NATIONAL ACFC- ’ ’ ‘“CAL ESTABLISHMEN

Ll’ii RARY

C.P. No. 25 12649

A.R.C. Technlcal Report

MINISTRY OF SUPPLY

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS

The Effect of Variation of Air Density and Temperature on the Airflow Characteristics of Porous Fabrics

1. Picken, B.Sc.

Crown Copyrrght Reserved

LONDON: HIS MAJESTY’S STATIONERY OFFICE

1950

Price 1s. 9d. net.

C.?. No.25 __------

i

Teohnxal Noze vo. M.C.3&5

ROYAL, AIRCRAFT ESTABLISHIEWT -.-..----_.--_-_--_.-

The iffect of Vwxatlon of Au? Density and Temperature on the Au-flm Clm.racxrlstux of Porous Fabrics

J. Pxken, B.Sc.

SUMNARY .--_.--

Thxs note describes a semes of tests made at low au denslt;les and temperatures and establishes that the airflow through porous fabrics obeys t;he laws of dynamic smllar~ty.

--

LIST OF COiWJZNTS

1 Introduction

2 i'iiethod

2.1 Apparatus

2.2 Fabrx Test Specimens

2.3 Measurements &lade

3 Results

3.1 Ducusslon of Results

3.2 Generalzsatlon ai' Previous Work

4 Conclusions

4.1 Further Action

References

LIST OF &?ENDICES

Lxst of symao1s

Relatlonshp between basic and measured quantities

LIST OF TABLES _

iletads of' Fabric Test Spccunens

LIST OF ILJXSTRATIOi'JS -..- -

Porosity Instrument

Vanatxon of' indwated earflow vath air pressure for a constant pressure dlf'ference

a

3

3

3

3

IL

0

7

Appencllx

I

II

Table

I

-2-

i

1 Introduction - -- ---

The airflow characteristics of most of the porous fabrics now used in the manufacture of parachutes were cxsmined during the Second World Var by Brown and Holford (Ref.1) at normal ground temperatures and pressures. They concluded that the porosity of these fabrics, and also of a fine wire mesh and ribbon mcshcs, increased vsith increasing pressure difference across them (that IS, that U is equal to f(p)\rp vhere f(p)

1s an lncrcasing function of p) and, further, that u PX

was independent

of P , vhcre x is a constant the value of which depended on whether the yarn vas composed of artificial or natural fibres. A limited number of cxpwxnents Voro also made by Duncan (R&.2). ' - vms consxlered an

\r, increasing function 13 speed. This was accepted as a characteristic of all parachute fabrics.

Taylor and Davies (Ref.3) measured the aerodynsmic forces on porous sheets including fabrics and found little variation due to Reynolds number over the ranges of their experiments.

Simons and Cmdrey (Ref.&) also measured the aerodynamic forces on fine wire mesh screens and noted but did not examine a 'speed affect'.

This note records the results of an investigation into the effects of variation of air temperature and density on the airflow characteristics of porous fabrics videly used for the manufacture of parachutes and indicates hov these illustrate a more general form of the conclusions reached in Refs.1 and 2.

A list of symbols is given in Appendix I.

2 Method

2.1 Apparatuc

In order that the arrflow through and pressure difference across the fabric test specimens could be varied and measured readily an instrument slrmlar to the High Pressure Porosity Instrument described in Ref.5 was used. It differed in that, to avoid the variable heating effect of tho blower on the air passing through the fabric test specimens, the dl?%tlOn of the mrflow was reversed - a ty{o stage exhauster driven by a five horsepozr electric motor replaced the single stage blcwer of the standard xk3trument. This modification also enabled greater pressure difference to bc obtained and thus extended the range of readings at lmr air densitlcs. The manameter board and certain other ancillary ccmponents wcrc rearranged in order that the instrument could be housed in the limited space available. The final assembly is illustrated in Fig.1. The measurements were made in the No.2 Cold and Decompression Chamber at Synehurst in order that the air density end temperature could be varied as required.

2.2 Fabric Test Specimens ---_I

Twelve types of fabrics widely used for the construction of para- chutes and differing from each other in porosity, treatment antior material were tested in order that any conclusions might have.a general application to parachutes. Details of porosity, specification, etc. are @ven in Table I. Each specimen was approximately one yard square and marked in ten positions by 3 inch diameter circles in such a way that no v<arp or weft threads were common to any two positions. An airflow measurement at scme particular pressure difference across a specimen was effected bY

-3-

tahng the mean of ten readings made at the centres of each of the marked posltaons as desor~bed an Ref.5

2.3 Keasur~ents Made

The tests carried out can be dlvacled into two series. In the first * the effect of low au denslty was exammod. The airflow through the twelve fabric test speolmens was measured at varaous pressure dlffarences end au- densltlcs oorrespondwg to those at he&ts above sea level of ' 0 to 30,000 ft. 1T1 lnorements of 5000 ft. The aar dens:lty v,as measured by a standard alrcrait altunetcr. Control of the temperature was dlrfa- cult and It varwd through a rsnge of O°C to 2CoC. Relatave humldlty lias not measured but was probably of the order of 90$ to 100,;.

In the second series the effect of low temperature was exemulcd. The mea;;urements were made m the same way as thoso of the farst series except that they covered a temperature range of -50°C to O°C and the air pressure was not varied from atmospheric. Although the operators -.iorc fabric face masks there was a oontanual suspcnslon of Ice partloles in the atmosphere of the chamber. This mdwated that the relatlvc humldaty must havt? been of the order of loo,&.

3 Results

Fig~.j - 14 gave the results of the tests &raphwal.ly. The rellabitaty of the measurements made at temperatures below O°C was seriously affected by the accumulation of ace particles in the lnterstloes of the fabrics. It was also aggravated by the imparted off lolency of the lnstrment . The clamping head did not move freely, the 'Sorbo' rubber rmg became hard, and ace accumulated in the exhauster causmg the eleotrlc motor to be overloaded frequently.

3.1 DYLSCUSS~O~ of Results

It has been suggested that moreaszng the pressure dtiferenoe across a fabrw ancreases the area of' the fabric lnterstaces relatlvc to the yarn and that this wall produce a change an porosaty chsracterastlcs. If this were the only effect we should expect the lndloated airflow to be andependent of azr density (or pr essure) for a given pressure dtifercnce across a fabric. Refs.1 ad 2 ~qLloatly accept thas explanation an therr conolusaons. Fag.2 shows however that the lnaicatod airflow lncraases wath ulcraasmng air pressure for a constant pressure dtierencc aoross the fabric test speounons.

To atteqt an lnterpretatlon of thas phenomenon let us assume that dlstortlon has no appreciable efiect on the porosrty cheracterlstics of a fabric. He ten then apply the laws of dynamo slmitarlty to the am- flow through the fabric obtalnlng the well known result that the nature of the flow and hence the Rorosity IS dependent on the Reynolds number. Thus If U IS the mean velocaty of the acflow through a fabric when the pressure ddference across It 1s &pV& then the relative porosity

U 7 = $(Rj where R = y . . . . . . . . . . (1,

* This RctatIous V IS -Lntroduoed an order that results mey be more directly applacable to parachutes. If &pV2 corresponds to the mean pressure dafferenoe across the l'abrlo of a Frachute canopy Inflated III a reiatlve slrstresm then the relatave velocity of the estream uLLl approxlloate to V.

-4-

Appendur II shows how ; and ; may be expressed ~fl terms of the

quantities measured, that w, expressed. as functions of air temperature and pressure snd, as read frcnn the prosxty mstrument, the arrflow through and pressure difference across the fabric test speolmens. All the constituent factors of R , except 8, were varxd..

In FlES.3, - 44 $ has been plotted agamst loge 5 for the twelve . spmens. It can be seen that where the air temperature was greater than

0 C the measurements appear to obey the relatIonship (1). Further, over this range of the uwestlgatlon, the relationship seems to be of the form

U - = m log CR V . . . . . . . . . . (2)

where m and o are constants dependent on the characterxstxcs of the fabric. Table I gives values of m and log, 04 for each of the speclmene a.nd the method by which they were derived from the measured quantltxes is outlined in Appendur II.

Where the air temperature was less than O°C the value of + was

mostly less than and never greater than the vslue to be expected from the relatlonshlp (1). As the oollectlon of Ice particles zn the fabrw lnterstxes was almost certain to effect a reduction in the value of thxs ratio the results in this series qxildat~vely support our assumption.

An examlnatlon of the results given in Ref.4 shows that the 'speed effect' on wue meshes also conforms to eyuatzon (2).

3.2 Cenerallsatlon of Previous Work

~upposa u relatlonshlp (1) that

$'(R) = lc5Rti - ' . . . . . . . . . . (3)

also

. . . . . . . . . , (4)

Thus oambitung (3), (4j and (51, (1) may be-m-leen ai

or

XJW Brown and Holford concluded (Ref. 1) tIw..r.

U -= PX

k6 where kg is independent of, p

This will conform to (I; provided

kg = k5 3 px-' 4 2x-' 0

Thus their relat1onshz.p may be generalised as

; = % F? where y : 2x - I

(8) may be related to (2) by

1 y = log, CR

ks = d!- YRY

,.......,, (7)

,. . . . . . , ..(Cj

*....,..*. (9)

. . . . . . . . . (loj

Over a narrow range of R for anal1 values of y equation (Sj approxlmatos * closely to equation (2) If the mean values of y and kg given by squa- tlons (Tj and. (loj are used.

4 Conclusions

The results tilcate that the laws of dynem~c sxumilardy hold for , parachute fabrics and suggest that over the range of the unrestlgatxon they may be conveniently summar lsed by the expresslan

U 7 = m log CR

where m end o may be regarded as fabrx charaoterzstlcs.

4.1 Further Action

The relatlonshlp between q(R) and the fabrzo parameters should be establxshed an&+.celly.

No. Author -

1 Brown and ' Holr*ord

2 Duncan

3 Taylor and _ Davies

4 smons and Cmdrey

5 Carlmg and Leigh

Title, etc. -

Porous pmpercies of various ~natenals liable to be used for malang parachutes. Current Paper No.24. Maroh, 1949.

The cause of The sponr;aneous opening and closing of parachutes (The phenomena of "Squdding"). R. & M.2119. December, 1943.

The aemdynanncs of porous sheets. R. & M.2237. April, 1944.

Measurements of the Aerodynaxkc fames aotlng on porous screens. R. & M.227b. Auyst , 1945.

The design of a high pressure porosity mstmment. Technxcal Noze No. Aero.1804. July, 1946.

-7-

APPlDnxXI

Llst of Symbols

c fabric constant

d density of alcohol used for porosity instrument manometers

f(P) function of p

y(T) runct1on of T

h height of the pressure dlfferenoe manometer of the porosity instrument

H heoght or" the flow reading manometer of the porosity instrument

kl a constant of the flow meter scale of the porosity lnstrurnent

k2 a constant of the venturi of the porosity vlstrwnent

k3 = 2 0

5 = 0.0151

k4

k5

constant = 2.23 x lOI

fabrx constant

e some suitable linew dunensxon of a fabric

m fabrio constant

P pressure differonce across a fabrx

P = k2 (;,,T U2)

T temperature m 'A, used as a suffix to denote the value of a physical quantity at a temperature T

U mean velocity of the alrflovr through a fabric when the pressure drfference aorvss lt 1s p

'i 1 = U when T = 288 and c = 1

x fabric constant

Y = 2x-l

rl v33oosity of air

-a-

P am density

u rclat 1ve al.r density U2B8 = re1at1vc air pressure ln standard atmosphere

u4 fur&xx of H

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APPENDIX II

Relatlonshlp between Basx and Measured Quantities

The follow-g relatxnshlps are either lmplud or their derwatwn from baac &ta 1s obvious. The slug foot second systa of units 1s used.

p = &PTV2 .,....*... (1)

p = WI . . . . . . ..I. (2)

28% u uT= T 288 . . . . . . . . . . (4)

3/2 VT = 0.08% n288 TT+ ,20 ..*..*....(5)

_, .

TJi=UNhonT=28R!A~d~=l ,..........(6)

D = k2 (&pTU2) ..#.......(7)

a, = 1.64 x IO-3 (1260 - T) . . . . . . . ...(8)

Prom (1) and (7)

from (6)

WTP =-

= 2 [288;q [Liz 10-3 (1260 - T} h.J

,3/z 2 o*0835q288 T +

I ,20

from (21, CL). (5) a-d (8)

where

= k4 c288 b F(T)

F(T) = (1260 - T) (!I! + 120) 2

& sna.

k4 = 2 x 288 x 1.64 x IO-3

421 x 0.08352~2288

. . . . . . . . . . (9)

..*...... (10)

In m.gs.3 - 14 ; 1s plotted against log, 2 for each fabru test specmen, the values of these being obtained from the meas- quant‘itlee by means of equations (9) end (IO).

These figures ud.cate that the results may be expressed IX-I the form U 7 = m log CR where m and c are constants dependent on the nature of the fabric. Because no comparative measwents of 8 were possible numerical values of o can not be derlvd. The followmg shows how m

Oe. can be obtund fboti-%tie measured. quantities through squnt~ons

-ll-

= m b&3 0 E .&

+ log, ce

where the suffices 1 and 2 denote-values st any two points,m the curve and

. . . . . . . . . ..(I21

Nuwxicd. values of m and log, c.3 are given m Table I for eaoh of the fabrm test specmen~.

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’ .

TABLE I

Details of Fabric Test ~pecmens

!

I

1

!

3.T.D.583

o.r.D.633

D.T.D 556A

If I

ti1276

7J-7721

D.T D.69A

1

El

?ppox. No. of

rids Picks

99 105

105 106

131 140

131 138

55 57

63 65

95 98

129 117

126 1%

103 100

57 51

108 98

?.Yd,

I

1 .4

1 .4

1.6

1.6

2.8

3.2

1 .3

1 .6

1 .7

0.8

2.9

1 .4

pprox. waght In .Gg. f 9,ooc metres f yarn

52

50

47

45

195

196

51

50

50

30

207

55

I?

a. 0

1 a

d

oromty at pressure lffW%llCC?

f IO" ".g. t 15% ma tmospherlc ~,ressure

f.P.S.

4.7 . 3

38.3

25.3

20.5

32.6

17.3

24.0

14.2

9.4

25.8

22.4

12.8

m

I.043 8.1

I.043 9.1

1.032 9.6

I.029 9.8

3.030 8.1

1.022 9.6

0.017 6.6

0.013 8.3

0.013 9.9

0.012 2.7

0.015 6.0

0.01: 9.4

-, log,ce,

, This fabric r-as 2roduced for supplies droppmg parachutes and is smilar m construction to fabric to Speclflcatlon D.T.D.55& except that It has fearer ends and p~.cks. To prevent "sllppmg" the yarn was treated vath bedafln resin In the manufacturmg process.

- 13 - .

it.mm. CPZ5.‘v. plrnted tn m3eat arzta%n.

. .

.I. T ITV I

FIG. 2.

1

.

A,R PRES~URC i=XPRESSED AS ALTITU# IN 1.CA.N. ATMOSPIIERE

fl~.z.vARl~TlON Of INUCkifED AIRFLOW WITH AIR PRESSURE FOR A CONSTANT

PRESSURE MfFERENCE.

FIG. 3 8 4.

a24-

0.14- 61 . 11.5 It.0

FIG.3

MATERI 3

COTTON SPECIFI TION DTO4186 ‘OROSITY 47 3 FP3 x 4T 40 INS OF WATER

t2.0 12.5 130

0 L”Ge i

13 5 14 0 14 5

MATERliL 5PEUFIC4TION POROSIN AT i0 INS OF WATER AT CjROlJND LEVEL AND 15%

61 ItaO it.5 (2 0 t3 5 14 0 44.5

FIC.4.

REL~tl0~9ilP BETWEEN bx AnvE POROSITY AND LOG, &)

l

.

.

c

FIG. s 8 h I 1 MATLRIAL COTTON I I 0T.D 5e4 P&S c.P.5. ~-‘. u

04c

6.

FIG I

RELATIONSHIP BEWEEN RELATIVE POROSITY AND LOG,@-)

+-

l

FIG. 7 8 8.

b .I ISPfCiFICATlON DTb5831 I 1 IMATERIAL

I POROSITY

COTTON 1 I

32.6 Fd I

AT E,FtOUND LEVEL

FIG. 7.

OIO-

oos-

‘I>0 og- c ZJ 0 007- cc a0

“>och-

F 4 ~035- -

004- I ;

POROSITY AT IO INS OF WATER AT GR6LlNn I-EVFI

b

.

RELATIONSHIP BETWEEN RELATIVE POROSITY AND LOG, (3).

0’0

O-3

FIG. 9.

FIG.9 & lo MA’ThRIAL SPfClhCAlION

NYLON SEE TABLE I

-

MATERIAL NYLON

SPECIFICATION 74Tf $“A POROBITY . . AT10 INS OF

c WATER AT GROUND LEVEL AN0 l5k

Fffi. IO. LO4 c(T)

RELATIONSHIP BETWEEN RELATIVE POROSITY AND LOCc(~)

FIG.11 & 12.

MATERAL SPECIFICATION POROSITY

5 -- ’ a.nrl ! !

G /

xl+

i Q

FIG II. LO% @)

!I;,, 90 I I SPECIFICATION l-l (276

POROSITY 258 FPS I I 0 14

AT IOINS OF WATER _ 2x 0 450 AT CjROUNO LEVEL

70 0 !Bt AT 15%

3ASO!325 4 0 10.0 23 0

140

FIG. 12.

41 5 I2 0

RELATIONSHIP BETWEEN RELATIVE POROSITY AND LOG@)

FIG. I5 & 14, I I 1 MATERIAL VlbcObE

CIfIcATDN V. 7721 5IT-f 22.4 6P.S.

A-r IOINS w I--’ -WATER AT qROUN0 s-6

- ‘55 LEVEL AN0 Ib’C

35 3.6 075

FIG IJ.

MATERIAL 1 a.

SILK SPCCIFICATICW

AT IO INS OF wAT-- .- ---. .~ .-

LEVEL AND IS’ C

J I , Il.5 I20 a5 ~~ Aa\ ‘30 ta5 l4.0 I

FIG 14. LOGe (j?-)

RELATIONSHIP BETWEEN POftOSiTY ANO

C.P. No. 25 12b.49

._ . A.R.C. TechnIcal Report

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