BLAST PRESSURE DISTRIBUTION AROUND LARGE STORAGE TANKS

Transcription

1 Research & development BLAST PRESSURE DISTRIBUTION AROUND LARGE STORAGE TANKS Written by: S. Yasseri Safe-Sight Technology, United Kingdom Abstract Correct distribution of the blast loading is important for storage tanks, as it is the local load acting on local imperfections, especially for thin walled structure, that can cause collapse. This paper reports results of a series of experiments on the distribution of blast pressure around a large storage tank. These results are applicable for tanks (LNG or oil) whose height is less than their diameter. Using regression analysis, expressions that fit the experimental results very well were derived. The derived expressions are also compared with results reported in the literature. Keywords: LNG Storage tanks; Oil storage tanks; Blast load distribution 1 Introduction Large hydrocarbon storage tanks are vulnerable to external pressure due to their sensitivity to imperfections. Blast pressure can accentuate imperfections, which enhances storage tanks vulnerability to collapse. Collapse of tanks in a tank farm (Figure 1) can put other tanks at risk of fire and explosion. Hence, correct load determination and analyses are important. Figure 1 Tank Farm in Wilmington, California There have been several accidental explosions in tank farms around the world which led to collapse of other tanks (Figure 2). In all cases, investigators attributed collapse to the intensity of the blast pressure and its distribution did not receive as much attention. As tanks are sensitive to imperfections, naturally the distribution of blast pressure is worthy of equal attention. This issue is addressed much better for tanks subjected to the effect of hurricanes; see for example Godoy & Flores [5]. This paper presents analytical expressions which can be used to determine the pressure distribution around large tanks. The investigation considered LNG tanks (Figure 3), which have heavier walls than oil storage tanks. Figure 2 Puerto Rico Refinery/Tank Farm Explosion on 23 October Review of Blast Time-history TNT is used as a reference for determining the blast overpressure and a scaled distance, Z (Equation 3). For this purpose, the explosive mass 22

2 There are more correlation relationships reported in literature, e.g. Miles [7] proposed the following expression: = , kpa (4) Z 3 Z 2 Z Brode [2] also proposed the following expression for p --, the maximum value of negative pressure (pressure below ambient pressure) in the negative phase of the blast. p - = , bar for Z > 1.6 (5) Z The explosion wave front speed, U s, and the maximum dynamic pressure, q s, are defined by Mays & Smith [6] Figure 3 Typical LNG tank is converted into and equivalent mass of TNT. To do this, the mass of fugitive gas is multiplied by a correlation factor based on the specific energy of the explosive charge (usually TNT) and the gas. The specific energies of different explosive types and their correlation factors to that of TNT can be found in Table 1 (from [15]). EXPLOSIVE Brode [2] gives the following expressions for the peak static overpressure for a medium to far distance: where Z is the scaled distance, given by: SPECIFIC ENERGY Qx (kj/kg) TNT EQUIVALENT Qx/QTNT Compound B (60 % RDX, 40 % TNT) RDX (Ciklonit) HMX Nitroglycerin (liquid) TNT Explosive Gelatin (91% Nitroglycerin, 7,9% nitrocellulose, 0,9 % Antracid, 0,2 % water) % Nitroglycerin dynamite Semtex C Table 1 Conversion factors for explosives = , bar for p > 10 bar (1) Z 3 s = Z , bar for 0.1< < 10 bar (2) Z 2 Z 3 R Z = 3, where (3) W R = distance from the centre of a spherical charge in meters W = mass of explosive expressed in kilograms of TNT U s q = s Where: = peak static wave front overpressure in bar p 0 = ambient air pressure (atmospheric pressure) in bar a 0 = speed of sound in the air in m s As the wave propagates through the air, the wave front encircles the structure and all its surfaces so that the whole structure is exposed to the blast pressure. The magnitude and distribution of the structural loading depends on the following factors: ÔÔ ÔÔ the characteristics of explosives that depend on the type of explosive material, released energy (size of explosion) and weight of explosive, the explosion location relative to the structure, intensity and magnification of pressure through interaction with the ground or the structure itself. The profile of the explosion pressure wave is usually described as an exponential function in the form of Friendlander s equation [9], in which b is the parameter of the waveform: Where: 6ps = a +7p 0 0 (6) 7p 0 5ps 2 2 ( p + 7p ) s 0 t bt p (t) = 1- t exp - (8) 0 t0 t 0 = duration of the positive phase during which the pressure is greater than the pressure of the surrounding air. For many purposes, such approximation is satisfactory and the pressure profile (over time) is shown in Figure 4. Rankine and Hugoniot [17] derived an equation for refracted overpressure P r : p r = 2+ (γ + 1) q s (9) For air, γ air 1.4 [17] Substituting Equation 7 into Equation 9: 7p Pr = 2p 0 +4 s (10) 7p 0 + (7) 23

3 Research & development BLAST PRESSURE DISTRIBUTION AROUND LARGE STORAGE TANKS Considering a cylindrical shell engulfed in a blast wave due to a major explosion of chemicals or hydrocarbon products, the blast load results from the reflected pressure and the drag loading based on the dynamic pressure. The effective pressure depends on time and the angle between the wave front and the cylindrical wall (Noret et al [10]): P r (Ө, t ) = p (t) (Ө) + q (t) Cd (11) V Figure 4 Schematic of the blast wave 3 Literature review A limited literature review is presented in this section. Figure 5 shows the flow field around a single cylinder. The transition from a laminar to a turbulent flow depends on the Reynolds number, and at some stage the flow becomes fully turbulent. The drag and lift coefficients are closely related to these transitions. Figure 5 shows that the pressure distribution around a large cylinder is not uniform. Thus, applying the total blast load to the front of a tank does not predict how the tank fails. The tank is considered to be in the far-field from the explosion origin so that drag loading is neglected (q(t)=0). It is further assumed that the pressure is positive and constant along the height. The function Λ(θ) is considered uniform around the shell for buckling behaviour. For the global behaviour of the tank, Λ(θ) is considered as a cosine function. Noret [10] don t provide the shape of Λ(θ), but it can be deduced from the calculation that cos θ is used, which equals to one at the front face θ=0. The fluid-solid interactions are neglected. Rotzer, J. and Douglas [11] proposed a distribution as shown in Figure 7. This figure shows a peak at 60 degrees, which is very different from what is known about pressure distribution p 0.5 p 60 p 0.1 p Figure 7 Distribution of blast pressure around an LNG tank according to Rotzer, J. and Douglas [11] Figure 5 Flow Field around Circular Cylinder Most articles addressing the design of storage tanks apply the blast over-pressure to the front face of the tank. A departure from that approach is used by Noret et al [10]. They have generated four different overpressure time histories (as shown in Figure 6) representing the positive phase of an exponential detonation (Signal 1), a typical vapour cloud deflagration (Signal 2), a quick deflagration (Signal 3) and a classical linear signature used for detonation (Signal 4). The effect of hurricane wind on the storage tank cannot be very dissimilar. There is a large amount of literature on the collapse of storage tanks in hurricanes. Figure 8 presents circumferential variations of wind pressure around cylinders based on different experimental results, and measured from the angle of wind incidence to one half of the diameter. The values presented correspond to the ACI-ASCE Committee 334 [1] and Rish [14]. Other distributions have been developed for long as well as short tanks. Overpressure (mbar) Signal 1 Detonation b=1 Signal 2 Deflagration b=1 Signal 3 Deflagration b=0 Signal 4 Detonation b= Time duration (ms) Figure 6 Various overpressure signatures (P (t)-p a ) ( =0.50 MPa, t 0 = 50ms) Figure 8 Wind pressure distribution around a cylinder 24

4 In some circumstances, when a cylindrical structure comprises openings, an additional uniform negative pressure is added due to the internal suction generated. Similar behaviour is possible in tanks with opened roofs as presented in Schmidt [13], which sometimes are reinforced with a ring stiffener at the top. Figure 8 also presents differences between the wind pressure distributions of close and open tanks (Resinger and Greiner [12]). The Rish [14] and ACI-ASCE [1] expressions are the two most popular distributions. Both have the following format: of the negative phase is very small and hence the drag force can be neglected. The free field incident blast overpressure time-history curve is described by a triangle, which is commonly assumed to have equal rise and fall. This section describes a method for determining the average pressure on projected areas of cylindrical objects when the direction of blast wave propagation is normal to the axis of the cylinder. Figure 9 shows a blast wave approaching a cylindrical object. p = 7 0 C i cos (iө) (12) Where: C i = Coefficient of external pressure. The ACI-ASCE [1] equation has 8 terms while the Rish [14] equation has 7 terms. p = External wind pressure λ = Parameter used to increase the pressure Table 2 gives C i for both expressions. C i ACI-ASCE 1991 Rish 1967 Figure 9 Blast wave approaching a cylindrical object C C C C C C C C N/A Table 2 4 Blast Pressure on Closed Cylindrical Objects There are two types of structures when calculating blast wave loading: ÔÔ ÔÔ Coefficients for ACI-ASCE and Rish equations Diffraction type; Drag type. A diffraction-type structure is primarily sensitive to the peak overpressure of the shock wave; a large storage tank without opening for example. When the pressure on different areas of a structure rapidly equalise due to its small size, the diffraction forces only last for a very short time. The response of such structure is then primarily due to the dynamic pressure (or drag forces) of the blast wind. The loading analysis of a diffraction dominated structure considers only the positive phase of the overpressure until it falls to zero on the front surface. This is due to the fact that the dynamic loading The interaction of blast waves with cubical objects which are now commonly used (see [16] for example) may be generalised for cylindrical objects such as storage tanks and pressure vessels. The ratio of reflected overpressure to the incident overpressure at the blast front depends on the angle at which the blast wave strikes the object. For a curved surface, the reflection varies from point to point on the front surface. The time of decay from reflected to stagnation pressure then depends on the size of the object and location on the front surface where the blast wave strikes. The drag coefficient varies with the shape of the structure. In most cases, an average drag coefficient is adequate to determine the net blast forces. The rise time of average pressure on the back surface depends on the size and, to some extent, on the shape of the object. If parts of the object can be blown out by the initial impact of the blast wave, then the shape of the object changes and the subsequent loading may also change. For example, when windows of a building are blown out, the blast wave enters the building and tends to equalise the inside and outside pressures. If a structure can be designed so as to allow certain parts to be blown out, then the net effect of blast on other portions of the building will reduce. In principle, the response of certain portions/elements of a structure may alter the overall blast loading on the structure. There is some interaction between blast and deformation of the structure, but such integration is neglected for design purpose. The blast loading on an object is a function of both the incident blast wave characteristics i.e. the peak overpressure, dynamic pressure, 25

5 Research & development BLAST PRESSURE DISTRIBUTION AROUND LARGE STORAGE TANKS decay, duration, size, shape, orientation, and the response of the object. The interaction of the incident blast wave with an object is a complex phenomenon. To reduce the complex problem of blast loading for practical use, it is assumed that (a) the over-pressures are less than 3.5 bar (dynamic pressures less than ~2.75 bar), and (b) the object being loaded is in the region of Mach reflection. Figure 10 shows a cylindrical tank with a diameter/height ratio lower than 3. The blast wave strikes the surface of the tank at a zero angle at time t=0 and the time of arrival at point A (Figure 10) is equal to X U s regardless of its position (whether it is on the front or back half). At time t 1, the overpressure rises to the reflected value P 1. t 1 is therefore the rise time. The reflected pressure P 1 varies with the position of A on the tank. Vortex formation causes the above pressure to drop to P 2 ; and is then followed by an increase to P 3, the stagnation pressure. From then on, the pressure is equal to (t)+c d q(t); where C d is the appropriate drag coefficient, which decays in the normal manner. Figure 10 Approaching of a blast wave - cross-section of Figure 9 The dependence of the pressures P 1 and P 2 and the drag coefficient C d on the angle θ is discussed later in this paper. The pressure values are expressed as the ratios to P r, where P r is the ideal reflected pressure for a flat surface. When θ is zero i.e. where the blast wave first strikes the tank, P 1 is the same as P r, but for larger angles its value decreases. The rise time t 1 and the time intervals t 2 and t 3, respectively corresponding to vortex formation and attainment of the stagnation pressure once the blast wave has passed the tank, are also shown in Figure 11 (expressed as the time unit H/U, with H being the radius of the tank). There is a zero rise time for the front half of the arc i.e. for θ between 0 and 90, but it increases on the back half i.e. for θ between 90 and 180. The times t 2 and t 1 are independent of the angle θ. Figure 11 The pressures P 1 and P 2 and the drag coefficient Cd are dependent on the angle θ (see Figure 10) Since the procedures described above give the loads normal to the surface at any arbitrary point A (see Figure 10), the net horizontal loading is not determined by simply subtracting the loading on the back from that on the front. To determine the net horizontal loading, it is necessary to sum the horizontal components of the loads over the two areas and then subtract them. In practice, an approximation may be used to obtain the required result, if the net horizontal loading is considered to be important. For large storage tanks, because of sensitivity to imperfections, it is the local loading rather than the net loading which is damaging [13]. In the approximate procedure for determining the net loading, the overpressure loading during the diffraction stage is considered to be equivalent to an initial impulse equal to P r A(2H U), where A is the projected area normal to the direction of the blast propagation. It will be noted that 2H U is the time taken for the blast front to pass the structure. The net drag coefficient for a single cylinder is about 0.4 in the considered range of blast pressures [15]. Hence, in addition to the initial impulse, the remainder of the net horizontal loading may be represented by the force 0.4 q (t) A, as seen in Figure 12, which applies to a single structure. Figure 12 Approximate equivalent net horizontal force on cylindrical structure 5 Experiments Three small scale experiments were conducted using a disused 2.5m diameter and 2m high tank as the target. The maximum pressure was measured via two rows of pressure transducers spaced around the perimeter 10 degrees from each other and on two planes at 0.9m and 1.5m above the foundation (Figure 13). The TNT charge was placed 2m away from the tank on the zero degree line. The intention was to determine pressure distribution around the tank from a nearby explosion. The blast wave was 26

6 Figure 17 compares the fitted curves (lines) with results reported in Reference 4 (shown as dots). For all parameters the difference is less than 6%; this is acceptable and there is no need to complicate the equations. Figure 13 Experimental set up normal to the tank face (zero degree). The measurements from these six experiments at 18 locations were averaged. The scatter of results was not large and the difference between the fitted curves and the experimental results, at any θ, was less than 12%. This gap could be closed by adding more terms in Equation 13, but the accuracy of the experimental results doesn t warrant more complexity. 6 Fitting Curves to the Experimental results A collection of cosine curves can represent circumferential pressures on shells. For this reason, most of the formulations which define circumferential patterns of pressure employ Fourier cosine series. The equation of the fitted curves has the following general form: p = 6 i = 0 c i cos iө The variable i stands for terms of the series (seven terms) and an increment of the angle measured from windward direction. C i is a constant representing the contribution of each term and the amplitude of the pressure coefficient wave. The pressure value at a specific height (λ) is multiplied by the external pressure coefficient represented by the summation expression. Table 3 gives the values for C i for the fitted curve as shown in Figures 14 to 16. Points shown as shapes in these figures correspond to the experimental values. The solid lines are the fitted curves using the cosine function. Coefficient P 2 /P r P 1 /P r C d C C C C C C C Table 3 Parameters of fitted curves shown in Figures 14 to 16 (13) The rise time t 1 and the time intervals t 2 and t 3, respectively corresponding to vortex formation and attainment of the stagnation pressure, and measured from the time when the blast wave first reaches the tank, are shown in Figure 18 (in terms of the time unit H/U). The rise time t 1 is zero for θ between 0 and 90. It increases but remains finite for a θ between 90 and 180. The times t 1 and t 2 are independent of the angle θ (Glasstone and Dolan 1977). The difference between the fitted curves at any angle θ is less than 12% for smaller values, and the difference is less for the larger numbers. This gap could be closed by adding more terms, but the accuracy of the experiment doesn t warrant more complexity. 7 Pressure distribution Over the Roof The distribution of the blast loading on the roof is not well researched. A suggested distribution is schematically shown in Figure Concluding Remark Expressions which are suitable for determining the distribution of the blast pressure around a large storage tank are given in this paper. These expressions are for isolated thanks. In principle, tanks within tank farms are separated enough from each other for these expressions to be applicable. The modification of the flow by adjacent structures is known as interference. If tanks are in close proximity to each other or to other buildings, they influence each other. However, interference with an adjacent structure can be accounted using a gust factor, similar to what is used in design for wind loading. The internal hydrostatic pressure by liquid can significantly enhance the buckling strength, but high internal pressures also lead to severe local bending near the base. Local yielding then precipitates an early elastic-plastic buckling failure. A damaged geometry due to blast triggers imperfection-sensitivity. API allowable buckling stress is based on the classical value of buckling stress under axial load, significantly factored down due to shell imperfections and also increased to account for the effects of internal liquid pressure. 9 Acknowledgements The author acknowledges the support provided by his colleagues David Walker, and Chris Millyard in testing and collating the material used in this paper. Many helpful comments of Mr Guillaume Vannier are also gratefully acknowledged. 27

7 Research & development BLAST PRESSURE DISTRIBUTION AROUND LARGE STORAGE TANKS Figure 14 Variation of drag coefficient around a tank Figure 15 Variation of pressure ratios around a tank Figure 16 Variation of pressure ratios for a tank 28

8 Figure 17 Comparison of the current results with results in [4] Figure 18 Interval time Figure 19 (a) Roof uplift pressure will occasionally damage tanks, (b) Roof to shell Joint may tear and peel away roof plate, (c) Roof structure may be dislodged by distortion of shell 29

9 Research & development BLAST PRESSURE DISTRIBUTION AROUND LARGE STORAGE TANKS 10 References [1] ACI-ASCE Committee 334 (1991), Reinforced concrete cooling tower shells-practice and commentary, ACI 334,2R,91. American Concrete Institute, New York. [2] Brode, H. L. Numerical solution of spherical blast waves, Journal of Applied Physics, American Institute of Physics, Ney York, [3] James I. Chang, Cheng-Chung Lin, 2006, A study of storage tank accidents, Journal of Loss Prevention in the Process Industries 19, pp [4] Glasstone, S. and Dolan, P., The effect of Nuclear Weapon, DOE & DOD, Chapter IV. Also available on [5] Godoy, L.A. and Flores, F.G., 2002, Imperfection sensitivity to elastic buckling of wind loaded open cylindrical tanks, Structural Engineering and Mechanics, Vol. 13, No. 5. [6] Mays, G. C.; Smith, P. D; Blast Effects on Buildings Design of Buildings to Optimize Resistance to Blast Loading, Tomas Telford, [7] Mills, C. A. The design of concrete structure to resist explosions and weapon affects, Proceedings of the 1st Int. Conference on concrete for hazard protections, Edinburgh, UK, pp , [8] Newmark, N. M.; Hansen, R. J. Design of blast resistant structures. // Shock and Vibration Handbook, Vol. 3, Eds. Harris and Crede. McGraw-Hill, New York, USA [9] Ngo, T.; Mendis, P.; Gupta, A.; Ramsay, J. Blast Loading and Effects on Structures An Overview, EJSE Special Issue: Loading on Structures, [10] Noret, E., Prod homme, G., Yalamas, T., Reimeringer, M., Hanus, J-L. And Duong, D-H, Safety of atmospheric storage tanks during accidental explosions, Revue. Volume X n x/année, pages 1 à X. [11] Rotzer, J. and Douglas, H., Hazard and Safety Probes for LNG tanks, LNG journal, February 2006, pp [12] Resinger F., and Greiner R. (1982), Buckling of windloaded cylindrical shells-application to unstiffened and ring-stiffened steel tanks, in Buckling of shells, Ramn E. (ed.), Springer, Berlin, pp [13] Scmidt H., Binder B., and Lange H. (1998) Postbuckling strength design of open thin walled cylindrical tanks under wind load. First International Conference on Thin Walled Structures. Elsevier Science Ltd., pp [14] Rish, R. F. (1967), Forces in cylindrical shells due to wind, in: Proc. Inst. Civil Engineers. Vol. 36, pp [15] Unified Facilities Criteria (UFC), Structures to Resist the Effects of Accidental Explosions, U. S. Army Corps of Engineers, Naval Facilities Engineering Command, Air Force Civil Engineer Support Agency, UFC , 5 December [16] Yasseri, Portable Building within Processing Plants, FABIG Newsletter No. 51. [17] Wikipedia, Rankine Hugoniot conditions, last accessed 13/06/ Rankine%E2%80%93Hugoniot_conditions. For further information, please contact: Sirous Yasseri Safe-Sight Technology Ltd E: sirous.yasseri@gmail.com 30