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Computer modelling of electrostatic conditions and hazards in tank washing
Journal of Electrostatics, 9 (1980) 71--88
71
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
COMPUTER MODELLING OF ELECTROSTATIC CONDITIONS AND HAZARDS IN TANK WASHING
J.N. CHUBB*, K.P. BROWN and G.J. BUTTERWORTH
Culham Laboratory, Abingdon, Oxfordshire 0X14 3DB (Gt. Britain) (Received September 11, 1979; accepted in revised form December 18, 1979)
Summary The paper describes how a computer program developed at Culham Laboratory for solving Poisson's equation in complex three-dimensional structures can be used for quantitative interpretation of electrostatic fieldmeter observations in practical situations. Computations are presented relating to interpretation of electrostatic conditions during shipboard studies of tank washing operations in the cargo tanks of crude oil carriers. The paper also discusses how the program was used to assess electrostatic ignition hazards by modelling possible discharge situations involving slugs of water and calculating the discharge energies which would be available as a function of geometric and electrostatic conditions.
1. Introduction A computer program, THREED, has been developed at Culham Laboratory to model electrostatic conditions within complex three-dimensional structures [1]. This paper describes the use of this program for investigations which have been carried out by the Electrostatics and Applied Physics Unit at Culham into the electrostatic ignition hazards which may arise during tank washing operations on large crude oil tankers. The computer program THREED was used in these investigations to assist the interpretation of shipboard observations of electrostatic conditions created during tank washing, and to assess prospective ignition risks by modelling likely ignition mechanisms. The particular computer calculations described in this report relate to the BP Tanker British Purpose on which shipboard studies were carried out during April and May 1977 [2]. 2. General background During the washing of cargo tanks with high pressure water jets (delivering typically up to 120 tons per hour per jet at 10 bar) a fine electrostatically *Present address: Linotype-Paul Limited, Chelham House, Bath Road, Cheltenham.
72 charged mist is formed. This mist has a fairly uniform electrostatic charge density, which may be positive or negative depending upon conditions, and may have a value up to 30 × 10 -9 C m -3 [3, 4]. The maximum space charge potential towards the centre of the tank may reach 40 kV [3]. Ignition hazards may arise if a flammable atmosphere is present in the tank and if sizeable lumps of wash water travel from occluded regions of the tank space, where electric fields are low, and approach large projections into the tank space such as washing machines or girders, where high electric fields exist [5, 6]. Alternatively, it is thought that hazards could arise if lumps of water leave such projections and travel without breakup to regions of the tank space where the electric field is low. The criterion to be satisfied before hazards arise is the release of more than 0.2 mJ of electrostatic energy in the form of a spark t y p e discharge between high conductivity surfaces with a discharge voltage greater than a b o u t 5 kV [7, 8]. The calculations described in this paper were concerned firstly, with providing a m e t h o d by which shipboard observations of the generation of electrostatically charged mist could be interpreted quantitatively in terms of mean electrostatic charge density and maximum space charge potential. Secondly, they were concerned with quantifying the discharge energies and potentials for a number of plausible spark discharge events. It was expected that such studies would enable some significance to be placed on practical observations of electrostatic conditions and on radio and flash photographic observations of the circumstances in cargo tanks associated with the occurrence of sparks during tank washing [2, 8].
3. Interpretation of field meter observations The electrostatic conditions created by washing operations in cargo tanks are normally observed or monitored by field meters [3, 9]. The field meter is very small compared to the dimensions of the cargo tank space and acts essentially as a potential probe. For the sizes of field meter head used by KSLA and b y Culham (about 90 mm diameter) the conversion factor between the electric field reading and the local potential is a b o u t 11 kV m -1 per kV [3, 10]. This conversion factor may be determined experimentally [3]. One m e t h o d of using the field meter is to lower it as a potential probe through the volume of tank space to observe the maximum potential in the centre of the tank volume. This approach is constrained in practice by the availability of suitable holes in the deck surface and by the risks to the equipment by the impact of the wash water jets throwing the field meter head against the internal structure. The approach we have adopted is to rigidly m o u n t the field meter head just a few meters below the deck surface. This rigid mounting and a suitable design of field meter head [10] allows continuous observations to be made during the course of washing operations. During a break or after completion of washing operations, the field meter may be safely lowered into the tank space to observe the potential distribution by vertical traverses at various locations.
73
These observations can then be compared with the values of potential observed at the normal field meter mounting position. Correlation of the forms of variations observed in such traverses with the predictions of computer calculations, and the accumulations of such experience justifies some confidence in the scaling of numerical values for maximum space charge potentials and mean space charge densities from computer calculations. Figure 1 shows a sketch of the basic structure within the wing tank 4P of the tanker British Purpose [2]. In the computer calculations the tank structure was simulated using individual rectangular parallelepipeds to define the bulkheads and the major girder structures of the tank. The boundaries of the tank were set to zero potential and a mesh grid was defined across the simulated tank with grid lines concentrated in the vicinity of the girder structures. By placing grid lines through the centres of the deck holes and requesting output for planes containing these grid lines, potential distributions were obtained for direct comparison with experimental vertical traverse observations with the field meters. For the purpose of the calculations the tank space was considered to be filled with electrostatic charge of uniform density 10 X 10 -9 C m -3. Figures 2, 3 and 4 show some of the patterns of potential distribution calculated by the program within the wing tank 4P. For the charge density used the maximum
+.
I II
Y
LLI
X
,
I I
!
;
o
Deck holes f o r equipment
~
Fixed washing machine
Fig. 1. Structure of wing tank 4P as represented for computer calculations,
74 Contours of potential in plane Z = 21 5 6 7
lo
Y
5
0
10
15
20
25
3O
Fig. 2. Computed potential distribution in XYplane through the field meter position in tank 4P. For charge density of 10 nC m -3, the maximum space potential in the tank is 10 kV, the highest potential contour 8.5 kV and the interval between contours 0.5 kV. space charge potential was around 10 kV. This value c o r r e s p o n d e d to a field m e t e r reading o f a b o u t 96 kV m -1 at the n o r m a l field meter m o u n t i n g position. A c o m p a r i s o n o f experimental and c o m p u t e d potential variations with depth b e n e a t h the d e c k level is s h o w n in Figure 5. Further c o m p a r i s o n in relation to earlier studies on a centre tank o f the BP tanker British C e n t a u r is s h o w n in Contours of potential in plane X = 12.51 2(5
1 24~
Contours of potential in plane Y= 7 1 3 0 22-
2520 ~
20161415-
12~ 10-
10-
867
4 2-
0
2
~1
&
8
1Q 12-
1~,
5-
I x0
O
5
10
15
20
25
Fig. 3. Computed potential distribution in YZ plane through the field meter position in tank 4P. For charge density of 10 nC m -3, the maximum space potential in the tank is 10 kV, the highest contour potential 9.5 kV and the interval between contours 0.5 kV. Fig. 4. Computed potential distribution in ZX plane through the field meter position in tank 4P. For charge density of 10 nC m -~, the maximum space potential in the tank is 10 kV, the highest potential contour 9.5 kV and the interval between contours 0.5 kV.
30
75 2 3 . 4 '77 4 Pa
2.~'77 5C
0 *°*o
•
e°
•
~o
~o ~o =. =
1
~ ,o
~ 20
~ C o m p t t t e d curve
I
2~
1
I
,
°~oPwering ,i=dmeter
25 r~ 1n e , : , . ~: FilT[id~~n: 0 1 2 3 4 5 6
A On r= J ~ing ,ietdmeter
2 3 4 5 6 Space potential (kV)
7
8
s p i c e potential
t 7
8
(kV)
(b}
Ca)
Fig. 5. Comparison of measured and computed potential variations with depth below deck level in tanks of British Purpose. (a) Tank 4P, aft section, from deck hole 3; (b) tank 5C from hole 4. Fieldmeter
0
20
2
(kV m-I) 60
80
100
o Fieldmeter measurement
~
4
~ o
reading
40
Calculated ver'(Ical component ~-of e l e c t r i c field in a b s e n c e
~_
e
~ 1(? i:512
o
18
0
J
~'xCurve of calculate 0
2
4 Space
potential
6 (kV)
8
10
Fig. 6. Comparison of measured and computed potential variations with depth below deck level in tank 3C of British Centaur. Figure 6. The satisfactory agreement between experimental and computed curves provides support for the method of computer analysis and the possibility of quantitative interpretation of electrostatic conditions from field meter observations. 4. Computer modelling of hazard mechanics Four main routes can be identified by which isolated conductors such as lumps of wash water may be involved in the acquisition and discharge of electrostatic energy [5, 6] :
76 (a) Acquisition of induction electrostatic charge by a body leaving a conducting projection where there is a concentration of electric field and moving to a discharge surface in a relatively field-free region of the tank. (b) Creation of polarisation charges on a relatively uncharged body as it approaches a conducting projection at which the electric field is concentrated. As the body approaches contact with the projection the component of the polarisation charge towards the projection may discharge in the form of a spark. (c) Acquisition of a net charge by a body close to the projection through part neutralisation of the polarisation charge by corona or water spray discharges. This net charge could then be released when the body arrived at the discharge surface in the region of low electric field. (d) Acquisition of a net electrostatic charge by aerodynamic sweep-up of charged mist particles and discharge of the body at a surface in a region of low electric field. Previous considerations of the above mechanisms [6] indicated that under the conditions of tank washing, aerodynamic sweep-up processes (route (d)) could not create hazardous electrostatic discharges (see Appendix), while corona water-spray processes (route (c)) could not create hazards any worse than those arising by discharge of induction or polarisation charges (routes (a) and (b)). The amounts of electrostatic energy available for release would be the same for discharge routes (a) and (b), so long as the capacitance of the body at the discharge point was the same in both cases. This is because the amount of electrostatic polarisation charge which would be discharged from the body with net zero charge (route (b)) would be the same as the amount of charge which the same body would acquire by induction on leaving the projection (route (a)). The capacitance of the body at its discharge position, however, depends upon its physical shape and also on the shape of the discharge surface approached.
Electrostatic calculations The electrostatic energy released at the discharge of an isolated conductor is given by
V= ½ (~Q)2/C where AQ is the net charge transferred in the discharge and C the capacitance of the body. The value of capacitance required in this expression is the capacitance of the body at the position where discharge occurs and this may be appreciably higher than the free space capacitance. Computer calculations with the program THREED were therefore carried out to provide values for both A Q and C for a number of plausible discharge situations involving washing machines and girders typical of the types of deep projections found in oil cargo tanks. The examples described below were carried out in relation to the cargo tank and washing machine geometries corresponding to tank 5C of the BP Tanker British Purpose. This situation was chosen because the main
77
Z
o
Deck holes for equipment
~ ) Fixed washing machine
Fig. 7. Structure of centre tank 5C as represented for computer calculations. C o n t o u r s of potential in plane X=18,85 26 24 25 20. 18 16 14 12 10 8
6 Z
t
4.
0
2
4
6
8
10
12
14
16
18
Fig. 8. Computed potential distribution in Y Z plane through the field meter position in tank 5C. For charge density of 10 nC m -3, the maximum space potential in the tank is 25.0 kV, the highest potential contour is 14.5 kV and the interval between contours 0.7615 kV.
78 purpose of the calculations was to provide specific background information against which to assess the expected results of shipboard flash photographic studies on this particular tanker. Figure 7 shows a sketch of the general structural form of cargo tank 5C of the British Purpose. The computer calculations started with a preliminary "macro" calculation involving the whole cargo tank structure filled with electrostatic charge of uniform density 10 × 10 -9 C m -3. Figures 8, 9 and 10 Contours of potential inplane Y=10.37 J
i
i
i
i
J
J
J
t
J
i
26 24 22 20 18 16 14 12 10
J
26 24 22 20
18 16 14 12 10
8
6
4
0
X=
|
0
Fig. 9. Computed potential distribution in Z X plane through the field meter position in tank 5C. For charge density of 10 nC m -3, the maximum space potential in the tank is 25.0 kV, the highest potential contour 23.0 kV and the interval between contours 1.211 kV. Contours of potential In plane Z =22.225 18
1,4
12J 10
~ X
O0
}
~,
g
g
10 17 1'4 16 1'8 2'0 2'2 2'4
Fig. 10. Computed potential distribution in X Y plane through the field meter position in tank 5C. For charge density of 10 nC m -3, the maximum potential in the tank is 25.0 kV, the highest potential contour 12.3 kV and the interval between contours 0.6448 kV.
79 show general potential distributions from these calculations in the planes X = 18.85, Y = 10.37 and Z = 22.25. From these computations separate calculation routes were then pursued for the interaction of water slugs with the nozzle of a washing machine and for interaction with the webs of the structural girders. F r o m the "macro" view of the whole tank a "mid z o o m " calculation was performed for a region of the tank including the whole Of a washing machine and with the boundary of the region only sufficientlyfar from the machine as not to be influenced by the presence of the machine. Closer boundaries would have been feasible if sufficientgrid spacings were available to include the basic structure of the washing machine in the macro view. The level of influence was monitored by looking for changes of potential at the next mesh Z
4 m m Gap
I
44
mm
C
/
Washing machine nozzle
Z
L_x
Washing machine nozzle
\
I50mm.~
I44mm
/ i 4ram Gap
\
Slug of water
~ ~ .
Slug of water
Fig. 11. Schematic diagrams of the washing machine--slug configurations studied. Contours of potential in plane Y =10 3700
Z
13.6513.60135513501345 1340 1335 13.30 13.25 13.20 13.15 13.10 13.05
I
Fig. 12. Potential distribution around water slug 150 mm in length for V -- 0.
80
lines in from the mid z o o m boundary which were also used in the macro view calculations. The washing machine was simulated as a cylindrical down pipe of 100 mm diameter, 2.725 m long with a horizontal nozzle of 44 mm diameter and 682 mm long mounted from its lower end. From this "mid zoom" calculation a set of "micro zoom" calculations was made for a region including only the tip of the washing machine nozzle and water slugs simulated as hemispherically ended cylinders of 50 mm diameter and 150 and 250 mm long approaching the side and end of the nozzle. The slugs were spaced a nominal 4 mm from the end of the nozzle. The geometric arrangements studied are shown schematically in Figure 11. Figure 12 shows a computer-drawn illustration of the potential distribution around a 150-mm-long water slug at zero potential near the tip of the washing machine nozzle. C h a r g e d e n s i t y = 1.0 x l O - a C m - 3 S l u g of w a t e r o n t o w a s h i n g m a c h i n e n o z z l e 1 5 0 m m long x 813 x 10-e Coulombs)
50 mm diameter Gap = 4 mm
l
1
i 0 ×
E
o
. ['Charge = 0.0 k 7VJ LPotential = 2.85
0
\ z o o m 5 ( - 4 . 2 5 6 x lO-ilCoulomb$ )
o u
u
-2 × 10-8 Coulombs)
I
I
0
1
I
I
I
2 4 6 P o t e n t i a l of slug (kV) =C h a r g e s calculated by p r o g r a m C H A R G E u s i n g o u t p u t from Zooms 3,4&5
Fig. 13. Graph s h o w i n g the relationship b e t w e e n the charge and p o t e n t i a l on a water slug 1 5 0 m m l o n g x 50 m m diameter coaxial w i t h the washing m a c h i n e n o z z l e and separated from it b y a 4 m m gap.
81
Estimation of the a m o u n t of electrostatic energy liberated at the discharge of the slugs of water as t h e y approach the washing machine tip with zero net charge requires information on the charge transferred (A Q) and the capacitance (C) of the b o d y at the discharge distance. Values for the net quantities of electrostatic charge induced on a water slug as a function of its potential were obtained using a computer program CHARGE. This program was written to calculate the net charge within any chosen rectangular parallelepiped region by application of Gauss's law to the values of electric flux density calculated by T H R E E D and written to magnetic tape. Two calculations were performed with the program T H R E E D for each physical arrangement, one calculation with the water slug at the zero potential and the other at a potential judged likely to give a b o u t zero net charge on the slug. It has previously been noted [6] (and confirmed in the present work by making additional calculations for one or two cases) that a linear relationship exists between the potential of the bodies and their net charge. This is illustrated graphically in Figure 13. Such graphs for each physical arrangement give values for the potential of the body for zero charge and, from the slope of the line, the actual capacitance of the b o d y can be determined. The discharge TABLE 1 Results of computer calculations for 50 mm-diameter water slugs of 150 and 250 m m interacting with washing machine nozzles and girder
length
Calculations relating to tank 5C of British Purpose filled with a uniform charge density of 10 n C
m -3
Slug potential
Charge Energy transferred released
for zero (nC) net charge
(~J)
Body capacitance
(pF)
(kV)
Water slugs approaching washing machine nozzle
15o
2.85
21.6
30
3.55
35.3
63
3.95
28.4
50
2~o
1.6
20.6
16.3
13.0
2~o
1,7
21.6
18.5
12.7
2~o
7.6 10
I ,50
7.2
Water slugs approaching girder edge
C
82 of an uncharged b o d y approaching the nozzle tip is modelled by discharge of the b o d y initially at the potential needed for net zero charge, with a transfer of charge equal to that necessary to achieve a final condition of zero potential. For an ignition hazard in the presence of hydrocarbon vapour/air mixtures, the discharge potential needs to be above the minimum value of a b o u t 5 kV. When considering the breakdown voltage for the gap between the water slug and the nozzle, it should be noted that electrical breakdown involving conducting fluid surfaces can take place at much lower electric field values than would apply with rigid electrodes [11]. However, some experiments at Culham indicated that with approach velocity greater than 0.5 m s -1 water surfaces exhibit breakdown voltage characteristics more similar to those of rigid electrodes. The results of the above computer calculations for water slugs interacting with washing machine nozzles are shown in Table 1. z
z
Girder~.~
T
Shaped
girder E E
i T Slug of water
4mmGap
Slug of water
4mmGap
Fig. 14. Schematic diagrams of the water slug--glrder configurations studied.
Similar calculations to those described above were carried out for water slugs approaching the top central girder structure. The calculation started from the results of the "mid z o o m " view calculations, and used a region of the results on the other side of the central girder structure so as to minimise the influence of the washing machine structure on the potential distribution. The " m i c r o - z o o m " calculations were performed with water slugs of 50 mm diameter and 250 mm length approaching a central girder of both simple rectangular and conventional web form. The geometric arrangements for this study are sketched in Figure 14. "Micro-zoom" calculations were made with the slugs at zero potential and at a potential judged likely to give near-zero net charge so as to provide, as for the discharges near the washing machine nozzle, information on the charge transfer and effective b o d y capacitance. The results of these calculations are shown in Table 1. Figures 15 and 16 show computer generated illustrations of the potential distribution around 250 mm × 50 mm water slugs near a girder for V = 0 and for V = 5 kV.
83 C o n t o u r s of potential in plane L _ _ J -
Z: 23.404
l
±
_
_
9.0-
8.8-
8.8-
8,4-
J
~
82
x 12.6
l 1 28
T 130
T 13 2
7 134
13.(5
Fig. 15. Computed potential distribution in Y X plane for 250-ram-long slug approaching simple girder in tank 5C. Uniform charge density 1 × 1 0 - ' C m -3, potential o f slug = 0 kV, highest contour potential = 5.4 kV, interval between contours = 0.2 kV, charge on slug = --2.06 X 1 0 - ' C. C o n t o u r s of potential in plane Z = 2 3 4 0 4
9.0-
88-
86-
84-
82
x
12G
128
1310
132
134
J
136
Fig. 16. Computed potential distribution in Y X plane for 250-mm-long slug approaching simple girder in tank 5C. Uniform charge density 1 × 10 - a C m - 3 , potential o f slug = 5 kV, highest contour potential = 5.4 kV, interval between contours = 0.2 kV, charge on slug = 4.44 × 10 - 8 C.
84
Results The results presented in Tables 1 and 2 show that the interaction of a lump of water with a relatively narrow projection such as a washing machine nozzle involves the release of appreciably larger amounts of electrostatic energy than interaction with structures such as girder webs. However before the particular interactions considered would have involved discharge energies above the minimum ignition energy for hydrocarbon vapour/air mixtures (0.2 mJ) it would have been necessary for the mean charge density in the tank to exceed a b o u t 18 nC m -3 and the maximum space potential to exceed a b o u t 45 kV. These values are based on the fact that discharge energies scale with the square of the mean space charge density, and the square of the maximum space charge potential. While the above comments suggest that ignition hazards in tank washing require fairly large isolated bodies and strong electrostatic conditions in the tank space, the present studies are not sufficiently detailed or extensive to allow any significant c o m m e n t on the ease or difficulty with which ignition hazards may arise in practice. The present results do however demonstrate that meaningful calculations are feasible for the various parameters (charge transfer, effective capacitance and discharge energy) relevant to the assessment of hazard mechanisms. It is likely that the hazards of discharge events involving isolated water slugs will vary with position in the cargo space in ways which may be related fairly simply to some local electrostatic potential or electric field value. The present calculations, however, have not been sufficiently extensive to test this proposition. If scaling with b o d y dimensions, form of structure and local electrostatic conditions is demonstrated then it will be feasible to at least estimate the prospective ignition hazards presented by particular events observed (for example by triggered flash photography) at any place in a cargo tank from a limited number of actual c o m p u t e r calculations. 5. Conclusions The studies described in the present paper demonstrate that electrostatic conditions and ignition hazard mechanisms in complex practical situations can be examined and assessed with the aid of computer calculations using a computer program such as the T H R E E D program developed at Culham.
Acknowledgements The work described in this paper was supported by the Marine Division of the Department of Trade. The work described in the Appendix was performed during 1972 for J.M. Houlder, Furness Withy and Co. Ltd., and the authors are grateful for his permission to publish it. The assistance of the BP Tanker Company in providing facilities for the shipboard experimental work is gratefully acknowledged.
85 APPENDIX Collection o f charge by aerodynamic sweep-up A.1. General features A body moving through a mist of charged particles can collect charge by aerodynamic processes. This process of charge collection is relevant to two aspects of the tanker explosion problem: (1) If incendiary quantities of electrostatic energy can arise by aerodynamic processes then such safety measures as dividing wire systems which limit the m a x i m u m space potential and m a x i m u m field concentrations would be only partially effective because aerodynamic collection is independent of potential and electric field. (2) The ability of water to form large physical bodies that can survive projection across a tank space is limited by surface tension and aerodynamic effects. Large lumps of crude oil and of waxy deposits retain their form much more easily because of a greater viscosity. However, the possibility that incendiary discharges could be drawn from such bodies will depend on the maintenance of a conducting layer of water on the surface. Simple laboratory tests at Culham failed to demonstrate the occurrence of incendiary discharges from a simulated body of crude oil -- a plastic ball coated with crude oil which was sprayed with a dilute solution of salt, detergent and glue to try to create a conducting surface coating. If a suitable layer of water could be maintained dynamically by aerodynamic sweep-up, then it might be necessary to reconsider lumps of crude oil as possible sources of incendiary discharges. A.2. Influence of electrostatic effects It might be expected that the collection of charge by a body moving through a charged mist would be determined by both electrostatic and aerodynamic effects. Van der Weerd quotes [3] the mobility of mist particles as being below 3 X 10 -7 m 2 V -1 s -1. If we consider a 200-mm-radius sphere carrying a typical value of induced charge of 2.8 X 10 -7 C then the electric field at the sphere surface is 6.3 × 104 V m -1. The drift velocity of mist particles in this field could be below 2X 10 -2 m s -1. This velocity is very small compared to the travel velocity of thrown or falling bodies, and thus it is clear that electrostatic force effects are not likely to significantly affect charge collection processes. A.3. Calculations of charge collection Langmuir [12] examined the collection of fine water droplets by cylindrical and spherical bodies moving through ~he air in relation to aircraft icing. He derived expressions which related the collection efficiency E for mist particles within the projected cross-section of the body to a parameter K which relates
86 to droplet size, droplet density, the velocity of the body, the radius of the b o d y and the viscosity of air. For a spherical b o d y in the Stokes' Law regime: Z / ( 1 - E ) = 0.82 (K - 1/12) 1"°4
and for a cylinder for K between 0.125 and 1.1: E = 0.466(log10 8K) 2 and for K above 1.1: E = K / ( K + ~/2).
The parameter K is defined in c.g.s, units as: K = 2pa2V/97?R
where p is the density of the airborne mist particles, a the radius of the mist particles, v the velocity of the body, ~ the velocity of air, and where R is the radius of the body. The total charge which a sphere would collect aerodynamically can be obtained by integrating the collection efficiency over the distance of travel: Q = nq~R 2 f Edl
where n q is the charge density, and R is the radius. The energy will then be: U = ½ Q2/C = ½ ( n q ~ R 2 f E d/)2/4~ e o R = ~ n ~ q2 ( ~ R 3 / e o ) ( f E d/) 2.
The minimum size of sphere which could possibly acquire sufficient energy to be incendiary (2 × 10 -4 J) can be found by assuming the collection efficiency to be unity and setting the integral equal to the maximum path of travel. For example, taking a 50-m path length as a plausible maximum within a ship's cargo tank and a charge density of 3 × 10 -8 C m -3, the minimum b o d y size is about 0.13 m radius. A simple computer program was written using the above expressions to see h o w much charge and energy would in fact be collected'by spherical and cylindrical bodies larger than this minimum size. The bodies were assumed to be thrown on an upward trajectory across a cargo tank a b o u t 40 m wide and a b o u t 20 m high with a 10 m s -1 horizontal velocity and 20 m s - 1 upward vertical velocity. The cylindrical bodies were assumed to be of 1 m length and thrown with the cylinder axis perpendicular to the direction of travel. A charge density of 30 nC m -3 was assumed. The results obtained were as shown in Table 2. It is clear that even taking large bodies and assuming a long trajectory through a charged mist consisting of large particles that the final energies are well below the 200 # J minimum ignition energy for hydrocarbon vapour/air
87 TABLE 2 Sphere or cylinder diameter (m)
Mist particle diameter (microns)
Charge collected (nC)
Energy (p J)
20 40 20 40
10.8 36.1 7.1 21.2
3.5 39 2.3 20
20 20 40
19.3 19.8 29.2
14.7 9.9 33.8
Spheres 0.3 0.3 0.2 0.2
Cylinders 0.02 0.1 0.02
m i x t u r e . I s o l a t e d l u m p s o f m a t t e r are n o t l i k e l y t o survive a n y s u c h t r a j e c t o r y . It is c o n c l u d e d t h a t a e r o d y n a m i c s w e e p - u p o f c h a r g e d m i s t p a r t i c l e s d o e s n o t p r o v i d e a m e c h a n i s m o f a n y s i g n i f i c a n c e in r e l a t i o n t o i g n i t i o n h a z a r d in t h e c a r g o t a n k s o f c r u d e oil t a n k e r s .
References 1 C.L. Thomas, THREED -- A digital computer code for the design and analysis of three-dimensional electrostatic fields, Papers for IEE Conference on Computer Aided Design 8-11 April, 1974, at the University of Southampton. 2 G.J. Butterworth, I.E. Pollard, B. Jaffrey, C.J. Mottershead, and J.N. Chubb, Studies of tankwashing on British Purpose during ballast voyage from Isle of Grain to Cape of Good Hope, April 7 to May 5, 1977. Culham Report CLM/RR/D2/34 Feb. 1978. 3 J.M. van der Weerd, Electrostatic charge generation during washing of tanks with water sprays. II Measurements and interpretation, Proceedings 3rd Conference on Static Electrification, Institute of Physics, London, May 1971, pp. 158. 4 R.L. Lindbauer, Static electricity measurements on board SS British Surveyor: Evaluation and interpretation, KSLA Report AMSR.0037.72 1972. 5 J.M. van der Weerd, Spark mechanisms in tanks filled with charged mists, Paper presented at the Special Symposium on Tanker Explosions at the 2nd Int. Conference on Static Electricity, Frankfurt, April 1973. 6 J.N. Chubb, Practical and computer assessments of ignition hazards during tank washing and during wave action in part ballasted OBO tanks, J. Electrostatics, 1 (1975) 61. 7 B. Lewis and G. yon Elbe, Combustion, Flames and Explosion of Gases, New York, Academic Press 1961. 8 J.N. Chubb and G.J. Butterworth, Instrumentation and techniques for monitoring and assessing electrostatic ignition hazards, Electrostatics 1979, Institute of Physics Conference Series, No. 48, 1979, p. 85. 9 R.J. Klaver and V.A. Dayot, An investigation of electrostatic charge generation during cargo tank washing on the Ralph B. Johnson, Chevron Research Co. Report, 27 July 1970.
88 10
I.E. Pollard and J.N. Chubb, A n instrument to measure electric fields in adverse conditions, Static Electrification,Institute of Physics Conference Series No. 27, 1975, p. 182. 11 G.I. Taylor and A.D. McEwan, The stability of a horizontal fluid interface in a vertical electric field, J. Fluid Mech., 22 (1965) 1. 12 I. Langmuir, Mathematical investigation of water droplet trajectories, Report No. RL-224. The Collected Works of Irving Langmuir, G. Suits (Ed.), Vol. X, Pergamon, 1961.
71
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
COMPUTER MODELLING OF ELECTROSTATIC CONDITIONS AND HAZARDS IN TANK WASHING
J.N. CHUBB*, K.P. BROWN and G.J. BUTTERWORTH
Culham Laboratory, Abingdon, Oxfordshire 0X14 3DB (Gt. Britain) (Received September 11, 1979; accepted in revised form December 18, 1979)
Summary The paper describes how a computer program developed at Culham Laboratory for solving Poisson's equation in complex three-dimensional structures can be used for quantitative interpretation of electrostatic fieldmeter observations in practical situations. Computations are presented relating to interpretation of electrostatic conditions during shipboard studies of tank washing operations in the cargo tanks of crude oil carriers. The paper also discusses how the program was used to assess electrostatic ignition hazards by modelling possible discharge situations involving slugs of water and calculating the discharge energies which would be available as a function of geometric and electrostatic conditions.
1. Introduction A computer program, THREED, has been developed at Culham Laboratory to model electrostatic conditions within complex three-dimensional structures [1]. This paper describes the use of this program for investigations which have been carried out by the Electrostatics and Applied Physics Unit at Culham into the electrostatic ignition hazards which may arise during tank washing operations on large crude oil tankers. The computer program THREED was used in these investigations to assist the interpretation of shipboard observations of electrostatic conditions created during tank washing, and to assess prospective ignition risks by modelling likely ignition mechanisms. The particular computer calculations described in this report relate to the BP Tanker British Purpose on which shipboard studies were carried out during April and May 1977 [2]. 2. General background During the washing of cargo tanks with high pressure water jets (delivering typically up to 120 tons per hour per jet at 10 bar) a fine electrostatically *Present address: Linotype-Paul Limited, Chelham House, Bath Road, Cheltenham.
72 charged mist is formed. This mist has a fairly uniform electrostatic charge density, which may be positive or negative depending upon conditions, and may have a value up to 30 × 10 -9 C m -3 [3, 4]. The maximum space charge potential towards the centre of the tank may reach 40 kV [3]. Ignition hazards may arise if a flammable atmosphere is present in the tank and if sizeable lumps of wash water travel from occluded regions of the tank space, where electric fields are low, and approach large projections into the tank space such as washing machines or girders, where high electric fields exist [5, 6]. Alternatively, it is thought that hazards could arise if lumps of water leave such projections and travel without breakup to regions of the tank space where the electric field is low. The criterion to be satisfied before hazards arise is the release of more than 0.2 mJ of electrostatic energy in the form of a spark t y p e discharge between high conductivity surfaces with a discharge voltage greater than a b o u t 5 kV [7, 8]. The calculations described in this paper were concerned firstly, with providing a m e t h o d by which shipboard observations of the generation of electrostatically charged mist could be interpreted quantitatively in terms of mean electrostatic charge density and maximum space charge potential. Secondly, they were concerned with quantifying the discharge energies and potentials for a number of plausible spark discharge events. It was expected that such studies would enable some significance to be placed on practical observations of electrostatic conditions and on radio and flash photographic observations of the circumstances in cargo tanks associated with the occurrence of sparks during tank washing [2, 8].
3. Interpretation of field meter observations The electrostatic conditions created by washing operations in cargo tanks are normally observed or monitored by field meters [3, 9]. The field meter is very small compared to the dimensions of the cargo tank space and acts essentially as a potential probe. For the sizes of field meter head used by KSLA and b y Culham (about 90 mm diameter) the conversion factor between the electric field reading and the local potential is a b o u t 11 kV m -1 per kV [3, 10]. This conversion factor may be determined experimentally [3]. One m e t h o d of using the field meter is to lower it as a potential probe through the volume of tank space to observe the maximum potential in the centre of the tank volume. This approach is constrained in practice by the availability of suitable holes in the deck surface and by the risks to the equipment by the impact of the wash water jets throwing the field meter head against the internal structure. The approach we have adopted is to rigidly m o u n t the field meter head just a few meters below the deck surface. This rigid mounting and a suitable design of field meter head [10] allows continuous observations to be made during the course of washing operations. During a break or after completion of washing operations, the field meter may be safely lowered into the tank space to observe the potential distribution by vertical traverses at various locations.
73
These observations can then be compared with the values of potential observed at the normal field meter mounting position. Correlation of the forms of variations observed in such traverses with the predictions of computer calculations, and the accumulations of such experience justifies some confidence in the scaling of numerical values for maximum space charge potentials and mean space charge densities from computer calculations. Figure 1 shows a sketch of the basic structure within the wing tank 4P of the tanker British Purpose [2]. In the computer calculations the tank structure was simulated using individual rectangular parallelepipeds to define the bulkheads and the major girder structures of the tank. The boundaries of the tank were set to zero potential and a mesh grid was defined across the simulated tank with grid lines concentrated in the vicinity of the girder structures. By placing grid lines through the centres of the deck holes and requesting output for planes containing these grid lines, potential distributions were obtained for direct comparison with experimental vertical traverse observations with the field meters. For the purpose of the calculations the tank space was considered to be filled with electrostatic charge of uniform density 10 X 10 -9 C m -3. Figures 2, 3 and 4 show some of the patterns of potential distribution calculated by the program within the wing tank 4P. For the charge density used the maximum
+.
I II
Y
LLI
X
,
I I
!
;
o
Deck holes f o r equipment
~
Fixed washing machine
Fig. 1. Structure of wing tank 4P as represented for computer calculations,
74 Contours of potential in plane Z = 21 5 6 7
lo
Y
5
0
10
15
20
25
3O
Fig. 2. Computed potential distribution in XYplane through the field meter position in tank 4P. For charge density of 10 nC m -3, the maximum space potential in the tank is 10 kV, the highest potential contour 8.5 kV and the interval between contours 0.5 kV. space charge potential was around 10 kV. This value c o r r e s p o n d e d to a field m e t e r reading o f a b o u t 96 kV m -1 at the n o r m a l field meter m o u n t i n g position. A c o m p a r i s o n o f experimental and c o m p u t e d potential variations with depth b e n e a t h the d e c k level is s h o w n in Figure 5. Further c o m p a r i s o n in relation to earlier studies on a centre tank o f the BP tanker British C e n t a u r is s h o w n in Contours of potential in plane X = 12.51 2(5
1 24~
Contours of potential in plane Y= 7 1 3 0 22-
2520 ~
20161415-
12~ 10-
10-
867
4 2-
0
2
~1
&
8
1Q 12-
1~,
5-
I x0
O
5
10
15
20
25
Fig. 3. Computed potential distribution in YZ plane through the field meter position in tank 4P. For charge density of 10 nC m -3, the maximum space potential in the tank is 10 kV, the highest contour potential 9.5 kV and the interval between contours 0.5 kV. Fig. 4. Computed potential distribution in ZX plane through the field meter position in tank 4P. For charge density of 10 nC m -~, the maximum space potential in the tank is 10 kV, the highest potential contour 9.5 kV and the interval between contours 0.5 kV.
30
75 2 3 . 4 '77 4 Pa
2.~'77 5C
0 *°*o
•
e°
•
~o
~o ~o =. =
1
~ ,o
~ 20
~ C o m p t t t e d curve
I
2~
1
I
,
°~oPwering ,i=dmeter
25 r~ 1n e , : , . ~: FilT[id~~n: 0 1 2 3 4 5 6
A On r= J ~ing ,ietdmeter
2 3 4 5 6 Space potential (kV)
7
8
s p i c e potential
t 7
8
(kV)
(b}
Ca)
Fig. 5. Comparison of measured and computed potential variations with depth below deck level in tanks of British Purpose. (a) Tank 4P, aft section, from deck hole 3; (b) tank 5C from hole 4. Fieldmeter
0
20
2
(kV m-I) 60
80
100
o Fieldmeter measurement
~
4
~ o
reading
40
Calculated ver'(Ical component ~-of e l e c t r i c field in a b s e n c e
~_
e
~ 1(? i:512
o
18
0
J
~'xCurve of calculate 0
2
4 Space
potential
6 (kV)
8
10
Fig. 6. Comparison of measured and computed potential variations with depth below deck level in tank 3C of British Centaur. Figure 6. The satisfactory agreement between experimental and computed curves provides support for the method of computer analysis and the possibility of quantitative interpretation of electrostatic conditions from field meter observations. 4. Computer modelling of hazard mechanics Four main routes can be identified by which isolated conductors such as lumps of wash water may be involved in the acquisition and discharge of electrostatic energy [5, 6] :
76 (a) Acquisition of induction electrostatic charge by a body leaving a conducting projection where there is a concentration of electric field and moving to a discharge surface in a relatively field-free region of the tank. (b) Creation of polarisation charges on a relatively uncharged body as it approaches a conducting projection at which the electric field is concentrated. As the body approaches contact with the projection the component of the polarisation charge towards the projection may discharge in the form of a spark. (c) Acquisition of a net charge by a body close to the projection through part neutralisation of the polarisation charge by corona or water spray discharges. This net charge could then be released when the body arrived at the discharge surface in the region of low electric field. (d) Acquisition of a net electrostatic charge by aerodynamic sweep-up of charged mist particles and discharge of the body at a surface in a region of low electric field. Previous considerations of the above mechanisms [6] indicated that under the conditions of tank washing, aerodynamic sweep-up processes (route (d)) could not create hazardous electrostatic discharges (see Appendix), while corona water-spray processes (route (c)) could not create hazards any worse than those arising by discharge of induction or polarisation charges (routes (a) and (b)). The amounts of electrostatic energy available for release would be the same for discharge routes (a) and (b), so long as the capacitance of the body at the discharge point was the same in both cases. This is because the amount of electrostatic polarisation charge which would be discharged from the body with net zero charge (route (b)) would be the same as the amount of charge which the same body would acquire by induction on leaving the projection (route (a)). The capacitance of the body at its discharge position, however, depends upon its physical shape and also on the shape of the discharge surface approached.
Electrostatic calculations The electrostatic energy released at the discharge of an isolated conductor is given by
V= ½ (~Q)2/C where AQ is the net charge transferred in the discharge and C the capacitance of the body. The value of capacitance required in this expression is the capacitance of the body at the position where discharge occurs and this may be appreciably higher than the free space capacitance. Computer calculations with the program THREED were therefore carried out to provide values for both A Q and C for a number of plausible discharge situations involving washing machines and girders typical of the types of deep projections found in oil cargo tanks. The examples described below were carried out in relation to the cargo tank and washing machine geometries corresponding to tank 5C of the BP Tanker British Purpose. This situation was chosen because the main
77
Z
o
Deck holes for equipment
~ ) Fixed washing machine
Fig. 7. Structure of centre tank 5C as represented for computer calculations. C o n t o u r s of potential in plane X=18,85 26 24 25 20. 18 16 14 12 10 8
6 Z
t
4.
0
2
4
6
8
10
12
14
16
18
Fig. 8. Computed potential distribution in Y Z plane through the field meter position in tank 5C. For charge density of 10 nC m -3, the maximum space potential in the tank is 25.0 kV, the highest potential contour is 14.5 kV and the interval between contours 0.7615 kV.
78 purpose of the calculations was to provide specific background information against which to assess the expected results of shipboard flash photographic studies on this particular tanker. Figure 7 shows a sketch of the general structural form of cargo tank 5C of the British Purpose. The computer calculations started with a preliminary "macro" calculation involving the whole cargo tank structure filled with electrostatic charge of uniform density 10 × 10 -9 C m -3. Figures 8, 9 and 10 Contours of potential inplane Y=10.37 J
i
i
i
i
J
J
J
t
J
i
26 24 22 20 18 16 14 12 10
J
26 24 22 20
18 16 14 12 10
8
6
4
0
X=
|
0
Fig. 9. Computed potential distribution in Z X plane through the field meter position in tank 5C. For charge density of 10 nC m -3, the maximum space potential in the tank is 25.0 kV, the highest potential contour 23.0 kV and the interval between contours 1.211 kV. Contours of potential In plane Z =22.225 18
1,4
12J 10
~ X
O0
}
~,
g
g
10 17 1'4 16 1'8 2'0 2'2 2'4
Fig. 10. Computed potential distribution in X Y plane through the field meter position in tank 5C. For charge density of 10 nC m -3, the maximum potential in the tank is 25.0 kV, the highest potential contour 12.3 kV and the interval between contours 0.6448 kV.
79 show general potential distributions from these calculations in the planes X = 18.85, Y = 10.37 and Z = 22.25. From these computations separate calculation routes were then pursued for the interaction of water slugs with the nozzle of a washing machine and for interaction with the webs of the structural girders. F r o m the "macro" view of the whole tank a "mid z o o m " calculation was performed for a region of the tank including the whole Of a washing machine and with the boundary of the region only sufficientlyfar from the machine as not to be influenced by the presence of the machine. Closer boundaries would have been feasible if sufficientgrid spacings were available to include the basic structure of the washing machine in the macro view. The level of influence was monitored by looking for changes of potential at the next mesh Z
4 m m Gap
I
44
mm
C
/
Washing machine nozzle
Z
L_x
Washing machine nozzle
\
I50mm.~
I44mm
/ i 4ram Gap
\
Slug of water
~ ~ .
Slug of water
Fig. 11. Schematic diagrams of the washing machine--slug configurations studied. Contours of potential in plane Y =10 3700
Z
13.6513.60135513501345 1340 1335 13.30 13.25 13.20 13.15 13.10 13.05
I
Fig. 12. Potential distribution around water slug 150 mm in length for V -- 0.
80
lines in from the mid z o o m boundary which were also used in the macro view calculations. The washing machine was simulated as a cylindrical down pipe of 100 mm diameter, 2.725 m long with a horizontal nozzle of 44 mm diameter and 682 mm long mounted from its lower end. From this "mid zoom" calculation a set of "micro zoom" calculations was made for a region including only the tip of the washing machine nozzle and water slugs simulated as hemispherically ended cylinders of 50 mm diameter and 150 and 250 mm long approaching the side and end of the nozzle. The slugs were spaced a nominal 4 mm from the end of the nozzle. The geometric arrangements studied are shown schematically in Figure 11. Figure 12 shows a computer-drawn illustration of the potential distribution around a 150-mm-long water slug at zero potential near the tip of the washing machine nozzle. C h a r g e d e n s i t y = 1.0 x l O - a C m - 3 S l u g of w a t e r o n t o w a s h i n g m a c h i n e n o z z l e 1 5 0 m m long x 813 x 10-e Coulombs)
50 mm diameter Gap = 4 mm
l
1
i 0 ×
E
o
. ['Charge = 0.0 k 7VJ LPotential = 2.85
0
\ z o o m 5 ( - 4 . 2 5 6 x lO-ilCoulomb$ )
o u
u
-2 × 10-8 Coulombs)
I
I
0
1
I
I
I
2 4 6 P o t e n t i a l of slug (kV) =C h a r g e s calculated by p r o g r a m C H A R G E u s i n g o u t p u t from Zooms 3,4&5
Fig. 13. Graph s h o w i n g the relationship b e t w e e n the charge and p o t e n t i a l on a water slug 1 5 0 m m l o n g x 50 m m diameter coaxial w i t h the washing m a c h i n e n o z z l e and separated from it b y a 4 m m gap.
81
Estimation of the a m o u n t of electrostatic energy liberated at the discharge of the slugs of water as t h e y approach the washing machine tip with zero net charge requires information on the charge transferred (A Q) and the capacitance (C) of the b o d y at the discharge distance. Values for the net quantities of electrostatic charge induced on a water slug as a function of its potential were obtained using a computer program CHARGE. This program was written to calculate the net charge within any chosen rectangular parallelepiped region by application of Gauss's law to the values of electric flux density calculated by T H R E E D and written to magnetic tape. Two calculations were performed with the program T H R E E D for each physical arrangement, one calculation with the water slug at the zero potential and the other at a potential judged likely to give a b o u t zero net charge on the slug. It has previously been noted [6] (and confirmed in the present work by making additional calculations for one or two cases) that a linear relationship exists between the potential of the bodies and their net charge. This is illustrated graphically in Figure 13. Such graphs for each physical arrangement give values for the potential of the body for zero charge and, from the slope of the line, the actual capacitance of the b o d y can be determined. The discharge TABLE 1 Results of computer calculations for 50 mm-diameter water slugs of 150 and 250 m m interacting with washing machine nozzles and girder
length
Calculations relating to tank 5C of British Purpose filled with a uniform charge density of 10 n C
m -3
Slug potential
Charge Energy transferred released
for zero (nC) net charge
(~J)
Body capacitance
(pF)
(kV)
Water slugs approaching washing machine nozzle
15o
2.85
21.6
30
3.55
35.3
63
3.95
28.4
50
2~o
1.6
20.6
16.3
13.0
2~o
1,7
21.6
18.5
12.7
2~o
7.6 10
I ,50
7.2
Water slugs approaching girder edge
C
82 of an uncharged b o d y approaching the nozzle tip is modelled by discharge of the b o d y initially at the potential needed for net zero charge, with a transfer of charge equal to that necessary to achieve a final condition of zero potential. For an ignition hazard in the presence of hydrocarbon vapour/air mixtures, the discharge potential needs to be above the minimum value of a b o u t 5 kV. When considering the breakdown voltage for the gap between the water slug and the nozzle, it should be noted that electrical breakdown involving conducting fluid surfaces can take place at much lower electric field values than would apply with rigid electrodes [11]. However, some experiments at Culham indicated that with approach velocity greater than 0.5 m s -1 water surfaces exhibit breakdown voltage characteristics more similar to those of rigid electrodes. The results of the above computer calculations for water slugs interacting with washing machine nozzles are shown in Table 1. z
z
Girder~.~
T
Shaped
girder E E
i T Slug of water
4mmGap
Slug of water
4mmGap
Fig. 14. Schematic diagrams of the water slug--glrder configurations studied.
Similar calculations to those described above were carried out for water slugs approaching the top central girder structure. The calculation started from the results of the "mid z o o m " view calculations, and used a region of the results on the other side of the central girder structure so as to minimise the influence of the washing machine structure on the potential distribution. The " m i c r o - z o o m " calculations were performed with water slugs of 50 mm diameter and 250 mm length approaching a central girder of both simple rectangular and conventional web form. The geometric arrangements for this study are sketched in Figure 14. "Micro-zoom" calculations were made with the slugs at zero potential and at a potential judged likely to give near-zero net charge so as to provide, as for the discharges near the washing machine nozzle, information on the charge transfer and effective b o d y capacitance. The results of these calculations are shown in Table 1. Figures 15 and 16 show computer generated illustrations of the potential distribution around 250 mm × 50 mm water slugs near a girder for V = 0 and for V = 5 kV.
83 C o n t o u r s of potential in plane L _ _ J -
Z: 23.404
l
±
_
_
9.0-
8.8-
8.8-
8,4-
J
~
82
x 12.6
l 1 28
T 130
T 13 2
7 134
13.(5
Fig. 15. Computed potential distribution in Y X plane for 250-ram-long slug approaching simple girder in tank 5C. Uniform charge density 1 × 1 0 - ' C m -3, potential o f slug = 0 kV, highest contour potential = 5.4 kV, interval between contours = 0.2 kV, charge on slug = --2.06 X 1 0 - ' C. C o n t o u r s of potential in plane Z = 2 3 4 0 4
9.0-
88-
86-
84-
82
x
12G
128
1310
132
134
J
136
Fig. 16. Computed potential distribution in Y X plane for 250-mm-long slug approaching simple girder in tank 5C. Uniform charge density 1 × 10 - a C m - 3 , potential o f slug = 5 kV, highest contour potential = 5.4 kV, interval between contours = 0.2 kV, charge on slug = 4.44 × 10 - 8 C.
84
Results The results presented in Tables 1 and 2 show that the interaction of a lump of water with a relatively narrow projection such as a washing machine nozzle involves the release of appreciably larger amounts of electrostatic energy than interaction with structures such as girder webs. However before the particular interactions considered would have involved discharge energies above the minimum ignition energy for hydrocarbon vapour/air mixtures (0.2 mJ) it would have been necessary for the mean charge density in the tank to exceed a b o u t 18 nC m -3 and the maximum space potential to exceed a b o u t 45 kV. These values are based on the fact that discharge energies scale with the square of the mean space charge density, and the square of the maximum space charge potential. While the above comments suggest that ignition hazards in tank washing require fairly large isolated bodies and strong electrostatic conditions in the tank space, the present studies are not sufficiently detailed or extensive to allow any significant c o m m e n t on the ease or difficulty with which ignition hazards may arise in practice. The present results do however demonstrate that meaningful calculations are feasible for the various parameters (charge transfer, effective capacitance and discharge energy) relevant to the assessment of hazard mechanisms. It is likely that the hazards of discharge events involving isolated water slugs will vary with position in the cargo space in ways which may be related fairly simply to some local electrostatic potential or electric field value. The present calculations, however, have not been sufficiently extensive to test this proposition. If scaling with b o d y dimensions, form of structure and local electrostatic conditions is demonstrated then it will be feasible to at least estimate the prospective ignition hazards presented by particular events observed (for example by triggered flash photography) at any place in a cargo tank from a limited number of actual c o m p u t e r calculations. 5. Conclusions The studies described in the present paper demonstrate that electrostatic conditions and ignition hazard mechanisms in complex practical situations can be examined and assessed with the aid of computer calculations using a computer program such as the T H R E E D program developed at Culham.
Acknowledgements The work described in this paper was supported by the Marine Division of the Department of Trade. The work described in the Appendix was performed during 1972 for J.M. Houlder, Furness Withy and Co. Ltd., and the authors are grateful for his permission to publish it. The assistance of the BP Tanker Company in providing facilities for the shipboard experimental work is gratefully acknowledged.
85 APPENDIX Collection o f charge by aerodynamic sweep-up A.1. General features A body moving through a mist of charged particles can collect charge by aerodynamic processes. This process of charge collection is relevant to two aspects of the tanker explosion problem: (1) If incendiary quantities of electrostatic energy can arise by aerodynamic processes then such safety measures as dividing wire systems which limit the m a x i m u m space potential and m a x i m u m field concentrations would be only partially effective because aerodynamic collection is independent of potential and electric field. (2) The ability of water to form large physical bodies that can survive projection across a tank space is limited by surface tension and aerodynamic effects. Large lumps of crude oil and of waxy deposits retain their form much more easily because of a greater viscosity. However, the possibility that incendiary discharges could be drawn from such bodies will depend on the maintenance of a conducting layer of water on the surface. Simple laboratory tests at Culham failed to demonstrate the occurrence of incendiary discharges from a simulated body of crude oil -- a plastic ball coated with crude oil which was sprayed with a dilute solution of salt, detergent and glue to try to create a conducting surface coating. If a suitable layer of water could be maintained dynamically by aerodynamic sweep-up, then it might be necessary to reconsider lumps of crude oil as possible sources of incendiary discharges. A.2. Influence of electrostatic effects It might be expected that the collection of charge by a body moving through a charged mist would be determined by both electrostatic and aerodynamic effects. Van der Weerd quotes [3] the mobility of mist particles as being below 3 X 10 -7 m 2 V -1 s -1. If we consider a 200-mm-radius sphere carrying a typical value of induced charge of 2.8 X 10 -7 C then the electric field at the sphere surface is 6.3 × 104 V m -1. The drift velocity of mist particles in this field could be below 2X 10 -2 m s -1. This velocity is very small compared to the travel velocity of thrown or falling bodies, and thus it is clear that electrostatic force effects are not likely to significantly affect charge collection processes. A.3. Calculations of charge collection Langmuir [12] examined the collection of fine water droplets by cylindrical and spherical bodies moving through ~he air in relation to aircraft icing. He derived expressions which related the collection efficiency E for mist particles within the projected cross-section of the body to a parameter K which relates
86 to droplet size, droplet density, the velocity of the body, the radius of the b o d y and the viscosity of air. For a spherical b o d y in the Stokes' Law regime: Z / ( 1 - E ) = 0.82 (K - 1/12) 1"°4
and for a cylinder for K between 0.125 and 1.1: E = 0.466(log10 8K) 2 and for K above 1.1: E = K / ( K + ~/2).
The parameter K is defined in c.g.s, units as: K = 2pa2V/97?R
where p is the density of the airborne mist particles, a the radius of the mist particles, v the velocity of the body, ~ the velocity of air, and where R is the radius of the body. The total charge which a sphere would collect aerodynamically can be obtained by integrating the collection efficiency over the distance of travel: Q = nq~R 2 f Edl
where n q is the charge density, and R is the radius. The energy will then be: U = ½ Q2/C = ½ ( n q ~ R 2 f E d/)2/4~ e o R = ~ n ~ q2 ( ~ R 3 / e o ) ( f E d/) 2.
The minimum size of sphere which could possibly acquire sufficient energy to be incendiary (2 × 10 -4 J) can be found by assuming the collection efficiency to be unity and setting the integral equal to the maximum path of travel. For example, taking a 50-m path length as a plausible maximum within a ship's cargo tank and a charge density of 3 × 10 -8 C m -3, the minimum b o d y size is about 0.13 m radius. A simple computer program was written using the above expressions to see h o w much charge and energy would in fact be collected'by spherical and cylindrical bodies larger than this minimum size. The bodies were assumed to be thrown on an upward trajectory across a cargo tank a b o u t 40 m wide and a b o u t 20 m high with a 10 m s -1 horizontal velocity and 20 m s - 1 upward vertical velocity. The cylindrical bodies were assumed to be of 1 m length and thrown with the cylinder axis perpendicular to the direction of travel. A charge density of 30 nC m -3 was assumed. The results obtained were as shown in Table 2. It is clear that even taking large bodies and assuming a long trajectory through a charged mist consisting of large particles that the final energies are well below the 200 # J minimum ignition energy for hydrocarbon vapour/air
87 TABLE 2 Sphere or cylinder diameter (m)
Mist particle diameter (microns)
Charge collected (nC)
Energy (p J)
20 40 20 40
10.8 36.1 7.1 21.2
3.5 39 2.3 20
20 20 40
19.3 19.8 29.2
14.7 9.9 33.8
Spheres 0.3 0.3 0.2 0.2
Cylinders 0.02 0.1 0.02
m i x t u r e . I s o l a t e d l u m p s o f m a t t e r are n o t l i k e l y t o survive a n y s u c h t r a j e c t o r y . It is c o n c l u d e d t h a t a e r o d y n a m i c s w e e p - u p o f c h a r g e d m i s t p a r t i c l e s d o e s n o t p r o v i d e a m e c h a n i s m o f a n y s i g n i f i c a n c e in r e l a t i o n t o i g n i t i o n h a z a r d in t h e c a r g o t a n k s o f c r u d e oil t a n k e r s .
References 1 C.L. Thomas, THREED -- A digital computer code for the design and analysis of three-dimensional electrostatic fields, Papers for IEE Conference on Computer Aided Design 8-11 April, 1974, at the University of Southampton. 2 G.J. Butterworth, I.E. Pollard, B. Jaffrey, C.J. Mottershead, and J.N. Chubb, Studies of tankwashing on British Purpose during ballast voyage from Isle of Grain to Cape of Good Hope, April 7 to May 5, 1977. Culham Report CLM/RR/D2/34 Feb. 1978. 3 J.M. van der Weerd, Electrostatic charge generation during washing of tanks with water sprays. II Measurements and interpretation, Proceedings 3rd Conference on Static Electrification, Institute of Physics, London, May 1971, pp. 158. 4 R.L. Lindbauer, Static electricity measurements on board SS British Surveyor: Evaluation and interpretation, KSLA Report AMSR.0037.72 1972. 5 J.M. van der Weerd, Spark mechanisms in tanks filled with charged mists, Paper presented at the Special Symposium on Tanker Explosions at the 2nd Int. Conference on Static Electricity, Frankfurt, April 1973. 6 J.N. Chubb, Practical and computer assessments of ignition hazards during tank washing and during wave action in part ballasted OBO tanks, J. Electrostatics, 1 (1975) 61. 7 B. Lewis and G. yon Elbe, Combustion, Flames and Explosion of Gases, New York, Academic Press 1961. 8 J.N. Chubb and G.J. Butterworth, Instrumentation and techniques for monitoring and assessing electrostatic ignition hazards, Electrostatics 1979, Institute of Physics Conference Series, No. 48, 1979, p. 85. 9 R.J. Klaver and V.A. Dayot, An investigation of electrostatic charge generation during cargo tank washing on the Ralph B. Johnson, Chevron Research Co. Report, 27 July 1970.
88 10
I.E. Pollard and J.N. Chubb, A n instrument to measure electric fields in adverse conditions, Static Electrification,Institute of Physics Conference Series No. 27, 1975, p. 182. 11 G.I. Taylor and A.D. McEwan, The stability of a horizontal fluid interface in a vertical electric field, J. Fluid Mech., 22 (1965) 1. 12 I. Langmuir, Mathematical investigation of water droplet trajectories, Report No. RL-224. The Collected Works of Irving Langmuir, G. Suits (Ed.), Vol. X, Pergamon, 1961.