Graphite dust deposition in the HTR-10 steam generator

Particuology 11 (2013) 533–539

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Graphite dust deposition in the HTR-10 steam generator Wei Peng ∗ , Yanan Zhen, Xiaoyong Yang, Suyuan Yu Institute of Nuclear and New Energy Technology of Tsinghua University, The Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 19 September 2012 Received in revised form 11 December 2012 Accepted 12 January 2013 Keywords: Graphite dust High-temperature gas-cooled reactor Steam generator Deposition

a b s t r a c t Graphite dust has an important effect on the safe operation of a high-temperature gas-cooled reactor (HTR). The present study analyzes temperature and flow field distributions in the HTR-10 steam generator. The temperature and flow field distributions are then used to study thermophoretic deposition and turbulent deposition. The results show that as the dust diameter increases, the thermophoretic deposition decreases, while the turbulent deposition first decreases and then increases. The thermophoretic deposition is higher at higher reactor powers, with turbulent deposition growing more rapidly at higher reactor power. For small particles, the thermophoretic deposition effect is greater than the turbulent deposition effect, while for large particles, the turbulent deposition effect is dominant. © 2013 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

1. Introduction Safety has always been an important consideration in the development of nuclear power. The pebble-bed high-temperature gas-cooled reactor (HTR), which is a fourth-generation reactor (U.S. DOE, 2002), uses spherical graphite elements in the fuel cycle. The graphite surfaces wear and generate graphite dust. The dust circulates with helium inside the primary loop. Large graphite dust particles deposit at the bottom of the reactor core owing to gravity, while small ones flow in the primary circuit carried by the helium. The suspended dust particles then deposit on the primary loop surface and affect the heat transfer as a fouling resistance. Fission products released by the fuel elements also enter the primary loop and combine with the dust, resulting in the dust having high loads of cesium, strontium, iodine, and tritium (Kissane, 2009). This complicates the maintenance and repair of the steam generator. In addition, during a depressurization accident, such as the breakage of a fuel pellet discharge pipe, helium is rejected at sonic speed owing to a large pressure difference. The graphite dust with the deposited fission products is then carried by the helium into the environment (Moormann, 2008). Therefore, the behavior of the graphite dust in the HTR must be carefully studied. The graphite dust particles in the HTR are very fine. The dust in the AVR (Arbeitsgemeinschaft Versuchsreaktor) was found much

∗ Corresponding author. Tel.: +86 010 62783709; fax: +86 010 62794678. E-mail address: [email protected] (W. Peng).

finer (<2 ␮m) than was expected (IAEA, 1997). Luo, Yu, Sheng, and He (2005) and Luo, Yu, Zhang, and He (2005) estimated the graphite dust generation in normal working conditions by conducting graphite wear tests and found that most dust particles had diameters in the range of 0.1–10 ␮m. Fachinger et al. (2008) found the median number-related size of dust particles in the pipes and joints of the AVR was between 0.2 and 0.7 ␮m whereas the median weight-related size was in the range of 0.8–1.5 ␮m. In recent years, there have been a few studies on the generation of graphite dust in the HTR. Cogliati and Ougouag (2008) used the discrete element method to investigate dust production in production-sized reactors. Rostamian, Potirniche, Cogliati, Ougouag, and Tokuhiro (2012) used the finite element code ABAQUS to analyze the contact between graphite pebbles and predict dust generation in a reactor core. Rostamian et al. (in press) and Hiruta et al. (in press) predicted dust generation in numerical simulations and experiments. Luo, Zhang, and Yu (2004) studied the effect of normal loads on the wear performance of graphite used in an HTR-10 steam generator; both the wear between graphite and graphite and the wear between graphite and stainless-steel were included. Luo, Yu, Sheng, and He (2005) and Luo, Yu, Zhang, and He (2005) experimentally measured the graphite–graphite and graphite–stainless-steel wear at various temperatures, and found that there were different wear mechanisms at different temperatures. Troy, Tompson, Ghosh, and Loyalka (2012) set up an experimental apparatus to generate graphite particles from preformed graphite hemispheres with rotational/spinning abrasive loading to study the size distributions and concentrations of the graphite particles produced by wear.

1674-2001/$ – see front matter © 2013 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.partic.2013.01.005

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W. Peng et al. / Particuology 11 (2013) 533–539

Nomenclature Cc Cm Cs Ct d dp dm d+ f g g+ J k k+ kg kp Kth Kn L0 N n Nu P q Qs Rp Re Pr Sc S0 T T u u* Vd+ Vth

Cunningham–Millikan–Davies correction factor momentum exchange coefficient thermal slip coefficient temperature jump coefficient hydraulic diameter (m) particle diameter (m) collision diameter of the gas molecules (m) dimensionless particle diameter friction factor gravitational acceleration (m/s2 ) dimensionless gravitational acceleration particle deposition flux (m−2 s−1 ) surface roughness (m) dimensionless mean height of the surface roughness thermal conductivity of gas (W/(m K)) thermal conductivity of particle (W/(m K)) thermophoretic coefficient Knudsen number cross section perimeter (m) dust concentration (m−3 ) molecular concentration of the gas (m−3 mol−1 ) Nusselt number pressure drop (Pa) heat flux (W/m2 ) volumetric flow rate (m3 /s) particle radius (m) Reynolds number Prandtl number Schmidt number cross section area (m2 ) temperature (K) temperature gradient velocity (m/s) friction velocity (m/s) dimensionless particle deposition velocity velocity of the thermophoretic deposition (m/s)

Greek symbols  density (kg/m3 )  mean free path of the gas (m) dynamic viscosity (Pa s)   kinematic viscosity (m2 /s) + dimensionless relaxation time Subscripts p particle gas g Superscripts + dimensionless variable * friction

gas-cooled reactors. The present study investigates the deposition characteristics of graphite dust in the steam generator using a semiempirical deposition model (Fan & Ahmadi, 1993; Talbot, Cheng, Schefer, & Willis, 1980). 2. Model 2.1. Physical model Fig. 1 shows the modular helical tube of the HTR-10 steam generator, which is a once-through steam generator. Hightemperature helium flows outside the heat transfer tube, while water flows inside the heat transfer tube. The HTR-10 steam generator consists of 30 mono-spiral helical tubes. The axial cross section of the steam generator is shown in Fig. 2. The diameter (D) of the heat transfer tube is 18 mm, the diameter of the cylindrical helix is 112 mm, the diameter of the central tube is 84 mm and the diameter of the casing tube is 140 mm. The heat transfer tubes are installed as a spiral coil. The temperature gradients within the steam generator are quite large, and the thermophoretic force thus plays an important role in the deposition of graphite dust. Moreover, the flow in the steam generator is turbulent, and the effect of turbulence on graphite dust deposition should thus be considered. The present study considers the effects of both thermophoretic deposition and turbulent deposition. 2.2. Thermal hydraulics model Helium flows in a single phase through the steam generator. The Nusselt number for the helium flow is calculated as Nu = 0.094Re0.72 Pr 0.33

(1)

The pressure drop for the helium flow through the heat transfer tube bundle is calculated as  P = Zf u2 , (2) 2 where Z is the number of laps of the heat transfer tube,  is the gas density, u is the velocity of gas, and f is a friction factor, which is calculated as f = 0.288Re−0.074 , Re =

ud , 

(3) (4)

where d is the particle diameter,  is the kinematic viscosity of the gas. The water changes from sub-cooled to superheated steam in the steam generator. The flow in the heat transfer tube can be divided into regions of sub-cooled flow, nuclear boiling, film boiling and super-heated steam. The average heat flux distributions at 100% power for these four segments are shown in Fig. 3. The thermal hydraulic analysis of the steam generator is based on these heat fluxes. 2.3. Thermophoretic deposition model

However, these previous studies mainly focused on the mechanism generating graphite dust or on the particle size distribution. Few studies have analyzed the behavior of graphite dust in the HTR. The performance of steam generator, which is the main heat transfer equipment in the primary loop and also the most important component in terms of maintenance and repair, may be affected by dust deposition. The behavior of graphite dust in the steam generator is important to the safety of high-temperature

The thermophoretic force in the steam generator due to the temperature gradient between the helium and tube wall causes the graphite dust to deposit on the surface. The velocity of the thermophoretic deposition is given by (Talbot et al., 1980) Vth = −

Kth  ∇ T, T

(5)

where Vth is the velocity of the thermophoretic deposition, Kth is the thermophoretic coefficient,  is the kinematic viscosity of helium, T

W. Peng et al. / Particuology 11 (2013) 533–539

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Fig. 1. Sketch of the steam generator. (1) casing tube; (2) annular cavity; (3) central tube; and (4) helical tube.

Fig. 2. Cross-sectional view of the steam generator.

is the helium temperature, and T is the temperature gradient near the heat transfer surface of the steam generator. The temperature gradient is then related to the heat flux according to

∇T =

q , kg

(6)

where q is the wall heat flux shown in Fig. 3 and kg is the helium thermal conductivity. Since the Knudsen number of helium in this geometry is less than 2, the Brock–Talbot formula (Talbot et al., 1980) gives a good result for Kth : Kth =

2Cs Cc ((kg /kp ) + Ct (/Rp )) , (1 + 3Cm (/Rp ))(1 + 2(kg /kp ) + 2Ct (/Rp ))

(7)

where Cs = 1.17 is the thermal slip coefficient, Ct = 2.18 is the temperature jump coefficient, and Cm = 1.14 is the momentum exchange coefficient. The coefficient Cc is Cunningham–Millikan–Davies correction factor, which is a function of Kn: Cc = 1 + Kn(1.2 + 0.41e−0.88/Kn ).

(8)

kg and kp are the thermal conductivities of the helium and dust, respectively, and Rp is the dust particle radius. The continuity equation gives −Vth N · ds = Qs · dN,

(9)

where N is the dust concentration, ds is the deposition area and Qs is the volumetric flow rate. Therefore the thermophoretic deposition is given by therm = 1 −

N = 1 − exp N0

 −V s  th

(10)

Qs

2.4. Turbulent deposition model Various studies (Friedlander & Johnston, 1957; Liu & Agarwal, 1974; Wells & Chamberlain, 1967) have indicated that the deposition of particles in turbulent flows varies with the particle size. The turbulent deposition model can be expressed as (Papavergos & Hedley, 1984). Vd+ = f ( + ),

(11)

Vd+

+

where is the particle deposition velocity and is the dimensionless relaxation time. Deposition experiments conducted by Wood (1981) and Papavergos and Hedley (1984) revealed that the particle deposition can be divided into a diffusion regime ( + < 0.1), diffusionimpaction regime (0.1 <  + < 10) and inertia-moderated regime ( + > 10). In the diffusion regime, the main deposition mechanism is the diffusion of small particles, such as Brownian diffusion. In the diffusion-impaction regime, both the particle inertia and the eddy in the turbulent core play important roles in the deposition. The inertia-moderated regime is for large particles with the particle inertia the determining factor of deposition. The dimensionless relaxation time is defined as (Wood, 1981) + =

Cp dp2 u∗2 18v2

,

(12)

where C is the Cunningham slip correction factor, p is the particle density and  is the gas density, dp is the particle diameter,  is the gas kinematic viscosity, u* is the friction velocity obtained from the mean fluid velocity and ff is the Fanning friction factor:



u∗ = um

ff 2

(13)

Since the flow in the steam generator is in the hydraulic smooth region of turbulent flow, ff is calculated as (Frank, 1999) ff = 0.158Re−0.25 ,

(14)

where Re is the Reynolds number, defined as Re = Fig. 3. The calculated average heat flux distributions along the axial direction of the steam generator.

um d0 , v

and d0 is the hydrodynamic diameter of the duct.

(15)

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In the present study, the Cunningham slip correction factor, C, was calculated with the correction (Allen & Raabe, 1985): C =1+

 dp





2.34 + 1.05 exp

−0.39

dp 



Operation condition

,

1 = √ 2 2 ndm

(17)

Here, n is the molecular concentration of the gas and dm is the collision diameter of the gas molecules. The turbulent deposition velocity is calculated using the formula of Fan and Ahmadi (1993); the turbulent deposition velocity is given as a function of the particle-to-gas density ratio, surface roughness, gravity, and gas flow Reynolds number. The semiempirical relation is

Vd+ =

⎪ ⎩

 0.084Sc −2/3

1 + 2

2

2

(0.64k+ + (d+ /2)) + (( + g + L1+ )/(0.01085(1 +  + L1+ ))) 2

Reactor power

(16)

where  is the mean free path of the gas, defined as

⎧ ⎪ ⎨

Table 1 Calculation conditions.

3.42 + (( +2 g + L1+ )/0.01085(1 +  +2 L1+ ))

Helium inlet velocity (m/s) Helium inlet temperature (K) Pressure (MPa) Graphite dust diameter (␮m) Graphite thermal conductivity (W/(m K)) Graphite density (kg/m3 )

30%

60%

80%

100%

8.28 973.15 3 0.1–7 25 1720

16.56 973.15 3 0.1–7 25 1720

22.08 973.15 3 0.1–7 25 1720

27.6 973.15 3 0.1–7 25 1720

shown in Fig. 5. Since the fluid mass of the primary and secondary loops of the HTR-10 changes in proportion to the plant power, the helium temperature in the steam generator is nearly the same for full power and partial power.

1/(1++2 L1+ ) [1 + 8e−(

+ −10)2 /32

]

0.037 1 −  +2 L1+ (1 + (g + /0.037))

,

if Vd+ < 0.14

(18)

otherwise.

0.14,

k+

where Sc is the Schmidt number, is the dimensionless mean height of the surface roughness, ku*/, d+ is the dimensionless particle diameter, dp u*/, g+ is the dimensionless gravitational acceleration, g/u*3 , L1+ is defined as 3.08/Sd+ (where, S is the particle-to-gas density ratio). The turbulent deposition velocity is defined as Vd+ =

J , u∗ N

The temperature gradient along the flow direction defined by Eq. (6) was calculated and is shown in Fig. 6. The results show that the temperature gradient increases as the reactor power increases owing to greater heat transfer as the velocity increases with the

(19)

where J is the particle deposition flux and N is the dust concentration over the cross-section. The continuity equation applied to an infinitesimal distance, dL, along the steam generator axis is JL0 dL = um S0 dN,

(20)

where L0 and S0 are the perimeter and cross section area. Thus the turbulent deposition is



tur = 1 − exp

+ L0 Vd u∗ − L S0 um



(21)

2.5. Graphite dust particle size Graphite-wear experiments for the HTR-10 gave a geometricmean particle diameter of about 2.2 ␮m (Luo, Yu, Zhang, & He, 2005). However, Fig. 4 shows that about 90% of the particles (in terms of numbers) are no more than 6 ␮m in diameter. Thus, the present study assumed the graphite dust particle diameters were between 0.1 and 7 ␮m.

Fig. 4. Graphite dust size distribution.

2.6. Calculation conditions The conditions used in the present study and listed in Table 1 are based on the HTR-10 operation conditions. 3. Results and discussion 3.1. Temperature gradient distribution A Fortran code based on the thermal hydraulics model of Section 2 was use to calculate the temperature and flow field in steam generator. The calculated average helium temperature distribution at 100% reactor power along the helium flow direction, which is defined as the x-direction for the HTR-10 steam generator, is

Fig. 5. Average temperature distribution along the axial direction of the steam generator.

W. Peng et al. / Particuology 11 (2013) 533–539

Fig. 6. The calculated temperature gradient distribution along the axial direction of the steam generator at different reactor powers.

power. Therefore, the increase in heat flux results in higher temperature gradients. 3.2. Thermophoretic deposition Fig. 7 shows the relationship between the thermophoretic deposition (calculated according to Eq. (10)) and particle size. As the diameter of particle increases, the thermophoretic deposition first rapidly declines and then gradually levels off. Since the temperature gradient shown in Fig. 6 increases with the reactor power, the thermophoretic force acting on the particles increases too, and the thermophoretic deposition seems likely to behave similarly. However, the results in Fig. 7 show that thermophoretic deposition is nearly independent of the reactor power. This may be attributed to the decreased residence time of the graphite dust in the steam generator with the increase of helium flow rate as the power increases, resulting an almost constant thermophoretic deposition. 3.3. Turbulent deposition The relationship between the turbulent deposition (calculated according to Eq. (21)) and the particle size is shown in Fig. 8. As the graphite dust diameter increases, the turbulent deposition first decreases and then increases. Fig. 9 shows that when the dimensionless relaxation time,  + , is small, that is, for particle diameters less than 1 ␮m, the turbulent deposition of the graphite dust is in the diffusion regime since particle diffusion is important to deposition, resulting in an initial decrease of the turbulent deposition

Fig. 7. Effect of particle size on thermophoretic deposition at different reactor powers.

537

Fig. 8. Effect of particle size on turbulent deposition at different reactor powers.

as the particle diameter increases. For larger particles, the turbulent deposition is then in the diffusion-impaction regime or even the inertia-moderated regime. Despite the effect of diffusion on the deposition decreases in these regimes, the effect of the particle inertia then increases, resulting in a rapid increase of the particle deposition. Fig. 8 also indicates that the turbulent deposition increases more rapidly as the power increases since the particle velocity increases as the power increases, which increases the particle inertia, resulting in more fast particles penetrating the boundary layer and depositing on the tube surface. 3.4. Comparison of thermophoretic deposition and turbulent deposition Fig. 10 compares thermophoretic deposition with turbulent deposition. It is seen that thermophoretic deposition dominates turbulent deposition for smaller particles. Thermophoretic deposition thus decreases as the particle size increases, because the thermophoretic force decreases as the particle size increases. As seen in Fig. 10, when the reactor is at 100% power, the thermophoretic deposition is the main deposition mechanism for a particle diameter less than 3 ␮m. For a particle diameter larger than 3 ␮m, the turbulent deposition is as great as the thermophoretic deposition. For particles larger than 4 ␮m, turbulent deposition is the main deposition mechanism.

Fig. 9. Dimensionless relaxation time vs. dust particle size at different reactor powers.

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Fig. 11. Particle size distributions of graphite dust at the inlet and outlet of steam generator.

Fig. 10. Comparison of thermophoretic and turbulent deposition rates at different reactor powers.

Fig. 12. Effect of particle size on total particle deposition at different reactor powers.

3.5. Total deposition The results show that both thermophoretic deposition and turbulent deposition contribute to total deposition of graphite dust in the steam generator. Brockmann (1993) indicated that thermophoretic deposition and turbulent deposition are independent. Therefore, the total deposition should be calculated as total = therm + turb − therm turb .

(22)

Fig. 11 shows the particle size distributions at the inlet and outlet of the steam generator. It is seen that most large particles are deposited on the tube surface. At 100% reactor power, almost all particles larger than 4 ␮m are deposited in the steam generator. As the power decreases, fewer larger particles are deposited. The figure also indicates that fewer small particles are deposited. Fig. 12 shows the total deposition rate as a function of particle diameter at different reactor powers. It is seen that the total deposition first decreases slightly and then increases with the particle diameter. For large particles, turbulent deposition plays a significant role and the turbulent deposition rate is high. Particles with diameters between 0.1 and 3 ␮m have a relatively low total deposition rate. Thus, new measures are needed to remove large particles or prevent large particles from entering the steam generator and ensure system safety and the proper heat transfer rate in the steam generator.

4. Conclusions The present study investigated the effects of both thermophoretic deposition and turbulent deposition of graphite dust in the HTR-10 steam generator. The model predicted the graphite dust deposition rates in the HTR steam generator for various conditions. The following are the main conclusions drawn from the study. (1) As the particle diameter increases, the thermophoretic deposition rapidly decreases initially and then gradually levels out. (2) As the particles diameter increases, the turbulent deposition decreases initially and then increases. (3) At 100% power, the thermophoretic deposition is the main deposition mechanism for particles less than 3 ␮m. The turbulent deposition rate is as high as the thermophoretic deposition rate for particles in the range of 3–4 ␮m, while turbulent deposition becomes the main deposition mechanism for particles larger than 4 ␮m. (4) Most large particles are deposited in the steam generator. When the detachment force due to fluid–wall stress exceeds the retention force due to adhesion, particles are resuspended in the exhaust helium flow, which affects the particle deposition rate. Future studies will consider the resuspension effect.

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