NASA Contractor Report 3373 

NASA 

CR 

3373 

c.1 

J et Array Impingement With 

Crossflow - Correlation of 

Streamwise Resolved Flow and 

Heat Transfer Distributions 

L. W. Florschuetz, D. E. Metzger, 

and C. R. Truman 

GRANT NSG-3075 

JANUARY 1981 
TECH LIBRARY KAFB, NM 

NASA Contractor Report 3373 

Jet Array Impingement With 

Crossflow - Correlation of 

Streamwise Resolved Flow and 

Heat Transfer Distributions 

L. W. Florschuetz, D. E. Metzger, 

and C. R. Truman 

Arizona State University 

Tempe, A rizona 

Prepared for 

Lewis Research Center 

under Grant NSG-3075 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Branch 

1981 
. . ., 
CONTENTS 

Page 

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V 

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 

2. EXPERIMENTAL FACILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

3. FLOW DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

3.1 Pressure Traverses and Discharge Coefficients .................. 13 

3.2 Flow Distribution Results ...................................... 18 

3.3 Flow Distribution Model ........................................ 20 

4. HEAT TRANSFER COEFFICIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 

4.1 Effect of Crossflow ............................................ 29 

4.2 Effect of Hole Pattern ......................................... 32 

4.3 Effect of Jet Plate Thermal Boundary Condition ................. 32 

4.4 Effect of Roughness Elements on Plenum Side of Jet Plate ....... 36 

5. CORRELATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 

6. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 

iii 

NOMEINCLATURE 

A 

A:, 

b 

l3 

P 

C 

CD 

d 

h 

= coefficient of Reynolds number in power function fit or correlation 

equations 

= ratio of jet hole area to opposing heat transfer surface area (open 

area ratio) 

= thickness of jet plate 

= coefficient in crossflow function of correlation equation 

= flow distribution parameter introduced following Eq. (3.71, 

CD fl(n/4)/[y,/d)/(x/d)l 

= constant appearing in correlation equation 

= jet plate discharge coefficient 

= jet hole diameter 

= crossflow mass velocity based on channel cross-sectional area 

= jet mass velocity based on jet hole area 

= superficial jet mass velocity based on jet plate or equivalent 

opposing heat transfer surface area 

= convective heat transfer coefficient resolved in streamwise 

direction, averaged across span 

= spanwise hole row number 

= thermal conductivity of fluid 

= streamwise length of heat transfer surface 

= Reynolds number exponent in power function fit or correlation 

equation 

= flow distribution parameter introduced at Eq. (3.4),flAzCDlx 

= dynamic viscosity 

= exponent in crossflow function of correlation equation 

nxsny,nz = constants appearing in correlation equation 

V 
Nu 

N", 

NC 

NS 

NH 

P 

pe 

PO 

Pr 

Rej 

P 

TO 

Tr 

TS 

X 

XII 

Yn 

z 

Subscripts 

IorS = 

Nusselt number resolved in streamwise direction, averaged across 

span, hd/k 

value of Nu at first upstream spanwise row of holes where Gc/Gj = 0 

number of spanwise rows of jet holes 

number of jet holes across span of heat transfer surface 

number of jet holes across span of channel 

channel pressure 

channel exhaust pressure 

plenum pressure 

Prandtl number 

jet Reynolds number, Gjd/p 

fluid density 

plenum air temperature 

recovery or adiabatic wall temperature at impingement surface 

impingement surface temperature 

streamwise location along heat transfer surface measured from 

upstream end of channel 

streamwise jet hole spacing 

spanwise jet hole spacing 

channel height (jet plate-to-impingement surface spacing) 

where distinction is required I refers to inline hole pattern, S 

refers to staggered 

Superscripts 

t-1 = overbar refers to mean value 

vi 
I --- -.- 

SUMMARY 

Correlations for heat transfer coefficients for jets of air issuing from 

arrays of circular orifices and impinging on a surface parallel to the jet 

orifice plate are presented. The air, following impingement, is constrained 

to exit in a single direction along the channel formed by the jet orifice 

plate and the heat transfer (impingement) surface. Cutlet flow from upstream 

jets imposes a crossflow on those downstream. Impingement surface heat 

transfer coefficients resolved to one streamwise jet orifice spacing, averaged 

across the channel spanr are correlated with the associated individual 

spanwise orifice row jet and crossflow velocities, and with the geometric 

parameters. The correlations are based on an extensive set of heat transfer 

data previously obtained and documented in an earlier NASA Contractor Report. 

The configurations tested model those of interest in current and contemplated 

designs for cooling of the midchord region of gas turbine airfoils. Both 

inline and staggered patterns of jet orifice arrays were included in the test 

program. 

The streamwise distributions of jet and crossflow velocities utilized in 

developing the correlations are based on a theoretical model which was 

verified by extensive flow distribution measurements obtained as a part of the 

same test program which resulted in the heat transfer data. The model is a 

discrete application of a continuous one-dimensional momentum-flux analysis 

which results in a simple closed form expression for the flow distribution. 

Both the model and the flow distribution measurements are presented, discussed 

and compared in this report. Discharge coefficients for each jet orifice 

plate included in the test program were also measured. 

Streamwise hole spacings ranged from 5 to 15 jet hole diameters for 

inline patterns and 5 to 10 diameters for staggered patterns, spanwise 

spacings were 4 to 8 diameters, and channel heights (jet plate-to-impingement 

surface spacings) were 1 to 3 diameters. Hole pattern aspect ratios (ratio of 

streamwise-to-spanwise hole spacing) ranged from 0.625 to 3.75. The number of 

spanwise rows of jet holes was fixed at 10 for all configurations. Mean jet 

Reynolds numbers ranged from about 5x10' to 5x10'. Overall, individual 

spanwise row jet Reynolds numbers were as low as 2.5~10~ and as high as 7x10'. 

The ratio of the channel crossflow velocity to the jet velocity ranged from 

zero (at the first upstream row) to as high as 0.8 downstream. 

Streamwise jet flow distributions ranged from highly nonuniform for a 

spanwise hole spacing of four hole diameters and a channel height of one 

diameter to essentially uniform for a spanwise spacing of eight diameters and 

a channel height of three diameters. The distributions were essentially 

independent of streamwise hole spacing and hole pattern. 

Separate correlations were required for the inline and staggered hole 

patterns, since the staggered patterns resulted in smaller heat transfer 

coefficients than their inline counterparts as hole spacings were decreased 

and channel height was increased. The correlations are, however, of the same 

form. Overall, 95% of the total of 2080 data points on which the correlations 

are based fall within 11% of the corresponding values predicted by the 

correlations. 
1. INTRODUCTION 

Impingement with high velocity gas jets has become an established method 

of convectively cooling or heating surfaces in a wide variety of process and 

thermal control applications. Examples include cooling of gas turbine 

airfoils and electronic equipment, drying of paper and textile or other thin 

layers of films, annealing of metals, and glass tempering operations. The 

most commonly used jet openings are slots and circular holes. For 

applications requiring highly localized heating or cooling a single circular 

jet may suffice. For long, but very narrow areas a single row of circular 

jets or a single slot jet may be appropriate. The single row or slot may also 

be adequate, in some cases, for treating sheets of material which can be moved 

continuously past the row or slot. However, where all portions of a surface 

of larger expanse must be continuously heated or cooled, multiple slot jets or 

two-dimensional arrays of jet orifices are required. 

For gas turbine engines a signif icant application utilizing a 

two-dimensional array of jets is the cooling of the midchord region of gas 

turbine airfoils. One such arrangement is illustrated in Fig. 1.1. 

Impingement air from the midchord array flows rearward along the channel 

formed between the inlet plenum and the airfoil envelope, discharging at the 

trailing edge. Flow from the upstream jets in the array imposes a crossflow 

on those located downstream. In this arrangement air discharged from the jet 

row provided for cooling of the leading edge is then used to provide localized 

film cooling, and does not interact with the midchord array jets. However, in 

alternate arrangements, leading edge cooling air is permitted to flow rearward 

inside the airfoil envelope where it becomes an initial crossflow influence on 

the midchord array. 

In addition to the increased heat rates attainable relative to 

nonimpinging flows, the jet array provides the designer with potential for a 

high degree of control of the distribution of surf ace heat transfer 

characteristics. By varying the flow and geometric parameters, including the 

number, size, and spat ing of the jet orifices as well as the orifice 

plate-to-cooled surface height, the potential exists for adjustment of the 

2 
heat transfer coefficients to achieve a specified distribution in surface 

temperature or heat flux. 

For the cooled gas turbine airfoil, it should ultimately be possible to 

account for the variation in the external hot gas heat transfer coefficients 

and arrive at an optimum internal impingement array that minimizes the 

required amount of coolant flow. Such an optimum array will, in general, be 

irregular, but modern chemical machining methods make this quite feasible. 

Such optimization will require a detailed knowledge of the effect of array 

geometry on the internal impingement heat transfer characteristics including 

the effect of the crossflow. 

It appears that knowledge of the effects of array configuration on heat 

transfer characteristics has been inadequate for achievement of optimal 

designs, even when consideration is restricted to uniformly spaced arrays. 

Gauntner, et al Ill, recently reported results of measurements on an actual 

gas turbine vane with midchord cooling provided by a uniformly spaced 

two-dimensional jet array. These results illuminated the inadequacy of 

existing correlations for predicting heat transfer performance of such arrays. 

In particular, the study revealed that questions remained unanswered 

concerning the important crossflow influence on downstream heat transfer as a 

function of array geometry. 

The present investigation was initiated with the primary objective of 

determining heat transfer behavior for a range of uniformly spaced array 

configurations which model those of interest in current and contemplated gas 

turbine airfoil cooling applications. The first phase of the test program was 

designed to model impingement cooling of the midchord region according to the 

scheme indicated in Fig. 1.1. The laboratory configuration used to model this 

midchord cooling scheme is illustrated schematically in Fig. 1.2. The test 

facility was designed, however, to also permit subsequent testing in the 

presence of an initial crossflow introduced upstream of the array. 

The original test program included the measurement of both mean and 

chordwise (or streamwise) resolved heat transfer coefficients for uniform 

rectangular (inline) arrays of jets as a function of flow rate and geometric 

parameters, with the objective of developing a correlation which would be of 

direct use to the designer. Subsequently, the program was expanded to include 

3 
Fig. 1.1 Example of cooled gas turbine airfoil with midchord cooling by jet 

array impingement scheme. 

JET PLATE 

0 0 0 0 

TEST SURFACE 

Fig. 1.2 Basic test model geometry and nomenclature. 

4 
staggered jet hole array patterns as well as determination of chordwise jet 

flow distributions. The overall objective, then, became that of developing, 

for design application, correlations of chordwise resolved heat transfer 

coefficients as a function of: (1) jet and crossflow rates associated with 

the individual spanwise jet rows, and (2) geometric parameters. 

A previous report 121 provided a detailed description of the basic heat 

transfer test rig, documented the extensive chordwise resolved and mean heat 

transfer results obtained for both the inline and staggered patterns as a 

function of overall or mean flow rate, and presented and discussed the 

observed trends and characteristics of the data. 

Subsequently, the use of a simple one-dimensional momentum flux model was 

found to quite accurately predict the row-by-row streamwise flow distribution. 

In this report both development of the model and experimental determination of 

the flow distributions are presented and the results compared. These flow 

distributions then provide the means by which the spanwise averaged, 

streamwise resolved Nusselt numbers are examined as a function of the 

individually associated spanwise row jet Reynolds numbers and crossflow-to-jet 

velocity ratios. Correlations are then presented for both inline and 

staggered hole patterns for Nusselt numbers resolved to one streamwise hole 

spacing. Specifically, these Nusselt numbers are correlated in terms of the 

individual spanwise row jet Reynolds number (Rej) and crossflow-to-jet 

velocity ratio (Gc/Gj); and in terms of three geometric parameters: the 

streamwise hole spacing, the spanwise hole spacing, and the channel height 

each normalized by hole diameter (x,/d, yn/d, and z/d). The overall ranges of 

these variables are for Rej, 2.5~10" to 7x104; for Gc/Gj, zero to 0.8; for 

x,/d, 5 to 15 for inline hole patterns and 5 to 10 for staggered patterns; for 

yn/aJ 4 to 8; and for z/d, 1 to 3. The aspect ratios, x,/y,, for the jet 

arrays ranged from 0.625 to 3.75. 

The number of spanwise rows of holes for each array was fixed at ten. 

The range of mean jet Reynolds numbers (FEj) was 5x103 to 5x104. The 

thickness of the jet orifice plate was maintained equal to the hole diameter. 

The thermal boundary condition at the impingement surface was isothermal. 

Tests were run for geometrically similar configurations of different sizes in 

order to examine scaling effects. Overall, hole diameters ranged from 

5 
0.0635 cm (0.025 in.) to 0.762 cm (0.3 in) and heat transfer surface lengths 

from 6.35 cm (2.5 in) to 38.1 cm (15.0 in.). The larger size configurations 

permitted better spatial resolution of heat transfer coefficients. The 

highest streamwise resolution obtained was one-third of the streamwise hole 

spat ing . This resolution permitted observation of pronounced periodic 

streamwise variations in the heat transfer coefficients C2,31. Heat transfer 

coefficients resolved to one or two streamwise hole spacings did not reflect 

the periodic variations, but showed the streamwise trends smoothed across the 

periodic variations [2,41. 

Prior heat transfer studies for two-dimensional arrays of circular 

impinging jets with flow constrained to exit in a single direction parallel to 

jet hole rows were reported by Friedman and Mueller 151, Huang 161, Kercher 

and Tabakoff 171, and Chance CSI. These studies provided either mean heat 

transfer results or were limited to spatial resolutions greater than or equal 

to one streamwise hole spacing. Studies which included some high resolution 

measurements, but in which the flow was not constrained to exit in a single 

direction were carried out by Gardon and Cobonpue [91 and Hollworth and Berry 

1101. A recent review of impinging jet flow heat and mass transfer was 

provided by Martin 1111. Metzger and Korstad [12l measured mean heat transfer 

coefficients for a single row of circular impinging jets normal to a 

cross-flowing air stream. High resolution studies of a single circular 

impinging jet in the presence of a crossflow were carried out by Bouchez and 

Goldstein [13l and by Sparrow, Goldstein and Bouf 1141. 
2. EXPERIMENTAL FACILITY 

A detailed description of the test facility may be found in [21. 

However, for the convenience of the reader in interpreting subsequent material 

in this report, a shortened but essentially complete description is included 

here along with a complete summary of the significant characteristics of the 

jet array geometries tested. 

The test facility consists overall of a compressed air supply, an air 

flow metering section, and interchangeable plenum/ jet plate assemblies which 

produce arrays of jets impinging on an instrumented heat transfer test 

surface. Chordwise (i.e., streamwise) and spanwise cross-sectional views of 

the assembly of the major components are shown in Fig. 2.1 for one plenum 

size. A single test plate unit consisting of a segmented copper test plate 

with individual segment heaters, the necessary thermal insulation, and the 

test plate support structure, is utilized for all tests. The segmented design 

provides for control of the streamwise thermal boundary condition at the heat 

transfer test surface, as well as for determination of spatially resolved heat 

transfer coefficients in the streamwise direction. The jet plate under test, 

positioned by the jet plate holder, is bolted to the lower flange of the 

plenum, which in turn, is bolted to the test plate unit. The jet plate lower 

surface is positioned relative to the heat transfer surf ace via 

interchangeable spacers to permit covering the desired range of z/d. 

Laboratory compressed air is piped to the plenum and passed through the 

plenum packing to provide a uniform flow upstream of the jet plate. After 

passing through the jet plate the air exhausts to atmospheric pressure by 

flowing along the channel formed by the jet plate, the test surface, and the 

spacer. 

There are four interchangeable plenums, each of a different streamwise 

length. Thus, the channel length varies depending on the size of the 

particular plenum/jet plate assembly being utilized. The thermally active 

length of the test plate consists, for a given test, of those test plate 

segments which are immediately opposite the jet plate. The maximum active 

chordwise length is 38.1 cm (15 in.) (30 segments by 1.27 cm (0.5 in.) per 

segment), with an additional segment at the downstream end to serve as a guard 

7 
+ 

AIR INLET 

PLENUM (INTERCHANGEABLE) 

JET PLATE HOLDER 

(INTERCHANGEABLE) 

i- SPACER (INTERCHANGEABLE) INSULATION -l 

CHORDWISE VIEW 

SPANWISE VIEW 

Fig. 2.1 Test unit assembly. 
element. For tests in which only a fraction of the test plate was thermally 

active the segment immediately downstream of the active portion served as a 

guard element. 

The jet plate thickness, b, at each hole location is equal to the jet 

hole diameter. This was achieved by appropriately counterboring plates of 

larger overall thickness (Fig. 2.1). This design feature was dictated 

primarily by the need to insure accurate channel heights during test runs, a 

particularly critical requirement for the narrowest channel height t.0635 cm). 

The counterbore was three jet hole diameters, except for the narrowest hole 

spacing where two jet hole diameters was used. In one test with z/d = 1, a 2d 

counterbore plate was used with the counterbored holes subsequently bored out 

t0 3a, and the test repeated. The results were identical to within 

experimental uncertainty. 

The significant dimensions and geometric characteristics unique to the 

interchangeable plenums and matching jet plates for which data was obtained 

are summarized in Table 2.1. The smallest jet hole diameter is near prototype 

size for the gas turbine application, while the larger sizes provided for 

improved streamwise resolution of heat transfer coefficients. The relation 

between the spanwise jet hole rows and the test plate segments is indicated in 

Fig. 2.2 for jet plates corresponding to each plenum size. Emphasis in this 

report is placed on results from the B, C, and D sizes since, for these, heat 

transfer coefficients can be resolved to at least one streamwise hole spacing. 

Note that the number of spanwise rows of holes was fixed at 10 for all jet 

plates. The first row (counting from upstream) was always displaced x,/2 from 

the upstream end of the channel (Fig. 2.2). Each jet plate with a staggered 

hole pattern was identical to its inline counterpart, except that alternating 

spanwise rows were offset by one-half the spanwise hole spacing (Fig. 2.3). 

Each individual configuration tested can be uniquely identified by 

specifying a size designation (A, B, C, or D), a set of geometric parameters 

(x,/d,y,/d,z/d), and a hole pattern (I or S). For brevity, specific 

configurations will be referred to by designations such as B(5,8,2)1; or when 

it is unnecessary to indicate in this way a specific size, hole pattern, 

and/or geometric paramter value, obvious notations such as B(5,8)1, B(5,8), or 

simply (5,8) will be used. 

9 
Table 2.1 Geometric Characteristics of Configurations Tested 

lenum 

Size 

A 

B 

D 

0.762(0.300) 

38.1(15.0) 

, 

4 / '92.3 I 6 9 0.81 -- 

5 6 1 1.2.3 I 4 6 1 0.77 -- 

8 1,233 1.S 31 4 0.78 0.78 

4 1 1,2,3 ( 1,s 1 12 ] 18 ( 0.82 1 

20 

0.83 

10 t-i 4 1,2,3 1 I 

8 1.2.3 _ . 1 I 

4 '.2,3 I 12 18 0.83 30 -- 

15 6 1 ,2 33 I 8 12 0.80 -- 

8 '.2,x I 6 9 0.79 -- 

Maximum 

Chordwise 

Resolution 

2xn 

xn 

1 

T xn 

1 

3 xn 

4 

!, 

F 

Channel 

Length 

cm (inches) 

10.8(4.25) 

17.1(6.75) 

29.8(11.75) 

41.3(16.25) 

Notes: 1 8 I denotes inline hole pattern, S denotes staggered. 

2 The number of holes across the test plate span, N,, 

was fixed at 10 for all tests reported herein. 

varies depending on hole spacing; the number along the chord, NC = !Ux,, 
A-SIZE 

C-SIZE 

Fig. 2.2 Location of spanwise jet hole rows relative to test plate segments. 

Attention is called to the fact that a number of the configurations of 

different sizes listed in Table 2.1 are geometrically similar. Considering 

sizes B, C, and D the maximum length scale factor is 3; including A-size, the 

maximum factor is 6. 

The discharge coefficients summarized in Table 2.1 were employed in 

determination of the row-by-row streamwise flow distributions, as discussed in 

the next section. 

11 
. . . . . . . . . 

. . . . . . . . 

(I’ 

. . . . . . . . . 

@ . . 

* 

. . 0’ . . . . 

0 . 

. . . . . . . . . 

. . . . . . . . . 

. . . . . . . . . 

In1 ine Pattern 

. . . . . . . . 

:@ ......... l 

. . . . . . . . 

;* @ 

. . . . . . . . . 

. . . . . . . . 

,@ e. 

. . . . . . . . . 

. . 

l •*****~e 9 

. . . . . . . . . 

,@ l ’ l ’ ’ l . 

. . . 0 

. . . . . . . . . 

0 l 0 0 0 0 l 0 0 

Flow 

Direction 

(Chordwise) 

Staggered Pattern 

Fig. 2.3 Corresponding inline and staggered jet array hole patterns 

illustrated for configuration B(5,8). 

12 
3. FLOW DISTRIBlTITON 

The determination of the distribution of the jet flow among the 

individual spanwise rows was an essential step prior to attempting correlation 

of the streamwise resolved heat transfer coefficients with the individual row 

jet and crossflow rates. The flow distributions were determined from measured 

streamwise channel pressure profiles and jet plate discharge coefficients. A 

one-dimensional incompressible momentum flux model was also developed which 

predicted the experimentally determined flow distributions quite 

satisfactorily. 

3.1 Pressure Traverse+ and Discharge Coefficients 

Streamwise channel pressure traverses were accomplished with static 

pressure probes inserted from the downstream end of the channel. The probes 

were stainless steel tubes of 0.0635 to 0.124 cm (0.025 to 0.049 in.) outside 

diameter closed at the upstream end, with a single orifice of 0.0254 cm (0.010 

in.) diameter located 0.318 cm (l/8 in.) from the end. For a given run the 

tube was positioned along one lower corner of the channel and pressed against 

the channel side wall and bottom by slightly bowing the tube. This 

positioning provided support of the tube, thus preventing vibration and 

possible whipping in the presence of a strong channel flow. The larger 

diameter tubes were used with larger channel heights which were also 

associated with longer channel lengths, thus requiring a stiffer probe. 

For a given traverse the orifice was positioned either facing upward 

toward the jet plate, downward toward the channel lower surface, or toward the 

channel sidewall. For each jet plate configuration, two or three traverses 

were usually made, each utilizing a different one of these orifice positions. 

Manometer readings of the channel pressure were normally made at each spanwise 

jet row location, midway between jet rows, and in some instances at the 

farthest possible upstream position, x = 0.318 cm (l/8 in.). Readings were 

also normally taken at several positions in the channel downstream of the last 

(tenth) row of jet holes, the channel exit section. 

13 
The pressure profile results for the B(10,8,3)1 configuration are plotted 

in Fig. 3.1 in terms of the ratio of the channel pressure, P, to the plenum 

pressure, P,. The locations of the spanwise jet rows are indicated by the 

vertical arrows along the abscissa. Comparison of results for the three 

orifice positions as well as the smoothness of the points in traversing from 

locations immediately opposite jet rows to midway between rows indicates that 

dynamic pressure effects were not significant. 

For the larger channel heights, z/d = 3 as in Fig. 3.1, the channel 

pressure was fairly uniform, resulting, as will be seen, in a fairly uniform 

flow distribution. In these cases most of the pressure drop from plenum to 

exit occurs across the holes rather than along the channel. The pressure 

I 

0 

0. 

0. 

to 0. 

a 

0. 

0.1 

0. 

0.: 

.O- 

.9- 

.6- 

7- 

6- 

5- 

4- 

t 

3- 

2- 

0 

I I I I I I I I I ’ 101 kPa’ 1- 

uuPuuuuDP~uea~4.~Puuuueosa 

n n n n n n n n n n n n n n n n n n n n n 

19.8K IO5kPa 

ue~~eee~~gg~g~~~~~~u**u* 

9.0 K II6 kPa 

RGj- 18.8 K P, =lGOkPa 

fJtiw3~g~uEi 

B(lO,EI,3)1 d = 0.127 cm 

Probe Orif ice Facing 

UP cl 

Side 0 

Down A 

D(lO,8,3)1 d = 0.381 cm 

Probe Orifice Facing 

UP n 

52.0 K 

Nominal To - 300 K -flQ* 

Nominal Pe = 96 kPa 

FJa 0 

1 I I I I I I ~IIL!!I14kll I I 

I 2 3 4 5 6 7 0 9 IO II I2 

x/x, 

Fig. 3.1 Channel pressure traverses for (10,8,3)1 geometry. 

14 
ratio, P/P,, decreases significantly with increasing Rej. For Gj = 52K, the 

pressure ratio across all holes is below the ,critical value for isentropic, 

one-dimensional flow of air, 0.53, indicating the flow is choked across all 

holes. The effect of hole diameter is indicated by comparing the results for 

the geometrically similar larger size case, D(lQ,8,3)1, at the nominal Bej of 

19K. The pressure ratio is significantly increased with increasing hole 

diameter. 

Comparable B-size results, but for the narrow channel height of z/d = 1, 

are plotted in Fig. 3.2 for the up-facing probe orifice traverses. Here the 

pressure gradients along the channel are larger, with a smaller fraction of 

I 

0 

0 

0 

to 0 

a 

0 

0 

0 

0 

.o1.8 - 

.7 - 

.6 - 

.5- 

.4 - 

.3- 

.2- 

0 

~ ~ $=4.9K ‘PO= 106kPc 

lu,~ll n M uil 9.7 K 

B(lO.8.1 1 I 

Probe Orif ice 

UP 0 

d-0.127 cm 

Facing 

Fig. 3.2 Channel pressure traverses for (10,8,1)1 geometry. 

15 

I 

t 

I 

-..-- -.--- _ ---- 

n n 

23.7K 

l9.4K 

q 

q 0 

n m 

132 kPa 

n 

139 kPa 

C(lO.8, 111 d=0.254 cm 

Probe Orifice Facing 

UP n 0 

q q o 214 kPa 

q o q 

q 

36.8K 

q 

Nominal To = 300K 

Nominal Pe = 96kPa 

365 kPa 

t 14 IC II II 14 1 c I I 14 I I I I 1 

I 2 3 4 5 6 7 8 9 IO II 12 

x/x, 
the pressure drop occurring across the holes than in the z/d = 3 case of Fig. 

3.1. The pressure ratio is less sensitive to increases in flow rate (as 

reflected by Bej). The flow is just approaching a choked condition at the 

last (tenth) row of holes for the largest Ej = 36.8K. The effect of hole 

diameter is again evident by comparing the C!(10,8,1)1 profile. 

A final illustration of pressure traverse results is shown in Fig. 3.3 

for two A-size configurations, A(10,8,3)1 and A(10,6,2)S. Traverses for 

z/d = 1 in A-size were not obtained because the narrow channel height required 

such a small diameter probe that the orifice diameter required in the side 

wall of the probe would have been excessively small. In Fig. 3.3, the 

A(10,8,3)1 configuration is choked across all holes at Ej = 21K (compare 

1.0 I I I I I I I I I I I I 

q oooo 

0 A (10.8.311 

0 A (IO, 6.2)s 

d = 0.0635 cm 

Probe Orifice Facing Side 

t 

0 0 0 0 

0.4 O 0 0 

t 

Nominal To =3OOk 

0.3 Nominal @ = 96kFu 

0 

0 

0 

0 

cl 

0 

Rej q 5.3 k 

0 

17.4 k 

0 

2l.Ok 

0 

PO = IlPkPa 

0 0 0 

269 kPo - 

El q 0 

308 k PO 

0 0 0 

0.21 + ’ + I + ’ 4 1 1 1 1 1 1 1 4 1 1 1 4 1 I I 

0 I 2 3 4 5 6 7 8 9 IO II I2 

X/X” 

Fig. 3.3 Channel pressure traverses for two A-size geometries. 

16 
-_ ..-d’-‘-‘. . 

._ -,.I -... . _.,’ ‘. 

-~ 

Fig. 3.11, and the A(10,6,2)S configuration shown for Ej = 17.4K apparently 

becomes choked at the last row of holes. 

It should be emphasized that the choked flow conditions occurred only for 

the smaller hole diameters at the larger jet Reynolds numbers. This results 

from the low laboratory pressure levels and the resulting relatively large 

pressure drops required for these cases. The effects of these conditions on 

the heat transfer coefficients were noted in a previous report 121 and will be 

referred to again in the heat transfer and correlation sections of this 

report. 

A discharge coefficient for each jet plate was determined from a separate 

test conducted with the plenum/jet plate assembly removed from the test plate 

unit and discharging directly to the laboratory environment at atmospheric 

pressure. Plenum pressure and temperature were measured to calculate the 

ideal flow rate, assuming one-dimensional isentropic compressible flow, while 

the actual flow rate was determined via the standard sharp edge orifice in the 

flow metering section upstream of the plenum. Discharge coefficients were 

measured over a range of Rej spanning that for which data was obtained in the 

heat transfer tests. In most cases at least 16 points were taken spread over 

the necessary range. The results for jet plate E(5,8)1 for which the largest 

number of points was taken are shown in Fig. 3.4. These CD values are 

CD 

1.00 I I I IIIll( I I I IIIIIBE,811 CD = 0.80 

0.80 - 0 O 0 oooao&o~ 

00° 

0.60 I I I IIIII I I I Illll 

IO3 IO' IO5 

Rej 

Fig. 3.4 Jet plate discharge coefficient as a function of jet Reynolds 

number. 

17 
- ‘_ 

.:. -:_ .- ..- ..l 

essentially independent of Rej over the range 2.5~10~ to 5~10~. The mean 

values of CD for each jet plate are listed in Table 2.1. These values were 

used in determining the flow distributions. While discharge coefficients for 

individual holes were not determined, each jet plate was checked for flow 

uniformity with very satisfactory results as detailed in [2l. 

3.2 Flow Distribution Results 

The distribution of the jet flow as calculated from the pressure traverse 

and discharge coefficient results is illustrated by the data points plotted in 

Figs. 3.5, 3.7, and 3.8. The ordinate, Gj/gj, represents the jet mass 

velocity for the individual spanwise rows normalized by the mean of the 

individual values over all ten rows. The points for the crossflow parameter, 

G,/Gj t corresponding to those for Gj/Ej in Fig. 3.5, are plotted in Fig. 3.6 

[excepting the C(5,6,1)1 case, omitted for clarity]. The crossflow velocity, 

G C’ immediately upstream of a given row was determined by summing the 

individual row jet flow rates upstream of that row. In these Figures the 

vertical arrows along the abscissa indicate the row locations. Results are 

included for various mean jet Reynolds numbers and configuration sizes, and 

span the range of geometric parameter values. For ten of the twelve cases 

shown in these Figures the sum of the flow rates over all rows closed to 

within 3% or better of the total flow rate measured upstream of the plenum. 

For the remaining two cases one closed within 4%, the other within 6%. The 

better mass closures tended to occur for the higher flow rates for which the 

pressure drops across the holes were larger. 

The curves in these Figures are based on the one-dimensional model 

presented in the next sub-section. The agreement is quite satisfactory. Some 

flow distribution test results obtained exhibited less precise and consistent 

agreement with the model than those displayed in Figs. 3.5 through 3.8. In 

general, however, the mass closures were also less satisfactory for such cases 

indicating increased uncertainty associated with the pressure traverses. The 

model leads to the result that the flow distribution is independent of the 

streamwise hole spacing, x,/d, depending, for a given discharge coefficient 

and number of rows, only on the geometric parameter (y,/d)(z/d). This result 

18 

--- ..-- -_---. - _: -.- --_~_ .-,-.- -. --.---.-, 

. - 

-. 

‘! 

. 

I 
0 B(5,4,l)I 

IS C (5, 6, I)1 

A B (5, 4,211 IO. 0 K 

Cl B (5,4,3)1 

V B (5,8,3)1 

0 t ItI I It I+ I I I I I c Ii 14 I!I 

0 I 2 3 4 5 6 7 8 9 IO 

X/X” 

Fig. 3.5 Streamwise distribution of jet velocities-- 

Comparison between measured values and model, Eq. (3.7). 

is corroborated by the data of Figs. 3.5 through 3.7. The range of this 

parameter covered in Figs. 3.5 and 3.6 matches that for the heat transfer 

tests. For the largest value, 24, the distribution is essentially uniform 

(Fig. 3.5) with a corresponding linear increase in the crossflow parameter, 

G,/Gj (Fig, 3.6). For the smallest value, 4, the distribution is highly 

nonuniform with the jet velocity as small as one-half the mean at the first 

row, and as large as twice the mean at the tenth row: Gc/Gj increases linearly 

upstream but levels off quickly downstream to a maximum value of about 0.75. 

The streamwise flow distributions are also independent of whether the 

hole pattern is inline or staggered as indicated by Fig. 3.8. This Figure 

includes a comparison for the (5,4,3) configuration. This configuration, with 

the smallest hole spacings and largest channel height, exhibited the most 

19 

- -~-_ - 
Loor I 1 I I I I I I I 

o-B8(5,4,1)1 

A- 8(5,4,2)1 

Yn z ( 7-d >( > 

6 

X/X” 

Fig. 3.6 Streamwise distribution of crossflow-to-jet velocity ratio-- 

Comparison between measured values and model, Eq. (3.8). 

significant differences in heat transfer coefficients of all configurations 

tested, when inline and staggered hole patterns were compared C2,3,41. These 

differences cannot be attributed to differences in individual spanwise row jet 

Reynolds numbers because the streamwise flow distributions are the same 

(Fig. 3.8). Rather, as previously discussed [2,31, it is suggested that the 

observed differences in heat transfer coefficients are due to differences in 

the spanwise distribution of the crossflow which develop as one proceeds 

downstream along the channel. This point will again be referred to in the 

heat transfer and correlation sections of this report. 

3.3 Flow Distribution Model 

The discrete hole array is imagined to be replaced by a surface over 

which the injection is continuously distributed (Fig. 3.9). The jet velocity 

Gj is related to the continuously distributed injection velocity G! through 

the open area ratio, G? = GjAz. Thus, assuming incompressible flow, the 

20 

- ---A. -- 

l_. ._ -. . - . .._ - -__ 
0 B(5,8,l)I 

Cl B(10, 8,l) I 36.8K 

A D(15, 8, I) I 

0 I 2 3 4 5 6 7 8 9 IO 

21 

_~. -_ --I__~- -_ ._. _ -----'.., --.- .' .:. -;,. ,: ,, 

-; -: _ .-- 

. 

x/x, 

Fig. 3.7 Effect of streamwise hole spacing on streamwise distribution of jet 

velocities. 

distributed injection velocity may be written in terms of the discrete hole 

discharge coefficient as 

63 = A*, CD [2p(P,- P)]1/2 (3.1) 

The streamwise pressure gradient in the channel is assumed to be primarily due 

to the acceleration of the flow caused by the injected fluid, with negligible 

influence of the wall shear. Accordingly, a force-momentum balance on the 

control volume indicated in Fig. 3.9a results in 

2G,dG, 

dP = - (3.2) P 
-. 

_- -. 

~ 

. . .:-, 

__-. - .--;--.-.LL ..1-1- .- . L.. :. _ . . 

2.41 I I I I I I I I I 

B&4) Nominal Rej = IOK z/d= I 

2.0 0 lnline 0 

0 Staggered 

- Model / 

6- 

2- 

Fig. 3.8 Effect of inline vs. staggered 

distribution of jet velocities. 

6 7 8 

hole pattern on 

9 IO 

streamwise 

A mass balance leads to 

*= % 

Gj '- dx (3.3) 

For constant CD and PO, the elimination of Gs and P from (3.11, (3.21, and 

(3.3) in favor of G, yields 

d2Gc 

- - WG, = 0 dx2 (3.4) 

where N = flAz CD/Z. The upstream boundary condition is G, = 0 at x = 0. A 

second boundary condition results from an overall mass balance for a channel 

length L written in terms of the overall mean injection velocity: i.e., 

G, = 6TL/z at x = L. Integration of (3.4) then gives 

22 

-----~_- 

. . - . . . . 

; .- ‘,’ 1. .‘. ---- - --. - .- 

: :.a .:. I. 
Fig. 3.9a Continuous injection model. 

Gi 

Fig. 3.9b Discrete hole injection model. 

23 
Gc L sinh Wx 

q = z sinh ML (3.5) 

for the crossflow distribution. The corresponding injected flow distribution 

obtained from (3.3) with the aid of (3.5) is given by 

63 ML cash Mx 

fjF= (3.6) 

J sinh ML 

The discrete hole array jet velocity distibution is determined from (3.6) 

by assuming that the value of Gj for a given spanwise row of holes is that 

corresponding to G!(x) with x evaluated at the centerline of the row. For 

the uniform rectangular arrays of interest here A: = (~/4)/[(xn/d)(yn/d)I, 

L = xnNc, and the first row is at x = x,/2. Noting also that “3 = EjAg, the 

jet velocity distribution based on (3.61, may be written as 

Gj PN, cash J3(x/xn) 

-= 

Gj sinh I3 N, (3.7) 

where 

p = cD~(,/4)![(y,/d)(z/d)I 

and 

x = xn(i-l/2) i = 1,2,3 . . .N, 

Besides the jet array velocity distribution given by (3.71, an additional 

flow parameter relevant to the correlation of the streamwise resolved heat 

transfer coefficients is the ratio of the crossflow velocity immediately 

upstream of a given spanwise row to the jet velocity of that row. This may be 

satisfactorily approximated utilizing G, from (3.5) evaluated one-half a hole 

spacing upstream of the given row (Fig. 3.9b), divided by Gj from (3.7). This 

results in 

Gc 1 sinh p(x/x,-l/2) 

-= m Gj Gosh p(x/xn) (3.8) 

where the spanwise hole row locations are the same as previously indicated 

following (3.7). 

24 
The curves shown in Figs. 3.5, 3.7, and 3.8, previously discussed, are 

based on Eq. (3.7). Those shown in Fig. 3.6, also previously discussed, are 

based on Eq. (3.8). 

The model developed above is similar to that presented by Martin 1111 for 

an array of slot nozzles in which the outlet flow is constrained to exit 

parallel to the slots. The present results, as illustrated by Figs. 3.5 

through 3.8, indicate the applicability of this type of model for discrete 

hole arrays as well, at least over the range of parameters covered by the test 

program. 

Though the model is based on the assumption of an incompressible flow, 

Eqs. (3.7) and (3.8) apply satisfactorily for the present geometries even when 

pressure ratios are such that the flow is choked across the holes or nearly 

so. This occurred only for geometries having the largest spanwise spacings 

and channel heights, (yn/d,z/d) = (8,3), and then only for the larger flow 

rates and smaller hole diameters. In these cases the jet flow distribution 

predicted by the model is uniform [Fig. 3.5, (y,/d)(z/d) = 241 to within a few 

percent. Thus, it essentially matches the uniform experimentally determined 

distributions which result when the flow is choked across all the holes. 

25 
4. HEAT TRANSFER COEFFICIENTS 

Both mean and streamwise resolved heat transfer coefficients for jet 

plate configurations summarized in Table 2.1 were previously presented and 

discussed as a function of mean jet Reynolds number and geometric parameters 

C2,3,41. Heat transfer coefficients resolved to one or two streamwise hole 

spacings [2,4] and to one-third the streamwise hole spacing [2,3] were 

considered. The heat transfer test plate (impingement surface) was 

isothermal. Experimental procedures and data reduction techniques were 

outlined in 141 and were further detailed in [Z], which includes a complete 

tabulation of mean and resolved Nusselt numbers. In reducing the data, the 

resolved heat transfer coefficients were defined in terms of the difference 

between the impingement surf ace temperature, T,, and the corresponding 

adiabatic wall (recovery) temperature, T,. This was essential in determining 

heat transfer coefficients from the test results, since for some geometries, 

especially at the higher flow rates, the difference between T, and the plenum 

air temperature, To, was quite significant compared with the surface-to-plenum 

air temperature differences (T, - To) at which the tests were conducted 

(normally 15 to 3OK). For the gas turbine application, however, conditions 

are such that one may take T, E To, since (T, - To) is negligible compared 

with (T, - To). Therefore, knowledge of the heat transfer coefficient and the 

surface and plenum temperatures is adequate for calculating heat fluxes in 

this anticipated application of these results. 

The present objectives are to examine the heat transfer coefficients 

resolved to one streamwise hole spacing as a function of the associated 

spanwise row jet velocity, crossflow velocity, and geometric parameters; and 

to achieve a correlation in terms of these quantities. Thus, we consider 

h = f(Gj,Gc,xn,Yn,zsd) 

or in dimensionless form, taking account also of relevant fluid properties, 

NU = f(Rej, Gc/Gj, Pr, x,/d, ynId, z/d) (4.1) 

Since the flow distribution model presented in the previous section was 

well supported by the flow distribution data, this model was used for 

26 
determination of Rej and Gc/Gj. It should be emphasized, however, that only 

the distribution of Rej relative to the mean, i.e., Rej/Kj = Gj/gj was 

determined from (3.7). The mean values were taken from the sharp-edge orifice 

total flow rate measurements upstream of the plenum since they are more 

accurate than the sum of the individual row flow rate measurements. 

The maximum nominal range of REj for which heat transfer data was 

obtained was 5~10~ to 5x104, though the full range was not covered for every 

individual geometry. Considering the geometries with the most highly 

nonuniform flow distribution, (yn/d)(Z/d) = 4, the maximum nominal range of 

Rej was 2.5~10~ to 1.75~10~ for RO\Y 1 (Gc/Gj = 0) and 104 to 7~10~ for ROW 10 

(G,/Gj g 0.75). For the most nearly uniform flow conditions, 

(y,/d)(z/d) = 24, the Rej range for all IOWS (0 i Gc/Gj L 0.28) was 

essentially the same as the range for Rej. 

Normally, for a given configuration, heat transfer coefficients were 

obtained for three values of Ri?j over its range. However, in some cases data 

were obtained at four or five values while for a few of the C-size geometries 

data were taken at just two values. Least squares Rower function fits of the 

form N" = A Re? 

were applied separately to individual data sets, with A and m 

permitted to be adjustable constants for each set. A data set for this 

purpose consisted of the measured Nu values at each Reynolds number for a 

given geometric size, (x,/d,y,/d,z/d), hole pattern, and spanwise row. 

Ninety-five percent of the data points deviated from these fit lines by less 

than 3%, 99% by less than 4%, and 100% by less than 9%, which compares quite 

favorably with the estimated uncertainty for the Nu data which was 25% for 95% 

confidence 121. Thus, the confidence which may be placed in interpolated data 

points based on these individual fits may be considered as good as that for 

the original data points. Results based on these fits were used in examining 

the effects of geometric parameters and crossflow at fixed values of Rej as 

discussed in the paragraphs below. 

Examination of Fig. 4.1"' indicates that Nuz, for which Gc/Gj = 0, 

decreases significantly with both x,/d and yn/d for fixed Rej. The points 

*The points for each specific hole spacing combination (x,/d, y,/d) are drawn 

from the same geometric sizes (B, C, or D) identified in Fig. 4.2. 

27 
7c 

;> 

I I 

Re- = IO 4 

J t/d 

0 -I 

60 B 13 -2 

!i! A -3 

0 

50 A x,/d 

83 

O 5 

% !z! 

40 

I 

6 

y,/d 

Fig. 4.1 Effect of geometric parameters on Nusselt number for initial 

upstream row of array (Gc/Gj = 0). Inline hole pattern. 

shown are for Re- = 104; J however, the trend with geometric parameters is 

similar over the Rej range of the tests. The sensitivity to z/d is quite 

small except for the highest hole density configuration, (x,/d,y,/d) = (5,4), 

where Nu, for z/d = 1 is significantly larger than the values for z/d = 2 and 

3. This is not a spurious data point because the data for the corresponding 

geometrically similar sizes corroborate this behavior. The trend of Nu, with 

z/d is decreasing for small values of x,/d and y,/d, but increasing for large 

values. This type of behavior tends to work against development of a tight 

correlation of simple form. 

28 

__- - ---- 

. . _ . .; .- _- - - ‘. 
4.1 Effect of Crossflow 

The matrix of plots in Fig. 4.2 shows the effect of the crossflow 

parameter, Gc/Gj, on Nu where Mu is normalized by Nu,. Each plot presents 

results for z/d = 1,2, and 3 for a single hole spacing combination (x,/d, 

Yn/d) l The data shown in each plot are for the smallest geometric size 

tested for that combination (excluding A-size for which Nu could not be 

resolved to one streamwise spacing). All points are for Rej = 104 but in this 

normalized form are representative of the general trends over the full Rej 

range. 

The trend of Nu/Nu, with G,/Gj shifts from a monotonic decreasing 

function to a form which exhibits a broad minimum as xn/d and y,ld increase, 

and as z/d decreases. Thus, for x,/d 1 10, yn/d 1 6, z/d = 1, and 

G,/Gj 2 0.4, Nu/Nu, increases slowly. A plausible explanation for this 

behavior, consistent with the fact that it occurs for large hole spacings and 

small channel heights, is that the crossflow provides an increasingly 

significant direct contribution to the heat transfer rate but does not cause a 

large degradation in the direct contribution from jet impingement. It may be 

remarked that results for heat transfer coefficients resolved to better than 

one streamwise hole spacing indicate that for these geometries the jets still 

impinge on the surf ace at the final downstream row: and, indeed, the 

impingement point is deflected downstream only a small fraction of the hole 

spacing 12,31. This inference is further corroborated by observations of 

discoloration patterns made subsequent to these test runs on the copper heat 

transfer surface. These observations clearly indicate impingement of all jets 

with only slight deflection even at the final downstream row. In contrast, 

for smaller hole spacings and/or larger channel heights the jets are deflected 

and diffused more by the crossflow, and though they still impinge on the heat 

transfer surface, their cooling effectiveness is more significantly reduced. 

At the same time there is less surface area available for direct cooling by 

the crossflow. 

The effect of increasing z/d, where significant, is to decrease NnlNu, at 

fixed G,/Gj. This trend is consistent with the results of Metzger and Korstad 

Cl21 for a single row of jets tranverse to a crossflow. The sensitivity of 

29 
.’ ’ 

I I 

17-L -’ 

I 

-*1 

1.0 I I 

-El 

I I 

0.8 - agdh 

mA' F!,A~~~ __ 

QBshl0a 0 000 -oaf% 0 000 

0.6 - B(5,4)1 

I I 

C(5,6)1 

I I 

B(5,8)1 

1.0 I 

I 

I 

I I I I I I I 

0.8 - doA e AfP 00 0 0 oo~-q~~g~~u"ouo oooo--~~&)&~uo oooo 

Q,Dh;% A 

0.6 - B(lO,4)1 C(lO,6)1 B(10.811 

1.0 I I I I I I I I I 

I I 

ooooo 0.8 - 

““2 no 

AA 

’ ’ om-_4h0&# && 0 q IJUOO 

AAA~ 

0.6 - 

AAA~ 

q - 2 

m5,4)r D(l5,6)1 D(l5,8)1 A- 3 

na’ I I I I I I I I I I I J 

V. I 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 

G,/Gj 

Fig. 4.2 Effect of crossflolv and geometric parameters on streamwise resolved 

Nusselt numbers emphasizing effect of z/d. Inline hole pattern. 
Nu/Nu, vs G,/Gj to z/d increases with x,/d but decreases with yn/d. Thus, the 

effect of z/d is significant for (x,/d, yn/d) = (15,4), the lower left plot, 

but essentially disappears for (5,8), the upper right plot. Or, stated 

another way the sensitivity of the crossflow effect to z/d appears to increase 

as the aspect ratio xn/yn increases. The complexity of the interacting 

jet/crossflow phenomena in the two-dimensional array precludes arriving with 

high confidence at a particular explanation, at least on the basis of 

currently available information. However, it may be appropriate to note 

several factors which contribute to the complexity, and may be involved in 

potential explanations. 

First, the crossflow velocity appearing in the crossflow parameter Gc/Gj 

as used in characterizing the present results is a mean value over the channel 

cross-section. Consider the distribution across the channel span of the 

crossflow velocity averaged over the channel height. There is some evidence, 

e.g., flow visualization, indicating that for the inline arrays the crossflow 

tends to become channelized between adjacent streamwise jet rows. Thus, the 

spanwise flow distribution would be nonuniform with velocities between jets 

larger than those directly approaching the next downstream jet. The degree of 

nonuniformity would vary with array geometric parameters. Thus ) the crossflow 

velocity immediately upstream of a given jet in an array would be smaller than 

the mean velocity over the cross-section by differing amounts depending on 

array geometry. Heat transfer coefficients obtained during preliminary tests 

with a spanwise uniform initial crossflow approaching the array were smaller 

than those measured following a certain downstream location for the same array 

without initial crossflow, but with total upstream jet flow rate adjusted so 

as to provide the same value of Gc/Gj approaching the downstream location. 

Second, the values of Nu being compared for various (xn/d,yn/dI 

combinations are averages over rectangles of widely varying aspect ratios, 

from xnlyn = 0.625 for the (5,8) case where no z/d effect is apparent to 3.75 

for the (15,4) case where the effect is significant. 

Third, results for potential core length obtained by Stoy and Ben-Haim 

cl51 for a single jet in a confined crossflow indicate that for the present 

range of z/d, impingement may occur for certain jets before they are 

developed, and for others (even in the same array) after they are developed. 

31 
The identical data points plotted in Fig. 4.2 are replotted in Fig. 4.3, 

but rearranged with x,/d rather than z/d as the parameter within each 

individual plot. At z/d = 1 the points for x,/d = 5 fall below those for 

x,/d = 10 which in turn fall below those for x,/d = 15. On the other hand, 

for z/d = 2 and 3, points for x,/d = 5 fall between or above those for 

x,/d = 10 and 15 depending on the value of yn/d. The amount of spread among 

the data points in each plot decreases with increasing yn/d and z/d. Thus, 

the largest spread occurs for (yn/d,z/d) = (4,1), the upper left plot, while 

the spread nearly disappears for (y,/d,z/d) = (8,3), the lower right plot. 

Or, put another way, Nu/Nu is not sensitive to x,/d when yn/d and z/d are 

large, but is sensitive whei they are small. 

4.2 Effect of Hole Pattern 

This effect is illustrated in Fig. 4.4 where Nusselt numbers for 

staggered hole patterns normalized by those for their counterpart inline 

patterns are plotted against the crossflow parameter. The effect is not 

significant for the largest hole spacing, (x,/d,y,/d) = (10,8). However, as 

x,/d and yn/d decrease, and as z/d increases, the staggered pattern results in 

increasingly reduced heat transfer coefficients relative to the inline values 

for increasing crossflow. 

This behavior is thought to be associated with differences in spanwise 

distribution of the crossflow in the two cases [2,31. The tendency of the 

crossflow to become channelized between adjacent streamwise rows of the inline 

pattern reduces the direct influence it can exert on each downstream jet. In 

contrast, the spanwise crossflow distribution presumably remains more nearly 

uniform for the staggered patterns; hence the crossflow approach velocity 

directly upstream of each jet is somewhat larger than for the matching inline 

case. 

4.3 Effect of Jet Plate Thermal Boundary_Condition 

Throughout the major heat transfer test program an isothermal boundary 

condition was utilized at the impingement surface. In general, no provision 

32 
t 

Q r; A A'AA AbA 

00 

a 0 B&%0 

0 0.2 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 

G,/Gj 

Fig. 4.3 Effect of crossflow and geometric parameters on streamwise resolved 

Nusselt numbers emphasizing effect of x,/d. Inline hole pattern. 
1.2 I I I I I I 

I I 

0.6 

t B(l0.4) 

Fig. 4.4 

0.2 0.4 0.6 0 

7 

- 

0.4 0.6 0.8 

Effect of hole pattern (staggered VS. inline) on streamwise resolved 

Nusselt numbers as function of crossflow and geometric parameters. 
was made to idependently control the thermal boundary condition at the exit 

plane of the jet plate: i.e., the channel wall opposite the impingement 

surface. It was not expected that this boundary condition would significantly 

affect the heat transfer coefficients to be determined at the impingement 

surface. However, early in the program it was deemed wise to verify this 

expectation, particularly for the narrowest channel height of z/d = 1. 

‘Accordingly, jet plate A(10,8)1 was fitted with resistance heating wires 

attached to and distributed uniformly over the plenum side of the plate. By 

adjusting the power input to this heating element the channel wall temperature 

at the exit plane of the aluminum jet plate could be controlled independently 

of the impingement surface and plenum air temperatures. 

During the initial heat transfer tests conducted with jet plate A(10,8)1, 

mounted with a channel height z/d = 1, impingement surface heat transfer 

coefficients were measured (at each Reynolds number level) not only with zero 

power input to the jet plate heater (the reference or normal condition) but 

for two finite jet plate heater power input levels: one equal to the maximum 

power input to the impingement surface test plate heaters, and one equal to 

half that value. To within experimental uncertainty the impingement surface 

heat transfer coefficients were unaffected by the power input level to the jet 

plate heater element. 

The special tests utilizing the jet plate heater were discontinued when 

the heat transfer measurements were made for this jet plate at z/d = 2 and 3, 

it being reasoned that if the effect discussed above were negligible for a 

channel height of 1 it would certainly be also for larger channel heights. 

However, the jet plate heater wires were left in place. 

As the test program proceeded and heat transfer data for the larger B, C, 

and D sizes of the (10,811 configuration became available, it was noted that 

the Nusselt numbers for the B, C, and D sizes, compared at the same mean jet 

Reynolds numbers, were, in general, more consistent with each other than with 

the corresponding A-size values. This was detailed in 121 (see, in 

particular, Fig. 4.5 of that report), where it was suggested that some 

differences observed at larger Reynolds numbers may be due to compressibility 

effects, while differences at smaller Reynolds numbers where compressibility 

35 
effects could not be a factor, may be due to effects of turbulence 

characterist its. 

Subsequently, it was decided to rerun several of the A(10,8)1 tests with 

the jet plate heater wires removed, motivated by the thought that the physical 

presence of these wires, originally installed for heating purposes, may be 

affecting the turbulence characteristics of the jets enough to cause 

observable effects on the heat transfer coefficients. Tests conducted at 

z/d = 1 and 3 with the heater wires removed gave results which, for z/d = 1, 

differed from the original A-size results but were now more consistent with 

the corresponding B, C, and D size results. For z/d=3, the results were 

essentially unchanged. 

It was then decided to run a series of comparative tests using the 

A(10,8)1 jet plate with and without wires, now considered as roughness 

elements, in order to further characterize the effects of their presence, 

especially since the initially observed effect was to enhance the heat 

transfer. The results of this series of tests are detailed in the next 

section. 

4.4 Effect of Roughness Elements on-Plenums Sideeof Jet Plate 

As indicated above a series of comparative tests was performed with and 

without roughness elements attached to the plenum side of the A(10,8)1 jet 

plate. The detailed geometry and method of attachment of the elements for 

these tests was patterned after that of the original installation of heater 

wires on this jet plate, since it was the presence of these wires which lead 

to the initial observation of the effect in question. Strips of double-sided 

masking tape were placed between the streamwise rows of jet holes on the 

plenum side of the jet plate. A single 0.0254 cm (0.010 in.) diameter wire 

was placed along each strip positioned midway between adjacent rows. Strips 

of plastic tape were then pressed down tightly over the wires. 

Heat transfer tests were run for z/d = 1, 2, and 3 at nominal mean jet 

Reynolds numbers of 5, 10, and 20K with the roughness elements in place, and 

with the elements removed. The results are compared in Fig. 4.5. Results for 

the cases with the elements removed are denoted as “Standard,’ ’ while those 

36 
I I 

z/d = I 

-1 I 

z/d q 2 

8 

z/d = 3 

I -- I I I I I 

2o 

17 

0 

8 2P 

5 

B 

I _I. I I I I 

0 Roughened - Case I 

A Roughened - Case II 

0 Standard 

v Standard (Repeat 1 

tltltltltltltltltltl 

“0 I 2 3 4 5 6 7 8 9 IO 

X/X” 

Fig. 4.5 Effect of jet plate plenum side roughness elements on Nusselt 

numbers for A(10,8)1 configuration. 

37 
with the elements in place are denoted as “Roughened-Case II.” Results 

from the original A(10,8)1 tests conducted when the original heater wires were 

in place are also included, denoted as “Roughened-Case I. ” Overall there 

is little difference between the standard and roughened cases for z/d = 2 and 

3. Most of the points are consistent to within experimental uncertainty. 

However, for z/d = 1 the Nusselt numbers for the roughened cases are uniformly 

higher than those for the standard case by about 15% over the entire Reynolds 

number range and at all positions along the impingement surface. 

The A-size data for the standard case at z/d = 1 is also more consistent 

with the data for the geometrically similar B, C, and D size cases than is the 

data for the roughened cases. Deviations from least squares power function 

fit lines to the combined data of all four sizes for the (10,811 configuration 

at z/d = 1 were summarized in Table 4.4 of a previous report [al. The A-size 

data considered there was from the original tests with the heater wires in 

place (Roughened--Case I). The corresponding fit lines and deviations have 

since been recalculated with the A-size data replaced by that from the more 

recently obtained data for the standard A-size case (wires removed). The 

relevant portion of Table 4.4 from 121 is reproduced below with the revised 

deviations included in parentheses immediately following the corresponding 

original values. The improved overall consistency for z/d = 1 is reflected by 

Sizes 

Included 

in Fits 

Nusselt Maximum Absolute Percent Total 

Number Deviation for Confidence Level of Number 

z/d (Mean of 

ResEtved) 

Points 

95% 99% 100% Involved 

Nii 14(7) 14(7) 14(7) 13 

1 

Nu(2x,) 18(11) 26(U) 26(11) 65 

Nii 11(9) U(9) H(9) 12 

A, B, C, D 2 

Nu(2xJ 13(12) 14(12) 14(12) 60 

mi 12(12) 12(12) 12(12) 13 

3 

Nu(2x,) 12(12) 16(16) 16(16) 65 

38 
the significantly reduced deviations. The consistency for z/d = 2 and 3 where 

the presence or absence of the wires had little effect remains essentially 

unchanged. 

Garden and Akfirat 1171 observed a significant increase in stagnation 

point heat transfer for small nozzle-to-plate spacings, when screens were 

placed in their slot nozzles immediately upstream of the nozzle exit plane. 

At larger spacings the effect of the screens was much smaller. This behavior 

was attributed to the effect of increased turbulence due to the screens, which 

caused the enhanced heat transfer for the small nozzle-to-plate spacings. 

However, as the spacing was increased, the high levels of turbulence generated 

by the jet mixing began to dominate and the turbulence characteristics 

affecting the heat transfer became independent of the characteristics induced 

just upstream of the nozzle exit plane. Apparently, for the present tests, 

even the presence of the wires attached to the plenum side of the jet plate 

midway between adjacent streamwise jet hole rows increased the turbulence 

levels enough to cause the observed 15% enhancement in heat transfer 

coefficients for z/d = 1, but this effect was suppressed at z/d = 2 and 3 due 

to turbulence generated by jet mixing. 

39 
5. CORRELATION 

Correlation attempts were carried out primarily in terms of the 

variables indicated in Eq. (4.1). Consideration of the number of these 

variables (six in all, excluding Prandtl number 1 coupled with close 

examination of the data indicated the improbability of achieving a really 

tight correlation of simple form. 

As alluded to earlier, least squares fits of the form Nu = A Rey to data 

sets for individual sizes at fixed values of the other parameters (G,/Gj 8 

x,/d, y,ld, and z/a) were excellent, though there was an apparently complex 

but not extremely sensitive variation of m with these parameters. 

The plots in Fig. 4.2, previously examined, indicate that a crossflow 

functional form representing the dependence on Gc/Gj must, in general, be 

sensitive to xnla, y,/a, and z/a; and that the sensitivity to z/d varies with 

x,/a and Ynla. For precise representation such a crossflow functional form 

would have to be monotonic decreasing for most values of x,/d, y,Id, and z/d, 

but for some cases with z/d = 1 would have to allow a broad, shallow minimum. 

Also, as previously discussed, Fig. 4.3 shows that for a given value of 

G,IGj > 0, NuINu, increases monotonically with x,/d, for z/d = 1, but is not 

monotonic with x,ld for z/d = 2 and 3. In general, the form and sensitivity 

of the dependence of both Nu, (Fig. 4.1) and Nu/Nu, (Figs. 4.2 and 4.3) on any 

one of the independent variables can change depending on the values of the 

remaining independent variables for which it is examined. Also note that Fig. 

4.4 indicates a different specific correlation is required for the staggered 

hole pattern, though the same functional form as for the inline pattern may be 

satisfactory. 

A functional form which would properly incorporate in detail all the 

above features, even if it could be determined, would undoubtedly be extremely 

cumbersome and complex. After a number of attempts utilizing forms of varying 

types and complexity, the following form was finally adopted: 

Nu = A Req (1 - ~[(zId)(G,/Gj)ln}Pr113 (5.la) 

where the coefficients A and B, and the exponents m and n are each permitted 

to depend on the geometric parameters in the form of simple power functions. 

40 
That is, 

A, m, B, and n = C(xn/d)nx(yn/d)ny(z/d)nz. (5.lb) 

The form (5.1) was applied separately to the inline and staggered hole 

pattern data for B, C, and D sizes. The analyses were carried out using a 

multivariable nonlinear regression routine with a least squares objective 

function C161. The objective function was based on the logarithm of the 

dependent variable (Nu). In this way, the relative deviations rather than the 

absolute magnitudes were minimized. The resulting best fit values for the 

coefficients and exponents are summarized in Table 5.1 for both inline and 

staggered hole patterns. 

Table 5.1 Constants for Use in Correlation Equation (5.1) 

Inline Pattern Staggered Pattern 

C nX nY nZ C nX nY nZ 

A 1.18 -0.944 -0.642 0.169 1.87 -0.771 -0.999 -0.257 

m 0.612 0.059 0.032 -0.022 0.571 0.028 0.092 0.039 

B 0.437 -0.095 -0.219 0.275 1.03 -0.243 -0.307 0.059 

n 0.092 -0.005 0.599 1.04 0.442 0.098 -0.003 0.304 

The inline correlation, based on a total of 1400 data points, produced a 

standard error of the deviations of 5.6%. By actual count 95% of the points 

fall within 11% of the fit line, while 99% fall within 16%. All the points 

fall within 19%, save one which deviated by 26%. The staggered correlation, 

based on a total of 680 points, produced a standard error of 6.1%. 

Ninety-five percent of these points were within 12% of the fit line, 99% were 

within 161, and all the points fell within 18%, save one which again deviated 

by 26%. The bulk of the points having the larger deviations tended to occur 

for upstream rows for small Rej at z/d = 1. 

41 

- 
In an earlier report 121, the degree of consistency of the results 

obtained for geometrically similar configurations was assessed in detail. 

Least squares fits in the form Nu = A Rey were carried out for the combined 

data of the several sizes for each set of geometrically similar 

configurations. In effect, A and m were permitted to be adjustable constants 

taking different best fit values for each parameter set ~x,/d,y,/d,z/d~ and 

each spanwise row number (i.e., each value of G,IGj). Ninety-five percent of 

the points were within 7% of the respective fit lines, 99% were within 10%, 

and all were within 14%. These percentages give some indication of the best 

that might be done if the optimum functional form were to be found. Viewed in 

this context the proposed correlations appear to be quite acceptable. 

Correlation lines calculated from Eq. (5.1) using values of the constants 

summarized in Table 5.1 are compared individually with the data for each 

inline geometry in Fig. 5.1 for z/d = 1, Fig. 5.2 for z/d = 2, and Fig. 5.3 

for zIa=3. In each individual graph of these Figures the shaded area 

represents the envelope of all data points for that geometry. The legend in 

each graph indicates the geometric sizes included, the geometric parameter 

values, the overall jet Reynolds number range, and the total number of points. 

The ordinate is the Nusselt number resolved to one streamwise hole spacing 

normalized by the value for the first upstream row Nu,, at which G,/Gj = 0. 

It should be emphasized that in preparing these plots the experimental values 

for Nu were normalized by the corresponding values of Nu, as calculated from 

the correlation equation. With corresponding correlated and experimental 

values of Nu normalized by the same value of Nul, a true comparison between 

the correlation and the data is maintained. It may also be emphasized that 

while the correlation is compared individually for each geometry in Figs. 5.1 

through 5.3, the correlation itself is based on the data for all geometries. 

Obviously, improved correlations w0da result if limited to a single geometry. 

Overall the correlation appears to do an excellent job for z/d = 2 and 3 

(Figs. 5.2 and 5.31, and an adequate job for z/d = 1 (Fig. 5.1). 

me data for the A-size geometries listed in Table 2.1 were excluded from 

the data sets relied on for correlation for two reasons. First, the maximum 

heat transfer coefficient resolution for these data was two rather than one 

streamwise hole spat ings . Second, as previously pointed out 12,41, 

42 
. . . . ““.. . . . . . . . . 

0.6- 

B.C,D (5,4, I) I C(5,6,1 )I B,C(5,8.I)I 

0,4- 2.5K < Rej < 70K - 3.6K < Rej < 30K -- 3.8K< Rej < 26K 

< 90 points < 20 points < 50 points < 

0. I I I I I I I I I 

0.6 - 

D(l5,4,I)I 

0.4 _ 2.5K < Rej < 70K _ 3.4K< Rej <29K 

G, /Gj 

Fig. 5.1 Heat transfer correlation Eq. (5.1) compared with data for 

individual inline jet plate geometries, da = 1. 
0.6 - 

B,C,D (5,4,2) I C(5,6,2)1 B,C(5,8,211 

0.4 _ 3.9K < Rej < 46K -- 

< 80 points 

4.6K < Rej <22K 

< 20 points 

-- 4.6K<Rej <23K 

< 

0 I I I I I I 

5 50 points 

I I I 

: .;:.. 

zit 

z 

0.6- 

B,C,D (10,4,2)1 C(lO,6,2)1 

z 

B.C.D(l0,8.2)1 

__ 5.5KC Rej <22K _- 

5 30 points 

4.4K < Rej < 57K 

I 

<, 90 points 

I I I 1 I 

I 

0.6 

D(l5,6,2) I D(l5,8,2)1 

_ 4.3K<Rej<2lK __ 

( 20 points 

4.6K< Rej < 55K 

r’ 

( 30 polnts 

I I I r I I I 

0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 

G, /Gj 

Fig. 5.2 Heat transfer correlation Eq. (5.1) compared with data for 

individual inline jet plate geometries, da = 2. 
C (5,6,3) I 8,C (5,8,3) I 

0.4 - 4.4K < Rej < 40K -- 5.8K< Rej < 20K -- 4.5K< Rej < 21K 

90 points 20 points 60 points < 

I I I I I I I I I 

C(10,6,3)1 B.C.D(10,8,3) I 

0.4 _ 4.2K < Rej < 40K 

< 90 points 

-_ 5.2K<Rej <2lK 

30 points 

__ 4.6K< Rej <55K 

90 points 

0 I I I I I I I I I 

I 

1. 

:. 

D(l5,4,3)1 

o.4- 4.3K< Rej <4lK 

30 points 

I I 

0 0.2 0.4 

I 

0.6 

D(l5,6,3) I D(l5,8,3)1 

__ 4.4K< Re j < l8.5K __ 4.6K < Rej < 56K 

20 paints 30 points 

I I I I I I 

0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 

G, /Gj 

Fig. 5.3 Heat transfer correlation Eq. (5.1) compared with data for 

individual inline jet plate geometries, z/a = 3. 
compressibility effects were present for these cases at the higher Reynolds 

numbers. This was due to the relatively low laboratory temperature and 

pressure levels at which the tests were run, combined with the small hole 

sizes and channel heights for A-size, resulting in pressure drops which were 

quite large relative to the pressure levels. This leads in some cases to 

choked flow conditions (see, e.g., Fig. 3.3). 

The pressure and temperature levels in the anticipated turbine 

application are much higher with correspondingly lower Mach numbers. 

Therefore, considering the full range of Reynolds numbers, it is expected that 

the present data for sizes larger than A-size best model the prototype heat 

transfer characteristics for the gas turbine engine application. Many 

applications which, in fact, operate at low pressures utilize larger hole 

sizes and channel heights than for the present A-size. Thus ) neither are 

compressibility effects present to a significant degree in these applications. 

It is of interest, nevertheless, to compare the A-size data with the 

correlation. This was done for Nu resolved to 2x,. Despite the Mach numbers 

for some of these cases approaching or equal to unity, 95% of the points still 

fall within 16% of the correlation, with only one of 140 points deviating by 

more than 20% to a value of 27%. (The data used for the A(10,8,1)1 case are a 

revised set recently obtained, which is more consistent with the corresponding 

B, C, and D size data than the original set documented in 121 and reported in 

141. This is the data obtained with no wire roughness elements present on the 

plenum side of the A(10,8)1 jet plate, which was presented and discussed in 

Section 4.4.) 

In developing the correlations, 50 data points for the highest flow rates 

for several B-size configurations (TGj from 2.6 to 5 .3x104) were also omitted 

because choked or nearly choked flow occurred (see, e.g., Fig. 3.1). However, 

when compared with the correlation 95% of these points are within 1540, the 

largest deviation being 18%. 

Prior heat transfer measurements involving two-dimensional arrays of 

circular orifices in which the orifice plate and the heat transfer surface 

form a channel of uniform height with flow constrained to exit in a single 

direction parallel to jet hole rows were reported by Friedman and Mueller 151, 

Huang C61, Kercher and Tabakoff [7], and Chance 181. These studies reported 

46 
mean heat transfer coefficients for the entire surface opposite the array 151, 

or values for spatial resolutions greater than or equal to one streamwise hole 

spacing C6,7,81. Only Kercher and Tabakoff, and Chance measured streamwise 

flow distributions and suggested correlations for streamwise resolved heat 

transfer coefficients in terms of individual spanwise row jet and crossflow 

velocities. Kercher and Tabakof f’s study included measurements for 16 

different combinations of hole spacing and channel height. Only two of these 

combinations provided streamw’ise resolutions down to one streamwise hole 

spacing, and these had just four rows of holes. All were inline arrays with 

an aspect ratio (x,/y,) of unity. Their correlation requires use of three 

graphical presentations. Chance tested square, equilateral triangular, and 

rectangular arrays, but did not report specific hole spacings or numbers of 

holes for his jet plates, nor does his correlation include any distinction 

based on hole pattern. 

Values of Nu, based on the present correlation are compared with those 

based on the Kercher and Tabakoff correlation in Fig. 5.4. The comparison is 

for square, inline arrays at the extreme values of the geometric parameters 

which fall within the ranges covered by both investigations. Results based on 

the correlation of Chance are also shown for cooling of the surface by the 

jets, which is the same condition under which Kercher and Tabakoff’s and the 

present data were obtained. Chance’s correlation for data with heating of the 

surface falls 1Wo above that shown in the Figure. The effect of crossflow as 

calculated from these same correlations is compared in Fig. 5.5 for the same 

geometries as Fig. 5.4. 

Permitting both the coefficients and exponents in Eq. (5.la) to depend on 

the geometric parameters provided the flexibility to achieve a reasonably 

tight overall correlation. This correlation is recommended for detailed 

analysis and design calculations, particularly when incorporated in computer 

programs where the larger number of specified constants is not a disadvantage. 

An alternate correlation, more convenient for hand computation or 

examination of trends, is presented below. This correlation is of the same 

form as (5.la), but with exponents m and n not permitted to depend on 

geometric parameters: 

47 
NulNu, = 1 - C(xnld)nx(yn/d)ny(z/d)nz(Gc/Gj)n (5.2a) 

where 

and the constants in (5.2a) take the following values: 

C nX nY nZ n 

In1 ine 0.596 -0.103 -0.380 0.8?3 0.561 

Staggered 1.07 -0.198 -0.406 0.788 0.660 

This correlation is essentially as good as that of Eq. (5.1) in terms of 

standard error and 95% confidence levels, but is not as tight overall. 

2 

IO2 

a 

6 

Nul 5 

4 

I03 

I I III, I I 

Present Work 

--- Kercher & Tabakoff / * 

--- 

z/d Chance 

(x, id, y,/d) 

4 5 6 a 

Re j 

2 3 

Fig. 5.4 Nusselt number for initial upstream row of array-- 

Correlations compared. 

48 
-- - Chance 

0.4 I I I I 

0 0.4 0.8 1.2 1.6 

Fig. 5.5 Effect of crossflow on streamwise resolved Nusselt numbers-- 

Correlations compared. 

49 
6. CONCLUSIONS 

Experimentally determined heat transfer characteristics have been 

presented for jets of air issuing from arrays of circular orifices and 

impinging on a surf ace parallel to the jet orifice plate. Following 

impingement the air is constrained to exit in a single direction along the 

channel formed by the orifice plate and the impingement surface. Outlet flow 

from upstream jets imposes a crossflow on those downstream. The 

configurations tested model those of interest in current and contemplated 

designs for cooling of the midchord region of gas turbiine airfoils. Uniform 

rectangular hole patterns of both inline and staggered arrangements were 

included in the test program. Streamwise resolved, spanwise averaged heat 

transfer coefficients were measured for an isothermal impingement surface. 

Discharge coefficients for the jet orifice plates, as well as streamwise 

variations of the jet and channel crossflow velocities for the various 

configurations were also experimentally determined. 

Streamwise hole spacings ranged from 5 to 15 jet hole diameters for 

inline patterns and 5 to 10 diameters for staggered patterns, spanwise 

spacings were 4 to 8 diameters, and channel heights (jet plate-to-impingement 

surface spacings) were 1 to 3 diameters. Hole pattern aspect ratios (ratio of 

streamwise-to-spanwise hole spacing) ranged from 0.625 to 3.75. The number of 

spanwise rows of jet holes was fixed at 10 for all configurations. Mean jet 

Reynolds numbers ranged from about 5~10~ to 5x104. Overall, individual 

spanwise row jet Reynolds numbers were as low as 2.5~10~ and as high as 7x104. 

The ratio of the channel crossflow velocity to the jet velocity ranged from 

zero (at the first upstream row) to as high as 0.8 downstream. 

Conclusions reached are as follows: 

(1) A simple one-dimensional, incompressible, momentum-flux model was 

found to satisfactorily predict the experimentally determined streamwise 

distributions of jet and channel crossflow velocities. 

50 
(2) Impingement surface heat transfer coefficients resolved in the 

streamwise direction to one streamwise hole spacing, averaged across the 

span, were satisfactorily correlated with the associated individual 

spanwise row jet and crossflow velocities, and with the geometric 

parameters. Separate correlations were required for the inline and 

staggered hole patterns, since the staggered patterns resulted in smaller 

heat transfer coefficients than their in1 ine counterparts as hole 

spacings were decreased and channe 1 height was increased. The 

correlations are, however, of the same form. Overall, 95% of the total 

of 2080 data points on which the correlations are based fall within 11% 

of the corresponding values predicted by the correlations. 

(3) Jet plate discharge coefficients were found to be relatively 

insensitive to jet Reynolds number over the ranges covered. Mean values 

for individual jet plates ranged from 0.73 to 0.85. The mean value 

considering all jet plates was 0.79. 

(4) Streamwise jet flow distributions ranged from highly nonuniform for 

a spanwise hole spacing of four hole diameters and a channel height of 

one diameter to essentially uniform for a spanwise spacing of eight 

diameters and a channel height of three diameters. The distributions 

were essentially independent of streamwise hole spacing and hole pattern 

(inline vs. staggered). 

(5) Nusselt numbers varied with jet Reynolds numbers raised to a nominal 

power of 0.73. 

(6) For a fixed jet Reynolds number and geometry the effect of 

increasing crossflow was to monotonically decrease the heat transfer 

coefficients, except for geometries having both larger hole spacings and 

channel heights of one hole diameter. In these latter cases decreases in 

heat transfer coefficients were followed by small increases, exhibiting a 

broad minimum over an intermediate range of crossflow-to-jet velocity 

ratios. 

51 
(7) Reduced values of heat transfer coefficients for staggered hole 

patterns relative to their inline counterparts are due to differences in 

the spanwise distribution of the crossflow. The crossflow for inline 

patterns tends to be channelized between adjacent streamwise jet rows, 

whereas for staggered patterns the crossflow is more nearly uniform 

across the channel span. 

(8) The impingement surface heat transfer coefficients were independent 

of the thermal boundary condition existing at the surface of the jet 

plate which coincides with the orifice exit plane (the channel wall 

opposite the impingement surface). 

(9) Roughness elements (wires) attached to the plenum side of one of the 

jet plates, midway between streamwise jet hole rows, increased the heat 

transfer coefficients by about 15% for the narrowest channel height of 

one hole diameter. The wires were originally installed for use as 

heating elements to control the jet plate surf ace thermal boundary 

condition resulting in conclusion (8) above. 

(10) Caution should be exercised in applying the flow distribution model 

and the heat transfer correlations beyond the parameter ranges for which 

they have been verified. 

(11) At the relatively low laboratory pressure levels at which the tests 

were conducted choked or nearly choked flow across the jet orif ices 

occurred in several cases with small hole diameters at large flow rates. 

This heat transfer data was excluded from that on which the correlations 

are based. Nevertheless, 95% of these data points fall within 15% of the 

correlation. 

52 
REFERENCES 

1. Gauntner, J.W., Gladden, H.J., Gauntner, D.J., and Yeh, F.C., "Crossflow 

Effects on Impingement Cooling of a Turbine Vane," NASA TM X-3029, March 

1974. 

2. Florschuetz, L.W., Metzger, D.E., Takeuchi, D.I., and Berry, R.A., 

Multiple Jet Impingement Heat Transfer Characteristic -- Experimental 

Investigation of Inline and Staggered Arravs with Crossflow, NASA 

Contractor Report 3217, Arizona State University, Tempe, January 1980. 

3. Florschuetz, L.W., Berry R.A., and Metzger, D.E., '*Periodic Streamwise 

Variations of Heat Transfer Coefficients for Inline and Staggered Arrays 

of Circular Jets with Crossflow of Spent Air," ASME Journal -- of Heat 

Transfer, Vol. 102, 1980, pp. 132-137. 

4. Metzger, D.E., Florschuetz, L.W., Takeuchi, D.I., Behee, R.D., and Berry, 

R.A., "Heat Transfer Characteristics for Inline and Staggered Arrays of 

Circular Jets with Crossflow of Spent Air," ASME Journal of Heat 

Transfer, Vol. 101, 1979, pp. 526-531. 

5. Friedman, S.J., and Mueller, A.C., "Heat Transfer to Flat Surfaces," 

Proceedinps, General Discussion on Heat Transfer, The Institute of 

Mechanical Engineers, London, England, 1951, pp. 138-142. 

6. Huang, G.C., "Investigations of Heat Transfer Coefficients for Air Flow 

Through Round Jets Impinging Normal to a Heat Transfer Surface," m 

Journal of Heat Transfer, Vol. 85, 1963, pp. 237-243. 

7. Kercher, D.M., and Tabakoff, W., "Heat Transfer by a Square Array of 

Round Air Jets Impinging Perpendicular to a Flat Surface Including the 

Effect of Spent Air," m Journal of Engineering for Power, Vol. 92, 

1970, pp. 73-82. 

8. Chance, J.L., "Experimental Investigation of Air Impingement Heat 

Transfer Under an Array of Round Jets," Tanpi, Vol. 57, No. 6, 1974, pp. 

108-112. 

9. Gardon, R., and Cobonpue, J., "Heat Transfer Between a Flat Plate and 

Jets of Air Impinging on It," International Developments in Heat 

Transfer, Proceedinps of 2nd International Heat Transfer Conference, ASME, 

New York, 1962, pp. 454-460. 

10. Hollworth, B.R., and Berry, R.D., "Heat Transfer from Arrays of Impinging 

Jets with Large Jet-to-Jet Spacing,'* ASME Journal -- of Heat Transfer, Vol. 

100, 1978, pp. 352-357. 

11. Martin, H., "Heat and Mass Transfer Between Impinging Gas Jets and Solid 

Surfaces," Advances in Heat Transfer, Vol. 13, Academic Press, New York, 

1977, pp. l-60. 

53 
12. Metzger, D.E., and Korstad, R.J., "Effects of Cross Flow in Impingement 

Heat Transfer," ASME Journal of Engineering for Power, Vol. 94, 1972, pp. 

35-41. 

13. Bouchez, J.P., and Goldstein, R.J., "Impingement Cooling from a Circular 

Jet in a Crossflow," International Journal of Heat and Mass Transfer, 

Vol. 18, 1975, pp. 719-730. 

14. Sparrow, E.M., Goldstein, R.J., and Rouf. M.A., "Effect of Nozzle-Surface 

Separation Distance on Impingement Heat Transfer for a Jet in a 

Crossflow," ASb5 Journal of Heat Transfer, Vol. 97, 1975, pp. 528-533. 

15. Stoy, R.L., and Ben-Bairn, Y., "Turbulent Jets in a Confined Crossflow," 

m Journal of Fluids Engineering, Vol. 95, 1973, pp. 551-556. 

16. Kuester, J.L., and Mize, J.H., Gotimization Techniques with Fortran, 

McGraw-Hill, New York, 1973, pp. 240-250. 

17. Gardon, R., and Akfirat, J.C., "The Role of Turbulence in Determining the 

Heat Transfer Characteristics of Impinging Jets," International Journal 

of Heat and Mass Transfer, ---- Vol. 8, 1965, pp. 1261-1272. 

54