The effect of vent ducts on the reduced explosion pressures of vented dust explosions

Review The effect of vent ducts on the reduced explosion pressures of vented dust explosions Geoff Lunn, David Crowhurst* and Michael Hey Explosion and Flame Laboratory, Health and Safety Executive, Harpur Hill, Buxton, Derbyshire, UK *Fire Research Station, Boreham wood, Hertfordshire, UK

An investigation into the effects of vent ducts on reduced explosion pressures is described. Experiments were made using an 18.5 m3 explosion vessel and a modified 20 I sphere, with dusts having K.r values ranging from 144 barms~’ to 630 barms”. The vent area/vessel volume ratio, bursting pressure of the vent cover, and the length to diameter ratio of the vent duct have been varied. Straight vent ducts, and ducts containing sharp 45O and SO’ bends have been used. A simple model to describe the effect of vent ducts on the reduced explosion pressure has been derived and compared with the experimental results. Agreement is shown to be satisfactory in nearly all cases. A comparison between the experimental results and guidance on the effect of vent ducts already available in the literature is discussed. (Keywords:

vents; explosion;

modelling)

materials, when dispersed in air in a finely divided form, at a suitable concentration and in the presence of an effective ignition source, are explosible. In enclosed vessels the pressures generated in these explosions may reach 10 bar for organic dusts, and still higher values for metal dusts such as aluminium. Such pressures cannot be contained by most industrial dust handling equipment, and measures need to be taken either to prevent the explosion or to protect plant against the effects. A method of protection used widely in industry is explosion relief venting. In this technique, panels or membranes covering openings in the walls of the equipment open at low overpressures in the event of an explosion, and thus the pressure is released’. The highest pressure attained in a vented explosion is known as the reduced explosion pressure, Pred. and is much less than the explosion pressure generated in an enclosed vessel. When the explosion relief is properly designed, Prcd is not high enough to cause damage to the plant. The nesessary vent area depends on several factors: the volume of the equipment, V (m3); the opening pressure of the vent covering, Pstat (bar a); the strength of the equipment or the reduced explosion pressure, which must not be exceeded, P,d (bar a) and the explosibility of the dust as characterized by the K,, value (bar m s-i) (Ref. 2). The K,, value of the dust is measured in the standard 20 1 sphere apparatus’. The maximum rate of pressure Many

Received

I March

0950-4230p8/040182Q 1988 Butterworth

182

1988; revised

13 June I988

15$3.00 & Co. (Publishers) Ltd

J. Loss Prev.

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lnd.,

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Vol

1, October

rise, (dP/dt)mar (bar s-i) is measured over a range of dust concentrations in air, using a standard technique. The highest value of the maximum rate of pressure rise is used to calculate the K,, value of the dust:

The K,, value is essentially defined as the maximum rate of pressure rise measured under standard conditions in a 1 m3 vessel, and is used to characterize the explosibility of the dust by reference to four groups: KM

: Grout

0 c K,, < 200

: Group

200 < K,, < 300: Group 300 < K,, : Group

St& Non-exolosible St1 Increasing St2 explosibility St3 I

The equation for K,, is referred to as the cube root law and expresses the relation between the rate of pressure rise and the volume of the vessel when standard conditions are maintained. A theoretical analysis of the venting process in compact vessels by Heinrich3 has led to a series of nomographs that allow estimates of the vent area when P,,,,, P& V and the K,, value are known. These nomographs are published in VDI 3673 (Ref. 4). The results obtained using this method are usually conservative, and for a given set of conditions the calculated vent areas can be up to three times experimentally determined values. This is because the apply to dusts with maximum K,, nomographs explosion pressures in enclosed explosions, Pmax, of 11 bar a when the K,, value is less than 300 bar m s-’

The effect

of vent

ducts

on the reduced

explosion

and 13 bar a when the K,, value is greater; most dusts have P,=, values less than these5. Nevertheless. it can be argued that this is a valuable safety factor, especially when conditions are somewhat different to those in the standard test, and the nomograph method has found wide favour. The nomograph method is designed for unobstructed vents. Vented dust explosions, however, are usually of large volume, and the burning material that ejects from dust handling equipment during a vented dust explosion cannot be allowed merely to disperse into the work place. The danger to personnel that the cloud of hot gas and dust poses is an obvious one. In practice the combustion products are guided to a safe place through a duct fitted to the vent opening. The presence of the duct, however, alters the explosion characteristics, and changing the system in this way is bound to affect the reduced explosion pressure. Thus fitting a vent duct may result in explosion pressures that unwittingly exceed the strength of the vessel. There are no truly satisfactory methods for predicting the effects of vent ducts. A rule of thumb used in the UK is that the duct should not exceed 3 m in length, should be straight, and should have an area not less than the area of the vent itself. VDI 3673 contains some guidelines4 but these are only for straight ducts and give only limited help on the one hand for ducts 3 m in length and on the other for those more than 3 m in length. This paper describes a project in which the effect of vent ducts on reduced explosion pressures has been studied. The results are discussed, and a method of calculation is described. This project was carried out for the British Materials Handling Board, which has brought together some 30 sponsors from industry and government to finance the project. The experiments were carried out at the Explosion and Flame Laboratory of the Research and Laboratory Services Division (RLSD) of the Health and Safety Executive at Buxton and at the Fire Research Station, Borehamwood. This paper is a shortened version of the report provided to sponsors of the project.

Experimental The dusts Three dusts were originally chosen to cover the range of explosibilities likely to be found in industrial dust handling processes, and to be representative of the three groups of dust explosibility. The St 1 dust was coal dust; the St2 dust was aspirin dust; the St3 dust was aluminium flake. Two other dusts, toner dust and polyethylene, were used in a short series of tests to check that the behaviour of the three main dusts was typical of the St-Groups.

The explosion

vessels

The 18.5 m’ explosion

vessel.

The

large

scale

tests

pressures

of vented

dust

explosions:

G. Lunn et al.

were conducted in an 18.3 m3 explosion vessel at the Explosion and Flame Laboratory, Buxton. A drawing of the vessel showing the dimensions of the explosion chamber has been published6. The length to diameter (L/D) ratio of the explosion chamber is approximately 1.6, and it thus qualifies as a compact enclosure to which the VDI venting nomographs apply. The explosion chamber is designed with a working pressure of 14 bar. Various ports in the chamber walls were utilized as entry points for the ignition source connections, and for attaching the dust injection cylinders. One end of the vessel contained a centrally positioned circular vent opening, diameter 1.1 m. A blanking plate was fitted over this opening to seal the chamber when enclosed explosions needed to be carried out. The dust injection system comprised three pressure vessels with pepper pot nozzles. The vessels were spaced along the top of the explosion chamber, and their positions have been shown6. The injection vessels were connected to pepper pot-type dispersion nozzles via ball valves. These injection devices are different to the ring system employed in the standard 20 1 sphere, but have the advantage that the scale of the dust injection process is larger and thus conforms, approximately, to the larger scale of the explosion chamber. In any event, a series of calibration tests carried out with enclosed explosions minimized the effects of differences in injection techniques. Prior to an experiment the dust was divided equally between the three injector cylinders and stored under the required injection pressure. This pressure was determined in the series of enclosed explosion calibration tests. The dust was released into the explosion chamber through the ball valves operated by air cylinders. Because of the large volume of the explosion chamber, the dust injection did not contribute significantly to the explosion pressure. The ignition source was positioned at the centre of the explosion chamber and comprised a 30 g charge of black powder ignited by an electrically fired powder fuse. The ignition source did not contribute to the explosion overpressure or to the maximum rate of pressure rise. The ignition delay between initiation of the dust injection and firing of the powder fuse was determined in the series of enclosed explosion calibration tests. A circular vent opening of 1.1 m diameter was positioned centrally in one end of the explosion chamber. Orifice plates were fitted over this opening when smaller vent diameters were required. These plates had bolt holes around the central opening to which both the explosion relief bursting discs and ducting could be fastened. The details of the vent opening are given in Table 1. The bursting discs were designed for three static bursting pressures: 1.1 bar a, 1.2 bar a and 1.5 bar a. These bursting pressures conform to those for which the VDI nomographs are applicable4. A bursting disc in position is shown in Ref. 6. Some experiments using open vents have also been carried out.

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183

The effect

Table 1

of vent

ducts

on the reduced

explosion

pressures

Details of the vent openings in the 18.5 m3 vessel

Vent diameter (m) 1.1

0.9 0.7 0.5

Vent area, A, (rn?

K-Factor fVU3/A.)

K-factor (cross section of chamber/A,)

0.950 0.636 0.385 0.196

7.38 11.0 18.18 35.71

4.93 7.35 12.15 23.87

of vented

dust

explosions:

G. Lunn et al.

Table 2 Values of K., and Pm,. for test materials at the concentration used in small scale vented explosions

Powder Silkstone coal Polyethylene Aspirin* Aspirin” Toner powder Aluminium flake’ Aluminium flakeb * The concentration * The concentration

Concentration (kgm-‘)

fbarms-‘1

0.6 0.25 1 .o 1.5 0.25 0.5 1 .o

193 220 254 236 272 333

KS, 144

P fba:) 8.4 8.8 8.6 8.7 ::: 9.3

used was not that which gave maximum used in a limited number of experiments

Ka

Igniter / Vent timer/ pressure tran

Figure 1

Explosion chamber and ducting

The vent ducts were of circular cross-section with diameters and areas equal to the four vent openings. For each vent diameter four straight lengths of duct were prepared, three of 5 m length and one of 1 m length; one sharp 90” bend and two sharp 45’ bends were also prepared for each duct size. In Figure I, 16 m of 0.5 m diameter duct is shown fitted to the explosion vessel. The 20 1 explosion vessel. The 20 1 spherical vessel was used to carry out the initial classification of materials. This vessel, when operated in accordance with the specified test procedure**‘, is acepted internationally 4*8~9as a suitable instrument for the determination of the maximum pressure (P,,,) and rate of pressure rise (dP/dt), and hence values of K,,. All the materials used were classified according to the standard test procedure and the results are summarized in Table 2. To carry out explosions vented through relief ducts, the standard 20 1sphere had to be modified to accept the vent cover and ducting. The top igniter support assembly and top flange were removed and replaced by a vent support plate and ducting adaptor. Two new support arms for the igniters were made and mounted through spare 14 mm holes in the small flange plate used to mount the sphere pressure transducer. The whole assembly was then mounted onto a new stand, which allowed the sphere to be rotated through 90” so that the ducting when fitted lay in a horizontal position. The modified sphere is shown in Figure 2. For vented explosions the energy of the ignition source was reduced from the standard 10 kJ to I kJ. This was done to reduce the pressure generated by the

184

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7. October

support

Figure 2

frame

Modified

20 litre sphere

ignition source upon activation from approximately 1 bar (approximately S-10 times the vent bursting pressure) to a negligible level thereby preventing bursting of the vent cover as a result of the ignition source. Classification tests on each of the powders to be used showed that reducing the ignition energy had no effect on the value of K,r obtained. For all vented explosions all other parameters (ignition delay, pre-dispersion pressure in vessel, dispersion pressure in the dust hopper) were the same as for the standard test. Three vent diameters were investigated; 76 mm, 100 mm and 128 mm. To seal the vent simple vent covers, made from thin (50pm) polythene film lightly glued to a cardboard frame to form a diaphragm, were used for all experiments. The external diameter of the frame was 140 mm while its internal diameter varied to match the diameter of the vent. The diaphragm was sandwiched between a vent cover support grid and the ducting adaptor flange and the complete assembly bolted to the sphere (see Figure 4). The support grid was made from 220 mm diameter 1.5 mm stainless steel plate with a hole cut from the centre to match the diameter of the duct, into which was welded a 2.5 mm wire mesh with a grid size of approxi-

of vent ducts on the reduced explosion pressures of vented dust explosions:

The effect

mately 25 mm. This grid supported the diaphragm against the evacuated pressure of 0.4 bar absolute (-0.6 bar gauge) during the pre-dispersion phase of each test. The presence of the grid reduced the effective area available for venting by 15-18%, thus the vent coefficient, normally given by V2’3jA,

K=

where A, equals the vent area, was increased for each vent by a corresponding amount, i.e. is given by

where AfV is the free vent area. Values of the vent coefficient, for each of the vent diameters used are presented in Table 3. All the ducting was made from galvanized heavy weight steel pipe to BS 1387, fitted with galvanized steel flanges to BS 10 Table E. Up to four lengths of pipe could be connected to form the duct; these had nominal lengths of 100 mm (adaptor flange), 400 mm, 900 mm and 1900 mm allowing various duct lengths up to a maximum of approximately 3400 mm to be investigated . Enclosed explosion tests The Kst value was chosen as the indicator of dust explosibility in both series of tests, so that comparisons between the results from the 20 1 sphere test investigation and the 18.5 m3 vessel investigation could be made. A preliminary series of enclosed explosions was conducted in the large scale vessel. Changes were made to the ignition delay and dust injection pressure until the maximum rate of pressure rise corresponding to the K,, value and the cube root law was obtained, at the same dust concentration. In terms of the rate of combustion in an enclosed explosion as measured by the maximum rate of pressure rise, this procedure effectively calibrated the vessel for the dusts used in the tests5. The injection pressures and time delays for each dust are given in Table 4.

The injection conditions altered from dust to dust. However, for the three dusts that did not coagulate (coal, toner and aluminium) the conditions were the same. More rigorous conditions have been necessary for aspirin dust, perhaps because it coagulates and the large injection ports in the 18.5 m3 vessel do not break it up as well as the ring system in the 20 1 sphere. The highest K,, value obtained for the polyethylene dust was 106 harms-t (compared with 190 bar m s- ’ in the 20 1 sphere), again because the dust coagulates readily. Vented tests without ducts Comparison with nomograph predictions. As a preliminary to the main work, a series of tests was carried out without the fitting of vent ducts. The reduced pressures measured in these tests have been compared with predictions from the VDI venting nomographs. The reduced explosion pressures cover a wide range of values from as low as 1.12 bar a to as high as 8.2 bar a. The results of the tests are given in Table 5. In all cases other than aluminium flake, the measured explosion pressure is below the predicted value. The predicted overpressure can be up to three times the measured overpressure. These results are in keeping with expected comparisons between nomograph predictions and measurements with dusts of P,,, around

Table

Results

5

and

comparison

by the Vent

VDI area

venting

Vent

areas

used

in small

scale

Vent

diameter

Total

(mm)

vent

A,

area,

Free

vent

At, (mm’1

(mm’)

76

4536

3720

100

7854

6519

19.8 11.3

128

12868

10552

7.0

coal

4

Details

of dust

injection

and

ignition

dust

DUST Coal Aspirin TOflW Polyethylene Aluminum

18.5 Ill3 K,-value lbarms-‘I

Cogcentrstion

20 30 20 30 20

760 540 760 540 760

144 254 236 106 630

0.5 1 .o 0.25 0.5 0.25

lkgm

‘1

barms

oredicted

‘) 0.50

7.36

i.l

0.2

0.25

0.56

1.1

0.5

0.61

1.04

0.9

0.1

0.24

0.84

0.636

0.9

0.2

0.64

1.03

0.9

0.5

1.24

1.64

0.385

0.7

0.1

0.58

1.52

0.7

0.2

1.56

1.83

0.7

0.5

1.38

2.81

0.5

0.1

2.44

3.13

0.5

0.2

2.58

3.68

0.5

0.5

3.77

35.7

Vented

explosions:

aspirin

dust

(K,, = 254

5.47 ‘)

1.1

0.1

0.71

1.04

7.36

1.1

0.2

0.94

1.26

1.1

0.5

1.04

1.97

.0.7

0.1

2.45

2.80

0.7

0.2

2.96

3.28

0.7

0.5

3.10

4.93

0.385

explosions:

aluminium

flake

1.1

0.636 0.9

11.00

” Dust

bar m s

0.95

pnl.x (bar al 8.5 8.3 8.8 7.9 11.0

= 144

measured

0.21

7.36

Ignition delay Imsl

Pred (bar g)

IK,,

0.95 InjectIon pleSS”W (bar a)

Pred bar gl

0.1

Vented

procedure

P (barStat g)

(ml

1.1

18.18

Table

m3 vessel,

0.95

coefficient K = pi3/Ati

18.5

predicted

Vent

0.196

area,

in the

overpressures

11.00

experiments Vent

Tests

explosion

nomographs

diameter

explosions:

explosion

reduced

(m’l

K factor Vented

of vented with

18.10

Table 3

G. Lunn et.al.

concentration

J. Loss Prev.

Process

= 0.5

kg m

Ind.,

(K,, = 630

bar m s

‘1

0.1

4.15

0.2

3.85

2.81 3.32

0.5 0.5”

4.83 7.12

4.95

0.5”

7.23

0.1

3.10

4.21

0.2

5.0

4.93

0.5

4.76

7.25

3

1988,

Vol 7, October

185

The effect

of vent

ducts

on the reduced

explosion

pressures

9 bar a (Ref. 5). Generally, the nomographs give conservative results for St1 and St2 dusts, as has been pointed out by Eckhoffg. It is clear from work by Eckhoff ” that in most industrial processes the dust clouds produce less violent explosions than those to which the nomographs apply. However, the nomograph method is a well used approach to calculating venting requirements and the conditions in the dust cloud to which the nomographs apply (central ignition and a state of turbulence producing a combustion rate generating the rate of pressure rise expected from the dust’s K,, value and the cube root law) have been used in the present tests so that comparisons can be made with previously published explosion data obtained under the same conditions. In the case of aluminium flake, the comparison between estimation and measurement of the reduced pressures suggestions that the Kst value can be estimated only approximately. The results suggest that in some of the tests the Kst value was above 630 bar m s-l. Tests done with a concentration of 0.5 kgme3 indicate a KS1 value well in excess of 630 harms-‘. Vented tests with ducts A method for the prediction of the eflect of vent ducts on the reduced explosion pressure. The measured explosion pressures are tabulated in Tables 6-9. The ducts were empty of dust prior to the experiment, and the only dust taking part in the experiment was that injected into the main vessel. Some examples of the measured effects of vent ducts on reduced explosion pressures are shown in Figures 3-10. The lines in these graphs represent the results of calculations using a simple model of the effect of vent ducts on the reduced explosion pressure.

Table 6

Experiments

of vented

dust

explosions:

G. Lunn

et

al.

Experimental tests are useful for measuring the effect of vent ducts in particular circumstances, but more general guidelines are needed for users of dust handling equipment. A simple empirical model has been derived that predicts the reduced explosion pressure that can be expected in a vented vessel, when a vent duct of given L/D ratio is fitted. The model does not attempt to describe the complicated processes of combustion that must take place in a vented vessel/vent duct system. In outline, the model considers the explosion to take place in two parts-the explosion in the main vessel, followed by a secondary explosion in the duct. The explosion in the main vessel is assumed to generate a pressure throughout the system, and the explosion in the vent duct causes a further increase in this pressure. In reality, the explosion process will be a continuous one, although much of the increase in explosion pressure caused by the vent duct will occur because the volume of the system has been increased while the vent area has remained essentially the same. The empirical nature of the model arises from the specification of a combustion rate in the explosion in the vent duct. This has been done as simply as possible and the information required to use the model consists of the duct configuration (L/D ratio, number and type of bend), the K,, value of the dust and the reduced explosion pressure in the vessel when the duct is absent. This latter value may either be measured or estimated from the Kst nomographs in VDI 3673 (Ref. 4). Thus apart from the duct parameters, the information required for the vent duct model is the same as is needed to use the Kst nomographs. Comparisons between predictions and experimental results are shown in Figures 5-12. Vented explosions

when the vent is unobstructed.

The

in 18.5 m3 vessel with a straight duct

Vent Vent

area Im2)

Dust

diameter lm)

(bar a) Open vent

Reduced explosion pressure (bar al and duct (L/D) ratio

P stat

Coal

0.95

1.1

Coal

0.95

1.1

1.2

Aspirin

0.95

1.1

open vent

Coal

0.196

0.5

open vent

Coal

0.196

0.5

1.5

Coal

0.385

0.7

Open vent

LID PW LID PWd LID PW, LID PWJ LID P red

0 1.12 0 1.20 0 1.60 0 2.55 0 4.8

LID

0

PM

1.8 0 3.4 0 1.25

Aspirin

0.385

0.7

1.1

LID

Coal

0.636

0.9

Open vent

I$ PWd

Aspirin

0.636

0.9

Open vent

Toner

0.636

0.9

Open vent

LID

Aluminium flake (0.25 kgm ? Aluminium flake (0.5 kgm ?

0.95

1.1

1.5

0.95

1.1

1.5

:jL; P reo LID Pr.0

LID P,X

186

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Ind.,

7988,

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0

2.1 0 2.05 0 5.7 0 8.1

0.90 1 .l 0.90 1.20 0.90 2 2.35 2 4.5 1.4 1.55 1.4 3.4 1.1 1.15 1 .l 2.4 1.1 2.2 0.9 6.5 0.9 a.4

5.5 1.20 5.5 1.55 5.5 2.45 12 2.4 12 4.8 8.6 2.4 8.6 6.7 1.3

6.7 2.8 6.7 3.3 5.5 7.8 5.5 8.8

10.0 2.0 10.0 10.0 2.55 22 4.0 22 15.7 2.4 15.7 4.0 12.2 2.03 12.2 3.97 12.2 3.6 10.0 8.1 10.0 9.5

14.5 2.3 14.5 2.6 14.5 3.00 32 4.0 32 5.4 22.8 3.7 22.8 5.8 17.8 1 .a5 17.8 4.3 17.8 4.1 14.5 7.9 14.5 9.1

The effect

Table 7

of vent

Experiments

ducts

on the reduced

explosion

pressures

of vented

dust

explosions:

G. Lunn

et al.

in 20 I vessel with straight ducts

Dust

Vent area (m*f

Coal

0.00454

Vent diameter tm)

Maximum reduced explosion pressure (bar a) and duct (L/D) ratio 1

0.076

.o

LID

pm,

1.2 1.37

6.6 1.97

13.0 2.5

17.3 2.9

26.2 3.25

31.8 3.55

38.4 3.62

43.6 3.8

30.0 3.0

33.7 2.6

Coal

0.00788

0.1

1 .o

LID Pred

0.9 1.15

5.1 1.26

10.3 1.30

14.3 1.75

20.5 2.20

24.3 2.02

Coal

0.0129

0.128

1 .o

LID P,*,

0.8 1.15

3.9 1.22

7.8 1.25

11.1 1.32

18.9 2.06

25.8 2.25

Polyethylene

0.0129

0.128

1 .o

LID P
0.8 1.25

3.9

7.8 1.9

11.1 2.1.

18.9 2.75

25.6 2.85

Aspirin

0.00454

0.076

1 .o

LID P red

1.2 2.8

6.6 2.9

13.0 3.52

17.3 3.40

26.2 3.70

31.8 3.67

38.4 3.75

43.6 3.57

Aspirin

0.00786

0.1

1 .o

LID PM

0.9 1.32

5.1 1.42

10.3 2.32

14.3 2.57

20.5 2.57

24.3 1.85

30.0 2.35

33.7 3.20

Aspirin

0.0129

0.128

1 .o

0.8

3.9 1.08

7.8

11.1 1.35

18.9 1.73

25.8 2.22

Toner

0.0129

0.126

1 .o

LID pm LID

0.8 1.35

3.9 2.25

7.8

P red

1 T.l 2.90

18.9 3.05

25.8 3.2

LID Pm.3

0.8 2.67

3.9 5.3

7.8 5.15

11.1 5.52

18.9 5.05

25.8 5.25

Aluminium flake

Table 8

Dust Coal

0.0129

Experiments

Vent area (m*) 0.95

0.128

1 .o

in 18.5 m3 explosron vessel with 45O bend in vent duct Vent diameter fm)

Pstat (bar a)

1.1

Open vent

Reduced explosion pressure (bar a) Vent duct L/D ratio and number and positions of the bends

LID

0

Bend

P,&

1.12

Coal

0.95

1.1

1.2

LID Bend

0

P,a,

1.25

Aspirin

0.95

1.1

Open vent

LID

0

Bend

Coal

0.196

0.5

Open vent

Pred

1.58

LID

0

Bend

Coal

0.196

0.5

1.5

P red

2.55

LID

0

PWd

4.75

LID

0

Bend

Coal

0.365

0.7

Open vent

Bend

Aspirin

0.385

0.7

1.1 Bend 3.40

Coal

0.636

0.9

Open vent

Toner

0.636

0.9

Open vent

0

PIed

1.25 0

$Z Bend

2.0

2.7 1 m from duct exit 1.25

7.3 1 m from duct exit 1.75

11.9 1 m from duct exit 2.1

16.4 1 from duct exit 2.3

2.7 1 m from duct exit 1.25

7.3 1 m from duct exit 1.80

11.9

16.4 6 m from duct exit 2.20

2.7 1 m from duct exit 2.25

7.3 1 m from duct exit 3.6

11.9 1 m from duct exit 3.1

16.4 1 m from duct exit 3.9

6.0 1 m from duct exit 2.7

16.0 1 m from duct exit 3.85

26.0 1 m from duct exit 3.8

36.0 6 m from duct exit 4.05

30.0 2 bends

6.0 1 m from duct exit 4.50

16.0 1 m from duct exit 5.20

26.0 1 m from duct exit 4.75

36.0 6 m from duct exit 5.8

30.0 2 bends

4.3 1 m from duct exit 1.5

11.4 1 m from duct exit 2.9

18.5 6 m from duct exit 3.15

25.7 10 m from duct exit 3.4

28.5 2 bends

4.3 1 m from duct exit 3.9

11.4 1 m from duct exit 5.2

18.5 6 m from duct exit 5.85

25.7 10 m from duct exit 5.9

3.33 1 m from duct exit 1.35

8.9 1 m from duct exit 1.65

14.4 1 m from duct exit 1.90

20.0 1 m from duct exit 2.10

3.33 1 m from duct exit 3.0

8.9 1 m from duct exit 4.35

14.4 1 m from duct exit 4.55

20.0 1 m from duct exit 4.15

J. Loss Prev.

Process

lnd.,

1988,

Vol I, October

13.6 2 bends 3.0

4.90

5.3

4.05

187

The effect

Table

9

of vent

Experiments

ducts

in 18.5

on the reduced

m3 vessel

with

90’

explosion

pressures

bend

duct

in vent

of vented

dust

explosions:

G. Lunn

et al.

vent Vent Dust

Coal

area

diameter

(rn’)

(ml

0.95

1.1

Reduced

P,,,, (bar a) Open

vent

Vent

LID

0

Bend

Coal

0.95

1.1

1.2

P red

1.12

LID

0

Bend

Aspirin

0.95

1.1

Open

vent

P red

1.25

LID

0

Bend

Coal

Coal

0.196

0.196

0.5

Open

vent

1.5

0.5

P red

1.58

LID

0

PTd

2.55

LID

0

Bend

Coal

0.385

0.7

Open

vent

P red

4.75

LID

0

Bend

Aspirin

0.385

1 .l

0.7

p,ed

1.8

LID

0

Bend

Coal

0.636

0.9

Open

vent

P.ed

3.40

LID

0

Bend

Toner

0.636

0.9

Open

vent

P&

1.25

LID

0

Bend P&

2.02

model uses as a starting point the conditions expected in the vented vessel when the vent duct is absent. For a compact vessel, the reduced explosion pressure can be obtained from the Kst nomographs in VDI 3673 (Ref. 1) when the vessel volume, v(m3), the vent area, A, (m’), the dust Kst value (bar m s-i), and the bursting pressure of the vent cover, PSt,, (bar a), are known. This value of the reduced pressure is usually a conservative estimate, and a measured value would be lower. Nevertheless, whether either measured or estimated, a value or Pred for an unobstructed vent (i.e. one without a vent duct) can be obtained, (Pred)& The Kst nomographs are developed from an equation derived by Heinrich3. The basis of this equation is that at the reduced pressure the rate of pressure rise due to the combustion equals the rate of pressure fall due to outflow of material through the vent. A simple equation can be derived to calculate the rate of mass outflow if the pressure in the vessel is known. A standard orifice flow equation equates the pressure loss to a number of velocity heads:

L/D ratio

duct

explosion and

number

pressure and

7.3

2.8

(bar

a)

positions

of the

bends

16.4

11.8

1 m from

1 m from

1 m from

1 m from

duct

duct

duct

duct

exit

exit

exit

2.15

1.90

1.25

16.4

7.3

11.8

1 m from

1 m from

1 m from

duct exit 1.45

duct

duct

2.8

exit

2.8

exit

2.50

1.90

exit

2.75 1 m from duct

exit

2.90 16.4

11.8

1 m from

7.3 1 m from

1 m from

1 m from

duct

duct

duct

duct

exit

exit

4.3

2.5

16

6

exit

4.0 1 m from

1 m from

1 m from

26 6 m from

duct

duct

duct

exit

exit

6

16

1 m from

1 m from

duct

duct

exit

exit

5.90

5.05

6 m from

duct

duct

exit

2.2

exit

3.0

exit

26 1 m from

1 m from

duct exit 5.50

36 duct

exit

6.15 25.7

18.5

1 em from

duct 4.9

11.4

4.3

exit

36

4.6

4.0

3.65

exit

3.1

1 m from

1 m from

duct exit 3.0

duct

exit

4.0 25.7

4.3 1 m from

1 m from

1 m from

6 m from

duct

duct

duct

duct

18.5

11.4

exit

4.50

exit

exit

exit

5.8

6.05

5.54

3.33

8.9

1 m from

1 m from

1 m from

20.0 1 m from

duct

duct

duct

duct

exit

14.4 exit

exit

1.8

2.05

3.33 1 m from

8.9 1 m from

1 m from

duct

duct

duct

exit

4.05

exit

20.0

14.4 exit

1 m from duct

exit

4.9

5.0

3.3

exit

2.00

1.40

which can be written 105((

Pred)O-

pO)=zpu2

1

(1)

where ( Pred)e has already been defined as the reduced explosion pressure (bar a) in a vessel with an unobstructed vent; PO is the atmospheric pressure when the orifice flow is subsonic (taken as I bar a in these calculations); p is the density (kgmm3); u is the velocity at the vent opening (ms-‘); and C, is an orifice contraction coefficient which has a value of 0.61 for a vent area small in comparison with other flow areas in the system. This is assumed to be the case for a vent discharging into the open air. Thus lo5 (( &d)O - PO) = 2.687(; pu2) The rate of mass discharge,

kgs-‘,

is given by

dm dt = WA, where A, is the area of the vent (m’). Substitution of Equation (3) into Equation

188

J. Loss Prev.

Process

lnd.,

1988,

Vol

I, October

(2) gives,

The effect

of vent

ducts

on the reduced

explosion

pressures

m

Vent

duct

dust

G. Lunn et al.

explosions:

a

k 5 -E PL

ratio

LID

of vented

0

4

8

12

16

Vent

20

duct

24

28

32

36

ratio

LID

I

4,

1L 0

I

’

2

4

I

I

I

I

1

1

6

6

10

12

14

16

Vent

duct

f&q--i

I

18

r&o

L/D

0

4

8

12

16

Vent

31 0

I

1

4

I

8

I

12 Vent

I

I

16 duct

,

20

24

LID

ratio

32

a

4

I 12

I 8

I 4

Vent

Figure 3 vessel

Effect

volume

meter = 1 .l vent

of

vent

= 18.5

m;

duct

duct

m’,

on

straight

area = 0.95

f 16

reduced duct:

= 1 .l

m; area = 0.95

m2; open

m area = 0.196

m2 P,,*

diameter

= 0.7

m; area 0.385

4

0

8

dust;

duct

vent;

= 1.5

m2 P,,,,

12

Vent

vent

2

c, coal

dust;

= 1.1 bar a

16

20

24

ratio

L/D

4

8

12

Figure

4

vessel

volume

Effect

I

I

I

I

1

I

6

8

10

12

14

16

meter = 0.9 diameter

m:

of

= 19.5

vent ms,

duct

on

straight

area = 0.636

LID

16

24

28

ratio

L/D

explosion

a, coal

vent;

b,

dust; toner

. .

1 0

ratio

reduced duct:

m* open

20

16 duct

ratio

L/D

1

duct

28

bar a; d. aspirin

4

Vent

24

20 ratio

LID

dia-

2*

0

16

duct

dust;

Vent

duct

36

Figure 5 Effect of vent duct on reduced explosion pressure vessel volume = 20 I, straight duct: a, coal dust; vent diameter = 0.1 m; area = 0.00706 m2 P,,=, E 1 .O bar a; b, aspirin dust; vent diameter = 0.1 m; area = 0.00786 m2 P_, z 1 .O bar a; toner dust; vent diameter = 0.129 m; area = 0.129 m’ C.

0

Vent

32

P,,,, G 1 .O bar a

a, coal

= 0.5

28

pressure

m*; PSI,, = 1.2 bar a; b, aspirin

diameter vent

24

explosion

vent diameter dust;

I 20

ratio

L/D

ratio

12 Vent

0

24

L/D

36

0

2

20

I

I

28

duct

I 4

dust;

die vent

= 0.9 m; area = 0.636 m2 open vent; c, aluminium flake; vent diameter = 1 .l m; area = 0.95 m* Pst,, = 1.5 bar a. 0, 0.25 kgm ;‘ q , 0.5 kgm~3

I 12 Vent

pressure vent

I a

duct

I 16 L/D

I 20

1 24

ratio

Figure 6 Effect of vent duct on reduced explosion pressure vessel volume = 20 I. straight duct: a, polyethylene dust; vent diameter = 0.128 m; area = 0.0129 m*; P,,., I 1 .O bar a; b, aluminium flake; vent diameter = 0.128 m; area = 0.0129 mz; P,,,, - 1 .O bar a

J. loss

Rev.

Process

Ind.,

1988,

Vol

1, October

189

The effect

0

of vent

2

ducts

4

6 Vent

on the reduced

8 10 duct L/D

12 ratio

explosion

14

16

pressures

of vented

2

11 0

4

6 Vent

I

I

2

4

I

8 duct

10

31

I

6

8

Vent

duct

12 ratio

L/D

I

10

14

16

I

I

I

12

14

16

G. Lunn

et al.

1 4

I 8

I

12 Vent duct

I

I

I

16

20

24

L/D

ratio

18

I

la

ratio

LID

explosions:

18 0

0

dust

Figure 7 Effect of vent duct on reduced explosion pressure vessel volume = 18.5 m3: a, coal dust; vent diameter = 1.1 m; area = 0.95 mp; P,r,? = 1.2 bar a; duct = 45O; b, coal dust; vent diameter = 1 .l m; area = 0.95 m’; PS,.t = 1.2 bar a; duct = 90°; c, aspirin dust; vent diameter = 1.1 m; area = 0.95 mz open vent, duct = 45O. q , single bend 1 m from duct exit; n , single bend 6 m from duct exit; l , two bends

Vent

duct

Vent

duct L/D

ratio

L/D

ratio

Figure 9 Effect of vent duct on reduced explosion pressure vessel volume = 18.5 m3 a, aspirin dust; vent diameter = 0.7 m; area = 0.385 m2; P,, = 1.1 bar a; duct = 90°; b. coal dust; vent diameter = 0.9 m; area = 0.636 m2, open vent, duct = 45O; c, coal dusti vent diameter = 1.1 m; area = 0.95 m*, open vent, duct = 45 A, single bend 1 m from duct exit; A, single bend From duct exit

ii 0

2

0

4

i$;

4

8

6 Vent

a 10 duct LID

12

16

Vent

duct

12 ratio

20

24

L/D

ratio

14

28

5 0

4

12 16 Vent duct

8

20 L/D

24 ratio

28

32

0

4

0

24 ratio

28

32

4

a

12 Vent duct

16 L/D

20

24

1 28

ratio

Figure 8 Effect of vent duct on reduced explosion pressure vessel volume= 18.5 m3 a, coal dust; vent diameter =0.5 m; area = 0.196 m’; P,,,, = 1.5 bar a; duct = 45O. b. coal dust: vent diameter = 0.5 m: area = 0.196 mz; PSt,r = 1.5 bar a; duct = 90’; c, coal dust; vent diameter = 0.7 m: area = 0.385 m2 open vent, duct = 90°. q , single band 1 m from duct exit; n , single band 6 m from duct exit; 0, two bends

190

J. Loss Prev.

Process

lnd.,

7988,

Vol

36

n

I

1

a

12

I

16

I

I

20

24

L/D

ratio

I

I

28

32

1

36

36

0

11 0

I

4

Vent duct 12 16 20 Vent duct LID

18

C

21

6

32

n

36

ZG;

16

I, October

4

12

8 Vent

duct

16 L/D

20

24

28

ratio

Figure 10 Effect of vent duct on reduced explosion pressure vessel volume = 18.5 m3 8, aspirin dust; vent diameter = 0.9 m; area = 0.636 m’, open vent, duct = straight; b, coal dust; vent diameter = 0.5 m; area = 0.196 m’, open vent, duct = 45O; c, coal dust; vent diameter = 0.5 m; area = 0.196 m*, open vent, duct = 90’; d. vent diameter = 0.7 m; coal dust: area = 0.385 m2, open vent, duct = 45O. d, single band 1 m from duct exit; I, single bend 6 m from duct exit; l , two bends; A, single bend 10 m from duct exit

The effect

after

g

of vent

ducts

on the reduced

explosion

Ad&d)0

2 x 10s

-

I’*

(. >

pO)L’2P”2

(4)

2687

Substituting p = (P,d)oM,/RT, where M, is taken as of air (0.029 kg mol- ), ‘ the molecular weight R = 82.0552 x lo-$ m3 bar/Kmole and T (K) is the temperature assumed to be obtained by adiabatic compression from ambient (T = 298(( P,,~)o/Po)“~286), into Equation (4) gives dm dt

A, = ~‘/2

(&d)Ci’*((&dh

-

f’o)“*5128

(9

Equation’ (5) is suitable only when the flow through the vent is subsonic. When (Pred)O > 1.89P0. the flow is choked, and

dm -=-

Thus, 10’ and,

- $!$

for choked X 0.47(Pred)O

= 2.687(;pu2)

by the same procedure A, T,,2

dm -=-

dt

(6)

as for subsonic

flow:

(p&o3516

The rate of mass outflow (Pred)O and A, are known.

(7)

can

thus

The changes to jlow resistance caused

be calculated

if

by fitting a duct.

Fitting a duct to the outside of a vent opening changes the resistance to flow. The pressure loss is now made up of three components: the loss at the duct exit, the frictional loss along the duct and the loss at the duct entrance. For the moment any effect of an explosion in the duct is neglected, and a procedure is described for estimating the new reduced pressure resulting from an explosion in the vessel under the new conditions for flow discharge. The area of the duct is assumed equal to the vent area, and of the same shape. Data’* has been used to calculate the pressure losses at various pipework configurations in terms of velocity heads. The pressure loss at the end of a duct discharging to atmosphere is equal to one velocity head: AP=fpu’

Thus 105(P2

-

PO) = ;&Iu*

(8)

where P2 (bar a) is the pressure inside the duct at the exit, and u is the flow velocity (ms-‘) inside the duct. Substituting for u in Equation (8) gives an expression for dmldt: $

= (Pz (Pz - Po))lf2 +2

8407

(9)

T, the temperature (K), is calculated by assuming adiabatic compression from ambient (298K) to P2. Equation (9) is suitable for subsonic flow at the duct

explosions:

G. Lunn et al.

> 1.89Po, the flow is choked

4

T,/2

and

5776

To estimate the new reduced pressure caused by explosion in the vessel some comparison has to be made with the. situation when the vent duct is absent. It is assumed here that the rate of mas outflow remains the same as at (Pred)~ and as calculated by either Equation (5) or Equation (7). Knowing the value of (dm/dt) means that the pressure 9 can be calculated by either Equation (9) or Equation (10). The pressure loss along the duct depends on the length to diameter (L/O) ratio of the duct and the friction factor. The general equation is: - Pz) = 8f

= 0.47( Prcd jo

flow

dust

P2A,

dt

105(p,

AP = (P&O

of vented

exit. When

some algebra

=

pressures

$ $ (. >

(11)

where PI is the pressure inside the duct at the entrance (bar a); f is the friction factor; p is the density (kg me3); and u is the velocity in the duct at the entrance (m s-l). A satisfactory engineering approximation is 8 f = 0.025 (Ref. 12) and this value has been used in all the calculations. Substituting dm/dt = puA, and the equation of state into Equation (11) gives PI (PI -

P2)

= y

(5)

&

(!$)*(0.0283

x 10-6)

(12) where T is calculated by assuming adiabatic compression from ambient (298K) to PI. PI can be calculated from Equation (12) by trial and error. The pressure loss at the entrance to the duct from the vessel depends on the configuration of the entrance. The general equation for this pressure loss is 105((P,,d),

- P,) = F* fpU2

(13)

where (Prcd)r is the new reduced pressure for the vessel explosion (bar a) and F is a factor, which depends on the configuration of the junction between the vessel and the duct. When the cross-section of the vent and the crosssection of the duct are the same for area, shape and possible, Fdepends on the area ratio of the duct and the vessel. Data is given in Ref. 12. Substituting dmldt = pA,u and the equation of state in Equation (13) gives: 2 lo’((Pred),

-

8)

=;

$7 (

RT

PI MwA,Z

)

(14)

and so p,((p,d),-~,)=E;

$ (

2(O.O293xlO-6) >

(15) where T is obtained assuming adiabatic compression from ambient to PI. (p&)1 can be calculated by Equation (15) using trial and error. The pressures throughout the vessel-duct system can now be calculated. Unless the duct length is very long

J. Loss Rev.

Process

lnd.,

1988,

Vol

I, October

191

The effect

of vent

ducts

on the reduced

explosion

pressures

(P&)1 will be less than (Prcd)O because the resistance to flow is less than the duct is fitted than for the orifice alone. When the duct contains bends, the restriction to outflow is increased. The following has been presented for sharp bends IL: AP = 1.2(1 - cos a)$pu2

for circular

ducting,

where CYis the angle of the bend. When several bends are present, the pressure loss can sometimes be obtained by simple summation. Thus the equation for the pressure loss along the duct when bends are present is

where N is the number of bends of a given angle; FF is the relevant loss term; and the summation sign implies bends of different angles. Using dmldt = pAu and the equation of state gives a variation of Equation (12) lO’(P,

0.025 $+EN*

- P2)Pl =

of vented

and thus PI can be found and error.

(0.0283 x 10-6)

by the usual

means

of trial

This model considers the The explosion in the duct. explosion in the vessel-duct system to take place in two stages. Heinrich’s model assumes that at (Pred)O, combustion inside the vessel is essentially complete. Similarly, the present model assumes that at (Pr&)[, combustion inside the vessel is ended, and that any further increase in explosion pressure due to the duct is caused by the flame entering the duct and burning the dust/air mixture therein. It is the net creation of volume from this secondary explosion that is assumed to cause the increase in the explosion pressure. The conditions of the start of this secondary dust explosion are first, the pressure in the explosion vessel equals (PI&)], and second, the pressure in the duct is taken to be constant along the duct and equal to PI. The volume of dust, VE, ejected from the vessel through the duct, is given by VE

=

vl

_

y,

- PO) (Pm - PO)

((Predh

(16)

where VI is the vessel volume, and P,,,,, is the maximum explosion pressure generated in an enclosed explosion. P,,,,, can be measured either in the vessel under consideration or obtained from tests in the Standard 20 1 sphere test. The value of Pmax should represent the energy release of the dust explosion only; when applied to the 20 1 sphere results, 1 bar has been subtracted from the measured value of Pm,, to compensate for the energy imparted by the igniter. VE is the volume of dust cloud measured at 1 bar pressure, and to take into

192

J. Loss Prev.

Process

lnd.,

1988,

Vol

I, October

G. Lunn et al.

account the overpressure in the duct, the right hand side of Equation (16) is multiplied by the density ratio be/pn) to give the volume of the dust cloud at the conditions in the duct. pD is the density assuming adiabatic compression from ambient pressure to the duct pressure, PI. The volume of dust taking part in the explosion in the duct depends on the relative values of the ejected volume of dust and the volume of the duct, VD,, where vu” = AVL. If VE > VD”, then the volume of dust to be burnt equals vu”, if VE < VDu, then the volume of dust to be burnt equals VE. The net rate of volume generation depends on the rate of combustion of this dust cloud compared with the rate of outflow from the duct to the open air. However, the rate of combustion depends on many factors that make an accurate assessment difficult. A simple empirical model utilizing the K,, value of the dust and the cube-root law has been used throughout these calculations. A simple formulation for the rate of expansion due to combustion, Rr, is

VDu

”

explosions:

V2d,3 VDu RE=-!$.-=K,,_

FF) : s

-$

dust

PO

PO

(17)

Equation (17) is the cube root law applied to the duct volume using the K pf value measured by a standard method. Normally, scaling the rate of pressure rise by the K,, value and the cube root law is only applicable to vessels with L/D ratio less than 5 : 1, and its use here is not intended to suggest any similarity between the advancing flamefront that would be generated by an ignition source in the duct and the combustion resulting from an explosion surging into the duct from the main vessel. Equation (17) is used only as an empirical formula and makes no statement about the actual rate of pressure rise taking place in the duct volume; it is assumed to describe the number of cubic metres at atmospheric pressure generated per second by combustion. The model does not calculate pressure changes throughout the system with either time or position; it calculates a final reduced explosion pressure by assuming the explosion volume increase is evenly distributed. Equation (17) does not imply any consideration of the method of combustion; however, in the initial surge of the explosion into the duct, combustion can be expected to be dispersed throughout a length of the duct. Thus, when the L/D ratio is short, combustion is likely to take place throughout the entire duct volume, but for longer L/D ratios the initial surge is likely to extend only part way along the duct, the rest of the dust being consumed as the explosion propagates. It is thus unlikely that the rate of expansion will continue to increase indefinitely with duct volume as the L/D ratio increases. To take this into account, when the L/D ratio > 10. the rate of expansion is assumed to stay constant at the value appropriate for L/D = 10. The progress of the duct explosion is followed by calculating the amounts of volume created and lost during small time steps until the dust initially in the duct

The effect

of vent

ducts

on the reduced

explosion

has been either burnt or ejected. The time step, dt, is chosen so that the final pressure is independent of dt. The volume expansion in the time step, is given by

Pl

VEX=RE-

PO

dt

(18)

The ratio (PI/PC,) has been introduced to take into account the effect of initial pressure on the expansion due to combustion. This ratio changes as the duct explosion progresses. The amount of dust air mixture burnt in a time step to give this expansion is given in volume terms by vB

=

RE

dt

I(pma;;po)

(19)

factor of the where (P,,,,, - Po)/Po is the expansion combustion. Vn is assumed to remain constant throughout the duct explosion; its value is subtracted from the volume of dust initially in the duct at the end of each time step. The volume lost from the duct through the open end is given by v

I.

=dmdt dt

P

The rate of outflow from the duct, dm/dt, is calculated assuming that there is a constant pressure, PI, throughout the duct. As the explosion continues, this pressure rises. The equation for rate of mass outflow includes pressure losses due to friction along the pipe and at bends, and at the duct exit. For subsonic flow the equation is

+CN*

where FF is a restriction number of bends. For choked flow dm _ PIA, dt-T’/ZX

factor

5764

1 + 0.025 LID

FF

>

for bends

and N is the

(22)

The rate of volume outflow is calculated by dividing Equations (21) and (22) by the density. Both density and temperature T are obtained by assuming adiabatic compression from ambient to PI. No account is taken of hot gas; the outflow is assumed to be always of unburnt material. The outflow equations used during the duct explosion incorporate the loss terms for the bends. The length of duct incorporated in the L/D term is shown on the appropriate figures. Generally, it is taken as the shortest length of duct, and terms are added to the usual L x A, method of calculating the duct volume to take into account the volume of the corners. Essentially, this procedure assumes that for a given duct volume, the effect of a bend on the reduced explosion pressure is due to the influence of the increased resistance and not to any increase of the

pressures

of vented

dust

explosions:

G. Lunn et al.

combustion rate compared with that in a straight duct. When the bend is close to the vent opening, however, its presence is likely to accelerate the combustion rate. The net volume expansion is given by: VN= VEX-

V,

(23)

The increase in pressure is obtained by dividing VN by the appropriate volume. At the start of the duct explosion the pressure in the duct is lower than in the vessel, and so initially the pressure is allowed to rise only in the duct, and thus the appropriate volume is the duct volume. When the pressure is uniform throughout the vessel-duct system, the appropriate volume is the sum of the vessel plus duct volumes. The amount of dust left is obtained from the following equation: Vo”sT=(vn”ST)r-C

va+

t5.p

i(

PI > i

(24)

where i is the number of the time step and ( VDUST)Iis the volume of dust initially present in the duct. pi is the density in the duct at the start of the duct explosion. The density ratio in Equation (24) is present to convert the volume lost at the conditions within the duct at time step i, to the volume at conditions initially present in the duct. When the amount of dust left is zero, the final explosion pressure is reached. A simple calculation after the last time step (which overshoots) brings the final pressure back to the actual amount of dust present. Comparison

with experiment

The model predictions have been compared with the reduced explosion pressures measured in the explosion vessel. Generally the agreement between prediction and experiment is satisfactory. The poorest agreement occurs with explosions in the 18.5 m3 vessel and with open vents, when in some sets of results the measured pressures regularly exceed the predicted values as the L/D ratio increases. In some of the open vent tests agreement between prediction and measurement is good, but ducts added to an open vent sometimes produced pressures ranging from 0.3 to 1 bar higher than expected, especially when ( PXd)O exceeded 2.0 bar a. In themselves however, the open vent results are consistent; the addition of bends to the duct increases the reduced explosion pressure by the expected amount, and the trend of the reduced pressure with increasing L/D ratio is satisfactorily calculated by the model, as Figure 12 shows. The discrepancies between prediction and experiment are greatest with coal dust, at the smallest diameter of vent and when the opening overpressure of the vent is low or non-existent. It may be that when dust is ejected into a narrow duct well in advance of the flame’s arrival, increased turbulence in the dust cloud can raise the combustion rate enough to show an effect on the explosion pressure, especially with dusts in the St1 group but not when the dust has a higher K,, value. When Psratis relatively high, the flame follows close behind the entry of dust into the duct, and does not propagate into dust which has increased turbulence.

J. Loss Prev. Process

Ind.,

1988,

Vol

I, October

193

The effect

of vent ducts on the reduced

explosion

pressures

Straight vent ducfs. Some examples of the comparisons between the maximum reduced explosion pressures measured inside the explosion vessel and the explosion pressures calculated by the model are shown in Figures 5 and 6. Generally, both the trend of the explosion pressure as the L/D ratio increased and the numerical value of the explosion pressure are well predicted. Figure 6b shows some results with an open vent. Although the trend of the changes in explosion pressure as the L/D ratio increases is satisfactorily predicted by the calculations, the experimental points all lie on one side of the calculated line. An attempt to calculate a line passing through the points, by choosing a slightly higher (Prcd)O would have been successful in this example. The results of the aluminium flake tests are shown in Figure 6~. Approximate values only for the K, and P,,,,, are available; these have been taken as 630 bar m s-i and 11 bar a respectively. In any event the experimental reduced pressures are much less than predicted by the model described earlier. However, if Equation (24) is modified to give: (vB+

&“ST=(h3”ST,I-~

& PI

(

>

(25)

i

and the model used as before, the calculated reduced pressures fall closer to the measured values. Considering the uncertainties typical of the high K,, value tests the agreement is probably reasonable. Some results from the 20 1 explosion vessels tests are compared with calculations in Figures 7 and 8. No measurements at L/D = 0 were taken in these tests, so the comparison is used to demonstrate that the trend of the results as L/D ratio increases is satisfactorily predicted. Generally, the trend is calculated satisfactorily. However, the agreement between calculation and experiment for the aspirin explosions in the 20 1 sphere is not good, except in the example shown (Figure 7b). Usually the measured pressures are much lower than predicted. When the calculations are compared with toner dust results, however, under similar conditions and a similar value of K,,, the agreement is satisfactory as can be seen in Figure 7c. This result suggests that the 20 1 sphere apparatus had not given true values in some of the aspirin dust tests. The trend in the aluminium flake explosions is calculated, as shown in Figure 8b, although the Ksr value is much lower than in the 18.5 m3 aluminium flake tests.

Vent ducts with bends. In Figuresg-II, calculations for a single 45” and a single 90” bend in the duct are compared with some of the values of the explosion pressure measured in the explosion vessel. As for the linear ducts, the trend of reduced explosion pressure with the L/D ratio is generally satisfactory, and in many cases the numerical value of pressure has been satisfactorily calculated also. On some of the figures, two measurements for pressure are shown at some values of L/D ratio. These results demonstrate the effect of position of the bend along the pipe. The bend was usually positioned at the end of the ducting, with a 1 m length of duct after the

194

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et al.

bend. Some tests were repeated with the bend closer to the explosion vessel. Usually the closer the bend was to the vent opening the higher the pressure measured, but in one case the higher pressure was measured when the bend was at the end of the duct. Generally the position of the bend did not have a large influence on the explosion pressure, only about 0.3 bar, although tests were not done with bends closer than 2 m to the explosion vessel. The effect of two 45” bends in the vent duct is shown in some of the figures. These results demonstrated that in some cases the effect of multiple bends on the explosion pressure was greater than expected from calculations assuming bend restrictions to be simply additive. Some measurements using a single curved bend rather than a sharp bend in the 20 1 sphere tests showed that explosion pressures were not noticeably different to those when the duct was straight, and of equal (LID) ratio. The eflect of duct closure and other auxiiiary experirnen ts

The effects of obstructing the end of the vent duct with either a grid or a membrane are demonstrated in Figure 1I. The conditions for these tests were a Pstat of 1.1 bar a, a vent diameter of 0.5 m and coal as the explosible dust. In these experiments, the membrane increased the reduced explosion pressure by about 0.3 bar, whereas the grid has little effect. Figure Ii also shows two examples of a vent explosion with the ignition source at the back end of the explosion vessel and not at the centre. In the test conducted without a vent duct, the reduced explosion pressure was increased by approximately 0.5 bar, whereas with a short vent duct present moving the position of the ignition source had no effect on the reduced explosion pressure. Comparisons

with data from other sources

Some tests on the effect of vent ducts have been carried out in the LJSAi2. The conditions of dust injection and ignition are different to those in the present tests and the K,, values of the dusts are not known. However, a comparison between calculated and measured reduced explosion pressures was made for some coal dust tests. A K,, value of 144 bar m s-’ was used in the calculations. In general, the agreement between calculation and experiment was reasonable, considering all the unknowns, and it

8

5

4 t 3

8 I

2L 0

I 4

I 6

I 12 Vent

* 16 duct

I 20 LID

I 24

I 28

I 32

I 36

ratio

Figure 11 Effect of vent duct closures on reduced explosion pressure; volume = 18.5 m3; vessel COSI dust (K,=144barms-‘): vent area=0.136m2; P,,=l.l bar a; straight duct; vent diameter = 0.5 m; 0, 0.5 kg me3 central ignition; q , 0.5 kg mm3 back ignition: 0, mesh fitted to duct end; A, membrane fitted to duct end

The effect

of vent

ducts

on the reduced

explosion

pressures

of vented

dust

explosions:

et al.

G. Lunn

v 4 PO1 P red

overpressure

(bargl

without

Figure 12 Comparison of results with guidance 18.5 msvessel. ~3 m duct; 0, 18.5 m3 vessel. sphere.

3 m

duct;

_,

guidance

Ref.

12;

vent

0.1 P red

duct

from Ref. 3 m duct; ----,

,’ ‘0.01

equal

14: n

A,

, 20 I

reduced

pressures

Figure 13

overpressure

Comparison

Vent duct length 7 K,,=300barms

P Sfaf= 1 .l bar

I

t

1.0

10

(bar

g)

of prediction

> 3 m. c, KS,= ‘,PS,,,=1.2bar

without

with

300

guidance

barme’, a; 0,

K,,=lOObarms~‘,

a;

K,,=lOObarms~‘.

1 IO

vent

duct from

Ref.

P,,,, = 1.5 K,,=300barms

a;

o,

7;

,

P,,,=1.5bar

PS,,,=1.2bar

14.

bar

l,

a;

K,,=lOObarms

‘,

P 5,at= 1 .l bar a

can be concluded that the American tests show that the effect of vent ducts on the reduced explosion pressure is of approximately the same degree as found in the present tests. The results of the present tests are compared in Figure 12 with the vent duct guidance from VDI 3673 (and given in Ref. 13). Reasonable correspondence is found when the vent duct is greater than 3 m in length. The recommendations are slightly higher than the measurements made in the 18.5 m3vessel, probably because the recommendations are an envelope of experimental measurements. When the vent duct length is 3 m the measured pressures in the 18.5 m3 vessel are lower than the recommendations. In all the present results for straight ducts, the rise in reduced pressure caused by a vent duct either starts off gradually or decreases at low vent duct lengths. The graphs of reduced explosion pressure against vent duct length given in Ref. 13 do not show this behaviour, and it does not appear to have been taken into account in deriving the recommendations. The present results at low duct level, would therefore be expected to fall below the recommendations. The results from the 20 1 sphere tests are also shown in Figure 12 for a duct length of 3 m, and do not coincide with the guidance. One further comparison can be made with the present results and the recommendations given in Ref. 13. If the vessel volume, the K,, value of the dust, the bursting pressure of the vent cover and the vent area are known, then (P&)0 can be obtained from the nomographs and the model described earlier applied. When the K,, value is equal to 300 bar m s-i (the top of the St2 group) and P,, equals 11 bar a, the results given by the model for a vent duct greater than 3 m in length coincide with the guidance in Ref. 13, as Figure I3 shows. When the K,, value is 100 barms -I, however, the increase in pressure caused by the vent duct is not as great. This comparison suggests that current guidance is a conservative estimate applicable to the top of the St2 group, and that at lower Kst values that effect of vent ducts on the reduced explosion pressure will not be as great.

4.0

b

3.0

0

4.0

4.0

-

0

Figure meter

200

14

duct

600 (msl

Pressure

= 0.9

explosion

400 Time

m:

open

vessel;

entrance;

d,

800

traces:

vent;

straight

b.

0.48

11

.O m from

m from

0

200

o-

1000

time

FL 0

toner duct

600 fms)

400

600

Time

fms)

200

vent

duct

400 Time

dust: duct

entrance;

800 1

800 11

vent

11 m c,

6.1

dia-

long.

a;

m from

entrance

Pressure measurements in the duct A typical example of pressure time traces in the vessel duct system is shown in Figure 14. The empirical model does not attempt to reproduce pressure changes with time or position, only to calculate the final reduced explosion pressure in the explosion vessel. However, pressure measurements along the duct generally showed maximum pressures somewhat less than the pressure measured in the explosion vessel. Often the pressure trace at a point in the

J. Loss Rev.

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1988,

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195

The effect

of vent

ducts

on the reduced

explosion

pressures

duct was double peaked and on some occasions the first peak did register a higher pressure than measured in the explosion vessel. However, this result was rare and these results support the general conclusion that the ducts should be made as strong as the explosion vessel.

Conclusions The effect of vent ducts on the reduced explosion pressures of vented dust explosions has been investigated and a simple empirical model has been shown to calculate adequately the pressure increases that result, except in some examples with vents of low bursting pressure or open vents. The obvious use of this data and model is to provide practical guidance for industrial dust handling equipment. Because of the experimental conditions used in this series of tests, this guidance could be directly associated with the K,, nomograph method for estimating venting requirements. It has been demonstrated that such guidance would agree with that already available at the top of the st2 dust explosibility Group (IL = 300 bar m s- ‘), but would enable users to take into account a wide range of variables and so design for lower explosion pressures than at present for K,, values less than 300 harms-‘.

Acknowledgements The extensive

196

contributions

J. Loss Prev.

Process

to

this project

lnd.,

1988,

of D. E.

Vol

1, October

of vented

dust

explosions:

G. Lunn

et al.

Brookes, A. Nicol, B. Quince, W. Wardle and H. Goodwin are acknowledged.

References 1 Schofield, C., in ‘Guide to Dust Explosion Prevention and Protection, Part l-Venting’. IChemE Rugby, UK. 1985 2 Bartknecht, W., in ‘Explosions Course Prevention Protection’, Springer Verlag, Berlin, 1981 1966, 38, 1125 3 Heinrich, H. .I. Chemie-lng-Tech. 4 VDI 3673, Pressure Release of Dot Explosions, Verein Deutscher Ingeneiure, 1983 5 Bartknecht, W. Plant/Operations Progress 19%. 5 (4), 1% 6 Lunn, C., J. Loss Prev. Process Ind. 1988, 1, 123 7 Operating Manual for 20 I Spherical Explosion Vessel 8 British Standards Institute, BS 6713, Part 1, Explosion Protection Systems, London, 1986 9 National Fire Protection Association. Guide for Explosion Venting, NFPA 68 Boston, MA, USA, Draft 1987 10 Eckhoff, R. K. Bulk Solids Handling 1986, 6 (5), 913 I1 Eckhoff, R. K., and Fuhre, K. Dust Explosion Experiments in a vented 500 m3 vessel, Fourth International Symposium on Loss Prevention and Safety Promotion in the Processing Industries, 1983, IChemE Symposium Hazards Series No 82 I2 ‘The Efficient Use of Fuel’, HMSO, 1958 13 Nagy, J.. and Verakis, H. C. in ‘Development and Control of Dust Explosions’, Marcel Dekker Inc. New York, 1983 14 Siwek, R. Additional Considerations Concerning an Effective Pressure Venting: paper presented at the Europex Seminar Course 1986. Dust Explosion Venting, Amsterdam, 17-19 November, 1986