Fossil-fuel fired boiler designers need to evaluate furnace wall temperature and heat flux, flue gas tem- perature, and furnace exit gas temperature. These pa- rameters are required to determine materials and their limits, and to size heat transfer surface.
An analytical solution for heat transfer in a steam generating furnace is extremely complex. It is not pos- sible to calculate furnace outlet temperatures by theo- retical methods alone. Nevertheless, this temperature must be correctly predicted because it determines the design of the superheater and other system components. In a boiler, all of the principal heat transfer mecha- nisms take place simultaneously. These mechanisms are intersolid radiation between suspended solid par- ticles, tubes, and refractory materials; nonluminous gas radiation from the products of combustion; con- vection from the gases to the furnace walls; and con- duction through ash deposits on tubes.
Fuel variation is significant. Pulverized coal, gas, oil or waste-fuel firing may be used. In addition, dif- ferent types of the same fuel also cause variations. Coal, for example, may be high volatile or low vola- tile, and may have high or low ash and moisture con- tents. The ash fusion temperature may also be high or low, and may vary considerably with the oxidizing properties of the furnace atmosphere.
Furnace geometry is complex. Variations occur in the burner locations and spacing, in the fuel bed size, in the ash deposition, in the type of cooling surface, in the furnace wall tube spacing, and in the arch and hopper arrangements. Flame shape and length also affect the distribution of radiation and heat absorp- tion in the furnace.
High intensity, high mixing burners produce bushy flames and promote large high temperature zones in the lower furnace. Lower intensity, controlled mixing burners frequently have longer flames that delay com- bustion while controlling pollutant formation.
Surface characteristics vary. The enclosing furnace walls may include any combination of fuel arrange- ments, refractory material, studded tubes, spaced tubes backed by refractory, close-spaced tubes, membrane con- struction or tube banks. Emissivities of these surfaces are different. The water-cooled surface may be covered with fluid slag or dry ash in any thickness, or it may be clean.
Temperature varies throughout the furnace. Fuel and air enter at relatively low temperatures, reach high temperatures during combustion, and cool again as the products of combustion lose heat to the furnace enclo- sure. All temperatures change with load, excess air, burner adjustment and other operating conditions.
Accurate estimates of furnace exit gas temperature are important. For example, high estimates may lead to over-estimating the heat transfer surface, while low estimates may cause operational problems. These are discussed in Chapter 19.
Empirical methods Considering the fuel type, fir- ing rate and furnace configuration, empirical meth- ods as illustrated in Fig. 31 have long been used to
predict local absorption rates in the furnace. These methods, although largely empirical, contain engi- neering models which are based on fundamentals. Data and operating experience are used to tune the models employed in the design envelope. Fig. 31 shows typical vertical and horizontal heat flux distributions for furnace walls.
Deviations in the heat flux distribution are caused by unbalanced firing, variations in tube surface condition, differences in slagging, load changes, sootblower opera- tion and other variations in unit operation. A typical upset heat flux distribution is shown in Fig. 31. These upset factors are typically a function of vertical/horizontal lo- cation, firing method and fuel, and furnace configura- tion. They are derived from operating experience.
The heat flux applied to the tubes in the furnace wall is also nonuniform in the circumferential direc- tion. As shown in Fig. 32, the membrane wall is ex- posed to the furnace on one side while the opposite side is typically insulated to minimize heat loss. The result- ing heat flux distribution depends upon the tube out- side diameter, wall thickness, and spacing, as well as the web thickness and materials. The fluid tempera- ture and inside heat transfer coefficient have second- ary effects. This distribution can be evaluated using commercially available computer codes.
To correlate data and calculations for different fur- naces, methods for comparing the relative effectiveness of different furnace wall surfaces are needed. The ef- fectiveness and spacing of tubes compared to a com- pletely water-cooled surface are shown in Fig. 33. A wall of flat-studded tubes is considered completely water- cooled. The effectiveness of expected ash covering, com- pared with completely water-cooled surfaces, can also be estimated. The entire furnace envelope can then be evaluated in terms of equivalent cold surface.
The heat energy supplied by the fuel and by the preheated combustion air, corrected for unburned com- bustible loss, radiation loss, and moisture from the fuel, may be combined into a single variable, known as heat
available. The heat available divided by the equiva-
lent flat projected furnace enclosure plus furnace Fig. 32 Typical circumferential heat flux distribution for a furnace
membrane wall panel tube.
Fig. 31 Typical vertical and horizontal heat flux distributions for
furnace walls.
Fig. 33 Furnace wall area effectiveness factor (1.0 for completely
water-cooled surface). A reduced area (equivalent cold surface) is determined from these curves for walls not completely water cooled. (Adapted from Hottel4.)
platen area is called the furnace heat release rate. The heat input from fuel divided by the furnace volume is called the furnace liberation rate. The furnace exit
plane defines the boundary of the furnace volume and
flat projected furnace enclosure area. The furnace exit plane area and back spacing between the furnace platen tubes are included in the flat projected area calculation. For furnace platens and membrane wall furnace enclosure, the effectiveness factor for all ex- amples given in this and other chapters is equal to 1.00. Furnace exit gas temperature (FEGT) is primarily a function of heat release rate rather than liberation rate. The furnace exit is commercially defined as be- ing located at the face of the first tube bank having a tube spacing of less than 15 in. (38.1 cm) side centers because, as can be inferred from Fig. 39, convection conductance typically becomes the predominant heat transfer mode at this side spacing. The furnace exit plane, generally used for the accurate calculation of overall heat transfer, is normally set at the face of the first tube bank having a tube spacing of 36 in. (91.4 cm) side centers or less in order to include the convec- tion conductance in the heat transfer calculations. At tube side centers of 36 in. (91.4 cm) or less, the convec- tion conductance is too significant to ignore as a portion of total heat transfer. The approximate relation of FEGT to heat release rate at the furnace exit plane for a typi- cal pulverized bituminous coal is given in Fig. 34.
Furnace exit gas temperatures and related heat absorption rates, as functions of furnace heat release rate for most pulverized coal-fired furnaces, lie within
the shaded bands shown in Figs. 35 and 36. The lim- its indicated serve only as a general guide and may vary due to combustion system type, burner and air port placement, stoichiometry, fuel characteristics and cleaning cycle. The bands for dry ash and for slag-tap furnaces overlap between 100,000 and 150,000 Btu/ h ft2 (315,460 to 473,190 W/m2), but different types of
coal are involved. To be suitable for a slag-tap furnace, a bituminous coal should have an ash viscosity of 250 poises at 2450F (1343C) or lower. In the overlapping range, dry ash and slag-tap both have about the same heat absorption rate, or dirtiness factor, as shown in Fig. 36. Both bands are rather broad, but they cover a wide range of ash characteristics and a considerable diversity in waterwall construction and dirtiness.
The heat leaving the furnace is calculated from the exiting gas flow rate (the gas enthalpy values evalu- ated at the furnace exit gas temperature) plus the net radiative transfer at the furnace exit. The heat ab- sorbed in the furnace is the difference between the heat available from the fuel, including the preheated combustion air, and heat leaving the furnace.
Numerical methods Empirical design methods are
gradually being supplemented with numerical meth- ods, as the level of detail increases and confidence is improved. Radiation heat transfer in furnace enclo- sures can now be solved on computers, in combina- tion with turbulent flow, energy, and combustion. Ra- diation properties of gases, particles, and fuel specific properties of ash deposits can be included in the analy- sis with more advanced engineering models and cor- relations. The effects of spectral radiation from gases and particles can also be included to improve accuracy of the analysis. Detailed results include the three-di- mensional distribution of radiation intensity, gas tem- perature, and heat flux on the furnace walls. Numeri-
Fig. 35 General range of furnace exit gas temperature for dry ash
and slag-tap pulverized coal-fired furnaces.
2600 (1427) 2200 (1204) 1800 (982) 1400 (760)
Furnace Exit Gas Temperature, F
(C)
100
(315)
Heat Release Rate, 1000 Btu/h ft2 (kW/m2)
200 (631) 300 (946) 400 (1262) 500 (1577) 0 3000 (1649) 3400 (1871) Slag-Tap Dry Ash
Fig. 34 Approximate relationship of furnace exit gas temperatures to
heat release rate for a typical pulverized bituminous coal.
2800 (1538) 2600 (1427) 2200 (1204) 2400 (1316) 2000 (1093) 1800 (982) 1600 (871) 1400 (760) 0 (-18)
Furnace Exit Gas Temperature, F
(C) 0 20 (63) 60 (189) 100 (315) 140 (442) 180 (568) 220 (694)
cal methods have the potential for more accurate pre- diction of heat flux distribution on furnace walls and convective surfaces. However, further validation of results and improvements in computational efficiency are needed to make numerical methods more practi- cal for routine engineering applications.
A numerical model was created for the furnace of a 560 MW supercritical steam pressure boiler firing high volatile eastern United States bituminous coal. A sche- matic of the furnace is shown in Fig. 37. The sloping furnace walls of the ash hopper, the furnace nose, and
the horizontal section of the convection pass were in- cluded in the model. Inlet fuel, inlet air and exit streams were properly located around the boundaries. An example of the predicted heat flux distribution is shown in Fig. 38. The predicted furnace exit gas tem- perature for this case was 2242F (1228C), while the observed average value was 2276F (1247C). Relative magnitudes of convective and radiative heat transfer at various locations are shown in Fig. 39 for a 650 MW boiler. The furnace area is dominated by radiation while the back-end heat transfer surfaces in the di- rection of flow are increasingly dominated by convection. Convection banks
Tube spacing and arrangement In addition to heat absorption and resistance to gas flow, other important factors must be considered in establishing the opti- mum tube spacing and arrangement for a convection surface. These are slagging or fouling of surfaces, ac- cessibility for cleaning, and space occupied. A large longitudinal spacing relative to the transverse spac- ing is usually undesirable because it increases the space requirement without improving performance. These are discussed further in Chapter 21.
Tube diameter For turbulent flow, the heat trans- fer coefficient is inversely proportional to a power of the tube diameter. In Equations 57 and 60 the expo- nent for longitudinal flow is 0.20; for cross flow it is 0.39. These equations indicate that the tube diameter should be minimized for the most effective heat trans- fer. However, this optimum tube diameter may require
Fig. 38 Numerical model – predicted furnace wall flat projected heat
flux distribution. (1 W/m2 = 0.317 Btu/h ft2) Fig. 37 560 MW utility boiler schematic used for numerical model
(see Fig. 38).
Fig. 36 General range of furnace heat absorption rates for dry ash
an arrangement that is expensive to fabricate, diffi- cult to install, or costly to maintain. A compromise between heat transfer effectiveness and manufactur- ing, erection, and service limitations is therefore nec- essary in selecting tube diameter.
Penetration of radiation A convection bank of tubes bordering a furnace or a cavity acts as a blackbody radiant heat absorber. Some of the impinging heat, however, radiates through the spaces between the tubes of the first row and may penetrate as far as the fourth row. The quantity of heat penetration can be established by geometric or analytical methods. The effect of this penetration is especially important in establishing tube temperatures for superheaters lo- cated close to a furnace or high temperature cavity. Consider 2.0 in. (50.8 mm) OD tubes placed in an ar- ray of tubes on a 6.0 in. (152.4 mm) pitch. Fig. 33, curve 1 can be used to estimate the remaining radia- tion. For a given radiant heat flux, 45% is absorbed in the first tube row, and 55% passes to the second row. 45% of this reduced amount is again absorbed in the second tube row. After the fourth row, less than 10% of the initial radiation remains.
Effect of lanes Lanes in tube banks, formed by the omission of rows of tubes, may decrease the heat ab- sorption considerably. These passages act as bypasses for flowing hot gases and radiation losses. Although the overall efficiency decreases, the high mass flow through the lanes increases the absorption rate of the adjacent tubes. Critical tube temperatures in super- heaters or steaming conditions in economizers may develop. Whenever possible, lanes should be avoided within tube banks and between tube banks and walls; however, this is not always possible. A calculation ac- counting for the lanes is necessary in such cases.
Heat transfer to water
Water heat transfer coefficient The heat transfer co- efficient for water in economizers is so much higher than the gas-side heat transfer coefficient that it can be neglected in determining economizer surface.
Boiling water heat transfer coefficient The combined gas-side heat transfer coefficient (convection plus
intertube radiation) seldom exceeds 30 Btu/h ft2 F (170
W/m2 K) in boiler design practice. The heat transfer
coefficient for boiling water [l0,000 Btu/h ft2 F (56,784
W/m2 K)] is so much larger that it is generally ne-
glected in calculating the resistance to heat flow, al- though Equation 4 in Chapter 5 can be used to calcu- late this value.
Effect of scale Water-side and steam-side scale de- posits provide high resistance to heat flow. As scale thickness increases, additional heat is required to maintain a given temperature inside a furnace tube. This leads to high metal temperatures and can cause tube failure. Deposition of scale and other contami- nants is prevented by good feedwater treatment and proper operating practices.
Heat transfer to steam In superheaters, the steam- side convection constitutes a significant resistance to heat flow. Although this resistance is much lower than the gas-side resistance, it can not be neglected in com- puting the overall heat flow resistance or the heat transfer rate. It is particularly significant in calculat- ing superheater tube temperatures, because the mean tube wall temperature is equal to the steam tempera- ture plus the temperature drop through the steam film plus half of the metal temperature drop.
The steam-side heat transfer coefficient is calculated from Equation 58 using information from Figs. 13, 16 and 17. If the steam heat transfer coefficient is desig- nated as h, the film temperature drop, ∆Tf, is q/(hA), using the outside surface area of the tube as the base in each expression.
It is imperative to prevent scale deposits in super- heater tubes. Because of its high resistance to heat flow and due to the elevated temperatures, even a thin layer of scale may be sufficient to overheat and fail a tube. Cavities
Cavities are necessary between tube banks of steam generating units for access, for sootblowers, and for possible surface addition. Hot flue gas radiates heat to the boundary surfaces while passing through the cavity. The factors involved in calculating heat trans- fer in cavities are as follows.
Temperature level Radiation from nonluminous
gases to boundary surfaces and radiation to the gas by the surroundings increase approximately by the fourth power of their respective absolute tempera- tures. Remembering that Eb = σ T4, Equations 39 and 40 illustrate this relationship.
Gas composition Carbon dioxide and water vapor
are the normal constituents of flue gases which emit nonluminous radiation in steam generating units. The concentrations of these constituents depend on the fuel burned and the amount of excess air.
Particles in the gas The particles carried by flue gases receive heat from the gas by radiation, convec- tion, and conduction, and emit heat by radiation to the furnace enclosure.
Size of cavity The heat transfer rate increases with cavity size. Thick layers of gas radiate more vigorously than thin layers. The shape of the cavity can also com- plicate heat transfer calculations.
Fig. 39 Comparison of radiative and convective heat transfer
contributions to absorption in various locations within a large utility boiler (SH = superheater; RH = reheater; 1 in. = 2.54 cm).
Surfaces in Zone 60 (189.3) 50 (157.7) 40 (126.1) 30 (94.6) 20 (63.1) 10 (31.5) 0
Heat Flux, 1000 Btu/h ft
2 (kW/m 2) 1 2 3 4 5 6 7 8 9 10 Convective Radiative 1 6 8 9 7 10 2 3 5 24 in. SH Platens Cavity 12 in. SH 9 in. RH Cavity 9 in. RH Cavity
48-54 in. Platens + Enclosure
Receiving surface A refractory surface forming part of a cavity boundary reaches a high temperature by convection and radiation from the flue gas. It also reradiates heat to the gas and to the other walls of the enclosure. Reradiation from a clean, heat-absorbing surface is small unless the receiving surface tempera- ture is high, as is the case with superheaters and reheaters. Ash or slag deposits on the tube reduce heat absorption and increase reradiation.
In boiler design, there are two significant effects of cavity radiation: 1) the temperature of flue gas drops, from several degrees up to 40F (22C), in passing across a cavity, and 2) gas radiation increases the heat ab- sorption rates for the tubes forming the cavity bound- aries. The second effect influences superheater tube temperatures and the selection of alloys.
Insulation
The calculation of heat transfer through insulation follows the principles outlined for conduction through a composite wall. Refer to Chapter 23 for more infor- mation regarding insulating materials.
Hot face temperature In a furnace with tube-to-tube walls, the hot face temperature of the insulation is the saturation temperature of the water in the tubes. If the inner face of the furnace wall is refractory, the hot face in- sulation temperature must be calculated using radiation and convection heat transfer principles on the gas side of the furnace wall, or estimated using empirical data.
Heat loss and cold face temperature The heat loss to the surroundings and the cold face temperature de- crease as the insulation thickness increases. However, once an acceptable layer of insulation is applied, ad- ditional amounts are not cost effective. Standard com- mercial insulation thicknesses should be used in the composite wall.
The detailed calculation of overall heat loss by ra- diation and convection from the surfaces of a steam generating unit (usually called radiation loss) is te- dious and time consuming. A simple approximate method is provided by the chart prepared from the American Boiler Manufacturers Association (ABMA) original. (See Chapter 23, Fig. 12.)
Ambient air conditions Low ambient air tempera- ture and high air velocities reduce the cold face tem- perature. However, they have only a small effect on total heat loss, because surface film resistance is a