CHAPTER V JET FLOW PAST A CYLINDER - MKO …psc.tamu.edu/files/library/center-publications/theses-and...CHAPTER V JET FLOW PAST A CYLINDER ... Figure 35 shows a close-up of the non-conformal

1

CHAPTER V

JET FLOW PAST A CYLINDER

Problem Description

Silane is used with other gases like nitrogen and hydrogen, so accidental leaks of silane

can occur near a gas cylinder. Two different cylinder sizes were considered. The

standard outer diameter for gas cylinders is 9 inches. Silane is available in 9 inch

cylinders or smaller cylinders with an outer diameter of 6 inches. Since leak size can

vary, two different nozzle diameters were considered, D0 = 4.6 mm and D0 = 3.2 mm.

The distance, L, between the nozzle diameter and the cylinder’s closest side varied. The

boundary conditions used before are the same. Figure 34 shows a schematic of the

problem. The flow around a cylinder is not axisymmetric but three-dimensional, so a

three-dimensional grid modeled the flow. Since there are two lines of symmetry (top

half and front half in Figure 34), only one fourth of Figure 34 was modeled with

FLUENT.

Grid

The grid for this problem was divided into two regions. The nozzle’s grid was

developed separately and merged with the rest of the computational domain to create a

non-conformal mesh (nodes do not line up at interface, as shown in Figure 35). The

boundary type of interface was specified on both grids at the nozzle’s exit. The grid was

created this way to control weighting factors around the nozzle. The grid’s nodes were

2

concentrated around the jet exit, between the nozzle and cylinder, and around the

cylinder. Figure 35 shows a close-up of the non-conformal mesh at the jet exit, and

Figure 36 shows a typical grid for flow past a cylinder.

Pressure Inlet Atmosphere

v = 100 m/s SiH4 line of symmetry Dcylinder

D0

Pressure Inlet Cylinder

L

Figure 34. Problem Description for Flow past a Cylinder

3

Figure 35. Zoomed in Portion of Three Dimensional Grid near the Nozzle

Figure 36. Sample Grid for Flow past a Cylinder

4

Normalization and Non-Dimensionalization

The same dimensionless variables, L/LLEL, V/Vjet, VSiH4/Vjet,SiH4, are used to normalize

the data for jet flow past a cylinder. The data are scaled for comparative purposes, but

they are not completely generalized for any leak size or cylinder diameter.

Results

Figures 37a and 37b show the effect of a jet of silane from a nozzle diameter of 4.6 mm

blocked by cylinder with diameters of 9 in and 6 in. The volumes increase linearly as

the cylinder distance increases. Figures 38a and 38b (The yellow line behind the cylinder

is a line of symmetry from the grid.) show side views and isometric views of a jet of

silane blocked by a cylinder that is close to the nozzle (L/LLEL = 0.2, L = 0.460 m). The

jet initially behaves like a free jet, as shown in Figure 5. When the jet encounters the

cylinder the flow is deflected, and it flows along the cylinder and around the cylinder. It

is evident in Figures 38a and 38b that most of the explosive volume is along the

cylinder, and there is hardly any silane directly behind the cylinder. As the cylinder

distance increases so does the free jet contribution to the volume, and the explosive

volume increases. As distance increases the volume contribution along and around the

cylinder decreases, because the concentration and velocity decrease. Figures 39a and

39b show a cylinder distance that is farther from the nozzle (L/LLEL = 0.6, L = 1.15 m).

Note again that there is very little jet flow directly behind the cylinder.

5

Figure 37a. Effect of Cylinder Diameter and Distance on the Explosive Volumefor D0 = 4.6 mm

Figure 37b. Effect of Cylinder Diameter and Distance on the Volume of Silanefor D0 = 4.6 mm

Effect of Cylinder Diameter and Distance on the Explosive Volume for D0 = 4.6 mm

00.20.40.60.8

11.2

0 0.2 0.4 0.6 0.8 1

L/LLEL

V/V

jet

Dcyl = 9 inDcyl = 6 in

Effect of Cylinder Diameter and Distance on the Volume of Silane for D0 = 4.6 mm

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

L/LLEL

VS

iH4/V

SiH

4,je

t


6

Figure 38a. Side, Explosive Volume for L/LLEL = 0.2, Dcyl = 9 in, D0 = 4.6 mm

Figure 38b. Isometric, Explosive Volume for L/LLEL = 0.2, Dcyl = 9 in, D0 = 4.6 mm

7



8

With the cylinder diameters of 9 in and 6 in, the nozzle diameter was decreased to

3.2 mm which decreases the size of the explosive volume. Since the nozzle diameter

was decreased and the explosive volume decreases, the 9 in and 6 in cylinder are more

effective at confining the explosive volume. Figures 40a, 40b, 41a, 41b, 42a, and 42b

show side views and isometric views of the explosive volumes with the smaller nozzle

diameter at distances of L/LLEL = 0.2 (L = 0.236 m), 0.4 (L = 0.472 m), and 0.8 (L =

0.944 m). Note that the cylinder mostly confines the volume, and there is no silane

behind the cylinder with a concentration above the LEL. In other words, the explosive

volume does not reattach behind the cylinder as it did for the larger nozzle diameter. If

the nozzle diameter decreases further or the cylinder diameter increases, the results

would be very similar to a plate confining a jet. This case with the cylinder is analogous

to a plate confining the entire volume within the plate radius.

9



10



11



12

Figures 43a and 43b show the effect on the volumes of reducing the nozzle diameter.

The plots in Figure 43a and 43b are similar to the plots in Figures 18a and 18b, which

show the effect of plate distance on the volumes (when the volume is confined within the

plate). When the cylinder is near the nozzle, the volume contribution along the cylinder

dominates the explosive volume compared to the free jet contribution as shown in

Figures 40a and 40b. As the cylinder distance increases so does the free jet contribution

to the volume, and the contribution along the cylinder decreases, such as the volume

shown in Figure 42a and 42b. In Figures 18a and 18b the volumes achieve a minimum

when neither contribution dominated the volume, and the same effect occurs for a

cylinder (if the diameter is large enough to confine the jet) which is evident in Figures

43a and 43b. Figures 41a and 41b show the explosive volume at the explosive volume

minimum when neither the free jet contribution nor the volume along the cylinder

dominates.

13

Figure 43a. Effect of Cylinder Diameter and Distance on the Explosive Volumefor D0 = 3.2 mm

Figure 43b. Effect of Cylinder Diameter and Distance on the Volume of Silanefor D0 = 3.2 mm

Effect of Cylinder Diameter and Distance on the Explosive Volume for D0 = 3.2 mm

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

L/LLEL

V/V

jet


Effect of Cylinder Diameter on the Volume of Silane for D0 = 3.2 mm

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

L/LLEL

VS

iH4/V

SiH

4,je

t


14

In Figures 37a, 37b, 43a, and 43b, the volumes are greater for the 6 in cylinder compared

to the 9 in cylinder. Compared to the larger cylinder, the smaller cylinder is narrower

than the jet width for 1.4 vol%, and the jet can flow around the smaller cylinder. This

case is analogous to the volumes increasing when the plate diameter decreases such as

the volumes shown in Figures 27, 29 or 30 (but not as drastic). Figures 44a, 44b, 45a,

and 45b show a jet of silane from the 3.2 mm nozzle flowing past a 6 in cylinder at

L/LLEL = 0.2 (L = 0.236 m) and 0.8 (L = 0.944). If these volumes are compared with the

volumes in Figures 40a, 40b, 42a, and 42b, it is evident that the volumes increase

because of the smaller cylinder diameter. In Figures 44a, 44b, 45a, and 45b, the

volumes reattach behind the cylinder, but they do not reattach for the larger cylinder

diameter. Eventually, as the diameter of the cylinder decreases the volumes approach

the volumes of the free jet.

Another practical comparison is to determine if a cylinder or a wall can confine the

explosive volume more effectively by minimizing the explosive volume. Figures 46a

and 46b compare the normalized explosive volume for a plate (plate completely confines

the volume) with the normalized explosive volumes for a cylinder. Clearly from Figure

46a and 46b, the cylinder minimizes the explosive volume when the obstacle is near the

nozzle. For the smaller nozzle diameter, the cylinder is more effective in minimizing the

explosive volume compared to the plate.

15



16



17

Figure 46a. Comparison of Explosive Volume Confined by a Plate and by a Cylinder

Figure 46b. Comparison of Volume of Silane Confined by a Plate and by a Cylinder

Comparison of Explosive Volume Confined by a Plate and by a Cylinder

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

L/LLEL

V/V

jet

Plate

Dcyl = 6 in, D0 = 3.2 mm

Dcyl = 9 in, D0 = 3.2 mm

Dcyl = 6 in, D0 = 4.6 mm

Dcyl = 9 in, D0 = 4.6 mm

Comparison of Volume of Silane Confined by a Plate and by a Cylinder

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

L/LLEL

VS

iH4/V

SiH

4,je

t

Plate

Dcyl = 6 in, D0 = 3.2 mm

Dcyl = 9 in, D0 = 3.2 mm

Dcyl = 6 in, D0 = 4.6 mm

Dcyl = 9 in, D0 = 4.6 mm

18

CHAPTER VI

CONCLUSIONS AND FUTURE WORK

Conclusions

The realizable k-ε turbulence in FLUENT predicts the axisymmetric, turbulent free jets

accurately. The realizable k-ε turbulence model therefore can be used to predict trends

for obstacle impingement of a round turbulent jet.

The volume above the LEL and the amount of silane in the total volume are functions of

obstacle radius and obstacle location. When the plate or cylinder confines the entire

explosive volume, the volumes decrease with increasing obstacle distance when the

radial contribution dominates; and the volumes increase with increasing obstacle

distance when the axial contribution dominates. For the smaller nozzle diameter the

cylinder was more effective at minimizing the explosive volume. The plate radius that

confines the entire volume decreases as the plate distance increases. The volumes

increase, decrease, or remain constant depending on the diameter of the plate. The

normalized volumes from the plate-impinging jet apply for other nozzle diameters and

concentrations (within the self-similar region) and for high Reynolds number flow.

Leak sizes cannot always be predicted, but if a leak occurs because of a disconnected

hose the diameter of the hose is known. If this diameter is known, one could determine

the volume of a flammable mixture. If the leak occurs near a wall and the goal is to

19

minimize the flammable volume, one could determine the best location for possible

silane storage and position of tubing. Also, if it is important to keep expensive

equipment away from potential leaks, Equation (3) can be used to determine a safe

distance to separate equipment from silane.

Future Work

The properties of silane (LEL and density) were considered for this problem, but the

results from the flat plate could easily be checked for other flammable gases like

methane, ethane, propane, etc. Equations (3), (49), and (50) already consider the density

of the source fluid so the LLEL (or LLFL), Vjet, and Vfuel, jet could be determined for the

other fuels’ LFL (lower flammability limit). The scaled results were shown to apply to

other concentrations and leak sizes.

The standard ambient conditions of T = 300 K and P = 1 atm were used to calculate the

density for the source fluid, surroundings, and mixture with the ideal gas model.

However, leaks are not always isothermal or near 1atm. The source fluid temperature

and the temperature of the surroundings might vary, or the system could be at higher

pressures. Assuming a constant temperature or ideal gas mixing can in certain

applications result in higher uncertainties.

Flow past a cylinder was considered for only a few cases, and the results were not

generalized. Generalized correlations could presumably be developed for any nozzle

20

diameter, cylinder radius, and distance. The same dimensionless variables used for the

plate-impinging jet could be used for the cylinder, but rplate would be rcylinder.

Other geometries for a wall-impinging jet could be considered. Leaks near walls are not

always axisymmetric, and might occur at an angle to the wall. This is now three-

dimensional flow, and the angle could vary between the jet flow and the wall. Leaks

could also occur near a corner, under a cabinet or the ceiling which are also three-

dimensional flows.

Other geometries for flow past a cylinder could also be considered. Leaks near cylinders

might occur off center, so they are not necessarily symmetric around a cylinder. Leaks

of silane might occur near the top of the cylinder or where the gas cylinder meets the

floor. The effect of the cylinder height could be considered also.

21

LITERATURE CITED

Becker, H. A., H. C. Hottel, G. C. Williams, “The Nozzle-Fluid Concentration of theRound, Turbulent, Free Jet, Journal of Fluid Mechanics, 30, 285 (1965).

Becker, H. A., S. H. Cho, B. Ozum, H. Tsujikawa, “Turbulent Mixing in theImpingement Zone of Dual Opposed Free Jets and of the Normal Wall-Impinging Jet,”Chemical Engineering Communication, 67, 291 (1988).

Bird, R. B., W. E. Stewart, E. N. Lightfoot, Transport Phenomena John Wiley and Sons,New York, NY (1960).

Britton, L. G., “Combustion Hazards of Silane and Its Chlorides,” Plant/OperationsProgress, 9, 16 (1990).

Chen, C. J. and W. Rodi, Vertical Turbulent Buoyant Jets – A Review of ExperimentalData, Pergamon Press, New York, NY (1980).

Chowdhury, N., “Silane Safety Study: Compressed Gas Association Performs LargeScale Tests,” Semiconductor Safety Association, 11, 47 (1997).

Corrsin, S. and M. S. Uberoi, “Further Experiments on the Flow and Heat Transfer in aHeated Turbulent Air Jet,” NACA Tn-1865 (1949).

Cruice, W., “Effects of Releases of Silane Mixtures in Ambient Air,” HRC Report 4007,Mt. Arlington, NJ (1978).

Cruice, W., “Leakage of Silane in Cabinets and Ducts,” HRC Report 5038, Mt.Arlington, NJ (1982).

Dahm, W. J. A. and P. E. Dimotakis, “Measurements of Entrainment and Mixing inTurbulent Jets,” AIAA Journal, 25, 1216 (1987).

FLUENT 5 User’s Guide, Fluent Inc., Lebanon, NH (1998).

Keagy, W. R. and A. E. Weller, “A Study of Freely Expanding Inhomogeneous Jets,”Heat Transfer and Fluid Mechanics Institute, 2, 89 (1949).

Lockwood, F. C. and H. A. Moneig, “Fluctuating Temperature Measurements in aHeated Round Free Jet,” Combustion Science and Technology, 22, 63 (1980).

22

Pitts, W. M., “Effects of Global Density Ratio on the Centerline Mixing Behavior ofAxisymmetric Turbulent Jets,” Experiments in Fluids, 11, 125 (1991).

Roiglestad, T., J. Mosovsky, J. Valdes, and C. P. Lichtenwalner, “Silane SafetyImprovement Project S71 Final Report,” SEMATECH Technology Transfer94062405A-Eng, www.sematech.org/public/docubase/techrpts.htm, Austin, TX (1994).

Schefer, R. W. and R. W. Dibble, “Mixture Fraction Measurements in a TurbulentNonreacting Propane Jet,” AIAA Paper, 86-0278 (1986).

Smith, J. M., H. C. Van Ness, and M. M. Abbott, Introduction to Chemical EngineeringThermodynamics, McGraw Hill, New York, NY (1996).

Tamanini, F., J. L. Chaffee, and R. L. Jambor, “Reactivity and Ignition Characteristics ofSilane/Air Mixtures,” Process Safety Progress, 17, 243 (1998).

Tamanini, F. and A. Braga, “A New Perspective on the Behavior of Silane Leaks inVentilated Enclosures – Implications for the Design of Protection Measures,”Semiconductor Safety Association, 11, 21 (1997).

Tamanini, F. and J. Chaffee, “Ignition Characteristics of Releases of 100% Silane,”SEMATECH Technology Transfer 9601367A-Eng,www.sematech.org/public/docubase/techrpts.htm, Austin, TX (1996).

Thring, M. W. and M. P. Newby, “Combustion Length of Enclosed Turbulent JetFlames,” 4th (International) Symposium on Combustion, Williams and Wilkins, 789,Pittsburgh, PA (1952).

Visokey, M., F. Tamanini, and J. L. Chaffee, “Effects of Leak Size and Geometry onReleases of 100% Silane,” SEMATECH Technology Transfer 96083168A-Eng,www.sematech.org/public/docubase/techrpts.htm, Austin, TX (1996).

23

APPENDIX A

DATA FROM FLUENT

Free Jet

Table A – 1. Comparison Between BHW and FLUENT’s Prediction for the IG Model(ρ0/ρa = 1.11)

BHW Real. k-ε Std. k-ε Real. k-ε Std. k-εx (m) x/r0 Y0/YC Y0/YC Y0/YC % error % error1.869 817.7 71.41 69.80 93.49 2.31 23.61.751 766.2 66.88 65.03 82.50 2.85 18.91.641 717.9 62.64 60.78 74.30 3.05 15.71.537 672.6 58.66 56.96 67.98 2.98 13.71.440 630.1 54.93 53.42 62.82 2.82 12.61.349 590.3 51.43 50.11 58.42 2.63 12.01.264 552.9 48.15 47.00 54.54 2.44 11.71.184 518.0 45.08 44.08 51.02 2.27 11.61.109 485.1 42.20 41.32 47.76 2.11 11.71.039 454.4 39.49 38.73 44.73 1.97 11.7

0.9728 425.6 36.96 36.29 41.89 1.84 11.80.9110 398.5 34.59 34.00 39.23 1.72 11.80.8531 373.2 32.36 31.85 36.73 1.61 11.90.7988 349.4 30.27 30.13 34.39 0.49 12.00.7479 327.2 28.32 27.92 32.20 1.42 12.10.7001 306.3 26.48 26.14 30.14 1.32 12.10.6554 286.7 24.76 24.46 28.22 1.23 12.20.6134 268.3 23.15 22.89 26.41 1.13 12.30.5741 251.1 21.64 21.42 24.72 1.01 12.50.5372 235.0 20.22 20.05 23.14 0.87 12.60.5027 219.9 18.89 18.76 21.65 0.70 12.70.4702 205.7 17.65 17.56 20.26 0.49 12.90.4399 192.4 16.48 16.44 18.95 0.22 13.00.4114 180.0 15.39 15.40 17.73 0.10 13.20.3847 168.3 14.36 14.43 16.58 0.49 13.40.3596 157.3 13.40 13.53 15.51 0.97 13.60.3362 147.1 12.50 12.69 14.50 1.52 13.80.3142 137.4 11.65 11.91 13.56 2.17 14.10.2935 128.4 10.86 11.18 12.68 2.92 14.30.2742 119.9 10.11 10.51 11.85 3.76 14.6

24

Table A – 2. Comparison Between BHW and FLUENT’s Prediction for the VW Model(ρ0/ρa = 1.07)

BHW Real. k-ε Real. k-εx (m) x/r0 Y0/YC Y0/YC % error1.869 817.725 72.77 72.48 0.401.751 766.181 68.16 66.88 1.911.641 717.861 63.83 62.12 2.751.537 672.559 59.78 58.02 3.021.440 630.092 55.97 54.35 2.981.349 590.276 52.41 50.96 2.841.264 552.948 49.07 47.79 2.671.184 517.957 45.94 44.82 2.501.109 485.1 43.00 42.02 2.341.039 454.4 40.25 39.38 2.19

0.9728 425.6 37.67 36.91 2.050.9110 398.5 35.25 34.58 1.920.8531 373.2 32.98 32.40 1.790.7988 349.4 30.85 30.34 1.680.7479 327.2 28.86 28.41 1.570.7001 306.3 26.99 26.59 1.470.6554 286.7 25.23 24.89 1.370.6134 268.3 23.59 23.30 1.260.5741 251.1 22.05 21.80 1.140.5372 235.0 20.61 20.40 1.000.5027 219.9 19.25 19.09 0.830.4702 205.7 17.98 17.87 0.620.4399 192.4 16.79 16.73 0.370.4114 180.0 15.68 15.67 0.060.3847 168.3 14.63 14.68 0.320.3596 157.3 13.65 13.76 0.770.3362 147.1 12.73 12.90 1.300.3142 137.4 11.87 12.11 1.930.2935 128.4 11.06 11.37 2.650.2742 119.9 10.31 10.68 3.47

25

Plate Impinging Jet

Table A – 3a. Effect of Plate Distance Volumes above 1.4 vol% Confined within thePlate’s Radius for the IG Model

L/D 0 L (m) L/L LEL V (m 3) V/V jet VSiH4 (mL) VSiH4/V SiH4,jet

35 0.160 0.09197 0.02805 0.9508 587.8 0.946570 0.320 0.1839 0.02391 0.8105 500.7 0.8062

100 0.457 0.2628 0.02260 0.7661 485.7 0.7821125 0.572 0.3284 0.02240 0.7593 490.1 0.7892150 0.686 0.3941 0.02179 0.7385 488.1 0.7860175 0.800 0.4598 0.02220 0.7525 503.0 0.8100200 0.914 0.5255 0.02440 0.8271 543.5 0.8752250 1.14 0.6569 0.02706 0.9173 596.1 0.9599275 1.26 0.7226 0.02895 0.9814 617.3 0.9940300 1.37 0.7883 0.03013 1.021 630.7 1.0156350 1.60 0.9197 0.03265 1.107 671.4 1.0812375 1.71 0.9853 0.03355 1.137 685.1 1.1032400 1.83 1.051 0.02950 1.000 621.0 1.000

Table A – 3b. Effect of Plate Distance on Volumes above 4.0 vol% Confined within thePlate’s Radius for the IG Model

L/D0 L (m) L/LLEL V (m3) V/Vjet VSiH4 (mL) VSiH4/VSiH4,jet

35 0.160 0.2635 0.00095 0.7361 58.5 0.754870 0.320 0.5271 0.00106 0.8179 67.7 0.8735

100 0.457 0.7530 0.00131 1.009 78.8 1.016

Table A – 4a. Effect of Plate Distance on Explosive Volume above 1.4 vol% Confinedwithin the Plate’s Radius for the VW Model


35 0.160 0.0941 0.02633 0.9222 538.2 0.903070 0.320 0.1883 0.02247 0.7870 471.0 0.7903

100 0.457 0.2689 0.02120 0.7424 456.1 0.7653150 0.686 0.4034 0.02003 0.7016 451.0 0.7567200 0.914 0.5379 0.02317 0.8116 516.3 0.8663250 1.14 0.6724 0.02739 0.9593 589.4 0.9889300 1.37 0.8068 0.02880 1.009 600.2 1.007

26

Table A – 4b. Effect of Plate Distance on Volumes above 4.0 vol% Confined within thePlate’s Radius for the VW Model


35 0.160 0.2658 0.0008706 0.7021 54.1 0.730670 0.320 0.5316 0.001046 0.8435 65.7 0.8872

100 0.457 0.7595 0.001276 1.029 76.2 1.029

Table A – 5a. Minimum Plate Radius to Confine Entire Volume above 1.4 vol% for theIG Model

L/D0 L (m) L/LLEL r (m) r/LLEL

35 0.160 0.09197 0.7537 0.433270 0.320 0.1839 0.6704 0.3853

100 0.457 0.2628 0.6208 0.3568125 0.572 0.3284 0.5620 0.3230150 0.686 0.3941 0.5020 0.2885175 0.800 0.4598 0.4676 0.2687200 0.914 0.5255 0.4353 0.2502250 1.14 0.6569 0.3648 0.2097275 1.26 0.7226 0.3390 0.1948300 1.37 0.7883 0.2848 0.1637350 1.60 0.9197 0.1977 0.1136

Table A – 5b. Minimum Plate Radius to Confine Entire Volume above 4.0 vol% for theIG Model


35 0.160 0.2635 0.2045 0.336870 0.320 0.5271 0.1471 0.2423

100 0.457 0.7530 0.1087 0.1790

27

Table A – 6a. Minimum Plate Radius to Confine Entire Volume above 1.4 vol% for theVW Model


35 0.160 0.0941 0.7319 0.430570 0.320 0.1883 0.6835 0.4021

100 0.457 0.2689 0.5856 0.3445150 0.686 0.4034 0.4594 0.2702200 0.914 0.5379 0.4189 0.2464250 1.14 0.6724 0.3602 0.2119300 1.37 0.8068 0.2689 0.1582

Table A – 6b. Minimum Plate Radius to Confine Entire Volume above 4.0 vol% for theVW Model


35 0.160 0.2680 0.1989 0.330470 0.320 0.5361 0.1425 0.2367

100 0.457 0.7658 0.0948 0.1575

28

Table A – 7a. Effect of Plate Radius on Volumes above 1.4 vol% for L/D0 = 35 (L =0.160 m)

rplate (mm) rplate/L V (m3) V/Vjet VSiH4 (mL) VSiH4/VSiH4,jet

1000 6.250 0.02905 0.9847 587.8 0.9465754 4.713 0.02905 0.9847 587.8 0.9465500 3.125 0.02091 0.7087 460.6 0.7417400 2.500 0.01756 0.5953 396.8 0.6390300 1.875 0.01539 0.5217 347.4 0.5594200 1.250 0.01310 0.4441 293.6 0.4728100 0.6250 0.0120 0.4061 256.1 0.412450 0.3125 0.0117 0.3949 244.2 0.393235 0.2188 0.0115 0.3902 242.6 0.390725 0.1563 0.0122 0.4142 254 0.409020 0.1250 0.1864 6.319 4192 6.75015 0.0938 0.0754 2.557 1643 2.64610 0.0625 0.0470 1.593 1000 1.6100 0 0.0295 1.000 621 1.000

Table A – 7b. Effect of Plate Radius on Volumes above 4.0 vol% for L/D0 = 35 (L =0.160 m)

rplate (mm) rplate/L V (mL) V/Vjet VSiH4 (mL) VSiH4/VSiH4,jet

400 2.500 895 0.6906 55.7 0.7187200 1.2500 885 0.6829 55.4 0.7148100 0.6250 623 0.4807 42.9 0.553550 0.3125 507 0.3912 35.7 0.460635 0.2188 442 0.3410 32.3 0.416825 0.1563 461 0.3557 32.8 0.423220 0.1250 2350 1.813 114.4 1.47615 0.0938 5080 3.920 281.2 3.62810 0.0625 3420 2.639 179.5 2.3160 0 1296 1.000 77.5 1.000

29



1000 3.125 0.0239 0.8105 500.7 0.8063670.4 2.095 0.0239 0.8105 500.7 0.8063500 1.563 0.0201 0.6797 441.2 0.7105300 0.9375 0.0139 0.4705 330.3 0.5319100 0.3125 0.0110 0.3715 253.8 0.408740 0.1250 0.0103 0.3492 237.0 0.381635 0.1094 0.3087 10.46 4895 7.88230 0.09375 0.1416 4.800 2935 4.72625 0.07813 0.0828 2.807 1778 2.86315 0.04688 0.0444 1.505 954.1 1.53610 0.03125 0.0350 1.186 748.3 1.2050 0 0.0295 1.000 621.0 1.000



500 1.563 1090 0.8410 68.5 0.8839300 0.938 1030 0.7948 66.9 0.8632100 0.3125 980 0.7562 63.6 0.820650 0.1563 858 0.6620 57.5 0.741935 0.1094 833 0.6427 55.8 0.720030 0.09375 967 0.7461 61.8 0.797425 0.07813 1940 1.497 104.0 1.341915 0.04688 1850 1.427 103.0 1.329010 0.03125 1560 1.204 89.8 1.15870 0 1296 1.000 77.5 1.000

30



914.4 2 0.0226 0.7661 492.1 0.7924620.8 1.358 0.02307 0.7820 492.1 0.7924500 1.094 0.02124 0.7200 465.8 0.7501400 0.8749 0.01853 0.6281 423.9 0.6826300 0.6562 0.01573 0.5332 372.8 0.6003200 0.4374 0.01267 0.4295 314.9 0.5071100 0.2187 0.01072 0.3635 270.1 0.434975 0.1640 0.01100 0.3728 271.1 0.436645 0.09843 0.1015 3.441 1718 2.76740 0.08749 0.1710 5.797 3073 4.94835 0.07655 0.1005 3.406 1971 3.17325 0.05468 0.06000 2.034 1217 1.96015 0.03281 0.03785 1.283 777.1 1.2510 0 0.0295 1.000 621 1.000



700 1.531 1310 1.011 78.9 1.018300 0.6562 1280 0.9877 77.8 1.004200 0.4374 1280 0.9877 77.6 1.001100 0.2187 1330 1.026 79.5 1.02675 0.1640 1340 1.034 79.99 1.03250 0.1094 1180 0.9105 73.7 0.951035 0.07655 1140 0.8796 71.99 0.928915 0.03281 1340 1.034 79.5 1.02610 0.02187 1390 1.073 83 1.0730 0 1296 1.000 77.5 1.000

31

Table A – 10a. Effect of Plate Radius on Volumes above 1.4 vol% for L/D0 = 150 andD0 = 4.57 mm (L = 0.686 m)


1000 1.458 0.02179 0.7385 488.1 0.7860500 0.7291 0.02179 0.7385 488.1 0.7860400 0.5833 0.02062 0.6990 467.5 0.7528300 0.4374 0.01860 0.6305 438.9 0.7068200 0.2916 0.01630 0.5525 396.7 0.6388100 0.1458 0.01381 0.4681 349.9 0.563475 0.1094 0.01340 0.4542 340.7 0.548665 0.09478 0.02354 0.7980 494.4 0.796160 0.08749 0.06242 2.116 1087 1.75055 0.08020 0.08694 2.947 1514.1 2.43850 0.07291 0.09474 3.212 1652 2.66035 0.05104 0.06461 2.190 1197 1.92825 0.03645 0.05102 1.729 994 1.60115 0.02187 0.03374 1.144 694 1.1180 0 0.02950 1.000 621 1.000

Table A – 10b. Effect of Plate Radius on Volumes above 1.4 vol% for L/D0 = 150 andD0 = 3.18 mm (L = 0.477 m)


1000 2.096 0.007235 0.7303 161.9 0.7754358.8 0.7522 0.007235 0.7303 161.9 0.7754250 0.5241 0.006584 0.6646 152.0 0.7280150 0.3145 0.005175 0.5224 128.5 0.615475 0.1572 0.004615 0.4658 111.6 0.534550 0.1048 0.004270 0.4310 108.9 0.521640 0.08386 0.02593 2.617 454.8 2.17835 0.07338 0.03223 3.253 562.7 2.69525 0.05241 0.02157 2.177 406.4 1.94610 0.02096 0.01129 1.140 232.5 1.1140 0 0.009907 1.000 208.8 1.000

32

Table A – 11. Effect of Plate Radius on Volumes above 1.4 vol% for L/D0 = 200 (L =0.914 m)


1000 1.094 0.024393 0.8269 543 0.8744443.5 0.4850 0.024393 0.8269 543 0.8744350 0.3828 0.024250 0.8220 542.3 0.8733300 0.3281 0.023490 0.7963 528.8 0.8515200 0.2187 0.021240 0.7200 494.5 0.7963100 0.1094 0.017630 0.5976 432.3 0.696180 0.08749 0.02090 0.708 470.4 0.75775 0.08202 0.03058 1.036 613.1 0.98770 0.07655 0.04309 1.461 809.0 1.30365 0.07108 0.04349 1.474 828.5 1.33450 0.05468 0.042859 1.453 831.4 1.33935 0.03828 0.03841 1.302 761.8 1.22725 0.02734 0.03195 1.083 668.7 1.0770 0 0.0295 1.000 621 1.000

Table A – 12. Effect of Plate Radius for Volumes above 1.4 vol% for L/D0 = 250 (L =1.14m)


1000 0.875 0.02844 0.9641 615.5 0.9911364.8 0.3192 0.02844 0.9641 615.5 0.9911300 0.2625 0.02797 0.9481 611.9 0.9853250 0.2187 0.02705 0.9169 591.1 0.9519200 0.1750 0.02647 0.8973 581.9 0.9370150 0.1312 0.02470 0.8373 554.7 0.8932100 0.08749 0.02287 0.775 523.7 0.84380 0.06999 0.02755 0.934 582.9 0.93975 0.06562 0.03042 1.031 620.4 0.99965 0.05687 0.03234 1.096 653.5 1.05250 0.04374 0.03119 1.057 640.5 1.03135 0.03062 0.03052 1.035 629.2 1.0130 0 0.02950 1.000 621 1.000

33

Table A – 13. Effect of Plate Radius for Volumes above 1.4 vol% for L/D0 = 300 (L =1.37 m)


1000 0.729 0.031117 1.0548 656.3 1.0568284.8 0.2076 0.031117 1.0548 656.3 1.0568200 0.1458 0.030749 1.0423 648.8 1.0448150 0.1094 0.029186 0.9894 624.9 1.0063100 0.0729 0.027800 0.9424 604.3 0.973190 0.0656 0.026840 0.9098 581.1 0.935780 0.05833 0.02688 0.911 580.4 0.93570 0.05104 0.02966 1.005 620.3 0.99965 0.04739 0.03125 1.059 645.2 1.03950 0.03645 0.03100 1.051 642.4 1.0340 0 0.029500 1.000 621.0 1.000

Cylinder Impinging Jet

Table A – 14. Effect of Cylinder Distance for Volumes above 1.4 vol% for Dcyl = 9 inand D0 = 4.6 mm

L/LLEL V (m3) VSiH4 (mL) V/Vjet VSiH4/VSiH4,jet

0.2 0.01774 357.0 0.6014 0.57490.4 0.02184 450.8 0.7403 0.72590.6 0.02609 548.4 0.8843 0.88310.8 0.03204 653.6 1.086 1.052



0.2 0.01982 402.0 0.6717 0.64730.4 0.02410 491.0 0.8168 0.79070.6 0.02837 577.2 0.9618 0.92950.8 0.03275 663.6 1.110 1.069

34



0.2 0.005356 110.7 0.5406 0.53010.4 0.004760 107.8 0.4805 0.51610.6 0.005636 130.4 0.5689 0.62450.8 0.007252 161.6 0.7320 0.7741



0.2 0.006720 132.5 0.6783 0.63470.4 0.005952 125.7 0.6008 0.60190.6 0.007282 153.7 0.7350 0.73610.8 0.008660 180.5 0.8741 0.8644

35

APPENDIX B

DERIVATION OF Vjet AND VSiH4, jet

Derivation of Vjet (Equation 49)

BHW’s correlations (with density modification) to determine the concentration field for

subsonic axisymmetric turbulent jets are integrated to determine the volume of a

flammable mixture above a specific concentration and nozzle diameter. The following

equations from Chen and Rodi and BHW will be used to express the axial, x, and radial,

r, decay of source material concentration, Y (mass fraction) or X (volume fraction).

(Technically the virtual origin – when the line to predict concentration from the distance

is extrapolated to the y-axis – should be included in Equations (B –1a) and (B – 1b), but

for distances far from the nozzle it is negligible compared to x).

21

01

0 185.0

∞

−

∞∞ ρρ

Dx )Y - (Y = Y - YC (B – 1a)

Converted to volume fractions:

( )( )

21

01

000 185.0

11

−+−+

∞

−

∞∞ ρρ

Dx

YRYYRY

)X - (X = X - XCC

C (B – 1b)

)57exp()(exp 2

2

xr

YY)br (- )Y -(Y = Y - Y C2

2

C −−= ∞∞∞ (B – 2a)

Converted to volume fractions:

36

)xr (-

YYRYRY

)X - X( = X - X2

2CC

C 57exp1

1

−+−+

∞∞ (B – 2b)

x 0.1 = b 1.2 = b 1/2 32550 (B – 3)

In the above equations, the subscripts 0, C, and ∞ refer to conditions in the source flow, on

the jet’s centerline, and in the surrounding environment, respectively. D refers to diameter

of the nozzle, b is the jet width, and b1/2 is the radial distance at which the concentration of

the source material dropped to 50% of the centerline value. R is the density ratio, ρ∞ /ρ0

used to convert the mass fractions to volume fractions. According to Chen and Rodi the

radial distance of the jet is nearly independent of the density ratio.

An expression will be derived for the volume of the jet above a specific source fluid

concentration, YLEL, will be derived as a function of downstream distance. The volume per

unit length is expressed by the following integral:

)Y - Y

Y - Y( b = r = dr r 2 =’ V

LEL

C2LEL

r0jet

LEL

∞

∞∫ ln2 πππ (B – 4)

where rLEL is the radius where the concentration is equal to YLEL. Equation (B – 2a) was

substituted into the above equation for rLEL to obtain the last equality. To determine the

volume, Equation (B – 4) is integrated in the axial direction.

dx )Y - Y

Y - Y( b = dx’ V = VLEL

C2x0jet

x0jet

∞

∞∫∫ lnπ (B – 5)

37

By substituting Equation (B – 1a) and (B – 3) in for (YC - Y ∞ ) and b, all the terms in the

integral are now a function of x. The following expression results from analytical

integration:

] 31 + )

x 0.185D

Y - YY - Y

( [ 3x 10. =V

LEL

32

jet

21

00ln325

∞∞

∞

ρρπ (B – 6)

If Equation (B – 1a) is solved for x and substituted in to Equation (B – 6) the following

expression results for the volume of a jet.

31 +

Y - YY - Y

DY - YY - Y

= VLEL

C

Cjet

∞

∞

∞∞

∞ ln902.2

3

21

00

ρρ

(B - 7)

If the quantity of interest is the portion of the volume of the jet where the downstream

location on the axis, YC is equal to YLEL, Equation (B – 7) becomes:

DY - Y

Y - Y = V

LELjet

3

21

009672.0

∞∞

∞

ρρ

(B – 8)

If there is no source material initially in the surrounding medium, the expression (with

nozzle radius) becomes

r Y

Y = V

aLELjet

3

21

00

0738.7

ρρ

(B – 9)

which is the same as Equation (49).

38

Derivation of VSiH4, jet (Equation 50)

The derivation for the amount of source fluid within the jet is fairly similar to the derivation

of the volume of a jet above a specific concentration. First the volume is integrated in the

radial direction and Equation (B – 2b) is substituted into the equation.

XX - XX

YRYYRY

+ YRYYRY

X - XX - X X

b = dr r 2 X =’ V

LELCLELLEL

CC

LELLEL

CC

LEL

C

2r0f

LEL

+−−+−+

−+−+

∫∞∞

∞

∞∞

)(1

1

11

lnππ (B – 10)

where rLEL is the radius where the concentration is equal to YLEL(mass fraction) or XLEL

(volume fraction). Equation (B – 10) must be integrated in the axial direction to determine

the volume where the centerline concentration is XLEL.

∫∫

+−−+−+

−+−+

=

∞∞

∞

∞∞x

LELCLELLEL

CC

LELLEL

CC

LEL

C

2x

ff dx XX - XX

YRYYRY

+ YRYYRY

X - XX - X X

b dxV = V00

'

)(1

1

11

lnπ (B - 11)

Again equations (B – 1b) and (B – 2b) are substituted into Equation (B – 11) for (XC -

X ∞ ) and b to obtain an expression in terms of x.

( )

dx

XXx

DYRYYRY

XX

+ x

DYRYYRY

X - XX - X

X

x = Vx

LELLELLEL

LELLELLEL2

f ∫

+−

−+−+−

−+−+

∞∞

∞

∞∞

∞∞

021

0000

21

0000

185.011

185.011

ln

)1325.0(

ρρ

ρρ

π

39

(B - 12)

After integration the following expression results.

]185.01

1)(

23

34

)185.01

1ln([

31325.0

21

0000

21

00003

2

−+−+−+−

+

−+−+

−−=

∞∞∞

∞∞

∞∞

ρρ

ρρπ

xD

YRYYRY

XXXX

xD

YRYYRY

XXXX

XxV

LELLELLEL

LELLELLELf

(B - 13)

Equations (B –1a) and (B – 1b) are solved for x and substituted into Equation (B - 13). The

following expression results:

)](1

123

34

)1

1ln([902.2

3

21

00

∞∞

∞

∞∞

∞∞

∞

−−+−++−+

−+−+

−−

XXYRYYRY

XX

YRYYRY

XXXX

X DY - YY - Y

= V

CLELLEL

CCLEL

LELLEL

CC

LEL

C

Cf ρ

ρ

(B – 14)

For the volume of source fluid in the portion of the jet where the centerline concentration,

XC is equal to the XLEL (or YC is equal to YLEL), Equation (B – 14) simplifies to

XX DY - Y

Y - Y = V LEL

LELf

−

∞∞∞

∞

21

239672.0

3

21

00

ρρ

(B – 15)

40

If there is no source fluid in the surroundings, Equation (B – 14) simplifies further to

yield Equation (50) in the main body of the text:

X r Y

Y = V LEL

aLELf

23738.7

3

21

00

0

ρρ

(B – 16)

41

APPENDIX C

GUIDE TO DEVELOPMENT OF GRIDS AND FLUENT

Axisymmetric Problems

Free Jet

The grid in Figure 2 was created with GAMBIT 1.1. This grid is fairly straightforwardto create. Refer to GAMBIT tutorial manual for familiarity with the interface and mousefunctions. This grid was created with the “bottom-up” approach. Bottom-up means thatthe grid was created with vertices, then the vertices were connected with straight lines.Note that the grid was created in millimeters. It is extremely important that one uses aconsistent unit system when creating a grid. The grid must be created with the sameunits in mind.

Procedure1. Start GAMBIT: type gambit –id filename at the prompt (filename is

the any name you want to call it)2. Choose solver from main menu bar Solver à FLUENT 53. Create initial vertices (dimensions for grid in Figure 2 are used)

a) Click on Geometry à Click on Create Real Vertexb) Enter coordinates of vertices (x, y)

Nozzle:1. (0,0)2. (-5, 0)3. (-5, 2.286)4. (0, 2.286)

Atmosphere:5. (0, 250)6. (2000, 250)7. (2000, 2.286)8. (2000,0)

Note: The radius of the nozzle was entered since theproblem is axisymmetric.

4. Connect the verticesa) Click on Geometry à Click on Edge à Create Edgeb) Connect vertices

42

1. Select (shift-left-click) vertices 1 and 2, click on apply2. Connect vertices 2 and 33. Connect vertices 3 and 44. Connect vertices 4 and 55. Connect vertices 5 and 66. Connect vertices 6 and 77. Connect vertices 7 and 88. Connect vertices 8 and 1

5. Connect straight edges to create a facea) Geometry à Face à Create Face from Wireframeb) Select all edges (shift-left click individually, shift-left-drag mouse

over all edges, click on edges arrow and pick all edges) and apply(edges turn blue – created a face)

6. Mesh edgesa) Mesh à Edge à Mesh edgesb) Zoom in on nozzle (control-left click)

1. Select all edges (Edges 1, 2, and 3) in nozzle (shift-leftclick)

2. Select interval count from option menu under spacing,enter a 2 in the text entry box. Click apply

c) Mesh edge 7 (straight across from nozzle)1. This has the same grading as nozzle so the grid lines

are straight across2. Mesh edge with same interval count as before (enter a

2 in text entry box)d) Mesh top and bottom (Edge 5 and 8) (they have the

same number of intervals and grading so the lines are straightacross)

1. Zoom in around nozzle2. Select interval count, enter number of intervals (like

50)3. Select successive ratio (see GAMBIT Lecture Notes

for different types of spacing and their definitions)from type option menu under grading- Want the grading to be concentrated towards the

nozzle- This is trial and error a enter value (slightly above

or below 1)- Want interval sizes to increase smoothly- If the grading is in the reverse direction there are

several ways to fix this: shift-middle click on the

43

edge, select the edge and click on reverse, invertratio under successive ratio)

4. Zoom out and see if spacing is smooth for rest of edgee) Mesh left and right (Edges 4 and 6), again they have

the same number of intervals and grading so the lines arestraight

1. Procedure is same as part d)2. Do not want abrupt changes in mesh

7. Mesh Facea) Mesh à Face à Mesh Facesb) Shift-left-click the facec) Click on the apply buttond) GAMBIT connects the nodes created along the edges

8. Set Boundary Typesa) Change entity to edges by selecting edges in the option menu

below entityb) Zoom in on the nozzlec) Select the top edge (edge 3) of the nozzle, enter a name (such

as nozzle) in the name text entry box, select wall in the typeoption menu

d) Select the left edge (edge 2) of nozzle, enter a name (such asfuel inlet) in the name text entry box, select velocity-inlet asthe boundary type

e) Select the entire lower edge (Edges 1 and 8) of thecomputational domain, enter a name (such as axis), select axisas the boundary type

f) Select the left and top edge (Edges 4 and 5) of computationaldomain, enter a name (such as air-inlet), select pressure-inletas the boundary type

g) Select the right edges (Edges 6 and 7), enter a name (such asoutlet), select pressure-outlet as the boundary type

9. Export Mesha) File à Export à Meshb) Enter file name (filename.msh) and click accept

After the grid was created it must be imported into FLUENT 5.1. The physics of theproblem are entered into FLUENT, and it solves the transport equations in the cells ofthe grid.

10. Import Mesh into FLUENTa) Type fluent 2d at prompt

44

b) File à Read à Case à filename.msh

11. Scale mesha) By default FLUENT assumes that grid was created in meters

and FLUENT uses SI units for data entryb) Grid à Scale

- Grid was created in mm and FLUENT uses SI units- Under Units Conversion select mm from list- Click scale- Now FLUENT scales grid to meters

12. The equations and physics models that FLUENT solves must bespecified

a) Define à Models à Solver – Select axisymmetrica) Define à Models à Viscous – Select appropriate model

(realizable k-ε model under the k-ε model panel)c) Define à Models à Species – Select multiple species model

(if a surface or volume reaction is modeled that would beselected here)

13. The species in the mixture must be specifieda) Define à Materialsb) Click on database, change mixture to fluid under material

type, scroll through database and select appropriate fluid(silane), and click copy

c) Close databased) Change fluid to mixture under material type, models to

calculate mixture properties such as density, viscosity, etc., areselected here, to select species in the mixture click on the editbutton to the right of mixture species, select appropriatespecies in mixture

e) If a reaction is modeled the reaction specifications are alsoentered here

f) Click on Change/Create button

14. Setting the Boundary Conditionsa) Define à Boundary Conditionsb) Click on the boundary of silane-inlet (velocity-inlet)

- Change velocity specification method to magnitudeand direction

- Set velocity magnitude to specified velocity (100 m/s)- Axial component of flow direction is 1 and 0 for radial

component of flow direction

45

- Change turbulence specification method to desiredmethod (intensity and hydraulic diameter) and enterappropriate values for them (5% and 0.0046 m)

- Change mass fractions to appropriate values (1.0 forsilane), note that one species will be missing since itsvalue can be determined by knowing all fractions addto one

c) Click on the boundary of air-inlet (pressure-inlet)- Keep default value of 0 for gauge pressure (models

atmosphere)- Specify turbulence method (for external boundary

conditions FLUENT recommends intensity andviscosity ratio) and specify reasonable values

- Change mass fractions (0 for silane)d) Click on the boundary of outlet (pressure-outlet)

- This is practically the same as pressure inlet- Reasonable values should be assigned and are utilized

if backflow occurs

15. Initialize the solutiona) Solve à Initialize à Intialize

- Select all-zones in the Compute from drop-down list- Click init to initialize the variables, close panel

b) Set the under-relaxation factors (these help stabilize thesolution)

- Usually the default for momentum, turbulence are fine,but the value of 1 is too high for the species (silane), itshould be changed to 0.8 or 0.9

- Click OKc) Save case filed) Start iterating

- Solve à Iterate- Change number of iterations (like 500)- Click iterate

16. After all the equations residuals are less than 0.001, FLUENT stopsiterating

17. Postprocessinga) To see the contours of volume fraction

- Display à Contours- Select contours of species and then select desired

species (mass fraction, mole fraction, etc)- Use clip to range to set min and max contours

46

b) To find volume between min and max concentrations- Adapt à Iso-value- Select Species and volume fraction, enter min and max

contours, click on mark- Grid à Separate Cells, under registers select the

register (cells just marked), select the cell zone to beseparated, click on separate (cell zone is split into twozones)

- Report à Volume integrals, select zone just created,click on calculate to volume of mixture. To calculatevolume of source fluid in mixture select species andvolume fraction of silane and click on calculate.

Normal Plate-Impinging Jet

The development of the grid in Figure 8 is very similar to the procedure to develop thegrid in Figure 2, which was just outlined. There are a couple of significant differences:

1. The dimensions are different.

2. The grading along the axis and top boundary was concentratedtowards the nozzle and the plate.

- Under grading select the type as successive ratio andclick on double sided so the grading applies to bothsides

- Enter values for ratio 1 and ratio 2 (care should betaken that the interval size increases and decreasessmoothly)

3. The boundary type of pressure outlet (left edge) should be theboundary type of wall (with a name like plate).

4. Commands in FLUENT are the same.

The development of the grid in Figure 19 is also similar to the procedure just outlined,but there are some major differences. The grid is also created with the bottom upapproach, and the major changes are outlined as follows. (For this particular procedurethe plate distance was assumed to be 0.686 m and radius was 50 mm.)

Procedure1. Create initial vertices (dimensions for grid in Figure 19 are used).

47

a) Click on Geometry à Click on Create Real Vertexb) Enter coordinates of vertices (x, y)

Nozzle:1. (0,0)2. (-5, 0)3. (-5, 2.286)4. (0, 2.286)

Atmosphere:5. (0, 50)6. (0, 1000)7. (686, 1000)8. (688, 1000)9. (3000, 1000)10. (3000, 50)11. (3000, 2.286)12. (3000, 0)

Plate:13. (688, 0)14. (688, 2.286)15. (688, 50)16. (686, 50)17. (686, 2.286)18. (686, 0)

2. Connect the verticesa) Click on Geometry à Click on EdgeàCreate Edgeb) Connect vertices

1. 1 and 22. 2 and 33. 3 and 44. 4 and 55. 5 and 66. 6 and 77. 7 and 88. 8 and 99. 9 and 1010. 10 and 1111. 11 and 1212. 12 and 1313. 13 and 1414. 14 and 1515. 15 and 1616. 8 and 1517. 7 and 16

48

18. 16 and 1719. 17 and 1820. 1 and 18

3. Connect straight edges to create a facea) Geometry à Face à Create Face from Wireframeb) Three faces will be created

1. Face left of plate – Connect edges 1 through 6, 17through 20

2. Face above plate – Connect edges 7, 15 through 173. Face left of plate – Connect edges 8 through 14, 16

4. Mesh edgesa) Mesh à Edge à Mesh edgesb) Edges are meshed in sets so the grid lines are straight horizontally and

vertically1. The following sets of edges are meshed identically

- Edges 1 and 3 are meshed the same- Edges 2, 11, 13, and 19 are meshed identically- Edges 4, 10, 14, and 18 (mesh is dense radially

toward the axis of rotation)- Edges 5, 9, 16, and 17 (mesh is dense toward plate)- Edges 6 and 20 (double sided grading)- Edges 7 and 15- Edges 8 and 12 (mesh is dense toward plate)

2. There should be no abrupt changes in mesh

5. Mesh Facea) Mesh à Face à Mesh Facesb) Mesh each face individually – grid lines will be horizontal and

vertical

6. Specify Boundary Conditionsa) Edges 1, 12 and 20 are boundary type, axisb) Edge 2 is the silane-inlet (velocity – inlet)c) Edge 3 is the nozzle (wall)d) Edges 4 through 8 are the air-inlet (pressure-inlet)e) Edges 9 through 11 are the outlet (pressure-outlet)f) Edges 13 through 15, 18 and 19 are the plate (wall)

7. Export the mesh

49

8. Commands in FLUENT are the same as before

Three – Dimensional Flow

Flow past a cylinder

The procedure to create the grid in Figures 36 and 37 was very different from theprocedure for the axisymmetric grids. The 3D grid was created with the top-downgeometry construction method in GAMBIT (creating a volume using solids). Also, thegrid was created by merging two separate grids to form a hybrid grid with anonconformal grid interface (such as the interface in Figure 37). This allows control ofmeshing around the nozzle.

Procedure to create the nozzle1. Geometry à Volume à Create Volume

a) Select Cylinder1. Enter dimensions (Height and radius of cylinder)2. Axis location is Positive Z (the default)

b) Select Brick1. Enter Dimensions (Height is same as the height for

cylinder, width and depth are larger than the cylinderradius)

2. Direction is +X +Y +Z

2. Want the intersection of the cylinder and the brick and leave onefourth of the nozzle (due to symmetry)

a) Geometry à Volume à Boolean Operations à Intersectb) Intersect cylinder with brick

3. Mesh Edgesa) Mesh à Mesh Edgesb) Edges directly across from each other have the same number

of intervals

4. Mesh Volumea) Mesh à Mesh Volumeb) Mesh Volume

5. Set Boundary Typesa) Curved surface is the nozzle (wall)b) The quarter circle in front is the silane-inlet (velocity-inlet)c) The quarter circle in back is the nozzle-interface (interface)

50

d) The vertical and horizontal rectangles are symmetry types inthe x-direction and y-direction (symmetry)

6. Export mesh (nozzle.msh)

Procedure to Create the Atmosphere with the cylinder

1. Geometry à Volume à Create Volumea) Select Cylinder

1. Enter dimensions (Height and radius of cylinder)2. Axis location is Positive Y (the default)

b) Select Brick1. Enter Dimensions (Height is the same as the height of

the cylinder)2. Axis location is +X +Y –Z

2. Translate the cylindera) Geometry à Volume à Move/Copy/Align Volumesb) Select the cylinderc) Translate is already set as the defaultd) Under Global enter a negative number in the box next to z to

translate volume (number is negative since the axis location is+X +Y -Z)

Note: Follow the cylinder’s center to translate the volume

3. Subtract the cylinder from the bricka) Geometry à Volume à Boolean Operations à Subtractb) Order is important here – Brick subtract cylinder

4. Apply boundary layer radially outward from cylindera) Mesh à Boundary Layer à Create Boundary Layerb) Select top and bottom of cylinderc) Fill in width of first layer (a), growth factor (b/a – ratio of

distances between consecutive rows), and the number of rows

5. Mesh Edgesa) Mesh à Mesh Edgesb) Vertical edges are meshed the same (nodes are concentrated

downward towards the nozzle)c) Mesh top and bottom edges between the nozzle and cylinder

with the double sided successive ratiod) Mesh top and bottom edges behind the nozzle with successive

ratio

51

e) The other edges will be meshed with the default values whenthe volume is meshed

7. Mesh Volumesa) Mesh à Mesh Volumesb) Select the volumec) Under spacing select interval count to mesh the rest of the

edgesd) Mesh the volume

8. Setting Boundary Typesa) Left face is the air-inlet interface (interface)b) Top and front faces are the air-inlet (pressure-inlet)c) Right face is the outlet (pressure-outlet)d) Bottom face is a symmetry face in the y-direction (symmetry)e) Back faces (either side of cylinder) are symmetry faces in the

x-direction (symmetry)f) Cylinder is a wall (wall)

9. Export Mesh (cylinder.msh)

10. Merge the two gridsa) At prompt type tgrid 3d (tgrid is the software that merges the

two different grids)b) Read both meshes (nozzle.msh and cylinder.msh)c) Zoom in around nozzle to make sure there is some overlap

between intervals on both sides of interface (see Figure 37)d) Write mesh file

The procedure for the 3D grid in FLUENT is also fairly different from the axisymmetricgrid

18. Import Mesh into FLUENTa) Type fluent 3d at promptb) File à Read à Case à filename.msh

19. Scale the grid (same as before)

20. Define the physics equationsa) Define à Models à Viscous – Select appropriate model

(realizable k-ε model under the k-ε model panel)b) Define à Models à Species – Select multiple species model

52

21. The species in the mixture must be specified (this is the same asbefore)

22. Define the grid interfacea) Define à Grid Interfaceb) In interface zone 1 select the smaller interface zone (nozzle

interface)c) In interface zone 2 select the other interface zone (air-inlet-

interface)d) Give it a name like junctione) Click Createf) FLUENT creates two new wall boundary zones

- Boundary zone 1 is the overlap region- Boundary zone 2 is the non-overlap region- FLUENT by default assigns boundary zone 2 with the

boundary type of wall (name is wall-# – this will bechanged when boundary conditions are assigned

23. Setting the Boundary Conditionsa) Define à Boundary Conditionsb) For the silane-inlet (velocity-inlet)

- Change velocity specification method to magnitudeand direction

- Change coordinate system to cylindrical- Radial direction should be 0 and axial direction should

be –1 (since grid is in the –Z direction)- Enter velocity magnitude- Enter turbulence specification method and parameters- Enter 1 for mass fraction of silane

c) For wall-# change the boundary type to pressure-inlet- Inlet conditions are same as inlet conditions for the

axisymmetric cased) For the air-inlet (pressure-inlet) and out

- The conditions are the same as the conditions for theaxisymmetric case

24. Initialize the solution (this is the same as the axisymmetric case)

25. Postprocessinga) To see the contours of volume fraction

- Display à Contours- Select contours of species and then select desired

species (mass fraction, mole fraction, etc)

53

- Use clip to range to set min and max contours- Select surfaces to display volume (recommended

surfaces are cylinder and lines of symmetry)b) To find volume between min and max concentrations

- Delete the grid interface: Define à Grid interface àSelect junction and click delete

- Adapt à Iso-value- Select Species and volume fraction, enter min and max

contours, click on mark- Grid à Separate Cells, under registers select the

register (cells just marked), select the cell zone to beseparated, click on separate (cell zone is split into twozones)

- Report à Volume integrals, select zone just created,click on calculate to calculate the volume of mixture.To calculate volume of source fluid in mixture selectspecies and volume fraction of silane and click oncalculate.

- Note volumes need to be multiplied by 4 since only ¼of the computational domain was modeled

54

VITA

Christina F. Sposato was born in Charleston, SC and grew up in Lincoln, NE. She

received a B.S. in Mathematics and Chemistry from the University of Nebraska –

Lincoln in May 1997. She spent one year studying undergraduate Chemical Engineering

at the University of Nebraska – Lincoln and joined Texas A & M University as a

graduate student in Chemical Engineering in September of 1998.

While attending the University of Nebraska, she worked as Mathematics Counselor for

the Mathematics Department’s Math Resource Center for two years. She also worked

for the Chemistry Department as a student assistant to a professor. She helped prepare

and conduct the workshop, Operation: Chemistry, which is a workshop to help

elementary school teachers introduce chemistry to young students. She also performed,

wrote, and edited several candidate laboratories for the new edition of the Chemistry 110

Lab Manual. Her last year at the University of Nebraska - Lincoln, she worked for the

USDA in the Soil Survey Laboratory. Her mailing address is 7155 S. 75th St., Lincoln,

NE 68516.

Documents

CHAPTER V JET FLOW PAST A CYLINDER - MKO …psc.tamu.edu/files/library/center-publications/theses-and...CHAPTER V JET FLOW PAST A CYLINDER ... Figure 35 shows a close-up of the non-conformal