Spreadsheet calculations of jets in crossflow: opposed rows of inline and staggered round holes
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Abstract
The objective of this study was to demonstrate and analyze empirical model results for jet-in-crossflow configurations which are typical in gas turbine combustors. Calculations in this paper, for opposed rows of round holes in both inline and staggered arrangements, were made with an Excel® spreadsheet implementation of a NASA-developed empirical model for the mean conserved scalar field. Results for cases of opposed rows of jets with the orifices on one side shifted by half the orifice spacing shows that staggering can improve the mixing, particularly for cases that would overpenetrate if the orifices were in an aligned configuration. For all cases investigated, the dimensionless variance of the mixture fraction decreased significantly with increasing downstream distance. The variation between cases at a given downstream location was smaller, but the “best” mixers for opposed rows of jets were found to be inline and staggered arrangements at an orifice spacing that is optimum for inline jets.
Keywords
Mixture Fraction Optimum Configuration Downstream Distance Round Hole Stagger ArrangementList of symbols
- AJ/AM
Jet-to-mainstream area ratio = (π/4)/((S/H)(H/d)2)
- C
(S/H)(sqrt (J)) same as Eq. 3
- Cd
Orifice discharge coefficient = (effective area)/(physical area)
- d
Actual physical diameter of a round hole
- DR
Jet-to-mainstream density ratio, ρ J /ρ M
- H
Duct height (called H 0 in several previous publications)
- H/d
Ratio of duct height to orifice diameter
- Heq
Effective duct height = H in this paper
- H0
Duct height at axial location of jet center
- J
Jet-to-mainstream momentum-flux ratio, (ρ J V J 2 )/(ρ Μ U M 2 )
- JIC
Jet(s) in crossflow
- mJ
Jet mass flow
- mM
Mainstream mass flow
- mT
Total mass flow, m J + m M
- MR
Jet-to-mainstream mass-flow ratio = m J /m M = (ρ J /ρ M )(V J /U M )(C d )(A J /A M )
- mJ/mT
Jet-to-total mass-flow ratio
- S
Lateral spacing between equivalent locations of adjacent orifices, e.g. between orifice centerplanes
- S/d
Ratio of orifice spacing to orifice diameter = (S/H)(H/d)
- S/H
Ratio of orifice spacing to duct height
- SX/H
Ratio of axial orifice spacing between rows to duct height
- T
Local scalar variable
- TJ
Scalar variable at jet exit
- TM
Scalar variable in unmixed mainstream flow
- U
Axial velocity
- UM
Unmixed mainstream velocity
- Us
Unmixedness = θvar/(θave(1 − θave)); same as Eq. 2
- VJ
Jet exit velocity
- x
Downstream coordinate; x = 0 at center of the first row of orifices
- y
Cross-stream coordinate; y = 0 at wall
- yc
Scalar trajectory, location of maximum scalar difference ratio, θ c
- z
Lateral coordinate
- θ
Dimensionless scalar, (T M − T)/(T M − T J ); same as Eq. 1
- θave
Fully-mixed scalar difference ratio ~m J /m T
- θc
Maximum scalar difference ratio, defines location of scalar trajectory, y c /H
- θvar
Variance of scalar difference ratio
- ρJ
Density of jet flow
- ρM
Density of mainstream flow
Notes
Acknowledgments
The authors would particularly like to thank Mr. Richard E. Walker (Aerojet Liquid Rocket Company, ret.) and Dr. Ram Srinivasan (then of Garrett Turbine Engine Company) for their contributions to the NASA JIC empirical model, and to Professor William E. Lear of the University of Florida for suggesting that the original computer code, written in the 1980s on a 64K Apple//e® in Applesoft® BASIC accompanied by a HyperCard® slideshow, could be rendered in an Excel® spreadsheet and for directing the development of the JIC spreadsheet.
References
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