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Journal of Loss Prevention in the Process Industries 23 (2010) 373e378

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Journal of Loss Prevention in the Process Industries

journal homepage: www.elsevier .com/locate/ j lp

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

* Tel.: þ44 (0) 1483225062; fax: þ44 (0) 14835592E-mail address: benintendi@libero.it

0950-4230/$ e see front matter � 2009 Elsevier Ltd.doi:10.1016/j.jlp.2009.11.004

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:

65.

All rights reserved.

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).

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

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

x

De

)x(r)x,0(v

)x,r(v)x(R

α

a=De gtc2/ α

noitisnarT wolfdepolevedylluFeroC

Fig. 1. Jet flow.

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:

vðr; xÞvð0; xÞ ¼ exp

�� 12$� r0:082$x

�2�(12)

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

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

R. Benintendi / Journal of Loss Prevention in the Process Industries 23 (2010) 373e378376

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:

vðr; xÞvð0; xÞ ¼ exp

�� 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

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°

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

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

Vz

Fig. 3. Jet calculation procedure.

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.

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.

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

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