30079_45b.pdf

Fig. 45.31 Gas radiation (Hr) and convection (Hc) coefficients for flue gas inside radiant tubes.1

perature. The gas radiation factor depends on temperature and inside diameter. The effect of flame

luminosity has not been considered.

45.9 FLUID FLOW

Fluid flow problems of interest to the furnace engineer include the resistance to flow of air or flue

gas, over a range of temperatures and densities through furnace ductwork, stacks and flues, or re-

cuperators and regenerators. Flow of combustion air and fuel gas through distribution piping and

burners will also be considered. Liquid flow, of water and fuel oil, must also be evaluated in some

furnace designs but will not be treated in this chapter.

To avoid errors resulting from gas density at temperature, velocities will be expressed as mass

velocities in units of G = Ib/hr • ft2. Because the low pressure differentials in systems for flow of

air or flue gas are usually measured with a manometer, in units of inches of water column (in. H2O),

that will be the unit used in the following discussion.

The relation of velocity head hv in in. H2O to mass velocity G is shown for a range of temperatures

in Fig. 45.32. Pressure drops as multiples of hv are shown, for some configurations used in furnace

design, in Figs. 45.33 and 45.34. The loss for flow across tube banks, in multiples of the velocity

head, is shown in Fig. 45.35 as a function of the Reynolds number.

The Reynolds number Re is a dimensionless factor in fluid flow defined as Re = DGI jx, where

D is inside diameter or equivalent dimension in feet, G is mass velocity as defined above, and JJL is

viscosity as shown in Fig. 45.9. Values for Re for air or flue gas, in the range of interest, are shown

in Fig. 45.36. Pressure drop for flow through long tubes is shown in Fig. 45.37 for a range of Reynolds

numbers and equivalent diameters.

45.9.1 Preferred Velocities

Mass velocities used in contemporary furnace design are intended to provide an optimum balance

between construction costs and operating costs for power and fuel; some values are listed on the next

page:

Fig. 45.32 Heat loss for flow of air or flue gas across tube banks at atmospheric pressure (ve-

locity head) x F x R

Velocity Head

Medium

Mass Velocity G

(in. H2O)

Cold air

15,000

0.7

800°F air

10,000

0.3

2200°F flue gas

1,750

0.05

1500°F flue gas

2,000

0.05

The use of these factors will not necessarily provide an optimum cost balance. Consider a furnace

stack of self-supporting steel construction, lined with 6 in. of gunned insulation. For G = 2000 and

hv = 0.05 at 1500°F, an inside diameter of 12 ft will provide a flow of 226,195 Ib/hr. To provide a

net draft of 1 in. H2O with stack losses of about 1.75 hv or 0.0875 in., the effective height from Fig.

45.38 is about 102 ft. By doubling the velocity head to 0.10 in. H2O, G at 1500°F becomes 3000.

For the same mass flow, the inside diameter is reduced to 9.8 ft. The pressure drop through the stack

increases to about 0.175 in., and the height required to provide a net draft of 1 in. increases to about

110 ft. The outside diameter area of the stack is reduced from 4166 ft2 to 11 X 3.1416 x 110 =

3801 ft2. If the cost per square foot of outside surface is the same for both cases, the use of a higher

stack velocity will save construction costs. It is accordingly recommended that specific furnace de-

signs receive a more careful analysis before selecting optimum mass velocities.

Stack draft, at ambient atmospheric temperature of 70°F, is shown in Fig. 45.38 as a function of

flue gas temperature. Where greater drafts are desirable with a limited height of stack, a jet-type

stack can be used to convert the momentum of a cold air jet into stack draft. Performance data are

available from manufacturers.

45.9.2 Centrifugal Fan Characteristics

Performance characteristics for three types of centrifugal fans are shown in Fig. 45.39. More exact

data are available from fan manufacturers. Note that the backward curved blade has the advantage

Fig. 45.33 Pressure drop in velocity heads for flow of air or flue gas through entrance configu-

rations or expansion sections.1

of limited horsepower demand with reduced back pressure and increasing volume, and can be used

where system resistance is unpredictable. The operating point on the pressure-volume curve is de-

termined by the increase of duct resistance with flow, matched against the reduced outlet pressure,

as shown in the upper curve.

45.9.3 Laminar and Turbulent Flows

The laminar flow of a fluid over a boundary surface is a shearing process, with velocity varying from

zero at the wall to a maximum at the center of cross section or the center of the top surface for

liquids in an open channel. Above a critical Reynolds number, between 2000 and 3000 in most cases,

flow becomes a rolling action with a uniform velocity extending almost to the walls of the duct, and

is identified as turbulent flow.

With turbulent flow the pressure drop is proportional to D; the flow in a large duct can be

converted from turbulent to laminar by dividing the cross-sectional area into a number of parallel

channels. If flow extends beyond the termination of these channels, the conversion from laminar to

turbulent flow will occur over some distance in the direction of flow.

Radial mixing with laminar flow is by the process of diffusion, which is the mixing effect that

occurs in a chamber filled with two different gases separated by a partition after the partition is

removed. Delayed mixing and high luminosity in the combustion of hydrocarbon gases can be ac-

Head loss through orifice

Velocity heads at diameter D

Head loss in pipe or duct elbows

Proportioning Piping for uniform distribution

Total pressure = static pressure + velocity head

Area at D should exceed 2.5 X combined areas of A, B, and C

Fig. 45.34 Pressure drop in velocity heads for flow of air or flue gas through orifices, elbows,

and lateral outlets.1

Staggered Tubes

Tubes in Line

Factor F for x/D

x/D Factor F y/D 1.5

1.5

2.00 1.25 1.184 0.576 0.334 0.268

1.47 1.5 1.266 0.656 0.387 0.307

1.22 2

1.452 0.816 0.497 0.390

1.14 3

1.855 1.136 0.725 0.572

2.273 1.456 0.957 0.761

complished by "diffusion combustion," in which air and fuel enter the combustion chamber in parallel

streams at equal and low velocity.

45.10 BURNER AND CONTROL EQUIPMENT

With increasing costs of fuel and power, the fraction of furnace construction and maintenance costs

represented by burner and control equipment can be correspondingly increased. Burner designs should

be selected for better control of flame pattern over a wider range of turndown and for complete

combustion with a minimum excess air ratio over that range.

Furnace functions to be controlled, manually or automatically, include temperature, internal pres-

sure, fuel/air ratio, and adjustment of firing rate to anticipated load changes. For intermittent oper-

ation, or for a wide variation in required heating capacity, computer control may be justified to

Staggered tubes Tubes in line

Fig. 45.35 Pressure drop factors for flow of air or flue gas through tube banks.1

Staggered Tubes

Tubes in Line

Factor F for x/D

x/D Factor F y/D 1.5

1.5

2.00

1.25 1.184 0.576 0.334 0.268

1.47

1.5 1.266 0.656 0.387 0.307

1.22

1.452 0.816 0.497 0.390

1.14

1.855 1.136 0.725 0.572

2.273 1.456 0.957 0.761

anticipate required changes in temperature setting and firing rates, particularly in consecutive zones

of continuous furnaces.

45.10.1 Burner Types

Burners for gas fuels will be selected for the desired degree of premixing of air and fuel, to control

flame pattern, and for the type of flame pattern, compact and directional, diffuse or flat flame coverage

of adjacent wall area. Burners for oil fuels, in addition, will need provision for atomization of fuel

oil over the desired range of firing rates.

The simplest type of gas burner comprises an opening in a furnace wall, through which combus-

tion air is drawn by furnace draft, and a pipe nozzle to introduce fuel gas through that opening.

Flame pattern will be controlled by gas velocity at the nozzle and by excess air ratio. Fuel/air ratio

will be manually controlled for flame appearance by the judgment of the operator, possibly supple-

mented by continuous or periodic flue gas analysis. In regenerative furnaces, with firing ports serving

alternately as exhaust flues, the open pipe burner may be the only practical arrangement.

For one-way fired furnaces, with burner port areas and combustion air velocities subject to control,

fuel/air ratio control can be made automatic over a limited range of turndown with several systems,

including:

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