Laminar Diffusion Flame Shapes Under Earth- Gravity and Microgravity Conditions

Transcription

1 Laminar Diffusion Flame Shapes Under Earth- Gravity and Microgravity Conditions Jason Abshire Graduate Research Assistant Sivakumar Krishnan Assistant Professor, (Advisor) 1

2 Outline Motivation, Background, and Objectives Earth-Gravity (1g) and Microgravity (µg = 10-6 g) Experimental Setup and Methods Normal Diffusion Flames, NDF Inverse Diffusion Flames, IDF Analytical Models Spalding Model Modified Roper Model Microgravity Flames Test Conditions Results and Discussion Earth-gravity Flames Test Conditions Results and Discussion Summary of Results Conclusions and Recommendations 2

3 Motivation Fire on board the Mir space station, 1997 Microgravity High Oxygen Inverse diffusion flames Flame shape is a fundamental parameter used to describe flames Fire safety of future manned space missions 3

4 Literature Burke, S.P., Schumann, T.E.W., (1928) Roper, F.G., (1977) Spalding, D.B., (1979) Baukal, C.E., (1998) Sunderland, P.B., Yuan, Z.G., Urban, D.L., (1999) Sunderland, P.B., Krishnan, S.S., Gore, J.P., (2004) 4

5 Objectives Experimentally observe flame shapes Length Width Contours Luminosity To predict analytically the flame shapes of NDF s and IDF s under buoyant (earth-gravity) and non-buoyant (microgravity) conditions with varying oxygen content in the oxidizer Understand the range of applicability of analytical models and the limitations of the assumptions through comparisons with experimental flame shapes 5

6 1g Laboratory Setup 6

7 1g Laboratory Setup NDF Burner IDF Burner 7

8 µg Laboratory 8

9 Experimental Methods NDF and IDF of C 2 H 6 and CH 4 were studied 5.5 mm Dia. ~ Microgravity (quiescent oxidizer/fuel) 11.1 mm Dia. ~ Earth-Gravity (co-flowing oxidizer/fuel) Oxygen concentration in the oxidizer: 21% to 100% Oxidizer volumetric consumption rate was held constant Image acquisition and processing by: Panasonic CCD video (Microgravity) and Nikon D-100 digital cameras (Earth-gravity) 9

10 Analytical Models 1. Axial diffusion is neglected Modified Roper Model Assumptions Soot Region 2. T f = constant in regions where diffusion is dominant, but allowed to vary in the axial direction Stoichiometric Flame Sheet Zone L 3. Axial velocity, v z is assumed to vary in the axial direction but is a constant at each z location w d 4. Due to assumption #3, buoyant acceleration and jet deceleration effects can be built into the model 5. Mixture fraction is solved using a similarity transformation, the flame sheet is located where the mixture is stoichiometric 10

11 Analytical Models 1. Axial diffusion is neglected Spalding Model Assumptions 2. Temperature and density are assumed to be constant throughout 3. Axial velocity, v z follows the Schlichting jet velocity profile 4. Due to assumption #3, buoyant jet acceleration effects cannot be accounted for, hence the model is much more suited for microgravity flames 5. Momentum equation is solved and through similarity the velocity is related to the mixture fraction 11

12 Modified Roper Model v r C( r, z) C D C ( r, z) + vz ( z) = 0 r z r r r (1) Conservation of a conserved scalar (Cylindrical Cord.) r, z, v r, and v z radial and axial coordinates and velocities D, mass diffusivity C = ( f ( f o f f a a ) ) (2) Conserved scalar approach, concentration utilizing mixture fraction, where f = nx f X O2 Mixture Fraction: The mass fraction of material having its origin in the fuel stream 12

13 Modified Roper Model C 0 In the far field C( r,0) = 1 2 r < d C( r,0) = 0 r > d 2 (3) Boundary Conditions for eq. 1 t( z) d ln r dt dt = z 0 vz D = v r r η( r, z) = θ ( t) = D r D r ( z) t dt 0 2 r D (4) Utilizing the transformations we convert from r and z to a new η and θ coordinate system t is the elapsed residence time on the flame axis r D is the characteristic scale of diffusion 13

14 Modified Roper Model C( η, θ ) 1 C = η θ η η η (5) After simplification and transformation eq. 1 becomes eq. 5 C C( η,0) = 1 η < 1 0 In the far field (6) Eq. 5 is now subject to the boundary conditions following the previous boundary conditions C( η, θ ) = η 2 e 4θ 4θ 1 0 e η1 4θ I o η η 1 dη1 2θ (7) Thus the solution to eq. 5 Known as the P-Function I o is the modified Bessel function of the first kind of order zero 14

15 Model Solution C3H8 C4H10 r d = η 2 T T f o z 2 d uz T = θ 4 D T o f 6 θ C2H6 C2H4 C2H2 CH µg 1g u T z u f T z f ( z) T = constant ( z) = f ( z) u = constant = o z ( z) = To + ( T f To ) L f T 2 f = uo g T o z η Roper Contours for Various Fuels 15

16 µg Conditions * % O i 30 30i 50 50i i 30 30i 50 50i i Flame # C 2 H 6 C 2 H 6 C 2 H 6 C 2 H 6 CH 4 CH 4 CH 4 C st T ad, (K) m& x 10 kg ( s ) u0 x Re Q, W * Fr f = Ethane Flames conducted at NASA by Dr. Sunderland ( m s )

17 Results and Discussion Microgravity Ethane NDF s Fuel: Ethane Co-flow: Zero Burner Dia.: 5.5mm Configuration: NDF 21% O 2 30% O 2 50% O 2 100% O 2 Soot obscures comparison, however modified Roper agrees well with luminous flame shape Neglecting axial diffusion results in inability of the prediction to move below the 17 burner

18 Results and Discussion Microgravity Methane NDF s Fuel: Methane Co-flow: Zero Burner Dia.: 5.5mm Configuration: NDF 30% O 2 50% O 2 100% O 2 18

19 µg Normal Experimental Correlations 40 C 2 H 6 Normal Flame Lengths 60 C 2 H 6 Normal Flame Widths Sunderland (1999) 40 Spalding (1979) Lf (mm) Sunderland (1999) Spalding (1979) Roper (1977) w (mm) Present Study (Modified Roper) 0 Adjusted Length Sunderland (1999) O 2 % O 2 % Lf (mm) CH 4 Normal Flame Lengths Sunderland (1999) Spalding (1979) Roper (1977) w (mm) CH 4 Normal Flame Widths O 2 % 10 0 Sunderland (1999) Spalding (1979) Present Study (Modified Roper) O 2 % 19

20 Results and Discussion Microgravity Ethane IDF s Fuel: Ethane Co-flow: Zero Burner Dia.: 5.5mm Configuration: IDF 21% O 2 30% O 2 50% O 2 100% O 2 Model predicts the stoichiometric flame lengths fairly accurately Widening effect was seen near the burner, linear interpolation has been used at z = 5mm 20

21 Results and Discussion Microgravity Methane IDF s Fuel: Methane Co-Flow: Zero Burner Dia.: 5.5 mm Configuration: IDF 30% O 2 50% O 2 100% O 2 21

22 µg Inverse Experimental Correlations Microgravity Ethane & Methane IDF s 50 C 2 H 6 Inverse Flame Lengths 30 CH 4 Inverse Flame Lengths Lf (mm) Sunderland (1999) Spalding (1979) Roper (1977) Lf (mm) Sunderland (1999) 10 Spalding (1979) Roper (1977) O 2 % O 2 % 22

23 1g Conditions Fuel O 2 % O 2 Flame # T ad, (K) C st mg mg m& ( ) m& ( ) u ( mm ) 21 C 2 H s s o s u / u CF 1.0 o Re 24 Fr (x 10-4 ) Q, W 90 21i C 2 H i C 2 H i C 2 H i CH i CH i CH i CH i

24 Results and Discussion Gravity Ethane NDF s Fuel: Ethane Co-Flow Ratio: 1 Burner Dia.: 11.1 mm Configuration: 1.25 X 21% O 2 30% O 2 50% O 2 100% O 2 Soot obscures comparison, however modified Roper agrees well with luminous flame shape 24

25 Results and Discussion Gravity Methane NDF s Fuel: Methane Co-Flow Ratio: 3 Burner Dia.: 11.1 mm Configuration: 2.0 X 21% O 2 30% O 2 50% O 2 100% O 2 25

26 1g Normal Experimental Correlations L f (mm) C 2 H 6 Normal Flame Lengths Present Study Roper (1977) w (mm) C 2 H 6 Normal Flame Widths O 2 % Present Study Modified Roper O 2 % CH 4 Normal Flame Lengths CH 4 Normal Flame Widths 80 Present Study Roper (1977) 14 Lf (mm) w (mm) Present Study 20 4 Modified Roper O 2 % O 2 % 26

27 Results and Discussion Fuel: Ethane Co-Flow Ratio: 1 Burner Dia.: 11.1 mm Configuration: 1.25 X Gravity Ethane and Methane IDF s Annular Soot Layer 21% O 2 30% O 2 50% O 2 100% O 2 Fuel: Methane Co-Flow Ratio: 1 Burner Dia.: 11.1 mm Configuration: 2.0 X The use of a 430 nm CH Bandpass Filter removes obstructing soot annulus 21% O 2 30% O 2 50% O 2 100% O 2 Due to highly convective nature of IDF s, buoyancy is expected to have little effect on IDF s 27

28 1g Inverse Experimental Correlations Microgravity Ethane & Methane IDF s Lf (mm) C 2 H 6 Inverse Flame Lengths Lf (mm) CH 4 Inverse Flame Lengths Present Study Roper (1977) 5 0 Present Study Roper (1977) O 2 % O 2 % 28

29 Results Summary Froude number describes the ratio between the inertial momentum and the buoyancy forces Fr f ( u0yf, = Tf L f g T stoic 2 ) 1 Region A Fr f < (u b /u o 17.5) Region B < Fr f < 0.4 (1.5 u b /u o 17.5) ub = (uo 2 +2aLf) 1/2 - uo (mm/s) Buoyant Velocity Vs. Burner Velocity (Points on the 'X' Axis are Non-Buoyant Flames) Buoyancy - Dominant Flames Frf < (Region A) Mixed Region (Buoyancy - Convection) < Frf < 0.4 (Region B) NDF C2H6 NDF CH4 IDF C2H6 IDF CH4 NDF 1g Sunderland (2003) IDF 1g Sunderland (2003) NDF 0g Sunderland (2003) IDF 0g Sunderland (2003) Convection - Dominant Flames Frf > 0.4 (Region C) Region C Fr f > 0.4 (u b /u o 1.5) u o (mm/s) 29

30 Results Summary Region A: Shows good agreement with Roper Region B: Significant scatter Region C: Shows good agreement with Roper Lf Roper (mm) Roper Vs. Experimental Data Present Study and Sunderland Data [2] y = x R 2 = Region A Region B Region C L f Exp (mm) 30

31 Results Summary L f /u o d 2 Vs. Ln(1+S -1 ) -1 NDFs L f /u o d 2 Vs. Ln(1+S -1 ) -1 IDFs NDF C2H6 NDF CH4 NDF C2H6 R % O2 Increasing %O2 100% O2 L f/uo d 2 (mm -2 s) NDF CH4 R NDF 1g Sunderland (2003) NDF 0g Sunderland (2003) Experimental Correlation (Present Study) y = 0.001x R 2 = % O 2 Decreasing %O 2 21% O Ln(1+S -1 ) -1 L f/uo d 2 (mm -2 s) y = 7E-05x R 2 = Ln(1+S -1 ) -1 IDF C2H6 IDF CH4 IDF C2H6 R IDF CH4 R IDF 1g Sunderland (2003) IDF 0g Sunderland (2003) Experimental Correlation (Present Study) NDFs: The experimental flame lengths are luminous flame lengths IDFs: The experimental flame lengths are stoichiometric flame lengths (using CH filter) 31

32 Conclusions 1. For Microgravity NDFs become longer, wider, and generally sootier in comparison to earth-gravity NDFs. Gravity level had a negligible effect on the IDF due to the large convective velocities 2. Increasing the oxygen concentration for NDFs and IDFs causes an increase in soot production and luminosity 3. Comparisons of NDF and IDF shapes using both analytical and experimental techniques have been successfully completed in both earth-gravity and microgravity environments Earth-gravity: Linear temperature distribution accelerating velocity profile Microgravity: Constant temperature distribution and a constant velocity profile 32

33 Conclusions Continued 4. In a flow regime identified by flame Froude numbers lying between and 0.4 (mixed regime), the Modified Roper Model predictions deviated substantially from the experimental flames. In this region convection and buoyancy effects are comparable 5. The Modified Roper Model performed well for buoyant normal diffusion flames with varying oxidizer concentrations (Fr f < ) and for some buoyant IDFs (Fr f > 0.4 ) where convection was dominant. The model also performed well for all non-buoyant (Fr f = ) NDFs and IDFs 33

34 Recommendation & Future Work 1. Higher flow rates are needed for larger flames which will be more suitable for comparison with the Roper model. The use of a Critical Flow Orifice (CFO) meter is recommended 2. Future studies will help establish the exact Froude numbers where flame shape curvature changes 3. A more complete numerical method which includes detailed chemistry, species diffusion effects, and flame radiation is needed for further study 4. Flame radiation, species, and flame temperature and soot measurements will aid in identify the stoichiometric flame length and other parameters of importance to fire safety researchers 34

35 Acknowledgments Wife and Parents Dr. Siva Krishnan (Graduate Advisor) Dr. Razi Nalim (Advisory Committee) Dr. Hasan Akay (Advisory Committee) Prof. Jay Gore (Purdue West Lafayette) Dr. Peter Sunderland & Dr. Zeng-Guang Yuan (NCMR) 35

36 Thank You 36