sc.) 49(3) 469 Flame temperature The fuel and oxygen would be completely consumed at any stochometrc mxture rato whch produced the maxmum temperature of gaseous burnng (McAllster et al., 2011). The maxmum temperature for the combuston of the pure methane and oxygen dd not alter wth the dfferent methane flow rates and the envronmental pressures; therefore, t was useful to specfy the flame length. The flame surface occurred n the temperature contour of the CFD results where the percentage of the maxmum temperature was collected and s defned by a whte color. Fgure 3 shows an example to dentfy the flame shape based on the whte color for maxmum temperature ranges usng a methane flow rate and an envronmental pressure of mg.s -1 and 100 Pa, respectvely. However, 100% of the maxmum temperature could not depct the jet flame surface but rather t depcted the temperature contour of the combustng result. The contnuous jet flame surface appeared n the range % of the maxmum temperature whch was more approprate to specfy the flame length than other percentage ranges. Oxygen consumpton Oxygen remanng after the combuston was another result of the dffuson jet flame smulaton. The mass fracton of oxygen was llustrated by a gray-colored contour as shown n Fgure 4. The blac color represents the mnmum oxygen fracton magntude equal to 0.00 n the combustng doman. In contrast, the whte color represented the maxmum oxygen fracton magntude equal to 0.23 n the combustng doman. The percentages of oxygen remanng from the oxygen fracton were defned to depct the flame surface by the whte color. There was no vsble flame shape at 0% of oxygen remanng from the oxygen fracton. An explct whte lne occurred as a jet flame as the amount of oxygen remanng n the oxygen fracton ranged from 0.01% to 5.00%. The flame had a smlar shape but the lengths were dfferent. Therefore, a certan value for dentfyng the flame length would be obtaned after comparson wth experments. Fgure 3 Identfcaton of the jet flame structure usng the percentage of maxmum temperature of computatonal flud dynamcs (CFD) results wth a methane flow rate of mg.s -1 and an envronmental pressure of 100 Pa. Fgure 4 Identfcaton of the jet flame shape usng the percentage of oxygen remanng from the oxygen fracton n computatonal flud dynamcs (CFD) results wth a methane flow rate of mg.s -1 and an envronmental pressure of 100 Pa.

6 470 Kasetsart J. (Nat. Sc.) 49(3) Heat release rate The heat release rate was the drect result of the dffuson jet flame smulaton. The whte color could be used to specfy the total heat release rate and to depct the jet flame n the contour of the combustng temperature as shown n Fgure 5. The whte surface appeared n the secton vew and formed to be the shape of the jet flame. Consequently, t was unnecessary to estmate the heat release rate range to specfy the flame shape Fgure 5 Jet flame shape usng the heat release rate wth a methane flow rate of mg.s -1 and an envronmental pressure of 100 Pa. for ths method. Valdaton of flame length The flame length was measured from the jet flame model when t had settled to a steady shape. A tme perod of 5.0 sec for smulatng the jet flame was performed and the results were shown by so-surface flame propagaton (Fgure 6). Repetton of the jet shape could be observed from a burnng tme from 1.0 to 5.0 sec of the smulated result. The top of the flame was shaped le an arrowhead at tme 1.0 sec and was buoyant to the open boundary condton on the top surface of the CFD doman at tme 2.90 sec whch prolonged the shape of the jet flame. The expanson of the flame ndcated the cyclc steady state. Therefore, the flame length was collected at the startng tme of the cycle whch was at 5.0 sec n every CFD case used n ths research. The flame length n the range % of the maxmum temperature the of CFD results were measured and compared wth the experment. The comparson s shown wth the related graph between flame lengths and pressures for the methane flow rates of 5.95, 11.90, and mg.s -1 n Fgure 7. The CFD results had good agreement wth the expermental results. Average errors between the CFD and expermental flame lengths were 31.02, 2.78, 2.66 and 1.57% for methane flow rates of 5.95, 11.90, and mg.s -1, respectvely. An amount of 1.0% of oxygen remanng depcted the flame length n close agreement wth the experments of Zeng et al., (2013). Subsequently, the flame lengths of CFD results were measured and compared wth the experment. The related graph of flame lengths and pressures for methane flow rates of 5.95, 11.90, and mg.s -1 s shown n Fgure 8. The CFD results had very good agreement wth the expermental results. Average errors between the CFD and expermental flame lengths were 23.66, 5.93, 2.95 and 1.75% for methane flow rates of 5.95, 11.90, and mg.s -1, respectvely. The flame length was llustrated by the heat release rate whch was compared wth the experment as shown n Fgure 9. The related graph of flame lengths and pressures for any methane flow rate of CFD had very good agreement wth the experment; the average errors between the CFD and expermental flame lengths were 21.86, 2.13, 2.28 and 1.11% for methane flow rates of 5.95, 11.90, and mg.s -1, respectvely.

7 Kasetsart J. (Nat. Sc.) 49(3) 471 Fgure 6 Sequence of the flame propagaton up to a tme of 5 s n three-dmensonal form under a methane flow rate of mg.s -1 and an envronmental pressure of 100 Pa. Fgure 7 Graph of flame lengths n the range % of the maxmum temperature and pressures for methane flow rates of 5.95, 11.90, and mg.s -1, respectvely. (Exp = Experment; CFD = Computatonal flud dynamcs smulaton.) Fgure 8 Graph of flame lengths wth 1% oxygen remanng and pressures for methane flow rates of 5.95, 11.90, and mg.s -1, respectvely. (Exp = Experment; CFD = Computatonal flud dynamcs smulaton.)

8 472 Kasetsart J. (Nat. Sc.) 49(3) Fgure 9 Graph of flame lengths wth the heat release rate and pressures for methane flow rates of 5.95, 11.90, and mg.s -1, respectvely. (Exp = Experment; CFD = Computatonal flud dynamcs smulaton.) CONCLUSION Ths research used three methods to determne the shape of the jet flame. The frst was the % range n the maxmum temperature. The second was 1% of the oxygen whch remaned nsde the doman and the last was the heat release rate of combuston. Flame lengths dstnctly ncreased dependng on the value of the methane flow rate. The envronmental pressure was almost unaffected by the flame length. The reducton n flame lengths was slght when the envronmental pressure was ncreased. Valdaton of the jet flame length from the CFD results ndcated an average error from 5.84% to 9.51%. The developed C++ code was the best way to determne the jet flame model usng the heat release rate. Ths methodology utlzes the flame structure from burners for analyss whch can reduce expermental costs. In partcular, burner mprovements can be developed by applyng ths CFD code. LITERATURE CITED Ferrars, S.A. and J.X. Wen Large eddy smulaton of a lfted turbulence jet flame. Combust Flame 150: Hu, L., Q. Wang, F. Tang, M. Delchatsos and X. Zhang Axal temperature profle n vertcal buoyant turbulent jet fre n reduce pressure atmosphere. Fuel 106:

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