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PRESENTATION WITH SLIDE NUMBERS INDICATED

SINGLE POINT FLOW CALCULATIONS FOR LIQUEFIEDCOMPRESSED GAS FIRE FX TI NG UI SH IN G AC;_EKTS

by Tom WysockiGuardian Services,

Inc

HISTORY Whether the agent is water, dry chemical, inert gas or a liquefiedcompressed gas, engineered system design demands that we deliver a specifiedquantity of agent to the fire zone in a specified time. The science of hydraulicsenables us to predict the flow of substances in networks of pipe and nozzles.Predicting the flow of liquefied compressed gases used for special fire fightingapplications present a unique challenge.

The liquefied compressed gas which has had the longest history of continuous usefor fire suppression is carbon dioxide. The NFPA Standard 12 on Carbon Dioxidesystems gives a method of calculating flow of COz based on the doctoral

dissertation of Dr. James Hesson. This same basic methodology was adapted byMr. Vic Williamson and later refined by the author to predict flow parameters forHalon 1301. In 1977, the WilliamsonlHesson two-phase flow methodology wasrecognized in NFPA 12A, the Standard on Halon 1301 Systems.

During the 1970s and 1980s, numerous laboratory and countless field testsshowed the WilliamsonlHesson method of predicting Halon 1301 flow to besufficiently accurate to design Halon 1301 pipe and nozzle systems. Nonethelessthere has been considerable debate over the validity of the approach. As with mostevery mathematical model of physical reality, there are limits which must berecognized.

The approach has been successfully applied to predict flow of Halon 1301, carbondioxide, HFC227ea, and HFC23. In this paper, we will review the flow theory forliquefied compressed gases. We will also present the enhancements which mustbe incorporated in order to use the WilliamsonlHesson method for complex pipenetworks.

FLOWEQUATIONS

Bernoullis equation is a fundamental equation of hydrodynamics.statement of this equation is that the sum of any changes in pressurehead, velocity head, friction head and elevation head in a system is zero

assuming no heat input or loss from the system. In its basic form, thisequation can calculate hydraulic parameters for substances whose density isessentially constant with changes inpressure -- in other words, for non-compressible flow.

A qualitative

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H

144P z+- -

P

2g

Figure 1Bernoullis Equation

Hessons adaptation of Bernoullis equation permits calculations for substanceswhose density changes with changing pressure.

Both of these equations relating pressure, flow rate, pipe diameter, and pipe lengthreauire knowledge of the densitv of the flowing media as a function of the pressurein the pipe.

LIQUEFIED COMPRESSED GAS DISCHARGE

Liquefied compressed gases exhibit the characteristics of compressible flow. Inother words, the density of the agent changes considerably as the pressure in thepipeline decreases. These agents also exhibit two-phase flow in that the flowingagent is comprised of a mixture of liquid and vapor.

One of the major problems inpredicting pressure drop and flow rate insuch asystem is deriving an accurate relation between agent density and pressure.Depending on the degree of accuracy needed for the type of fire suppression

system, a more or less rigorous approach will be required to calculate the pressure-density relationship.

For high pressure carbon dioxide system work, the pressure in the storagecontainer is set to 750 PSI. Density as a function of pressure is calculated byassuming that the carbon dioxide liquidwill expand from a saturated conditionat750 PSI with the enthalpy held constant.

This approach provides the required degree of accuracy for calculating flow ratesand system pressures for C02. For large complex carbon dioxide systems,transient conditions at the start and end of discharge may also need to beconsidered.

Halon system work and Halon alternative system work generally require muchgreater accuracy. We are working toward quite accurate predictions of the amountof agent which will be discharged from individual nozzles ina system. ANSIStandard limits require we predict the quantity per nozzle to within -5% and +IO%.Discharge times may vary by no more than 1second predictedto actual.

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To start out our calculation of density as a function of pressure, we first considerthe discharge of the agent from the storage container. We assume that the agentleaves the storage container as pure liquid with appropriate amounts of nitrogen insolution. We assume constant entropy conditions as each increment of liquidleaves the storage container. Pressure recession curves such as those shown forFE13 HFC23) or FM200 HFC227ea) may be calculated.

FE13 PRESSURE RECESSION IN CYLINDER ASSUMINGCONSTANT ENTROPY

625

600

575

550%

w 525

500

K

I)

475

a 450

425

400

0 10 20 30 40 50 60 70 80 90 100PERCENT DISCHARGED

[ -30 Ib/cu ft. *40 Ib/cu.ft.t

49 b./cu. f t .I

Here we see a theoretical cylinder pressure recession based on constant entropycondition for FE 13 HFC23) discharge. Cylinder fill density affects the recession.Filldensities of 30, 40 and 49 pounds per cubic foot are shown.

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NITROGEN SUPERPRESSURIZEDFM200CYLINDER PRESSURE RECESSION CONSTANT ENTROPY

400

350

a

300

250

-

v

W

150

Tj 200

E

100

50

0

0 0.2 0.4 0.6 0.8 1

FRACTION DISCHARGED1

-

70 LB./CU.FT.4-60 LB./CU. FT.0

50 LB./CU.FT. +40 LB./CU. FT.1

Here we see similar theoretical curves for FM200 superpressurized with nitrogen.

HFC227ea (FM200) DISCHARGE TEST I

70 LB/CU FT FILL DENSITY

400

350

5 250g

300

W

Tj 200

100

3 150

a50

0

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3

TIME (SEC)

-CYLINDER NO2 1

This pressure versus t ime tracing taken during a FM200 discharge shows thecontinual variation in cylinder pressure and a lesser variation in pressure at the

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nozzleduring the course of discharge. The peak in the nozzle pressure trace at 9.6seconds indicates a change from two-phase flow to vapor flow.

Both the theoretical and experimental data indicate that pressure in the storagecylinder will vary considerably from the start of discharge until the end. Two basicapproaches were considered and tested for calculating the essential hydraulicparameters of flow rate and pressure drop. One approach is to do multiplecalculations for increments of agent leaving the cylinder. Any number ofincrements could be chosen -- for example, a calculation could be done for each10% increment to leave the cylinder. The other approach is to work toward anaverage condition during the discharge and do a single calculation based on theaverage condition.

Intuitively one would expect that doing multiple calculations for increments leavingthe cylinder would yield more accurate results. This is true for relatively simplesystems - yet for simple systems, the accuracy achieved by doing a singlecalculation is extremely good -- much better than that required by the ANSI

standard. For complex systems, involving unbalanced flow splits at tees, adifficulty with any theoretical approach surfaces -- and this difficulty obviates anyadvantage in the accuracy which might be gained by the multiple incrementapproach.

PIPELINE PRESSURE AND AGENT DENSITY In determining a single pointin the discharge which approximates an overall average condition offlow,consider that in a well designed system the conditions at the discharge nozzle willcontrol the agent flow rate. A good average condition would be approximated bythe mid discharge condition at the nozzles. Neglecting initial transient conditions,the mid discharge condition will be the point in time at which of the agent has

been discharged from the nozzle.

The reference point on the cylinder pressure recession curve for the mid dischargecondition will vary depending on the amount of agent which the pipeline contains.

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400

350

300

a 250

{ 150

100

50

0

-

u

f: 200

FM200 CYLINDER PRESSURE RECESSION70 LBlCU FT FILLDENSITY

0 10% 20% 30% 40 50 60% 70% 80 90 100

PERCENT DISCHARGED FROM CYLINDER

If the discharge nozzle is close coupled to the storage cylinder outlet, the pipe willhold zeroagent during discharge. 50% of the agent will have left the nozzlebasically when 50% of the agent leave the cylinder. This graph shows mid

discharge storage cylinder pressure for such an arrangement..

FM200 CYLINDER PRESSURE RECESSION 70 LBlCU FT FILLDENSITY

400

350

-3004v

W

250

5

200

I00

150

50

0

\

MID-DISCHARGE

PRESSUREIN -

0% 20% 40% 60 00% 100%

PERCENT DISCHARGED FROM CYLINDER

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Most often there will be considerable pipe between the cylinder outlet and thedischarge nozzles. The graph shows the middischargecondition for a systemwhere the pipeline holds 20% by weightof the agent under flowing conditions. 50%will have left the nozzle at the point in time when 70% of the agent has left thestorage container.

PIPELINE DENSITY

For very rapid discharges and relatively short pipelines, heat exchange betweenthe flowing agent and the pipe is usually negligible. An exception might be theinitial increment of cold liquid flowing into a relatively warm pipe. The initialincrements are offen vaporized before they reach the discharge nozzle. Once theinitial flow of agent has cooled the pipe, relatively little heat will be exchangedbetween the agent and its surroundings. For purposes of calculating density as afunction of pressure in the pipe, we can assume no heat exchange or a constantenthalpy condition of the saturated agent.

PIPELINE DENSITY VS PRESSURENITROGEN SUPERPRESSURIZED

FM200 60 LBKU FT FILL DENSITY

- 100

t

80Q

m60

2

40

20

0

W

250 200 150 100 50 0

PRESSURE (PSIA)

1-0% +27 -47 ]

The graph shows theoretical agent densities in the pipe for FM200 (HFC227ea)

based on constant enthalpy conditions. The calculation is shown for systemscontaining 0%(close coupled nozzle cylinder), 27% and 47% of the agent in thepipe.

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CORRELATIONOF PRESSURE DROP CALCULATION WITH EXPERIMENT

PRESSURE DROP VERIFICATIONHFC227ea (FM200)

180

160

- 1403

rz 120e

w

100

80

60

a 40

20

0

[L

v

0 10 20 30 40 50 60

EQUIVALENT LENGTH (FEET)

I-CALCULATED PRESSURE TEST IPRESSURE- .TEST 2 PRESSURE..

Experimental verification of the pressure drop predicted using the constant enthalpyassumption for density has been done for many agents. The figure shows the

results fortwo

test done withFE13. The system consistedof 60 equivalent feet ofXpipe. Agreement of calculated and experimentally measured pressure anddischarge time was excellent. The ANSI Standard which United States approvaland testing laboratories apply to such flow calculations requires that predictednozzle pressures be within 10%of measured nozzle pressures at the specifieddesign reference point. Test results for single nozzle and balanced systemstypically agree to within5% for the liquefied compressed gases tested.

ADDITIONAL THEORETICAL CONSIDERATIONS The example we have seen is

typical of the correlation between calculated and predicted pressures for singlenozzle systems. More

comdex

svstems can be accurately calculated with

additional theoretical considerations. The following must be considered:

Flow regime - turbulent, laminar, transition zone flow

Velocity changes

Transient conditions

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TURBULENCE When using the WilliamsonlHesson method for pressure dropcalculation, it is important to maintain flow densities which will result in a fullyturbulent mixture of the liquid and vapor phases of the agent as it flows through thepipe. The Moody friction factor varies with Reynolds number until flow reaches afully turbulent state. For flow densities above the fully turbulent threshold, the

Moody friction factor becomes a constant.

Although it is possible to vary the friction factor in the calculation with Reynoldsnumber, there are a number of practical difficulties in system performance whichoccur at low flow densities. The major difficulty is unpredictable liquid-vapor phaseseparation when flow splits at tee junctions.

FE13 MINIMUMFLOW RATE FOR COMPLETE TURBULENCE

1

I

I

0

0 1 2 3 4 5 6

INTERNAL PIPE DIAMETER (INCHES)

The graph shows theoretical minimum flow rates for FE13 to give completeturbulence.

VELOCITY CHANGES Conversions of energy between static pressure head andvelocity head must be calculated when flow density (Ibs./sec./cross sectional area

of pipe) changes.

TRANSIENTS Transient effects such as compensation for initial heat entry into theagent and time delays for the agent to travel from cylinder outlet to various nozzlesin the system must be considered. If systems are unbalanced, additionalconsiderations must be made for transient conditions which occurs as the last

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increment of liquid agent leaves the cylinder and the trailing vapor expands into thepipe. All of these considerations can be made on the basis of standardthermodynamic and hydraulic theory. All of these consideration must likewise bedone if a multiple increment approach to pressure drop calculation is used.

MECHANICAL EFFECTS A phenomenon which has been noted for variousmulti-

phase flow regimes is that of mechanical separation of phases which occurs whenflow changes direction. As a mixture of heavier particles or liquid drops and lightervapor moves into a bend ina pipe, the heavy particles because of their greaterinertia tend to continue in a straight line toward the outer radius of the bend.

Assuming turbulent flow and that the flow stream is not split near the outlet of thebend, any phase separation quickly is eliminated and the density of the flowingmixture behaves essentially as predicted by thermodynamics.

Mechanical Effects on Density

Flow direction

33

Although this potential was recognized as a possibility for agents such asC 0 2

compensation for the effect was not considered necessary. In 1973, Williamsonand Wysocki documented the effect for Halon

1301.

They developed empiricalcorrections to produce more accurate calculations of pressure drop and quantity ofagent discharged from nozzles.

In recent work on unbalanced system calculations with HFC227ea, the effect wasagain noted.

When liquid and vapor mechanically separate at a tee junction, the density justdownstream of the tee departs from the density predicted by thermodynamics. Allpressure drop and flow downstream of the tee is affected by this density change.

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BULLHEAD TEEMechanical Effects on Density

Greater flow rate

Flow direction

Liquid droplet

35

For a bull head tee configuration more liquid tends to flow into the outlet branchcarrying the lesser flow rate.

125%

120%

115%

flow gases

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