Zone Method_furnce.pdf

APPLICATION OF RADIATIVE ZONE METHOD IN MODELING OF HEAT TRANSFER IN A BOILER FURNACE Mohammad Hadi Bordbar Timo Hyppänen Department of Energy and Environmental Technology, P.O.Box 20, FIN-53851 Lappeenranta University of Technology, Lappeenranta, Finland [email protected]

Abstract: Radiative heat transfer in the freeboard of large pulverized fuel utility boilers was analyzed by applying one of the most accurate radiation models, the zone method of analysis, to the prediction of incident radiative heat fluxes on the furnace walls. Modeling the cooling water tubes in the freeboard was quite challenging and using this method for unstructured mesh was leading to computationally demanding calculations. By using this model, the behavior of temperature and heat flux within the furnace and on the heat surfaces has been investigated. The velocity field of the combusted fuel from burner has been modeled by using the existing formula for the velocity field of turbulent jet exit from the burner orifice. The accuracy of the method was tested by comparing its predictions with experimental measured radiative fluxes on the walls. The final aim of the study was to find the needed changes in boiler’s burners and load in order to change fuel quality from Mazut to Methane without any damages in heat surfaces. By comparing the results of our simulation for methane-state with experimental results for Mazut state, we found that for preventing any damage in heat surfaces due to aforementioned fuel changes, the load of the boilers should be decreased by 12%. By this fuel changing, the efficiency of the boiler will increase and the boiler will work with a cleaner fuel. Keywords: Boiler modeling, Zone method, Fuel changing, Green Energy.

1 INTRODUCTION In recent years, many researches have been done in the field of the performance optimization of large power plant boilers. The main aims have been at extending the boiler’s lifetime, increasing the thermal efficiency and reducing the pollutant emissions in the boilers. A good design of the furnace, as the most important part in energy conversion process in the boilers, has a key role in achieving aforementioned targets. A Furnace is the space that the fuel can burn over there and the chemical energy is converted into heat to be transferred into the water walls of steam boilers. The temperatures in the pulverized fuel furnaces are high enough that the radiation becomes the most important mechanism in heat transfer. Due to complexity of radiation mechanism and its dependence to enclosure’s geometry, the analytical solution does not exist except for very simple problems. This fact along with expensive

experimental modeling leads researchers to develop numerical models for analyzing these enclosures. The most usual numerical methods for analyzing the radiative spaces are Monte-Carlo method, heat flux method and zone method. Indeed, by using these methods the radiative heat transfer in an absorbing, emitting, scattering medium can be analysed. In this article, the zone method has been employed for predicting temperature and heat flux on the water walls of steam boiler’s furnace. Hottel and Cohen have created this model first time in 1935 for analyzing the radiation heat transfer in an enclosure containing gray gas with certain properties. Later, Hottel and Sarofim in 1967 used this method for more complex geometries. Since that time, this model has been widely used by researchers for modeling the industrial radiative enclosures such as boiler’s furnaces (Diez et al. 2004; Batu and Selcuk 2001).

In this research, zone method was employed for predicting heat flux on the side walls of enclosures and temperature distribution within the furnace. In this method, whole space of the furnace is split into zones and the enclosure’s walls are divided into some finite surface parts (zones). The main assumption is using an existing uniform temperature and properties within the volume and surface zones. After dividing the space and surfaces to finite zones, by using the existing flow pattern and combustion model, the rate of mass transfer from/to each volume zone to/from other neighboring zones, the amount of combusted fuel, and convection coefficient (in the volume zone that have at least one neighbor surface zone) will be obtained. By writing energy balance equation for all surface and volume zones in steady state, we will end up to nonlinear equations system for temperature field on volume and surface zones. By solving this nonlinear equations system, we can find temperature distribution, heat flux on heat surfaces and total value of radiation heat transfer between the zones. For pulverized fuel utility boilers, we can assume the flow of combusted material as a free jet that exit from an orifice. By using, experimental formulas that describe free jet from orifice we will end up to velocity field of gas within the furnace that will be used for driving energy balance equations for zones. The updating existing furnace in the way that they can work with more efficient and cleaner fuel is very important for industry. The furnace that is modeled with zone method was originally fired with Mazut as the fuel. This fuel produced high level of pollutions, so the final target of this research was to find a good approximation for changing the boiler performance in a way that the furnace can work with methane as a main fuel without any damages in heat surfaces. The result of this research will be useful for investigating the heat transfer of boilers when fuel properties are changed. The validity of this model has been addressed by comparing the result of simulation for Mazut with experimental data that are reported by manufacturing company. By using this valid model for new fuel, the amount of heat flux and temperature on the furnace’s walls has been investigated. This result will be useful for designing the new operation range of a boiler, burners and the whole power plant. In section 2, calculation of radiative heat transfer between zones by zone method will be explained. A new method for calculating direct exchange area between zones - that have main role in amount of radiation between the zones - will be explained in this section. The experimental formulas that were used for investigating flow pattern and their result will be reported in section 3. In section 4, the energy balance equation for volume and surface zone will be explained. In section 5, the simplified model that was used for simulating our boiler’s furnace will be interpreted. In section 6, the result of our model will be explained. The conclusions and remark points of this research will be presented in the last section.

2 RADIATIVE HEAT TRANSFER BETWEEN LARGE ZONES The heat transfer between a pair of zones depends on coefficients that are called heat flux area. For example, the amount of heat transfer between a volume zone (i) and surface zone (j) will be: → ← Qi € j = Gi S j Eg ,i − Gi S j E j (1) → ← Where Gi S j and Gi S j are heat flux area between

volume zone i and surface zone j, Eg , i is black emissive power of gas and E j is black emissive power of surface. In the same way, we can write following equations for radiative heat transfer between surface-surface zones and volume-volume zones, respectively: → ← Qi € j = Si S j Ei − Si S j E j → ← Qi € j = GiG j Eg ,i − GiG j Eg , j

(2)

(3) Recall that the radiative emissive power of each zone depends to temperature (e.g. Ei = σ T 4 ; where σ is the Stephan-Boltzman constant). The directed flux area is calculated from some other coefficient which are called total exchange area, and this coefficient also can be calculated from other coefficient has been called directed exchange area. In table 1 the symbols that are used for representing this kind of coefficient, and the parameter that has effect on these coefficients has been shown. Table 1 The important coefficients in radiation calculation in zone method. Name of Symbol Effective parameters Coefficient Directed si s j , gi s j , Enclosure’s geometry, Exchange Absorption coefficient gi g j , Area of gray gas Total Exchange Area

GiG j

Directed Flux Area

Si S j , Gi S j ,

Si S j , Gi S j , Enclosure’s geometry,

→

→

→

GiG j

Absorption coefficient of gray gas,surface emissivity coefficient Enclosure’s geometry, Absorption coefficient of gray gas,surface emissivity coefficient, Temperature of redatiobn source

The directed exchange area coefficients can be calculated according to following expressions: cosθi cos θ j exp(− krij )

si s j = ∫ ∫ A A i

j

gi s j = ∫ ∫ A V j

i

π rij2 k cos θ j exp(-krij )

π rij2

dAi dA j

dVi dA j

(4)

(5)

gi g j = ∫ ∫ VV i

k 2 exp(-krij )

π rij2

j

(6)

dV j dAi

n

In these equations, rij is the size of the vector that connects center of two elements to each other, θ i and θ j are the angle between the normal vector of surface elements and aforementioned vector, and k is emissivity coefficient of gas. The order of these integrals is so high that analytical solutions for them are not possible except of some simple states, so for calculating them we employed some mathematical technique we decrease the order of integrals in a way that they can be calculated by numerical method. For example for surface-surface zones and for parallel zones, if we assume the (0, 0, 0) and (a, b, c) as the coordinates of two point of these zones, we can change the equation 4 to the expression: ( si s j ) B2

c2 = π

1

∫ ∫

dx dy × (1 − x)(1 − y )   0 0

where f ( x, y ) = and

1

e

− k g B rij

rij4

gray gases. In this method, the following expression is considered for emissive coefficient of real gas:

∑

f ( ± x, ± y )   12

,

(7)

∑ f ( ± x, ± y ) = f ( x, y ) + f ( − x, y ) + f ( x, − y ) + f ( − x, − y )

In this equation B represents characteristic length of gray gas. Therefore by using this technique, the order of integral will decrease and the numerical calculations will be much easier and more accurate. This technique has also been used for other state of surface-surface zones and surface-volume and volume-volume zones. During calculation of directed exchange area for some elements we will be exposed to singularity points for solving this kind of problem we separate the integrals into two separate parts, the first part consist of singular points which has been solved by analytical techniques and second one was an integral without singular points which was solved by numerical method. Between several formulations of Simpson method for calculating integrals numerically, the Simpson 1/3 has been chosen because of its simplicity and generality. For verifying validity of directed exchange area values, we used the analytically calculated value that was reported for a simple case (Hotel and Sarofim, 1967). By using the aforementioned methods and techniques the values of directed exchange area has been calculated numerically for different possible states (singularity), the calculated values showed very good conformity with aforementioned reference values. After calculating directed exchange area, the total exchange area can be calculated from these values by using the method that Hotel and Cohen reported in 1935. We know that that the main products of combustion ( H 2O, CO2 )are not gray gases and by using gray gas assumption for them the large amount of error will enter to our calculation, but the exponent form of gray gas emission behavior can be good form for modeling real gas(combustion product). Therefore, a famous method for modeling the radiation behavior of real gas is weight summation of

∑a

g ,i (1 − exp(ki PL )

(8)

i =0

Where k , P and L represents the emissivity, partial pressure and effective path length of the gray gases, respectively. Term i = 0 is related to limpid gas. By using the method that described in (Viskanta and Mengae 1987) and by considering the water vapor and CO2 and a limpid gas as the main products of combustion the coefficients of ag ,i has been calculated for several states of partial pressures. These coefficients employed for calculating directed flux area from total exchange area by the following expression, for surface-surface zones: →

N

Si S j = ∑ a s,n (Ti ) SiS j   k = k n =1

←

and rij =  ( x + a ) + ( y + b)2 + c 2    2

εg =

n

(9)

N

Si S j = ∑ a s,n (Tj ) SiS j   k = k n =1

n

For surface-Volume zones: →

N

Gi S j = ∑ a g,n (Tg,i )  G iS j    k=k n =1

←

n

(10)

N

Gi S j = ∑ a s,n (T j )  G iS j   k=k n =1

n

For volume-volume zones: →

N

GiG j = ∑ a g,n (Tg,i ) G iG j   k = k n =1

(11) n

3 VELOCITY FIELD WITHIN THE FURNACE For calculating the convective heat transfer term in energy balances in surface zone we need to have velocity field within the furnace. In this order, we calculated velocity field within the furnace by some experimental formula. Almost all industrial flames are in the form of turbulent jet that exit from burner’s orifice. By defining an equivalence diameter for nonisothermal condition, velocity distribution and inlet mass from around to jet can be calculated from following equations (Beer, 1972): d e = do (Ts To )1 2

(13)

6.4 U = exp( −82( y x ) 2 ) U o ( x de )

(14)

m& e m& o = 0.32 ( x d e )

(15) Where d e is equivalence diameter , x, y is position of calculated point related to center of orifice , do is orifice diameter Ts is temperature of calculated point, To is inlet temperature, U is axial velocity in calculated point, U o is axial velocity in orifice, m& o is inlet mass and m& e is the mass that enter to jet region from neighbor regions.

4 ENERGY BALANCE EQUATIONS IN SURFACE AND VOLUME ZONES For every surface zone (s), energy conservation equation can be written as: (16) As + C s + Qs = Fs Where As : The amount of energy that is absorbed by surface zone (s) from the energy which is emitted from all zones (even itself). Cs : The convective energy that is transferred from/to surface zone (s) to/from neighbor volume zones. Qs : The amount of energy that exits from furnace to load by this surface zone (s). Fs : The amount of energy emitted from surface zone(s). By using the theory that was explained in section 1, this energy balance can be rewrite in better shape: m

←

L

→

∑ S S σ T + ∑G S σ T i j

j =1

4 j

j i

4 g, j

− Aiε iσ Ti4 + Ai qi,conv. = Q& i

j =1

(17) Where m and L represents number of surface zones and number of volume zones, respectively. The first term on the left hand side of this equation is summation of all radiation that reached to this surface zone from all surface zones in enclosure. The second term on the left hand side represents summation of all radiation that reached to this surface zone from all volume zones in the enclosure. The third term represents the radiation emits from this surface zone. The fourth term is the amount of convective energy from neighbor volume zone. The right hand side represents the amount of heat transfer to load (water walls) from this surface zone. This value can be approximated by having the condition of water in entering and exiting the boiler and dividing the whole enthalpy changes between surface zones, expect the burner’s surface zones, equally. For a furnace with m surface zones, we will have m energy balance in this shape. For volume zones, we should also write energy balance: Av + Bv + Cv + Dv − Ev = Fv (18) Av : The total radiative energy that is absorbed in volume v from all the energy that emitted from all zones in the system. Bv : The heat energy of the gas that is entered to this volume zone. Cv : The amount of energy that is transferred to/from neighbor surface zone by convection mechanism. Dv : The energy generated in this volume zone by the combustion mechanism. Ev : The heat energy of the gas that is exited from this volume zone. Fv : The total energy that is emitted from volume zone v. This equation can be explained in other shape:

Q& g ,net + Q& a + Q& g + Q& conv . + Q& rad . = 0

(19)

The first term on the left hand side is net heat generated from combustion can be calculated from Q& g ,net = V& × C (20) g v , net Where V&g the volume rate of inlet fuel to this volume zone and Cv , net is net heat of combustion for fuel. Q& a in eq.18 is the energy of combustion air at inlet

temperature and Q& g is the rate of decrease in sensible enthalpy of gas flowing through the zone. These two parameters can be calculated from:



 Q& a = V&G  Rs  1 + Q& g

   ρ a H a (Ta ) 100   X

(21)

  X   = V&G  Rs + Rs  ρ g H g (T g ) 100  

(22)

In these equations, we have: Rs : Volume rate of air to fuel in stoichiometric condition ρ a : Density of inlet air ρ g : Density of combustion product H a : Enthalpy of the air H g : Enthalpy of the fuel

x : Additional air (%) For radiative energy term in volume zone balance, we can write: l

←

m

←

N

4 4 Q& rad = ∑ Gi G j σ Tg , j + ∑ Gi S j σ T j − 4 ∑ an k g ,nVi σ Tg ,i j =1

j =1

n =1

(23) By substituting equations (20-23) into eq.19, we will have: l

←

m

←

N

∑ Gi G jσ Tg , j + ∑ Gi S j σ T j4 − 4∑ an k g ,nViσ Tg4,i − j =1

j =1

n =1

( Q& conv. ) + ( Q& g ,net )i + ( Q& a )i + ( Q& g )i

=0

(24)

Where Q& conv. represents the convective heat transfer to all surface zone that are in neighbor of this volume zone. Same as surface zone we can write one energy balance for every volume zones. By solving these nonlinear equations together, we will reach to final solution for temperature in all surface and volume zones. 5 INTRODUCING THE MODEL The boiler that is modeled in this research is made by CE Company. This kind of boiler has natural circulation for water and the furnace dimensions are 22.4 ft × 33.6 ft × 67.2 ft .The side walls of the furnace is made of the stainless steel tubes with 2.5in diameter. These tubes connect to each other by the plates with 0.5in thickness and the center to center distance of

the tube is 3in . All the walls are made by this kind of tubes and just there are no any tubes in the part of boiler that gas exits. This complex shape of walls has been replaced by an equivalent surface with emissivity of 0.85 . The method was explained by Hottel and Cohen in 1935 is used for calculating the amount of the equivalent surfaces. This boiler has 16 burners that are placed in two stages with different height in the front (8 burners) and rear (8 burners) walls of the boiler. Figure 1 shows a simplified model of this furnace that we used for our simulation. As illustrated in figure 1, by using asymmetric property of this furnace, we should just simulate a half of surfaces and volume.

amount of mass transfer between the volume zones which is necessary for completing the energy balance in surface and volume zones (Eq.17 and Eq.24), is calculated. According to the pattern in Fig. 2, the portion of convective term in whole heat transfer process is maximum in the chimney of the furnace relative to other parts.

Fig. 2. Velocity contours within the furnace. Figures 3 shows the radiative heat flux distribution in the front and side walls of furnace. The minimum value of radiative heat flux has been observed in the corners of the walls and also near the exit part and the maximum values has been observed in central regions. This kind of behavior is in conformity with related calculated value for directed heat flux area. It means that in the central region where the directed heat flux area is high, the amount of radiative heat transfer is maximum. Fig. 1. An illustration of our simplified model of the furnace ,The names that we used to address different parts of furnace with the volume and surface zones, position of the burners in front and rear walls. Recall that in both state of fuels (Methane and Mazut) the length of the flame is shorter that the length of the zone, therefore considering the constant temperature for the volume zones that are exactly in front of the burners will be acceptable assumption. The amount of inlet mass flow rate in burners was obtained by maintaining the overall heat value of fuels in both states equal. Therefore, by using the specific heat values for Mazut and Methane and existing inlet mass flow rate for Mazut state, the amount of equivalent mass flow rate in Methane state will be obtained. 6 RESULT AND DISCUSSION The flow pattern and velocity field of the gas within the furnace were calculated by using the equations that are explained in section 3. The velocity contours of the gas in one cross section area of the furnace are illustrated in figure 2. By using these results, the

Fig.3. (a) Radiative heat flux distribution on the front wall of furnace ( Btu ft 2 hr ). (b) Radiative heat flux distribution on the side wall of the furnace ( Btu ft 2 hr ).

The minimum value for directed flux area has been calculated for the regions which are in the corners of the furnace and it caused that the amount of radiative heat flux in these regions was less than in other regions of the walls. It makes sense because these central regions have better position for taking the radiation ray from other surfaces and gas.

Fig.4.Temperature distribution in volume zones; (a): j=1 the first row of volume zones near the sidewall. (b): j=2 the second row of volume zones. Figure 4 shows the temperature distribution in the volume zones in two rows of volume zones, near the side wall and in the central region (j=1, 2 in fig.1). The temperature behaviors in both rows are almost similar and in the most regions, the temperature is uniform. It means that the temperature in the gas is quite high and it decreases near the chimney because of its effect. Comparison between the calculated data from our simulation for methane state with experimental measured data which reported by manufacturer company, give us very useful information for predicting the actual differences between two states. This information will be useful for changing the load and work conditions of boiler and its burners in the way that boiler can work with new fuel, Methane, without any damages in heat surfaces. By comparing the calculated value for temperature in different regions of the boiler with experimental reported data, it is obtained that the temperature in Methane state is higher than Mazut state by approximately 20 %. 7 CONCLUSIONS AND REMARKS The zone method is one of the most accurate methods in simulation radiative heat transfer within the industrial furnaces but it has some limitation to apply on all furnaces. Complex geometries of real furnaces should be replaced by simpler shape to be suitable for using zone method. This method needs the high power of numerical calculations and finding the best size for zones is one of the major criteria in this method. Choosing very small sized meshing will lead us to very complex numerical calculation and it can increase the amount of truncation and round off error during the calculation. Whereas, the very coarse

mesh structure will not be able to explain adequately the details of the heat transfer phenomena within the furnace. In this article, the capability of zone method for analysing the heat transfer within an industrial furnace is shown. Solving the flow field within the furnace is necessary for calculating the convective heat transfer term in energy balance equations. Using the CFD method for solving the velocity field needs a suitable turbulence model and very fine mesh which will increase the calculation time. Furthermore, matching the large zones that are used in zone method with this very fine mesh that are used for CFD calculation will be complex. Due to these reasons, in this study we used some empirical equations for calculating the velocity field. An alternative approach in the further studies is to use finer mesh for CFD calculations and apply radiation energy transfer profile of zone method in source terms of CFD energy equations. The result of simulation has a good conformity with existing experimental data. These results are very useful for estimating the needed changes in the burners and the operating conditions of the boiler when changing the fuel. By comparing the results of our simulation with existing data, we found that the temperature of combustion product in the Methane state is higher than Mazut state by 200-300 Rankine. Due to higher temperature in Methane state, for preventing any damage in heat surfaces due to aforementioned fuel changes, we need to decrease total entered fuel value. It means that the load of the boilers should be decreased by 12%. By this fuel change, the efficiency of the boiler will increase and the boiler will work with a cleaner fuel. REFERENCES Batu, A. and Selçuk, N. (2002). Modeling of Radiative Heat Transfer in the Freeboard of a Fluidized Bed Combustor Using the Zone Method of Analysis. Turkish Journal of Engineering and Environmental Sciences 26, 49–58. Beer, J. M. (1972). Recent advances in the technology of the furnace flames. J. Inst. Fuel 45, 370–382. Díez L. I.,Cortés C. and Campo A. (2005). Modeling of pulverized coal boilers: review and validation of on-line simulation techniques. Applied Thermal Engineering 25, 1516–1533. Hottel H. C. and Cohen E. S. (1935). Radiant heat exchange in a gas-filled enclosure: Allowance for nonuniformity of gas temperature. AIChE Journal 4(1), 14–30. Hottel H. C. and Sarofim A.F., (1967). Radiative Transfer. McGraw-Hill Book Co. New York. Viskanta, R., Menguc, M.P. (1987). Radiation heat transfer in combustion systems. Progress in Energy and Combustion Science. 13, 97–160.