James D. Holdeman

Glenn Research Center, Cleveland, Ohio

James R. Clisset

University of Florida, Gainesville, Florida

Jeffrey P. Moder

Glenn Research Center, Cleveland, Ohio

Spreadsheet Calculations for Jets in Crossfl ow: 

Opposed Rows of Inline and Staggered Holes 

and Single and Opposed Rows With Alternating 

Hole Sizes

NASA/TM—2010-216100

July 2010
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 7115 Standard Drive

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James D. Holdeman

Glenn Research Center, Cleveland, Ohio

James R. Clisset

University of Florida, Gainesville, Florida

Jeffrey P. Moder

Glenn Research Center, Cleveland, Ohio

Spreadsheet Calculations for Jets in Crossfl ow: 

Opposed Rows of Inline and Staggered Holes 

and Single and Opposed Rows With Alternating 

Hole Sizes

NASA/TM—2010-216100

July 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors would particularly like to thank Mr. Richard E. Walker (Aerojet Liquid Rocket Company, retired) 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 (UF) for suggesting that the publicly available JIC 

computer code, written by the fi rst author in BASIC on a 64K Apple //e (Apple Inc.), could be converted to an Excel 

(Microsoft Corporation) spreadsheet and for directing the development of the spreadsheet at UF. The authors also wish to 

acknowledge the contributions to the spreadsheet made by Mr. Gilbert F. Canton (then an undergraduate student at UF) 

and Mr. Joel H. Scheuer (then a LERCIP intern at NASA Glenn) and appreciate the support and encouragement from 

Dr. Clarence T. Chang, Dr. C. John Marek (retired), Dr. Edward J. Mularz (retired), and Mr. Timothy D. Smith at the 

NASA Glenn Research Center (GRC), Mr. David S. Liscinsky of the United Technologies Research Center (UTRC), 

Professor John F. Foss of Michigan State University (MSU), Professor G. Scott Samuelsen of the University of 

California–Irvine (UCI), and the late Professor Arthur H. Lefebvre, author of Gas Turbine Combustion.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2010-216100 1 

Spreadsheet Calculations for Jets in Crossflow: Opposed Rows 

of Inline and Staggered Holes and Single and Opposed Rows 

With Alternating Hole Sizes 

James D. Holdeman 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

James R. Clisset 

University of Florida 

Gainesville, Florida 32611 

Jeffrey P. Moder 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The primary purpose of this jet-in-crossflow study was to calculate expected results for two 

configurations for which limited or no experimental results have been published, namely: 

(1) cases of opposed rows of closely-spaced jets from inline and staggered round holes and 

(2) rows of jets from alternating large and small round holes. Simulations of these configurations 

were performed using a Microsoft Excel (Microsoft Corporation) spreadsheet implementation of 

a NASA-developed empirical model which had been shown in previous publications to give 

excellent representations of mean experimental scalar results, suggesting that the NASA 

empirical model for the scalar field could confidently be used to investigate these configurations. 

The supplemental Excel spreadsheet is posted with the current report on the NASA Glenn 

Technical Reports Server (http://gltrs.grc.nasa.gov) and can be accessed from the Supplementary 

Notes section as TM-2010-216100-SUPPL1.xls. Calculations for cases of opposed rows of jets 

with the orifices on one side shifted show that staggering can improve the mixing, particularly 

for cases where jets would overpenetrate slightly if the orifices were in an aligned configuration. 

The jets from the larger holes dominate the mixture fraction for configurations with a row of 

large holes opposite a row of smaller ones although the jet penetration was about the same. For 

single and opposed rows with mixed hole sizes, jets from the larger holes penetrated farther. For 

all cases investigated, the dimensionless variance of the mixture fraction decreased significantly 

with increasing downstream distance. However, at a given downstream distance, the variation 

between cases was smaller. 

Introduction 

Jets in crossflow (JIC) have been extensively investigated in the literature. The studies of 

multiple jets that are summarized in Reference 1 were motivated by mixing of dilution jets in 

conventional gas turbine combustors; and the studies summarized in References 2 and 3 focused 

on optimizing the mixing section in the Rich burn/Quick mix/Lean burn (RQL) combustor 
NASA/TM—2010-216100 2 

scheme. Many of the studies summarized in Reference 4 were motivated by aerodynamics 

associated with vertical/short takeoff and landing aircraft. The summary in Reference 5 focused 

on calculation methods that have been used for JIC flow fields. References to many of the JIC 

studies that were published prior to References 1 to 5 are listed in their citations. Because these 

lists are extensive, older reports and papers are not cited in this publication unless specific results 

are mentioned. Secondary References are listed parenthetically if the primary Reference is the 

same as, similar to, or derived from, the secondary Reference. 

It was shown in References 1 to 3 that trends of a conserved scalar in JIC flowfields were 

independent of the duct shape and were similar whether conserved scalar results came from 

experimental or analytical studies. That is, trends from conserved scalar results could be from 

probe measurements, nonintrusive species measurements, empirical model calculations, or CFD 

calculations for nonreacting or reacting flows in a rectangular, annular, or cylindrical duct. 

Most JIC research prior to 1970 focused on the trajectory, centerline decay, and the shape of 

unconfined single jets. The (post 1970) studies in References 6 to 25 were motivated by mixing 

in the dilution zone of large annular gas turbine combustors, and were based on simplified 

combustor mixer geometries in a rectangular duct. From the data in Reference 8 a NASA JIC 

empirical model was reported in Reference 12, published in the journal paper in Reference 13, 

and used in Reference 15 to illustrate “basic” features of the scalar field downstream of a row of 

jets mixing with a confined crossflow. 

The original NASA JIC empirical model that was published in Reference 13 was 

subsequently extended to include variations typically found in gas turbine combustors; e.g., 

noncircular orifices, double and/or opposed rows of jets, with or without flow area convergence 

and/or a nonuniform mainstream scalar distribution. The experimental and modeling results from 

the work to include these variations are reported in References 14 and 17 to 19. The NASA JIC 

empirical model that resulted was used in Reference 20 to demonstrate flow and geometric 

effects in a rectangular duct. CFD calculations for many of the cases in Reference 14 are given in 

Reference 21. Journal publications using data from References 14 and 17 to 19 are given in 

References 1, 16, 22, and 23. 

The BASIC programs for the NASA JIC empirical model used in References 15 and 20 were 

later converted to an Excel (Microsoft Corporation) spreadsheet and reported in Reference 24. 

Discussions of spreadsheet specifics, cases of jet mixing in a confined crossflow, a slideshow, 

and a listing of the correlation equations in the NASA JIC empirical model were published in 

References 24 and 25. Suggested design procedures for cylindrical and rectangular ducts are 

given in References 2 and 3. Both NASA and Cranfield design methods are discussed in 

Reference 26. 

The primary purpose of this JIC study was to calculate expected results for two 

configurations for which limited or no experimental results have been published: (1) cases of 

opposed rows of closely-spaced jets from inline and staggered round holes and (2) rows of jets 

from alternating large and small round holes. Simulations of these configurations were 

performed using NASA JIC spreadsheet (described in References 24 and 25) which had been 

shown in previous publications to give excellent representations of mean experimental scalar 

results, suggesting that the NASA empirical model for the scalar field could confidently be used 

to investigate these configurations. The contour plots generated directly in the version of the 

spreadsheet used herein have considerably less resolution than those presented in Figures 4 to 14 

in Reference 25 that were generated with a graphics post processor using data exported from the 
NASA/TM—2010-216100 3 

spreadsheet. The NASA JIC spreadsheet also generates profile plots, as shown in Figures 4 to 26 

in Reference 24 and Figures 15 to 24 and the slideshow in Reference 25. 

The first configurations analyzed consist of opposed rows of both inline and staggered 

arrangements. Results for inline configurations were reported in References 1, 24, 25, and 27. 

Previously unpublished data for opposed rows of closely-spaced staggered jets from the United 

Technologies Research Center were used (with permission) in Reference 28. The data used 

therein were all on a plane of symmetry and were measurements of velocity magnitude rather 

than a conserved scalar. Some other unpublished measurements were made off a plane of 

symmetry (private communication with D.S. Liscinsky). 

The second configurations analyzed were rows of jets with alternating hole sizes. There are 

no data in the open literature for opposed rows of jets from alternating hole sizes, but there were 

experimental results for one-side injection from mixed size holes reported in Reference 8, and 

data were published in Reference 27 for opposed rows of aligned jets. Adjacent jets in 

Reference 27 were always the same size, but cases were investigated with different size holes on 

opposite sides. 

Nomenclature 

AJ/AM jet-to-mainstream area ratio = (π/4)/((S/d)(H/d)) = (π/4)/((S/H)(H/d)

2

) 

C jet penetration coefficient = (S/H)(√(J)); same as Equation (5) 

Cd orifice discharge coefficient = (effective area)/(physical area) 

d actual physical diameter of a round hole 

dj effective diameter = (d)(√(Cd)) 

DR jet-to-mainstream density ratio, ρJ /ρM

H duct height at center of row of holes (called H0 in several previous publications) 

H/d ratio of duct height to orifice diameter 

Heq effective duct height (= H except in the symmetry model for opposed rows of inline 

jets) 

J jet-to-mainstream momentum-flux ratio, (ρJVJ 

2

)/(ρΜUM 

2

)

mJ jet mass flow 

mM mainstream mass flow 

mT total mass flow, mJ + mM 

mJ/mM jet-to-mainstream mass-flow ratio = (ρJ/ρM)(VJ/UM)(Cd)(AJ/AM)) = (mJ/mT)/(1 – mJ/mT)

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 lateral orifice spacing to orifice diameter = (S/H)(H/d) 

S/H ratio of lateral orifice spacing to duct height 

SX/H ratio of axial orifice spacing 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 
NASA/TM—2010-216100 4 

Us unmixedness = θvar/(θave(1 – θave)); same as Eq. (4) 

VJ jet exit velocity 

− W1/ 2 jet half-value width on injection side of vertical distribution; i.e., for y/H < yc/H in 

Figure 2 (note that y = 0 is at the top wall) 

+ W1/ 2 jet half-value width on opposite side of vertical distribution; i.e., for y/H > yc/H in 

Figure 2 (note that y = 0 is at the top wall) 

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, θc

z lateral coordinate; z = 0 at centerplanes 

θ dimensionless scalar, (TM – T)/(TM – TJ); same as Equation (2)

θave fully-mixed scalar difference ratio = θEB

θc maximum scalar difference ratio, defines location of scalar trajectory, yc/H

θEB equilibrium θ (called TB in Reference 15) approximately mJ/mT −

min θ minimum scalar difference ratio on injection side of vertical distribution; (i.e., for 

y/H < yc/H in Figure 2) +

min θ minimum scalar difference ratio on opposite side of vertical distribution; (i.e., for 

y/H > yc/H in Figure 2) 

θvar variance of scalar difference ratio 

Flow Field Model 

Figure 1 is a schematic of the basic flow field for jets in a confined crossflow. The jets are 

shown entering the mainstream flow through orifices in the top duct wall. The primary 

independent geometric variables are the lateral spacing between similar locations of adjacent 

orifices S, the duct height H, and the orifice diameter d. S/H and H/d were chosen as independent 

dimensionless variables. The product of them, the ratio of the orifice spacing to orifice diameter 

S/d is a frequently cited dimensionless variable. Note that for round holes S/d cannot be less 

than 1. 

Downstream distances are specified in intervals of x/H because the objective in combustor 

design is usually to identify orifice configurations to optimize the mixing within a given length 

and the downstream locations of interest are usually independent of the orifice diameter. The 

ratio of the downstream distance to the orifice diameter x/d = (x/H)(H/d) is a common 

dimensionless parameter, particularly in unconfined flows. 

The empirical model for the conserved scalar field downstream of jets mixing with a 

confined crossflow is based on the observation that nondimensional vertical scalar distributions 

in the flow field can usually be expressed in the following form 

( / )

( ln 2)( / / ) exp θ θθ θ

W1/ 2 H

y H yc H

c min

min

± ±

± − − = −

− (1) 

where 

 θ = (TM – T)/(TM – TJ) (2) 
NASA/TM—2010-216100 5 

θc, +

min θ , −min θ , W H +1/ 2 , W H −1/ 2 , and yc/H in Eq. (1) are scaling parameters for θ profiles in a 

vertical x-y plane as shown in Figure 2. Note that x = 0 is at the center of the orifice and y = 0 is 

at the top in Figures 1 and 2, and that the jet trajectory yc/H is defined as the location of the 

maximum scalar difference in the profile in the centerplane (the x-y plane though the center of an 

orifice). Unmixed jet fluid is θ = 1 and unmixed mainstream fluid is θ = 0. A physically realistic 

θ should be neither <0 nor >1. Although θ was formulated from temperature data in an 

incompressible flow in References 8, 14, 17, and 18, θ applies to any conserved scalar. For 

example, species concentration was often used in the isothermal experimental studies 

summarized in References 2 and 3 and a carbon balance was used in the experiments results for 

reacting flows reported in References 2 and 29 to 31. 

Equation (1) was first applied to confined JIC data in Reference 11. It gives θ = (θc+ ±

min θ )/2 

at the half-value width W H ±

1/ 2 on the opposite or injection side of the trajectory as appropriate, 

but does not guarantee that θ = −

min θ at y = 0 or θ = +min θ at H. Usually +min θ ≠ −min θ and 

W H +

1/ 2 ≠ W H −1/ 2 . Off-centerplane values of θc and yc are dependent on z, and it is assumed in 

the empirical model that off-centerplane values of ±

min θ /θc and W H ±1/ 2 are equal to their values 

in the centerplane. Calculations at y/H should not be accepted if y/H<0 or y/H>1 and should be 

scrutinized carefully if y/H<yc/H and (yc/H–W H −

1/ 2 ) < 0 or if y/H > yc/H and (yc/H +W H +1/ 2 ) >1. 

An equation similar to Equation (1) was applied to data for a single, unconfined JIC ( ±

min θ = 0) in 

References 6 and 7. 

Correlation equations were developed for each of the scaling parameters and are given in 

Reference 24. For all calculations, the dimensionless flow and geometric variables that must be 

specified are the jet-to-mainstream density ratio DR, jet-to-mainstream momentum-flux ratio J,

jet discharge coefficient Cd, orifice-spacing-to-duct-height ratio S/H, duct-height-to-orificediameter ratio H/d, and the dimensionless downstream distance x/H. If there are multiple rows of 

jets, the axial distance between their centers SX/H must also be specified. 

The correlation equations used in the spreadsheet are the same as those included in 

Reference 1, but the equations published there are written in terms of Heq and H0 rather than H.

For all the cases considered here H0 = Heq = H, since H0 = H in a nonconverging duct and Heq is 

only ≠ H if the symmetry model is used for opposed rows of jets with their centerlines inline. 

Most of the cases for this application are in the near field of the JIC, so, although the trajectory 

becomes asymptotic in the axial direction, characterization of the flow depends on both 

downstream distance and JIC configuration. 

Three-dimensional oblique plots (herein called profile plots) and low resolution contour plots 

are the native displays in the spreadsheet. The dependent variable θ is shown on the horizontal 

axis in the profile plots and θ is the plotted variable in the contour plots. The vertical and oblique 

axes in the profile plots are the y and z directions, which are respectively in the direction of the 

jet injection and along the orifice row in an axial plane. These are the axes of ordinates and 

abscissas in the contour plots. There are 21 profiles in the z-span shown in the figures, but less 

than half of the jet profiles are actually calculated directly. The others are generated by assuming 

cyclic boundary conditions at the jet centerplanes or midplanes as appropriate. (The x-y plane 

through the orifice center is called the centerplane, and that halfway between orifices in each row 

is called the midplane.) 
NASA/TM—2010-216100 6 

The downstream distance x/H and orifice spacing S/H must be input in the top front row in 

the spreadsheet. S/H and x/H for other rows are dependent on, but may not be identical to, the 

values input there. The specifics and operation of the spreadsheet, the correlations in the NASA 

empirical model, the “closest” experimental data, and listings of the original BASIC programs 

are given in Reference 24. 

Because of the positive results using the superposition model for inline jets shown in 

Reference 25, the superposition model was used for all opposed row conditions. Profiles for 

multiple rows were obtained by combining independent calculations of the flow distributions 

according to the following equation: 

[ ]

[ ] 1 (θ )(θ )

θ θ 2(θ )(θ ) θ

1 2

1 2 1 2

−

+ − =

 (3) 

For opposed rows of jets with centerlines inline, θ1 is the distribution for the top and θ2 is the 

distribution for the bottom. If there are more than 2θ’s, Equation (3) is used up to three more 

times to get a function of, at most, five θ’s (a JIC spreadsheet maximum). 

Although superposition usually gives a good approximation to the experimental data, it 

should be realized that it is an approximation, since there may be an interaction between opposite 

and/or adjacent jets that is not accounted for in superimposing independently calculated 

distributions. 

The older symmetry model, described in e.g., References 1, 15, 20, and 23 to 25, is still the 

default method in the spreadsheet for opposed rows of jets with their centerlines aligned. 

Specifying anything other than slanted slots in the same row with all orifices aligned uses 

symmetry. To invoke the superposition model, one must not have the same configurations on 

both top and bottom in any row. The “solution” to get superposition for two opposed rows of jets 

with their centerlines aligned is to use row 1 top and row 2 bottom (or row 2 top and row 1 

bottom) and to specify SX/H = 0. 

The NASA JIC empirical model assumes the flows of interest will be confined and cannot be 

used for unconfined jet flows because the relations used for orifice size and spacing do not 

extrapolate properly as jet spacing and/or the distance to the opposite wall becomes large. 

Although it may work, the spreadsheet should not be used upstream of the trailing edge of the 

orifices. 

Per Reference 27, the unmixedness Us is defined as 

θ (1 θ )

θvar

ave ave

Us − = (4) 

where θvar is the mean squared deviation between θave and all θ values in the span shown at 

each axial x location for which calculations are performed (in this case, 2020 θ − values = 20 

profiles × 101 spanwise points, where the 21st profile is not included in the average because it is 

the beginning of the next cycle). θave is the fully-mixed mean value (usually = mJ/mT) and is not 

a function of the axial location x.

Analysis of the experimental data in References 8 and 14 suggested a coupling between the 

orifice spacing and the momentum-flux ratio, and led to the conclusion that similar penetration 

occurs independent of orifice size if the square root of the momentum-flux ratio J and orifice 

spacing S/H are inversely proportional. This relationship can be stated as 
NASA/TM—2010-216100 7 

 C = (S/H)(√(J)) (5) 

Equation (5) for the jet penetration coefficient C is not assumed in the correlations, so the 

empirical model results shown in References 1, 13, 15, 20, and 22 to 25 and this report provide 

verification for it. 

The coefficient C can be useful in characterizing the jet penetration. For one sided injection, 

optimum penetration was found to occur when C was approximately 2.5. Obvious underpenetration was observed when C was half the optimum value, and obvious over-penetration was 

observed when C was double the optimum value. For opposed rows of inline jets, the 

corresponding C values are half of those above; for opposed rows of staggered jets, the 

corresponding C values are double the single-side ones. As can be seen from Equation (5), and 

inferred from perusing the figures in References 24 and 25, there is usually a trade-off between 

momentum-flux ratio J and orifice spacing S/H. Note that C characterizes penetration rather that 

mixing, but it usually follows that an optimum C gives the best mixing at a given J. Mixing 

parameters, such as the standard deviation of the mixture fraction, and the “unmixedness” Us, 

should be consistent with the θ distribution. Having shown that it is, mixing parameter values can 

be compared, but comparing mixing parameters alone can be misleading as a nonoptimum 

configuration at one J can have, for example, a lower Us than for an optimum configuration at a 

lower J. 

Review of Significant Flow and Geometry Effects 

Figures 3 to 7 are similar to Figures 9 to 14 in References 24 and 25, except that both the 

contour and profile plots here are from the spreadsheet posted with this report, whereas the 

contour plots in Figures 4 to 14 in Reference 25 were done with a graphics post-processor from 

spreadsheet data. Although the same trends could be shown at different axial locations, results 

in Figures 3 to 7 are shown at a downstream distance equal to one half of the duct height 

(x/H = 0.5). These cases were initially run to check results from the current spreadsheet but 

are included in this report as they provide background material for the new results. 

Variation of θ Distributions With Momentum-Flux Ratio (J) 

The momentum-flux ratio J is the most significant flow variable. Figure 3 shows the increase 

in jet penetration that occurs with increasing momentum-flux ratio (6.6 ≤ J ≤ 105.6); here 

S/H = 0.5 and H/d = 5.66. Note that the jets are under-penetrating in Figure 3(a) (C = 1.28), 

optimum in Figure 3(b) (C = 2.57), and over-penetrating in Figure 3(c) (C = 5.14). Since the 

orifice size and spacing are constant the jet-to-mainstream mass-flow ratio MR increases with 

increasing momentum-flux ratio J. 

Variation of θ Distributions With Density Ratio (DR) for a Constant Momentum-Flux Ratio (J) 

Analyses of the experimental data in References 8 and 14 showed that the effect of varying 

the density ratio DR was minor when J was constant. This effect can be seen in Figure 4. In the 

figure, the density ratio varies from 0.5 (less dense jets) to 1 (equal density) to 2 (more dense 

jets). In Figure 4, J = 26.4, S/H = 0.5 (C = 2.57), with H/d = 5.66. Note that the magnitude of θ

increases slightly as the density ratio increases because the jet-to-mainstream mass-flow ratio 

increases as the density ratio increases. Other than this, there is not much difference between hotjets-in-a-cold-mainstream and cold-jets-in-a-hot-mainstream at a constant momentum-flux ratio. 
NASA/TM—2010-216100 8 

Variation of θ Distributions With Orifice Spacing (S/H and S/D) at a Constant Orifice Size (H/D) 

Figure 5 shows the effect of increasing the lateral spacing between orifices from S/H = 0.25 

to 1.0 (2 ≤ S/d ≤ 8) with J = 26.4 and H/d = 8. The jet penetration increases as S/H increases 

(1.28 ≤ C ≤ 5.14). Note that the lateral variation of the distribution also increases as orifice 

spacing increases. Both this and the increased jet penetration probably occur because there is less 

interaction between adjacent jets when they are farther apart. The jet-to-mainstream mass-flow 

ratio decreases as the spacing increases, since the orifice size is constant.

Variation of θ Distributions With Orifice Size (H/D) at a Constant Orifice Spacing (S/H) 

The jet penetration in Figure 6 remains very similar when the orifice diameter d increases 

(H/d decreases) at a constant S/H. (Note that S/H is constant, but S/d is proportional to H/d.) The 

orifice diameter doubles as H/d is varied from 8 to 4, resulting in a four-fold increase in the jetto-mainstream mass-flow ratio MR. The result is that the distributions shift to higher θ values as 

MR increases, but the jet penetration and shape of the distributions remains similar. The obvious 

conclusion from Figure 6 is that varying the orifice size has a secondary effect on jet penetration. 

Orifice size can be chosen to satisfy other considerations (e.g., the mass-flow ratio) provided S/H

is constant. Note that when S/H and x/H are constant both S/d and x/d decrease as H/d decreases.

Variation of θ Distributions With Coupled Orifice Spacing (S/H) and Momentum-Flux Ratio (J) 

The plots in Figure 7 show the inverse relationship between the orifice spacing S/H and 

the momentum-flux ratio J when they are related according to Equation (5); e.g., for J = 6.6, 

S/H = 1; for J = 26.4, S/H = 0.5; and for J = 105.6, S/H = 0.25. The conditions in Figure 7 

represent nearly optimum mixing conditions for a single row of jets (C = 2.57), although similar 

trends could be shown for over- and under-penetrating jets. In Figure 7 the mass-flow ratio MR is 

constant, because the orifice size was decreased as the momentum-flux ratio J was increased and 

the orifice spacing S/H was decreased. Clearly, similar penetration is obtained over a range of 

momentum-flux ratios if J and S/H are coupled, but note also that the flow is vertically and 

laterally less uniform for smaller momentum-flux ratios. This result was shown in Reference 1 

using experimental data. 

Results and Discussion 

Figures 8 to 20 show results for the primary configurations investigated here: (1) opposed 

rows of inline and staggered jets and (2) rows of jets from alternating large and small holes. 

Results for the conditions investigated computationally are shown in the contour and profile 

plots in Figures 8 to 20 and the conditions for the calculations are given in Table 1 and also 

identified in the titles of the figures. The downstream location and the unmixedness Us are given 

in the subtitle for each part of each figure. Recall that the x = 0 location is at the center of the 

holes, and note that the trailing edge of round holes is at x/H = (0.5)/(H/d). Because the 

“effective” duct height for opposed rows is often approximately half of the actual duct height, 

downstream locations of x/H = 0.125, 0.25, and 0.5 were chosen for opposed rows of jets and 

x/H = 0.25, 0.5, and 1.0 were chosen for most of the single-side injection cases.

Figures 8 to 15 show opposed rows of inline and staggered jets for cases that either are 

optimum configurations for one side injection or are optimum for opposed rows of inline jets. 

Figures 16 to 20 show a single row and opposed rows of jets from alternating large and small 

holes. There is a considerable decrease in Us with downstream distance for each case shown in 
NASA/TM—2010-216100 9 

Figures 8 to 20, however, there is also a smaller difference in Us between cases at a given 

downstream location. 

Opposed Rows of Inline and Staggered Jets 

Inline Jets 

The cases in Figures 8 and 9 are similar to the results for single and opposed rows of inline 

jets in References 1, 15, 20, 24, 25, and 27. The experimental data in Reference 27 show that jets 

from opposite walls penetrate similarly in inline configurations for the same momentum-flux 

ratio J even if the orifice sizes on opposite sides are different. 

Figure 8 is a nearly optimum configuration for opposed rows of inline jets. Note that the jets 

penetrate to approximately H/4 and that C = 1.28 for the configuration shown. Figure 9 has 

double the S/H, but the diameter of the holes is increased to give the same total area 

(AJ/AM = 0.098). For this case, the jets penetrate to approximately H/2 and C = 2.57. As this is a 

nearly optimum configuration for one side injection, the overpenetration shown in Figure 9 for 

opposed rows of inline jets is expected. Figure 10 has the same total area, momentum-flux ratio, 

and orifice spacing as Figure 9 but with smaller holes (H/d = 8) on top and larger ones 

(H/d = 4.62) on the bottom (C = 2.57 on both sides). The cases in Figures 9 and 10 confirm the 

earlier results that hole size has a minimal effect on penetration for jets at the same spacing S/H 

and momentum-flux ratio J. As the smaller holes get smaller (and eventually disappear), and the 

larger ones get larger, they approach the limit of optimum single-side injection, which is shown 

in Figure 11. 

The Us values for Figures 9 and 10 are similar, but the unmixedness for the case in Figure 10 

with different hole sizes on opposite walls is a little bit higher than the case in Figure 9 where the 

holes are all the same size. However, the Us values in Figure 11 for single-side injection with 

H/d = 4 is higher still. The lowest Us is for the optimum configuration for opposed rows as 

shown in Figure 8.

Staggered Jets 

A configuration for optimum penetration of staggered jets is shown in Figure 12 for 

AJ/AM = 0.098. A staggered optimum is obtained when every other hole of an optimum 

configuration for one-side injection is relocated to the opposite side. Thus, for an optimum 

staggered configuration, the spacing of adjacent jets is doubled from that for a single side 

optimum. The unmixedness Us is slightly less for the optimum staggered configuration than for 

the single side optimum, but Us for an optimum staggered configuration (Fig. 12) is significantly 

larger than for an optimum inline configuration (Fig. 8) probably because there are four times as 

many holes in an optimum inline configuration. 

Because C for an optimum staggered configuration is quadruple the optimum for opposed 

rows of inline jets, the diameter of round holes for an optimum staggered configuration is twice 

that for jets in an opposed inline optimum for the same area ratio. If C is less than the optimum 

for a staggered configuration, the penetration of staggered jets will be reduced. For example, 

note that the orifice spacing for the case in Figure 13 (S/H = 0.5) is half of that for the optimum 

staggered case in Figure 12 (S/H = 1.0). 

The cases in Figures 13 and 14 are similar respectively to those in Figures 9 and 10 except 

that the lower row of holes in Figures 13 and 14 are shifted by S/2. The staggered jet cases 

shown in Figures 13 and 14 overpenetrate if opposed jets are inline. In Figure 13 all the holes are 
NASA/TM—2010-216100 10 

the same size (H/d = 5.66), whereas the case in Figure 14 has smaller holes (H/d = 8) on top and 

larger ones (H/d = 4.62) on the bottom. The cyclical nature of the results shown in Figure 13 is 

confirmed by unpublished measurements from UTRC (private communication) for the staggered 

jet case described in Reference 28. As in Figures 9 and 10 which are inline configurations, the 

unmixedness Us in Figure 13 where the holes are all the same size is a little bit less than that in 

Figure 14 with different holes sizes on opposite sides. 

Also of interest is a comparison of inline and staggered configurations where the staggered 

one has a row shifted such that the centerplane of the jets from one side is opposite from the 

midplane of jets from the opposite side. θ distributions in Figures 9 and 13 and 10 and 14 suggest 

that an opposed row of staggered jets in a nearly optimum configuration for one-side injection 

mix better than an opposed row of inline ones at the same spacing and momentum-flux ratio, 

however the Us for the staggered cases are only slightly less than for the inline cases. For an 

optimal configuration for opposed rows of inline jets (as in Fig. 8), shifting does not make much 

difference as shown in Figures 8 and 15. 

Rows of Jets From Alternating Large and Small Holes 

One-Side Injection From Orifices With Mixed Hole Sizes 

The cases shown in Figures 16 to 18 are similar to those in Reference 8. In addition to the 

alternating size holes in Figure 18, these include the cases of only large holes at the spacing 

between holes of the same size in the alternating-size configuration (Fig. 16) and uniform size 

holes at the spacing between adjacent holes in the mixed configuration (Fig. 17). Note that the 

case shown in Figure 18 is a combination of the cases shown in Figures 16 and 17 so the total 

area in Figure 18 is AJAM = 0.098. Also note that two jets are shown in Figure 17, whereas four 

of the smaller jets are shown in Figure 18 and that the Us values in Figures 16 to 18 are 

comparable to many of those for the opposed row cases, but the downstream distances in 

Figures 16 to 18 are double those for opposed rows. Faster mixing is typical for opposed rows as 

there are usually more and smaller holes in configurations with opposed rows of inline jets than 

in one-side configurations. 

The penetration of the jets was shown previously, with both experimental and modeling 

results (e.g., Refs. 1, 15, 20, 24, and 25), to be largely independent of orifice size, so the jet 

penetration would be expected to be about the same for adjacent holes if the same spacing was 

used for both the large and small holes. This is contrary to the experimental results in 

Reference 8 that shows that jets from the larger holes penetrate farther. 

To implement mixed hole sizes in the JIC spreadsheet we used both rows on top with the 

axial spacing Sx/H = 0 and the lateral spacing S/H between large holes for the large holes and the 

lateral spacing between all holes for the small holes. Although the lateral spacing S/H is input 

only in row1-top in the spreadsheet, it is divided by two for the smaller holes by specifying four 

holes for them and two holes for the larger ones. This changes the penetration of adjacent jets 

significantly although they have the same J. 

This is shown in the spreadsheet calculations in Figure 18 for alternating size holes for 

injection from one side (here the top) for AJ/AM = 0.098. Each row of the mixed hole size 

configuration in this simulation is half of the total area. However, because there are only half as 

many large holes and because a larger hole is co-resident with a smaller one in the calculation, 

the effective area of the large holes is really three times that of the small ones. The jets from the 

large holes overpenetrate as expected, because the S/H between large holes is too big (S/H = 1) 
NASA/TM—2010-216100 11 

for this momentum-flux ratio (J = 26.4), whereas the spacing of the small holes is nearly 

optimum (S/H = 0.5). 

Opposed Rows of Jets With Mixed Hole Sizes 

The results in Figures 16 to 18 for one-side injection of jets in crossflow agree with the 

experimental data in Reference 8 so the JIC spreadsheet was used to calculate expected results 

for opposed rows of jets with mixed hole sizes. For opposed rows of mixed hole sizes, we used 

both rows on top and bottom with Sx/H = 0 and again used the lateral spacing S/H between large 

holes for the large holes and the lateral spacing between all holes for the small holes. 

For opposed rows with holes of mixed sizes, there are two possible configurations—holes of 

the same size can be opposite each other, or a larger hole can be opposite a smaller one. These 

are shown in Figures 19 and 20 for a total AJ/AM = 0.098. Although the θ distributions suggest 

significantly better mixing in the staggered configuration in Figure 20, the Us values are only 

slightly lower for the staggered configuration. The limiting cases are (1) all holes are of the same 

size and (2) only the large holes exist. These are shown in Figures 8 and 9 for opposed rows of 

inline jets for a nearly optimum opposed row configuration for inline jets (Fig. 8) and an opposed 

row configuration of larger holes with double the orifice spacing (Fig. 9). Corresponding 

staggered configurations are shown in Figures 15 and 13, respectively. The mixing for the case 

in Figure 13 of staggered jets at a spacing that is optimal for one-side injection (C = 2.57) 

appears to be significantly better than that for inline jets as in Figure 9, but for jets in a nearly 

optimal configuration for opposed rows of inline jets (C = 1.28), staggering does not make much 

difference, as shown in Figures 8 and 15. 

The Unmixedness Us for opposed rows of jets with mixed hole sizes is about the same for 

both inline (Fig. 19) and staggered (Fig. 20) configurations, but Us is usually slightly smaller for 

the staggered case. Also the Us values for both inline and staggered cases with mixed hole sizes 

are less than Us for only large holes with C = 2.57 as shown in Figures 9 and 13. However, the 

US for jets in a nearly optimal configuration for opposed rows of inline jets is about the same 

whether the jets are staggered or inline, as shown in Figures 8 and 15. 

Conclusions 

A spreadsheet which displays 3–D plots of the distributions of a conserved scalar 

downstream of jets mixing with a confined crossflow was used to investigate the cases of 

opposed rows of jets in inline and staggered configurations and single and opposed rows of 

alternating large and small holes. The spreadsheet used in this report is the same as that posted 

with NASA/TM—2006-214226 except that contour plots were added to the Excelspreadsheet. 

Previous publications showed that the NASA empirical model gave results that were an 

excellent representation of mean experimental results so that the model could confidently be 

used to investigate opposed rows of jets in inline and staggered configurations with uniform size 

and alternating large and small holes. Although closely-spaced staggered jets are usually not an 

optimum staggered configuration, shifting of one side to make a staggered configuration from 

one in which opposed jets are aligned can improve the mixing, particularly for cases that would 

overpenetrate slightly when the orifices are in an aligned configurations. For single and opposed 

rows of mixed size holes, jets from the larger holes penetrated farther and dominated the mixture 

fraction. For all cases investigated, staggered configurations mixed better than comparable 
NASA/TM—2010-216100 12 

unshifted inline ones. However, optimum configurations for opposed rows of inline jets mixed 

significantly faster than optimum one-side or optimum staggered opposed row configurations. 

The dimensionless variance of the mixture fraction decreased significantly with increasing 

downstream distance for all cases. Although the variation between cases at the same downstream 

distance was smaller, it was consistently lower for staggered configurations. The unmixedness 

for optimum configurations for opposed rows of inline jets was significantly less than the 

unmixedness for optimum one-side or optimum staggered opposed row configurations. 

References 

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and Combustion Science, Vol. 19, pp. 31–70, August 1993 (similar to AIAA Paper 91–2458 and 

NASA TM–104412, June 1991). 

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Clifford E., Mixing of Multiple Jets With a Confined Subsonic Crossflow: Part I—Cylindrical Ducts. 

Journal of Engineering for Gas Turbines and Power, Vol.119, October 1997 (same as ASME Paper 

96–GT–482 and NASA TM–107185, June 1996). 

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Crossflow: Part II—Opposed Rows of Orifices in Rectangular Ducts. Journal of Engineering for Gas 

Turbines and Power, Vol.121, July 1999 (same as ASME Paper 97–GT–439 and NASA TM–107461, 

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Experimental Assessment of Jets in Cross Flow, AGARD Conference Proceedings 534, April 1993. 

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Report No. 94–71), August 1994. 

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a Jet Injected Normal to a Crossflow. NASA TN D–6966, September 1972. 

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No.11, pp. 1425–1429, November 1972 (same as AIAA Paper 72–149, January 1972; derived from 

NASA CR–72893, June 1971). 

8. Walker, R.E. and Kors, D.L., Multiple Jet Study Final Report. NASA CR–121217, June 1973. 

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Airstream for Gas Turbine Combustors. AIAA Paper 73–1249, November 1973 (same as NASA TM 

X–71426). 

10. Walker, R.E., Kors, D.L., and Holdeman, J.D., Mixing of Multiple Jets of Cooling Air With 

Simulated Combustion Gases. CPIA Publication 243, Proceedings of the 10th JANNAF Combustion 

Meeting, Vol. I, pp. 377– 396, December 1973. 

11. Kamotani, Y. and Greber, I., Experiments on Confined Turbulent Jets in Cross Flow, NASA 

CR–2392, March 1974. 

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1975. 

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Journal, Vol. 15, No. 2, pp. 243–249, February 1977 (similar to AIAA Paper 76–48 and NASA TM 

X–71821, January 1976). 

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CR–168031 (Garrett 21–4302), November 1982. 

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Paper 83–1200 (same as NASA TM–83457), June 1983. 
NASA/TM—2010-216100 13 

16. Holdeman, J. D., Srinivasan, R., and Berenfeld, A., Experiments in Dilution Jet Mixing. AIAA 

Journal, Vol. 22, No. 10, pp. 1436–1443, October 1984 (same as AIAA Paper 83–1201 and NASA 

TM–83434, June 1983). 

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CR–174624 (Garrett 21–4804), June 1984. 

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Report. NASA CR–174884 (Garrett 21–5418), June 1985. 

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175043 (Garrett 21–5705), March 1986. 

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(same as NASA TM–87294), June 1986. 

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Program: Phase I Final Report, Volume II. NASA CR–168243 (Garrett 21–4742–2), August 1983. 

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Power, Vol. 2, No. 1, January–February 1986, pp. 4–9 (similar to AIAA Paper 84–1379 and NASA 

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Noncircular Orifices on Dilution Jet Mixing. Journal of Propulsion and Power, Vol. 3, No. 3, May–

June 1987, pp. 219–226 (similar to AIAA Paper 85–1104 and NASA TM–86996, July 1985). 

24. Holdeman, J.D., Smith, T.D., Clisset, J.R., and Lear, W.E., A Spreadsheet for the Mixing of a Row of 

Jets with a Confined Crossflow, NASA/TM—2005-213137, February 2005. 

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Rows of Jets With a Confined Crossflow, NASA/TM—2006-214226, October 2006. 

26. Lefebvre, Arthur H., Gas Turbine Combustion, Second Edition, Taylor and Francis, 1999. 

27. Liscinsky, D.S., True, B. and Holdeman, J.D., Effect of Inlet Flow Conditions on Crossflow Jet 

Mixing. AIAA Paper 96–2881 (same as NASA TM–107258), July 1996. 

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to complex geometries. International Journal of Heat and Fluid Flow, Vol, 29, pp.640–653, 2008. 

29. Leong, M.Y., Samuelsen, G.S., and Holdeman, J.D., Mixing of Jet Air With a Fuel-Rich, Reacting 

Crossflow, Journal of Propulsion and Power, Vol. 15, No. 5, September–October 1999, pp. 617–622 

(similar to WSS/CI Paper No. 97S–034 & NASA TM 107430, Apr. 1997, derived from NASA CR–

195375, Sept. 1996). 

30. Leong, M.Y., Samuelsen G.S., and Holdeman, J.D., Optimization of Jet Mixing into a Rich, Reacting 

Crossflow, Journal of Propulsion and Power, Vol. 16, No. 5, September–October 2000, pp. 729–735 

(same as AIAA–98–0156 and NASA/TM—1997-206294, Dec. 1997; derived from NASA CR–

195375, Sept. 1996). 

31. Holdeman, J.D. and Chang, C.T., Mixing of Multiple Jets With a Confined Subsonic Crossflow: Part 

III—The Effects of Air Preheat and Number of Orifices on Flow and Emissions in an RQL Mixing 

Section. NASA/TM—2008-215151, March 2008 (similar to Journal of Fluids Engineering, Vol.129, 

pp.1460–1467, November 2007; derived from NASA/TM—1999-209431, September 1999). 
NASA/TM—2010-216100 14 

TABLE 1.—CONDITIONS INVESTIGATED

Case/figure 

no. 

S/H S/d H/d AJ /AM J Ca

opposed row inline optimum 

8 top 0.25 2 8 0.0491 26.4 1.28 

bottom 0.25 2 8 0.0491 26.4 1.28 

opposed row inline 

9 top 0.5 2.83 5.66 0.0491 26.4 2.57 

bottom 0.5 2.83 5.66 0.0491 26.4 2.57 

10 top 0.5 4 8 0.0245 26.4 2.57 

bottom 0.5 2.31 4.62 0.0737 26.4 2.57 

single side optimum 

11 0.5 2 4 0.0982 26.4 2.57 

opposed row staggered optimum 

12 top 1 4 4 0.0491 26.4 5.14 

bottom 1 4 4 0.0491 26.4 5.14 

opposed row staggered 

13 top 0.5 2.83 5.66 0.0491 26.4 2.57 

bottom 0.5 2.83 5.66 0.0491 26.4 2.57 

14 top 0.5 4 8 0.0245 26.4 2.57 

bottom 0.5 2.31 4.62 0.0737 26.4 2.57 

15 top 0.25 2 8 0.0491 26.4 1.28 

bottom 0.25 2 8 0.0491 26.4 1.28 

single side limits 

16 1 4 4 0.0491 26.4 5.14 

17 0.5 2,83 5.66 0.0491 26.4 2.57 

single side mixed size 

18 1 4 4 0.0491 26.4 5.14 

+ 0.5 2,83 5.66 0.0491 26.4 2.57 

opposed row mixed size inline 

19 top 0.5 4 8 0.0245 26.4 2.57 

+ 0.25 2.83 11.31 0.0245 26.4 1.28 

bottom 0.5 4 8 0.0245 26.4 2.57 

+ 0.25 2.83 11.31 0.0245 26.4 1.28 

opposed row mixed size staggered 

20 top 0.5 4 8 0.0245 26.4 2.57 

+ 0.25 2.83 11.31 0.0245 26.4 1.28 

bottom 0.5 4 8 0.0245 26.4 2.57 

+ 0.25 2.83 11.31 0.0245 26.4 1.28 

a

C = (S/H)(√(J)) 
NASA/TM—2010-216100 15 

Figure 1.—Schematic for flow field for one side 

injection of a row of jets in a confined crossflow. 

(Shown for injection from the top duct wall.) 

Figure 2.—Schematic of a typical vertical scalar profile 

showing scaling parameters in the empirical model. 

(Shown for one side injection from the top duct wall.) 
NASA/TM—2010-216100 16 

x

(a) J = 6.6 

(b) J = 26,4 

(c) J = 105.6 

Figure 3.—Variation of scalar distributions with increasing momentum-flux ratio 

for S/H = 0.5, H/d = 5.66, DR = 2.2, and Cd = 0.64 at x/H = 0.5. 
NASA/TM—2010-216100 17 

(a) DR = 0.5 

(b) DR = 1.0 

(c) DR = 2.0 

Figure 4.—Variation of scalar distributions with increasing density ratio for S/H = 0.5, 

H/d = 5.66, J = 26.4, and Cd = 0.64 at x/H = 0.5. 
NASA/TM—2010-216100 18 

(a) S/H = 0.25, (S/d = 2)

(b) S/H = 0.5, (S/d = 4) 

(c) S/H = 1.0 (S/d = 8)

Figure 5.—Variation of scalar distributions with increasing orifice spacing for 

H/d = 8, DR = 2.2, J = 26.4, and Cd = 0.64 at x/H = 0.5. 
NASA/TM—2010-216100 19 

(a) H/d = 8 (S/d = 4, x/d = 4) 

(b) H/d = 5.66 (S/d = 2.83, x/d = 2.83) 

(c) H/d = 4 (S/d = 2, x/d = 2) 

Figure 6.—Variation of scalar distributions with increasing orifice diameter 

(decreasing H/d) for S/H = 0.5, DR = 2.2, J = 26.4, and Cd = 0.64 at x/H = 0.5. 
NASA/TM—2010-216100 20 

(a) J = 6.6, S/H = 1, H/d = 2.83, (x/d = 1.42) 

(b) J = 26.4, S/H = 0.5, H/d = 5.66, (x/d = 2.83)

(c) J = 105.6, S/H = 0.25, H/d = 11.32, (x/d = 5.66)

Figure 7.—Variation of scalar distributions with coupled momentum-flux ratio (J) 

and orifice spacing (S/H) for DR = 2.2 and Cd = 0.64 at x/H = 0.5. t x/H = 0.6. 

 
NASA/TM—2010-216100 21 

(a) x/H = 0.125 (x/d = 1); Us = 0.176 

(b) x/H = 0.25 (x/d = 2); Us = 0.068 

(c) x/H = 0.5 (x/d = 4); Us = 0.020 

Figure 8.—Variation of scalar profile and contour plots for opposed rows of inline jets 

for S/H = 0.25, H/d = 8 (total AJ/AM = 0.098), DR = 2.2, J = 26.4, and Cd = 0.64. 
NASA/TM—2010-216100 22 

(a) x/H = 0.125 (x/d = 0.71); Us = 0.185 

(b) x/H = 0.25 (x/d = 1.41); Us = 0.113 

(c) x/H = 0.5 (x/d = 2.83); Us = 0.084 

Figure 9.—Variation of scalar profile and contour plots for opposed rows 

of inline jets with S/H = 0.5, H/d = 5.66 (total AJ/AM = 0.098), DR = 2.2, 

J = 26.4, and Cd = 0.64. 
NASA/TM—2010-216100 23 

(d) 

(a) x/H = 0.125 (x/d|top = 1; x/d|bottom = 0.58). Us = 0.191 

(b) x/H = 0.25 (x/d|top = 2; x/d|bottom = 1.16); Us = 0.120 

(c) x/H = 0.5 (x/d|top = 4; x/d|bottom = 2.31); Us = 0.083 

Figure 10.—Variation of scalar profile and contour plots for opposed rows 

of inline jets with S/H = 0.5, H/d = 8 on top, H/d = 4.62 on bottom (total 

AJ/AM = 0.098), DR = 2.2, J = 26.4, and Cd = 0.64. 
NASA/TM—2010-216100 24 

(a) x/H = 0.125 (x/d = 0.5). Us = 0.318 

(b) x/H = 0.25 (x/d = 1); Us = 0.195 

(c) x/H = 0.5 (x/d = 2); Us = 0.096 

Figure 11.—Variation of scalar profile and contour plots for optimum single-side injection 

with S/H = 0.5, H/d = 4 (AJ/AM = 0.098), DR = 2.2, J = 26.4, and Cd = 0.64. 
NASA/TM—2010-216100 25 

(a) x/H = 0.125 (x/d = .5); Us = 0.406 

(b) x/H = 0.25 (x/d = 1); Us = 0.179 

(c) x/H = 0.5 (x/d = 2); Us = 0.042 

Figure 12.—Variation of scalar profile and contour plots for jets from optimum staggered 

holes with S/H = 1.0, H/d = 4 (total AJ/AM = 0.098), DR = 2.2, J = 26.4, and Cd = 0.64. 

 
NASA/TM—2010-216100 26 

(a) x/H = 0.125 (x/d = .71), Us = 0.165 

(b) x/H = 0.25 (x/d = 1.42); Us = 0.091 

(c) x/H = 0.5 (x/d = 2.83); Us = 0.083 

Figure 13.—Variation of scalar profile and contour plots for opposing rows of 

staggered jets with S/H = 0.5, H/d = 5.66 (total AJ/AM = 0.098), DR = 2.2, 

J = 26.4, and Cd = 0.64. 

 
NASA/TM—2010-216100 27 

(a) x/H = 0.125 (x/d|top = 1; x/d|bottom = 0.58); Us = 0.176 

(b) x/H = 0.25 (x/d|top = 2; x/d|bottom = 1.16); Us = 0.097 

(c) x/H = 0.5 (x/d|top = 4; x/d|bottom = 2.31); Us = 0.081 

Figure 14.—Variation of scalar profile and contour plots for opposing rows of 

staggered jets with H/d = 8 on top, H/d = 4.62 on bottom (total AJ/AM = 0.098), 

for S/H = 0.5, DR = 2.2, J = 26.4, and Cd = 0.64. 

 
NASA/TM—2010-216100 28 

(a) x/H = 0.125 (x/d = 1); Us = 0.175 

(b) x/H = 0.25 (x/d = 2); Us = 0.065 

(c) x/H = 0.5 (x/d = 4); Us = 0.018 

Figure15.—Variation of scalar profile and contour plots for opposed rows of 

staggered jets for S/H = 0.25, H/d = 8 (total AJ /AM = 0.098), DR = 2.2, J = 26.4, 

and Cd = 0.64. 
NASA/TM—2010-216100 29 

(a) x/H = 0.25 (x/d = 1); Us = 0.199 

(b) x/H = 0.5 (x/d = 2), Us = 0.099 

(c) x/H = 1.0 (x/d = 4); Us = 0.056 

Figure 16.—Variation of scalar profile and contour plots for one side injection 

with S/H = 1.0, H/d = 4 (AJ /AM = 0.049), DR = 2.2, J = 26.4, and Cd = 0.64. 
NASA/TM—2010-216100 30 

(a) x/H = 0.25 (x/d = 1.42); Us = 0.149 

(b) x/H = 0.5 (x/d = 2.83). Us = 0.078 

(c) x/H = 1.0 (x/d = 5.66); Us = 0.032 

Figure 17.—Variation of scalar profile and contour plots for one side injection 

with S/H = 0.5, H/d = 5.66 (AJ /AM = 0.049), DR = 2.2, J = 26.4, and Cd = 

0.64. 
NASA/TM—2010-216100 31 

(a) x/H = 0.25; Us = 0.177 

(b) x/H = 0.5; Us = 0.099 

(c) x/H = 1.0; Us = 0.028 

Figure 18.—Variation of scalar profile and contour plots for one side injection 

from alternating size holes for S/H = 1.0, H/d = 4 in row 1 and S/H = 0.5, 

H/d = 5.66 in row 2 with Sx /H = 0 (total AJ /AM = 0.098), DR = 2.2, J = 26.4, 

and Cd = 0.64. 
NASA/TM—2010-216100 32 

(a) x/H = 0.125; Us = 0.153 

(b) x/H = 0.25; Us = 0.061 

(c) x/H = 0.5; Us = 0.034 

Figure 19.—Variation of scalar profile and contour plots for opposed rows of 

alternating hole sizes with similar holes opposite each other for S/H = 0.5, 

H/d = 8 and S/H = 0.25, H/d = 11.31 on each side with Sx /H = 0 (total AJ /AM

= 0.098), DR = 2.2, J = 26.4, and Cd = 0.64. 
NASA/TM—2010-216100 33 

(a) x/H = 0.125; Us = 0.149 

(b) x/H = 0.25; Us = 0.047 

(c) x/H = 0.5; Us = 0.029 

Figure 20.—Variation of scalar profile and contour plots for opposed rows 

of alternating hole sizes with large and small holes opposite each other 

for S/H = 0.5, H/d = 8 and S/H = 0.25, H/d = 11.31 on each side with 

Sx/H = 0 (total AJ /AM = 0.098), DR = 2.2, J = 26.4, and Cd = 0.64. 
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1. REPORT DATE (DD-MM-YYYY)

01-07-2010 

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Technical Memorandum 

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4. TITLE AND SUBTITLE

Spreadsheet Calculations for Jets in Crossflow: Opposed Rows of Inline and Staggered Holes 

and Single and Opposed Rows With Alternating Hole Sizes 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Holdeman, James, D.; Clisset, James, R.; Moder, Jeffrey, P. 

5d. PROJECT NUMBER

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5f. WORK UNIT NUMBER

WBS 561581.02.08.03.16.03 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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E-17185 

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NASA/TM-2010-216100 

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Unclassified-Unlimited 

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Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

Jim Holdeman, retired. A supplemental Microsoft Excel (Microsoft Corporation) spreadsheet TM-2010-216100-SUPPL1.xls can be viewed 

on the Web at http://gltrs.grc.nasa.gov. 

14. ABSTRACT

The primary purpose of this jet-in-crossflow study was to calculate expected results for two configurations for which limited or no 

experimental results have been published: (1) cases of opposed rows of closely-spaced jets from inline and staggered round holes and (2) 

rows of jets from alternating large and small round holes. Simulations of these configurations were performed using an Excel (Microsoft 

Corporation) spreadsheet implementation of a NASA-developed empirical model which had been shown in previous publications to give 

excellent representations of mean experimental scalar results suggesting that the NASA empirical model for the scalar field could 

confidently be used to investigate these configurations. The supplemental Excel spreadsheet is posted with the current report on the NASA 

Glenn Technical Reports Server (http://gltrs.grc.nasa.gov) and can be accessed from the Supplementary Notes section as TM-2010-216100-

SUPPL1.xls. Calculations for cases of opposed rows of jets with the orifices on one side shifted show that staggering can improve the 

mixing, particularly for cases where jets would overpenetrate slightly if the orifices were in an aligned configuration. The jets from the 

larger holes dominate the mixture fraction for configurations with a row of large holes opposite a row of smaller ones although the jet 

penetration was about the same. For single and opposed rows with mixed hole sizes, jets from the larger holes penetrated farther. For all 

cases investigated, the dimensionless variance of the mixture fraction decreased significantly with increasing downstream distance. 

However, at a given downstream distance, the variation between cases was small.

15. SUBJECT TERMS

Jets in crossflow; Gas turbine combustors 

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