Prediction of sulfuric acid dew point temperature on heat transfer fin surface

Applied Thermal Engineering 98 (2016) 492–501

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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g

Research Paper

Prediction of sulfuric acid dew point temperature on heat transfer fin surface Y.C. Wang, G.H. Tang * MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

H I G H L I G H T S

• • • •

Local sulfuric acid dew point on fin surface is predicted for the first time. Wall temperature, flue speed and fin effects on acid dew point are firstly studied. Sulfuric acid dew point is higher on windward and first row of fin surface. Novel types of fin surfaces can reduce sulfuric acid dew point temperature.

A R T I C L E

I N F O

Article history: Received 22 April 2015 Accepted 15 December 2015 Available online 30 December 2015 Keywords: Sulfuric acid dew point temperature Local distribution Partial pressure Heat transfer fin surface Tube bank

A B S T R A C T

Sulfuric acid dew point temperature is an important parameter denoting the dew point corrosion. The sulfuric acid dew point temperature is calculated by considering both the vapor–liquid equilibrium effect and multi-component diffusion effect. In addition, the local distribution of acid dew point temperature on fin surface is numerically predicted for the first time. The influences of fuel type (sulfur content, water content and ash content), wall temperature, excess air ratio, flue gas inlet velocity, fly ash particle (size and quantity) and heat transfer fin structure on the sulfuric acid dew point temperature are discussed. The results show that different types of fuels (which differ in gas composition and combustion temperature) have a great impact on the sulfuric acid dew point temperature. The sulfuric acid dew point temperature decreases with the reduction of excess air ratio, the increasing of wall temperature, and the condensation of sulfuric acid vapor on ash particle surface. The sulfuric acid vapor condensates more seriously on the tube windward than on the leeward. The novel types of heat transfer fins with high heat transfer performance can also reduce the local sulfuric acid dew point temperature, and the maximum reduction of sulfuric acid dew point is 4.1 K between the novel fin surface and the original H-type fin surface. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction The sulfuric oxides and water vapor in flue gas can condense into sulfuric acid solution on the low temperature surface of heat exchanger when the wall temperature is below the local dew point temperature, which will corrode the wall and lead to equipment failure. Great attention has been paid to the sulfuric acid dew point corrosion and the corrosion rate and morphology have been studied [1–3]. The sulfuric acid dew point temperature plays an important role in the formation of sulfuric acid dew point corrosion. The existing research methods for the sulfuric acid dew point temperature of flue gas are mainly classified into chart method, empirical equation, neural network method, numerical analysis and experimental measurement etc. The Muller curve is the basis for

* Corresponding author. Tel.: +86 29 82665319; fax: +86 29 82665445. E-mail address: [email protected] (G.H. Tang). http://dx.doi.org/10.1016/j.applthermaleng.2015.12.078 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

predicting the sulfuric acid dew point temperature, and it shows the relationship between the sulfuric acid dew point temperature and the partial pressure of sulfur trioxide vapor in flue gas [4]. However, the influence of the water vapor partial pressure on the sulfuric acid dew point temperature was not considered. Pierce proposed an estimation method to calculate the sulfuric acid dew point temperature when the fuel characteristics and excess air ratio are provided [5]. But the error of this method was large due to the limited accuracy of thermodynamic parameters of sulfuric acid vapor and solution. Once the thermodynamic parameters of sulfuric acid solution and sulfuric acid vapor are calculated accurately [6], the sulfuric acid dew point formula proposed by Verhoff and Banchero [7] can be applied to high gas temperature. However, the error is still large for the low gas temperature. Okkes proposed a formula for sulfuric acid dew point temperature based on the experimental data from Muller, which is related to the partial pressure of sulfur trioxide vapor and water vapor in flue gas [8]. The Soviet standard formula [9] is widely used among the existing empirical formulas.

Y.C. Wang, G.H. Tang/Applied Thermal Engineering 98 (2016) 492–501

Recently, some other methods for the prediction of the sulfuric acid dew point have also been studied. ZareNezhad and Aminian presented a model of multi-layer feed forward neural network for predicting sulfuric acid dew point over sulfur trioxide and water vapor concentration [10]. A predictive tool was also proposed based on Vandermonde matrix, which accounts for fuel type, sulfur fraction and excess air ratio [11]. Shi et al. proposed the concept of engineering sulfuric acid dew point temperature, at which the heat transfer performance drops sharply due to the influences of both ash deposition and acid condensation in the experiment. It is about 30 K lower than the thermodynamic sulfuric acid dew point temperature [12]. Wang et al. studied the coupling mechanism between ash deposition and dew point corrosion and found that the acid vapor condensed in the main condensation zone rather than directly on the tube wall surface [13]. In summary, although many prediction methods for sulfuric acid dew point temperature have been studied, the effects of specific position and structure of heat transfer surface on the sulfuric acid dew point temperature have not yet been considered in the literature. In this work, we calculate the sulfuric acid dew point temperature of flue gas and compare it with the Soviet standard formula, and a variety of factors (such as fuel type, wall temperature, excess air ratio, inlet velocity, fly ash particles and fin structure) which affect the distribution of sulfuric acid dew point temperature on the heat transfer surface of H-type finned oval tube are evaluated. In addition, the distribution of sulfuric acid dew point temperature on the fin surfaces of tube bank is examined. 2. Model description and numerical method 2.1. Physical model A multiple-row oval tube bank based on the H-type fin with compound dimples and rectangular longitudinal vortex generators is shown in Fig. 1. Four types of fin tubes are studied, which are the original H-type finned oval tube, the fin surfaces with bleeding dimples (Dimple), with −30° rectangular longitudinal vortex generators (LVG) and with compound dimples and rectangular longitudinal vortex generators (Dimple-LVG). The dimple in the present study is modified by carving a bleed hole inside to make the fluid flow through. The geometry parameters of the oval tube bank and four types of fins are listed in Table 1. The flue gas consisting of air, water vapor and sulfuric trioxide flows across the tube while the water flows inside the tube. 2.2. Governing equations and boundary conditions The calculation domain is marked in the blue solid box, as shown in Fig. 1a and 1b. The extended zones are set at the inlet to ensure the uniform inlet flow and at the outlet to prevent the fluid backflow. The top and bottom surfaces of the calculation domain are periodic boundary, and the left and right surfaces are symmetry boundary. The velocity inlet and pressure outlet are adopted in the numerical simulation. Assumptions and simplifications performed in the present simulation are listed below. (1) The temperature of the tube wall is constant. (2) The thermal resistance of the liquid film on the fin surface is neglected as its contribution to the total thermal resistance is below 3% [14]. (3) The flue gas is assumed to be an ideal gas mixture with a variety of gas compositions. (4) Only the velocity of flue gas in the x direction is considered and the velocities in other directions caused by diffusion are ignored.

493

The mass, momentum and energy conservation equations and the RNG k-ε turbulence model are presented as follows. Continuity:

∇⋅U = 0

(1)

Momentum:

1 U ⋅∇U = υ∇ 2U − ∇P ρ

(2)

Energy:

⎛ λ ⎞ ∇ ⋅ (UT ) = ∇ ⋅ ⎜ ∇T ⎟ ⎝ ρc p ⎠

(3)

The Reynolds number of flue gas flow in the simulations ranges from 12,253 to 28,000, so the turbulent flow is considered and the RNG k-ε equation model is employed [15].

∂ ⎡ ∂ ∂k ⎤ α k (η + ηt ) − ρε + G k (ρkui ) = ∂x j ⎢⎣ ∂x i ∂x j ⎥⎦

(4)

∂ ⎡ ε2 ε ∂ ∂ε ⎤ α ε (η + ηt ) − C 2ε ρ − R ε + C 1εG k (ρεui ) = ⎢ ⎥ ∂x j ⎣ ∂x i ∂x j ⎦ k k

(5)

2 where the effective viscosity ηt = c μ ρk ε with c μ = 0.0845, and α k and α ε are the inverse effective Prandtl numbers for k and ε , respectively, G k is the generation of turbulence kinetic energy due to the mean velocity gradient with G k = ηt S 2, R ε is the rate of strain term, C 1ε = 1.42 and C 2ε = 1.68. The key to obtain the sulfuric acid dew point temperature is to solve the sulfuric acid vapor distribution in flue gas. And the distribution of sulfuric acid vapor partial pressure in flue gas is solved with the commercial software Fluent combined with the userdefined function, based on which the distribution of sulfuric acid dew point temperature, is calculated. We also simulate the condensation of the sulfuric acid vapor on the fly ash particle surface. They are discussed in the next subsection.

2.3. Theoretical and numerical models for sulfuric acid dew point temperature The sulfuric acid dew point temperature of flue gas can be solved by the thermodynamic theory [16], given by

R P ⎞ ⎛ 1 Ta = 1 ⎜ − ln a ⎝ T a,0 ΔQ c aP ⎟⎠

(6)

where Ta and Ta,0 are the sulfuric acid dew point temperature of flue gas and pure sulfuric acid vapor, respectively, ΔQ is the heat of vaporization for pure sulfuric acid estimated by the Watson formula and correlations [17], Pa is the sulfuric acid vapor partial pressure in flue gas, P is the pressure of flue gas, ca is the sulfuric acid solution concentration, and R is the ideal gas constant. To obtain the sulfuric acid dew point temperature, the sulfuric acid solution concentration and the sulfuric acid vapor partial pressure should be calculated. In the case of known fuel type, lower heating value and excess air ratio, the partial pressure of water vapor Pw and sulfuric acid vapor Pa in flue gas can be solved according to the material balance and heat balance equations [18], and the process is presented in Part I of Fig. 2. Different from Pa, the partial pressure of species i at the gas–liquid interface Pi is affected by the concentration and temperature of sulfuric acid solution at the interface. However, both ca and Pi are unknown. They can be calculated by iteration [19] from Eqs. (7)–(9), and the process is shown in Part II of Fig. 2.

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Y.C. Wang, G.H. Tang/Applied Thermal Engineering 98 (2016) 492–501

(a) left surface

fin domain

entrance area

S1

right surface tail extension area

S2 (b) top surface

F

Ft

bottom surface

(c)

(d)

(e)

(f)

Fig. 1. Schematic configuration of (a) top view of tube bank, (b) side view of tube bank, (c) H-type finned tube, (d) Dimple finned tube, (e) LVG finned tube and (f) DimpleLVG finned tube.

ln Pi = ai A + biB + c iC + ΔH ivD + ΔS ivE + C pilF + L ilG + α iH + ln ai (298)

(7)

Table 1 Geometry parameters of the studied heat exchanger. H(mm)

w(mm)

m(mm)

S1(mm)

S2(mm)

F(mm)

Ft(mm)

95

62

12

100

140

15

3

N

a(mm)

b(mm)

c(mm)

d(mm)

w1(mm)

w2(mm)

5

64

40

35

49

20

26

e(mm)

g(mm)

h(mm)

θ(°)

r1(mm)

r2(mm)

Fm(mm)

3

5

10

30

1

2

21.34

where A–H are the equation coefficients affected by the temperature of sulfuric acid solution, ai , bi, c i , ΔH iv and ΔS iv are the thermodynamic parameters for pure component at 298 K, and they are estimated based on experimental measurements and observed spectra [20]. C pil , L il and α i are the parameters dependent on the concentration change of composition when the temperature is 298 K, and lnai is the liquid activity logarithm. They are obtained based on experimental measurements and are forced to comply with the Gibbs–Duhem equation, when the concentration of sulfuric acid solution is in the range of 0.0177–0.999 [21]. The real-gas effect which indicates the dissociation of H2SO4 into H2O and SO3 in the vapor phase is introduced by using the apparent fugacity coefficient to improve the predictions from the acid vapor partial pressure calculation [22], given by

Y.C. Wang, G.H. Tang/Applied Thermal Engineering 98 (2016) 492–501

a

495

surface per unit volume of flue gas. The source term is N a = 0 if there is no ash particle in flue gas. Otherwise, the source term N a is calculated by

Qnet,ar

4π r 2D am dPa N a = ρp RT dr

T

Pw

where ρp is the number of particles per unit volume of flue gas, r is the radial coordinate of particle sphere, and T is the temperature of condensation sulfuric acid solution, which is equal to the particle surface temperature. When the temperature of the fly ash particle is lower than the critical super-saturation temperature, the sulfuric acid and water vapor start to condensate first on the largest particles. However, condensation does not take place on the particle surface [24] if the temperature is higher than the critical super-saturation temperature. The sulfuric acid vapor partial pressure in flue gas will decrease with the sulfuric acid vapor condensation on the ash particle surface, which has significant effect on the sulfuric acid dew point temperature [24]. The sulfuric acid flux on the particles is defined as the mass transfer rate of the sulfuric acid vapor around the particles within a unit volume of flue gas, based on the mass conservation principle. It can be determined from the Fick’s law and the state equation of ideal gas as shown in Eq. (11). The flux of sulfuric acid vapor on the particle surface is different from that on the flat surface, because the surface curvature can increase the droplet vapor pressure at the interface [25]. The flux of sulfuric acid vapor on the particle surface Pa,0 is calculated by

Pa i Pw,0 = Pwi

Tw

ca

i +1 Pa,0i +1 Pw,0

i +1 Pw,0 − Pwi+1 < 10−5

Fig. 2. Iterative solution of sulfuric acid vapor partial pressure and sulfuric acid solution concentration.

Pa,0 = Pi φa,0

φa,0 =

Pw 2 Pw + K 0 + K 1 (Pw )

(8)

Pa,0 = Pa*,0 exp (2σ M ρRTrp )

(12)

where Pa,*0 is the sulfuric acid vapor partial pressure at a flat surface under the same conditions of a particle surface, σ is the surface tension, ρ is the density of the condensation sulfuric acid solution, rp is the radius of particle sphere, and M is the molecular weight. 3. Results and discussion

(9) 3.1. Grid independence test and validation of the computation model

where Pa,0 is the real sulfuric acid vapor partial pressure at the gas– liquid interface, φa,0 is the apparent fugacity coefficient, Pw is the water vapor partial pressure in flue gas, and K0 and K1 are the reaction equilibrium constants [23]. In the heat exchanger, the sulfuric acid vapor partial pressure Pa in flue gas which flows outside the heat transfer tube changes along the flow direction. As shown in Eq. (10), it is numerically solved with the Fluent software combined with the user-defined function. The convection term, diffusion term and source term are defined by the macros (DEFINE_DIFFUSIVITY, DEFINE_UDS_FLUX, and DEFINE_SOURCE) while the boundary conditions are defined by the macro (DEFINE_PROFILE). The sulfuric acid solution concentration ca on different positions of fin surface is calculated by the iteration process schematic in Part II of Fig. 2. Firstly, we assume the values of water vapor partial pressure in flue gas and wall temperature to determine the acid solution concentration, and the acid solution concentration is calculated by iteration from Eq. (7) [19]. Secondly, the sulfuric acid partial pressures at the gas–liquid interface are solved from Eqs. (7)–(9). Thirdly, the real water vapor partial pressure by the sulfuric acid flux and sulfuric acid solution concentration is obtained. Repeat above three steps with the updated water vapor partial pressure at the gas-liquid interface until the iteration converges.

U ⋅∇Pa + N a = ∇ ⋅ (D am∇Pa )

(11)

(10)

where Dam is the effective diffusion coefficient for the sulfuric acid vapor, and N a is the flux of sulfuric acid vapor on the ash particle

The grid independence is carried out by simulating the average sulfuric acid dew point temperature of flue gas on the fin surface and the heat transfer coefficient of the single H-type finned oval tube. The hexahedral grid is applied in the model and the results are summarized in Table 2. It can be seen that the effect of grid number on the sulfuric acid dew point temperature is negligible. But the heat transfer coefficient changes obviously at different grid numbers. The solution of the grid system of 964,400 can be regarded as grid-independent. The grid numbers for other cases in the present simulations are also of the same order. To validate the present model, the predicted sulfuric acid dew point temperature is compared with the experimental data [10] in Fig. 3. Among the 48 data points, 12 points are in the SO3 concentration range of 1–6 ppmv and H2O content of 5–20% while the other 36 points are in the SO3 concentration range of 6–500 ppmv and H2O content of 5–30%. In Fig. 3, all the predictions fit well with the

Table 2 Grid independence test. Grid

Nu

Difference (%)

Ta (K)

Difference (%)

133,480 236,574 390,195 964,400 1,245,825

48.862 51.122 52.943 56.304 57.142

14.49 10.54 7.35 1.47 –

379.78 379.06 378.16 376.81 375.69

1.09 0.90 0.66 0.30 –

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Y.C. Wang, G.H. Tang/Applied Thermal Engineering 98 (2016) 492–501

460

510

Ta (K)

Numerical Ta (K)

420

+ 5%

450 420

- 5%

390

[9]

P.A. present

440

480

400 380 360

360 330 330

(a)

340 360

390

420

450

480

320

510

0

2

4

Experimental Ta (K) 1.0

Fig. 3. Comparison of sulfuric acid dew point temperature between the predictions and experimental results.

6 group

8

(b)

Ya (Pa)

12

[24]

numerical present

0.8 experimental data within a relative deviation of ±5%. It can be concluded that the present computation method meets the requirements for engineering applications in the specified ranges of SO3 concentration and H2O content. Generally the partial pressure of water vapor in gas is usually low in the coal-fired power plants due to the low water content of coal [18]. So the confidence limits of the predicted sulfuric acid dew point temperature are able to meet the requirement for coal-fired boilers. The studied 10 types of fuels including lignite, anthracite, meagre coal and bituminous coal from various origins are listed in Table 3 [18]. The theoretically predicted sulfuric acid dew point temperature is compared with the results calculated by the Soviet standard formula (Р.А. Лероеян) [9] as shown in Fig. 4a. All the deviations for the sulfuric acid dew point temperature are within 5%. A numerical simulation is conducted for the distribution of the sulfuric acid vapor partial pressure for the flue gas with fly ash particles at the passage wall in a circular tube. The geometry parameters and operating conditions are presented in Table 4, which are the same as Reference [24]. Fig. 4b shows that the deviations between the present work and the literature are quite small at the entrance of the tube because little sulfuric acid vapor condenses on the fly ash particle surface. However, the deviation expands with the increase of the condensation of sulfuric acid vapor on the fly ash particle surface in the streamwise direction. The deviation keeps unchanged after L = 230 mm and all the deviations are within 15%.

10

0.6 0.4 0.2 0.0 0

50

100

150

200

250

300

L (mm) Fig. 4. Model validation of (a) sulfuric acid dew point temperature and (b) sulfuric acid vapor partial pressure at the gas–liquid interface.

3.2. Sulfuric acid dew point temperature on the fin surface of single tube Figs. 5 and 6 show the distributions of wall temperature and the sulfuric acid dew point temperature on the fin surfaces. The studied fuel is the meagre coal of group 6 in Table 3. The velocity and temperature of the inlet flue gas are 8 m·s−1 and 415 K, respectively. The

Table 3 Model validation of sulfuric acid dew point temperature. Species

Lignite Anthracite Meagre coal Bituminous coal

Group

Group1 Group2 Group3 Group4 Group5 Group6 Group7 Group8 Group9 Group10

Lower heating value

Present

P.A. Лероеян

Car (%)

Har (%)

Oar (%)

Nar (%)

Sar (%)

Aar (%)

Mar (%)

Qnet,v,ar (kJ·kg−1)

Ta (K)

T (K)

34.65 36.50 51.53 65.65 57.93 63.57 38.46 44.90 55.82 58.30

2.34 3.03 1.98 2.64 2.69 3.00 2.16 3.03 4.95 3.88

10.48 10.40 2.71 3.19 2.11 1.79 4.65 8.23 8.77 6.53

0.57 0.95 0.60 0.99 1.14 0.96 0.52 0.94 1.04 1.07

0.31 0.69 3.14 0.51 2.58 1.54 0.61 0.88 0.51 1.40

17.02 28.40 32.74 19.02 27.75 23.24 43.10 29.03 16.71 19.92

34.63 20.03 7.30 8.00 5.80 5.90 10.50 12.99 12.20 8.90

12,280 13,440 19,530 24,420 22,100 23,810 15,530 16,860 22,380 23,320

384.0 392.3 399.0 373.3 396.1 389.3 378.6 389.0 379.4 388.4

382.0 391.7 410.7 360.7 402.4 386.1 375.8 387.4 373.4 390.3

Composition of coal

Y.C. Wang, G.H. Tang/Applied Thermal Engineering 98 (2016) 492–501

L(mm)

d(mm)

uin(m·s−1)

Tg(K)

Tw(K)

xa(ppm)

xw(%)

300

10

3.3

400

350

6

6

constant wall temperature (350 K) is assigned. Due to the cooling of the tube and the thermal resistance of fin, the wall temperature at the edges of fin is higher than that in the central zone of fin in Fig. 5. The maximum difference of the spanwise-average values of wall temperature in different zones of fin is up to 17 K. It can be seen from Fig. 6that the sulfuric acid dew point temperature reaches peak at the leading edge of fin, and then it decreases due to the development of sulfuric acid concentration boundary layer on the fin surface. The boundary layer weakens the mass transfer and leads to lower sulfuric acid vapor partial pressure at the gas–liquid interface. However, the fin structure and the horseshoe vortices (as shown in Fig. 7) before the front edge of tube wall will make more efficient mixing and enhance the mass transfer, so the sulfuric acid dew point temperature rises in this zone. It can be seen from Fig. 7 that there is backflow close to the surface of fin in the x direction, which leads to the horseshoe vortices, though not obvious. After that, the condensation of the sulfuric acid vapor leads to the re-

(a) 385.0 383.3 381.6 380.0 378.3 376.6 375.0 373.3 371.6 370.0 368.3 366.6 365.0

Ta (K) 390

(b)

385 380

Ta (K)

Table 4 Geometry parameters and physical properties for the validation of sulfuric acid vapor partial pressure.

497

375

(a) 372.0 370.6 369.1 367.7 366.3 364.9 363.4 362.0 360.6 359.1 357.7 356.3 354.9 353.4 352.0

370 365 -10

0

10 20 30 40 50 60 70 80 90 100

L (mm) Fig. 6. Sulfuric acid dew point temperature of flue gas along the flow direction on the fin surface. (a) Contours. (b) spanwise-average value.

Tw (K) 380

(b)

375

Tw (K)

370 365 360 355 350 -10

0

10 20 30 40 50 60 70 80 90 100

L (mm) Fig. 5. Wall temperature of fin surface along the flow direction. (a) Contours. (b) spanwise-average value.

Fig. 7. Local velocity distribution in x direction at y = 6.5 mm for the original H-type fin.

498

Y.C. Wang, G.H. Tang/Applied Thermal Engineering 98 (2016) 492–501

405

(a)

group10 group8 group6 group3 group2

400 395

Ta (K)

390 385 380 375 370 365 -10

0

10 20 30 40 50 60 70 80 90 100

L (mm) 395

(b)

α=1.50 α=1.45 α=1.40 α=1.35 α=1.30

390

Ta (K)

385 380

temperature on the same fin surface along the streamwise direction, all of which decrease by about 15 K. As shown in Fig. 8b, the sulfuric acid dew point temperature increases with the excess air ratio. The sulfuric acid dew point temperature increases by about 9.3 K when the excess air ratio varies from 1.30 to 1.50. It is because that the large excess air ratio will enhance the concentration of sulfur trioxide vapor in flue gas under the same conditions. We choose the meagre coal of group 6 as the calculated fuel in all the following discussion. From Fig. 9a, we can see that the inlet velocity of flue gas has little effect on the sulfuric acid dew point temperature, and the maximum temperature difference is only about 3 K when the velocity increases from 6 m·s−1 to 14 m·s−1. At both fin edges, the sulfuric acid dew point temperature decreases with the increasing of the inlet velocity of flue gas, but in the middle zone of the fin, the sulfuric acid dew point temperature increases with the increasing of the velocity. The sulfuric acid dew point temperature is affected by two opposite factors. It increases with the sulfuric acid vapor partial pressure while decreases with the sulfuric acid solution concentration based on Eq. (6). On one hand, the high velocity of flue gas accelerates the mass transfer and generates larger sulfuric acid vapor partial pressure over the fin surface. On the other hand, it raises the wall temperature and increases the sulfuric acid solution concentration on the fin surface. Obviously, the effect of sulfuric acid solution concentration is more dominant on the fin

390 375

-1

14 m·s -1 12 m·s -1 10 m·s -1 8 m·s -1 6 m·s

385

370 365

380

0

10 20 30 40 50 60 70 80 90 100

Ta (K)

360 -10

(a)

375

L (mm) Fig. 8. Effects of (a) fuel type and (b) excess air ratio on the spanwise-average sulfuric acid dew point temperature of flue gas along the flow direction for uin = 8 m·s−1, Tg = 414 K and Tw = 350 K.

370 365 -10

0

10 20 30 40 50 60 70 80 90 100

L (mm) 410

(b)

Tw=365 K Tw=355 K

400

Tw=345 K Tw=335 K

390

Ta (K)

duction of the sulfuric acid vapor partial pressure in flue gas and causes the sulfuric acid dew point temperature on the fin surface to decrease along the streamwise direction. The maximum difference among spanwise-average value of sulfuric acid dew point temperature on the fin surface is up to 15 K, and the sulfuric acid vapor condensates more seriously on the windward of tube than on the leeward. The fuel type and the excess air ratio are two important factors affecting the sulfuric acid dew point temperature, which are taken into account in most of the present calculations for the sulfuric acid dew point temperature. In Fig. 8a, we present the sulfuric acid dew point temperature of five types of coals in the streamwise direction, and their compositions are presented in Table 3. The differences in sulfuric acid dew point temperature are large among the five types of coals. It is about 10 K between the coal of group 3 and group 10 under the same conditions. With the information of sulfur content, water content and ash content, the production of sulfuric oxide and the combustion temperature can be calculated by the material balance and heat balance equations, which lead to different concentrations of sulfuric acid vapor and water vapor in flue gas. The fin structure affects the trend of sulfuric acid dew point temperature by changing the wall temperature and the velocity of flue gas, so the five types of coals have similar trend of sulfuric acid dew point

Tw=325 K

380 370 360 -10

0

10 20 30 40 50 60 70 80 90 100

L (mm) Fig. 9. Effects of (a) inlet velocity and (b) wall temperature on the spanwiseaverage sulfuric acid dew point temperature of flue gas along the flow direction for (a) Tg = 414 K and Tw = 350 K, and (b) uin = 8 m·s−1 and Tg = 414 K.

Y.C. Wang, G.H. Tang/Applied Thermal Engineering 98 (2016) 492–501

(a)

-3

-2

-3

ρp=1.65×10 kg·m

388

ρp=1.25×10 kg·m -3

-3

ρp=8.5×10 kg·m

384

Ta (K)

-2

ρp=4.5×10 kg·m -3

380

-3

no fly ash particle

376 372 368 -10

0

10 20 30 40 50 60 70 80 90 100

L (mm) 392

(b)

-5

rp=1.05×10 m

388

-6

rp=6.5×10 m -6

rp=3.5×10 m

384

-6

Ta (K)

rp=2.5×10 m

380

no fly ash particle

376 372 368 -10

0

10 20 30 40 50 60 70 80 90 100

L (mm) Fig. 10. Effects of (a) quantity and (b) size of fly ash particles on the spanwiseaverage sulfuric acid dew point temperature of flue gas along the flow direction for uin = 8 m·s−1, Tg = 414 K and Tw = 350 K.

edges. However, the effect of sulfuric acid vapor partial pressure is more significant in the middle zone of fin. The wall temperature is also an important factor affecting the sulfuric acid dew point temperature. As shown in Fig. 9b, the sulfuric acid dew point temperature decreases by 14–17 K when the wall temperature increases from 325 K to 365 K which indicates that the increasing of the wall temperature will raise the partial pressure of saturated sulfuric acid at the gas–liquid interface, weaken the mass transfer and decrease the sulfuric acid vapor partial pressure over the fin surface. It can be seen from Fig. 10 that both the size and quantity of fly ash particles affect the sulfuric acid dew point temperature more significantly at the tail of fin. The total condensed sulfuric acid on the particle surface increases gradually along the streamwise direction, which causes the decreasing of the sulfuric acid vapor partial pressure in flue gas. When the condensing sulfuric acid solution on the particle surface accumulates up to a certain amount, the temperature difference of the acid dew point becomes more obvious. As shown in Fig. 10a, the sulfuric acid dew point temperature decreases with the increase of the quantity of fly ash particles in flue gas under the same fly ash particle size. Among the five cases, the sulfuric acid dew point temperature achieves the lowest at the tail of fin when the fly ash quantity is 1.65 × 10−2 kg·m−3. And it is

about 2 K lower than that of the flue gas without any fly ash particles. The spanwise-average sulfuric acid dew point temperature on the fin surface decreases by 15.14, 15.45, 15.75, 16.06 and 16.40 K along the streamwise direction, when the fly ash quantity is 0, 4.5 × 10−3, 8.5 × 10−3, 1.25 × 10−2 and 1.65 × 10−2 kg·m−3, respectively. It is because that the high fly ash quantity will enhance the surface areas of the ash particles within unit volume of flue gas, and more sulfuric acid vapor will condense on the ash particle surface per unit volume of flue gas per unit time, which results in reduction of the sulfuric acid vapor partial pressure. In Fig. 10b, it can be observed that the sulfuric acid dew point temperature at the tail of fin increases with the ash particle size. The sulfuric acid dew point temperature for rp = 2.5 × 10−6 m is 1.4 K lower than the one for the flue gas without ash particles. The maximum temperature difference of the sulfuric acid dew point between the windward and the leeward of the fin is 15.14, 15.94, 15.64, 15.24 and 15.17 K for the flue gas without fly ash, rp = 2.5 × 10−6, rp = 3.5 × 10−6, rp = 6.5 × 10−6 and rp = 1.05 × 10−5 m, respectively. The reason is similar to that accounting for the effect of fly ash quantity on the sulfuric acid dew point temperature. It can be seen from Fig. 10 that the effects of both the quantity and size of fly ash particles on the sulfuric acid dew point temperature can be neglected except at the tail of fin. Three novel types of finned tubes (Dimple, LVG and DimpleLVG) were introduced in section 2.1. Here their influences on the sulfuric acid dew point temperature on the fin surface are examined. As shown in Fig. 11, the spanwise-average sulfuric acid dew point temperature on the front of the four types of fin surfaces is similar. However, the velocity of flue gas is low around the dimples, which weakens the mass transfer and results in the reduction of the sulfuric acid vapor partial pressure. So, the sulfuric acid dew point temperature on the Dimple and Dimple-LVG fin surfaces is lower than that on both the LVG and the original H-type fin surfaces around the dimple locations. As the longitudinal vortex structure could generate disturbance in the flue gas, the sulfuric acid dew point temperature decreases at first and then increases around the rectangular longitudinal vortex. With above analysis, it can be concluded that the spanwise-average sulfuric acid dew point temperature on the Dimple-LVG finned tube is the lowest among the four types of finned tubes. From the results shown in Figs. 10 and 11, we can also conclude that the effects of both fly ash particles and fin structure on the sulfuric acid dew point temperature vary

390 Dimple-LVG Dimple LVG H-type

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temperature is affected by two opposite factors presented in section 3.2. The effect of sulfuric acid solution concentration on the sulfuric acid dew point temperature gets more apparent with the decreasing of acid vapor partial pressure in flue gas. From Fig. 12b, it can be seen that most of the spanwise-average sulfuric acid dew point temperature on the dimple-LVG fin surface is lower than that on the H-type fin surface for the flue gas with fly ash particles. However, the maximum temperature difference is only about 4.7 K and most of the temperature difference is lower than 3 K. The difference of the average sulfuric acid dew point temperature is about 13 K between the first row and the fifth row of fin, which denotes that the wall temperature of the first-row fin surface is more likely below the local sulfuric acid dew point temperature under the same conditions, compared with other fin surfaces. Therefore the fluoropolymer composite coating [26] or the nickel coating [27] could be mainly applied onto the first-row fin surfaces, which have excellent corrosion resistance and can prevent the fin surface from acid corrosion. The fin structure affects the sulfuric acid dew point temperature by changing the flow disturbance, but the velocity of flue gas has little effect on it, so the temperature difference of flue gas with ash particles is small between on the H-type finned tube bank and on the Dimple-LVG finned tube bank. Our previous studies have shown that the Dimple-LVG tube bank can improve the comprehensive performance on heat transfer, anti-wear as well as anticondensation of sulfuric acid vapor [28,29]. The present result indicates that it is also able to decrease the sulfuric acid dew point temperature slightly. Therefore it can be concluded that the DimpleLVG tube bank is promising candidate for heat recovery of flue gas in engineering applications.

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L (mm) Fig. 12. Effects of (a) fly ash particle and (b) fin structure on the spanwise-average sulfuric acid dew point temperature of flue gas along the flow direction for uin = 8 m·s−1, Tg = 414 K and Tw = 350 K.

along the flow direction. Therefore, the sulfuric acid dew point temperature of flue gas with ash particles on the H-type fin surface and Dimple-LVG fin surface in tube bank is examined in the next section. 3.3. Effects of fly ash particle and fin structure on sulfuric acid dew point temperature on fin surfaces of tube bank The tube-bank with five-row finned tubes is studied. As shown in Fig. 12a, the sulfuric acid dew point temperature of flue gas with ash particles is lower than that of flue gas without ash particles on the fin surfaces of original H-type finned tube bank, and the temperature difference of sulfuric acid dew point increases with the tube row number. As the sulfuric acid vapor condenses on the particle surfaces, the sulfuric acid vapor partial pressure in flue gas will decrease along the streamwise direction. On the fin surface of the 5th-row tube, the temperature difference of sulfuric acid dew point between the two types of finned tubes varies from 2.3 K to 5.9 K, reaching the largest among the five fin surfaces. The sulfuric acid dew point temperature increases sharply at the tail of fin except for the 1st-row finned tube and it is remarkable in the 5th-row finned tube. The reason is that the sulfuric acid dew point

We have theoretically predicted the sulfuric acid dew point temperature of flue gas by considering both the vapor–liquid equilibrium effect and the multi-component diffusion effect. The predicted sulfuric acid dew point temperature is consistent with the calculated results from the Soviet standard formula. In addition, by incorporating the present theory and the iteration method into the userdefined function of the software Fluent, the local distribution of sulfuric acid dew point temperature on different positions and structures of fin surfaces were investigated. Typical factors on the distribution of sulfuric acid dew point temperature were discussed and the tube bank composed of Dimple-LVG fin surface was examined as well. Among the factors, the inlet velocity is not significant, but the fuel type, excess air ratio and wall temperature affect the sulfuric acid dew point temperature effectively. The sulfuric acid dew point temperature increases with the excess air ratio, while it decreases with the wall temperature. The influence of fly ash particles on the sulfuric acid dew point temperature mainly focuses on the tail of fin and it increases with the tube row number. The Dimple-LVG structure can reduce the local sulfuric acid dew point temperature on the heat transfer surface to some extent, though not obvious. The sulfuric acid dew point temperature on the windward of the tube is 15 K higher than on the leeward of the tube, and the difference in the average acid dew point temperature is up to 13 K between the first row and the fifth row of fin. The present results can provide important guidance for the local protection of heat transfer tube from sulfuric acid dew point corrosion. To achieve both high heat transfer performance and low coating cost, the fluoropolymer composite coating or the nickel coating could be mainly applied onto the first-row fin surface. In addition, the novel Dimple-LVG fin structure can be used in tube banks, which can enhance the heat transfer as well as prevent sulfuric acid dew point corrosion effectively.

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Acknowledgements

References

This work was supported by the National Basic Research Program of China (2011CB710702) and the National Natural Science Foundation of China (51222604).

[1] Y.G. Yang, T. Zhang, Y.W. Shao, G.Z. Meng, F.H. Wang, In situ study of dew point corrosion by electrochemical measurement, Corros. Sci. 71 (2013) 62–71. [2] V.F.C. Lins, E.M. Guimaraes, Failure of a heat exchanger generated by an excess of SO2 and H2S in the Sulfur Recovery Unit of a petroleum refinery, J. Loss Prev. Process Ind. 20 (1) (2007) 91–97. [3] R. Ebara, F. Tanaka, M. Kawasaki, Sulfuric acid dew point corrosion in waste heat boiler tube for copper smelting furnace, Eng. Fail. Anal. 33 (2013) 29–36. [4] P. Muller, A contribution to the problem of the action of sulfuric acid on the dew point temperature of flue gases, Chem. Eng. Technol. 31 (1959) 345–350. [5] R.R. Pierce, Estimating acid dew points in stack gases, Chem. Eng. 84 (8) (1977) 125–128. [6] S.M. Chackalackal, F.E. Stafford, Infrared spectra of the vapors above sulfuric and Deuteriosulfuric acids, J. Am. Chem. Soc. 88 (4) (1966) 723–728. [7] F.H. Verhoff, J.T. Banchero, Predicting dew points of flue gases, Chem. Eng. Prog. 70 (8) (1974) 71–72. [8] A.G. Okkes, Get acid dew point of flue gas, Hydroc. Proc. 66 (7) (1987) 53– 55. [9] Методические указания по предупреждению низкотемпературной коррозии поверхностей нагрева и газоходов котлов, МУ 34-70-118-84, М., 1985, с.12. (in Russian). [10] B. ZareNezhad, A. Aminian, A multi-layer feed forward neural network model for accurate prediction of flue gas sulfuric acid dew points in process industries, Appl. Therm. Eng. 30 (6) (2010) 692–696. [11] A. Bahadori, Estimation of combustion flue gas acid dew point during heat recovery and efficiency gain, Appl. Therm. Eng. 31 (8) (2011) 1457–1462. [12] Y.T. Shi, X.Y. Zhang, F. Li, L. Ma, Engineering acid dew temperature: the limitation for flue gas heat recovery, Chin. Phys. Lett. 59 (33) (2014) 4418–4425. [13] Y.G. Wang, Q.Y. Zhao, Z.X. Zhang, Z.C. Zhang, Mechanism research on coupling effect between dew point corrosion and ash deposition, Appl. Therm. Eng. 54 (1) (2013) 102–110. [14] M. Goldbrunner, Lokale phänomene bei der kondensation von dampf in anwesenheit eines nichtkondensierbaren gases (Dissertation for Doctoral Degree), Universität München, 2003. (in Germany). [15] S.A. Orszag, V. Yakhot, W.S. Flannery, F. Boysan, D. Choudhury, J. Maruzewski, et al., Renormalization group modelling and turbulence simulations, In International Conference on Near Wall Turbulent Flows, Tempe, Arizona, 1993. [16] F.P. Wang, M. Li, H. Chen, X.G. Li, Thermodynamic analysis of dew point temperature in mixed flue gas system, Corros. Prot. Petrochem. Ind. 19 (2002) 56–58 (in Chinese). [17] L. Riedel, Liquid density in the saturated state. extension of the theorem of corresponding states II, Chem. Ing. Tech. 26 (1954) 259–264. [18] X.H. Wu, General Methods of Calculation and Design for Industrial Boiler, Standards Press of China, Beijing, 2003. [19] R.W. Wilson, Condensation of sulfuric acid and water mixtures in laminar flow (Dissertation for Doctoral Degree), Lehigh University, 1989. [20] D.R. Stull, H. Prophet, JANAF Thermochemical Tables, second ed., National Bureau of Standards Reference Data Service, Washington, 1971. [21] W.F. Giauque, E.W. Hornung, J.E. Kunzler, T.R. Rubin, The thermodynamic properties of aqueous sulfuric acid solutions and hydrates from 15 to 300 K, J. Am. Chem. Soc. 82 (1) (1960) 62–70. [22] T.W. Copeman, F.P. Stein, On the derivation and application of solution thermodynamics for reactive components, Fluid Phase Equilib. 9 (1982) 149–165. [23] J.I. Gmitro, T. Vermeulen, Vapor-liquid equilibria for aqueous sulfuric acid, AIChE J. 10 (1964) 740–746. [24] Z.T. Zhang, Mass transfer processes in flow passages of rotating regenerative air preheaters (Dissertation for Doctoral Degree), Lehigh University, 1991. [25] H. Ehrenreich, F. Spaepen, Solid State Physics, Academic Press, New York, 2001. [26] Y. He, D. Walsh, C. Shi, Fluoropolymer composite coating for condensing heat exchangers: characterization of the mechanical, tribological and thermal properties, Appl. Therm. Eng. 91 (2015) 387–398. [27] A. Sole, C. Barreneche, I. Martorell, L.F. Cabeza, Corrosion evaluation and prevention of reactor materials to contain thermochemical material for thermal energy storage, Appl. Therm. Eng. 94 (2016) 355–363. [28] Y.C. Wang, G.H. Tang, Acid condensation and heat transfer characteristics on H-type fin surface with bleeding dimples and longitudinal vortex generators, Chin. Phys. Lett. 59 (33) (2014) 4405–4417. [29] X.B. Zhao, G.H. Tang, X.W. Ma, Y. Jin, W.Q. Tao, Numerical investigation of heat transfer and erosion characteristics for H-type finned oval tube with longitudinal vortex generators and dimples, Appl. Energy 127 (2014) 93–104.

Nomenclature ai, bi, ci ai C 1ε , C 2ε ca cp C pil Dam Gk ΔH iv k K 0, K 1 L il M N N a P Pa Pa,0 Pi Pw Pw,0 ΔQ r rp R Re ΔS iv Ta Ta,0 T U u

Ideal-gas heat capacity coefficients Activity Turbulence model constants Concentration of sulfuric acid solution Specific heat, J·kg−1·K−1 Partial-molar heat capacity, J·mol−1·K−1 Effective diffusion coefficient for sulfuric acid vapor, m2·s−1 Generation of turbulence kinetic energy Heat of vaporization, J·mol−1 Turbulent kinetic energy, m2·s−2 Equilibrium constants Partial-molar enthalpy, J·mol−1 Molar mass, kg·mol−1 Number of tube bank Flux of sulfuric acid vapor, mol·m−3·s−1 Pressure of flue gas, Pa Sulfuric acid vapor partial pressure, Pa Real sulfuric acid vapor partial pressure at interface, atm Partial pressure at interface of species i, atm Water vapor partial pressure, atm Real water vapor partial pressure at the interface, atm Heat of vaporization for pure sulfuric sulfuric acid, J·mol−1 Radial coordinate of particle sphere, m Radius of particle sphere, m Ideal gas constant, J·mol−1·K−1 Reynolds number Entropy of vaporization, J·mol−1·K−1 Sulfuric acid dew point temperature of flue gas, K Sulfuric acid dew point temperature of pure sulfuric acid vapor, K Temperature, K Velocity vector, m·s−1 Velocity, m·s−1

Greek symbols φa,0 Apparent fugacity coefficient υ Kinematic viscosity, m2·s−1 αi Partial-molar heat capacity coefficient, J·mol−1 αk, α ε Inverse effective Prandtl numbers for k and ε ρ Density of sulfuric acid solution, kg·m−3 ρp Number of particles per unit volume flue gas, m−3 ε Turbulent energy dissipation rate, m2·s−3 Subscripts a Sulfuric acid g Flue gas in Inlet w Wall or water i Species i in flue gas