THE EFFECTS OF OBSTACLE GEOMETRY ON JET MIXING IN RELEASES OF SILANE

Transcription

1 1 THE EFFECTS OF OBSTACLE GEOMETRY ON JET MIXING IN RELEASES OF SILANE A Thess by CHRISTINA F. SPOSATO Submtted to the Offce of Graduate Studes of Texas A&M Unversty n partal fulfllment of the requrements for the degree of MASTER OF SCIENCE December 2000 Major Subject: Chemcal Engneerng

2 2 THE EFFECTS OF OBSTACLE GEOMETRY ON JET MIXING IN RELEASES OF SILANE A Thess By CHRISTINA F. SPOSATO Submtted to Texas A&M Unversty n partal fulfllment of the requrements for the degree of MASTER OF SCIENCE Approved as to style and content by: M. Sam Mannan Davd M. Ford (Char of Commttee) (Member) Malcolm J. Andrews Rayford G. Anthony (Member) (Head of Department) December 2000 Major Subject: Chemcal Engneerng

3 3 ABSTRACT The Effects of Obstacle Geometry on Jet Mxng n Releases of Slane. (December 2000) Chrstna F. Sposato, B.S., Unversty of Nebraska Lncoln Char Advsory Commttee: Dr. M. Sam Mannan Releases of slane nto ar and the effects of obstacles were modeled wth the Computatonal Flud Dynamcs (CFD) code, FLUENT. Frst the CFD code smulated the release of a free turbulent jet of slane nto ar to assure that the code agreed wth establshed trends for turbulent jets. Then FLUENT was used to model the flow of slane when confned by a wall, or mpnged by an obstacle such as a flat plate or a cylnder. Computer smulated concentraton profles of a slane and ar mxture were analyzed to determne mxture volumes between the mxture explosve lmts. For each volume of an explosve mxture, the volume of slane was determned. The volume of the flammable mxture and the amount of slane wthn the flammable mxture were normalzed and determned as functons of obstacle radus and obstacle dstance. If the obstacle confnes the entre volume, the volumes decrease as obstacle dstance ncreases when the radal contrbuton domnates the volume. As the dstance of the obstacle ncreases then the axal contrbuton domnates the volume so the volume ncreases. The volumes ncrease, decrease, or reman constant dependng on the obstacle dameter.

4 4 Dedcated to My Husband And My Famly

5 5 ACKNOWLEDGEMENTS I would lke to acknowledge Dr. Francesco Tamann for all hs nspraton, gudance, expertse, recommendatons, and help on ths project. He played an nstrumental role for startng and workng on ths project. I would lke to acknowledge Dr. Sam Mannan for all the support and gudance throughout the year. He was always encouragng throughout the course of ths project. I would lke to acknowledge Dr. Wllam Rogers for hs recommendatons, support, gudance, and help workng on ths project. I would lke to acknowledge Dr. Malcolm Andrews for hs help wth CFD code, development of grds, and general expertse. I would lke to acknowledge Dr. Davd Ford for hs support and agreeng to serve on my commttee. Fnally, I would lke to thank my husband who made t possble for me to attend graduate school, supported my decson to go, and sacrfced a lot for me to be here.

6 6 TABLE OF CONTENTS Page ABSTRACT... DEDICATION... v ACKNOWLEDGEMENTS...v TABLE OF CONTENTS... v LIST OF FIGURES...v LIST OF TABLES...x NOMENCLATURE... x CHAPTER I INTRODUCTION II PREVIOUS RESEARCH AND LITERATURE REVIEW...4 Prevous Research on Releases of Slane Prevous Research on Free Turbulent Jets...6 Ths Research III FREE JET Problem Descrpton...11 Flud Propertes...12 Boundary Condtons Grd Mathematcal Bass...17 Results...26 IV NORMAL PLATE-IMPINGING JET Effect of Plate Dstance on Releases of Slane Problem Descrpton 32 Flow Propertes and Boundary Condtons. 33

7 7 CHAPTER Page Grd...34 Normalzaton and Non-Dmensonalzaton..36 Results...36 Effect of Plate Radus on Releases of Slane..45 Results...45 Effect of Plate Radus and Dstance on Releases of Slane.. 55 Normalzaton and Non-Dmensonalzaton..55 Results...55 V JET FLOW PAST A CYLINDER...62 Problem Descrpton...62 Grd...62 Normalzaton and Non-Dmensonalzaton...65 Results...65 VI CONCLUSIONS AND FUTURE WORK...79 Conclusons...79 Future Work...80 LITERATURE CITED...82 APPENDIX A DATA FROM FLUENT...84 APPENDIX B DERIVATION OF V jet AND V SH4,jet APPENDIX C GUIDE TO DEVELOPMENT OF GRIDS AND FLUENT VITA...114

8 8 LIST OF FIGURES FIGURE Page 1 Problem Descrpton for a Free Jet Full Grd for a Free Jet.16 3 Close up of the Grd for a Free Jet Profle of Explosve Volume for a Free Jet of Slane for the Realzable k-ε Model Velocty Vectors for a Free Jet of Slane.27 6a 6b Comparson of the Realzable and Standard k-ε Models usng IG Model wth Expermental Data and Data Ft for Turbulent Free Jet.29 Comparson of the Realzable k-ε Model and VW Model wth Expermental Data and Data Ft for a Turbulent Free Jet 29 7 Problem Descrpton for a Plate-Impngng Jet 34 8 Sample Grd for a Plate-Impngng Jet 35 9 Close up of Grd near the Jet Axs Velocty Vectors for a Sample Plate-Impngng Jet Explosve Volume for a Slane/Ar Mxture at L/D 0 = Explosve Volume for a Slane/Ar Mxture at L/D 0 = Explosve Volume for a Slane/Ar Mxture at L/D 0 = Explosve Volume for a Slane/Ar Mxture at L/D 0 = Explosve Volume for a Slane/Ar Mxture at L/D 0 =

9 9 FIGURE Page 16 Explosve Volume for a Slane/Ar Mxture at L/D 0 = Mnmum Plate Radus to Confne the Entre Explosve Volume as Plate Dstance Increases a 18b Effect of Plate Dstance on the Explosve Volume..44 Effect of Plate Dstance on the Volume of Slane Sample Grd for Flow past a Plate Close up of Grd Flow past a Plate a 21b Effect of Plate Radus on the Explosve Volume at L/D 0 = Effect of Plate Radus on the Volume of Slane at L/D 0 = Explosve Volume for L/D 0 = 150 and r plate = 400 mm Explosve Volume for L/D 0 = 150 and r plate = 200 mm Velocty Vectors for L/D 0 = 150 and r plate = 65 mm Explosve Volume for L/D 0 = 150 and r plate = 65 mm Velocty Vectors for L/D 0 = 150 and r plate = 60 mm Explosve Volume for L/D 0 = 150 and r plate = 60 mm Velocty Vectors for L/D 0 = 150 and r plate = 50 mm Explosve Volume for L/D 0 = 150 and r plate = 50 mm Explosve Volume for L/D 0 = 150 and r plate = 35 mm a Effect of Plate Radus and Plate Dstance on the Explosve Volume b Effect of Plate Radus and Plate Dstance on the Volume of Slane a 32b Varaton of Explosve Volume for 1.4 vol% and 4.0 vol%.59 Varaton of Volume of Slane for 1.4 vol% and 4.0 vol%..59

10 10 FIGURE Page 33a 33b Effect of Nozzle Dameter and Plate Radus on the Explosve Volume at L/D 0 = Effect of Nozzle Dameter and Plate Radus on the Volume of Slane at L/D 0 = Problem Descrpton for Flow past a Cylnder Zoomed n Porton of Three Dmensonal Grd near the Nozzle Sample Grd for Flow past a Cylnder a Effect of Cylnder Dameter and Dstance on the Explosve Volume for D 0 = 4.6 mm b Effect of Cylnder Dameter and Dstance on the Volume of Slane for D 0 = 4.6 mm a Sde, Explosve Volume for L/L LEL = 0.2, D cyl = 9 n, D 0 = 4.6 mm b Isometrc, Explosve Volume for L/L LEL = 0.2, D cyl = 9 n, D 0 = 4.6 mm.67 39a Sde, Explosve Volume for L/L LEL = 0.6, D cyl = 9 n, D 0 = 4.6 mm b Isometrc, Explosve Volume for L/L LEL = 0.6, D cyl = 9 n, D 0 = 4.6 mm.68 40a Sde, Explosve Volume for L/L LEL = 0.2, D cyl = 9 n, D 0 = 3.2 mm b Isometrc, Explosve Volume for L/L LEL = 0.2, D cyl = 9 n, D 0 = 3.2 mm.70 41a Sde, Explosve Volume for L/L LEL = 0.4, D cyl = 9 n, D 0 = 3.2 mm b Isometrc, Explosve Volume for L/L LEL = 0.4, D cyl = 9 n, D 0 = 3.2 mm.71 42a Sde, Explosve Volume for L/L LEL = 0.8, D cyl = 9 n, D 0 = 3.2 mm b Isometrc, Explosve Volume for L/L LEL = 0.8, D cyl = 9 n, D 0 = 3.2 mm.72

11 11 FIGURE Page 43a 43b Effect of Cylnder Dameter and Dstance on the Explosve Volume for D 0 = 3.2 mm Effect of Cylnder Dameter and Dstance on the Volume of Slane for D 0 = 3.2 mm a Sde, Explosve Volume for L/L LEL = 0.2, D cyl = 6 n, D 0 = 3.2 mm b Isometrc, Explosve Volume for L/L LEL = 0.2, D cyl = 6 n, D 0 = 3.2 mm.76 45a Sde, Explosve Volume for L/L LEL = 0.8, D cyl = 6 n, D 0 = 3.2 mm b 46a 46b Isometrc, Explosve Volume for L/L LEL = 0.8, D cyl = 6 n, D 0 = 3.2 mm.77 Comparson of Explosve Volume Confned by a Plate and by a Cylnder.78 Comparson of Volume of Slane Confned by a Plate and by a Cylnder.78

12 12 LIST OF TABLES TABLE Page 1 Lterature Measurements for the Effect of the Densty Rato on the Centerlne Concentraton for a Free Jet. 9 2 Physcal Propertes of Ar and Slane Physcal Propertes of the Mxture Inlet Boundary Condtons Turbulence Parameters for the Standard and Realzable k-ε Models. 22 6a 6b Comparson of FLUENT s Predcton for Explosve Volume and Volume of Slane wth Analytcal Integraton of Jet Data for 1.4 vol% Comparson of FLUENT s Predcton for Explosve Volume and Volume of Slane wth Analytcal Integraton of Jet Data for 4.0 vol% Comparson of FLUENT s Predcton wth BHW for Dstance wth a Concentraton of 1.4 vol% and 4.0 vol%. 33

13 13 NOMENCLATURE FLUENT S Nomenclature for Transport Equatons A 0, A s Functons of velocty gradents for realzable k-ε turbulence model C µ,, C 1, C 1ε, C 2ε, C 2 Constant for turbulence models (C µ not constant n realzable k-ε model) D,m, D t Mass dffusvty D H Hydraulc dameter I Turbulence ntensty J, Dffuson flux k Turbulent knetc energy l Turbulence length scale m Mass fracton M Molecular weght p Statc pressure P Pressure r Radal coordnate R Unversal Gas Constant R j Reynold s stresses Re Reynold s number, ρ 0 U 0 D 0 /µ 0 S Modulus of the mean rate of stran tensor for turbulence models S j Rate of stran tensor for turbulence models Sc t Turbulent Schmdt number, µ t /ρd t T Temperature u Axal velocty (cylndrcal coordnates) u Velocty (Cartesan coordnates) u Instantaneous velocty U * Functon of velocty gradents for realzable k-ε turbulence model v Radal velocty (cylndrcal coordnates) W Functon of rate of stran tensor x Axal coordnate (cylndrcal coordnates) Coordnate drecton (cartesan coordnates) x Greek letters δ j ε jk φ η 0, = j Kronecker delta functon 1, j Turbulence dsspaton rate Alternatng tensor Functon of rate of stran tensor Sk/ε

14 14 µ Vscosty µ t Turbulent vscosty ν Knematc vscosty ρ Densty σ k, σ ε Turbulent Prandtl numbers for k and ε τ j Shear stress ω k Angular velocty Rate-of-rotaton tensor Ω j Subscrpts g Gauge, j, k Coordnate drecton (Cartesan coordnates), speces number ' Speces number (when used wth coordnate drecton, ) r, x, θ Coordnate drecton (Cylndrcal coordnates) op Operatng condtons Overscores ~ Root-mean-square value Average value Nomenclature for non-fluent equatons b Jet wdth (radal drecton) b 1/2 Jet wdth where the concentraton of the source flud s 50% of the centerlne value D Dameter IG Ideal gas model L Dstance from nozzle to obstacle L LEL Dstance from nozzle when concentraton along jet axs equals the lower explosve lmt (LEL) r Radus R Densty rato = ρ a /ρ 0 v Velocty V Volume of mxture above LEL V jet Volume of jet above LEL wthout obstacle V SH4 Volume of slane n the mxture above LEL V SH4,jet Volume of slane n mxture above LEL wthout obstacle VW Volume weghted mxng model x Dstance from nozzle along jet axs

15 15 X Y Volume fracton Mass fracton Greek Letters ρ Densty Subscrpts a, Ambent C Jet s centerlne ε Effectve LEL Lower Explosve Lmt 0 Nozzle

16 16 CHAPTER I INTRODUCTION Slane s a pyrophorc gas prmarly used n the semconductor ndustry for Chemcal Vapor Deposton (CVD) of thn delectrc flms on substrates. Slcon doxde flms form by reactng slane wth an oxdzer. Slane s also used to manufacture ICs and photovoltac cells. Uses of slane can potentally present fre and exploson hazards because of ts pyrophorc nature (Roglestad et al, 1994). In 1994 AT&T Bell Laboratores and SEMATECH surveyed varous ndustres that use slane lke semconductor, solar cell, and flat panel dsplay manufacturers and unverstes. Out of the 55 ncdent surveys returned, 38 of them reported an unplanned slane release durng the last fve years. Fre was often the consequence of a slane release. Injures n the ncdent surveys ncluded one serous burn, one mnor burn, and one temporary hearng loss. Most of the slane ncdents, 45%, occurred durng processng, 21% durng mantenance, and 21% durng cylnder changes (Roglestad et al, 1994). Ths document follows the style of the AIChE Journal

17 17 Slane s a pyrophorc gas because ts autognton temperature n ar, whch has been as low as C, s below the ambent temperature (Brtton, 1990). Because t s pyrophorc, slane can spontaneously gnte f t s exposed to the ar. For slane-ar mxtures less than or equal to 30 mole% slane the stochometrc combuston reacton of slane n ar s as follows: SH 4 + 2O 2 + N 2 SO 2 (s) + 2H 2 O + N 2 When slane s 70 mole% or greater slane reacts wth oxygen as follows: SH 4 + O 2 + N 2 SO 2 (s) + 2H 2 + N 2 For mxtures between 30 mole% and 70 mole%, both reactons take place (Chowdhury, 1997). Even though slane s pyrophorc t may not always gnte mmedately when exposed to oxygen. When released t may not gnte dependng on factors such as release velocty, pressure, temperature, humdty, presence of turbulence, and release geometry such as the cross sectonal area of release (Chowdhury, 1997). There are fve known slane gnton types: prompt gnton, gnton durng flow decay, gnton at shutoff, ploted gnton, and bulk autognton. Prompt gnton occurs when the reacton starts at the begnnng of a slane release. If the slane does not gnte promptly, then a slane/ar mxture forms. Ignton durng flow decay occurs when the flow of slane s gradually decreased. There s only mnmal pressure development from ths type of gnton.

18 18 Ignton at shutoff occurs when the flow of slane s suddenly stopped. The possblty for ths type of gnton s very lkely. Pressure development from the reacton can be hgh, because an explosve volume can form for concentratons between the explosve lmts. Ploted gnton occurs when the slane/ar mxture s gnted from an external gnton source (Tamann and Braga, 1997). From experments gntng stable slane/ar mxtures from an external source, the lower explosve lmt (LEL) was determned to be around 1.4 vol% of slane and the upper explosve lmt (UEL) was determned to be around 96 vol% (Tamann and Chaffee, 1996). Also, slane forms a metastable mxture wth ar at concentratons above 4.0 vol%. Bulk autognton s smlar to ploted gnton, but an external gnton source s not needed (Tamann and Braga, 1997).

19 19 CHAPTER II PREVIOUS RESEARCH AND LITERATURE REVIEW Prevous Research on Releases of Slane Some research has studed the gnton characterstcs of slane. The bulk of testng and research was performed by Hazards Research Corporaton (HRC) n the late 1970s and early 1980s, Unon Carbde n the late 1980 s and early 1990 s, and Factory Mutual Research Corporaton (FMRC) n the md 1990 s. The Compressed Gas Assocaton (CGA) s currently performng tests on slane releases. HRC conducted test wth releases of slane nto the ar through ¼, ½, and ¾ nch dameter tubes. These tests were conducted at ntal lne pressures of 50, 100, and 500 psg for the ½ and ¾ nch dameter tubes. For the ¼ nch tube, tests were only conducted at 500 psg. Prompt gnton was not observed at ntal pressures of 100 and 500 psg but was observed at 50 psg for the ¾ nch tubes (Cruce, 1978 and 1982). At Unon Carbde, Brtton presented data that show the effects of sudden releases of slane nto ar. Brtton concluded that the probablty of gnton of a released slane jet decreases wth ncreased flow velocty and decreased temperature. Therefore, autognton of the jet seems to take place f the ext velocty s below a crtcal value. The crtcal velocty depends on factors such as the dameter of the orfce, temperature

20 20 of the jet and the surroundng envronment, and the release geometres. Brtton reported crtcal veloctes n the range of m/s at an ambent temperature of 32 o F and 50 m/s at a temperature of 43 o F for a release from a ½ nch tube (Brtton, 1990). FMRC studed the gnton characterstcs of releases of 100% slane and the effects of leak sze and geometry on releases of 100% slane. Frst they smulated an accdental release of slane nto a ventlated cabnet from a regulated pressure lne of a ¼ nch OD tube (0.18 nch ID) at pressures rangng from 30 to 300 psg. For an ext lne of a ¼ nch OD, prompt gnton was very lkely wth a release pressure below 70 psg. For lne pressures between 100 psg and 300 psg, prompt gnton probablty was about 50/50. Igntons were observed when the flow of slane was termnated (Tamann and Chaffee, 1996; Vsokey, Tamann, and Chaffee, 1996). FMRC also studed the effects of leak sze and geometry on releases of 100% slane. The effect of leak sze was studed by releasng slane from a regulated pressure lne (8 100 psg) by varyng the dameter of the dscharge lne. These tests were conducted by releasng slane from a 1/8 nch tube (nstead of a ¼ nch tube). Only one of the twelve tests (at a pressure of 33 psg) gnted promptly. The slane dd not gnte promptly even at a lne pressure as low as 7.8 psg from a 1/8 nch tube whle t gnted around 70 psg for a ¼ nch lne. The results of these tests were qute surprsng and unexpected because the slane would not gnte for even very low lne pressures from a 1/8 nch. Igntons were observed at flow shutoff or flow decay. Leak sze certanly does seem to

21 21 be factor for a delayed gnton. Tests were carred out also when the release from a ¼ nch lne was amed at a flat plate. The plate s supposed to smulate an object lke a cabnet or a wall close to a leak. For a release from a ¼ nch dameter ext lne amed at a flat plate, prompt gntons were always observed for lne pressures below 130 psg. At hgher pressures, the splt between cases of prompt and delayed gnton was about 50/50 (Vsokey, Tamann, and Chaffee, 1996). Prevous Research on Free Turbulent Jets The concentraton and the effect of the source flud s densty on the concentraton along the centerlne of a free jet s axs have been studed qute extensvely. Along the jet s centerlne the tme-averaged concentraton s nversely proportonal to the dstance downstream from the nozzle. The tme-averaged concentratons obey the relatonshp: Y 0 x = slope * (1a) Y C r o where Y 0 s the concentraton of the source flud from the nozzle, Y C s the concentraton (mass fracton) of the source flud along the jet s axs, x s the dstance from the nozzle, and r 0 s the radus of the nozzle. The slope must be determned expermentally. Equaton (1) s vald when the flow s self-smlar. Some dstance downstream of the jet source, and wth Reynolds number above a certan mnmum to ensure adequate turbulence all free jets are dynamcally smlar (except for mcroscale pheneomena) (Thrng and Newby, 1952). Therefore, the turbulent flow depends only on the ntal

22 22 momentum flux, but does not depend on the exact condtons of the flow generaton. Smlarty analyss can provde some nformaton on the general behavor of jets. Ths nformaton s useful because t tells how the data must be expected to behave so that they can be condensed nto a few dmensonless parameters and profles. Flow s consdered self-smlar when one concentraton (Y 0 ) and one length scale (r 0 ) are suffcent to predct the dmensonless functons (x/r 0 and Y 0 /Y C ) of one geometrcal varable (Chen and Rod, 1980). Becker, Hottel, and Wllams (BHW) analyzed the nozzle flud concentraton for a jet of ar released nto ar. The ar orgnatng from the nozzle was marked wth ol smoke as a tracer. BHW determned how the concentraton along the jet s axs decreased as dstance from the nozzle ncreased from the followng data ft (Becker, Hottel, and Wllams, 1967): Y0 x = (1b) Y r C 0 Snce BHW s an ar/ar jet, the coeffcent of must be corrected for other source fluds. Thrng and Newby concluded for dstances that are far enough from the nozzle the densty of the mxture approaches the densty of the surroundng flud because the jet contnuously entrans ar. They ntroduced an effectve radus defned as 1 ρ 2 0 r = r ε (2) ρa 0

23 23 to take nto account for the dfference n densty. The effectve radus corresponds to the radus of a nozzle for a jet wth the same momentum and mass flux, but wth densty ρ a nstead ρ 0 (Thrng and Newby, 1952). To scale the concentraton for a compound other than ar, the coeffcent n Equaton (1) must be corrected wth Equaton (2): Y0 = Y C x r 0 ρ ρ a (3) where ρ 0 s the densty of the flud orgnatng from the jet, and ρ a s the densty of ar at ambent condtons (Chen and Rod, 1980; Thrng and Newby, 1952). Results from several studes that studed the effect of the densty rato for varous source fluds are lsted n Table 1. The results are compared wth Equaton (3) s predcton for the slope. It s evdent from Table 1 that the densty of the source flud has a strong effect on the centerlne s concentraton. There s some varaton, up to 28 %, between the slope from the expermental data and the slope predcted by Equaton (3). Ths could be attrbuted to expermental technque, measurement uncertantes, nozzle shapes and types, buoyancy effects, data was not taken n the self-smlar regon, etc. Also, for densty ratos much greater or much less than one Equaton (3) mght not accurately account for the densty dfference. For example, Ptts noted that for SF 6 there was a strong buoyancy effect. (Also, note for Ptts work the surroundng medum had a coflow velocty whch also could affect the results, and the Reynolds number, 4000, seemed a lttle low for the flow to be consdered fully turbulent.)

24 24 Table 1. Lterature Measurements for the Effect of the Densty Rato on the Centerlne Concentraton for a Free Jet Author Jet/Surroundng ρ 0 /ρ a Slope * (ρ a /ρ 0 ) 1/2 % error Becker Ar/Ar Lockwood Heated Ar/Ar Corrsn Heated Ar/Ar Ptts He/Ar CH 4 /Ar CF 4 /Ar SF 6 /Ar Schefer C 3 H 8 /Ar Keagy N 2 /Ar He/Ar Dahm Water/Water Ths Research Present research s focused on releases of slane that gnte when the flow of slane s shut off. The goal of the research s to determne the amount of slane that forms an explosve mxture wth ar before the mxture gntes. The research s concerned only wth the mxture that forms before a reacton and not durng or after a reacton. Determnng the amount of the slane nvolved n a reacton (concentratons above the LEL) can help determne the pressure development resultng from the mxture gnton. Ths wll nclude studyng the effects of plate or cylnder mpngement (to smulate a

25 25 release blocked by a wall, cabnet, or a gas cylnder) on the amount of slane nvolved and the volume occuped by the explosve mxture the volume above the LEL. The ultmate goal s to develop generalzed correlatons to determne the total mxture volume and amount of slane wthn the volume at any plate dstance wth any radus and to determne the effect of cylnder dstance and radus on the volume. Instead of conductng laboratory experments to determne the effects of obstacles on the explosve volume and amount of slane n the explosve volume, the Computatonal Flud Dynamcs (CFD) code, FLUENT, s used to smulate the release of slane and the effects obstacles have on the release. There are several reasons to use CFD code to approxmate ths system nstead of runnng a laboratory experment. Because slane forms a flammable mxture wth ar and can gnte at ambent condtons, t would be dffcult to estmate the amount of mass nvolved n the explosve mxture even f the mxture gntes when the flow s shutoff. In addton, t mght be dffcult to determne how much mass was ntally present that forms an explosve mxture before t gntes. Wth CFD code, one does not have to rsk formng an explosve mxture or have unaccounted mass. CFD code would be safer to use for ths system snce one does not have to be concerned about flammable chemcals and mxtures. Also t s less costly to use CFD code then buyng lab equpment and flammable chemcals. FLUENT was specfcally chosen to smulate ths scenaro. FLUENT can readly calculate concentratons and the volume between concentratons, whch can be used to determne the mass nvolved n gnton for axsymmetrc and turbulent systems.

26 26 CHAPTER III FREE JET Problem Descrpton The frst problem modeled wth FLUENT was a round turbulent free jet of slane. The term free means that the jet s unconfned. As noted before, much research has already been done on turbulent free jets and analyzng concentraton profles along the jet axs (Becker, Hottel, and Wllams, 1967; Chen and Rod, 1980). One purpose of smulatng a free jet of slane s to valdate FLUENT s predcton for the mean mxture fracton along the jet s axs for a turbulent jet. Another purpose s to provde a bass for normalzng the results. Fgure 1 shows the geometry of the problem. The nner dameter of the nozzle s 0.18 nches (4.6 mm). Because the jet s released nto an nfnte envronment, the computatonal doman must approxmate an nfnte doman, and must be large enough to contan the entre explosve volume, but not too large to waste CPU tme and memory. The length of the computatonal doman to smulate the atmosphere s 2 m, and the dameter of the computatonal doman s 0.5 m. FLUENT uses the boundary condton type of a pressure nlet to represent an unconfned boundary. A gauge pressure must be entered for a pressure nlet so a gauge pressure of zero s entered to model the atmosphere. Because the jet s round, and therefore axsymmetrc, only the upper half of Fgure 1 s modeled wth CFD code.

27 27 Pressure nlet Pressure outlet Atmosphere D = 1.0 m SH 4 v = 100 m/s Axs of Rotaton D = 4.6 mm Pressure nlet x = 2 m Pressure outlet Fgure 1. Problem Descrpton for a Free Jet Flud Propertes FLUENT contans a database of compounds, and the flud propertes for slane and ar are taken from the database and are lsted n Table 2. Physcal propertes for the mxture are calculated wth equatons avalable n FLUENT. The densty of the ar/slane mxture was estmated wth the deal-gas mxng law (IG) and the volume-weghted mxng law (VW): Pop ρ = (4) m RT M ρ = 1 m ρ (5) where R s the unversal gas constant, m s the mass fracton of speces, M s the molecular weght of speces, and P op s the operatng pressure (atmospherc pressure).

28 28 The mxture propertes of vscosty, mass dffusvty, and operatng pressure are taken as constant and agan are taken from the FLUENT database of compounds. Usng constant molecular transport propertes s acceptable because the flow s turbulent. The molecular transport propertes play a mnor role compared wth turbulent transport (FLUENT Inc, 1998). Physcal propertes calculated for the mxture and used by FLUENT are lsted n Table 3. The deal gas mxng model s acceptable for several reasons. The compressblty factor at P = 1 atm and T = 300 K for slane was calculated to be 0.995, and the second vral coeffcent was calculated to be cm 3 /mol (Smth, Van Ness, and Abbott, 1996). Therefore, the uncertanty ntroduced by usng the deal gas model for pure slane at near ambent condtons s 0.5 %, whch s small compared to the total modelng uncertanty. Also, ar s entraned nto the jet such that the densty of the fnal jet s approxmately equal to the densty of ar. See Table 1 for uncertantes encountered for usng ths model. Table 2. Physcal Propertes of Ar and Slane Ar SH 4 Molecular Weght (kg/kgmol) Densty, ρ (kg/m 3 ) Vscosty, µ (kg/m-s) * *10-5 Temperature, T (K)

29 29 Table 3. Physcal Propertes of Mxture Vscosty, µ (kg/m-s) 1.72*10-5 Mass Dffusvty, D j (m 2 /s) 2.88*10-5 Operatng Pressure, P op (Pa) 101,325 Temperature, T (K) 300 Boundary Condtons Boundary condtons for the jet ext and the ar flow must be entered nto FLUENT. The boundary type for the jet was set as a velocty nlet. The axal velocty from the slane jet s specfed as 100 m/s wth a slane mass fracton of 1.0. The Reynolds number based on the jet nozzle s nner dameter s approxmately 55,000. The turbulent parameters of turbulence ntensty, I, and hydraulc dameter, D H were specfed to approxmate turbulence. The FLUENT User s Gude recommends Equaton (6) for fully developed ppe flow: 1/ 8 I 0.16(Re D H ) (6) Equaton (6) was used to approxmate the turbulence ntensty for the jet. Wth a Reynolds number of 55,000, turbulence ntensty approxmately equals 4% (FLUENT Inc., 1998). The boundary type for ar s set as a pressure nlet wth zero gauge pressure and a slane mass fracton of 0. Turbulence parameters must also be specfed for a boundary type of pressure nlet. The FLUENT manual recommends usng turbulence ntensty and vscosty rato for an external flow boundary type. The vscosty rato s defned as the

30 30 rato of turbulent vscosty to lamnar vscosty, µ t /µ. Snce the flow at the pressure nlet s not very turbulent, very low turbulence parameters are used. A vscosty rato of 1 and a turbulence ntensty of 0.5% were specfed. Table 4 summarzes the nlet boundary condtons (FLUENT Inc., 1998). Table 4. Inlet Boundary Condtons Ar SH 4 Velocty, v, (m/s) N/A 100 Gauge Pressure, P g (Pa) 0 N/A Temperature, T (K) Turbulence Intensty, I (%) Hydraulc Dameter, D H (m) N/A Vscosty Rato, µ t /µ 1.0 N/A Mass Fracton of SH Grd The upper half of Fgure 1 was modeled wth a quadrlateral mesh. Weghtng factors were used to concentrate the grd at the symmetry axs and near the jet ext. Ths ensures that the regons wth large gradents n velocty and concentraton are accurately predcted. Also, the areas wth dense mesh were postoned where most of jet flow took place. Fgure 2 shows the full grd, and Fgure 3 shows a close up of the grd around the nozzle and jet ext.

31 31 Fgure 2. Full Grd for a Free Jet. Fgure 3. Close up of the Grd for a Free Jet.

32 32 Mathematcal Bass FLUENT solves the conservaton of mass and momentum equatons. Because ths problem s turbulent and also requres multple speces mxng, FLUENT also solves a speces conservaton equaton and two addtonal transport equatons for turbulence. All the transport equatons are dscretzed nto algebrac equatons and solved by teraton n the fnte cells of the grd. The equaton for the conservaton of mass, or the contnuty equaton, can be wrtten for steady state 2D axsymmetrc geometry as follows: ( ρu) + x ( ρv) + r ρv r = 0 (7) where x s the axal coordnate, r s the radal coordnate, u s the axal velocty, and v s the radal velocty. For steady state 2D axsymmetrc flow, the conservaton of momentum equatons, or the Naver-Stokes equatons n the axal and radal drecton, are wrtten as follows: 1 ( rρ uu) 1 ( rρvu) p 1 ( rτ rx ) + = r x r r x r r τ xx x (8) 1 ( rρuv) 1 ( rρvv) p 1 ( rτ rr + = ) r x r r r r r τ rx x + τθθ r (9)

33 33 where p s the statc pressure and τ j s the stress tensor. The stress tensors are defned as (FLUENT Inc., 1998; Brd, Stewart and Lghtfoot, 1960) u v τ rx = µ + r x (10) u 2 τ xx = µ 2 ( v) x 3 (11) v 2 τ rr = µ 2 ( v) r 3 (12) v 2 τ θθ = µ 2 ( v) r 3 (13) and u v v v = + + (14) x r r For speces transport, a conservaton equaton must be solved for each chemcal speces. FLUENT solves the local mass fracton of each speces, m, wth a convecton-dffuson equaton for the th speces. The speces conservaton equaton for the th speces s descrbed as follows (ρ J = (15) x x um ) ' ', where J, s the dffuson flux of speces ', whch arses from concentraton gradents and s defned as (FLUENT Inc., 1998)

34 34 m J ' ρ (16) ', = D', m x However, Equatons (8) through (16) are for low Reynolds flow. The Reynold s number based on the jet dameter was around 55,000. Therefore, the flow s turbulent and must be modeled wth turbulence models. Two turbulence models, the standard k-ε model and the realzable k-ε model, were used to smulate turbulent free jets. Turbulence s the unsteady, aperodc moton n whch the velocty components fluctuate. To model turbulence, the velocty s decomposed nto the mean and fluctuatng terms: u u + u ' (17) where u s the velocty, u s the mean velocty and u ' s the fluctuatng velocty. Smlar defntons exst for pressure and speces concentratons (FLUENT Inc., 1998). Instead of solvng the standard Naver-Stokes equatons, for turbulent flow the Reynolds Averaged Naver-Stokes equatons are solved. The Reynolds Averaged Naver-Stokes equaton n steady state form (and Cartesan coordnates) s wrtten as U p U R 2 j ρ U k = + µ + (18) xk x x j x j x j where R j are the Reynolds stresses (fluctuatons) and are defned as follows (FLUENT, Inc., 1998 ):

35 35 j j u u R ' ' ρ = (19) Introducng the Reynolds stresses ntroduces more unknowns so the set of equatons must be closed. The Boussnesq hypothess relates the Reynolds stresses to the mean velocty gradents (FLUENT Inc., 1998): j t j j t j x u k x u x u u u δ µ ρ µ ρ + + = 3 2 ' ' (20) For both k-ε models two more transport equatons, the turbulent knetc energy, k, and the turbulence dsspaton rate, ε are ntroduced. The turbulent vscosty, µ t, s a functon of k and ε. The k and ε are solved so that turbulent vscosty can be computed for the Reynolds Averaged Naver-Stokes equaton and close the set of equatons. 2 u u k (21) + j j j x u x u x u v ε (22) ε ρ µ µ 2 k C t (23) The k-ε turbulence model s a sem-emprcal model. It assumes that the flow s fully turbulent, and the effects of molecular vscosty are neglgble. The transport equaton for the turbulent knetc energy s the same for the standard k-ε model and the realzable k-ε model, and t s defned from the followng transport equaton:

36 36 ρε σ µ µ µ ρ = k t j j j t x k x x U x U x U x k U (24) The left hand sde of the equaton represents convecton. The frst term on the rght hand sde models the generaton of turbulent knetc energy due to mean velocty gradents. The mddle term represents dffuson, and the last term s the destructon of knetc energy (FLUENT Inc., 1998). σ k s the turbulent Prandtl number for k. The default value of σ k was used, and t was orgnally determned from experments and s generally accepted for a wde range of flows. All model constants for both turbulence models are lsted n Table 5. The transport equaton for the turbulent dsspaton rate for the standard k-ε model s gven as follows: ( ) + + = k C x x x U x U x U k C x U t j j j t / ε ε σ µ µ ε ε ρ ε ε ε (25) The left hand sde of the equaton represents convecton. The frst term on the rght hand models generaton of turbulent knetc energy. The mddle term agan represents dffuson, and the last term models destructon. Agan, σ ε, C 1ε, and C 2ε are emprcal constants for the model, and they are lsted n Table 5.

37 37 Table 5. Turbulence Parameters for the Standard and Realzable k-ε Models Standard Model Realzable Model C µ 0.09 vares σ k σ ε C 1ε C 2ε 1.92 N/A C 2 N/A 1.9 The standard k-ε model s the most common model used n ndustry. However, the standard k-ε model has one major weakness. It predcts planar jets farly accurately, but t does not predct round jets accurately. To correct the round jet anomaly the dsspaton transport equaton n the realzable k-ε model was modfed to predct axsymmetrc jets more accurately. The realzable k-ε turbulence s realzable because t ensures that the normal stresses are always postve, u 2 >0, so t satsfes the mathematcal constrants. Therefore, there are two man dfferences between the standard and realzable k-ε models. The transport equaton for the turbulent dsspaton s derved dfferently for each model, and C µ n the equaton for turbulent vscosty s allowed to vary n the realzable model (FLUENT Inc., 1998). The alternate form of the turbulent vscosty s defned as: 2 k t ρc (26) ε µ µ where C µ s now allowed to vary accordng to the followng equaton:

38 38 C µ 1 = (27) * U k A0 + As ε A 0, A s and U * are functons of the velocty gradents. They are defned as U * S j S j + ~ Ω j ~ Ω j (28) ~ Ω = Ω 2 j j jk ω k (29) Ω = Ω ω (30) j j jk k Ω j s the mean rate-of-rotaton tensor wth angular velocty ω k. The constants A 0 and A s are defned as follows where A 0 = 4.04 (31) A s = 6 cosφ (32) 1 φ = arccos( 6W ) (33) 3 Sj S jk S k W = ~ (34) S ~ S = S j S j (35) S j = 1 u 2 x j + u x j (36)

39 39 The modfed transport equaton for the turbulent dsspaton for the realzable k-ε model s ρu ε x µ t ε 2 ε = ρc Sε µ ρc 2 (37) x j σ x k vε ε j + η C 1 = max 0.43, (38) η + 5 S 2S j S j (39) and η = Sk /ε (40) Although the terms are dfferent, they model the same physcal features as the standard k-ε model. The left hand sde models convecton, the frst term on the rght hand sde models generaton, the mddle terms represents dffuson, and the last term s the destructon term. All the turbulence model constants are defned n Table 5 (FLUENT Inc., 1998). FLUENT requres turbulence parameters to be specfed at the nlet and outlet boundary types. The k and ε can be specfed explctly; or more convenent quanttes such as turbulent ntensty, turbulent vscosty rato, or turbulence length scale can be specfed to estmate k and ε (FLUENT Inc. 1998).

40 40 Τhe turbulence ntensty, Ι, s defned as the rato of the root-mean-square of the velocty fluctuatons, u, to the mean flow velocty, u avg. I u' = (41) u The FLUENT manual recommended Equaton (6) to estmate ntensty for fully developed ppe flow. Equaton (42) relates turbulent ntensty to turbulent knetc energy: k = ( uavg I) (42) The physcal quantty, turbulence length scale, l, s related to the large eddes n turbulent flow. Turbulence length scale s lmted to the sze of the duct. For the nozzle, the hydraulc dameter was specfed to estmate the turbulence length scale. Turbulence length scale determnes turbulent dsspaton, ε, from the followng equaton: k / 4 ε = C µ (43) l For the external boundary condtons, the turbulent vscosty rato, µ t /µ, was specfed. The ε can be derved from the turbulent vscosty rato from 1 2 k µ t = ρc (44) µ µ ε µ The equaton for the dffuson flux of speces, Equaton (16), must also be corrected for turbulent flows as follows (FLUENT Inc., 1998):

41 41 J ', = µ m t ' ρ D', m + Sc (45) t x where Sc t s the turbulent Schmdt number Sc t µ t = (46) ρd t Results Fgure 4 shows the upper profle of the explosve volume (volume above 1.4 vol%) created by a free jet of slane released nto ar. The upper concentraton was clpped to 7.9 vol% to see the resoluton better n the bulk of the jet and the contours of 4.0 vol% and 1.4 vol%, but the actual upper concentraton lmt should be 1.0 mole fracton of slane. Because the jet s axsymmetrc, the area n the Fgure 4 s rotated around the jet axs; and the resultng volume s the explosve volume. Very close to the nozzle the concentratons of slane are very hgh. As the jet entrans ar from the atmosphere the jet of slane becomes dluted. The slane concentraton decreases as the dstance from the nozzle ncreases. It s evdent n Fgure 4, that so much ar s entraned nto the jet that bulk of the volume s ar. As the concentraton decreases by a few percent, the volume ncreases sharply. Fgure 5 shows the velocty vectors, and the entranment of ar nto the hgh-velocty slane jet s clearly vsble n ths fgure.

42 42 Fgure 4. Profle of Explosve Volume for a Free Jet of Slane for the Realzable k-ε Model Fgure 5. Velocty Vectors for a Free Jet of Slane

43 43 The results from FLUENT s predcton for a free jet are compared wth generally accepted trends for subsonc, axsymmetrc, turbulent free jets expandng nto a quescent atmosphere. Fgures 6a and 6b shows how FLUENT s predctons compare wth BHW s expermental results and data ft wthn the self-smlar regon. (BHW noted that the flow became self-smlar 40 nozzle rad downstream from the nozzle.) Fgure 6a compares the realzable k-ε model and standard k-ε model wth Equaton (3) wth ρ 0 /ρ a = 1.11 (IG model), where ρ 0 s the densty of the source flud and ρ a s the densty of ar at ambent condtons. The maxmum offset n the self-smlar regon for the realzable k-ε model usng an deal gas assumpton to approxmate densty was 3.8% and 22% for the standard k-ε model. The average offset for the realzable k-ε model was 1.7% and 13% for the standard k-ε model. Fgure 6b compares VW mxng model and realzable k-ε model wth Equaton (3) wth ρ 0 /ρ a = The maxmum offset n the self-smlar regon was 3.5%, and the average offset was 1.7%. Self-smlarty for the jet of slane s not possble close to the nozzle because of the varaton n densty across the flow (Chen and Rod, 1980). From Fgures 6a and 6b, self-smlarty for the realzable k-ε model occurs around 120 nozzle rad. Clearly the realzable k-ε model predcts free jets better than the standard k-ε model especally n the self-smlar regon. Ths was actually expected snce the realzable k-ε model corrected the round jet anomaly from the standard k-ε model. Therefore, FLUENT s realzable turbulence model predcts the jet s centerlne concentraton to wthn 3.5% n the selfsmlar regon usng ether model to approxmate the densty.

44 44 Y0/YC Comparson of FLUENT's IG Model wth BHW for a Turbulent Free Jet BHW - Data Ft FLUENT - Realzable Model and IG FLUENT - Standard Model and IG BHW - Expermental Data x/r 0 Fgure 6a. Comparson of the Realzable and Standard k-ε Models usng IG Model wth Expermental Data and Data Ft for a Turbulent Free Jet (ρ 0 /ρ a = 1.11) Comparson of FLUENT's VW Model wth BHW for a Turbulent Free Jet Y0/YC BHW - Data Ft FLUENT - Realzable Model and VW BHW - Expermental Data Fgure 6b. Comparson of the Realzable k-ε Model and VW Model wth Expermental Data and Data Ft for a Turbulent Free Jet (ρ 0 /ρ a = 1.07) x/r 0

45 45 FLUENT can determne the total volume of the slane/ar mxture above the LEL (1.4 vol%). For an axsymmetrc problem, the volume s calculated by rotatng the area n Fgure 4 around the jet axs from 0 to 2π. The volume of the explosve mxture s calculated by summng the volumes of all the cells between the specfed concentratons. V jet = dv jet = n = 1 V (47) FLUENT can also calculate the amount of slane n the explosve volume. The volume ntegral s computed by summng the product of the cell volume by the volume concentraton of slane n that cell (FLUENT Inc. 1998). V SH n = dvsh = X SH V 4 4 4, (48) Equatons (49) and (50), whch are derved n Appendx B, can estmate the volume of a turbulent free jet above a specfed concentraton (Y s mass fracton, and X s volume fracton) and the amount of source flud wthn the volume for a gven nozzle radus. The equatons are vald n the self-smlar regon. = 1 V jet Y = Y 0 LEL ρ r0 ρ 0 a (49) V jet, SH 4 Y Y ρ r 0 ρ X = LEL LEL a 3 (50) Tables 6a and 6b compare FLUENT s predctons for the explosve volume and the volume of slane from both turbulence and densty models wth the analytcal ntegraton

46 46 of BHW s jet data to determne these volumes (Becker, Hottel and Wllams, 1965; Chen and Rod, 1980). Snce 4.0 vol% s also a sgnfcant concentraton for slane/ar mxtures, the volumes are also calculated for ths concentraton. Table 6a. Comparson of FLUENT s Predcton for Explosve Volume and Volume of Slane wth Analytcal Integraton of Jet Data for 1.4 vol% Integraton of Jet Data (ρ 0 /ρ a = 1.07) Realzable k-ε model VW (ρ 0 /ρ a = 1.07) Integraton of Jet Data (ρ 0 /ρ a = 1.11) Realzable k-ε model IG (ρ 0 /ρ a = 1.11) Standard k-ε model (ρ 0 /ρ a = 1.11) V jet (m 3 ) % error V SH4,jet (ml) % error Table 6b. Comparson of FLUENT s Predcton for Explosve Volume and Volume of Slane wth Analytcal Integraton of Jet Data for 4.0 vol% Integraton of Jet Data (ρ 0 /ρ a = 1.07) Realzable k-ε model VW (ρ 0 /ρ a = 1.07) Integraton of Jet Data (ρ 0 /ρ a = 1.11) Realzable k-ε model IG (ρ 0 /ρ a = 1.11) V jet (L) % error V SH4,jet (ml) % error

47 47 CHAPTER IV NORMAL PLATE-IMPINGING JET Effect of Plate Dstance on Releases of Slane Problem Descrpton Snce FLUENT accurately (wthn 3.5%) predcted the expanson of an axsymmetrc, turbulent jet nto stagnant surroundngs, the CFD code then was used to smulate a jet mpngng on a plate that s normal to the jet. To study the effect of the dstance of the plate from the nozzle on the volume of the mxture and the volume of slane, the poston of the plate was vared between L/D 0 = 35 (L = m) and L/D 0 = 400 (L = 1.83 m). Equaton (3) can be used to predct the dstance from the nozzle wth a centerlne concentraton of 1.4 vol% (1.55 mass%) or 4.0 vol% (4.41 mass%). FLUENT s predctons for the dstance at a concentraton of 1.4 vol% and 4.0 vol% are compared wth Equaton (3) s predcton for the IG (ρ 0 /ρ a = 1.11) model and the VW model (ρ 0 /ρ a = 1.07) n Table 7. Therefore, f the jet could fully expand to form the explosve volume, the length of the explosve volume would be about 1.70 m for ths specfc dameter. For other nozzle dameters, Equaton (3) can be used to determne the length of the flammable volume.

48 48 Table 7. Comparson of FLUENT s Predcton wth BHW for Dstance wth a Concentraton of 1.4 vol% and 4.0 vol% IG (ρ 0 /ρ a = 1.11) LEL = 1.4 vol% VW (ρ 0 /ρ a = 1.07) LEL = 1.4 vol% IG (ρ 0 /ρ a = 1.11) LEL = 4.0 vol% VW (ρ 0 /ρ a = 1.07) LEL = 4.0 vol% L (m) - FLUENT L (m) - BHW (Equaton 3) % error Fgure 7 shows a schematc of the problem. The dameter of the nozzle, D 0, s 4.6 mm (0.18 n). The dstance of the plate from the nozzle, L, vares. The plate radus s large enough to confne the entre explosve mxture wthn the plate. Agan the boundary of pressure nlet smulated the boundares of the atmosphere. Ths problem s also axsymmetrc, so only the top half of Fgure 7 s modeled wth FLUENT. Flow Propertes and Boundary Condtons The materal propertes lsted n Table 2 and Table 3 and the boundary condtons lsted n Table 4 are the same for the jet confned by a plate. The realzable k-ε model was used to model turbulence, and both the deal gas model and volume weghtng mxng model were used to calculate the densty of the mxture.

49 49 Pressure Inlet Atmosphere v = 100 m/s SH 4 axs of rotaton D plate D 0 = 4.6 mm Pressure Inlet Plate L Fgure 7. Problem Descrpton for a Plate-Impngng Jet Grd Fgure 8 shows a typcal grd for a jet mpngng onto a plate, and Fgure 9 shows a close up of a typcal grd around the nozzle and the plate. Large gradents n flow occur around the nozzle and the plate. To model these gradents accurately, the nodes of the grd were concentrated along the jet axs around the nozzle and plate. The nodes were also concentrated radally toward the symmetry axs and along the plate. In general, the grd should be densest where jet flow occurs and the velocty and concentraton gradents are largest.

50 50 Fgure 8. Sample Grd for a Plate-Impngng Jet (for L = m and r plate = 0.70 m) Fgure 9. Close up of Grd near the Jet Axs

51 51 Normalzaton and Non-Dmensonalzaton For a free jet the tme averaged concentraton feld s characterzed by the dmensonless ratos L/D 0 (D 0 s the dameter of the nozzle) and Y 0 /Y C. Another varable of nterest s the axal dstance, L LEL, when the centerlne concentraton s equal to the LEL. Equaton (3) can be used to determne L LEL at the LEL for any nozzle dameter. Equatons (49) and (50) can be used to determne the volume of the free jet, V jet, and the volume of slane n the jet, V SH4,jet, above the LEL for any nozzle dameter. The followng dmensonless ratos, V/V jet, V SH4 /V SH4, jet, and L/L LEL are used to normalze the data. Therefore, the volumes and the length of the flammable volume for a plate mpngng jet can be estmated for other nozzle dameters and concentratons. Results The jet ntally behaves lke a free axsymmetrc turbulent jet as shown n Fgure 5, and then t enters a zone near the plate of strong deflecton and momentum change n the radal drecton. Further downstream, a turbulent radal wall jet forms (Becker, Cho, Ozum, and Tsujkawa, 1988). Fgure 10 shows a close up of the velocty vectors around the nozzle and plate to show the change n drecton of flow for a typcal platempngng problem. Also, the pcture shows that ar s beng entraned nto the jet.

52 Fgure 10. Velocty Vectors for a Sample Plate-Impngng Jet 52

53 53 Fgures 11 through 16 show the top profle of the slane/ar mxture above 1.4 vol% that forms. Snce the problem s axsymmetrc the pcture must be rotated around the jet centerlne to vsualze the explosve volume. The concentraton of slane s hgh very close to the nozzle. As the jet entrans ar, the slane concentraton decreases away from the nozzle. As the dstance of the plate from the nozzle ncreases, the axal contrbuton to the volume ncreases, and the radal contrbuton decreases. The radal contrbuton decreases as plate dstance ncreases because the concentraton decreases at further dstances from the nozzle. Therefore, the locaton of the concentraton of 1.4 vol% slane along the plate decreases as dstance ncreases. Fgures 11 through 16 show the effect of plate dstance on the volume of the explosve mxture. (Agan note that upper concentraton n the fgures s set at 7.9 vol% to show resoluton n the volume of the jet and the contours of 4.0 vol% and 1.4 vol%, and not all the fgures are zoomed to the same scale.) As these fgures ndcate, the plate radus requred to confne the entre explosve volume wthn the plate decreases as the plate dstance from the nozzle ncreases. Fgure 17 shows the how the normalzed mnmum radus to confne the entre explosve volume decreases as the normalzed plate locaton ncreases. Snce 4.0 vol% s also a sgnfcant concentraton for slane/ar mxtures, the normalzed mnmum radus for 4.0 vol% s also ncluded to show the normalzaton s vald for other concentratons n the self-smlarty regon. Fgure 17 also shows that ether model to calculate the densty predcts smlar results.

54 54 Fgure 11. Explosve Volume for a Slane/Ar Mxture at L/D 0 = 35 (L = m) Fgure 12. Explosve Volume for a Slane/Ar Mxture at L/D 0 = 70 (L = m)

55 55 Fgure 13. Explosve Volume for a Slane/Ar Mxture at L/D 0 = 100 (L = m) Fgure 14. Explosve Volume for a Slane/Ar Mxture at L/D 0 = 150 (L = m)

56 56 Fgure 15. Explosve Volume for a Slane/Ar Mxture at L/D 0 = 250 (L = 1.14 m) Fgure 16. Explosve Volume for a Slane/Ar Mxture at L/D 0 = 350 (L = 1.60 m)

57 57 The Effect of Plate Dstance on the Mnmum Radus to Confne the Entre Volume r/llel vol% = 1.4% IG vol% = 4% IG vol% = 1.4% VW vol% = 4% VW L/L LEL Fgure 17. Mnmum Plate Radus to Confne the Entre Explosve Volume as Plate Dstance Increases Fgures 18a and 18b show how the volumes change wth plate dstance. When the plate s very close to the nozzle most of the volume s n the radal drecton as n Fgure 11 and 12. Therefore, the radal contrbuton domnates the volume. The volume decreases as plate dstance ncreases when the flow s mostly n the radal drecton. As the plate dstance ncreases the axal contrbuton to the volume ncreases, so the volume ncreases

58 58 as n Fgures 15 and 16. In Fgures 18a and 18b the volumes go through a mnmum between L/L LEL = and (L/D 0 = 100 and 150), because nether the radal or axal contrbuton domnates the volume. Fgures 13 and 14 show the volume for L/D 0 = 100 and 150. Note that for dstances greater than 375 nozzle dameters (L = 1.71 m) the volumes are no longer affected by the plate (FLUENT predcted the total length of the explosve volume for the unconfned jet to be L = 1.73 m). Ths can be seen n Fgure 18a and 18b. The total volume and the amount of slane n the total volume at 400 nozzle dameters was equal to the volumes for the unconfned jet expandng nto stagnant surroundng. About 300 nozzle dameters downstream from the jet orgn, FLUENT predcts a slghtly larger total volume and volume of slane than the volumes for the free jet. The reason for the slght ncrease n volume s probably due to the deflecton near the plate. The bulk of the volume s n the free jet part, but near the plate the flow s deflected radally. The concal secton of volume near the plate takes up more space than the small segment of the volume that would be past the plate dstance for the unconfned jet.

59 59 Effect of Plate Dstance on Volume of Mxture Normalzed Volume, V/V jet Vol% = 1.4% IG Vol% = 4% IG Vol% = 1.4% VW Vol% = 4% VW Normalzed Dstance, L/L LEL Fgure 18a. Effect of Plate Dstance on the Explosve Volume Effect of Plate Dstance on Volume of Slane Normalzed Volume, VSH4/VSH4, jet Vol% = 1.4% IG Vol% = 4% IG Vol% = 1.4% VW Vol% = 4% VW Normalzed Dstance, L/L LEL Fgure 18b. Effect of Plate Dstance on the Volume of Slane

60 60 Effect of Plate Radus on Releases of Slane The precedng secton studed the effect of plate dstance on the volume, and the entre explosve volume was confned wthn the plate. Ths secton shows the effect of decreasng the radus below the mnmum dameter that wll confne the entre volume at a gven plate dstance (L/D 0 = 150). The problem descrpton s the same as Fgure 7, and the boundary condtons and flud propertes are the same values, also. Smlar weghtng factors were used to create the grds. Weghtng factors were used to concentrate the grds near the nozzle ext and plate, towards the axs, along the plate, and also above and behnd the plate. The grd was dense where jet flow occurs. Fgure 19 shows a sample grd wth the weghtng factors, and Fgure 20 shows a close up of the grd. Results Fgures 21a and 21b show the effect of decreasng the plate dameter at 150 nozzle dameters (L = m) downstream from the nozzle. It s evdent from Fgure 21a and 21b that there are four dstnct ranges for the plate radus. The frst range s from a radus of 0 mm to a radus around 50 mm, the second range occurs between 50 mm to 65 mm, the thrd s from 65 mm to 500 mm, the fnal range s the constant volume greater than 500 mm. Each of the regons wll be explaned below.

61 61 Fgure 19. Sample Grd for Flow past a Plate Fgure 20. Close up of Grd for Flow past a Plate

62 62 Effect of Plate Radus on the Exsplosve Volume at L/D 0 = V (m 3 ) r plate (mm) Fgure 21a. Effect of Plate Radus on the Explosve Volume at L/D 0 = 150 Effect of Plate Radus on the Volume of Slane at L/D 0 = VSH4 (ml) r plate (mm) Fgure 21b. Effect of Plate Radus on the Volume of Slane at L/D 0 = 150

63 63 For a nozzle dameter of 4.6 mm, FLUENT predcted a mnmum radus of 502 mm to confne the entre explosve volume wthn the plate for the IG model. Therefore, the volumes are constant for any plate rad above ths mnmum plate radus. The mnmum plate radus and the effect of dstance on the radus to confne the entre volume were dscussed n the precedng secton. Fgure 14 shows a FLUENT plot wth a plate radus larger than 502 mm at L/D 0 = 150. As the plate radus decreases the plate no longer confnes the entre jet, and the volume fracton of 1.4 vol% s now past the plate s edge as shown n Fgures 22 and 23. The jet s momentum s stll n the radal drecton past the plate s edge. Fgures 21a and 21b show the volumes decrease farly lnearly as the plate s radus decreases untl 65 mm. The volume decreases because the plate no longer blocks ar from beng entraned nto the mxture from behnd the plate. As the plate dameter decreases the jet can entran ar sooner nto the mxture and dlute t, so the explosve volume wll decrease as the dameter of the plate decreases. Fgures 22 and 23 show examples of plate rad that do not confne the entre explosve volume wthn the plate. They also show that the volume decreases as the plate radus decreases.

64 64 Fgure 22. Explosve Volume for L/D 0 = 150 and r plate = 400 mm Fgure 23. Explosve Volume for L/D 0 = 150 and r plate = 200 mm

65 65 The volumes decrease when the plate radus decreases n Fgure 21a and Fgure 21b untl the plate radus s approxmately the wdth of the jet at 1.4 vol%. At a plate radus of 65 mm the vortex that develops behnd the plate s too wde for the concentraton contour for 1.4 vol% to flow past t. Ths s evdent n Fgure 24, whch shows the velocty vectors and the vortex behnd the plate. Fgure 25 shows the explosve volume, and the concentraton contour of 1.4 vol% does not flow past the vortex. As the plate radus decreases the vortex also decreases, and the jet can flow past the vortex. At a plate radus of 60 mm the concentraton contour for 1.4 vol% s wthn the vortex so the volume ncreases sharply as shown n Fgure 21a and Fgure 21b. Fgures 26 and 27 show the velocty vectors and the vortex for the plate rad where the large ncrease n the flammable volume occurs. Also, note that jet flow s not just n the radal drecton near the plate. As the plate dameter decreases, the jet flows n the radal and axal drecton past the plate.

66 66 Fgure 24. Velocty Vectors for L/D 0 = 150 and r plate = 65 mm Fgure 25. Explosve Volume for L/D 0 = 150 and r plate = 65 mm

67 67 Fgure 26. Velocty Vectors for L/D 0 = 150 and r plate = 60 mm Fgure 27. Explosve Volume L/D 0 = 150 and r plate = 60 mm

68 68 The large spke n Fgure 21a and Fgure 21b occurs when the plate radus s much less than the jet wdth at 1.4 vol%. The jet just flows past the plate. A vortex stll develops behnd the plate, but the vortex s small enough that the jet can flow past t. The plate and the vortex cause the jet to wden, whch ncreases the flammable volume untl t reaches a maxmum. As the plate dameter decreases further the vortex decreases so the jet s not as wde, whch decreases the flammable volume. Eventually the dameter of the plate wll be so small that t no longer affects the jet, and the volume the LEL approaches the volume for a free jet. Fgure 28 shows the velocty vectors for a plate radus of 50 mm at L/D 0 = 150. It s evdent from the pcture that vortex behnd the plate s much smaller, and the jet flows over the vortex. Fgures 29 and 30 are the profles of the flammable volumes at rad of 50 mm and 35 mm. Note that the wdth of the volume s smaller due to the smaller plate sze and vortex. Fgure 28. Velocty Vectors for L/D 0 = 150 and r plate = 50 mm