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Heat transfer and flow friction characteristics of perforated nickel plate-fin type heat transfer surfaces Bannon, John M. Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/31780 Downloaded from NPS Archive: Calhoun

John M. Bannon

•#

TA7 .U62 no. 52

-

HEAT TRANSFER AND FLOW FRICTION CHARACTERISTICS OF PERFORATED NICKEL PLATE-FIN TYPE HEAT TRANSFER SURFACES.

Library U. S. Nnval Postgraduate ScKodf

\ionterc#, California

USNPGS TR 52

UNITED STATES

NAVAL POSTGRADUATE SCHOOL

HEAT TRANSFER AND FLOW FRICTION CHARACTERISTICS OF PERFORATED NICKEL PLATE- FIN TYPE

HEAT TRANSFER SURFACES

J'.M.

BANNON //

C.H. PIERSALL.Jr.

P.F. PUCCI

30 JUNE 1965

Technical Report/Research Paper No. 52

TMA'i

\

S.

Naval Postgraduate

Monterey. California

iScoool

rary S.

Naval Postgraduate Scaou*

Monterey, California

UNITED STATES NAVAL POSTGRADUATE SCHOOL

Monterey, California

Rear Admiral E. J. O'Donnell, USN,

Dr. A.

E.

Vivell,

Academic Dean

Superintendent

ABSTRACT:

Experimental results for the convective heat transfer and flow friction characteristics of plate-fin type heat transfer surfaces are presented for eight surfaces. Six surfaces were fabricated of perforated nickel plate, one perforated nickel fins with solid nickel plate splitters and one of solid nickel plate. The heat transfer data were obtained by the transient technique and includes the effect of longitudinal conduction.

This task was supported by:

Bureau of Ships, Code 645

Prepared by:

Approved by: R.

W.

J. M.

Bannon

C.

H.

Piersall, Jr.

P.

F.

Pucci

Released by:

Bell,

C.

B.

Menneken

Chairman, Department

Dean of

of Aeronautics

Research Administration

U.

S.

Naval Postgraduate School 30 June 1965

UNCLASSIFIED ii

Technical Report No. 52

Table of Contents Page

Introduction

1

Description of Surfaces

1

Presentation of Results

3

Experimental Methods

3

Experimental Uncertainties

5

Discussion of Results

7

Conclusions

11 *

References

12

Figures 1.

Schematic of Test Apparatus

14

2.

Photograph of Test Apparatus

15

3.

Geometric and Physical Properties of Slotted Perforated Nickel (160/40 TV and 160/40 Q) "Parallel Plate" Matrices

16

4.

Geometric and Physical Properties of Round Perforated Nickel (125 M, 125 P, and 50 G) "Parallel Plate" Matrices

17

5.

Geometric and Physical Properties of Slotted Perforated Nickel Fin (160/40 TV) with Solid Splitters "Parallel Plate" Matrix

18

6.

Geometric and Physical Properties of Solid Nickel, "Parallel Plate" Matrix

19

7.

Geometric and Physical Properties of a Slotted Perforated Nickel (160/40 TV) 20° Skew Matrix

20

8.

Enlarged Photograph of the 160/40 TV Perforated Nickel Plate

21

9.

f

and

j

vs. N. 160/40 TV "Parallel Plate" Matrix

22

10.

f

and

j

vs. N_ 160/40 Q "Parallel Plate" Matrix

23

11.

f

and

j J

vs. N n 125 R

M "Parallel Plate" Matrix

24

12.

f

and

j

vs. N_ 125 P "Parallel Plate" Matrix K

25

K

iii

and

vs. N„ 50 G "Parallel Plate" Matrix R

26

13.

f

14.

f

15.

f

and

j J

vs. N„ Solid Nickel "Parallel Plate" Matrix

28

16.

f

and

j

vs. N_ 160/40 TV 20° Skew Matrix K

29

17.

Comparison of Slotted Perforated Nickel, 160/40 TV vs. Solid Stainless Steel, 20° Skew Matrices

30

18.

Comparison of Solid Nickel vs. Theoretical Solutions Parallel Plate Matrices

31

19.

Comparison of Slotted Perforated vs. Solid Nickel "Parallel Plate" Matrices

32

20.

Comparison of Round Perforated vs. Solid Nickel "Parallel Plate" Matrices

33

21.

Comparison of Slotted Perforated Fin with Solid Nickel "Parallel Plate" Matrices

34

22.

Comparison of Slotted Perforated Nickel "Parallel Plate: vs. Slotted Perforated Nickel 20° Skew Matrix

35

Flow Area Goodness Factors for the 160/40 TV Perforated Nickel and the Solid Stainless Steel 20° Skew Matrices

36

24.

Flow Area Goodness Factors for the Slotted Perforated Nickel and the Solid Nickel Parallel Plate Matrices

37

25.

Flow Area Goodness Factors for the Round Perforated Nickel and the Solid Nickel Parallel Plate Matrices

38

26.

Heat Transfer Power vs. Flow Friction Power Per Unit Area for the Slotted Perforated Nickel and Solid Nickel "Parallel Plate" Matrices

39

27.

Heat Transfer Power vs. Flow Friction Power per Unit Area for the Round Perforated Nickel and Solid Nickel and Solid Nickel "Parallel Plate" Matrices

40

28.

Heat Transfer Power vs. Flow Friction Power per Unit Area for the 160/40 TV Perforated Nickel and the Solid Stainless Steel 20° Skew Matrices

41

29.

Enlarged Photograph of the 20° Skew Matrix, 160/40 TV Perforated Nickel

42

30

Enlarged Photograph of the Modified Parallel Plate Matrix, 160/40 TV Perforated Nickel

42

.23.

J1

and j vs. N 160/40 TV Fin with Solid Nickel Splitters "Parallel Plate" Matrix

R

iv

27

31.

Matrix Holder (Upstream View)

43

32.

Matrix Test Section Disassembled (Downstream View)

44

33.

Velocity Profile and Temperature Distribution Measurement Device

45

34.

Nichrome Wire Heater (Upstream View)

46

35.

Close-up of Apparatus Test and Heater Sections

47

36.

Recorder Trace of Actual Cooling Curve for 160/40 Q Perforated Nickel, "Parallel Plate" Matrix

48

Summary of Heat Transfer and Friction Results 160/40 TV Perforated Nickel, "Parallel Plate" Matrix

49

Summary of Heat Transfer and Friction Results 160/40 Q Perforated Nickel, "Parallel Plate" Matrix

50

III

Summary of Heat Transfer and Friction Results 125 M Perforated Nickel, "Parallel Plate" Matrix

51

IV

Summary of Heat Transfer and Friction Results 125 P Perforated Nickel, "Parallel Plate" Matrix

52

Summary of Heat Transfer and Friction Results 50 G Perforated Nickel, "Parallel Plate" Matrix

53

Summary of Heat Transfer and Friction Results 160/40 TV Perforated Nickel Fins with Solid Nickel Splitters, "Parallel Plate" Matrix

54

VII

Summary of Heat Transfer and Friction Results Solid Nickel, "Parallel Plate" Matrix

55

VIII

Summary of Heat Transfer and Friction Results 160/40 TV Perforated Nickel, 20° Skew Matrix

56

Tables I

II

V

VI

C-l

Table of Geometric Properties of Perforated Nickel as Specified by the Manufacturer

NOMENCLATURE English Letter Symbols

Matrix total heat transfer area, ft 2

A A

c

Matrix minimum free flow area,* ft

2

2

A_

Matrix total frontal area,' ft

A

Solid matrix cross sectional area available for thermal o conduction, ft z

fr

s

A,

Conduction area corrected for effect of perforations, ft

A*

Plane surface area, ft

a

Plate thickness, ft

a

Short side of a rectangular flow passage, ft

b

Plate spacing, ft or in.

b

Long side of a rectangular flow passage, ft

C

Flow stream capacity rate, (mc ), Btu/fhr °F)

C s

Matrix capacity, W

c s

2

2

Btu/°F

,

s

Specific heat at constant pressure, Btu/(lbm°F)

c c 5

Matrix material specific heat, Btu/(lbm°F)

D„ n

Hydraulic diameter,

d

Inside pipe diameter, in.

E

Flow friction power per unit area, HP/ft

f

Mean friction factor, dimensionless. This is the "small" or "Fanning" friction factor. (Ratio of wall shear stress to the fluid dynamic head.)

4r,

n

2

»\

Exchanger flow stream mass velocity, (m/A ), lbm/(hr ft

Proportionality factor in Newton's Second Law, g - 32.2 C (lbm ft)/(lbf sec 2 ) Unit conductance for thermal convection heat transfer, Btu/(hr ft z F) , or heat transfer power per unit area per degree temperature difference, Btu/(hr ft 2 °F)

vi

)

English Letter Symbols (continued)

Colburn factor = Ng T dimensionless

j

j'

Colburn

j

2/3 fl

pR

,

heat transfer characteristic,

factor based on plane surface area, A*, dimension-

less

K

,

K

Contraction loss coefficient for flow at heat exchanger entrance or exit respectively, dimensionless

k

Unit thermal conductivity, Btu/(hr ft 2 °F/ft)

k

s

Matrix thermal conductivity, Btu/(hr ft

2

°F/ft)

L

Total matrix flow length, ft

m

Mass flow rate, lbm/hr

P

Pressure, lbf/ft

p

Porosity for matrix surfaces, dimensionless

q

Heat transfer rate, Btu/hr

R

Gas constant, (ft lbf)/(lbm °R)

,

r.

Hydraulic radius, (A L/A)

(4r,

s

Solidity of a perforated material, 1-u, dimensionless

T

Absolute temperature, degrees Rankine, °R

t

Temperature, degrees Fahrenheit, °F

2

,

ft,

(53.35 for air) = hydraulic diameter)

3

V

Matrix volume, ft

V

Material volume corrected for effects of perforations

m

W s

x

Mass of matrix,* lbm

Distance along the flow passage in direction of flow, ft

Greek Letter Symbols a

Aspect ratio of a rectangular flow passage, b/a, dimensionless

6

Comp actness; ratio of total heat transfer area to the volume between een the plates, ft /ft

A

Denotes difference

6

Fin thickness, ft

vii

Greek Letter Symbols (continued) C

Conduction area reduction ratio due to perforations in perforated material; cross sectional area of perforations/ cross sectional area, dimensionless Time

A

k A s s Longitudinal conduction parameter, tj

— C

,

dimensionless

P t

Time parameter

y

Fluid viscosity coefficient, lbm/hr ft

u

Area reduction ratio due to perforations in perforated material, dimensionless

p

Density, lbm/ft

3

Ratio of freeflow area to frontal area, A /A, c



8

,

Summation

Local atmosphere

f

Fluid

i

Initial, individual

k

Equivalent

m

Mean or matrix, as appropriate At orifice

s

STD

dimensionless

Compactness for perforated material including the effect of area reduction, A*s/V dimensionless

Subscripts

atm

,

Denotes "function of"

m

1

fr

(Matrix material) solid

Standard temperature and pressure

1

Upstream

2

Downstream

viii

Dimensionless Groupings N N

Reynolds number,

K

,

v

(4r,

n

G/u)

Stanton number, (h/Gc

N

Nusselt number, (h4r, /k)

N

Prandtl number, (uc /k) lu

j

f

a flow modulus

Reynolds number for pipe, (dG/u)

N„ bt

N_

,

)

a heat transfer

,

modulus

p

,

a heat

,

transfer modulus

a fluid properties modulus

Number of heat transfer units, (hA/mc

)

p

Generalized zed heat transfer grouping - Colburn "j" factor, 2 (Ng Np z/J This factor versus N R defines heat transfer ). t r characteristics of the surface. I

Mean friction factor. This is the "small" or "Fanning" friction factor (Ratio of wall shear stress to the fluid dynamic head) This factor versus N^ defines the friction characteristics of the surface. .

X

Conduction parameter, k g A s /mLc for solid material; kgAfc/mLcp for perforated material

A,

Equivalent conduction parameter (corrected for equivalent length in perforated material) Xtk hA Time parameter, rj ,

t

w c s

s

ix

INTRODUCTION

The present investigation is an outgrowth of the continuing program at Stanford University [8]

for the evaluation of heat transfer surfaces.

The experimental work reported by Howard [4] was performed at the U. S.

Naval Postgraduate School, Monterey, and a continuation of that work is

presented herein.

DESCRIPTION OF SURFACES The eight compact heat exchanger surfaces tested were: 1.

Skewed passage a.

2.

20° total skew angle;

160/40 TV perforated nickel

Modified parallel plate a.

160/40 TV perforated nickel

b.

160/40 Q perforated nickel

c.

125 M perforated nickel

d.

125 P perforated nickel

e.

50 G perforated nickel

f.

160/40 TV perforated nickel fins with solid nickel splitters

g.

solid nickel

The skewed passage surface employs corrugated sheets of 160/40 TV per-

forated nickel, stacked alternately with the lines of corrugations 10* from the flow direction, thereby forming a total angle of 20* between

Numbers in brackets refer to numbered items listed in References.

adjacent stacked plates.

Howard [4].

It is the same geometry as one employed by

The modified parallel plate surfaces were made by alternately

stacking a formed plate and a plane splitter plate to prevent nesting, as

shown in the sketch below and in the enlarged photograph of Figure 30.

T~

—^ vA v V^ -r V^—V^— 7^—

—v^—

a.

The flow channels formed by this geometry may be compared to rectangular

channels with an aspect ratio, a = b/a, of about

7.

The perforated nickel plate employed is an electro-deposited metallic sheet of integral structure manufactured by Perforated Products, Incorporated. This material is described in detail in Appendix C.

The geometrical and

physical properties of the surfaces are given in Figures

3

through

7

.

All matrices formed had a frontal cross section of approximately 3.2 inches square and a length of 2.0 inches in the flow direction.

matrices had flow passages with a hydraulic diameter of approximately .002 feet, thus the L/D

ratio in all cases was of the order of 83. rl

All

PRESENTATION OF RESULTS Heat transfer and flow friction data for each matrix investigated are given in both tabular and graphical form, TABLES I through VIII and

Figures

9

through 16, using the Colburn

and Reynolds number.

j

modulus, Fanning friction factor,

In evaluating the Reynolds number, the hydraulic

diameter, which is defined as four times the hydraulic radius, was used.

The effects of entrance, exit, and flow acceleration have been considered in the evaluation of

f.

(See Appendix A).

Figures 17 through 22 show heat transfer and friction comparisons

between various matrices investigated.

Also plotted in Figure 18 for

comparison purposes are the theoretical laminar flow solutions for parallel plates and rectangular passages [6, 8, 11].

Both solutions are

for an infinite length to hydraulic diameter ratio, and the heat transfer

solutions are for constant wall temperature.

In Figures 23 through 25,

"figure of merit" type curves are presented.

The j/f versus Reynolds

number thus plotted gives an indication of the required matrix flow frontal area for a given pressure drop.

Lastly, in Figures 26 through 28, heat transfer power versus flow

friction power curves on a unit area basis, evaluated for fluid properties at standard conditions of dry air at 500°F and one atmosphere, are

presented (See Appendix A).

EXPERIMENTAL METHODS To obtain the heat transfer data, a transient technique was employed.

Briefly, this method consists of heating the test matrix by heated air to a uniform temperature (approximately 20°F above ambient in these tests)

and then subjecting the matrix to a step change in the air flow tempera-

ture to ambient temperature

.

The air temperature ddwnstream of the

matrix is monitored and recorded versus time. of constructing such a test rig [4, 10, 12],

There are several ways

The one used in these tests

is shown in Figure 1, and described in detail in

Appendix

B,

A series of fine nichrome wire heaters were installed upstream of the matrix to heat the air.

Turning off the heaters provides the step

change in temperature of the air without disturbing the flow.

By

referencing the thermocouples downstream of the matrix to the thermocouples upstream of the heaters, the initial temperature difference can be very closely controlled.

This temperature difference is continuously

recorded by a strip chart recorder when a run is made.

This recorded

trace has the distinct advantage in that there is no transposition of

data required which would produce increased uncertainties.

Reduction of

the data follows the method of Locke [10] and Howard [5], whereby the N

of the surface can be evaluated by determining the maximum slope of

the fluid temperature difference versus time curve during the cooling

transient.

Pressure drop data for evaluating the friction factor were obtained from static pressure taps located in the test section immediately upstream and downstream of the matrix.

The static pressure immediately upstream

of the matrix was also recorded.

Velocity profiles were taken just

upstream of the matrix to assure that uniform flow conditions were being

maintained by the screen pack straightener and by the wire heaters.

The

flow was measured by an A.S.M.E. standard D and D/2 orifice meter with

:

changeable orifice plates [14], and was located downstream of the test section.

Various manometers were used consistent with the pressure

range encountered.

All pressure drop data for evaluating the friction

factor were taken under ambient air conditions (i.e., isothermal flow). The data reduction relationships are given in detail in Appendix A.

EXPERIMENTAL UNCERTAINTIES The experimental uncertainties can be considered to be in two catagories.

First, in the manner in which the experimental gear attempts to

meet the idealizations of the experimental method.

These are discussed

in detail by Howard in [A] and [5]. By insuring uniform flow to the matrix, minimizing the temperature

change to minimize fluid property changes, and in the careful design of the fluid heater, these idealizations are met.

The second catagory

can be grouped in three areas (1) uncertainty of physical constants,

(2)

inaccuracy in the geometric measurements , and

(3)

instrumentation inaccuracies.

For the determination of the uncertainties reported, the method of Kline

and McClintock [9] was used. (1)

[1],

Values for the physical constants required were obtained from

[2], and [3].

The uncertainties in these values, as best as can be

determined, are listed below: ±

0.5%

±

0.5%

N„ Pr

±

2.0%

k

*

o.5%

±

1.0%

c s

c

P

s

u

It is noteworthy that the accuracy for the value of c

the metal used.

depends upon

Where pure metals are used the accuracy quoted is

feasible; however, this is not the case with alloys.

Thus the tolerance

can be a major cause for inaccuracy [10].

of c

Due to inconsistencies in construction of the matrices, errors

(2)

in lineal dimensions are considered to be

±

0,5%.

Inasmuch as the

weight of the matrix can be determined as accurately as desired, the error in W

is considered negligible.

Based on this, the uncertainties

in geometric measurements are considered to be as follows:

A' A

fr'

VVV

'°*

*

l

L

±

0o5%

W


» 33

c o O,

s 5

o

o, ^^^^ {>>

-p •H CO

o ^ O cu

Ph

•H S3

•3

160/40 TV Fins Solid Nickel Splitters

Matrix Material Specific Heat (c g ) Btu/lb

0.1065

°F

Thermal Conductivity (k s ) Btu/ hr ft

°F

38.7

Fin Thickness, inches

0.0022

Splitter Thickness, inches

0.0020

Total Heat Transfer Area (A)

Frontal Area (A f

Total Conduction Area (A k ) Free Flow Area (A c )

Matrix Density

(

Porosity (p)

Figure 5.

0.00689 0.05883

ft3

0.011588 lb/ft 3

Hydraulic Diameter (D^)

Compactness (§)

ft

Tt*

^ m)

19.3084 0.06953

ft

)

Matrix Volume (Vm )

ft

ft 2/ft^

ft

69.1

0.00194 1666.2 O.846

Geometric and Physical Properties of Slotted Perforated Nickel Fin (160/40 TV) with Solid Splitters, "Parallel Plate" Matrix

Matrix Material

Solid Nickel

Specific Heat (c s ) Btu/lb °F

0.1065

Thermal Conductivity (kg ) Btu/ hr ft °F

38.7

Material Thickness, inches

0.0020 ft 2

Total Heat Transfer Area (A) Frontal Area (A fr )

ft

2

0.06953

Total Conduction Area (A g ) Free Flow Area (A c )

Matrix Volume (Vm ) Matrix Density

(

.-.....'.

'

0.01014 0.05939

0.011588 lb/ft 3

Hydraulic Diameter (D^)

Compactness

ft

3

m)

20.1875

2 3 ft /ft

ft

77.7

0.001961 1742.1

0.854

Geometric and Physical Properties of a Solid Nickel "Parallel Plate" Matrix

6

7

8

9

Q

THEL.S.STARRETTCO.

20 Degree Skew 160/40 TV Perf .Nickel

Matrix Material Specific Heat (c ) Btu/lb s

F

0.1065

Thermal Conductivity (k ) Btu/ hr ft s

Material Thickness, inches Total Heat Transfer Area (a)

Frontal Area (A ) fr

Matrix Density (^ ) m

ft 2

Porosity (p)

Figure 7.

ft 2 /ft 3

15.U

ft 2

0.00349 0.06412

0.01211

lb/ft 3

Hydraulic Diameter (D ) H

Compactness ($)

ft 2

0.0734

ft 3

Matrix Volume (V ) m

38o7

0.0022

ft 2

Total Conduction Area (A ) k Free Flow Area (A ) c

F

ft

50.1

0.00252 1272.8 0.873

Geometric and Physical Properties of a Slotted Perforated Nickel (I6O/4O TV) 20° Skew Matrix

-5

X3 0)

a.

> o

s -p

o j=

a

aj Sh

O -P a,

•a

v

hi-

ll a)

W CO

f-i

'

l

!

ms^

1.0 I

!.;:uii;uii:ritauiiuiiiiiiiiiite#E^

Modified Parallel Plate Perforated Nickel, 160/40 TV

.6

•4

f



.2

.1

K3 .06 S«*

.04

.02

.01

NsiW*

.006

/:;: ;j '''

.,:•'

;

'

f

*v!'

-'.-*

.004

;

j*g .#

.002

.001

Figure 9.

Surface Heat Transfer and Friction Data "Parallel Plate", 160/40 TV Perforated Nickel

'.

:

.

Figure 10.

Surface Heat Transfer and Friction Data "Parallel Plate", 160/40 Q Perforated Nickel

1.0

.6

.4 i

.2

.1

==

.06

.04

J

.02

.01

.006

.004

.002

.001

Figure 11.

Surface Heat Transfer and Friction Data "Parallel Plate", 125 M Perforated Nickel

Figure 12.

Surface Heat Transfer and Friction Data "Parallel Plate", 125 P Perforated Nickel

t

Modified Parallel Plate Perforated Nickel, 50 G -

Porosity, p = 0.883 Compactness,

@

=

966.8 f 2 /f\?

Hydr. Diana., D H = 0.002028 ft.

'«,.-

-

•':;

-

-.

:

40

'

60

NR

Figure 13.

Surface Heat Transfer and Friction Data "Parallel Plate", 50 G Perforated Nickel

\

\

.001

10

20

40

100

60

200

500

NR

Figure 14«

Surface Heat Transfer and Friction Data "Parallel Plate", 160/40 TV Fins with Solid Nickel Splitter Plates

1000

rmmiW

•'immimm i

#p

.006 ""

-

.004

Figure 15.

Surface Heat Transfer and Friction Data "Parallel Plate", 0.002" Solid Nickel

40

Figure 16.

60

100

Surface Heat Transfer and Friction Data 20* Skew, 160/40 TV Perforated Nickel

1.0

i Is

M

Figure 17.

Comparison of Slotted Perforated Nickel, 160/40 TV vs. Solid Stainless Steel, 20° Skew Matrices

.004

.002

(T)

Theoretical Solution, Infinite Parallel Plates

(2)

Theoretical Solution, Rectangular Passage b/a= 7.

(3)

Solid Nickel, Modified Parallel Plate Matrix:

,001

10

20

40

100

60

200

500

1000

II-

R

Figure 18.

Comparison of Solid Nickel vs. Theoretical Solutions Parallel Plat© Matrices

a?

-

.-.

*

*

3f

.

'*

'"-

;

r

- -t»'

U>

Figure 19.

60

100

Comparison of Slotted Perforated vs. Solid Nickel "Parallel Plate" Matrices

«s

.003.

10

20

Figure 20,

40

60

100

200

500

Comparison of Round Perforated vs. Solid Nickel "Parallel Plate" Matrices

1000

flW

;1

.1 "

'

.06 ;

.04 -

i

" -

.01 '

3

.006

-

.004

Wk --'

.002

.001

10

20

40

60

100 N

'*

Figure 21. :

200

500

1000

R

Comparison of Slotted Perforated Fin with Solid Nickel Splitters vs. Solid Nickel "Parallel Plate" Matrices

40

Figure 22.

60

100

Comparison of Slotted Perforated Nickel "Parallel Plate" vs. Slotted Perforated Nickel 20° Skew •

Matrix:



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CM (-• r-H

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.0188

L.

k i

The solid cross sectional area for heat conduction, the path length.

The area, A^

A,

Ki

varies along

selected was the cross sectional area

,

between the slots normal to the flow direction, i.e., = (0.0095) (0.0022) - 0.0000209 in.

A.

K

2

i

Just as L = EL is the flow length

and m _

is

A,

EA^

where L is the total matrix flow length and L

between two successive perforations; so does

In evaluating A^

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r employed and is defined as

therefore, i.e.

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,

A,

,

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,



,

c

,

=

L,

= ZL,

a conduction area reduction ratio



cross sectional area of: perforations c cross sectional area

is the solid cross sectional area multiplied by 1 - £

,

71

;

\

= A (l-C) s

- 1.6058

6102 in

- 0oG0424 £

160/400,

.00(0}"

A

=

ch

A



0063 )( 02 5) - =0001575 in. =

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SX

C

\

v = .1942

- A 8

(l-0 =

002887

ft.

- .8058

s

7— L

- .655

=0.3351, same

as

160/40TV

k

125M «

T .O07fsir\60

A

^

ch

A,

.

nole



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2

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c

v = s

no le

A

ch

- .8053

e

.00001052 00005404

H

0.19466



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T JLj, •

The equivalent conduction length, L^

,

s .00?$ sin 6o° =. 0QG84-

is computed in the case of

i

round perforations assuming the path to be as shown above, i.e.,

where

r,

Thus

.liX 1 22291.

-00827

k

3

l

.00684 = .82709 .00827

2

..

and

1^.

is determined as C

2Trr

—r

k

is the radial distance equal to one-half the center to center

distance.

A,

M

=

in the case of the slotted perforations.

diam. of hole x plate thickness center to center distance x plate thickness

_ (.00366)(.Q016) _

(,0079)(.0016)

Therefore,

A^ - A

^ DJ:>

(l-O - 1.1679

in.

2

(1-.4633)

2 - .6268 in. 2 = .00435 ft.

73

125P

d-JOQZ?!

A

=

.

en

(

Anole

o

-

.

00684)

f4

(o

0079) =

(,00291)

2

«

.

.

00005404

"

in'

A^ = A (1-;) = ,00640

00000665

ft'

v = 0,12307 i

= 0,8769

s

J

J

00827"

ki

= .82709

ki C

= 0,3684

50G

Jm.OtJt*

-

L^

A

=



ch

A

01706 XoQ197) s ,00033608 in

=7(,0138)

.

nole

4

2

= ,00014957 in.

c

2

= .82697 J

v s

Lk

.0\97 sin 60°

k.

l

.44504

= ,55496

C

- .02063"

= .7005

A^ - A (l-O = .00243 ft

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