1 / 21

Scalar Mixing in Turbulent, Confined Axisymmetric Co-flows

Scalar Mixing in Turbulent, Confined Axisymmetric Co-flows. C.N. Markides & E. Mastorakos Hopkinson Laboratory, Department of Engineering Monday, 6 th of February, 2006. 1/19. The Turbulent, Confined Axisymmetric Co-flow 1.

doris-hurley
Download Presentation

Scalar Mixing in Turbulent, Confined Axisymmetric Co-flows

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. 1/19 The Turbulent, ConfinedAxisymmetric Co-flow1 • Axisymmetric flow configuration (r,z) • Dimensions: • Quartz tube inner Ø D=33.96mm • Injector outer Ø do=2.975mm • Injector inner Ø d=2.248mm and 1.027mm • Domain (laser sheet) height 60mm • Co-flow air preheated to 200±1oC • Upstream (63mm from injector nozzle) perforated grid (M=3mm circular holes, 44% solidity) enhances co-flow turbulence level • Injected stream: • Begins as nitrogen-diluted fuel • YC2H2=0.73 C2H2/N2 or YH2=0.14 H2/N2 • Passes though seeder that introduces 20% acetone b.v. • For co-flow define: • Reco = UcoM/ν, or, Returb = u'coLturb/ν • Reco range: 395-950; ***Returb≈Reco/10*** • For injected stream define: • υinj=Uinj/Uco • υinj range: 1.1-4.9; ***Not a free jet*** • δinj= ρinj/ρco • δinj=1.2 forC2H2/N2/acetone • δinj=0.8 for H2/N2/acetone Laser Sheet Fuel Injection z Uinj, Tinj r Injector Quartz Tube Uco, Tco Air from MFC Acetone Seeded Fuel Grid 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.

  3. 2/19 Planar Laser-Induced Fluorescence Measurements (Brief Overview2) • Each ‘Run’ corresponds to a set of fixed Uco, Uinj and Yfuel conditions (i.e. Reco/Returb, υinj and δfuel) • 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) • Images are 2-dimensional planar measurements: • Smallest lengthscale in the flow is Kolmogorov (ηK) 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: • Two-dimensional scalar dissipation (the Greek one - χ) was calculated by: ***But before this was done the images of ξ were filtered and denoised*** 2. See Markides and Mastorakos (2006) in Chem. Eng. Sci.; Markides (2006) Ph.D. Thesis for details.

  4. 3/19 Quantifying Measurement Resolution

  5. 4/19 Obtaining the instantaneous χ2D field from the instantaneous ξ field (I) ξ χ2D

  6. 5/19 Obtaining the instantaneous χ2D field from the instantaneous ξ field (II) ξ χ2D

  7. 6/19 Obtaining the instantaneous χ2D field from the instantaneous ξ field (III) ξ χ2D

  8. 7/19 Obtaining the instantaneous χ2D 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 • Finally, need molecular diffusivity (D): • Consider ternary (acetone-’1’, nitrogen-’2’ and fuel-’3’) diffusion coefficients from binary diffusion coefficients (D11, D12, D13, D22, D23, D33) • Simplify by assuming that D12≈D13 or X1<<1 so that D12T<<D11T and calculate D1,mix at each point in the flow, given that we already have the instantaneous X1 (from ξ)

  9. 8/19 Calculating Mixing Quantities (I) • 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)

  10. 9/19 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) ηK 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 χ2D) • Calculate the local mean, variance, skewness and kurtosis of the logarithm of all versions of χ2D • Compile pdfs of all versions of all variables (ξ and χ2D) each composed of 90 and 30 points respectively spanning the min-max range (from about 140,000 data points) • Separate the χ2D data into 30 groups between the min-max range of ξ by considering the corresponding values of ξ (χ2D|ξ) • Calculate the local mean, variance, skewness and kurtosis of χ2D|ξ and ln(χ2D|ξ) • Compile pdfs of all versions of χ2D|ξ: • unless number of data points in the local pdf is less than 300 • each composed of 30 points respectively spanning the min-max range • from about 2,000-10,000 data points

  11. 10/19 Below: All are equal velocity cases (Uinj≈Uco; υinj=1.0±0.2) with the 2.248mm injector and varying Reco/Returb Right: Jet cases with the 2.248mm injector (υinj=3 and 4) Not affected by image processing Mean ξ (I)

  12. 11/19 Mean ξ (II)

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

  14. 13/19 Variance of ξ (II)

  15. 14/19 Mean χ2D (I) • Equal velocity case • Significantly affected by image processing

  16. 15/19 Mean χ2D (II)

  17. 16/19 (Non-strict) Isotropy in χ2D

  18. 17/19 Mean Scalar Dissipation Modelling and CD (I) • 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 χ2D (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 • Use (k/ε)/(Lturb/u')≈1.7±0.2 Pope (2000)

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

  20. 19/19 Mean Scalar Dissipation Modelling and CD (III) τturb/τturb(z/d=35)

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

More Related