1. Scalar Mixing in Turbulent, Confined Axisymmetric Co-flows C.N. Markides & E. Mastorakos Hopkinson Laboratory, Department of Engineering Monday, 6 th of February, 2006 Monday, 6 th of February, 2006

2. The Turbulent, Confined Axisymmetric Co-flow 1 Axisymmetric flow configuration (r,z) Axisymmetric flow configuration (r,z) Dimensions: Dimensions: –Quartz tube inner Ø D= 33.96mm –Injector outer Ø d o =2.975mm –Injector inner Ø d=2.248mm and 1.027mm –Domain (laser sheet) height 60mm Co-flow air preheated to 200±1 o C Co-flow air preheated to 200±1 o C Upstream (63mm from injector nozzle) perforated grid (M=3mm circular holes, 44% solidity) enhances co-flow turbulence level Upstream (63mm from injector nozzle) perforated grid (M=3mm circular holes, 44% solidity) enhances co-flow turbulence level Injected stream: Injected stream: –Begins as nitrogen-diluted fuel –Y C2H2 =0.73 C 2 H 2 /N 2 or Y H2 =0.14 H 2 /N 2 –Passes though seeder that introduces 20% acetone b.v. For co-flow define: For co-flow define: –Re co = U co M/ν, or, Re turb = u' co L turb /ν –Re co range: 395-950; ***Re turb ≈Re co /10*** For injected stream define: For injected stream define: –υ inj =U inj /U co –υ inj range: 1.1-4.9; ***Not a free jet*** –δ inj = ρ inj /ρ co –δ inj =1.2 for C 2 H 2 /N 2 /acetone –δ inj =0.8 for H 2 /N 2 /acetone 1. See Markides and Mastorakos (2005) in Proc. Combust. Inst.; Markides (2006) Ph.D. Thesis; Markides, De Paola and Mastorakos (2006) shortly in Exp. Therm. Fluid Sci. for details. Grid Injector Quartz Tube Air from MFC U co, T co Acetone Seeded Fuel Laser Sheet Fuel Injection U inj, T inj z r 1/19

3. Planar Laser-Induced Fluorescence Measurements (Brief Overview 2 ) Each ‘Run’ corresponds to a set of fixed U co, U inj and Y fuel conditions (i.e. Re co /Re turb, υ inj and δ fuel ) Each ‘Run’ corresponds to a set of fixed U co, U inj and Y fuel conditions (i.e. Re co /Re turb, υ inj and δ fuel ) The raw measurements are near-instantaneous (integrated over 0.4μs) images of size (height x width) 1280 x 480 pixels The raw measurements are near-instantaneous (integrated over 0.4μs) images of size (height x width) 1280 x 480 pixels For each ‘Run’ we generated 200 images at 10Hz (every 0.1s) For each ‘Run’ we generated 200 images at 10Hz (every 0.1s) Images are 2-dimensional planar measurements: Images are 2-dimensional planar measurements: –Smallest lengthscale in the flow is Kolmogorov (η K ) and was measured at 0.2-0.3mm –Laser-sheet thickness (spatial resolution) ≈ 0.10±0.03mm –Measured intensity at any image pixel is the spatial average over a square region of length 0.050- 0.055mm at that point in the flow –Ensemble spatial resolution is 0.09mm –Ability to transfer contrast information quantified by Modulation Transfer Function (MTF). Investigation revealed ability to resolve 70-80% of spatial detail with 4-5 pixels or 0.3mm –Local intensity proportional to local volumetric/molar concentration of acetone vapour, so that: Convert to mass-based mixture fraction by: Convert to mass-based mixture fraction by: Two-dimensional scalar dissipation (the Greek one - χ) was calculated by: Two-dimensional scalar dissipation (the Greek one - χ) was calculated by: 2. See Markides and Mastorakos (2006) in Chem. Eng. Sci.; Markides (2006) Ph.D. Thesis for details. ***But before this was done the images of ξ were filtered and denoised*** 2/19

4. Quantifying Measurement Resolution 3/19

5. Obtaining the instantaneous χ 2D field from the instantaneous ξ field (I) ξ χ2Dχ2D 4/19

6. Obtaining the instantaneous χ 2D field from the instantaneous ξ field (II) ξ χ2Dχ2D 5/19

7. Obtaining the instantaneous χ 2D field from the instantaneous ξ field (III) ξ χ2Dχ2D 6/19

8. Obtaining the instantaneous χ 2D field from the instantaneous ξ field (IV) At this stage have considered the squares of the spatial gradients of ξ, ( ∂ξ/∂r) 2 and ( ∂ξ/∂z) 2 ; we also have the spatial gradients of ξ', ( ∂ξ ' /∂r) 2 and ( ∂ξ ' /∂z) 2 At this stage have considered the squares of the spatial gradients of ξ, ( ∂ξ/∂r) 2 and ( ∂ξ/∂z) 2 ; we also have the spatial gradients of ξ', ( ∂ξ ' /∂r) 2 and ( ∂ξ ' /∂z) 2 Finally, need molecular diffusivity (D): Finally, need molecular diffusivity (D): – Consider ternary (acetone-’1’, nitrogen-’2’ and fuel-’3’) diffusion coefficients from binary diffusion coefficients (D 11, D 12, D 13, D 22, D 23, D 33) –Simplify by assuming that D 12 ≈D 13 or X 1 <<1 so that D 12 T <<D 11 T and calculate D 1,mix at each point in the flow, given that we already have the instantaneous X 1 (from ξ) 7/19

9. Calculating Mixing Quantities (I) For each ‘Run’ and at each pixel representing a location in physical space (r,z) loop through 200 images: For each ‘Run’ and at each pixel representing a location in physical space (r,z) loop through 200 images: –Of each version of ξ (raw and all stages of processing) to obtain the mean and variance of each version of ξ –Of each version of corresponding ( ∂ ξ/ ∂ r) 2 and ( ∂ ξ/ ∂ z) 2 to obtain the mean and variance of each version of ( ∂ ξ/ ∂ r) 2 and ( ∂ ξ/ ∂ z) 2 –Of each version of corresponding ( ∂ ξ'/ ∂ r) 2 and ( ∂ ξ'/ ∂ z) 2 to obtain the mean and variance of each version of ( ∂ ξ'/ ∂ r) 2 and ( ∂ ξ'/ ∂ z) 2 –Evaluate spatial 2-point autocorrelation matrices along centreline and at left/right half-widths –Compile radial volume-averaged quantities (i.e. at one z group all r data together) 8/19

10. Calculating Mixing Quantities (II) For each ‘Run’ and at each pixel representing a location in physical space (r,z) consider a window of size 1x1 (or 2x10) η K containing 40 (or 720) pixels and loop through 200 images: For each ‘Run’ and at each pixel representing a location in physical space (r,z) consider a window of size 1x1 (or 2x10) η K containing 40 (or 720) pixels and loop through 200 images: –At 15 axial locations from 1mm to 60mm in steps of 4mm –At 5 radial locations with r=0, ±d/2, ±d –Calculate the local mean, variance, skewness and kurtosis of all versions of all variables (ξ and χ 2D ) –Calculate the local mean, variance, skewness and kurtosis of the logarithm of all versions of χ 2D –Compile pdfs of all versions of all variables (ξ and χ 2D ) each composed of 90 and 30 points respectively spanning the min-max range (from about 140,000 data points) –Separate the χ 2D data into 30 groups between the min-max range of ξ by considering the corresponding values of ξ (χ 2D |ξ) –Calculate the local mean, variance, skewness and kurtosis of χ 2D |ξ and ln(χ 2D |ξ) –Compile pdfs of all versions of χ 2D |ξ: unless number of data points in the local pdf is less than 300 unless number of data points in the local pdf is less than 300 each composed of 30 points respectively spanning the min-max range each composed of 30 points respectively spanning the min-max range from about 2,000-10,000 data points from about 2,000-10,000 data points 9/19

11. Mean ξ (I) Below: Below: –All are equal velocity cases (U inj ≈U co ; υ inj =1.0±0.2) with the 2.248mm injector and varying Re co /Re turb Right: Right: –Jet cases with the 2.248mm injector (υ inj =3 and 4) Not affected by image processing Not affected by image processing 10/19

12. Mean ξ (II) 11/19

13. Variance of ξ (I) 12/19 Left: Left: –Equal velocity case Right: Right: –Jet case Affected by image processing Affected by image processing

14. Variance of ξ (II) 13/19

15. Mean χ 2D (I) 14/19 Equal velocity case Equal velocity case Significantly affected by image processing Significantly affected by image processing

16. Mean χ 2D (II) 15/19

17. (Non-strict) Isotropy in χ 2D 16/19

18. Mean Scalar Dissipation Modelling and C D (I) At each location in physical space where we would like to evaluate: At each location in physical space where we would like to evaluate: Firstly we need to recover the mean full 3-dimensional χ from the mean χ 2D (along the centreline by symmetry the mean gradients squared in the radial and azimuthal direction are equal) Firstly we need to recover the mean full 3-dimensional χ from the mean χ 2D (along the centreline by symmetry the mean gradients squared in the radial and azimuthal direction are equal) –Also examined isotropy of the two components We also need knowledge of the turbulent timescale (k/ε) where k is the turbulence kinetic energy and ε the mean turbulence dissipation We also need knowledge of the turbulent timescale (k/ε) where k is the turbulence kinetic energy and ε the mean turbulence dissipation –Use (k/ε)/(L turb /u')≈1.7±0.2 Pope (2000) 17/19

19. Mean Scalar Dissipation Modelling and C D (II) U/U co u'/U co 18/19 Centreline (z+63mm)/d

20. Mean Scalar Dissipation Modelling and C D (III) 19/19 τ turb /τ turb (z/d=35)

21. Scalar Mixing in Turbulent, Confined Axisymmetric Co-flows C.N. Markides & E. Mastorakos Hopkinson Laboratory, Department of Engineering Monday, 6 th of February, 2006 Monday, 6 th of February, 2006