Explosion Hazard Assessment: A Study of the Feasibility and ...

Explosion Hazard Assessment: A Study of theFeasibility and Benefits of Extending

Current HSE Methodology to take Account ofBlast Sheltering

HSL/2001/04

Project Leader: Dr M Ivings

Authors: Dr C Catlin, Dr M Ivings, Mr S MyattDr D Ingram, Prof D Causon, Dr L Qian

Fire and Explosion Group

© Crown copyright 2001

Broad Lane, Sheffield S3 7HQTelephone: 0114 289 2000Facsimile: 0114 289 2500

Summary

Objectives / Background

This study concerns the methodology used by MSDU, HSE in assessing Land Use Planningcases (LUP) near Hazardous Installations storing LPG and presenting a Vapour Cloud Explo-sion (VCE) hazard. The work is also relevant to all risk assessment and consequence modelsthat are used to assess the hazard posed by blast.

The methodology currently used by MSDU assumes that the blast propagates without interac-tion with any buildings or terrain features that may lie between the explosion source and theproposed site. Thus the estimate of the incident peak positive overpressure is likely to beconservative. The probability of fatality is then inferred from the peak positive overpressureusing war-time data. This allows the vulnerability of the public to be assessed from whichconsultation distance and hazard zone boundaries are determined.

The leading shock wave is the highest frequency component of the blast wave and will, there-fore, be the most affected by interaction with obstacles. A revised methodology which takesaccount of obstacle interaction will, therefore, exhibit sheltering effects. Thus there are situa-tions where buildings that lie between the explosion source and the proposed site will providesubstantial sheltering in the region of the proposed construction. In such situations it isconceivable that the existing methodology places the hazard zone boundaries at substantiallylarger distances than is required to maintain an acceptable probability of fatality. A revisedmethodology, therefore, which takes sheltering into account could potentially free-up substan-tial areas of land around existing and future hazardous installations.

Main Findings

Predictions of Computational Fluid Dynamic (CFD) simulations have been compared againsta limited number of field-scale experiments which investigate the effects on the blastoverpressure of the intervening obstacles. This has established that sufficient accuracy can beobtained using CFD methods without a prohibitive requirement of staff or computingresources. It has been shown that for simple linear rows of square cross-section buildings thatthree-dimensional CFD simulations provide a very accurate predictive method but requiresubstantial computing and staff-time resources. However the application of a two-dimensionalaxi-symmetric approximation can also be used in the computations to yield adequate accuracy using contemporary workstations and a simulation turnover of less than a day. This hasenabled the two-dimensional CFD to be used to simulate a range of cases for different build-ing layouts and sizes.

The peak positive overpressures determined from these simulations have provided sufficientdata with which to propose a preliminary methodology for incorporating the effects of shelter-ing into existing explosion hazard assessment models. The methodology amounts simply todetermining the TNT mass-scaled height of the buildings, and their intervening distances, andreferring to look up tables to determine the relevant sheltering factors. These can then be used

to determine the inward shifts of the hazard zone boundaries. The preliminary methodologyhas been applied to two representative scenarios, the larger being on the scale of the Flixbor-ough disaster, and has shown that the outer and inner boundaries of the Outer Zone can bemoved in by as much as 80 m and 50 m respectively. These distances represent substantialfree-up of land and therefore suggest that a revised methodology could significantly increasethe land available for development around a major hazard site and/or lead to less restraints onthe site owner.

Main Recommendations

A preliminary methodology for incorporating the effects of sheltering into existing explosionhazard assessment models has been proposed. MSDU can now decide on the appropriatenessof including the sheltering effects of buildings in their assessment of LUP cases. This willcrucially depend on the fact that intervening buildings are not necessarily permanent and theirremoval will change the consultation distance.

The further development of the methodology described in this report will lead to a useful toolthat could be used in the preparation or assessment of COMAH safety reports where blast is asignificant hazard.

The development of the methodology should be based on a programme of two and threedimensional CFD simulations validated against further blast experiments.

Contents

567. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55 6.1. Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .546. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53 5.3. Applicability of revised methodology . . . . . . . . . . . . . . . . .42 5.2. Two-dimensional CFD parameter variation study . . . . . .41 5.1. Extended TNT Methodology . . . . . . . . . . . . . . . . . . . . . . . . . .415. SHELTERING MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40 4.4. Parametric study CFD calculations . . . . . . . . . . . . . . . . . . .29 4.3. 2D Axisymmetric CFD calculations . . . . . . . . . . . . . . . . . . .27 4.2. Mesh refinement study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 4.1. The appropriateness of axi-symmetry . . . . . . . . . . . . . . . .244. VALIDATION OF THE METHODOLOGY . . . . . . . . . . . . . . . . . . .

20 3.5. Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 3.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 3.3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 3.2. Experimental method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 3.1. Nominal experimental programme . . . . . . . . . . . . . . . . . . . .73. METHODOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 2.4. LPG-RISKAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2.3. Consequence models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 2.2. TNO Multi-Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 2.1. TNT Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32. BLAST PREDICTION METHODS . . . . . . . . . . . . . . . . . . . . . . . . . .

11. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. INTRODUCTION

This study concerns the methodology used by MSDU, HSE in assessing Land Use Planningcases (LUP) near Hazardous Installations storing LPG and presenting a Vapour Cloud Explo-sion (VCE) hazard. This work is also relevant to all risk and consequence models that are usedto assess the hazard posed by blast. Necessarily the methodology must be quick to use yetconservative. Current methods assume unobstructed terrain and yet the fatality statistics arelargely based on war time data which would have involved the additional effects of blast struc-ture interaction, structural damage and projectiles. The current methodology, therefore, can beconsidered as conservative.

A revised methodology, which results in a substantial reduction in the consultation distances,would have large financial implications if blast waves were the only or dominant hazard at thatdistance. For example the sheltering effects of buildings sited on the hazardous installation couldbe taken into account and free up land space for development.

For the reasons outlined above the methodology must be simple but versatile enough to apply tothe many potential scenarios. The current methodology achieves this by assuming a flatunobstructed terrain between the blast source and the site. Thus the complexities of the effects ofthe intervening buildings are overlooked for the sake of versatility but with the assurance thatthe blast prediction is conservative. This is because for those instances when the blast frontcomprises a shock wave its interaction with buildings before arrival at the site will tend toremove energy from the blast wave and lessen the peak shock overpressure. The exceptionalcase might for example occur when the initial blast wave is preferentially aligned with the build-ings so as to amplify the incident shock overpressure relative to the standard methodology. Suchexceptions are presently addressed by basing the fatality data upon worst case data.

The time is also opportune for the development of more sophisticated blast prediction method-ologies since they at present lag behind those used for gas dispersion calculations. In manyinstances gas dispersion calculations are performed prior to a blast calculation in order toestimate the explosion inventory in the event of a flammable vapour release. Such dispersionmethods cater for the improved mixing caused when a vapour disperses over built up terrain.These methods have been implemented into PC software in a form that they can be easily andquickly used by MSDU.

This study necessarily considers the extension of the current TNT and TNO blast predictionmethods. Both of these methods cater for ideal blast waves for which sheltering or amplificationare most likely to occur. The shorter frequency component of the blast wave, namely the leadingshock wave and immediate later times, is the most likely to be affected through interaction withbuildings. The lower frequency components will be least affected. This study will be primarilyconcerned with peak incident overpressure in view of it being the principal measure of blastseverity in the RISKAT methodology.

One of the key issues concerns the representation of the complex variety of buildings and layoutpatterns. In the case of gas dispersion these can be adequately represented by roughness parame-ters that describe mean separation and building heights. In the case of explosions the scope for asimple approach is less obvious since we are studying the interaction of the higher frequencycomponent of the blast wave which, therefore, is sensitive to the details of the geometry. Thus

1

the development of a comprehensive methodology necessarily requires the investigation of alarge number of obstacle layouts and geometries and also a range of incident blast wave lengths.The effects of blast-structure interaction will be most pronounced when the blast wavelengthsare similar in size to that of the building whereas the effects will be negligible for much largerwavelengths.

In general there are many three dimensional layouts to be studied and in each case there can be alarge surface area of terrain to search over to find the maximum incident overpressures. Thus anexperimental programme alone has limitations in view of the need for the large number of blastmeasurements for each geometry studied as well as the large number of geometries. Computa-tional Fluid Dynamic methods have an excellent track history for simulating ideal blast wavepropagation and obstacle interaction but their accuracy can be questioned when applied for thefirst time to complex geometries. This question principally concerns the ability to capture theimportant physical features without the need for prohibitive computer and staff time. While inprinciple the methods can predict the near exact behaviour, in practice there are substantialconstraints placed by the size and speed of the computer. A limited experimental programmewas envisaged, therefore, to establish the sufficiency of the combined numerical and computa-tional resources.

The primary objective was to assess whether there was scope for developing a simple methodol-ogy. It was decided to investigate where significant effects of sheltering might be observed.Linear rows of buildings without gaps were therefore studied in the absence of obstructions tothe down wind side: Depending upon their proximity to the hazardous installation, downwindstructures could reflect and amplify the shock pressure incident upon the site. If, therefore, avaluable methodology could be distilled from these cases then this would provide a sound finan-cial incentive for future more exhaustive investigation. This approach has the additional benefitsthat the obstacle layouts used in the experiments were simple and needed few changes. It alsoallowed the numerical representation to be axi-symmetric thus making it feasible to service thelarger part of the study using standard workstations except for some isolated three-dimensionalruns which were used to validate the axi-symmetric approximation.

2

2. BLAST PREDICTION METHODS

2.1. TNT Equivalence

The longest established methods for estimating incident blast overpressure are based upon highexplosive (HE) blast. This approach is directly compatible with the estimates of damage which,having incorporated war-time data, are generally characteristic of high explosives. Because thesource of energy is concentrated into a small volume, ideally in a mathematical sense to aninfinitesimal point, the corresponding blast waves are considered ideal. The lack of geometricalscales results in the blast wave being characterised by only one effective length scale, namely thecube root of the charge mass. Thus the blast waves from different masses of TNT are all similarif the distance and time scales are normalized by the cube root of mass. This is the basis ofHopkinson scaling [1]. In practice the blast waves from a wide range of energetic explosions canbe adequately characterised by that of the detonation of a suitable mass of TNT provided that thecorresponding conversion efficiency of chemical energy into the blast wave energy is known. Itis noted that many of the blast parameters, e.g. peak negative overpressure, positive and negativeoverpressure phase impulses and durations can be normalised using Hopkinson scaling andrepresented by one family of graphs [1].

It is important to note that in this study the TNT blast wave parameters correspond to groundreflected overpressure, namely that achieved when the given mass of TNT is placed on theground and the overpressures measured at ground level. In many instances overpressures arequoted relative to free-air bursts, namely those not influenced by ground reflection, for whichtwice the mass of TNT is required to achieve the ground reflected overpressure. Clearly groundreflected overpressures are the more relevant to this application.

In general the blast waves generated by explosions are not the same as those from HE. This isparticularly true of Vapour Cloud Explosions (VCEs) in which the flame speeds are not suffi-ciently high to ensure a shock wave at the blast front. This limitation is addressed in the TNOMulti-Energy method described below. However for many vapour cloud explosions with highflame speeds [2] the blast from a VCE can be adequately determined by assuming a suitableconversion efficiency between the heat of combustion of the gas mixture and an equivalent massof TNT [2].

2.2. TNO Multi-Energy

The Multi-Energy methodology [3] was developed in recognition that many explosions, particu-larly VCE’s where flame acceleration is involved, can vary substantially in the efficiency withwhich the chemical energy released by the combustion is converted into mechanical energy ofthe blast wave. Detonation, whether of gas or HE is the most efficient conversion process andthe blast waves from detonations can therefore be accurately related to those of a suitableequivalent mass of TNT. In fact the Multi-Energy method categorises the explosion strength intoten levels, the peak incident overpressure and positive overpressure phase duration being givenin Figures 2.1 and 2.2. Normalization of distance and time scales is here performed in terms ofthe combustion energy (E/P0)1/3 to allow one set of graphs to be used for different inventories ofvapour cloud. HE blast corresponds to explosion strength 10. In fact it can be seen that in therange 70 mbar < Ps < 140 mbar there is effectively no difference in the peak incident

3

overpressure from explosion strengths 6 through 10. In the range 70 mbar < Ps < 140 mbar thereis at most 20% underestimate in the positive phase duration.

Explosion strengths 1 through 3 on the other hand are not sufficient to generate the lower peakoverpressure threshold (70 mbar) of interest in this study. This leaves explosion strengths 4 and5 neither of which is severe enough to produce shocks at the high level of relevance to thisstudy, namely 140 mbar. Explosion strength 5 only acquires the ideal blast wave-form at peakpositive overpressures substantially below 70 mbar. Outside the ideal blast wave region theMulti-Energy method assumes that the blast front has a finite rise time with total positive phaseduration between 2 to 3 times longer that the equivalent HE blast wave. In view of the absenceof the shock and the longer duration such blast waves will be far less susceptible to sheltering oramplification effects and have, therefore, not been considered in this study.

0.001

0.010

0.100

1.000

10.000

100.000

0.1 1 10 100

1 2 3 4 5 6 7 8 910600 mbar140 mbar 70 mbar

Dim

ensi

on

less

max

imu

m s

ide-

on

ove

rpre

ssu

re (

P s)

Combustion energy-scaled distance (R)

Ideal blast wave region

Figure 2.1 TNO Multi-Energy methodology : Decay with distance of peak positiveoverpressure for ten explosion strengths

4

0

1

10

0.1 1 10 100

1

2

3

4

5

6

7

8

9

10

600 mbar

140 mbar

70 mbar

Combustion energy-scaled distance (R)

Dim

ensi

on

less

po

siti

ve p

has

e d

ura

tio

n (

Ts)

Ideal blast wave region

Figure 2.2 TNO Multi-Energy methodology : Variation with distance of positive overpres-sure phase duration for ten explosion strengths

2.3. Consequence models

Consequence models are used by MSDU to assess Land Use Planning cases where sites are storing flammable substances and the dominant hazard is that of blast. These models may alsobe used by MSDU when assessing the predictive elements of COMAH safety cases where a‘snapshot’ of the blast hazard is required. In Land Use Planning cases decisions are made basedupon where the proposed site lies relative to the source of the explosion. The development iscategorised according to the vulnerability of those persons that will be at the development. Theadvice is determined by a matrix of overpressure versus distance (Table 2.1). The matrix isdivided into three zones (Inner, Middle and Outer) according to the peak incident shockoverpressure (Ps). Beyond the radius of the Outer Zone, the so called Consultation Distance(CD) where Ps < 70 mbar, fatalities are unlikely. The Outer Zone corresponds to the overpres-sure range 70 mbar < Ps < 140 mbar where a 1% chance of fatality amongst the general public isexpected. The Middle Zone is defined by the region 140 mbar < Ps < 600 mbar . It is assumedthat there is a near certain chance of a fatality in the Inner zone, where Ps > 600 mbar .

5

Table 2.1 Decision function used in the consequence model for assessing Land UsePlanning cases

Don’t Advise AgainstDon’t Advise AgainstDon’t Advise AgainstCategory BDon’t Advise AgainstConsultConsultCategory CDon’t Advise AgainstConsultAdvise AgainstCategory A

ConsultConsultAdvise AgainstCategory D

Outer Zone70 < Ps < 140

Middle Zone140 < Ps < 600

Inner ZonePs > 600

The vulnerability axis is split into four categories: A - residential such as houses and hotels, B - industrial namely factories and offices, C - leisure/retail which includes shops, restaurants, sports centres and D - institutional namely hospitals and schools.

A revised methodology which accounts for sheltering, for example, might propose a shift of thezone boundaries toward the source thus freeing up land for development.

2.4. LPG-RISKAT

LPG-RISKAT [4] is used by MSDU when assessing applications for the development of newmajor hazard sites. If a risk based decision matrix is used then the matrix given in Table 2.2 isadopted. It is similar to that for the consequence model above and uses the same categories forvulnerability.

Table 2.2 Decision matrix used in LPG-RISKAT (where DD is dangerous dose or worse and cpm is chances per million)

Don’t Advise AgainstDon’t Advise AgainstDon’t Advise AgainstCategory BDon’t Advise AgainstConsultConsultCategory CDon’t Advise AgainstConsultAdvise AgainstCategory A

ConsultConsultAdvise AgainstCategory D

Outer Zonerisk < 1/3 cpm DD

Middle Zone1< risk <10 cpm DD

Inner Zonerisk > 10 cpm DD

In the present case, where we are interested in blast effects, a dangerous dose is an overpressureof 140 mbar. In the case of fireball, the dangerous dose is 1000 tdu.

6

3. METHODOLOGY

3.1. Nominal experimental programme

As explained previously the terrain has been assumed flat in view of the relatively smalldistances (within a 500 m radius) between the centre of the blast source and the site in question.For example, if the TNT equivalent to the Flixborough disaster of 16 Te is assumed, thedistances to the 600 mbar, 140 mbar and 70 mbar are given respectively by 105 m, 254 m and413 m. The 600 mbar contour, therefore, is very close to the explosion source and the benefits ofsheltering are far less in terms of the distances by which the zone boundaries could be movedcloser. Thus the greatest significance of a revised methodology would be on the inner and outerboundaries of the Outer Zone since the distances involved are larger and, therefore, the area ofland affected larger.

As explained previously the generic scenario to be studied involves the placement, between theblast source and the site of interest, of unbroken rows of square cross-section obstacles. Obsta-cles on the downstream side of the site have been omitted since they could potentially counterany beneficial effect of sheltering.

The generic geometries chosen were based upon terraced housing, either separated by back-to-back gardens, or else an access street, and modern industrial layouts also separated by accessroutes. A survey of several industrial sites was conducted:

Older industrial sites were commonly housed in square cross-section brick buildings typicallycramped together. The layout was seldom alike the tidy linear rows in the tests but the gapsbetween buildings were on average one building height. The newer sites appeared to beconstructed from generic building pods whose base width to height ratio can vary between 2 to4. These were typically constructed on brown-field sites where the uncluttered start had enableda regular building pattern, alike that of the tests. The layout on a site depends upon the floorspace required by the businesses housed in each building and also the type of vehicle accessrequired. Many small businesses in consecutive buildings all requiring articulated lorry accesswould result in the widest gaps between buildings (typically equal to the base width of thegeneric building pod). When a single business is housed and the vehicle access is from thenarrower end of the building then the land space between buildings is less wide than the articu-lated lorry access described above. The limiting cases correspond to a large business requiringlarger than normal floor space. In this case there is no gap and the building pods are attached toone another to form a building with a many to one base width to height ratio. The obstacleslayout used in the study are shown in Figure 3.1. The proposed configurations, therefore,approximate the older industrial sites and also help to investigate the question of how arelatively narrow gap between rows affects the energy reflection. This configuration thenapproximates the newer industrial layouts of pods with the lowest base width to height ratio.

7

Figure 3.1 Layouts of obstacle rows used in field-scale experiments

The generic obstacle layout is shown in Figure 3.2 and is characterised by the dimensions H, W,D, Xs and G.

Xs

DG

H

W

Figure 3.2 Generic geometry and definition of parameters

It was important to specify the test conditions so as to identify a significant sheltering effect inthe pressure range of relevance to the consequence model, i.e. 70 mbar to 600 mbar, and whichcould also be effectively accommodated on the HSL test site. Too large a charge could result inground shock with disturbance to the neighbouring public. Too small a charge could result in

8

asymmetry of the blast wave and significant dissipation of the blast front energy through itsinteraction with the ground surface. Thus simple criteria were applied to size the charge weightsand obstacles. Namely, that the wave length of the positive overpressure phase of the free airblast wave should be of a similar size to the height of the obstacles. Thus a range of HE chargeweights were estimated, based upon the available obstacles (namely 0.6 m × 0.6 m square cross-section concrete blocks) that resulted in the appropriate blast wavelength at the 140 mbar and70 mbar distances. The smallest physical height possible therefore was 0.6 m and multiples of0.6 m achieved by placing the blocks next to and above one another. As explained previouslythis linear arrangement also had the advantage of simplifying the grid geometry used in thenumerical calculations. The parameters used in the test programme are given in Table 3.1.

Table 3.1 Configuration parameters used in experimental programme

0.5820.61401010.31.0960.6720.67016.2214.60.7351.3311.27016.2214.60.7341.1711.21401010.31.0930.8910.67016.29110.3120.7810.61409.977.70.461

H/M1/3

(m/kg1/3)W/HH

(m)Ps

*

(mbar)Xs/M1/3

(m/kg1/3)Xs

(m)M

(kg)Test no.

3.2. Experimental method

The experiments were performed on the Blast Range facility of the Health and Safety Labora-tory (HSL) at Buxton, Derbyshire by Explosives Section staff. The Section has great experiencein measuring overpressures from a wide variety of explosive events[5,6].

The range, 11 m wide and 112 m long, had a rolled hardcore surface which provides a flat areaon which the concrete pendine block obstructions could be built, and which reduced the likeli-hood of spurious shockwave reflections from reflecting surfaces.

PE4, a plastic explosive with a TNT equivalence of approximately 1.3 [7], was used for all thetests. The explosive was formed into a hemisphere, placed on a mild steel plate (500x500x28mm), and detonated remotely using an L2A1 detonator inserted into the top of the explosive(Figure 3.3).

9

Figure 3.3 Arrangement of explosive system

The pendine blocks (600x600x1800 mm) were arranged into obstructions as shown inFigure 3.1. Each obstruction extending over the middle 9 m of the range width for all tests.

Blast waves were measured using up to ten Meclec FQ11C piezo-electric gauges (resonantfrequency 80 kHz) mounted in B12 baffles (Figure 3.4), positioned as shown in Figures 3.1 and3.5. The gauges were mounted on steel supports with bases that were resting on 30 mm thickexpanded foam sheets in order to reduce the effects of ground shockwaves which could interferewith shockwaves propagated through the air.

The explosives were positioned centrally with the obstructions on one side. This allowedcomparison of the interaction of the blast wave with the obstructions and with those on the ‘clearfield’ side while using the same explosive source. A test using only a detonator was alsoperformed to determine its contribution to the shockwave; this was found to be small.

10

Figure 3.4: Photograph of Meclec FQ11C transducer in B12 baffle

Figure 3.5 File allocations for gauges used during tests

Generally, the gauges were positioned along the central axis of the range at the half height of theobstructions. However, a gauge at each end of the measured range was also positioned at 1.5times the height of the obstructions along the central axis, and two other gauges, one at eachend, were positioned in an offset position 2.125 m from the central axis. In some instances 11transducers were required when only 10 were available. In such cases the offset transducer atthe furthest point from the explosion on the clear field side was removed to a more usefulposition. Since complex blast wave interactions were not expected on the clear field side of theexplosion, and 2 transducers would remain at that distance (on the central axis), it was

11

considered that this would not compromise the results. A photograph of a typical experimentalset-up (Test 1) is shown in Figure 3.6.

Figure 3.6 Photograph of typical experimental arrangement (Test 1)

Because the number of gauges varied depending on the test being performed, the allocated gaugenumbers were not the same in all cases. Figure 3.5 shows the relative positions of the gaugesand their allocated numbers (their file identification codes are also provided).

The gauge closest to the explosion (Gauge 5) was positioned perpendicular to the central axisand was used to trigger the data logging system. The distance of the gauge from the centre ofthe explosive charge varied between tests as shown in Table 1.

Table 3.2 Distance of trigger gauge from centre of explosion

2.005&61.003&41.251&2 + Detonator test

Distance (m)Test No

Electrical signals from the gauges were amplified using Kistler 5011 charge amplifiers (having a200kHz frequency range), and recorded on a Nicolet 500 series datalogger. 12 bit samples weretaken at a sampling rate of 500kHz. The mean sensitivity of each transducer was programmedinto its associated charge amplifier so that the voltage readings obtained from all the transducerswere directly comparable. All of the equipment was calibrated and quoted results are traceableto national standards where appropriate.

12

Each test was performed in triplicate (except the detonator-only test) and the data was processedusing FAMOS software, a package designed to manipulate waveforms to enable quantitativedata to be obtained.

Where possible the following parameters were obtained for each trace:� Shock wave rise time� Peak pressure� Impulse � Time of peak pressure� Positive phase duration� Negative phase duration� Peak negative pressure

The traces from the obstructed side of the explosion did not mirror the clear field traces due tocomplex wave interactions. This made it more difficult to obtain accurate measurements of theparameters listed above. Generally, where broad pressure pulses were observed with sharperpulses superimposed on the broader peak, the peak pressure and its time were assigned to thelargest sharp peak.

3.3. Experimental results

Examples of shock wave traces from the clear field and obstructed sides of the explosion areshown in Figures 3.7 and 3.8, respectively (1 mV = 0.33 mbar). The repeatability of the threefirings for each of the tests was found to be high. Mean values averaged over the three firings foreach of the parameters measured in the tests are summarised in Tables 3.3 to 3.9.

Aaa005a Aaa002a Aaa003a Aaa004aAaa001a

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0V

-5 0 5 10 15 20 25

ms

TEST 1. Firing 1. (17/3/00)Clear field side of explosion

320.7g PE4 initiated by L2A1 detonator

Triggered by arrival of blast wave atfirst transducer (1.25m from explosion)

Gauge 51.25m from charge (30cm high)Rise Time: 67microsecondsMax pressure: 2278mbarTime of max pressure: 0.060ms

Gauge 42.9m from charge (30cm high)Rise Time: 60microsecondsMax pressure: 672.2mbarTime of max pressure: 3.26ms




Figure 3.7 Typical traces from clear field side of explosion (Test 1)

13

Aaa005b Aaa002b Aaa003b Aaa004bAaa001b

-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700mV

0 5 10 15 20 25 30

ms

Gauge 62.9m from charge (30cm high)Max pressure: 218.5mbarTime of max pressure: 3.96ms


Gauge 107.7m from charge (30cm high, OffsetMax pressure: 50.82mbarTime of max pressure: 18.7ms



TEST 1. Firing 1. (17/3/00)Obstructed side of explosion

320.7g PE4 initiated by L2A1 detonator

Triggered by arrival of blast wave atfirst transducer (1.25m from explosion)

Figure 3.8 Typical traces from obstructed side of explosion (Test 1)

The blast traces for some of the gauges had perturbations in the baseline prior to the arrival ofthe air blast. These perturbations were not always observed on the clear field side and are oftenmore prominent in data from the obstructed side of the explosion, Figure 3.9 shows a typicalexample.

These perturbations are likely to be due to ground shockwaves passing through the ground at afaster speed than the air blast.

14

Aal003a Aal004b

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280mV

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280mV

0 10 20 30 40 50 60

ms

Gauge 3Clear field trace

Gauge 9Obstructed field trace

Figure 3.9 Comparison of blast traces from the clear and obstructed side of Test 4.(Gauges 14.6 m from the explosion)

3.4. Discussion

The data obtained indicates that complex interactions occur between the air shockwave and theobstructions. Gauges positioned at the half height of the pendine block obstructions tended torecord much lower pressure values than gauges which were positioned above them. The signalsfrom the obstructed side were also much smaller than those recorded on the clear field side ofthe tests. These results indicate that the obstacles create a significant sheltering effect.

The presence of signals before the arrival of the air blast indicates that shockwaves are beingtransmitted through the ground. This occurs at a faster rate than shockwave propagation in theair. The ground shock signals are small in comparison to the air shockwaves on the clear fieldside of the tests, particularly close to the explosion, but can become significant when the airblast is small i.e. when ‘sheltering’ of the gauge has occurred. Where comparable ground shockdata are available on the clear and obstructed side of a test, it appears that the baseline perturba-tions due to ground shock are decaying by the time that the air blast arrives at the gauge (Figure3.10). The clear field trace is typical of results likely to be produced by an air blast i.e. the shockfront gives the characteristic step rise in pressure followed by a sharply decaying back slope.These observations indicate that data on the interaction of the air blast with the obstructions isunlikely to have been compromised by the ground shock effect acting directly on the gauges.

15

Aal004a Aal001b

-160-140-120

-100-80-60-40-20

020406080

100120140160180

200220240260280300320340

mV

-160-140-120

-100-80-60-40-20

020406080

100120140160180

200220240260280300320340

mV

0 10 20 30 40 50 60 70 80

ms

Gauge 4Clear field trace

Gauge 6Obstructed field trace

Figure 3.10 Comparison of blast traces from clear and obstructed sides of Test 4. (Gauges11.0 m from explosion point)

Since direct ground shock effects do not appear to affect the data significantly in the region ofinterest (ie. after the arrival of the air blast), the more complex traces from the obstructed side ofthe tests are likely to be caused by the interaction of the air blast with the obstructions ie. reflec-tions between blocks and diffraction from the block edges. These interactions are likely to causesome retardation of the blast propagation which is seen as a later arrival time of the air blast onthe obstructed side compared to that on the clear field side.

There is a possibility that ground shock could transmit into the pendine blocks which couldpropagate the shock wave back into the air at their surfaces. The waves generated in this mannerare likely to occur in the area of interest but the magnitude of their contribution is not known.The large difference between the density of air and the concrete pendine blocks suggests thatenergy transfer between the two would be inefficient and would result in small shock waves.However, the air waves generated by this process will be produced over a large flat surfacewhich may have the effect of amplifying the wave amplitude over the distances involved in thetests. No experimental work has been done to quantify these effects.

16

Table 3.3 Results from Detonator test (n/m = not measurable)

3.783.680.51n/m0.078.45725n/mn/mn/mn/m85.900.4321361.900.860.67n/m84.801.91494n/mn/mn/mn/m94.80n/mn/m7n/mn/mn/mn/m90.101.35633n/mn/mn/mn/mn/mn/mn/m9n/mn/mn/mn/m102.700.63452n/mn/mn/mn/m103.500.26n/m8n/mn/mn/mn/m102.700.59481n/mn/mn/mn/mn/mn/mn/m10

Duration(ms)

Peakpressure

(kPa)

Duration(ms)

Impulse(kPa.s)

Time topeak

pressure(ms)

Peakpressure

(kPa)

Rise time(ms)

Negative phaseparameters

Positive phase parameters

Gauge

Table 3.4 Mean results from Test 1; Mean mass of PE4 = 320.2g

12.1523.100.960.070.05296.8057539.3912.655.170.054.0121.22142612.9312.322.000.053.2872.8059441.446.655.930.0312.249.973452714.429.012.440.038.0038.1867340.952.536.600.0217.975.08752913.004.403.160.0216.1215.7169229.042.426.380.0117.387.8569813.574.513.070.0215.9815.3163153.563.416.560.0218.705.1581610

Duration(ms)

Peakpressure

(kPa)

Duration(ms)

Impulse(kPa.s)

Time topeak

pressure(ms)

Peakpressure

(kPa)

Rise time(ms)



Gauge

17

Table 3.5 Mean results from Test 2 ; Mean mass of PE4 =182.5g

11.3717.930.970.060.03236.4836554.336.275.150.0213.538.51346769.434.842.200.028.5322.4762458.573.456.320.0118.764.853566710.244.512.510.0213.7415.44357325.471.325.740.0128.052.67575910.082.862.600.0125.557.3365240.671.325.710.0127.393.0465811.612.203.060.0125.607.0661132.701.545.660.0128.252.4159910

Duration(ms)

Peakpressure

(kPa)

Duration(ms)

Impulse(kPa.s)

Time topeak

pressure(ms)

Peakpressure

(kPa)

Rise time(ms)



Gauge

Table 3.6 Mean results from Test 3 ; Mean mass of PE4 = 757.0g

18.6328.381.270.160.03913.335513.6911.698.750.0416.969.792169.418.363.500.0412.0929.4060414.093.9810.250.0223.5410.6665911.626.754.370.0321.9317.8517312.913.0810.850.0226.353.693812.006.704.230.0321.8815.1467214.842.979.160.0228.983.783712.366.504.350.0322.4915.53631

Duration(ms)

Peakpressure

(kPa)

Duration(ms)

Impulse(kPa.s)

Time topeak

pressure(ms)

Peakpressure

(kPa)

Rise time(ms)



Gauge

18


10.8729.261.100.120.00713.907511.774.528.770.0229.704.24368.563.184.270.0225.7811.1161412.871.496.010.0136.245.1610499.273.914.030.0135.208.9814310.281.1211.250.0139.162.23388.202.813.270.0135.127.6169215.321.738.240.0139.832.43378.421.713.850.0135.247.47711

Duration(ms)

Peakpressure

(kPa)

Duration(ms)

Impulse(kPa.s)

Time topeak

pressure(ms)

Peakpressure

(kPa)

Rise time(ms)



Gauge


13.0523.031.590.070.05212.732159.554.856.170.0227.566.593469.133.634.180.0224.9210.1072412.092.355.890.0134.465.035999.823.854.030.0134.298.0135313.561.394.38<0.0110.520.40388.382.603.340.0134.317.6568212.252.276.280.0135.923.383712.291.973.490.0134.326.79661

Duration(ms)

Peakpressure

(kPa)

Duration(ms)

Impulse(kPa.s)

Time topeak

pressure(ms)

Peakpressure

(kPa)

Rise time(ms)



Gauge

19

Table 3.9 Mean results from Test 6 ; Mean mass of PE4 = 757.0g (n/m = not measurable)

12.7724.621.480.100.06250.3143511.4811.125.850.0415.5313.5760613.888.153.430.0411.0129.7271435.385.526.420.0222.169.8265912.686.013.960.0320.5616.85473n/m1.39n/mn/m50.741.0838

11.687.014.300.0320.5816.3469213.773.917.190.0224.034.743714.694.764.310.0321.1118.21741

Duration(ms)

Peakpressure

(kPa)

Duration(ms)

Impulse(kPa.s)

Time topeak

pressure(ms)

Peakpressure

(kPa)

Rise time(ms)



Gauge

3.5. Numerical method

The hydrocode in this study has been under continuous development at Manchester MetropolitanUniversity (MMU) since the early 1990’s and is based on modern high resolution, finite volume,time marching methods. The hydrocode was originally developed using total variation diminish-ing (TVD) schemes developed for aeronautical applications [8]. The code has been updated toutilise solution methods based on MUSCL reconstruction [9] and approximate Riemann solvers[10,11] which more accurately represent the physics of wave propagation. The fully threedimensional/axi-symmetric hydrocode uses a structured body fitted grid topology, with a subgrid scale modelling capability, models chemistry using reduced reaction kinetics mechanisms[12,13] and solves either the inviscid Euler equations or the compressible Favre averaged formof the Navier-Stokes equations [14,13]. The code has been used to study a number of industrialblast wave and explosion hazard problems including the impact of the detonation of an explo-sive charge on a French blast shelter [15,8], the effect of blast wave impact on a Tank farm [16]and blast diffraction in a twin side-by-side jet engine configuration [17]. In addition the code hasbeen used for contract and consultancy work for the Defence Evaluation and Research Agency(DERA) and British Aerospace, plc and has attracted funding from the Research Councils [18].The code currently reflects the state of the art in blast and shock wave capturing methods andhas been proven to be accurate and robust.

Because of the simplicity of the geometry in the present study a rectangular, uniformly spaced,Cartesian grid has been used throughout and in most cases axi-symmetry has been assumed tominimise the computational costs. Furthermore, the inviscid, non-reactive, Euler equations havebeen solved since viscous effects are expected to be negligible in the region of interest and sincehigh explosive charges are being used, gaseous detonation models are not required. The initialconditions for the blast wave have been obtained using the balloon analogue [19,20]. Thisapproach has been chosen since a complete blast calculation requires a reactive-flow computa-tion for the detonation process within the solid charge, an approach which is both computation-ally expensive and only warranted where detailed data is required in the near field region. In theballoon analogue, initial flow conditions for a statically pressurised gas are specified within a

20

balloon of arbitrary shape. The blast propagation is initiated by the rupture of the balloon,causing the pressurised gas to expand outwards forming a shock wave while a rarefaction travelsinwards giving a blast wave like decay in the pressure behind the initial shock, see Figure 3.11.Control of the shape of the balloon and the internal conditions allows adjustment of the initialconditions to match a wide range of actual blasts waves in the mid to far-field. Figure 3.12shows the typical blast wave profile generated by the balloon analogue. The blast wave and itsdecay are generated by the shock and rarefaction waves which form when the balloon ruptures,while the subsequent reshock is generated by the reflection of the rarefaction waves from thecentre of the balloon. The magnitude of the blast wave, the positive and negative phasedurations, and the magnitude of the reshock are all determined by appropriate choices ofparameters. The energy potential of a balloon filled with ideal gas is given by [20]

(3.1)E = (P−P0)V�−1

where E is the total blast energy of the charge (in J), P is the initial static pressure within theballoon (in Pa), Po is the ambient pressure (in Pa), V is the volume of the balloon (in m3), and γis the ratio of specific heats for the gas inside the balloon. The values of the free parameters P, Vand γ, at t=0, together with the density of the gas inside the balloon, ρ (in kgm−3) are selected togive the best representation of the real blast wave. It is important to note that although the shapeof the balloon should be similar to the shape of the explosive charge, there is no requirement forthe volume of the balloon, V, to be equal to the charge volume. To simplify parameter selectionin the present study, the balloon pressure (P) is set to the detonation pressure of TNT (21.0 GPa)and the ratio of specific heats γ is set to that for air, (1.4). The volume of the charge can then becalculated using equation (3.1), leaving either the density (ρ) or temperature (T) inside theballoon as the sole free parameter.

In order to select an appropriate density for the gas inside the balloon, a series of numericalsimulations starting with varying initial density has been compared with the overpressuremeasured on the unobstructed side of the experiments. Figure 3.13 shows the pressure tracesobtained at Gauge 4 (2.9 m from the charge) with ρ = 8, 11 and 16 kg m−3 respectively for acharge weight of 0.461 Kg (TNT equivalent). All three values of density give good agreementwith both the peak overpressure and the decay rate in the post shock expansion. The main effectof varying density is to alter the magnitude and arrival time of the reshock. Higher air density inthe balloon results in lower pressures in the negative phase and a stronger, more delayed,reshock. As a result of these comparisons, an initial balloon ρ = 11 kg m−3 has been adopted asthe optimised value for the following calculations. It is important to note that unless the modelincludes a detailed gas dynamic representation of the flow conditions and chemical compositionof detonation products within the balloon, accurate prediction of the arrival time and magnitudeof the reshock is impossible. The reshock is a small feature in comparison to the main blastwave and will have a small effect on the overpressure and impulse loading at the points ofinterest.

21

Initial Balloon

Rarefaction

Shock Wave

Figure 3.11 Balloon analogue: Waves generated after the initial rupturing of the balloon

P

Reshock

Initial Shock

tNegative PhasePositive PhaseDurationDuration

Figure 3.12 Balloon analogue: Typical blast wave profile generated by the balloon rupture

22

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Gauge 4, DX=DY=0.01

Experiment8.0

11.016.0

Figure 3.13 Balloon analogue: Effect of the initial density of the balloon gas, ρ=8, 11 and16 kg m−3

23

4. VALIDATION OF THE METHODOLOGY

4.1. The appropriateness of axi-symmetry

In order to be able to simulate the large number of cases required by the parametric study it isnecessary for the computation to be as efficient as possible. This efficiency would be easilyobtainable if 2D axi-symmetric calculations can be shown to give sufficient agreement for thecentreline pressure measurements. In order to ascertain whether the axi-symmetric assumption isappropriate a three dimensional calculation has been performed and comparisons made bothwith experimental measurements and a two dimensional axi-symmetric simulation of the samecase. The configuration used is that from Test 1 (see Figure 4.1).

In the 3D simulation, the symmetry along the centreline of the experiment has been exploited toreduce the required mesh size. The charge is placed on the symmetry (Z=0) plane. In the simula-tion each of the Pendine blocks is 4.25 m long and 0.6 m wide with a square cross-section. Theinter-block spacing is 1.2 m. Pressure monitoring points are placed 0.3 m above the floor at themid-points of the cavities (0.6 m from each wall) on the symmetry plane (Z=0.0 m) and off theaxis (Z=2.125 m). Comparisons between the centre line and off axis predictions and the experi-mental measurements have been made. The computational mesh (8 m long, 4 m high and 6 mwide) contained 3 million grid cells with equal mesh spacing, ∆X=∆Y=∆Z=0.04 m. Because ofthe computational cost associated with the 3D calculations, it has been necessary to obtaintemporary access to a high performance α-powered workstation. The simulation was run on a600 MHz DEC-α RISC processor with 512 Mbytes of memory and took 23 hours 30 minutes tocompute. In addition to gaining access to the α workstation additional staff effort was requiredto port and optimise the code for the α processor.

Pressure histories at six measuring points as shown in Figure 4.1 are given in Figure 4.2. TheseFigures show a great deal of similarity between the centreline (Z=0.0 m) and off axis (Z=2.125m) histories. The only difference is a slight time lag (around 1.2 ms), which results from thedifferences in distance from the centre of the charge and the monitoring point. The numericalpredictions for peak overpressure and positive phase impulse agree to approximately 2%.Gauges 8 and 9, in the experiment, are at the same locations as the last two monitoring pointsand a similar time lag can be observed. The agreement between the experimental measurementsand simulated pressure histories is encouraging. It is worth noting that the oscillations whichoccur prior to the arrival of the incident shock in Gauges 8 and 9 are due to the detection of theground wave, which is not present in the simulations.

A further comparison between the 3D results, already discussed, and a 2D axi-symmetric calcu-lation (on an equivalent mesh) has been performed in order to establish equivalence between thecentre line and axi-symmetric monitoring points. Table 4.1 shows the peak overpressure andimpulse from both the 2D and 3D calculations together with percentage errors. This shows thatthe errors are acceptable. Figure 4.3 compares the pressure histories at Gauges 6, 7 and 9 fromboth the 2D and 3D simulations. This Figure shows good agreement between the 2D and 3Dsimulations during the positive phase of the blast wave, while in the negative phase somediscrepancies start to become apparent. Since the main focus of this study is the effects of theinitial blast wave, these discrepancies are acceptable

24

Table 4.1: Comparison between 2-D and 3-D calculated results

0.1418.0645.90.13(7.1%)18.10(0.2%)42.0(8.4%)90.2712.6671.30.26(3.7%)12.76(0.7%)73.9(3.4%)70.41 5.41148.80.42(2.4%)5.41(0.0%)146.2(1.7%)6

mbar smsmbarmbar smsmbar

Imp.TPmaxPmaxImp.(Err%)TPmax(Err%)Pmax(Err%)Gauge No.3-D 2-D

0.6m

4.25m

0.6m monitoring points

charge

Pendine blocks

2.125m

y

x

z

Figure 4.1 3D Test: Geometrical Layout

25

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

3-D, test 1, gauge 6, 200x100x150

Z=0.000mZ=2.125m

Experiment

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

3-D, test 1, gauge 7, 200x100x150

Z=0.000mZ=2.125m

Experiment

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

3-D, test 1, Gauge 9 & 10, 200x100x150

Z=0.000mZ=2.125mGauge 9Gauge 10

Figure 4.2 3D Simulation: Comparison between centre line and off axis pressure histories

26

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Test 1, Gauge 6, DX=DY=0.04

2-D3-D

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)


2-D3-D

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)


2-D3-D

Figure 4.3 Comparison between 2-D and 3-D pressure histories

4.2. Mesh refinement study

In order to examine the grid convergence of the numerical scheme a systematic mesh refinementstudy has been conducted using four grids, with mesh spacings of ∆X=∆Y=0.04 m,∆X=∆Y=0.02 m, ∆X=∆Y=0.01 m and ∆X=∆Y=0.005 m. Each of the grids was used to simulatethe unobstructed side of test 1. Figure 4.4 shows the pressure history obtained on each grid at themonitoring point furthest from the point of detonation. These results show the expected steepen-ing and gain in amplitude of the incident blast wave with reducing mesh spacing. This conver-gence can be better demonstrated by using the grid convergence index (GCI). If we choose themaximum positive overpressure Ps as the required indicator of the grid convergence, then giventhe Ps values at the same gauge location on a fine grid (PS1) and a coarse grid (PS2), the GCI canbe obtained from,

(4.1)GCI21 = 3 �21

rp−1

27

where p is the formal order of accuracy of the numerical method (2 in the present case), r is themesh refinement factor

(4.2)r = �X2

�X1

and ε21 is a measure of the percentage relative error between the two solutions at the givenlocation, i.e.

(4.3)�21 = 100Ps1−Ps2

Ps1

Table 4.2 shows the GCI for the three gauge positions used in the Test 1. The GCI estimates anerror of about 5% in the peak overpressure between the finest two grids, thus indicating thatacceptable accuracy can be obtained on mesh ∆X=∆Y=0.01 m.

Table 4.2: Maximum overpressure values (in mbar) at three gauge points on four gridswith the Grid Convergence Index (GCI) at each location

0.005 0.010.020.04∆X, ∆Y (m)

5.67 10.11217.15656.70619.44556.80461.3145.65 8.4616.42276.73261.09239.00199.7435.27 8.8216.3167.67158.82144.82121.172

GCI21 GCI32GCI43Ps1Ps2Ps3Ps4Gauge No.

In order to generalise these findings it is useful to non-dimensionalise the mesh spacing withrespect to the nominal blast wave length, λ. This length scale is related to the TNT equivalentcharge weight, W through a 1/3rd power scaling, i.e.

λ = W1/3

Figure 4.5, shows the peak overpressure, Ps, at the three gauge locations plotted against thenondimensionalised grid spacing λ/∆x. This graph indicates that acceptable ( ≈ 5%) accuracywill be obtained for 100 < λ/∆x < 150.

Finally, it is important to note that increasing the spatial accuracy of the grid will also increasethe temporal accuracy of the integration scheme. This is a direct consequence of the Courant-Friedrichs-Lewy (CFL) stability condition which states that

(4.4)

+∆

+∆<∆

ijijijijijij cv

Y

cu

Xt

max,

maxmin

where ∆t is the time step, ∆X and ∆Y are the grid density, uij and vij are the velocity componentsin the x and y coordinate directions and cij is the local sound speed.

28

-100

-50

0

50

100

150

200

250

300

-4 -2 0 2 4 6 8 10

Overpressure(mbar)

Time(ms)

Grid Convergence, Test 1, Gauge 3

0.040.020.01.005

Figure 4.4 Mesh refinement: pressure history at Gauge 3 (Test 1) on meshes with spacing∆X=∆Y=0.005, ∆X=∆Y=0.01, ∆X=∆Y=0.02 and ∆X=∆Y=0.04

100

200

300

400

500

600

700

0 50 100 150 200 250

Overpressure(mbar)

lambda/DX

Grid Convergence Study

Gauge 2Gauge 3Gauge 4

Figure 4.5 Mesh refinement: Peak overpressure vs. nondimensionalised mesh spacing

4.3. 2D Axisymmetric CFD calculations

All the two dimensional calculations have been carried out on a SGI workstation and the calcu-lations require about 0.11 ms per time step per control volume. Thus, for a typical case using800×400 grid points and 2000 time steps, the computational time would be around 22 hours.During the calculation, the time history of the overpressure at selected gauge points are recorded

29

at each time step. The flow variables such as pressure P, density ρ, temperature T, and totalenergy E etc. for the full domain are also recorded at a regular interval and post-processingsoftware developed at MMU is used to draw the contour plots. This provides a clear image ofthe position and strength of the shock waves and a useful mechanism to analyse the underlyingphysical processes of the blast-obstacle interactions. In all the two dimensional calculations theflow is assumed to be axi-symmetric about the vertical axis and comparisons are made withexperimental measurements from the central plane of the experiment (Figure 4.6).

(transmissive)boundaryDownrange

y

r(x)

Upper boundary (transmissive)

Ground Surface

Pendine blocks

AxisSymmetry

Charge

Figure 4.6 Set-up of the numerical modelling

Table 4.3: Experimental test configurations

1.2 1.20.6210.31.09461.2 1.20.6214.60.72951.2 1.21.2214.60.72941.2 1.21.2210.31.09431.2 0.60.6311.00.30821.2 0.60.637.70.4611

G(m)

W(m)

H(m)

No. ofobstacles

Xs(m)

M(kg TNT)

Test No.

Detailed comparisons have been made between experiments and simulations for six test cases(Table 4.3 shows the main parameters of each test). In all the experiments pressure historieswere recorded at various locations on both the obstructed and unobstructed sides of the charge.Figures 4.7-4.12 show simulated and experimental pressure histories at various gauges. Tables4.4-4.9 compare the peak pressure and positive phase impulse recorded at the same gauges.These tables also show the time of arrival of the pressure wave and the percentage errorsbetween the simulated and experimental peak pressures and impulses. In examining these resultsit is useful to note that Gauges 2, 3, 4 and 5 are on the unobstructed side of the charge while

30

Gauges 6, 7, 8 and 9 are on the obstructed side. Difficulties with Gauge 8 during Tests 5 and 6prevents meaningful comparisons to be made at this station for these cases.

One trend that can be seen in all the comparisons is that the errors observed at Gauge 5 tend tobe quite high, this is a direct result of the proximity of Gauge 5 to the charge and the consequentstrength of the pressure pulse. Two problems arise - firstly, the blast wave at this location has avery small wavelength and is not well resolved by the grid. Increased mesh resolution wouldimprove this measurement but would dramatically increase the computational costs without anysignificant improvement of the results in the medium to far field. Secondly, the pressure trans-ducers used in the experiment have a finite response time and are unlikely to measure the peakoverpressure accurately in this case. Due to the short wavelength of the blast wave, missing thepeak by a fraction of a millisecond can result in a dramatic reduction in pressure.

In all the Figures the experimental and numerical pressure histories closely agree in terms ofunderlying trends. This is particularly clear in Tests 1 and 2 (Figures 4.10 and 4.11) whereGauges 6 and 7 show quite complex patterns of multiple spikes during the initial blast wave.These spikes are caused by the blast wave reverberating in the street canyons between thependine blocks. The reverberation effects can lead (see Gauge 7) to peak pressure beingobserved after the initial blast wave. The peak pressures in this case are predicted to around 10%by the numerical method (see Table 4.4 and 4.5).

In all the experiments, but particularly in the latter cases, the measurements from the pressuretransducers have been contaminated by ground shocks. This causes oscillations in the pressuretrace prior to the arrival of the blast wave. In these cases comparisons between the CFD predic-tions (which assumes a perfectly rigid ground) and the experiments must be treated with caution.However, there is a high level of agreement between the CFD and the experiment in many caseson both the clear field and obstructed sides of the explosion, for example see the Gauge 6 resultsin Figures 4.10 and 4.11. These results give strong support to the earlier argument that the effectof the ground shock has decayed before the arrival of the air blast. Furthermore, there is suffi-cient experimental data, where ground shocks do not interfere with the experimental data, thatare in good agreement with the CFD predictions to give confidence in the numerical simulations.Thus indicating that the 2D axi-symmetric simulations will provide a reasonable basis for thedevelopment of a sheltering methodology.

31

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Test 1, Gauge 2

SimulationExperiment

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Test 1, Gauge 3


-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Test 1, Gauge 4


-2

0

2

4

6

8

10

12

14

-0.005 0 0.005 0.01 0.015 0.02 0.025

Overpressure(V)

Time(s)

Test 1, Gauge 5


-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Tset 1, Gauge 6


-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Test1, Gauge7


-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Test 1, Gauge 9


Figure 4.7 Test 1: Computational and Experimental pressure histories.

32

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

Test 2, Gauge2


-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

Test 2, Gauge 3


-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

Test 2, Gauge 4


-1

0

1

2

3

4

5

6

7

8

9

-0.01-0.005 0 0.005 0.01 0.015 0.02 0.025

Overpressure(V)

Time(s)

Test 2, Gauge 5


-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

Test 2, Gauge 6


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

Test 2, Gauge 7


-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Overpressure(V)

Time(s)

Test 2, Gauge 9


Figure 4.8 Test 2: Computational and Experimental pressure histories

33

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.0160.018 0.02 0.0220.0240.0260.028 0.03

Overpressure(V)

Time(s)

Test 3, Gauge 2


-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.0160.018 0.02 0.0220.0240.0260.028 0.03

Overpressure(V)

Time(s)

Test 3, Gauge 3


-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.005 0.01 0.015 0.02 0.025 0.03

Overpressure(V)

Time(s)

Test 3, Gauge 4


-5

0

5

10

15

20

25

30

35

40

-0.01 0 0.01 0.02 0.03 0.04

Overpressure(V)

Time(s)

Test 3, Gauge 5


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.01 0.02 0.03 0.04 0.05

Overpressure(V)

Time(s)

Test 3, Gauge 6


-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.01 0.02 0.03 0.04 0.05

Overpressure(V)

Time(s)

Test 3, Gauge 8


-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.01 0.02 0.03 0.04 0.05

Overpressure(V)

Time(s)

Test 3, Gauge 9



34

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 4, Gauge 2


-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(S)

Test 4, Gauge 3


-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 4, Gauge 4


-5

0

5

10

15

20

25

-0.01 0 0.01 0.02 0.03 0.04

Overpressure(V)

Time(s)

Test 4, Gauge 5


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 4, Gauge 6


-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 4, Gauge 8


-0.05

0

0.05

0.1

0.15

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 4, Gauge 9



35

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 5, Gauge 2


-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 5, Gauge 3


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 5, Gauge 4


-1

0

1

2

3

4

5

6

7

8

-0.005 0 0.005 0.01 0.015 0.02

Overpressure(V)

Time(s)

Test 5, Gauge 5


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 5, Gauge 6


-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 5, Gauge 9



36

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 6, Gauge 2


-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 6, Gauge 3


-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 6, Gauge 4


-1

0

1

2

3

4

5

6

7

8

-0.01 0 0.01 0.02 0.03 0.04 0.05

Overpressure(V)

Time(s)

Test 6, Gauge 5


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 6, Gauge 6


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Overpressure(V)

Time(s)

Test 6, Gauge 9



37

Table 4.4: Comparison Between Computational Results and Experiments measurementsfor Test 1

11.82.214.2 17.9750.816.117.7549.793.06.429.4 12.2499.730.311.9593.372.111.345.9 4.01212.246.94.03188.1634.742.869.77 0.052968.094.040.064214.150.79.250.07 3.28728.050.433.22660.944.324.034.56 8.00381.833.077.73289.936.811.719.04 16.12157.120.3415.88138.72

Imp.(%)

Pmax

(%)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Gauge No.

ErrorExperimental Simulated


6.87.87.7 26.7326.78.2327.1428.8922.90.216.1 18.7648.512.417.9148.673.012.823.0 13.5385.422.310.9274.468.915.861.70 0.032364.867.210.082739.651.612.821.24 8.53224.721.589.11195.946.818.617.16 13.74154.415.9814.10125.6310.47.78.97 25.6070.69.9125.9765.12

Imp.(%)

Pmax

(%)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Gauge No.



43.228.7231.88 23.54106.6131.5122.4475.994.69.2193.05 26.3536.9184.0725.0240.389.78.6440.55 16.9697.9483.4116.13106.3628.224.91630.2 0.039133.32090.30.03211410.050.015.0400.95 12.09294.0400.7311.86249.2410.026.0284.13 21.93178.5255.4722.06132.031.712.1259.16 21.88151.4263.8021.68133.02

Imp.(%)

Pmax

(%)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Gauge No.


38


3.623.374.91 36.2451.677.6035.0939.6925.02.2139.04 39.1622.3104.3037.7522.8830.419.8183.37 29.7042.4239.0528.5450.861.56.81213.3 0.007139.01194.70.0696654.857.911.5173.80 25.78111.1187.5724.5098.344.826.5134.09 35.2089.8140.4634.9966.0318.312.0119.68 35.1276.1141.5434.7267.02

Imp.(%)

Pmax

(%)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Gauge No.



28.227.8102.52 34.4650.3131.4133.8636.398.512.3220.55 27.5665.9239.2926.8557.8617.113.3713.35 0.052127.3835.550.0561844.754.42.3179.96 24.92101.0187.8123.4798.744.417.6135.41 34.2980.1141.3633.7766.0319.013.7119.02 34.3176.5141.6433.7266.02

Imp.(%)

Pmax

(%)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Gauge No.



29.826.1183.37 22.1698.2237.9821.3172.6926.40.7393.80 15.53135.7497.7015.24136.669.64.2957.22 0.062503.11059.60.1262607.050.515.9403.92 11.01297.2402.0710.10249.846.321.7281.82 20.56168.5263.9521.04132.031.119.2262.24 20.58163.4265.0120.95132.02

Imp.(%)

Pmax

(%)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Imp.(Pa s)

TPmax

(ms)Pmax

(mbar)Gauge No.


39

4.4. Parametric study CFD calculations

In order to provide data for the parametric study a series of CFD calculations were carried outgiving rise to peak pressures of 140 mbar and 70 mbar at the point of interest. For both peakpressures the number of obstacles upstream of the point of interest has been varied betweennone, one and two. In all cases an array of computational pressure transducers has been used togive measurements over a range of normalized distances (-2/M1/3....+2/M1/3) around the point ofinterest. The array extends vertically from ground level up to 1 or 2 building heights(0 < Y < 2H) depending on the case. For each of these locations the peak positive and negativeover pressures, the positive and negative impulses and the positive and negative phase durationshave been computed. The resulting parametric data was post processed and presented in theform of a series of spreadsheets.

40

5. SHELTERING MODEL

5.1. Extended TNT Methodology

The approach toward developing a revised model must necessarily be compatible with the exist-ing TNT and TNO models. This warrants representing geometrical features in terms of normal-ized dimensions, such as the building height, the distance from the obstacles to the 140 mbar or70 mbar point and, for more than one row of obstacles, the gap distance between the obstacles.Thus dimensions have been normalized against the cube root of the ground reflected TNTcharge mass. This is merely a convention which could be readily converted to other forms ofnormalization such as the combustion energy scaled distance used in the TNO Multi-Energymethodology. These normalized distances are interrelated via appropriate constant multiplyingfactors.

It becomes possible, therefore, to determine the inward displacements of the normalized zoneboundaries from the sheltering parameter, here defined as the ratio of the sheltered and free airincident peak positive overpressure (Ps/Ps

*). The more effective the sheltering, the smaller Ps andthe closer the zone boundary can be moved toward the explosion source. The relationshipsbetween the shifts in the 140 mbar and 70 mbar boundaries and the sheltering parameter aregiven approximately in Figure 5.1. These are calculated by assuming that the overpressure at theshifted zone boundary, when multiplied by the sheltering factor, gives the nominal zone bound-ary peak overpressure (i.e. 140 mbar or 70 mbar). As previously explained the same degree ofsheltering gives rise to a larger inwards shift of the 70 mbar boundary compared to that of the140 mbar boundary.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 2 4 6 8 10 12 14 16 18 20

140 mbar

70 mbar

Sh

elte

rin

g f

acto

r (P

s/P

s*)

Normalized distance (Xs/M1/3)

Figure 5.1 Zone boundary shifts corresponding to sheltering factors

41

5.2. Two-dimensional CFD parameter variation study

The scope of the two-dimensional parameter variation study is shown in Table 5.1. Two genericbuilding geometries have been considered, namely one or two building-rows of square cross-section buildings. In the case of two building-rows they have been assumed to be one building-height apart. This corresponds to an intermediate level of separation between buildings as foundin both housing and industrial estates (see Section 3.1). Two placements for the site have beenconsidered namely distances of two building-heights (D = 2H) and four building heights(D = 4H) downwind of the nearest building row. This was done to establish to what extentsheltering was confined to the immediate down wind vicinity of the buildings. It was also neces-sary to investigate the effect of the ratio of building-height to the blast wavelength. This wasdone by varying the TNT mass-normalized building heights between 0.5 and 1.0. In the limitedscope offered by this study these values were chosen to correspond to representative buildingheights (10 m) for inventories similar to the Flixborough disaster. Calculations were done for alleight of these cases for the two boundaries of the Outer Zone, namely incident peak overpres-sures of 140 mbar and 70 mbar respectively, thus making sixteen simulations in all.

Table 5.1 Configuration parameters for the two-dimensional CFD calculations

421N/A1.00.517014021D/HG/HH/M1/3W/HPs

*Rows

The accuracy of the numerical calculations were maintained by selecting the same computa-tional cell dimensions, when normalized against the cube root of charge weight. In addition tomaintaining accuracy this had the additional benefit of enabling the pressure monitoringpositions to be placed at the same normalized distances relative to the nominal zone boundary.Pressure-time variation was, therefore, calculated in all cases on the same array of forty fivecells whose centres extended horizontally ±2 m/kg1/3 to either side of the zone boundary andfrom ground level to two building heights (0 < Y < 2H).

42

0.0

0.5

1.0

1.5

2.0

8 10 12 14 16 18 20

Free air Obstructed140 mbar 70 mbar

No

rmal

ized

po

siti

ve p

eak

ove

rpre

ssu

re (

Ps/P

s*)


Height range {0<Y<2H}

Figure 5.2(a) Maximum positive overpressure (0<Y<2H) for one building row

The case of 1-building row was considered first, of which there are four geometries in all,namely D = 2H, D = 4H, H/M1/3 = 0.5 and H/M1/3 = 1.0. The normalized peak positive phaseoverpressure in the height range 0 <Y < 2H are plotted in Figure 5.2(a) for the 140 mbar and 70mbar zone boundaries together with the corresponding free air predictions at ground level shownas a solid line. Clearly all but very few of the monitoring positions fall significantly below thefree air value indicating that sheltering is significant in the majority of cases. Similar compari-sons of the positive phase impulse in Figure 5.2(b), however, show it to be reduced by shelteringbut to a lesser extent than that for the peak overpressure. Figure 5.2(c) shows the positive phaseduration in all cases to be larger than the free air value. It is evident that the free air values areonly exceeded on the source side of the obstacles and therefore one might assume that they arisefrom amplified overpressures that propagate over the top of the obstacles.

43

0.000

0.001

0.002

0.003

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

has

e im

pu

lse

(I s/[

Ps*M

1/3 ])



Figure 5.2(b) Maximum positive phase impulse (0<Y<2H) for one building row

0.000

0.002

0.004

0.006

0.008

0.010

8 10 12 14 16 18 20

Free Air Obstructed140 mbar 70 mbar

No

rmal

ized

po

siti

ve p

has

e d

ura

tio

n (

T s/M

1/3 )



Figure 5.2(c) Maximum positive phase duration (0<Y<2H) for one building row

This hypothesis is confirmed in Figures 5.3(a-c) which show the peak positive phase overpres-sure, impulse and duration up-to one building height above the ground. In all the cases the peakpositive overpressure generates substantial sheltering at the zone boundary. Impulse andduration however still approximate the free air values. However fatality levels are convention-ally correlated against peak positive overpressure suggesting that it is the action of the shock andits amplification which is primarily responsible for fatality whether through its direct effect onpersonnel or indirectly through damage it causes to property. Thus to maintain consistency withexisting fatality estimates the observed reduction in the magnitude of incident peak overpressure

44

has been associated with a reduction in the probability of fatality. It is important to note,however, that should positive phase impulse be used instead there would be a much reducedbeneficial effect of sheltering.

A repeat of the above analysis was also performed for the case of two building-rows (SeeFigures 5.4(a-c) and Figures 5.5(a-c). Again, the incident peak overpressure is substantiallyreduced and the magnitude of sheltering found to be greater than for the case of 1 building-row.Corresponding observations were made for positive phase impulse and duration.

0.0

0.5

1.0

1.5

2.0

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

eak

ove

rpre

ssu

re (

P s/P

s*)



Figure 5.3(a) Maximum positive overpressure (0<Y<H) for one building row

0.000

0.001

0.002

0.003

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

has

e im

pu

lse

(Is/[

Ps*M

1/3 ])



Figure 5.3(b) Maximum positive phase impulse (0<Y<H) for one building row

45

0.000

0.002

0.004

0.006

0.008

0.010

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

has

e d

ura

tio

n (

T s/M

1/3 )



Figure 5.3(c) Maximum positive phase duration (0<Y<H) for one building row

0.0

0.5

1.0

1.5

2.0

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

eak

ove

rpre

ssu

re (

Ps/P

s*)



Figure 5.4(a) Maximum positive overpressure (0<Y<2H) for two building rows

46

0.000

0.001

0.002

0.003

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

has

e im

pu

lse

(I s/[

Ps*M

1/3 ])



Figure 5.4(b) Maximum positive phase impulse (0<Y<2H) for two building rows

0.000

0.002

0.004

0.006

0.008

0.010

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

has

e d

ura

tio

n (

T s/M

1/3 )



Figure 5.4(c) Maximum positive phase duration (0<Y<2H) for two building rows

47

0.0

0.5

1.0

1.5

2.0

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

eak

ove

rpre

ssu

re (

P s/P

s*)



Figure 5.5(a) Maximum positive overpressure (0<Y<H) for two building rows

0.000

0.001

0.002

0.003

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

has

e im

pu

lse

(I s/[

Ps*M

1/3 ])



Figure 5.5(b) Maximum positive phase impulse (0<Y<H) for two building rows

48

0.000

0.002

0.004

0.006

0.008

0.010

8 10 12 14 16 18 20


No

rmal

ized

po

siti

ve p

has

e d

ura

tio

n (

T s/M

1/3 )



Figure 5.5(c) Maximum positive phase duration (0<Y<H) for two building rows

The above observations indicate a way in which the results can be condensed into a simplesheltering principle. Namely, to maintain conservatism, the maximum values of the peakpositive phase overpressure for both 0 <Y < H and 0 <Y < 2H can be plotted at both zoneboundaries in relation to their corresponding free air values. Thus for one building row withnormalized building heights of H/M1/3 = 0.5 and 1.0 we obtain the results in Figures 5.6(a-b). Itcan be seen that the maximum peak positive phase overpressure between the ground and onebuilding height remains fairly constant and little changed whether the zone boundary is 2H or4H down wind of the building-row or which of the two zone boundaries is being considered. Inaddition the magnitude of sheltering increases slightly as the normalised building height isincreased. This latter observation is consistent with the building being larger relative to the wavelength of the positive overpressure phase of the wave.

Figures 5.6(a-b) also clearly show that it is the component of the blast wave which propagatesover the top of the building that approaches the free air value. This is consistent with the earlierinterpretation of the reflected blast wave energy being directed upwards above the building. Thelarger building is responsible for deflecting more blast wave energy which results in reducedblast wave sheltering in the upper region H < Y < 2H.

49

0.00

0.25

0.50

0.75

1.00

1.25

1.50

8 10 12 14 16 18 20

D=2H ; Max{0<Y<2H} D=2H ; Max{0<Y<1H}D=4H ; Max{0<Y<2H} D=4H ; Max{0<Y<1H}140 mbar 70 mbar

Normalized distance (Xs/M1/3)No

rmal

ized

pea

k p

osi

tive

ove

rpre

ssu

re (

P s/P

s*)

______ Free air

Figure 5.6(a) Sheltering factors for one building row with height (H/M1/3=0.5)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

8 10 12 14 16 18 20



rmal

ized

pea

k p

osi

tive

ove

rpre

ssu

re (

P s/P

s*)

______ Free air

Figure 5.6(b) Sheltering factors for one building row with height (H/M1/3=1.0)

50

The above observations also follow for two building-rows as shown in Figure 5.7(a-b) exceptthat the sheltering factors are significantly larger. The observations concerning the blast waveenergy diffracted above the building are also equally valid. The larger sized building is responsi-ble for diffracting more energy. Thus sheltering factors for the region H < Y < 2H are smallerthan for 0 < Y < H. Note also that the sheltering factors in this region are less at the outer zoneboundary

There are immediate conclusions from these observations. First of all global sheltering factorsfor the region 0 < Y < H can be assigned to both zone boundaries and that these can be shown tobe a simple functions of the normalized building height and the particular building geometry (inthis case either 1 building-row or 2 building-rows with a gap of one building height). Suchrepresentation is shown in Figure 5.8 highlighting areas of uncertainty remaining from thisanalysis.

Second the benefits of sheltering are far less if the proposed construction is substantially higherthan the average building height on its upwind side. This observation stands to sense because theupwind obstacles tend to deflect blast energy upwards and, therefore, toward the upper level ofthe proposed building.

0.00

0.25

0.50

0.75

1.00

1.25

1.50

8 10 12 14 16 18 20



rmal

ized

pea

k p

osi

tive

ove

rpre

ssu

re (

Ps/P

s*)

______ Free air

Figure 5.7(a) Sheltering factors for two building rows with height (H/M1/3=0.5)

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0.00

0.25

0.50

0.75

1.00

1.25

1.50

8 10 12 14 16 18 20



rmal

ized

pea

k p

osi

tive

ove

rpre

ssu

re (

Ps/P

s*)

______ Free air

Figure 5.7(b) Sheltering factors for two building rows with height (H/M1/3=1.0)

0.00

0.25

0.50

0.75

1.00

0 0.5 1 1.5

1 Building row 2 Building rows

Normalized building height (H/M1/3)No

rmal

ized

pea

k p

osi

tive

ove

rpre

ssu

re (

P s/P

s*)

??

?

MAX{0 <Y <1H ; ∆ Ps* < 140 mbar ; D < 4H)

Figure 5.8 Sheltering factors as a function of building height showing areas of uncertainty

.

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5.3. Applicability of revised methodology

In order to provide an assessment of the applicability of the new methodology two scenarioshave been considered in which buildings are assumed to have a nominal height of 10 m. Twoscenarios have been considered. The larger inventory scenario (A) concerns one on the scale ofthe Flixborough disaster, namely a TNT equivalent (in ground burst TNT mass equivalent) of16 Te (16,000 kg). Comparison with a smaller scenario (B) of 2 Te has also been considered. Inthe following calculation we shall determine the shift in meters of the Outer Zone boundaries forthe two cases of one and two building rows. The calculation values are provided in Table 5.2.

Table 5.2 Calculated values for scenarios used in methodology assessment

246817466919446120Land free-up (1000 m2)3562233948833149Boundary shift (m)14070140701407014070Zone boundary (mbar)

0.610.750.740.84Sheltering factor2121no. building rows

216TNT mass (Te)BAScenario

First we determine the TNT equivalent mass-normalised height (H/M1/3) of the building rowwhich yields H/M1/3 = 0.4 and 0.8 for scenarios A and B respectively. Referring to Figure 5.8 wecan now calculate the corresponding sheltering factors for the two scenarios for the 1 and 2building-row cases. These are found to range between 0.74-0.84 for scenario A and 0.61-0.75for scenario B. These four sheltering factors can then used in conjunction with Figure 5.1 todetermine the TNT mass normalized shifts for the 70 mbar and 140 mbar boundaries of theOuter Zone. The absolute boundary shift distances are given for the cases of 1 and 2 building-rows in Table 5.2. In Case A, which has a comparable scale to the Flixborough disaster, theabsolute shifts for the Outer Zone boundaries in the case of 2 building-rows are 48 m and 83 mrespectively. For the case of 1 building-row these reduce to 31 m and 49 m . The correspondingzone boundary shift for the smaller inventory scenario (Case B) are 35 m and 62 m for the caseof 2 building-rows and 23 m and 39 m for the case of one building-row.

Clearly the zone shift distances for the larger inventory scenario represent substantial free-up ofland. When the whole perimeter of the inner and outer boundaries of the Outer Zone are takeninto account these can be expressed as areas lying between the concentric circles given by theexisting and revised zone boundaries (see Table 5.2).

These calculations of land free-up are approximate conservative values based upon the smallestsheltering values for a site centred within four building heights of the last building-row. Clearlysubstantial improvement might be expected if there were more rows of buildings between theproposed site and explosion source.

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6. CONCLUSIONS

A review of TNT and TNO Multi-Energy explosion hazard methodologies has established thatthere is an opportunity to reduce the conservatism of current methods used by MSDU to adviseplanning authorities. This is because the models apply to the ideal blast wave regime in whichthe leading shock is most affected by interaction with structures.

Comparison between CFD calculations and measurements of overpressure in field-scale experi-ments has established that sufficient accuracy can be established in the prediction of blast waveparameters. The ability to predict the detailed pressure-time histories in three-dimensions hasalso been established when suitably powerful (workstation) computers can be dedicated to thestudy. Simplified geometries however allow 2-dimensional computational representations whichhave the benefit that individual calculations can be performed within a day using present dayworkstations. Thus, without prohibitive investment of staff-time or computing resources manycalculations can be performed to explore the effects of blast interaction with simplified buildinggeometries in the ranges of existing consultation distances.

The scope for field-scale experimental studies at HSL has been found limited by the size of thecharge weight necessary. Larger charges generate ground shocks which cause substantial lowfrequency corruption to the far field overpressure signals and can also propagate off-site to causeinterference to the general public. The high quality of agreement between experiment and CFDfor the uncorrupted measurements however has established that, provided due consideration istaken to the choice of grid cell sizes, then adequate accuracy can be determined from the CFDpredictions. The investigation of more general geometries however, will require the applicationof three-dimensional methods with a corresponding need for suitably high-performance worksta-tions and proportionally more staff time in servicing the calculations.

The parameter variation exercises offered by the computational study have enabled a simplemethodology to be proposed which takes account of sheltering caused by buildings on theupwind side of the proposed site. This methodology employs TNT mass scaling as is consistentwith existing TNT and TNO Multi-Energy methods. By calculating the mass normalized build-ing height for the given scenario a simple reference to graphs can establish the worst casesheltering factors for the building layouts of relevance. In this study the extended methodologyis limited to one and two continuous rows of buildings oriented at right angles to the linebetween the explosion source and the proposed site. Given the sheltering factors, and the build-ing geometry, the TNT inventory masses are then used to determine the shift in the inner (140mbar) and outer (70 mbar) boundaries of the Outer Hazard Zone. For a representative buildingheight of 10 m two typical scenarios were selected, the largest of which is on a scale with theFlixborough disaster. The sheltering has the effect of moving the inner and outer boundaries ofthe Outer Zone up to 50 m and 80 m respectively. These distances represent substantial free-upof land.

Buildings that provide a sheltering effect may collapse as a result of the blast overpressure.However, the time-scale for the building collapse is large compared to the time-scale of the blastwave and therefore the building collapse will not decrease the sheltering effect of the building.

It is important to note that intervening buildings that provide a sheltering effect may be demol-ished within the lifetime of the proposed new development. This in turn will change the

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consultation distance and will clearly have an effect on MSDU’s assessment of the LUP case.Therefore MSDU need to make a policy decision on whether the sheltering effect of buildingsshould impact on their methodology used for assessing LUP cases. However, in COMAH safetyreports, where a ‘snapshot’ of the blast hazard is required, such considerations do not need to betaken into account. Therefore these sheltering factors could be used and potentially lead tosignificant financial savings for major hazard site owners.

6.1. Recommendations

The new blast sheltering methodology proposed in this report needs further development beforeit can be used for realistic scenarios. The scope of the CFD simulation study should be widenedto cover more building sites and layouts primarily to establish whether the extended findingssupport the conclusions of this study, namely that a simple revision can be made to existingmethodologies to account for sheltering.

A further limited field-scale experimental programme should be considered for more generalthree-dimensional building layouts, provided the difficulties caused by ground-shock aremanaged to acceptable levels, to establish whether the CFD methods can yield satisfactoryagreement with experiment without the need for excessive computational or staff resources.Suggestions for study concern gaps between buildings, different heights of buildings on theupwind side, orientation of the building rows to the direction of the incident shock and buildingson the downwind side of the proposed site.

Following the successful conclusion of the above studies an extensive three-dimensional simula-tion study should be considered to provide the necessary blast data upon which to base a revisedmethodology.

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7. REFERENCES

[1]. W Baker, P Cox, P Westine, J Kulesz and R Strehlow Explosions Hazards andEvaluation, volume 5 of Fundamental Studies in Engineering, Elsevier, 1983

[2]. R J Harris, M J Wickens Understanding of Vapour Cloud Explosions – AnExperimental Study, Institute of Gas Engineers, 55th Autumn Meeting,Communication 1408, 1989; Advisory Committee on Major Hazards, 2nd report,Health and Safety Executive, 1979

[3]. J B M M Eggen, GAME: development of guidance for the application of themulti-energy method, TNO Prins Maurits Laboratory, 1995

[4]. N W Hurst, R D Fitzpatrick, G Clay Development of RISKAT for LPG Part I. WholeTank Failures, Calculation of Overpressure and Radiation, IR/L/HA/89/1, HSE

[5]. S A Formby and R K Wharton. ‘Blast characteristics and TNT equivalence values forsome commercial explosives detonated at ground level’, J Haz. Mats., Volume 50,p183 (1996).

[6]. S A Formby. ‘Quantification of the air blast characteristics of commercialexplosives’, I Chem E. 2nd Eur. Conf. Major Hazards Onshore and Offshore’, UMIST. p147, (1995).

[7]. S A Formby. ‘Assessment of the explosion hazard of low order detonating explosives- final report’. HSL Report IR/EX/96/01

[8]. DM Ingram. Numerical Prediction of Blast Wave Flows around Rigid Structures. PhDthesis, Department of Mathematics and Physics, Manchester Metropolitan University,November 1992.

[9]. B van Leer. On the relation between the upwind-differencing schemes of Godunov,Engquist-Osher and Roe. SIAM Journal on Scientific and Statistical Computing,5(1):1-20, 1984.

[10]. A Harten, PD Lax, and B van Leer. On upstream differencing and Godunov-typeschemes for hyperbolic conservation laws. SIAM Review, 25(1):35-61, 1983.

[11]. EF Toro, M Spruce, and W Speares. Restoration of the contact surface in the hllRiemann solver. Shock Waves, Vol 4, pages 25-34, 1994.

[12]. B Jiang, DM Ingram, DM Causon, and R Saunders. A global simulation method forobtaining reduced reaction mechanisms for use in reactive blast wave flows. ShockWaves, 5(1/2):81-87, 1995.

[13]. DM Ingram, B Jiang, and DM Causon. On the role of turbulence in detonationinduced by mach stem reflection. Shock Waves, 8(6):327-336, 1998.

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[14]. P Batten, DM Ingram, R Saunders, and DM Causon. An implicit viscous solver for thecompressible navier-stokes equations. Computers and Fluids, 25(4):421-341, 1996.

[15]. DM Ingram, N.S. Ellis, and DM Causon. Hydrodynamic code calculations of anairburst. In K. Takayama, editor, Shock Waves: Procceedings of the 18th InternationalSymposium on Shock Waves, Sendai, Japan, 1991, volume II, pages 905-910, Berlin,Germany, 1992. Springer-Verlag.

[16]. DM Ingram, P Batten, C Lambert, and DM Causon. Hydrodynamic code calculationsof a blast on a tank farm. In R. Brun and L.Z. Dumitrescu, editors, Shock Waves @Marseille: Proceedings of the 19th International Symposium on Shock Waves,Marseille, France 1993, volume IV, pages 419-424, Berlin, Germany, 1995.Springer-Verlag.

[17]. DM Causon and DM Ingram. Numerical simulation of unsteady flow in a twinside-by-side intake system. Aeronautical Journal, 101(1008):365-370, 1997.

[18]. DM Causon, R Saunders, DM Ingram, and P Batten. Numerical modelling of blastwave in the process industry. Final report - SERC grant GR/H18654, Centre forMathematical Modelling and Flow Analysis, Department of Mathematics and Physics,Manchester Metropolitan University, Manchester M1 5GD, December 1993.

[19]. W Baker, P Cox, P Westine, J Kulesz, and R Strehlow. Explosions Hazards andEvaluation, volume 5 of Fundamental Studies in Engineering. Elsevier, 1983.

[20]. DV Ritzel and K Matthews. An adjustable explosion-source model for CFD blastcalculations. In AFP Houwing and A Paull, editors, Proceedings of the 21stInternational Symposium on Shock Waves, page Paper 6590. Panther Publishing,Fyshwick Australia, 1998.

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