hac-model

Turbulent jet modelling for hazardous area classification

Renato Benintendi*

Megaris Ltd, 57 Send Barns Lane, Woking, Surrey GU23 7BS, United Kingdom

a r t i c l e i n f o

Article history:Received 5 March 2009Received in revised form20 November 2009Accepted 20 November 2009

Keywords:ATEXHazardous areas classificationTurbulent jetGasdynamicsExplosionEN 60079-10

a b s t r a c t

Hazardous area classification, as per EN 60079-10, is based on the explosive gas volume of the clouds inwhich the average gas concentration is related to the Low Explosion Limit (LEL). The higher Reynoldsnumber, the less this approach is valid, because of the development of a concentration gradient due tothe momentum driven flow. The resulting areas and volumes may be overestimated by two or threeorders of magnitude, which is often critical in equipment design and selection. This paper proposes andtechnically justifies an overview of turbulent jet flow modelling, with the aim at developing a morerealistic calculation method of the hazardous areas, within the ATEX approach.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Hazardous Area Classification is a primary concern of processsafety and design. Within ATEX approach, the sizing of gaseousexplosive clouds is generally carried out in accordance with EN60079-10 (2002). This is based on the hypothetical volume Vz,which is the volume over which the mean concentration of flam-mable gas or vapour is either 0.25 or 0.5 times the Low ExplosionLimit (LEL). The result generally overestimates the real size ofvolumes, that is often an unacceptable outcome. This has beenunderlined and proven also by Gant and Ivings (2005), througha CFD modelling of gas jets. The present work aims at developing,relatively to turbulent jets, a simple and rigorous hazardous areacalculation method, which gives more realistic results, than the socalled Vz volume approach.

2. Vz volume approach: estimation of explosive clouds

Section B.4.2 of EN 60079-10 presents the following formula forestimating the hypothetical volume Vz of explosive gas atmospheredue to an emission:

VZ ¼ f $��

dVdt

�min

.C�

(1)

and:

�dVdt

�min

¼�dGdt

�max

$

�T

k$LEL$293

�(2)

where (dV/dt) min is the minimum volumetric flow rate of fresh air(m3/s), (dG/dt) max the maximum release rate at source (kg/s), LEL isthe lower explosive limit (kg/m3), k is a safety factor, T is theambient temperature (K), C the number of fresh air changes perunit time (s�1).

The estimated volume has an average concentration related tothe LEL. A similar procedure is recommended by the Italian code CEI31-35 (2007) also for calculating the so called hazardous distancedz, that is the distance from the emission source at which the gasconcentration is lower than the LEL. This method refers again to theLEL. No importance is given to the gas concentration and velocitydistribution in the cloud, which is, at the contrary, well charac-terised and strongly marked, particularly for the high Reynoldsnumber flow jets, such as pressure relief valve discharges orreleases from high pressure pipelines. The related influence on theresulting cloud size is so expectedly high.

3. Turbulent jets

Jets may be generally regarded as turbulent or laminar alsodependently on their mixing efficiency as well as on the ambient airentrainment. This is very high when the Reynolds number, referredto the exit zone, equals or is higher than 104, which may beassumed as a lower border line in applying the theory of the fullydeveloped jet, according tomany research and practice suggestions(f.i. Yujiro Suzuki and Takehiro Koyaguchi, 2007, API RP 521, 2008).

* Tel.: þ44 (0) 1483225062; fax: þ44 (0) 1483559265.E-mail address: [email protected]

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Moreover, no further change in the jet behaviour is expectedincreasing Reynolds number beyond this value.

3.1. Gas conditions at the exit plane

To calculate the fluid properties downstream, further to a highpressure jet release, gas characteristics at the exit plane must beknown. Isentropic expansion hypothesis may be assumed and,accordingly, the gas characteristics obtained. Indicating withsubscript v the calm gas state and with subscript e the exit sonicflow condition, it will be:

PePv

¼�

2gþ 1

� gg�1

(3)

TeTv

¼�

2gþ 1

�(4)

rerv

¼�

2gþ 1

� gg�1

(5)

ve ¼�

2$ggþ 1

$R$Tv

�1=2(6)

The mass flow through the exit is given by the expression:

me ¼ re$ve$p$D2

e4

(7)

3.2. Mach disc

A high velocity (momentum driven) gas jet from a stagnantvolume is choked at the exit. Immediately downstream, it expandsand velocity increases so that supersonic conditions occur. Jets witha high jet pressure ratio are classified as underexpanded. Theoriginated expansion waves meet the jet boundary and are reflec-ted as compression waves. The overall result is the well knownbarrel-shaped shock, which covers a jet zone substantially unaf-fected by any entrainment contribution from the surrounding calmgas, as remarked by Xu, Zhang, Wen, Dembele, and Karwatzki(2005). Jet gas recompression creates a normal shock, the Machdisc, downstream of which the flow becomes sonic.

The knowledge of the Mach disc distance from the exit plane isessential to identify the position of the first jet section whereentrainment begins, that is the door of a transition zone of the jet. Ifa combustible gas is emitted to calm air, then this is the first sectionwhere a gas-fuel mixing takes place. The mentioned distance maybe estimated according to the following empirical formula of Ash-kenas and Sherman (1966):

zM ¼ 0:67$D$�PvPa

�1=2(8)

where Pa is the atmospheric pressure and x is the distance alongthe jet axis.

The Mach disk section is also the place where the flow condi-tions become sonic again. Accordingly, indicating this section withthe subscript M, the equation of continuity including the same(sound) velocity:

p$D2e4$re$ve ¼ p$

D2M4

$rM$vM (9)

and the ideal gas law application, will give:

p$D2e4$Pe ¼ p$

D2M4

$PM (10)

where PM is not strictly the calm ambient pressure, but, accordingto Xu et al. (2005), it is generally a little bit higher. Downstream,a further transition zone exists, which drives the jet to the so calledsimilarity zone.

3.3. Transition zone

The existence of a transition zone has been broadly recognisedand studied. It has typically the following characteristics:

e the turbulent intensity is not completely developed, to a vari-able extent, also depending on the Reynolds number; numericalvortices, presumably due to the curved slip stream boundary,have been found to exist by Prudhomme and Haj-Hariri (1994);

e the velocity profile follows a decay law approximatelyproportional to x�0.5 according to Yue (1999);

e entrainment takes place, as stated by Boguslawski and Popiel(1979) and Hill (1972), with a lower coefficient with respect tothe fully developed jet;

e the transition zone terminates at a distance that depends onthe Reynolds number. For momentum driven high velocity jets,this distance from the exit plane may be assumed to be atx � 25O30 according to Bogey and Bailly (2006). It is inter-esting to note that this is also the distance at which a fullvorticity is supposed to begin.

3.4. Profile similarity zone

Beyond the transition zone, the jet forms a conical shape volumewith a virtual origin placed at a distance a from the opening (Fig. 1),which, for simplicity's sake, has been assumed equal to zero in thenext calculations. Reichardt (1942) supposed an axial similarvelocity profile following a Gauss error function, which has beenconfirmed by Shepelev (1961) and other authors.

Accordingly, the velocity profile in any section may be repre-sented by the following general equation:

vðr; xÞvð0; xÞ ¼ exp

�� A$

�rx

�2�(11)

in which v(r,x) is the velocity at the distance r from the axis andv(0,x) is the centreline maximum velocity, both at the point x.Shepelev (1961) proposed:


�� 12$� r0:082$x

�2�(12)

x

De

)x(r)x,0(v

)x,r(v)x(R

α

a=De gtc2/ α

noitisnarT wolfdepolevedylluFeroC

Fig. 1. Jet flow.

R. Benintendi / Journal of Loss Prevention in the Process Industries 23 (2010) 373e378374

Along the axis, within the third zone, the momentum conser-vation equation may be applied. So, being:

Me ¼ re$p$D2e4$v2e (13)

and

Mx ¼ 2$p$Z RðxÞ

0r$vðr; xÞ2$r$dr (14)

the jet momentum at the exit plane and at the distance x of theaxis respectively, it will result:

Me ¼ Mx (15)

where R(x) is the maximum radial width at the axis point x.Concerning the centreline velocity v(0,x), the following hyper-

bolic decay law may be assumed in the similarity zone, as:

vð0; xÞve

¼ B$De

xþ a(16)

The momentum conservation assumption has been stressedby several researchers. It is generally agreed that the fully devel-oped zone terminates to a fourth zone, where the jet momentumloss is expected due to dissipation. Nottage (1951) drew thebehaviour of the Mx/Me ratio vs x/De ratio, at constant values ofReynolds number. Specifically, the higher this is, the more thementioned ratio keeps equal to 1. In correspondence to differentReynolds number values, Mx/Me decreases linearly with the x/De

ratio approximately with the same slope.

3.4.1. The entrainmentAs mentioned, ambient fluid entrainment begins downstream

the Mach disk and fully develops in the similarity zone. The generalentrainment equation is the following:

dmðxÞdx

¼ Ce$me

De(17)

where me and m(x) are the initial and the overall entrained gasmass flow rates at x respectively.

By integration, it will give:

mðxÞme

¼ Ce$xDe

(18)

Equation (18) might be considered valid from the Mach diskdistance up to approximately x z 120De, even if the entrainmentcoefficient in the transition zone should be assumed equal to 1/3the coefficient valid for the similarity zone, as reported by Hill(1972). Here, it is broadly accepted that, until the fourth zone isreached, Ricou and Spalding (1961) entrainment coefficientapplies:

mðxÞme

¼ 0:32$xDe

(19)

Similarly, the API RP 521 (2008) standard recommends:

mðxÞme

¼ 0:264$xDe

(20)

In the present work, coefficients reported in eqs. (19) and (20)have been assumed as the upper and lower limit respectively of thepracticable range.

3.5. Approximation of Thring and Newby

The jet entrains air downstream the Mach disk, so that the gasdensity at the boundary approaches the air density ra not farfrom the nozzle exit. Thring and Newby (1953) introduced theconcept of equivalent nozzle, which has the same momentumand velocity as the operating nozzle, Me and ve, but the density ofthe entrained fluid, i.e air in the present paper. More recently,further alternative equivalent diameter (nozzle) theories havebeen developed, (f.i. Birch et al. (1987) and Schefer et al. (2007)).Application of the equivalence criterion will give:

Deq ¼ De$

ffiffiffiffiffirera

r(21)

being the subscript a referred to ambient air.The equivalence allows to consider constant the density in the

model development, provided that the equivalent nozzle isadopted.

4. The flammable gas cone

The characterisation of the fully developed jet zone and itsstability along the axis allow to identify the hypothetical volume Vz

of explosive gas atmosphere, differently from the EN 60079-10method. With reference to Fig. 2, this volume will be completelyknown, once the following will have been defined:

ethe cross sections corresponding to the UEL and LEL,respectively

ethe cross section diameter variation law along the axis

4.1. Concentration gradient along the axis

Independently of the transversal concentration profile, an(assumed) cross sectional isoconcentration may be easily deter-mined along the axis, so that any given molar fraction of flammablegas, progressively mixed with the ambient air, may be exactly

x ,LEL X LEL

x ,LEU X LEU

D LEL

D LEU

Fig. 2. Explosive volume.

R. Benintendi / Journal of Loss Prevention in the Process Industries 23 (2010) 373e378 375

localised. Indicating with Xf the mean molar fraction of the flam-mable gas and with MWf and MWa the molecular weight of the gasand of the air respectively, it will be:

Xf ¼ me=MWf

½mðxÞ �me�=MWa þme=MWf(22)

and, through the (18):

Xf ¼ 1=MWfhCe$ x

De� 1

i.MWa þ 1=MWf

(23)

Being the explosive cloud a truncated conical volume limiteddownward by the LEL section and upward by the UEL section, thesewill be identified writing:

XUEL ¼ 1=MWfhCe$xUELDe

� 1i.

MWa þ 1=MWf

(24)

XLEL ¼ 1=MWfhCe$xLELDe

� 1i.

MWa þ 1=MWf

(25)

where XUEL and XLEL are the molar fractions corresponding tothe UEL and LEL respectively, and xUEL and xLEL the relatedcoordinates.

Equations (24) and (25) may be solved for x, obtaining:

xUEL ¼

"�1

XUEL$MWf� 11=MWf

�$MWa þ 1

#$De

Ce(26)

xLEL ¼

"�1

XLEL$MWf� 11=MWf

�$MWa þ 1

#$De

Ce(27)

4.2. Diameter of the cone cross sections

To complete the full characterisation of the spatial distributionof the flammable gas concentration, the size of the mixture circulararea at any distance x must be calculated. To do that, the equationof the entrainment:

2$p$Z RðxÞ

0rðr; xÞ$vðr; xÞ$r$dr ¼ me$Ce$

xDeq

(28)

has been simplified assuming a constant value of the density,according to Thring and Newby (1953):

2$p$ra

Z RðxÞ

0vðr; xÞ$r$dr ¼ me$Ce$

xDeq

(29)

Again:

p$ra

Z RðxÞ

0vðr; xÞdr2 ¼ me$Ce$

xDeq

(30)

Expressing v(r,x) according to Shepelev:


�� 12$� r0:082$x

�2�(31)

p$ra$vð0;xÞ$Z RðxÞ

0exp

��12$� r0:082$x

�2�dr2 ¼me$Ce$

xDeq

(32)

Integrating:

Rx ¼ffiffiffi2

p$0:082$x

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ln

"1� me$Ce

2$p$ra$vð0;xÞ$Deq$x$0:0822

#vuut (33)

Concerning centreline (maximum) velocity, the constant B ineq. (16) has been plotted slightly bigger than 6 by Pope (2000),equals 6.06 according to Panchapakesan and Lumley (1993), and5.8 according to Hussein et al. (1994). A value ¼ 6 has beenselected.

vð0; xÞ ¼ 6$Deq$ve

x(34)

Substituting in eq. (33):

Rx ¼ffiffiffi2

p$0:082$x

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ln

1� Ce

8$6$ð0:082Þ2

!vuut (35)

and, relatively to the angle of spread:

a ¼ tg�1

" ffiffiffi2

p$0:082

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ln

1� Ce

8$6$ð0:082Þ2

!vuut375 (36)

Rx calculated through eq. (35) will correspond to an angleof 14.2�, according to Ricou and Spalding entrainment coefficient,and 8.3�, according to API RP 521 coefficient. Conservatively, anangle of 15� shall be assumed.

Introducing the value of xUEL and xLEL obtained from eq. (26) and(27) in the eq. (35), the diameters of the UEL and LEL sections willbe calculated. In doing that, it must be considered that, the lower isthe entrainment coefficient, the larger is the truncated conevolume. It is so recommended to use the Ricou and Spaldingentrainment coefficient for the spread angle and the API RP 521entrainment coefficient for the volume sizing.

5. Comparative results

In order to test the method, two different comparative estima-tions have been analysed, relatively to natural gas. Specifically, theyrefer respectively to:

eAn example proposed by the Italian Code CEI 31-35/A, whichcarries out the calculation of the volume Vz in accordance withthe EN 60079-10

eA CFD simulation carried out by the Gant and Ivings (2005),which quantifies the size of the cloud to which a meanconcentration of 50% LEL corresponds.

The summary of the input data and the results are given inTables 1 and 2 respectively. As expected, the volume Vzobtainedthrough the jet method is largely smaller than the one sizedaccording to the EN 60079-10. Differently, the agreement with CFD


simulation seems really good. In the application of the presentmethod, for simplicity's sake, the Thring and Newby approximationhas not been applied.

6. The method

The analysis carried out in the previous paragraph can be usedfor developing a more realistic method for sizing volumes resultingfrom turbulent jets, to be used in hazardous areas classification. Therelevant steps of the method have been represented in the blockdiagram (Fig. 3).

The adoption of both Ricou and Spalding and API RP 521coefficients of entrainment is effective, with the aim at fitting themost conservative pathway. The method is valid for turbulent jetswith Reynolds number higher than 104. In general, the LELsection is reached before the initial momentum is lost accordingto Nottingham, i.e. the so-called fourth zone begins. This isunderlined also by API RP 521, which reports that, with referencewith hydrocarbons, the LEL section is reached within a distancefrom the exit approximately equal to twelve times the nozzlediameter.

7. Concluding remarks

The necessity to develop an alternative method for estimatingthe volume Vz provided by EN 60079-10 has been originated by theevidence that it overpredicts the resulting explosive volumes, withrespect to verification performed with alternative techniques. Forhigh Reynolds numbers, the overestimation is expected to be larger,since the high entrainment coefficient makes the gas rapidlyapproach the LEL condition. The analysis of the existing data hasallowed to identify a relatively simple and reliable sizing method,essentially based on the entrainment equation. In using it, a lowerand upper limit of the applicable entrainment coefficient rangehave been assumed, in accordance with API RP 521 and Ricou andSpalding data, respectively.

The method could be adopted for hazardous area classificationwithin the ATEX frame, both with the aim at improving the reli-ability of the results and at avoiding the oversizing of the classifiedzones, which is often unacceptable.

References

API RP 521. (2008). Guide for pressure-relieving and depressuring systems. AmericanPetroleum Institute.

Ashkenas, H., & Sherman, F. S. (1966). Rarefied gas dynamics. In J. H. De Leeuw (Ed.),Proc. 4th int. symp. rarefied gas dynamics, vol. II (pp. 84e105). New York:Academic Press, 1966.

Birch, A. D., Hughes, D. J., & Swaffield, F. (1987). Velocity decay of high pressure jets.1563-521X. Combustion Science and Technology, 52(1), 161e171.

Bogey, C., & Bailly, C. (2006). Computation of the self-similarity region of a turbulentround jet using large-eddy simulation. Netherlands: Direct and Large-EddySimulation VI. Springer.

Boguslawski, L., & Popiel, Cz. O. (1979). Flow structure of the free round turbulentjet in the initial region. Journal of Fluid Mechanics, 90(3), 531e539, CambridgeUniversity Press.

CEI 31-35. (2007). Electrical apparatus for explosive atmospheres e Guide forclassification of hazardous areas. Comitato Elettrotecnico Italiano.

Gant, S. E., & Ivings, M. J. (2005). CFD modelling of low pressure jets for areaclassification. Health and Safety Laboratory.

Table 2Summary of Gant and Ivings CFD results.

e Lupton natural gas

Molecular weighta kg/kmol 18.7LELa % vol 4.3UEL % vol 17Specific heat ratioa e 1.265Mass flow rate kg/s 0.416Stagnation pressurea barg 5Exit pressureb barg 2.31Stagnation temperature K 283Exit temperatureb K 249.89Stagnation density kg/m3 6.93Safety coefficient for LEL e 0.5Vent diametera m 0.0105Exit densityb kg/m3 4.34Viscosity at exitb Pa s 9.26 � 10�6

Reynolds numberb e 4.16 � 105

Vz volume as per CFD m3 0.0275Vz volume as per jet method m3 0.0233Vz CFD vs Vz jet method e 1.18Diameter number to full LEL 134

a Values reported in the Gant and Ivings document.b Values calculated.

Pre-emission condition

Pv, ρv

Emission condition

Pe, ρe, ve, m e

Eq. 3, 5, 6, 7

Equivalent Nozzle Diameter

Dv, ρv

Eq. 21

MWa, MWf, XLEL, XUELEq. 26, 27

Isoconcentration sectionscoordinates

xLEL, xUEL

Isoconcentration sectionsradii

RLEL, R UEL,Spread angle = 15°

Vz

Fig. 3. Jet calculation procedure.

Table 1Summary of “CEI 31-35/A e GE-2.5.3 example” results.

e Natural gas

Molecular weighta kg/kmol 17.77LELa % vol 4.43UEL % vol 17Specific heat ratioa e 1.31Mass flow ratea kg/s 0.416Stagnation pressurea Pa 28.613 � 105

Exit pressureb Pa 15.6 � 105

Stagnation temperature K 293Exit temperatureb K 254Stagnation density kg/m3 21.136Safety coefficient for LELa e 0.6Vent diametera m 0.0105Exit densityb kg/m3 11.54Viscosity at exitb Pa s 9.7 � 10�6

Reynolds numberb e 5.47 � 106

Vz Volume as per CEI 31/35A m3 264Vz Volume as per jet method m3 0.0213Vz CEI vs Vz jet ratio e 12395Diameter number to full LEL 130.5

a Values reported in the Code.b Values calculated.

R. Benintendi / Journal of Loss Prevention in the Process Industries 23 (2010) 373e378 377

Hill, B. J. (1972). Measurement of local entrainment rate in the initial region ofaxisymmetric turbulent air jets. Journal of Fluid Mechanics, 51(4), 773e779,Cambridge University Press.

Hussein, J. H., Capp, S. P., & George, W. K. (1994). Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent Jet. Journalof Fluid Mechanics, 258, 31e75, Cambridge University Press.

EN 60079-10. (2002). Electrical apparatus for explosive gas atmospheres e part 10:classification of hazardous areas edition: 4.0. International ElectrotechnicalCommission.

Nottage, H. B. (1951). Report on ventilation jets in room air distribution. Cleveland,Ohio: Case Inst. of Technology.

Panchapakesan, N. R., & Lumley, J. L. (1993). Turbulence measurements inaxisymmetric jets of air and helium. I: Air jet. Journal of Fluid Mechanics, 246,197e223, Cambridge University Press.

Pope, S. B. (2000). Turbulent Flows. Cambridge University Press.Prudhomme, S. M., & Haj-Hariri, H. (1994). Investigation of supersonic under-

expanded jets using adaptive unstructured finite elements. Finite Elements inAnalysis and Design, 17, 21e40.

Reichardt, H. (1942). Gesetzmässigkeiten der freien Turbulenz, V.D.I. For-schungsheft 414 (2. Auflage 1051)

Ricou, F. P., & Spalding, D. B. (1961). Measurements of entrainment by axisym-metrical turbulent jets. Journal of Fluid Mechanics, 11(1), 21e32, CambridgeUniversity Press.

Schefer, Houf, Williams, Bourne, & Colton. (2007). Characterization of high-pres-sure, under-expanded hydrogen-jet flames. International Journal of HydrogenEnergy, 32(13), 2081e2093.

Shepelev, I. (1961). Air supply ventilation jets and air fountains. Proceedings of theAcademy of Construction and Architecture of the USSR, 4.

Thring, M.W. & Newby, M.P. (1953). Combustion length of enclosed turbulentjet flames. in: Proceedings of 4th International Symposium on Combustion,Pittsburgh, PA, 789e796

Xu B.P., Zhang J.P., Wen J.X., Dembele S. & Karwatzki J. (2005) Numerical study ofa highly underexpanded hydrogen jet, in: Proceedings of the InternationalConference on Safety 2005, Sept 8e10, 2005, Pisa, Italy.

Yue, Z. (1999). Air jet velocity decay in ventilation applications. InstallationsteknikBullettin, n. 48, ISSN 0248-141X.


Ventilation theory and dispersion modelling appliedto hazardous area classification

D.M. Webber, M.J. Ivings*, R.C. SantonHealth and Safety Laboratory, Harpur Hill, Buxton SK17 9JN, UK

a r t i c l e i n f o

Article history:Received 15 November 2010Received in revised form6 April 2011Accepted 8 April 2011

Keywords:Area classificationJetsFlammable gasIntegral modelVentilation

a b s t r a c t

Critical formulae given in the current Explosive Atmospheres Hazardous Area Classification Standard IEC60079-10-1 (2008) [BS EN 60079-10-1, 2009] to determine the expected gas cloud volume which is usedto determine area classification do not have any scientific justification. The standard does allow thealternative use of Computational Fluid Dynamics (CFD) methods, which serve to compound the concernwith these formulae: the predicted volume of the gas cloud from CFD models being several orders ofmagnitude smaller than that given by the formulae in question. To resolve such major discrepancies,replacement of the current formulae with a scientifically validated approach is proposed. Integral modelsof dispersion and ventilation have been used routinely for many years in the analysis of major hazards inthe chemical industry. This paper presents an adaptation of these models to determine the expectedvolume of a gas cloud arising from a release of gas from a pressurised source. A very simple integral jetmodel is presented for outdoor dispersion, extended to the case of indoor dispersion, from which thevolume of the gas cloud is derived. The single free parameter, an entrainment coefficient, is fixed bycomparison with data on a free jet, and then predictions of the model are compared with CFD calcula-tions (which themselves have been validated against experimental data) for dispersion within anenclosed volume. The results of this simple integral model are seen to agree very well with the CFDpredictions. The methodology presented here is therefore proposed as a scientifically validated approachto Hazardous Area Classification.

Crown Copyright � 2011 Published by Elsevier Ltd. All rights reserved.

1. Introduction

The control of sources of ignition by the use of specially pro-tected equipment in areas where flammable gases or vapours mayarise has been a fundamental safety measure for many years.Following the availability of specially protected electrical (flame-proof) equipment for use in mines in the early 20th century, it wassoon adapted for use in surface chemical industries. The classifi-cation of hazardous areas into “divisions” (later called “zones”) wasintroduced in the 1960s. It was recognised that the highest level ofprotection is requiredwhere the risk of a release is highest, and thatlower levels of protection could be used where the risk of release islower without prejudice to overall safety.

Thus hazardous areas are classified into zones based on theexpected frequency of occurrence and the expected duration of anexplosive gas atmosphere. The zones are currently defined in the

relevant International Standard IEC 60079-10-1, 2008 (published inthe UK as BS EN 60079-10-1, 2009) (hereinafter “the standard”) as:

Zone 0 e a place in which an explosive gas atmosphere ispresent continuously or for long periods or frequently. (Exam-ples e inside a closed vessel, near the liquid surface in an openvessel.)Zone 1 e a place in which an explosive atmosphere is likely tooccur in normal operation occasionally. (Examples e Samplepoints, relief valves, drainage points.)Zone 2 - a place inwhich an explosive atmosphere is not likely tooccur in normal operation but, if it does occur, will persist fora short time only. (Examples e near flanges, pipe fittings, valvestems, pump glands.)

The ATEX 137 Workplace Directive (1999/92/EC) has beenimplemented in the UK as DSEAR, the Dangerous Substances andExplosive Atmospheres Regulations (2002) and by similar regula-tions in other EU member states. These regulations requireHazardous Area Classification (HAC) to be carried out where theremay be a risk of explosion due to the presence of flammablesubstances in the form of gases, vapours, mist or dust. To ensure

* Corresponding author. Tel.: þ44 1298 218133; fax: þ44 1298 218840.E-mail address: [email protected] (M.J. Ivings).

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0950-4230/$ e see front matter Crown Copyright � 2011 Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.jlp.2011.04.002

Journal of Loss Prevention in the Process Industries 24 (2011) 612e621

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safe operation, any equipment (electrical or non-electrical) used ina classified hazardous area falls within the scope of the regulationsand must be suitable for use in the respective zone. Accurate andjustifiable area classification is therefore not just a technical safetyrequirement but also, in the EU, a legal requirement. Specifically, toensure safety and legal compliance, the methodology used for HACneeds to be both proven and reliable. Without this, the level ofsafety realised will be uncertain and the cost of providing thespecially protected equipment for use in the Hazardous Areasdetermined, to be unjustified, or potentially worse, insufficient.

This can only be avoided if there is a proper understanding ofthe physical processes leading to the hazard, in terms of bothexperiment and theory. If a scientific analysis can be done whichleads to a ‘best estimate’ of the hazard, then it can be examinedcarefully to reveal the circumstances under which it might be anunderestimate, and appropriate allowance made in order toproduce a conservative estimate. If there is no scientific basis, thenany safety factors introduced into an estimate (however that isdone) remain in the realm of conjecture and the overall level ofsafety realised must be uncertain.

The methods presented here focus on the science and makinga best estimate, but one particularly clear danger will becomeapparent: the hazard is very sensitively dependent on the hole sizeleading to a release, and an underestimate of that size will poten-tially lead to severe non-conservatism. We therefore emphasisethroughout that the results presented here, if they are used for areaclassification, must be interpreted with care if a conservative esti-mate is to be guaranteed.

The existing standard classifies hazardous areas on the basis ofthe size of an expected “hazardous volume” Vz of gas. If this volumeis less than 0.1 m3, it is suggested that, if ignited, the cloud wouldproduce such small overpressure and thermal effects that it may beregarded as insignificant. In this case the area classification isdesignated as of “Negligible Extent” (NE) and no further action isrequired. Therefore protected equipment and controls over sourcesof ignition are not required. Accepting that there is empiricalevidence for this classification (Ivings et al., 2008), this paper willfocus on methods for estimating Vz.

The hazardous volume Vz is defined as a volume within whichthe volume average concentration of the cloud is equal to a certainthreshold, depending on the Zone classification. For Zone 2conventionally the threshold is taken as 50% of the lower explosivelimit (LEL); for Zones 0 and 1 it is taken as 25% of LEL. This paperwill denote this threshold as the ‘critical threshold concentration’(Ccrit) and not explore further which of these values might bea better choice in what circumstances, but it should be borne inmind that these are the sort of figures of interest e typically molefractions of no more than a few percent.

Other aspects of IEC 60079-10-1 are more confused however.The parameter Vz is used in the standard to differentiate between‘high’, ‘medium’, and ‘low’ ventilation in an enclosed room. Thismisses the essential point that Vz may depend also on the source ofgas, and in many cases it may be more sensitively dependent on thesource than on the ventilation of the room. This misunderstandingis taken to its logical conclusion in the case of outdoor jet releases,which in reality can dilute essentially independently of the state ofthe atmosphere, but where Vz in the standard is determined by the‘ventilation’ of a fictitious cube with sides of 15 m by an imaginedair flow of 0.5 m/s. The introduction of these spurious dimensions,and neglect of genuine factors determining dispersion, producea completely arbitrary result for Vz.

As an alternative to the formulae it presents, the standardexpressly allows the use of Computational Fluid Dynamics (CFD) tocalculate an estimate of Vz. But it is now clear (Benintendi, 2010;Gant & Ivings, 2005; Ivings et al., 2008) from the use of CFD and

other methods that values of Vz can result which are up to 3 ordersof magnitude smaller than those arising from using the formulae inthe standard.

It is clearly inappropriate that a standard should give the optionof using two methodologies where the results between these showsuch wide and inconsistent discrepancy. New methodologies aretherefore required for those who do not have access to, or choosenot to use CFD for the estimation of Vz indoors and outdoors basedon sound scientific theory to address this concern.

In fact the methodology required is not entirely ‘new’. Integralmodels of dispersion and ventilation have already been developedfrom the 1970s onwards for the analysis of ‘major industrialhazards’ following the explosion involving cyclo-hexane at Flix-borough in 1974; the 1976 Seveso dioxin incident in Italy (leading tothe EU’s so-called ‘Seveso directive’); and the toxic cloud from theUnion Carbide plant in Bhopal (1984). These incidents and othershave spawned an immense amount of experimental and theoreticalresearch into the behaviour of gas clouds, which can be adaptedquite straightforwardly to provide simple formulae for the esti-mation of Vz. This is the purpose of the current work.

As noted above, the simple Vz concept is a useful and practicalone. It must be noted, though, that the standard stresses that Vz isonly to be used as an assessment of the ‘degree of ventilation’ andnot as having any relation to the location of the hazardous zone. Forexample the standard makes no reference to how the potentiallyexplosive mixture is distributed (although it has in fact sometimesbeen used with spurious geometric considerations). In the processof adapting fluid models to the estimation of Vz some indications ofthe distribution of the cloud will emerge, in some cases at least, butwe emphasise that these should be interpreted with care. And Vz

will be shown to be dependent not only on the ‘degree of ventila-tion’ but also, and often more significantly, on the source of gas.

The prime objective here is to provide a scientifically-basedestimation of Vz, specifically in the case of a hazard from pressur-ised vessels or pipe-work, which can be used in themanner definedby the standard, but with a much greater degree of confidence.

2. The current standard e a summary

For indoor situations, in a ‘room’ of volume V0, the currentstandard defines a volume Vk by

Vk ¼ qminq1

V0 (1)

where q1 is the ventilation volume flux (volume of air per unit timeflowing into and out of the room) and qmin is the value of q1 whichresults in a room-average concentration equal to the criticalthreshold concentration of interest (Ccrit). Vz is found by multiplyingthis volume by a factor f, ranging from 1 to 5 according to whetherventilation is considered ‘ideal’or ‘impeded’ to somedegree. Asnotedin the introduction, no justification at all is provided for this formula.

Out of doors the ‘room’ is considered to be a cube of 15 m side,‘ventilated’ by a breeze of 0.5 m/s entering and leaving by oppositefaces of the cube e thus prescribing q1 ¼ 112.5 m3/s. Curiously (inview of the immense amount of knowledge gained about thesubject in the last 40 years) the standard makes essentially nomention of the concept of ‘dispersion’.

3. Ventilation theory

Consider a room of volume V0 containing a source of hazardousgas released at a rate (volume per unit time) qs. Let the rate of airinflow from ventilation be q0 and the total outflow be q1, as shownin Fig. 1.

D.M. Webber et al. / Journal of Loss Prevention in the Process Industries 24 (2011) 612e621 613

Assuming that the concentration of gas at the outflow apertureis C1, a balance of fluxes yields:

Volume : q1 ¼ q0 þ qs (2)

Contaminant : V0dCbdt

¼ Csqs � C1q1 (3)

where Cs is the concentration at the source and Cb is the back-ground concentration.

The solution of these equations requires an assumption abouthowwell-mixed the air is within the room away from the jet. If thisis optimally efficient, then the background concentration will beessentially uniform, and wewill have C1 ¼ Cb. More generally let usassume

C1 ¼ 3Cb (4)

with a constant 3, which we shall denote the ‘efficiency of back-ground mixing’ as 3 ¼ 1 defines a well-mixed room volume. If theventilation flux enters and leaves in a part of the room distant fromthe gas source, thenwemay expect 3< 1: the room is ventilated butthe backgroundmixing is such that the air is not having the optimaleffect in diluting the jet.1

These equations are solved straightforwardly to give

CbðtÞ ¼ Ceh1� e�3nt

i(5)

where the equilibrium room-average concentration Ce (achievedasymptotically at large time) is

CehCbðt/NÞ ¼ Csqs3q1

¼ Csqs

3ðqs þ q0Þ(6)

and

n ¼ q1V0

(7)

is the air change rate (frequency) from ventilation. Note that theasymptotic room-average concentration depends on the source andventilation fluxes; the air change rate determines how rapidly it isachieved.

If we require the room-average concentration to remain lowerthan the critical threshold concentration Ccrit, then we mustdemand a minimum degree of ventilation:

q1 >

�CsCcrit

��qs3

�hq*min �

�CsCcrit

�qshqmin (8)

where the last inequality applies when 3 � 1. The final value qmin isthe minimum required ventilation flux (in the absence of anyknowledge of how well distributed the ventilation flow is withinthe room), and is exactly the minimum ventilation rate mentionedin the standard IEC 60079-10-1 (2008). It must be emphasised thatit is based entirely on the existence of solid walls, and onconstraints on room-average concentration. It has nothing to dowith the distribution of gas in the room, nor with any Vz whichmight be significantly smaller than the room volume, and abso-lutely nothing to do with outdoor dispersion.

Ventilation considerations alone tell us very little about thehazardous volume itself, but one further consideration linksventilation theory with the standard, which defines a volume

Vkhqminn

(9)

based on the minimum required ventilation flux and the airexchange frequency. The standard then asserts that the resultanthazardous volume Vz is equal to f$Vk without any form of deriva-tion. The factor f is defined to have a value between 1 and 5, and isdescribed as the “efficiency of ventilation” (presumably meaning“inefficiency” as the hazard increases with f) due to “impeded airflow”.

The physical significance of these volumes can be clarified usingthe following thought experiment employing Maxwell’s Demon2 totake all of the contaminant gas in the room and mix it with justenough air to give a uniform concentration Ccrit. This leaves theroom divided into two zones: one containing contaminant mixedwith air to a uniform concentration Ccrit, and the other containingpure air e see Fig. 2.

This must be done so that the room-average concentrationremains as Ce as predicted by ventilation theory (including thecirculation efficiency factor 3). It is readily found that the volume ofthe mixture in these circumstances is:

CeCcrit

V0 ¼ CsCcrit

qs3q1

V0 ¼ CsqsCcrit

V03q1

¼ qmin3n

¼ Vk3

(10)

If we associate the standard’s “ventilation inefficiency” f withthe inverse of our “efficiency of background mixing” 3, then this isjust the hazardous volume asserted by the standard! Interestingly,under the assumptions of this derivation, the volume Vk/3 providesan absolute upper bound on Vz: there is no rearrangement ofmolecules in the room which can make Vz bigger than this. On theother hand, we had to employ Maxwell’s Demon to create thiscloud; in reality we expect any dispersion mechanism to producea hazardous volume very much less than this value.

Fig. 1. Volumetric fluxes in a ventilated room.

1 The term ‘efficiency’ must be taken somewhat loosely as a jet close to, anddirected at, the outlet, may result in a value 3 > 1. This situation is not of primaryinterest, however, as it would be a fortuitous circumstance producing an optimisticestimate of any hazard.

2 Conceived as a thought experiment by James Clerk Maxwell and subsequentlynamed by Lord Kelvin, the demon is a magical being who can open or close a doorin a wall when a molecule approaches from one side or the other depending simplyon whether or not he wishes to let it through. The demon can therefore arrangethat molecules with a given property congregate in one part of the room and othermolecules congregate elsewhere, separating, for example, faster molecules fromslower (hot gas from cold), or in this case contaminant from air. The question ofhow the demon thus apparently manages to reduce the entropy of the gas whiledoing no work, has been recurring theme of interest ever since; we shall not reviewthe subject here but simply take it for granted that this being is mythical.

D.M. Webber et al. / Journal of Loss Prevention in the Process Industries 24 (2011) 612e621614

In fact if we consider how Vk was derived above, then one thingbecomes clear immediately: there has been absolutely no consid-eration of how the gas actually disperses within the room. Theabove discussion of the factor f in the standard highlights the factthat the standard combines both the rate at which air enters theroom (ventilation), the way that air may be distributed around theroom (background mixing), and the way the gas mixes with airwithin the room (dispersion) under the single description ‘venti-lation’3, and this underlies much of its confusion. In reality it isdispersion, and not just ventilation, which determines the extent ofa hazardous cloud, and so it is to dispersion theory that we nowturn.

4. Dispersion of jets and plumes

In most cases of interest the hazard is a gas in a pressurisedvessel or pipe-work, and so this will be the primary considerationof this paper. A small breach will result in a jet. Gas jets have beenstudied since the 1960s and in great detail since the 1980s. Theirbehaviour is well understood. Many computerised safety analysisprogram suites contain gas jet modules, but the standard requiresa simple analytic formula for Vz. To this effect we present the lowestcommon denominator of suchmodels, which we denote QUADJET.4

For comparison purposes a simple model of a passive plume(denoted QUADPLUME) is presented in the same framework.

The notation will be as follows:

z [L] downstream distance coordinateA(z) [L2] the cross-sectional area (as a function of down-

stream distance)r(z) [L] the jet/plume radius (as a function of downstream

distance)u(z) [Lt�1] the downstream flow velocity (as a function of

downstream distance)C(z) [ML�3] the concentration of flammable gas (as a function of

downstream distance)r(z) [ML�3] the plume/jet density (as a function of downstream

distance)

where the square brackets indicate dimensions. It is also ofinterest to consider a jet within a large indoor volume in which

there is a background concentration of hazardous gas. Thereforedefine also

Cb [ML�3] the background concentration of flammable gasrb [ML�3] the background density

The case of outdoor dispersion in pure ambient air is recoverablein the limit (Cb, rb) / (0, ra). For indoor jets a non-zero value of Cbwill be taken from the ventilation theory presented above, definingour model, QUADVENT, of jet dispersion in a ventilated room.

4.1. Subsonic jets and plumes

Consider initially subsonic jets and passive plumes. The simple1-dimensional steady-state flow equations are derived by consid-ering conservation of momentum, mass, and contaminant gas.

Momentum :Jet Plume

d�ru2A

�dz

¼ 0 u ¼ ua(11)

Mass :Jet Plume

dðruAÞdz

¼ ð2prÞrbuEdðruAÞdz

¼ ð2prÞrbuE(12)

Contaminant :Jet Plume

dðCuAÞdz

¼ ð2prÞuECbdðCuAÞ

dz¼ ð2prÞuECb

(13)

Where the cross-section A and radius r are related by

A ¼ pr2 (14)

Looking first at the mass equation e which is of the same formfor jet and plume: this describes a mass flux in direction z whichincreases downstream owing to entrainment of ambient air ofdensity rb with some entrainment velocity uE(z), through theperimeter of the plume. (Again it is worth remembering that noabsolute boundary need exist: these concepts are valid in thecontext of self-similar profiles.)

The contaminant equation describes the contaminant concen-tration (mass per unit volume) in the same way.

The momentum equation is a genuine conservation ofmomentum flux for the jet case (the jet is considered to be in calmair), but in the plume case simply a statement of advection witha wind travelling at constant speed ua.

Treating the hazardous gas and air as ideal gases at constanttemperature and pressure with molecular weights Mg and Ma, thedensity and concentration of the mixture satisfy

r� ra ¼ lC (15)

where l ¼ 1�(Ma/Mg).Finally the models are completed by a sub-model for entrain-

ment. Under the assumption of fully turbulent flow (high Reynoldsnumber) the entrainment velocity is restricted by dimensionalconsiderations. In the case of a jet, the turbulence velocity in the jetwhich powers entrainment is simply proportional to the jetvelocity u. In the case of a plume in the open, the turbulence level isproportional to the ambient air speed. Therefore the entrainmentvelocity should be proportional to u in both cases. The simplest sub-model defined by uE ¼ au was originally proposed by Morton,Taylor, and Turner (1956) for buoyant plumes and is usuallyreferred to under their names. But a priori a dependence on the

Fig. 2. A cloud of uniform concentration Ccrit and volume Vk.

3 This leads further to the bizarre situation in which outdoor dispersion isconsidered by the standard to be a form of ventilation.

4 The name QUADJET is intended as a reminder of the fact that the model is to beconsidered as the absolutely simplest one possible: a QUick And Dirty JET model.


dimensionless ratio r/rb cannot be ruled out, and another popularmodel is the model of Ricou and Spalding (1961)

uE ¼ a

ffiffiffiffiffir

rb

ru (16)

which we shall adopt here. At the level addressed here, the choiceof model is not expected to make an enormous difference, and thisone leads to significantly simpler analytic formulae. Note howeverthat the entrainment coefficient amust be determined empirically,and that there is no reason to expect it to be the same for plumesand jets as the turbulence structure in the two cases may be verydifferent. (In fact for plumes in the open, it may depend on atmo-spheric stability.)

Equations (11)e(16) define the jet and plume models, in a waywhich makes the physical assumptions clear. The solutions arestraightforward. Denoting conditions at the source with subscript‘s’, they are

For the jet:

Jet Velocity : u ¼ us½1þ bðz=rsÞ� (17)

Jet Concentration : C � Cb ¼ ðCs � CbÞ½1þ mðz=rsÞ� (18)

Jet Radius : r ¼ rsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½1þ bðz=rsÞ�½1þ mðz=rsÞ�

q(19)

with constants

bh2affiffiffiffiffirbrs

rmh2a

ffiffiffiffiffirsrb

r(20)

For the passive plume:

Plume Velocity : u ¼ ua (21)

PlumeConcentration: C�Cb ¼ðCs�CbÞ

1þrsrb

hð1þbðz=rsÞÞ2�1

i (22)

Plumer Radius : r ¼ rs

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ rs

rb

hð1þ bðz=rsÞÞ2�1

is(23)

with

bha

ffiffiffiffiffirbrs

rh

b

2(24)

Consider the point zH downstreamwhere the concentration hasdecreased to a value CH. The volume of the cloud upstream of thatpoint is

VH ¼ZzH0

dz$AðzÞ (25)

and the volume averaged concentration hCiH within this volume isgiven by

hCiH ¼ 1VH

ZzH0

dz$CðzÞAðzÞ (26)

The results of these two integrals give VH and hCiH as functionsof zH, and eliminating zH will therefore give VH as a function of hCiH .Setting hCiH ¼ Ccrit will yield VZ as defined in the standard.

Following this procedure yields a relationship which is verysimple in the limit where the critical threshold concentration issmall compared with the source concentration (CH/Cs<<1):

Jet Plume

VZz9pr3s16a

�rbrs

�3=2� Cs � CbCcrit � Cb

�3VZz

pr3sffiffiffi3

p

a

�Cs � CbCcrit � Cb

�3=2

(27)

For a jet out of doors there is zero background concentration andthe background density is that of pure air. In this case therefore:

Jet Plume

VZz9pr3s16a

�rars

�3=2� CsCcrit

�3

VZzpr3s

ffiffiffi3

p

a

�CsCcrit

�3=2 (28)

4.2. Properties of jets and plumes

Two properties of these equations merit immediate comment.Firstly, the hazardous volume is proportional to the cube of the

source radius, multiplied by a dimensionless function of the ratio ofsource and critical threshold concentrations. This follows simplyfrom dimensional analysis. This dependence on source size issensitive (for example underestimating a breach radius by a factorof 2 will underestimate the hazardous volume by a factor of 8), andtherefore the choice of credible breach size will be crucial to esti-mating a hazardous volume. A particular point of concern is that athigh overpressures (typically higher than around 10 barg) aninitially small puncture may propagate into a larger breach. In thiscase, rather than trying to estimate a realistic hole size, it may bebetter, given this sensitivity, simply to estimate Vz as being largeenough to pose a significant hazard.

Secondly, there is no dependence of Vz on the velocity of thereleased gas in the case of the jet, or the ambient air speed in thecase of a passive plume. This contrasts starkly with the currentstandard, where results (for subsonic jets) depend both on sourceradius and source velocity through the mass release rate. The originof the lack of dependence on velocity is very simple. The entrain-ment rate is determined by the turbulence velocity scale in the jetor plume. And that scale is proportional to the jet velocity or theambient air velocity respectively. So the faster the gas moves, thefaster it entrains, and if one is interested purely in spatial concepts(like hazard range or hazard volume) then the velocity just cancelsout of the problem. A consequence is that there is no dependenceon storage pressure. This last conclusion is, however, only expectedfor subsonic jets; the extension of this analysis to sonic jets will begiven below.

Thirdly, if the hazardous concentration of interest, Ccrit, is small,then the jet has a larger hazardous volume than the passive plumeegiven the same source radius. This is because the jet velocity dies offindefinitely downstream (under the assumption of no ambientflow) and so also, therefore, does entrainment.

It is also interesting to consider how an ambient flow wouldaffect a jet release. Near the source, where the jet velocity is muchhigher than the ambient velocity, the jet equations may be taken asa good approximation to reality. Further downstream, as the jetvelocity decays to the ambient velocity, then plume behaviour mayset in, and the result for Vz may be between that of the two modelsgiven above. Significantly in the jet, both concentration andvelocity decay inversely as downstream distance, and so if thesource velocity obeys

usua

>CsCcrit

(29)


then one may assume that the hazardous zone lies entirely in theregion where jet behaviour is dominant. In any event, the jetformula, will be expected to give a conservative result for any givensource radius.

Finally, it must be acknowledged that one assumption under-lies all of this analysis: that of turbulent flow. This is expected forall but the very slowest releases in a very poorly ventilated room,but if such conditions prevail, then care should be taken ininterpreting this work. The defining quantity is the Reynoldsnumber Re ¼ usrs/n or Re ¼ uars/n where n here is the kinematicviscosity of air (approx 10�5 m2/s). A 1 mbar overpressure isexpected to result in a release of order 10 m/s release, and froma 1 mm radius hole therefore Rew 1000. For this or larger or fasterreleases the assumption of turbulent flow is acceptable. Fora passive plume from a 1 mm hole on a 0.5 m/s ambient flow thenRe w 50 and turbulent flow is not expected (but this impliesa release rate of only 1.6 � 10�6 m3/s and so a hazardous volumemay take some time to build up).

4.3. Sonic and subsonic jets

The above analysis is for subsonic jets. A sonic jet results fromchoked flow in the aperture. This occurs when the pressurebehind the breach exceeds a certain threshold. Immediatelyoutside the breach there is a region where the pressure in the jetis higher than atmospheric and, because of this, it is generallyconsidered that no air is entrained in this zone. Atmosphericpressure is achieved a few hole diameters from the source, andthis point can be considered a pseudo-source for an isobaric jetwhich behaves as described above. In this case rs in the aboveformulae is not the actual hole radius but the radius of thepseudo-source, which may be somewhat larger, as illustratedschematically in Fig. 3.

The high pressure zone is relatively small but complicated: thedepressurisation is accompanied by Mach discs and barrel shocks,as shown, for example, by Ewan and Moodie (1986) in a shadow-graph picture. Because the zone is generally small compared withthe overall jet volume of interest, the main objective in studyingthis zone is to find the ratio of the pseudo-source radius to theactual hole radius, rs/r0. The dependence of the jet volume on thestorage pressure enters via this quantity. The other question ofprime interest is, of course, whether a sonic, or subsonic, jet isexpected in any given source scenario.

Both of these questions are addressed in an extensive review byBritter (1994) which gives the following guidance.

The important parameter is the ratio of storage pressure toambient pressure p/pa. For punctured vessels the consensus is thatunchoked flow resulting in a subsonic jet will occur if

ppa

� B (30)

with

Bh�

2gþ 1

��ð gg�1Þ

/g/1:4

1:89 (31)

Results are not expected to depend significantly on the ratio ofspecific heats, g, and we shall adopt the typical value of 1.4 inorder to provide specific numerical results. In this case chokedflow is expected in releases from overpressures of 0.89 bar orhigher.

For unchoked flow, resulting in subsonic jets, Britter (1994)reports that an isobaric jet model of the form presented abovemay be used with source radius rs given directly by the aperturesize.

rs ¼ r0 (32)

The source velocity is approximated by

us ¼ffiffiffiffiffiffiffiffiffiffiffigRTa

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2641�

�2

g� 1

�0B@Bg�1g �

�ppa

�g�1g

1CA375

vuuuut

hffiffiffiffiffiffiffiffiffiffiffigRTa

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�

2g� 1

�0B@�ppa

�g�1g �1

1CA

vuuuut ð33Þ

Inwhich R is the universal gas constant divided by themolecularweight of the gas, and we have replaced the expected temperaturein the orifice by ambient temperature Ta (as the likely errorinvolved in this is only of order 10%).

For choked flow resulting in sonic jets, Bitter shows that liter-ature yields a plethora of estimates of rs/r0 all arising througha desire to find a simplified understanding of the very complicatedshock zone. A variety of authors, including Birch, Brown, Dodson,and Swaffield (1984), Birch, Hughes, and Swaffield (1987),Britter’s (1994) own recommendation, Ewan and Moodie (1986),find that this ratio increases proportionally with

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiðp=paÞp

at largevalues of p. The underlying reason is simple enough. As thepressure drops from p to pa, then the density drops also, and if,broadly speaking, the temperature change is bounded, the densitydrops by a factor comparable with the pressure drop. If thevelocity in the region from the nozzle to the pseudo-source isconstrained by the speed of sound, then a conserved mass fluxmeans that the jet cross-sectional area must grow to balance thedensity drop, yielding rs=r0w

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiðp=paÞp

. The coefficient of pro-portionality, and the deviation from this asymptotic behaviour atsmaller values of p/pa, differ from model to model, none of whichare entirely compelling. In view of this, a pragmatic approach issimply to set

rsr0

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ K

�ppa

� B�s

(34)

with a phenomenological constant K and Britter’s (1994) reviewsuggests that K z 0.5 is a reasonable value. This formula behavesaccording to the general consensus at large p/pa and is consistentwith the unchoked flow result when p/pa ¼ B.

The flow velocity at the pseudo-source is taken to be the speedof sound:

us ¼ffiffiffiffiffiffiffiffiffiffiffigRTa

p(35)

again giving continuity when p/pa ¼ B.Fig. 3. Radial expansion of a jet in the depressurisation zone immediately outside therelease aperture.


In both choked and unchoked cases, the (pseudo-) sourcedensity and concentration are

Cs ¼ rs ¼ paRTa

(36)

5. The entrainment coefficient

The value of the entrainment coefficient, a, must be found withrecourse to experiment. This is most conveniently done bycomparing the velocity decay of subsonic air jets, and thus avoidingcomplications due to density factors and the optimum value of thepseudo-source radius. Birch et al. (1987) give very clear data forsuch jets showing the centreline velocity decay of the form

u=usz4:89� 2� rs=z (37)

for z more than a few nozzle diameters downstream, from whichwe extract b ¼ 0.10 and hence

az0:05 (38)

6. Summary of predictions of Vz

6.1. Outdoors

The hazardous volume for outdoor jet releases is predicted byEquation (28) in which rs is the aperture radius for unchokedreleases (see criterion (30)) and a pseudo-source radius (Equation(34)) for choked releases. For a pure source it is convenient todefine the vol/vol concentration (or mole fraction)

xcrit ¼ Ccrit=Cs (39)

so that for the jet release

VZ ¼ 9pr3s16a

�rars

�3=2� 1xcrit

�3

(40)

6.2. Indoors

The hazardous volume for indoor jet releases is predicted byEquation (27) with the same source radius considerations. In thiscase there is also a dependence on the room background concen-tration, which we can take from the considerations of ventilationtheory. Taking into account the bounding value of Vz as the roomvolume, V0, we can estimate

VZ¼ min

(9pr3s16a

�rbrs

�3=2� 1� xbxcrit � xb

�3

;V0

); xb < xcrit

¼ V0 ; xb � xcrit

(41)

where the background vol/vol concentration is defined by consid-erations of ventilation and background mixing:

xb ¼ qs3q1

(42)

For any given size of hole, this provides an interesting rela-tionship between the hazardous volume and the room backgroundconcentration. For low background concentration the dependenceis weak: the hazardous volume depends essentially entirely onthe properties of the jet. For higher background concentrations, thehazardous volume depends more strongly on this: in this case thehazardous volume depends both on the source and on the degree ofventilation, and may also be sensitive to the efficiency of back-ground mixing 3. This is discussed further below.

6.3. Walls and obstructions

The above model neglects to consider walls and other obstruc-tions. Some qualitative arguments about their effect can be madehowever.

Small obstructions, such as pipe-work, should not change theresult for Vz by a large factor. If a jet encounters a small obstacle,then it may be deflected and/or envelop the obstacle. Turbulencegenerated in the wake will entrain more air, broadening the jet andslowing it down. But the turbulent energy responsible comes ulti-mately from the jet, and whilst the shape of the hazardous volumemay be different, we expect only a small difference in the magni-tude of the hazardous volume. In general, slowing the jet, andincreasing its radius, will not have a large effect on Vz as long as theprocess responsible primarily involves entrainment of air.

The meaning of ‘small’ in the above paragraph should bequantified. It means small on the scale of the jet radius at the pointwhere the obstacle is encountered. As an example, consider thatIvings et al. (2008) have performed CFD calculations which foundthat a cubic obstacle with the same width as the source diameter,and placed just over 5 source diameters from the release point inthe path of a jet, increased Vz by a factor of 2. A spherical obstacle insimilar circumstances had less effect. But a factor of 2 in Vz isequivalent to increasing the hole radius (or the linear dimension ofthe hazardous zone) by only 25%. Quantifying the effect of theobstacle in terms of linear dimensions, therefore puts it intoperspective as a ‘small’ effect. In fact regarding the larger Vz

essentially as a 25% increase in linear dimension invites theconjecture that it is related to the fact that the linear size of theobstacle is about 30% of what the free jet diameter would have beenat the point in question.

More significant may be what happens when a jet encountersa larger obstacle or a wall5. For this case it is pertinent to invert thequestion and ask howan obstruction could increase Vz significantly.The dependence on rs

3 again gives useful insight here. Sonic jetsgive a Vzwhich increaseswith pressure because rs is larger at higherpressure: the effective source is larger, but is still pure gas. Anobstruction which could significantly increase the effective sourceradius, without diluting the jet, would also lead to a larger value ofVz. It is possible to imagine exotic ways inwhich this might happen.For example, suppose that the jet enters a container through a smallhole, is partly blocked by internal obstructions, and leaves througha much larger hole. If the container prevents any air from entering,then it acts as a damping reservoir of gas, admitting a fast narrowjet and letting out a wider slower one, thus increasing the value ofVz. Of course in practice one does not expect there to be such anobstacle in exactly the right place, but consider now a jet directedfrom very short range into a corner of the room. One can imaginethat a certain amount of almost pure gas can gather in the corneritself, and that the reflected jet (or jets) may be slower and broader,and lead to a larger Vz.

Viewed from this perspective (in terms of linear dimensions) theprocess does not have to be very dramatic to have a significant effect:a factor 5 in the effective radius, for example, would result in a factorof 125 in Vz. CFD provides an appropriate framework in which toimprove upon these qualitative arguments, as will be seen below.

First however, let us note that the release point would have to bevery close to the wall or corner (and directed at it) to producea significant effect. While the room background concentrationremains low, Equation (18) tells us that a jet centreline

5 A model of a wall jet would be useful in this case but is outside the scope of thecurrent work. For example, the larger Vz found by Ivings et al. (2008) for a jet veryclose to, and parallel to, a wall should be accessible to integral modelling.


Fig. 4. Some of the volumes studied (not to scale), denoted “Very small” (1 m3), “Small” (8 m3), “Medium” (44.7 m3), and “Large” (400 m3), showing obstacles, and the Vz predictedby CFD from some of the jets considered. In each case air enters through openings on the right and leaves on the left.

0.0001

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Fig. 5. Predictions from CFD (filled symbols) and the integral model QUADVENT (hollow symbols) for Vz plotted against the concentration at the ventilation outflow. Pointscorresponding with different jet releases and ventilation rates are included in each figure. Circles e very small enclosure, Diamonds e small, Squares e medium, Triangles e Large.


concentration of 1% (say) is achieved when z is about 500*rs. Forrs ¼ 1 mm, that would mean that the jet must be released withinabout 0.5 m of the wall for the wall to have a significant effect on Vz.

7. Comparison of the integral model with CFD results

The current standard explicitly allows the use of CFD modellingto estimate Vz, though it makes no mention of the kind of integralmodelling presented above. It is therefore appropriate to compareour results with those of CFD computations.

7.1. Unobstructed jets in a room

Ivings et al. (2008) have performed CFD computations in roomsof different sizes with air entering through one or two apertures inone wall, and leaving through one or two in the opposite wall. Insome cases there was an ‘obstacle’ within the room in the form ofeither a large rectangular parallelepiped, or a large cylinder, atassorted positions. Jet releases were studied varying the position ofthe source, the direction of the jet, and the release rate. They alsostudied a variety of these configurations experimentally. The goodagreement found lends confidence to the CFD results in the wholeset of scenarios studied.

As a validation exercise on the simple integral model QUADVENT,let us look at a subset of the scenarii where the jet did not imme-diately impinge on a wall. These are described as “very small”,“small”, “medium” and “large”, according to the roomsize, and in thelast two cases, the roomcontained a large obstacle, as shown in Fig. 4.

In each case the jet is fairly central in the room and ventilationinlets and outlets are on oppositewalls with the jet in between. Thereis no reason to assume poor circulation within the room and so wetake 3 ¼ 1. Graphs of predictions of Vz using QUADVENT and CFDagainst the concentrationat theoutlet are shown in Fig. 5 foranumberof different jet sources and ventilation rates as documented by Ivingset al. (2008). Especially in view of the fact that no parameters havebeen tuned, the agreement is excellent. It could be improved furtherwith only a slight increase in the QUADVENT’s entrainment coeffi-cient, but the agreement (and, as it turns out, very slight conservatism)using the predetermined entrainment coefficient more thanadequately demonstrates the validity of the integral model approach.

7.2. Jets with a greater degree of obstruction

Ivings et al. (2008) also consider, as their most severelyobstructed case, a release directed at a wall and within the smallspace, 50 cm wide, between the rectangular object and the wall.This results in a significantly larger value of Vz as would be expectedfrom the discussion presented with the summary of integral modelpredictions. It is interesting that this might be approachable inintegral model terms, based on the relative dimensions of the freejet and the space into which it is directed, but following thisconjecture is beyond the scope of the current work.

8. Conclusions and recommendations

We have presented a simple integral model of a gas jet in thecontext of Hazardous Area Classification (HAC) relevant tothe standard IEC 60079-10-1, 2008. The standard is centred on theestimation of a ‘hazardous volume’, the magnitude of which is usedto classify the degree of ventilation and hence in turn the HAC.However, the formulae for Vz given in the current standard are notscientifically based, and in general cannot be expected to produceresults that reflect reality. Furthermore Vz isn’t even a measure ofthe degree of ventilation as it depends both on the ventilation andon the source of gas.

On the other hand, gas jet models of the kind presented herehave been used routinely for the assessment of major hazards formany years and, despite their essential simplicity, their scientificcredibility is well established. It is therefore natural to apply themto hazardous area classification of pressurised flammable gases.

Whilst the basic integral models presented here cannot beconsidered innovative, two relatively new features do emerge. First,an analytic formula for the hazardous volume Vz defined by thestandard can be derived from the model. Secondly, a standard jetmodel can be extended to cover jet dispersion in a room in whichthere is a non-zero background concentration of flammable gas.This results in a hazardous volume which depends not only on thedegree of ventilation of the room but also on the source.

The jet model itself has one free parameter, the entrainmentcoefficient, which has been fixed by comparison with the data ofBirch et al. (1987). The extension to indoor jet dispersion has beentested here, by comparingwith the CFD results of Ivings et al. (2008),with the predetermined entrainment coefficient, plotting hazardousvolume against the concentration in the flow leaving the ventilatedroom. The agreement is striking. Given that Ivings et al. (2008) alsocompared the CFD approach with experimental results, this must beconsidered as strong support also for the integral model approach.

The analysis presented here also suggests that more may begained by going further down this path e specifically in regard toobstructed jets, aerosol jets, and buoyancy. The detailed CFD work ofIvings et al. (2008) shows that larger values of Vz can result if the jetemerges very close to an obstacle of some kind. We have discussedhow the linear dimension of a small obstacle compared with thediameter of (what would otherwise be) a free jet at that pointsuggests an increased linear cloud dimension (on which Vz dependsas the cube) and thismay be a useful topic for a further investigation.Ivings et al. (2008) achieved a significant increase in Vz by directingthe jet into a very confined space constrained not only by the threesurfaces meeting at the corner of the room, but also by a large solidstructure very nearby. The analysis presented here points to the ideathat it may, in future, be possible to allow for such awkward config-urations with relatively simple rules of thumb. To that aim we alsorecommend furtherwork onmodellingwall jets in aventilated room.

The focus of this work has been on pressurised gas releases, butmodels for two-phase jets (e.g. from LPG storage) are used routinelyin major hazards analysis, and these too should be adaptable toExplosive Atmospheres Hazardous Area Classification.

In the case of pressurised releases, the jet is usually moving sofast that buoyancy is not an important factor. However buoyantreleases (see e.g. Fanneløp &Webber, 2003; Morton et al., 1956) canbe considered in the same framework: there are cases where theturbulence generated from buoyant plume rise can dominate thebackground turbulence in the room, and the methods equivalent tothose developed here for jets can also be used to estimate Vz in thiscase.

Our suggested formulae for Vz are therefore not the last word,but do provide a valid approach where the hazard is defined by therelease of flammable gas from a pressurised source. Analyses nomore complicated than the one presented here for gas jets can bestraightforwardly applied to other hazards, and would result informulae applicable to a wider range of hazard scenarios.

This publication and the work it describes were funded by theHealth and Safety Executive (HSE). Its contents, including anyopinions and/or conclusions expressed, are those of the authorsalone and do not necessarily reflect HSE policy.

References

Benintendi, R. (2010). Turbulent jet modelling for hazardous area classification.Journal of Loss Prevention in the Process Industries, 23, 373e378.


Birch, A. D., Brown, D. R., Dodson, M. G., & Swaffield, F. (1984). The structure andconcentration decay of high pressure jets of natural gas. Combustion Science andTechnology, 36, 249e261.

Birch, A. D., Hughes, D. J., & Swaffield, F. (1987). Velocity decay of high pressure jets.Combustion Science and Technology, 52, 161e171.

Britter R. E. (1994). Dispersion of two-phase flashing releases e FLADIS fieldexperiment. Cambridge Environmental Research Consultants report FM89/2 tothe Commission of the European Communities DG XIII.

Bs EN 60079-10-1. (2009). Electrical apparatus for explosive gas atmospheres. Part 10.Classification of hazardous areas.

DSEAR. (2002). The dangerous substances and explosive atmospheres regulations2002. UK Statutory Instrument 2002 No. 2776.

EU. (1999). Directive 1999/92/EC of the European Parliament and of the Council of16 December 1999 on minimum requirements for improving the safety andhealth protection of workers potentially at risk from explosive atmospheres.

Ewan, B. C. R., & Moodie, K. (1986). Structure and velocity measurements inunderexpanded jets. Combustion Science and Technology, 45, 275e288.

Fanneløp, T. K., & Webber, D. M. (2003). On buoyant plumes rising from area sourcesin a calm environment. Journal of Fluid Mechanics, 497, 319e334.

Gant, S. E., & Ivings, M. J. (2005). CFD modelling of low pressure jets for area classi-fication. Report HSL/2005/11. Buxton: Health and Safety Laboratory.

IEC 60079-10-1. (2008). Electrical apparatus for explosive gas atmospheres. Part 10.Classification of hazardous areas.

Ivings, M. J., Clarke, S., Gant, S. E., Fletcher, B., Heather, A., Pocock, D. J., et al. (2008).Area classification for secondary releases from low pressure natural gas systems,HSE Research Report RR630. HSE Books.

Morton, B. R., Taylor, G. I., & Turner, J. S. (1956). Turbulent gravitational convection frommaintained and instantaneous sources.Proceedingsof the Royal Society A, 234,1e23.

Ricou, F. P., & Spalding, D. R. (1961). Measurements of entrainment by axisym-metrical turbulent jets. Journal of Fluid Mechanics, 8, 21e32.


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