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air balancing in power plants
Applied Mathematical Modelling 30 (2006) 854–866 www.elsevier.com/locate/apm
CFD application for coal/air balancing in power plants Sowjanya Vijiapurapu a, Jie Cui a
a,*
, Sastry Munukutla
b
Mechanical Engineering Department, Tennessee Technological University, P.O. Box 5014, Cookeville, TN 38505, USA b Mechanical Engineering Department, Center for Energy Systems Research, Tennessee Technological University, P.O. Box 5014, Cookeville, TN 38505, USA Received 1 May 2004; received in revised form 1 May 2005; accepted 27 June 2005 Available online 18 August 2005
Abstract Unbalanced coal/air flow in the pipe systems of coal-fired power plants will lead to non-uniform combustion in the furnace, and hence a overall lower efficiency of the boiler. A common solution to this problem is to put orifices in the pipe systems to balance the flow. It is well known that if the orifices are sized to balance clean air flow to individual burners connected to a pulverizer, the coal/air flow would still be unbalanced and vice versa. However, the current power industry practice throughout the world is to size orifices for balancing the clean air flow and accept the resulting imbalance in coal/air flow. Field tests are mostly conducted to verify a balanced clean air flow. It is now proposed to size the orifices for balancing the coal/air flow and then calculate the unbalanced clean air flow distribution to be known as the ‘‘tailored clean air flow’’. Commercially available Computational Fluid Dynamics (CFD) code CFX was used to simulate the complex flows in the piping systems in a power plant. The two-phase modelling technique was employed to estimate the pressure drop coefficients with both clean air and coal/air flows in order to size the orifices. The results indicate that the pressure drop is strongly dependent on the piping system geometry. With this proposed method, field tests can be conducted to correspond with the tailored clean air flow, and the coal/air flow balancing would be achieved. 2005 Elsevier Inc. All rights reserved. Keywords: CFD; Numerical modelling; Coal/Air balancing; Power plant
*
Corresponding author. Tel.: +1 931 372 3357; fax: +1 931 372 6340. E-mail address: [email protected] (J. Cui).
0307-904X/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2005.06.005
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1. Introduction There are a number of operational problems of coal-fired boilers, which are suspected to be caused by non-uniform combustion in the furnace. One source of non-uniform combustion is uneven distribution of fuel inputs to the furnace. Several coal pipes connect the exit of the pulverizer to the individual burners, all of which are located at the same elevation in the furnace for that particular pulverizer [1]. Though the elevation change is identical for each system, the pipes have different horizontal, vertical, and inclined lengths, and bends. Thus, the resistance to flow is different for each system, leading to uneven distribution. The resistance of a system is different for single-phase flow (clean air) or two-phase flow (coal/ air) [2]. The resistance is expressed as a dimensionless pressure drop coefficient. Thus, the singlephase and the corresponding two-phase pressure drop coefficients for any given system are different. One significant point is that the pressure drop coefficient for a sharp edged orifice is the same for both single-phase and two-phase flows for dilute suspension flows encountered in power plants. A typical volume fraction of coal to air is 1/1600 [3]. Since the resistance coefficients are different for clean air and coal/air flows, the orifice sizes needed to balance the clean air flow would be different from the orifice sizes needed to balance the coal/air flow. The electric power industry practice throughout the world so far has been to size the orifices based on clean air flow pressure drop coefficients. The clean air flow would, therefore, be balanced but the corresponding coal/air flow would still be unbalanced. In one instance, it was reported that after the clean air flow was balanced to within 3%, the coal/air flow was still unbalanced by 27% [4]. On the other hand, if the orifice sizing is based on the coal/air flow balancing, the corresponding clean air flow would be unbalanced. This would not present a problem since coal/air balancing is what is needed for efficient combustion. For calculating the pressure drop coefficients, standard handbook data can be used [5]. However, the data for two-phase flow (coal/air) is found to be unreliable. So, the pressure drop coefficients for the coal/air as well as the clean air flow were calculated using CFD in the present work [6]. The multi-phase models were used to simulate the complex flow field of each phase and the interaction between air and coal particles. It is believed that the numerical solution was able to provide reasonable pressure drop coefficients in the current study. In most power plants the geometry for individual pipe systems is specified by the total horizontal run, total vertical run, number of bends, and bend geometry. Since exact geometry of the system is not specified, it is not possible to calculate the pressure drop of the entire system in one pass. It was therefore decided to calculate the pressure drop in a system by breaking it into individual components. The calculated pressure drops across various components were then added together, to estimate the pressure drop of the entire system. In the current paper, this procedure will be implemented in one of the coal-fired electric utilities. A description of this method and results from field experience will form the rest of the contents of this paper.
2. Use of CFD in power industry applications In the power generation industry, many processes involve multi-phase flow, phase transformation, combustion, and complex chemical reactions [7]. This is particularly true for coal fired power
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plants. However, due to the complex nature of these phenomena, traditional research approaches were not adequate in providing a thorough understanding of these processes. Recently, CFD has been used in power industry to gain a qualitative as well as quantitative understanding of these processes. Pulverized coal combustion in a 2.5 MW burner was modelled using two commercial CFD codes [8]. Despite discrepancies between the solutions of the two codes, the predicted velocity, temperature, and species concentration were in overall agreement with the experimental data, suggesting that the two codes were capable of predicting good ÔtrendÕ solutions. The Eulerian–Eulerian multi-phase model in conjunction with the k–e model was applied to predict erosion in slurry pipeline tee-junctions [9]. The CFD model was used to assess several potential solutions to the erosion problem, and the results demonstrated the effectiveness with which CFD techniques can be used in industrial applications. Similar multi-phase model was employed to develop a computational model of erosion in a fluidized bed [10]. It was shown that the model predictions were in good agreement with the experiment results. Stopford reviewed some of the recent applications of CFD to the power generation and combustion industries [11]. Examples included coal-fired low-NOx burner design, furnace optimization, over-fire air, gas reburn, and laminar flames. The results showed that CFD modelling was well established as a design tool and has been widely used in the power generation industry to help engineers reduce emissions, increase thermal efficiency, select fuel, and extend plant lifetime. In this paper, an attempt will be made to take this new approach—CFD—to a problem faced by the power industry for a number of years: coal/air balancing. The multi-phase model in the unstructured version of CFX (version 5.5.1) will be applied to determine pressure drop in the piping systems in a power plant. Based on the predicted pressure drop, orifices in the piping systems will be added or modified and balanced coal/air flow will be achieved.
3. Principle of the method Fig. 1 shows two systems with the same elevation change, but different horizontal, vertical runs, and bends. Both systems start at the same elevation at the pulverizer exit and discharge at the same elevation in the boiler. System 1 has one vertical run, one horizontal run, and one bend. System 2 has 3 vertical runs, 3 horizontal runs, and 5 bends. The total pressure drop consists of frictional loss over the horizontal and vertical pipe lengths, a loss due to bends, and a loss due to gravity. In general if the total flow rate is Q, with flow rate in system 1 being Q1 and that in system 2 being Q2, and the pressure drop coefficients being K1 and K2, respectively, we have Q ¼ Q1 þ Q2 ; K 1 Q21 ¼ K 2 Q22 ; Q qffiffiffiffi ) Q2 ¼ 1 þ KK 21
Q qffiffiffiffi . and Q1 ¼ 1 þ KK 12
ð1Þ
Let the pressure drop coefficients for clean air and coal/air for systems 1 and 2 be K1A, K2A, and K1C, K2C respectively. Then the flow distribution with clean air is given as
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Fig. 1. Illustration of two systems with the same elevations change, but different horizontal and vertical runs, and bends.
Q2A ¼
1þ
Q qffiffiffiffiffiffi K 2A K 1A
and Q1A ¼
Q qffiffiffiffiffiffi
ð2Þ
Q qffiffiffiffiffiffi .
ð3Þ
1þ
K 1A K 2A
and that with coal/air is given as Q2C ¼
1þ
Q qffiffiffiffiffiffi K 2C K 1C
and Q1C ¼
1þ
K 1C K 2C
In most cases, it has been observed that the ratio of K2C/K1C is very nearly equal to K2A/K1A. In other words, clean air and coal/air are unbalanced in a similar manner. The pressure drop coefficient KOR of the orifice plate is calculated as the absolute difference in the pressure drop coefficients of the pipes. In order to achieve clean air balance, an orifice yielding a pressure drop coefficient of KOrf,A = K2A K1A should be introduced. In order to achieve coal/air balance, an orifice yielding a pressure drop coefficient of KOrf,C = K2C K1C should be introduced. As a general rule the pressure drop coefficients for the coal/air (two-phase) flow K1C and K2C, are always greater than the corresponding clean air (single-phase) pressure drop coefficients K1A and K2A (typically by a factor of 2–3) [12]. Hence, the orifice diameters based on the clean air distribution are larger than those based on the coal/air distributions. As a result of the above, it has been a normal trend in the power industry to under estimate the pressure drop requirement. The diameter of the orifice can be calculated from available empirical equations [13], one of the commonly used equations is " 0.375 !#2 F1 F0 F0 1 þ 0.707 1 ; ð4Þ K OR ¼ F0 F1 F1 2 where FF 01 ¼ AA01 ¼ DD01 , A0, A1 correspond to the area of the orifice and pipe, respectively, and, D0, D1 correspond to the diameters of the orifice and pipe, respectively.
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4. The systems modelled The four systems modelled using the numerical method are given in Table 1. As shown in the Table, there are 4 systems that carry coal/air mixture from the pulverizer to the furnace. The individual lengths of the horizontal and vertical sections between the bends are not known. The only data available is the total horizontal and vertical length of the systems, and the number of different bends in each system. Also, the bend angles for each system are known. If K1, K2, K3, and K4 are the pressure drop coefficients for systems 1, 2, 3, and 4, respectively, flow distributions V1, V2, V3, and V4 can be calculated by extending Eq. (3) to a 4-branch system. rffiffiffiffiffiffi 400 K1 qffiffiffiffi qffiffiffiffi qffiffiffiffi ; V 2 ð%Þ ¼ V 1 ; V 1 ð%Þ ¼ K1 K1 K1 K2 1 þ K2 þ K3 þ K4 rffiffiffiffiffiffi rffiffiffiffiffiffi K1 K1 V 3 ð%Þ ¼ V 1 ; V 4 ð%Þ ¼ V 1 . ð5Þ K3 K4 Note that for a perfectly balanced system K1 = K2 = K3 = K4, and in that case V1 = V2 = V3 = V4 = 100%. For an unbalanced system V1, V2, V3, and V4 could be different from 100%, but however, would still add to 400%. It can be seen from Table 2 that in the existing system the clean air and coal/air flows are both unbalanced. It can also be observed that the two unbalances are not similar due to the presence of orifices. Hence, it is proposed to retrofit the whole orificing system based on the coal/air balancing. Since the two-phase flow in the existing systems is quite complex and the data from standard handbook is unreliable, it was decided to Table 1 Detail of four systems that exit from one pulverizer and feed the boiler at the same elevation System
Total vertical length (m)
Total horizontal length (m)
Bends in system
Diameters of existing orifices in system (mm)
1
10.39
48.11
150, 160, 160, 135
2
10.39
36.83
120, 135
3 4
10.39 10.39
64.34 75.62
165, 90, 135 135, 90, 160, 160, 135
442 at 1 m distance 442 at 56 m distance 437 at 1 m distance 437 at 45 m distance 442 at 1 m distance No orifices
Note: Orifices are inserted according to the maximum pressure drop in the systems. Calculated pressure drop in system 4 is the maximum. Therefore, orifices were inserted in systems 1–3 to balance the pressure drop.
Table 2 Existing flow distribution for clean air and coal/air flows System
Clean air flow distribution (%)
Coal/air flow distribution (%)
1 2 3 4
95 97 100 108
102 108 96 94
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utilize the two-phase modelling technique to obtain the pressure data in each system. Then the orifice diameters are recalculated based on the CFD results and a well-balanced system is obtained.
5. CFD application to calculate pressure drop As discussed in Section 2, the exact geometries of the individual systems in a power plant are not always available. This problem was overcome by breaking up the geometry of the system into various components like the horizontal section, vertical section, and various bends. The pressure drop across each component is calculated and then put together to give the pressure drop along the whole geometry of the system. Examples of the geometries used for the modelling are shown in Fig. 2. The pressure drops for the horizontal and vertical lengths were calculated initially for a 60D pipe, where D is the diameter of the pipe. The pressure drops across unit length were then calculated and applied to the existing lengths of the pipe. A length of 60D was chosen to ensure that the flow became fully developed. The pressure drop per unit length was calculated for the fully developed region. It was found that for the current configuration and flow condition (Reynolds number 9.15 · 105, surface roughness e = 0.0026 mm) the flow became fully developed within 30D from the inlet. Therefore, for the bends, the upstream length was assumed to be 40D and downstream to be 20D and the pressure drop across the bend was calculated. For calculation of the steady state flow in the piping systems, continuity and momentum equations were solved along with the standard k–e turbulence model. Two-phase flow calculations were adopted to simulate the air flow and coal particles. The equation of continuity for a mixed fluid is expressed by Eq. (6), where a is the phase, ra is the volume fraction of that phase, qa is the density of the fluid in the phase a, xj is the coordinate with the index j ranging from 1 to 3, and U ja is the mean velocity in the phase a along the direction j. The continuity equation expressed for each control volume is shown in Eq. (7).
Fig. 2. Schematics of the components modelled.
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oðra qa Þ oðra qa U ja Þ ¼ 0; þ ot oxj X 1 oðra qa Þ oðra qa U j Þ X a ¼ 0; ra ¼ 1 or þ j q ot ox a a a
ð6Þ ð7Þ
where repeated indices imply summation from 1 to 3. The equation of motion is expressed by Eq. (8) oðra qa U ia Þ oðra qa U ia U ja Þ op oðra sji Þ þ ¼ ra i þ ra qa gi þ ; j ot ox ox oxj where p is the pressure and sij is the stress tensor given by i oU oU j sij ¼ leff þ i ; oxj ox
ð8Þ
ð9Þ
where leff is effective viscosity, which is defined as the sum of dynamic viscosity l and eddy viscosity lt, leff = l + lt. The eddy viscosity is provided by the k–e turbulence model. lt ¼ C l q
k2 ; e
ð10Þ
where Cl is a constant and is equal to 0.09, k is the turbulent kinetic energy, e is the dissipation rate, and both are provided by the k–e turbulence model.
o o l þ a ok a j ðra qa k a Þ þ j ra ðqa U a k a Þ l þ ð11Þ ¼ ra ðP a qa ea Þ þ T kab ; ot ox rk oxj
o o l þ a oea ea ¼ ra ðC e1 P a C e2 qa ea Þ þ T eab ; ð12Þ ðra qa ea Þ þ j ra ðqa U ja ea Þ l þ ot ox re oxj ka where rk = 1.0, re = 1.3, Ce1 = 1.44, and Ce2 = 1.92 are constants from the k–e model. T kab and T eab are the terms that represent the inter-phase transfer for k and e respectively. P represents the shear production due to turbulence for that particular phase, which is oU j oU j oU k ð13Þ þ j . P ¼ lt k ox oxk ox The continuity equation, momentum equation, and the turbulence model equation were solved for each phase. The pipe diameter was 0.527 m. For clean air flow, the air density was taken as 1.284 kg/m3, which is the value at room temperature. For coal/air flow, the air density was 0.977 kg/m3, which is the value at 88 C, and the coal density was 1398 kg/m3. The coal flow rate was 2.36 kg/s and the air flow rate was 5.00 kg/s. The boundary conditions were assumed to be uniform velocity distribution at the inlet and zero gage pressure (open to atmosphere) at the outlet. Grid refinement near the walls was used for grid generation (Fig. 3). This allows for much better resolution of the velocity field near the wall where it changes rapidly. Reynolds Averaged Navier–Stokes equations (RANS) were solved using finite volume method on an unstructured mesh with the standard k–e model for turbulence.
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Fig. 3. Cross-section and plan view of the unstructured grid.
A typical mesh size for the CFD simulation was around 300,000 mesh cells, each steady state case took 11–16 wall clock hours on Dell Optiplex GX270 computers. These computers had 2 Intel P4 3.20 GHz processors with 2.00GB RAM. The steady state solutions used pseudo time step, which was determined by the CFL requirement of the solver. Convergence was claimed when a stable pressure drop was achieved, usually it took 7000 iterations. The friction factor was calculated by using the pressure drop in the fully developed region of the pipe. The friction factor for clean air was calculated by f ¼
DP L 1 qU 2avg D 2
;
ð14Þ
where f is the friction factor, DP is the pressure drop along the pipe over a distance of L in the fully developed region, q is the density of air, Uavg is the average velocity, and D is the diameter of the pipe. For a fully developed flow, the friction factor is a constant. From this calculation, the friction factor was found to be f = 0.0164. The results were compared to those in the Moody chart (Reynolds number 9.15 · 105, surface roughness e = 0.0026 mm, friction factor f = 0.017). The boundary conditions for the coal/air flow were imposed in the same manner as those for clean air flow. The boundary condition for the particles was no slip i.e., the particles stick to the surface if they hit the surface. The volume fraction for coal at inlet was considered to be uniformly distributed. The coal particles were all considered to be spherical and of the same uniform size (diameter 1 lm). Table 3 gives the pressure drop per unit length for the horizontal and vertical components and also the pressure drop across the bends for both clean air and coal/air flows. As can be seen, the pressure drop for the coal/air flow is always greater than that of the clean
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Table 3 Pressure drop across various components for clean air and coal/air flows Horizontal (Pa/m) Vertical (Pa/m) Bend angles 90 (Pa) 120 (Pa) 135 (Pa) 150 (Pa) 160 (Pa) 165 (Pa) Clean air 11.02 Coal/air 27.52
10.82 16.6
48.68 104.33
32.06 51.76
23.93 29.63
13.79 15.64
9.18 11.47
5.71 8.38
air flow. It can be said that this is mainly due to the resistance offered by the interaction between air and coal particles and among coal particles themselves, as well as blockage effects.
6. Results In this study, orifice sizes were calculated for coal/air balancing. Based on the given data, the calculations have been performed with the existing system configuration. The clean air and coal/ air pressure drop coefficients, and flow distributions were first calculated. Orifice sizes for coal/air balancing were then calculated. Note that in each system if one or more orifices already exist, then there was at least one orifice at 1-m distance from the pulverizer exit. It was then tacitly assumed that the new orifice would replace that orifice. Table 1 gives the data from the power plant. This table is self-explanatory. The existing flow distributions are given in Table 2, which are based on the pressure drop calculations shown in Table 3. The orifice diameters for balancing coal/air flow are shown in Table 4. The tailored clean air flow and the balanced coal/air flow distribution after insertion of new orifices is shown in Table 5. As can be seen from Table 5, the pressure drop for each system is the same and Table 4 Orifice diameter calculation for coal/air balancing System
K Loss coefficient
Existing orifice KOR
Total K
New KOR
Orifice diameter (mm)
1 2 3 4
5.84 4.73 7.78 9.10
0.95 1.07 0.00 0.00
6.79 5.80 7.78 9.10
2.32 3.31 1.32 0.00
401.78 389.08 427.85 –
Note: K is the pressure loss coefficient of each system and KOR is the pressure loss coefficient of the orifice calculated based on Eq. (4).
Table 5 Tailored clean air flow and balanced coal/air flow distribution after insertion of new orifices System 1 2 3 4
Clean air
Coal/air
Total K after retrofit
Flow distribution (%)
Total K after retrofit
Flow distribution (%)
5.25 6.01 3.88 3.01
91 85 105 120
9.10 9.10 9.10 9.10
100 100 100 100
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consequently the coal/air flow is balanced. In each instance, an existing orifice at 1 m distance is to be replaced by the new orifice. The CFD simulations also provide detailed information of the two-phase flow field. Fig. 4 shows the close-up view of the air velocity magnitude contours for bends with various angles. The gravity force is vertically downward (in the negative y-direction). All contours shown in Figs. 4 and 5 are on the center plane (xz-plane) that passes the axis of the bend. In the horizontal portion of the bend, all flows exhibit similar velocity distributions and there is no variation in the
Fig. 4. Air velocity magnitude contours for bends with various angles.
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Fig. 5. Contours of volume fraction of coal for bends with various angles.
streamwise direction. This is because the flow has gone through 40D upstream length before it reaches the bend, and flow has become fully developed. It is observed that the velocity is lower near the bottom of the horizontal portion. This is due to the higher resistance to the air induced by the coal particles when they deposit to the pipe bottom. For the flow conditions considered in the current study, the effects of coal particle deposition is significant. It can be clearly seen from Fig. 4 that the characteristics of the air flow downstream of the bend strongly depend on the bend angle. For sharp turns (Fig. 4a–c), the flow has to change direction quickly and the higher velocity flow is shifted towards the outer radius of the downstream bend. While near the inner radius of
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the bend, a lower velocity region can be identified. As shown in Table 3, this sharp flow direction change results in significant pressure loss, with the 90 bend giving the highest. For higher bend angles (Fig. 4d), the flow goes through the bend quite smoothly, and the pressure loss is insignificant compared to the sharp turning cases. Fig. 5 displays the contours of volume of fluid (VOF) of coal for bends with various angles. In the horizontal portion, all bends show similar coal VOF distribution, just like the velocity contours in Fig. 4. Higher coal VOF is found at the lower part of the upstream pipe. This is again attributed to the deposition of the coal particles. In the bend, maximum VOF of coal can be identified near the outer radius of the bend. This is explained by the flow impingement in the bend, and the attachment and accumulation of coal particles at this location. For sharp turning bends, the overall VOF of coal becomes much less downstream of the bend, indicating significant deposition and accumulation of coal particles in the bend and upstream pipe (Fig. 5a–c). While for smooth turning bend, the effects of coal particle deposition and accumulation are not as prominent (Fig. 5d). It should be pointed out that for the 90 bend, immediately downstream of the bend and close to the inner radius, there is a localized region with a higher coal VOF than its local ambient. This is the indication of flow separation. The local recirculating flow traps a significant amount of coal particles and a region of higher VOF of coal is formed. For 120 and 130 bends, this localized region can still be seen, but the size is much smaller. While for the 160 bend, it is not recognizable, suggesting negligible or non-existent flow separation downstream of the bend.
7. Conclusions There is currently no easy way of measuring coal/air flow in a power plant. In order to balance the coal/air flow to the individual burners, it would, therefore, be necessary to rely on clean air tests. The industry practice has so far been to balance the clean air flow and accept the resulting imbalance in the coal/air flow. It was observed in one specific case that, when the clean air is balanced with a maximum deviation of 3% from the average, the corresponding coal/air flow deviation was approximately 27%. This is unacceptable from the consideration of efficient unit operation. A new method in which creating a tailored imbalance in clean air flow corresponding to a balanced coal/air flow distribution has been successfully proposed in this paper. Commercially available software CFX was used to calculate pressure drops in systems. The two-phase flow phenomena was simulated using the multi-phase modelling technique. Using this, several geometries involving any number of independent lines starting from a mill and discharging to a given burner can be handled. The results show that the pressure drop in the systems strongly depends on the system geometry. Orifices are sized based on calculated coal/air pressure drops, and finally imposing a tailored imbalance in clean air flow distribution leading to a balanced coal/air distribution. It should be pointed out that in order to implement this method in power plant, verification can still be done by measuring the tailored clean air distribution. The numerical results also provide detailed information of the two-phase flow field in the piping systems in a power plant, based on which physical insights were obtained and better understanding of the complex flow phenomena was achieved. This study demonstrated that CFD can be used as an effective tool for design and research for power industry applications.
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References [1] A.A. Vetter, R.S. Vetter, Balancing pulverized coal flows in parallel piping, J. Eng. Gas Turb. Power 107 (July) (1985) 679–684. [2] R. Avancha, Coal/air balancing in pulverized coal fired units, MasterÕs Thesis, Tennessee Technological University, 1995. [3] M.P. Sharma, Numerical and experimental study of gas-particle flows in orifices and venturis: application to flowmeter design, Ph.D. Dissertation, Washington State University, 1977. [4] G.R. Jones, Pulverized Coal Mill Fuel/Air Ratio Testing, paper presented at EPRI Heatrate Improvement Conference, Knoxville, Tennessee, September 1989. [5] ASHRAE Handbook Fundamentals-2001, I.P. Edition. [6] AEA Technology, CFX-5.5.1 Flow Solver User Guide, AEA Technology Inc., 2003. [7] C. Yin, L. Rosendahl, S.K. Kar, T.J. Condra, Use of numerical modeling in design for co-firing biomass in wallfired burners, Chem. Eng. Sci. 59 (2004) 3281–3292. [8] C.N. Eastwick, S.J. Pichering, A. Aroussi, Comparisons of two commercial computational fluid dynamics codes in modeling pulverized coal combustion for a 2.5 MW burner, Appl. Math. Modell. 23 (1999) 437–446. [9] G.J. Brown, Erosion prediction in slurry pipeline tee-junctions, Appl. Math. Modell. 26 (2002) 155–170. [10] D. Achim, A.K. Easton, M.P. Schwarz, P.J. Witt, A. Zakhari, Tube erosion modelling in a fluidised bed, Appl. Math. Modell. 26 (2002) 191–201. [11] P.J. Stopford, Recent applications of CFD modelling in the power generation and combustion industries, Appl. Math. Modell. 26 (2002) 351–374. [12] A.A. Vetter, Theoretical Evaluation of the Differences Between Single and Two-Phase Flow as Applied to Coal Transport Piping, Humburg Mountain Research Laboratories Report, HMRL R—31:1, September 1981. [13] I.E. Idelchik, Handbook of Hydraulic Resistance, third ed., CRC Press, Inc., Boca Raton, 1994, p. 221.
CFD application for coal/air balancing in power plants Sowjanya Vijiapurapu a, Jie Cui a
a,*
, Sastry Munukutla
b
Mechanical Engineering Department, Tennessee Technological University, P.O. Box 5014, Cookeville, TN 38505, USA b Mechanical Engineering Department, Center for Energy Systems Research, Tennessee Technological University, P.O. Box 5014, Cookeville, TN 38505, USA Received 1 May 2004; received in revised form 1 May 2005; accepted 27 June 2005 Available online 18 August 2005
Abstract Unbalanced coal/air flow in the pipe systems of coal-fired power plants will lead to non-uniform combustion in the furnace, and hence a overall lower efficiency of the boiler. A common solution to this problem is to put orifices in the pipe systems to balance the flow. It is well known that if the orifices are sized to balance clean air flow to individual burners connected to a pulverizer, the coal/air flow would still be unbalanced and vice versa. However, the current power industry practice throughout the world is to size orifices for balancing the clean air flow and accept the resulting imbalance in coal/air flow. Field tests are mostly conducted to verify a balanced clean air flow. It is now proposed to size the orifices for balancing the coal/air flow and then calculate the unbalanced clean air flow distribution to be known as the ‘‘tailored clean air flow’’. Commercially available Computational Fluid Dynamics (CFD) code CFX was used to simulate the complex flows in the piping systems in a power plant. The two-phase modelling technique was employed to estimate the pressure drop coefficients with both clean air and coal/air flows in order to size the orifices. The results indicate that the pressure drop is strongly dependent on the piping system geometry. With this proposed method, field tests can be conducted to correspond with the tailored clean air flow, and the coal/air flow balancing would be achieved. 2005 Elsevier Inc. All rights reserved. Keywords: CFD; Numerical modelling; Coal/Air balancing; Power plant
*
Corresponding author. Tel.: +1 931 372 3357; fax: +1 931 372 6340. E-mail address: [email protected] (J. Cui).
0307-904X/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2005.06.005
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1. Introduction There are a number of operational problems of coal-fired boilers, which are suspected to be caused by non-uniform combustion in the furnace. One source of non-uniform combustion is uneven distribution of fuel inputs to the furnace. Several coal pipes connect the exit of the pulverizer to the individual burners, all of which are located at the same elevation in the furnace for that particular pulverizer [1]. Though the elevation change is identical for each system, the pipes have different horizontal, vertical, and inclined lengths, and bends. Thus, the resistance to flow is different for each system, leading to uneven distribution. The resistance of a system is different for single-phase flow (clean air) or two-phase flow (coal/ air) [2]. The resistance is expressed as a dimensionless pressure drop coefficient. Thus, the singlephase and the corresponding two-phase pressure drop coefficients for any given system are different. One significant point is that the pressure drop coefficient for a sharp edged orifice is the same for both single-phase and two-phase flows for dilute suspension flows encountered in power plants. A typical volume fraction of coal to air is 1/1600 [3]. Since the resistance coefficients are different for clean air and coal/air flows, the orifice sizes needed to balance the clean air flow would be different from the orifice sizes needed to balance the coal/air flow. The electric power industry practice throughout the world so far has been to size the orifices based on clean air flow pressure drop coefficients. The clean air flow would, therefore, be balanced but the corresponding coal/air flow would still be unbalanced. In one instance, it was reported that after the clean air flow was balanced to within 3%, the coal/air flow was still unbalanced by 27% [4]. On the other hand, if the orifice sizing is based on the coal/air flow balancing, the corresponding clean air flow would be unbalanced. This would not present a problem since coal/air balancing is what is needed for efficient combustion. For calculating the pressure drop coefficients, standard handbook data can be used [5]. However, the data for two-phase flow (coal/air) is found to be unreliable. So, the pressure drop coefficients for the coal/air as well as the clean air flow were calculated using CFD in the present work [6]. The multi-phase models were used to simulate the complex flow field of each phase and the interaction between air and coal particles. It is believed that the numerical solution was able to provide reasonable pressure drop coefficients in the current study. In most power plants the geometry for individual pipe systems is specified by the total horizontal run, total vertical run, number of bends, and bend geometry. Since exact geometry of the system is not specified, it is not possible to calculate the pressure drop of the entire system in one pass. It was therefore decided to calculate the pressure drop in a system by breaking it into individual components. The calculated pressure drops across various components were then added together, to estimate the pressure drop of the entire system. In the current paper, this procedure will be implemented in one of the coal-fired electric utilities. A description of this method and results from field experience will form the rest of the contents of this paper.
2. Use of CFD in power industry applications In the power generation industry, many processes involve multi-phase flow, phase transformation, combustion, and complex chemical reactions [7]. This is particularly true for coal fired power
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plants. However, due to the complex nature of these phenomena, traditional research approaches were not adequate in providing a thorough understanding of these processes. Recently, CFD has been used in power industry to gain a qualitative as well as quantitative understanding of these processes. Pulverized coal combustion in a 2.5 MW burner was modelled using two commercial CFD codes [8]. Despite discrepancies between the solutions of the two codes, the predicted velocity, temperature, and species concentration were in overall agreement with the experimental data, suggesting that the two codes were capable of predicting good ÔtrendÕ solutions. The Eulerian–Eulerian multi-phase model in conjunction with the k–e model was applied to predict erosion in slurry pipeline tee-junctions [9]. The CFD model was used to assess several potential solutions to the erosion problem, and the results demonstrated the effectiveness with which CFD techniques can be used in industrial applications. Similar multi-phase model was employed to develop a computational model of erosion in a fluidized bed [10]. It was shown that the model predictions were in good agreement with the experiment results. Stopford reviewed some of the recent applications of CFD to the power generation and combustion industries [11]. Examples included coal-fired low-NOx burner design, furnace optimization, over-fire air, gas reburn, and laminar flames. The results showed that CFD modelling was well established as a design tool and has been widely used in the power generation industry to help engineers reduce emissions, increase thermal efficiency, select fuel, and extend plant lifetime. In this paper, an attempt will be made to take this new approach—CFD—to a problem faced by the power industry for a number of years: coal/air balancing. The multi-phase model in the unstructured version of CFX (version 5.5.1) will be applied to determine pressure drop in the piping systems in a power plant. Based on the predicted pressure drop, orifices in the piping systems will be added or modified and balanced coal/air flow will be achieved.
3. Principle of the method Fig. 1 shows two systems with the same elevation change, but different horizontal, vertical runs, and bends. Both systems start at the same elevation at the pulverizer exit and discharge at the same elevation in the boiler. System 1 has one vertical run, one horizontal run, and one bend. System 2 has 3 vertical runs, 3 horizontal runs, and 5 bends. The total pressure drop consists of frictional loss over the horizontal and vertical pipe lengths, a loss due to bends, and a loss due to gravity. In general if the total flow rate is Q, with flow rate in system 1 being Q1 and that in system 2 being Q2, and the pressure drop coefficients being K1 and K2, respectively, we have Q ¼ Q1 þ Q2 ; K 1 Q21 ¼ K 2 Q22 ; Q qffiffiffiffi ) Q2 ¼ 1 þ KK 21
Q qffiffiffiffi . and Q1 ¼ 1 þ KK 12
ð1Þ
Let the pressure drop coefficients for clean air and coal/air for systems 1 and 2 be K1A, K2A, and K1C, K2C respectively. Then the flow distribution with clean air is given as
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Fig. 1. Illustration of two systems with the same elevations change, but different horizontal and vertical runs, and bends.
Q2A ¼
1þ
Q qffiffiffiffiffiffi K 2A K 1A
and Q1A ¼
Q qffiffiffiffiffiffi
ð2Þ
Q qffiffiffiffiffiffi .
ð3Þ
1þ
K 1A K 2A
and that with coal/air is given as Q2C ¼
1þ
Q qffiffiffiffiffiffi K 2C K 1C
and Q1C ¼
1þ
K 1C K 2C
In most cases, it has been observed that the ratio of K2C/K1C is very nearly equal to K2A/K1A. In other words, clean air and coal/air are unbalanced in a similar manner. The pressure drop coefficient KOR of the orifice plate is calculated as the absolute difference in the pressure drop coefficients of the pipes. In order to achieve clean air balance, an orifice yielding a pressure drop coefficient of KOrf,A = K2A K1A should be introduced. In order to achieve coal/air balance, an orifice yielding a pressure drop coefficient of KOrf,C = K2C K1C should be introduced. As a general rule the pressure drop coefficients for the coal/air (two-phase) flow K1C and K2C, are always greater than the corresponding clean air (single-phase) pressure drop coefficients K1A and K2A (typically by a factor of 2–3) [12]. Hence, the orifice diameters based on the clean air distribution are larger than those based on the coal/air distributions. As a result of the above, it has been a normal trend in the power industry to under estimate the pressure drop requirement. The diameter of the orifice can be calculated from available empirical equations [13], one of the commonly used equations is " 0.375 !#2 F1 F0 F0 1 þ 0.707 1 ; ð4Þ K OR ¼ F0 F1 F1 2 where FF 01 ¼ AA01 ¼ DD01 , A0, A1 correspond to the area of the orifice and pipe, respectively, and, D0, D1 correspond to the diameters of the orifice and pipe, respectively.
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4. The systems modelled The four systems modelled using the numerical method are given in Table 1. As shown in the Table, there are 4 systems that carry coal/air mixture from the pulverizer to the furnace. The individual lengths of the horizontal and vertical sections between the bends are not known. The only data available is the total horizontal and vertical length of the systems, and the number of different bends in each system. Also, the bend angles for each system are known. If K1, K2, K3, and K4 are the pressure drop coefficients for systems 1, 2, 3, and 4, respectively, flow distributions V1, V2, V3, and V4 can be calculated by extending Eq. (3) to a 4-branch system. rffiffiffiffiffiffi 400 K1 qffiffiffiffi qffiffiffiffi qffiffiffiffi ; V 2 ð%Þ ¼ V 1 ; V 1 ð%Þ ¼ K1 K1 K1 K2 1 þ K2 þ K3 þ K4 rffiffiffiffiffiffi rffiffiffiffiffiffi K1 K1 V 3 ð%Þ ¼ V 1 ; V 4 ð%Þ ¼ V 1 . ð5Þ K3 K4 Note that for a perfectly balanced system K1 = K2 = K3 = K4, and in that case V1 = V2 = V3 = V4 = 100%. For an unbalanced system V1, V2, V3, and V4 could be different from 100%, but however, would still add to 400%. It can be seen from Table 2 that in the existing system the clean air and coal/air flows are both unbalanced. It can also be observed that the two unbalances are not similar due to the presence of orifices. Hence, it is proposed to retrofit the whole orificing system based on the coal/air balancing. Since the two-phase flow in the existing systems is quite complex and the data from standard handbook is unreliable, it was decided to Table 1 Detail of four systems that exit from one pulverizer and feed the boiler at the same elevation System
Total vertical length (m)
Total horizontal length (m)
Bends in system
Diameters of existing orifices in system (mm)
1
10.39
48.11
150, 160, 160, 135
2
10.39
36.83
120, 135
3 4
10.39 10.39
64.34 75.62
165, 90, 135 135, 90, 160, 160, 135
442 at 1 m distance 442 at 56 m distance 437 at 1 m distance 437 at 45 m distance 442 at 1 m distance No orifices
Note: Orifices are inserted according to the maximum pressure drop in the systems. Calculated pressure drop in system 4 is the maximum. Therefore, orifices were inserted in systems 1–3 to balance the pressure drop.
Table 2 Existing flow distribution for clean air and coal/air flows System
Clean air flow distribution (%)
Coal/air flow distribution (%)
1 2 3 4
95 97 100 108
102 108 96 94
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utilize the two-phase modelling technique to obtain the pressure data in each system. Then the orifice diameters are recalculated based on the CFD results and a well-balanced system is obtained.
5. CFD application to calculate pressure drop As discussed in Section 2, the exact geometries of the individual systems in a power plant are not always available. This problem was overcome by breaking up the geometry of the system into various components like the horizontal section, vertical section, and various bends. The pressure drop across each component is calculated and then put together to give the pressure drop along the whole geometry of the system. Examples of the geometries used for the modelling are shown in Fig. 2. The pressure drops for the horizontal and vertical lengths were calculated initially for a 60D pipe, where D is the diameter of the pipe. The pressure drops across unit length were then calculated and applied to the existing lengths of the pipe. A length of 60D was chosen to ensure that the flow became fully developed. The pressure drop per unit length was calculated for the fully developed region. It was found that for the current configuration and flow condition (Reynolds number 9.15 · 105, surface roughness e = 0.0026 mm) the flow became fully developed within 30D from the inlet. Therefore, for the bends, the upstream length was assumed to be 40D and downstream to be 20D and the pressure drop across the bend was calculated. For calculation of the steady state flow in the piping systems, continuity and momentum equations were solved along with the standard k–e turbulence model. Two-phase flow calculations were adopted to simulate the air flow and coal particles. The equation of continuity for a mixed fluid is expressed by Eq. (6), where a is the phase, ra is the volume fraction of that phase, qa is the density of the fluid in the phase a, xj is the coordinate with the index j ranging from 1 to 3, and U ja is the mean velocity in the phase a along the direction j. The continuity equation expressed for each control volume is shown in Eq. (7).
Fig. 2. Schematics of the components modelled.
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oðra qa Þ oðra qa U ja Þ ¼ 0; þ ot oxj X 1 oðra qa Þ oðra qa U j Þ X a ¼ 0; ra ¼ 1 or þ j q ot ox a a a
ð6Þ ð7Þ
where repeated indices imply summation from 1 to 3. The equation of motion is expressed by Eq. (8) oðra qa U ia Þ oðra qa U ia U ja Þ op oðra sji Þ þ ¼ ra i þ ra qa gi þ ; j ot ox ox oxj where p is the pressure and sij is the stress tensor given by i oU oU j sij ¼ leff þ i ; oxj ox
ð8Þ
ð9Þ
where leff is effective viscosity, which is defined as the sum of dynamic viscosity l and eddy viscosity lt, leff = l + lt. The eddy viscosity is provided by the k–e turbulence model. lt ¼ C l q
k2 ; e
ð10Þ
where Cl is a constant and is equal to 0.09, k is the turbulent kinetic energy, e is the dissipation rate, and both are provided by the k–e turbulence model.
o o l þ a ok a j ðra qa k a Þ þ j ra ðqa U a k a Þ l þ ð11Þ ¼ ra ðP a qa ea Þ þ T kab ; ot ox rk oxj
o o l þ a oea ea ¼ ra ðC e1 P a C e2 qa ea Þ þ T eab ; ð12Þ ðra qa ea Þ þ j ra ðqa U ja ea Þ l þ ot ox re oxj ka where rk = 1.0, re = 1.3, Ce1 = 1.44, and Ce2 = 1.92 are constants from the k–e model. T kab and T eab are the terms that represent the inter-phase transfer for k and e respectively. P represents the shear production due to turbulence for that particular phase, which is oU j oU j oU k ð13Þ þ j . P ¼ lt k ox oxk ox The continuity equation, momentum equation, and the turbulence model equation were solved for each phase. The pipe diameter was 0.527 m. For clean air flow, the air density was taken as 1.284 kg/m3, which is the value at room temperature. For coal/air flow, the air density was 0.977 kg/m3, which is the value at 88 C, and the coal density was 1398 kg/m3. The coal flow rate was 2.36 kg/s and the air flow rate was 5.00 kg/s. The boundary conditions were assumed to be uniform velocity distribution at the inlet and zero gage pressure (open to atmosphere) at the outlet. Grid refinement near the walls was used for grid generation (Fig. 3). This allows for much better resolution of the velocity field near the wall where it changes rapidly. Reynolds Averaged Navier–Stokes equations (RANS) were solved using finite volume method on an unstructured mesh with the standard k–e model for turbulence.
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Fig. 3. Cross-section and plan view of the unstructured grid.
A typical mesh size for the CFD simulation was around 300,000 mesh cells, each steady state case took 11–16 wall clock hours on Dell Optiplex GX270 computers. These computers had 2 Intel P4 3.20 GHz processors with 2.00GB RAM. The steady state solutions used pseudo time step, which was determined by the CFL requirement of the solver. Convergence was claimed when a stable pressure drop was achieved, usually it took 7000 iterations. The friction factor was calculated by using the pressure drop in the fully developed region of the pipe. The friction factor for clean air was calculated by f ¼
DP L 1 qU 2avg D 2
;
ð14Þ
where f is the friction factor, DP is the pressure drop along the pipe over a distance of L in the fully developed region, q is the density of air, Uavg is the average velocity, and D is the diameter of the pipe. For a fully developed flow, the friction factor is a constant. From this calculation, the friction factor was found to be f = 0.0164. The results were compared to those in the Moody chart (Reynolds number 9.15 · 105, surface roughness e = 0.0026 mm, friction factor f = 0.017). The boundary conditions for the coal/air flow were imposed in the same manner as those for clean air flow. The boundary condition for the particles was no slip i.e., the particles stick to the surface if they hit the surface. The volume fraction for coal at inlet was considered to be uniformly distributed. The coal particles were all considered to be spherical and of the same uniform size (diameter 1 lm). Table 3 gives the pressure drop per unit length for the horizontal and vertical components and also the pressure drop across the bends for both clean air and coal/air flows. As can be seen, the pressure drop for the coal/air flow is always greater than that of the clean
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Table 3 Pressure drop across various components for clean air and coal/air flows Horizontal (Pa/m) Vertical (Pa/m) Bend angles 90 (Pa) 120 (Pa) 135 (Pa) 150 (Pa) 160 (Pa) 165 (Pa) Clean air 11.02 Coal/air 27.52
10.82 16.6
48.68 104.33
32.06 51.76
23.93 29.63
13.79 15.64
9.18 11.47
5.71 8.38
air flow. It can be said that this is mainly due to the resistance offered by the interaction between air and coal particles and among coal particles themselves, as well as blockage effects.
6. Results In this study, orifice sizes were calculated for coal/air balancing. Based on the given data, the calculations have been performed with the existing system configuration. The clean air and coal/ air pressure drop coefficients, and flow distributions were first calculated. Orifice sizes for coal/air balancing were then calculated. Note that in each system if one or more orifices already exist, then there was at least one orifice at 1-m distance from the pulverizer exit. It was then tacitly assumed that the new orifice would replace that orifice. Table 1 gives the data from the power plant. This table is self-explanatory. The existing flow distributions are given in Table 2, which are based on the pressure drop calculations shown in Table 3. The orifice diameters for balancing coal/air flow are shown in Table 4. The tailored clean air flow and the balanced coal/air flow distribution after insertion of new orifices is shown in Table 5. As can be seen from Table 5, the pressure drop for each system is the same and Table 4 Orifice diameter calculation for coal/air balancing System
K Loss coefficient
Existing orifice KOR
Total K
New KOR
Orifice diameter (mm)
1 2 3 4
5.84 4.73 7.78 9.10
0.95 1.07 0.00 0.00
6.79 5.80 7.78 9.10
2.32 3.31 1.32 0.00
401.78 389.08 427.85 –
Note: K is the pressure loss coefficient of each system and KOR is the pressure loss coefficient of the orifice calculated based on Eq. (4).
Table 5 Tailored clean air flow and balanced coal/air flow distribution after insertion of new orifices System 1 2 3 4
Clean air
Coal/air
Total K after retrofit
Flow distribution (%)
Total K after retrofit
Flow distribution (%)
5.25 6.01 3.88 3.01
91 85 105 120
9.10 9.10 9.10 9.10
100 100 100 100
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consequently the coal/air flow is balanced. In each instance, an existing orifice at 1 m distance is to be replaced by the new orifice. The CFD simulations also provide detailed information of the two-phase flow field. Fig. 4 shows the close-up view of the air velocity magnitude contours for bends with various angles. The gravity force is vertically downward (in the negative y-direction). All contours shown in Figs. 4 and 5 are on the center plane (xz-plane) that passes the axis of the bend. In the horizontal portion of the bend, all flows exhibit similar velocity distributions and there is no variation in the
Fig. 4. Air velocity magnitude contours for bends with various angles.
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Fig. 5. Contours of volume fraction of coal for bends with various angles.
streamwise direction. This is because the flow has gone through 40D upstream length before it reaches the bend, and flow has become fully developed. It is observed that the velocity is lower near the bottom of the horizontal portion. This is due to the higher resistance to the air induced by the coal particles when they deposit to the pipe bottom. For the flow conditions considered in the current study, the effects of coal particle deposition is significant. It can be clearly seen from Fig. 4 that the characteristics of the air flow downstream of the bend strongly depend on the bend angle. For sharp turns (Fig. 4a–c), the flow has to change direction quickly and the higher velocity flow is shifted towards the outer radius of the downstream bend. While near the inner radius of
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the bend, a lower velocity region can be identified. As shown in Table 3, this sharp flow direction change results in significant pressure loss, with the 90 bend giving the highest. For higher bend angles (Fig. 4d), the flow goes through the bend quite smoothly, and the pressure loss is insignificant compared to the sharp turning cases. Fig. 5 displays the contours of volume of fluid (VOF) of coal for bends with various angles. In the horizontal portion, all bends show similar coal VOF distribution, just like the velocity contours in Fig. 4. Higher coal VOF is found at the lower part of the upstream pipe. This is again attributed to the deposition of the coal particles. In the bend, maximum VOF of coal can be identified near the outer radius of the bend. This is explained by the flow impingement in the bend, and the attachment and accumulation of coal particles at this location. For sharp turning bends, the overall VOF of coal becomes much less downstream of the bend, indicating significant deposition and accumulation of coal particles in the bend and upstream pipe (Fig. 5a–c). While for smooth turning bend, the effects of coal particle deposition and accumulation are not as prominent (Fig. 5d). It should be pointed out that for the 90 bend, immediately downstream of the bend and close to the inner radius, there is a localized region with a higher coal VOF than its local ambient. This is the indication of flow separation. The local recirculating flow traps a significant amount of coal particles and a region of higher VOF of coal is formed. For 120 and 130 bends, this localized region can still be seen, but the size is much smaller. While for the 160 bend, it is not recognizable, suggesting negligible or non-existent flow separation downstream of the bend.
7. Conclusions There is currently no easy way of measuring coal/air flow in a power plant. In order to balance the coal/air flow to the individual burners, it would, therefore, be necessary to rely on clean air tests. The industry practice has so far been to balance the clean air flow and accept the resulting imbalance in the coal/air flow. It was observed in one specific case that, when the clean air is balanced with a maximum deviation of 3% from the average, the corresponding coal/air flow deviation was approximately 27%. This is unacceptable from the consideration of efficient unit operation. A new method in which creating a tailored imbalance in clean air flow corresponding to a balanced coal/air flow distribution has been successfully proposed in this paper. Commercially available software CFX was used to calculate pressure drops in systems. The two-phase flow phenomena was simulated using the multi-phase modelling technique. Using this, several geometries involving any number of independent lines starting from a mill and discharging to a given burner can be handled. The results show that the pressure drop in the systems strongly depends on the system geometry. Orifices are sized based on calculated coal/air pressure drops, and finally imposing a tailored imbalance in clean air flow distribution leading to a balanced coal/air distribution. It should be pointed out that in order to implement this method in power plant, verification can still be done by measuring the tailored clean air distribution. The numerical results also provide detailed information of the two-phase flow field in the piping systems in a power plant, based on which physical insights were obtained and better understanding of the complex flow phenomena was achieved. This study demonstrated that CFD can be used as an effective tool for design and research for power industry applications.
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