Flow and mass transfer downstream of an orifice under flow accelerated corrosion conditions

Nuclear Engineering and Design 252 (2012) 52–67

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Flow and mass transfer downstream of an orifice under flow accelerated corrosion conditions Wael H. Ahmed ∗ , Mufatiu M. Bello, Meamer El Nakla, Abdelsalam Al Sarkhi Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals (KFUPM), P.O. Box 874, Dhahran 31261, Saudi Arabia

h i g h l i g h t s     

Mass transfer downstream of orifices was numerically and experimentally investigated. The surface wear pattern is measured and used to validate the present numerical results. The maximum mass transfer coefficient found to occur at approximately 2–3 pipe diameters downstream of the orifice. The FAC wear rates were correlated with the turbulence kinetic energy and wall mass transfer in terms of Sherwood number. The current study offered very useful information for FAC engineers for better preparation of nuclear plant inspection scope.

a r t i c l e

i n f o

Article history: Received 27 March 2012 Received in revised form 16 June 2012 Accepted 27 June 2012

a b s t r a c t Local flow parameters play an important role in characterizing flow accelerated corrosion (FAC) downstream of sudden area change in power plant piping systems. Accurate prediction of the highest FAC wear rate locations enables the mitigation of sudden and catastrophic failures, and the improvement of the plant capacity factor. The objective of the present study is to evaluate the effect of the local flow and mass transfer parameters on flow accelerated corrosion downstream of an orifice. In the present study, orifice to pipe diameter ratios of 0.25, 0.5 and 0.74 were investigated numerically by solving the continuity and momentum equations at Reynolds number of Re = 20,000. Laboratory experiments, using test sections made of hydrocal (CaSO4 ·½H2 O) were carried out in order to determine the surface wear pattern and validate the present numerical results. The numerical results were compared to the plants data as well as to the present experiments. The maximum mass transfer coefficient found to occur at approximately 2–3 pipe diameters downstream of the orifice. This location was also found to correspond to the location of elevated turbulent kinetic energy generated within the flow separation vortices downstream of the orifice. The FAC wear rates were correlated with the turbulence kinetic energy and wall mass transfer in terms of Sherwood number. The current study found to offer very useful information for FAC engineers for better preparation of plant inspection scope. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Flow accelerated corrosion (FAC) is a major safety and reliability issue affecting carbon-steel piping in nuclear and fossil power plants. This degradation mechanism results in wear and thinning of large areas of piping and fittings that can lead to sudden and sometimes to catastrophic failures, as well as a huge economic loss. FAC is a process caused by the flowing water or wet steam damaging or thinning the protective oxide layer of piping components. The FAC process can be described by two mechanisms: the first mechanism is the soluble iron production (Fe2+ ) at the oxide/water interface, while the second mechanism is the transfer of the

∗ Corresponding author. Tel.: +966 3 860 7507; fax: +966 3 860 2949. E-mail address: [email protected] (W.H. Ahmed). 0029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2012.06.033

corrosion products to the bulk flow across the diffusion boundary layer. Although the FAC is characterize by a general reduction in the pipe wall thickness for a given piping component, it frequently occurs over a limited area within this component due to the local high area of turbulence. The rate of the metal wall loss due to FAC depends on a complex interaction of several parameters such as material composition, water chemistry, and hydrodynamic. Failures due to FAC degradation have been reported at several power plants around the world since 1981 (Kanster et al., 1990). However, a close attention to the FAC damage did not start before the severe elbow rapture downstream of a tee occurred at Surry Unit 2 power plant (USA) in 1989, which caused four fatalities and extensive plant damage and resulted in a plant shutdown. In 1999, an extensive steam leakage from the rupture of the shell side of a feed-water heater at the Point Beach power plant (USA) was reported by Yurmanov and Rakhmanov (2009). In 2004, a fatal pipe

W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

Nomenclature A Cf CP dH D Deff ID LRN MTC P PO Pin Pout Q r R Re Sc Sh Shfd u ¯ v¯ , w ¯ u, U UO V x y+ z

pipe cross-sectional area (m2 ) skin friction coefficient, Cf = W /(1/2UO2 ) pressure coefficient, CP = (P − PO )/(1/2UO2 ) hydraulic diameter (m) pipe diameter (m) effective diffusivity (m2 /s) internal diameter (m) low Reynolds number mass transfer coefficient (m/s) static pressure (N/m2 ) reference pressure taken at the outflow (N/m2 ) inlet fluid pressure (N/m2 ) outlet fluid pressure (N/m2 ) volume flow rate (m3 /s) radial co-ordinate (m) pipe radius (m) Reynolds number, Re = UD/ Schmidt’s number, Sc = /D Sherwood number Sherwood number for fully developed flow root-mean-square of velocity fluctuations (m/s) components of fluctuation velocity vector (m/s) axial component of mean velocity vector (m/s) free stream velocity (m/s) radial component of mean velocity vector (m/s) mass quality non-dimensional distance from the wall axial co-ordinate (m)

Greek letters dissipation rate of kinetic energy of turbulence ε (m2 /s3 )  kinematic viscosity (m2 /s) density (kg/m3 )  W wall shear stress (kg/ms2 ) ˛ volumetric void fraction Subscripts b bulk fluid value d diffusive value effective value (molecular + turbulent) eff i, j coordinates directions z, r wall value w 0 inlet value

rupture downstream of an orifice in the condensate system due to FAC occurred in the Mihama nuclear power plant Unit 3 (Japan) (Yurmanov and Rakhmanov, 2009). More recently, the pipe failure downstream of a control valve at Iatan fossil power plant in 2007 resulted in two fatalities and a huge capital of plant loss as reported by Moore (2008). The recent study by Ahmed (2010) indicated that a significant research has been conducted on investigating the effect of fluid chemical properties on flow accelerated corrosion (FAC) in power plants. However, the hydrodynamic effects of single and two-phase flows on FAC have not been thoroughly investigated. In order to determine the effect of the proximity between two components on the FAC wear rate, Ahmed (2010) has investigated 211 inspection data for 90◦ carbon steel elbows from several nuclear power plants. The effect of the velocity as well as the distance between the elbows and the upstream components was discussed. Based on the analyzed trends obtained from the inspection data, the author

53

indicated a significant increase in the wear rate of approximately 70% that was identified to be due to the proximity. The repeated inspections in both fossil and nuclear power plants systems have shown that piping components located downstream of flow singularities, such as sudden expansion or contractions, orifices, valves, tees and elbows are most susceptible to FAC damage. This is due to the severe changes in flow direction as well as the development of secondary flow instabilities downstream of these singularities (Ahmed, 2010). Moreover, in two-phase flows, the significant phase redistributions downstream of these singularities may aggravate the problem. Therefore, it is important to identify the main flow and geometrical parameters require in characterizing FAC damage downstream of pipe fittings. These parameters are: the geometrical configuration of the components, piping orientation, and the flow turbulence structure which will affect the surface shear stress and mass transfer coefficients. For single phase flow, the secondary vortices and/or flow separation downstream of pipe fittings considered to be important parameters need to be analyzed and modeled while predicting the highest FAC wear rate location. For example; the secondary flows in elbows induce a pressure drop along the elbow wall that can significantly increase the wall mean and oscillatory shear stresses as discussed by Crawford et al. (2007). Also, orifices and valves promote turbulence close to the wall in the downstream pipe and thus enhance the rate of mass transfer at the wall (Crawford et al., 2007). These mechanisms have been identified as the governing factors responsible for FAC as explained by Chen et al. (2006). On the other hand, the hydrodynamics parameters controlling FAC in two-phase flows are more complex than for single-phase flows due to the phase redistribution and the complex interactions between the gas phase and the liquid turbulence structures (Kim et al., 2007). The latter mechanism plays a major role in the mass, momentum, and energy transfer between the flow phases (Hassan et al., 1998). The two-phase flow regime at the inlet plays an important role in the flow dynamics downstream of the orifices since the phase redistribution downstream will primarily depend on the flow regime. For example, bubbles can have significant effects on the turbulent kinetic energy close to the wall, affecting the wall shear stress and pressure. Jepson (1989) showed that high velocity slugs can cause high turbulence and shear forces at the pipe wall and thus enhance the destruction of the protective inhibitor film. Moreover, in the oil and gas production industry, sand and water are commonly entrained in the fluid produced from the well (Zhang et al., 2007; Wang and Shirazi, 2003). These sand particles though only 150 ␮m in size can impact the inner walls of piping components, valves, and other fixtures and cause extensive erosion in addition to the corrosion damage. Erosion–corrosion of oil and gas field piping and equipment is very complex and can be affected by many factors. These factors, which can determine the severity of erosion damage, include the production flow rates, multiphase flow regimes, fluid properties, sand production rates, sand properties, sand shape, sand size distribution, equipment and piping wall materials, and geometry of the equipment. Computational fluid dynamic (CFD) analysis is used to predict turbulent fluid flow with great accuracy for many applications. However, only the recent advances in computational power have allowed the use of CFD for mass transfer and corrosion studies. This can be explained as the accurate prediction of mass transfer near the wall requires resolving the mass transfer boundary layer which may be an order of magnitude smaller than the viscous sub-layer. In order to perform the CFD calculations with good accuracy, fine near-wall grids with correct near-wall turbulence models can therefore provide mass transfer data for the corrosion species. In the cases where corrosion is controlled by the mass transfer, relation between the wall mass transfer coefficient and corrosion rate can be derived (Keating and Nesic, 1999). In formulating the

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W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

CFD codes, consideration is made to the hydrodynamic parameters affecting the mass transfer rate of the corrosion products to the bulk fluid and consequently the FAC rate. These hydrodynamic parameters are the flow velocity, pipe roughness, piping geometry, and steam quality or void fraction for two-phase flow. The hydrodynamic effects of the working fluid on FAC have been investigated by many researchers using CFD. Bozzini et al. (2003) adopted numerical simulations for investigating wall erosion/corrosion inside a pipe bend for a four-phase flow that comprised of two immiscible liquids, gas and particulate solids. Also, Chang et al. (2006) suggested an evaluation scheme to estimate the load carrying capacity of thinned-wall pipes exhibiting FAC. They employed a steady-state incompressible flow CFD code to determine the pressure distributions, which were used as input conditions for a structural finite element analyses to calculate local stresses. More recently, Ferng (2008) developed an approach that used an erosion/corrosion model and three-dimensional single and two-phase flow models to predict locations of serious FAC in power plant piping systems. Their predictions agreed quite well with plant measurements. Moreover, in the CFD analysis, secondary flows, i.e., secondary vortices and/or flow separation are considered two challenging parameters need to be understood and modeled while dealing with FAC downstream of flow in orifices. In order to resolve the mass transfer of the wall species, the concentration needs to be determined up to the wall surface which requires modeling the turbulent flow in the near wall region. Therefore, the conservation equations were solved using the low Reynolds number (LRN) K–ε turbulence model by Wang and Mujumdar (2005), Hrenya et al. (1995), Kechiche et al. (2004) and El-Gammal et al. (2012). The use of this model found to incorporates damping functions that consider the viscous effects in the near-wall region as indicated by El-Gammal et al. (2012). Consequently, the transport equations of the turbulence kinetic energy and turbulence dissipation are integrated in the solution through the viscous sub-layer. Also, according to Kechiche et al. (2004) who used various LRN K–ε models to study the heat transfer across a wall with a turbulent jet, these models were found very suitable for resolving the thermal characteristics close to the wall. Also, Wang (1997) found very good agreement between the numerical and experimental results of the concentration gradient of the wall species using Abe–Kondoh–Nagano (AKN) version of LRN K–ε model (Abe et al., 1994). Therefore, the AKN version of LRN K–ε is selected for the present study. In summary, the pipe downstream of an orifice is found to be one of the locations where aggressive FAC occurs. Therefore, the main objective of the present study is to characterize FAC downstream of an orifice in order to identify the location of the highest FAC wear rate. The effect of local flow and mass transfer parameters on FAC wear rate is evaluated. The findings will enable the mitigation of sudden and catastrophic failures due to FAC and consequently improve the plant capacity factor. 2. FAC rate and mass transfer The FAC process in carbon steel piping is described by four steps. In the first process, metal oxidation occurs at metal/oxide interface in oxygen-free water and explained by the following reactions: Fe + 2H2 O → Fe2+ + 2OH− + H2 2+

Fe

−

+ 2OH → Fe(OH)2

3Fe + 4H2 O → Fe3 O4 + 4H2

(1) (2) (3)

The second process involves the solubility of the ferrous species through the porous oxide layer into the main water flow. This transport across the oxide layer is controlled by the concentration

diffusion. The third step is described by the dissolution of magnetite at oxide/water interface as explained by the following reaction: (1/3)Fe3 O4 + (2 − b)H+ + (1/3)H2 ↔ Fe(OH)b (2−b)+ + (4/3 − b)H2 O

(4)

where Fe(OH)b (2−b)+ represents the different iron ferrous species b = (0,1,2,3). In the fourth step, a diffusion process takes place where the ferrous irons transfer into the bulk flowing water across the diffusion boundary layer. In this process, the species migrated from the metal/oxide interface and the species dissolved at the oxide/water interface diffuse rapidly into the flowing water. In this case, the concentration of ferrous iron in the bulk water is very low compared to the concentration at the oxide/water interface. It can be noticed that FAC mechanism involves convective mass transfer of the ferrous ions in the water. The convective mass transfer for single phase flow is known to be dependent on the hydrodynamic parameters near the wall interface such as flow velocity, local turbulence, geometry, and surface roughness. In addition, the physical properties of the transported species or the water do not affect the local transport rate in adiabatic flow especially when temperature changes in piping system are negligible. Over a limited length of piping component, FAC rate is considered as direct function of the mass flux of ferrous ions and can be calculated from the convective mass transfer coefficient (MTC) in the flowing water. Then, FAC rate is calculated from the MTC and the difference between the concentration of ferrous ions at the oxide/water interface (Cw ) and the concentration of ferrous in the bulk of water (Cb ) as: FAC rate = MTC(Cw − Cb )

(5)

Several research works (Poulson, 1987; Berge and Saint Paul, 1981; Bouchacourt and Remy, 1991) showed that MTC is one of the important parameters affecting FAC and the experimental data are often expressed in terms of Sherwood, Reynolds and Schmidt numbers as: Sh = a · Reb · Sc c

(6)

where a, b and c are related to mass transfer which occurs under a given flow condition and can only be obtained experimentally. Where Sh in the non-dimensional representation of MTC as a function of the local hydrodynamic parameters and expressed as: Sh =

MTC · dH D

(7)

where dH = hydraulic diameter and D = diffusion coefficient of iron in water.In Eq. (6), the velocity exponent varies between 0.8 for lower Reynolds numbers and 1.0 for very high Reynolds numbers. This difference in the velocity exponent is caused by the surface roughness. This indicates that the FAC rate increases as the surface roughness increases. It should be also noted that the experimental studies and the correlations developed for MTC were carried out under low flow rates conditions compared with common operating conditions in power generation industry. Therefore, the MTC data obtained in the literature for moderate and high Reynolds numbers at power plant conditions can lead to significant errors. Tagg et al. (1979) described the wear enhancement profile downstream of the orifice empirically. They expressed the maximum Sherwood number using Reynolds number at the vena contracta section downstream of the orifice (Reo ) as follows: Shmax = 0.27 · Reo0.67 · Sc 0.33

(8)

W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

On the other hand, the local enhancement profile downstream of the orifice at different axial locations (z) is described empirically by Coney (1980) referred to by Chexal et al. (1996) as



Shz = 1 + Az 1 + Bz Shfd





Reo0.67 − 21 0.0165 · Re0.86

(9)

∂u¯ i =0 ∂xi



∂ui ∂xi

 =0

(10)

Momentum equation: u¯ j

∂P¯ ∂ ∂u¯ i =− + ∂xj ∂xi ∂xj



1 ∂u¯ i − ui uj Re ∂xj

 (11)

Species mass transport equation for a steady process with no chemical reaction is:

∇ · (vYi ) = −∇ · Ji + Si

(12)

where Ji is the diffusion flux of species i, and arises due to concentration gradient, and Si is the source term. In Eq. (11), the Boussinesq (1877) eddy viscosity assumption is used for modeling the Reynold’s stress. The eddy viscosity model relation is expressed as:

 −ui uj = t

∂Ui ∂zj



 + (∂Uj ∂zi ) −

2kıij 3



k2 ε

(13)



(14)

The turbulence kinetic energy (k) and the turbulence kinetic energy dissipation rate (ε) are defined as follows:

k=

u2 + v2 + w2 , 2

 ε=v

∂ui ∂zj

2 (15)

Therefore, the equation for turbulence kinetic energy can be also expressed as follows: ∂(Uk) + ∂z +

 1  ∂(rVk) r

∂r

=

∂[(eff /k )(∂k/∂z)

 1 ∂[(r / )(∂k/∂r)] eff k r

∂r

∂z + Gk − ε

∂(Uε) + ∂z

(16)

 1  ∂(rVε) r

∂r

=

∂[(eff /ε )(∂ε/∂z)

 1 ∂[(r / )(∂ε/∂r)] ε eff r

∂r

∂z

+

ε k

(Cε1 f1 Gk − Cε2 f2 ε)

(17)

In Eqs. (16) and (17) the generation of kinetic energy of turbulence term (Gk ) can be written as



Gk = eff

 +

2

∂U ∂r

∂U ∂z

  +

2



+

∂V ∂z

∂V ∂z

2

+

 V 2



r

2  (18)

where the effective viscosity (eff ) is defined as =

eff

 effective

+



 molecular



(19)

t  turbulent

The calculation of the local MTC is obtained similar to El-Gammal et al. (2010) as MTC(z) =

−DSL ∂c/∂n|w cw − cb

(20)

where cw is the species concentration along the wall (obtained from hydrocal properties table), cb is the species concentration in the bulk flow beyond the diffusive boundary layer, n is the normal vector to the wall surface and DSL is the diffusive coefficient of the solid species, which is calculated by using Wilkie’s semi-empirical relationship (Chexal et al., 1996): DSL =

7.4 × 10−15 × T ×



× MS

× V 0.6

(21)

where T is the temperature (K), is the association factor for the solvent (2.6 for water), MS is the molecular mass for the solvent (18 g for water), is the solvent absolute viscosity (Pa s), V is the molecular volume of the dissolved species (144.86 cm3 /mol for hydrocal) at ambient temperature. The concentration of hydrocal species in the bulk of water cb is calculated as follows: cb (z) =

where t is defined as the “turbulent viscosity” and expressed as t = C f

and the equation for the turbulence kinetic energy dissipation expressed as

+

where Shfd is the Sherwood number for the smooth straight pipe, Shz is the Sherwood number at any axial location (z), Az and Bz are empirical constants. Once the relationship between mass transfer and FAC wear rate is established, the computational model for MTC downstream of an orifice can be formulated. Fully developed turbulent pipe flow is assumed in order to determine MTC profiles downstream of the orifice. ANSI specifications of orifice were used to construct the geometrical model. Since the experimental condition in the present study is carried out for straight pipe section fabricated from hydrocal (CaSO4 ·½H2 O) downstream of an orifice. The Solution is obtained for Renormalization Group (RNG) K–ε differential viscosity model for turbulent flow in conjunction with the species transport equations using FLUENT CFD code. The velocity field of the incompressible viscous flow is obtained using the one-dimensional Reynolds averaged governing equations as follows: Continuity equation:

55

1 UA



u(r)c(r)dA

(22)

where U is the area average velocity, u(r) is the instantaneous flow velocity, c(r) is the species concentration profile, and A is the crosssectional area of the pipe. The term ∂c/∂n|w (z) is calculated by taking the concentration gradient at the wall at an axial location (z). Substituting Eqs. (21) and (22) into Eq. (20), the cross-sectional average for MTC(z) along the axial direction can be calculated. 3. Experimental setup and procedure Experiments are conducted in a flow loop schematically shown in Fig. 1 that is designed to accommodate different test section geometries as well as running single and two-phase flow test conditions. Water is supplied from a 100 L tank through a centrifugal pump driven by a variable speed electric motor. In the present condition, the air line is shut off and only water is allowed through the test section. The flow rates are controlled by controlling the pump rotational speed in addition to a gate valve located on the water flow line. The water flow rate is measured using a turbine flow meter with an accuracy of 2% full scale, and the temperature is measured using thermocouples at various locations along

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W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

Fig. 1. Schematic diagram of the flow loop.

the flow loop. Experiments were performed using a 1-in. diameter straight tubing at a Reynolds number of 20,000. A straight section of approximately 75 diameters is installed upstream of the test section to ensure fully developed inlet flow conditions. An additional straight section of 100 diameters is installed downstream of the test

section. A standard ANSI orifice (Fig. 2) with orifice-pipe diameter ratios of 0.25, 0.5 and 0.74 were installed. The test section downstream of the orifice is made of hydrocal, as shown in Fig. 3, in order to obtain wall wear patterns in a reasonable test time. This technique has been applied and tested

Fig. 2. Sketch of the flow through orifice and the ANSI standard dimensions.

W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

57

Fig. 3. Hydrocal test section.

before by Poulson (1990) and the dissolution of the wall material depends on the mass transfer of hydrocal from wall into the bulk flow and used to simulate FAC wear in carbon steel piping components. Although the changes to the surface occurring from the mass transfer of the hydrocal to the flow may not be exactly the same as that would occur in carbon steel piping systems in power plants, the wear pattern developed from hydrocal is expected to be reasonably similar to that generated over a longer period of time in carbon steel piping component as explained by Wilkin et al. (1983). To determine the Saturation limit of the hydrocal in water, tests were performed using fine particles of hydrocal and dissolved in the water reservoir and the water conductivity were recorded as explained by El-Gammal et al. (2010). Running fully saturated solution through the hydrocal test section showed no-wear. This indicates that the measured wear in the present tests was entirely due to mass transfer and that the hydrocal test sections are not susceptible to mechanical wear. The overall mass transfer over the entire hydrocal test section surface is determined by measuring the electrical conductivity, using EU Tech-PC300 meter with an accuracy of ±1%, of the circulating water within the flow loop. The operating principle of this technique depends on the increase in the conductivity of the circulating water due to the dissolution of the hydrocal from the surface. The amount of hydrocal dissolution in the water was previously

obtained through a calibration curve relating the water conductivity to the amount of dissolved hydrocal shown in Fig. 4. A maximum concentration of 4% on volume basis (3.35 g hydrocal per 1 L of water) is identified as the limit where saturation is reached and the conductivity remain constant for high concentration values. Automatic temperature compensation is applied during the experiments to account for the changes in the water conductivity with temperature. The water conductivity measurement are recorded every 2 min during each experimental run. The tank is thoroughly cleaned after each test to ensure that no residual hydrocal deposits exist for the following experiments. Also, at the beginning of each experiment, the electrical conductivity of the distilled water in the reservoir was measured to ensure the zero conductivity.

7

Conductivity (milliSienmens)

6

Experiments region

5 4 3 2 1 0 0

2

4

6

8

10

Hydrocal Concentration by volume (%) Fig. 4. Calibration of the conductivity probe.

Fig. 5. Measurements using FARO-Axis CMM with Laser Scanner D100.

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W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

Fig. 6. Surface wear profiles using GEOMAGIC studio.

Fig. 7. Computational domain and grids.

W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

59

Fig. 9. Model validation for single-phase downstream an orifice with no species.

used for data processing for the each test section. After the cut-test section was scanned, the point cloud data was optimized by reducing the data noise, over lapping triangular mesh and overhanging data. Then data was merged into polygons and converted into one stretched water-polygon structure. It should be noted that no data modification or smoothing operation carried out in order to keep the original data trend. After the data imported into GEOMAGIC studio, reference CAD geometry was created to represent the new pipe. Then, the wear profiles are identified by the difference between the surface measurements after wear takes place and the original pipe surface. A sample of scanned profiles is shown in Fig. 6. 4. Results and discussions

Fig. 8. Axial velocity profiles at different number of grids.

The wear measurements were obtained using FARO-Axis CMM with Laser Scanner D100 attached to laser power source of Class 2M. The measured wear is calculated by measuring the difference between the actual corroded scanned surface and a CAD model representing the new pipe without corrosion. Wear measurements were obtained by scanning the cut pipe as shown in Fig. 5 with a measurement accuracy of ±0.037 mm. KUBE software was used to laser measurement capturing and GEOMAGIC studio software was

The problem considered is shown as an axisymmetric sketch in Fig. 7a, which refers to two-dimensional incompressible flow of water in a horizontal pipe of diameter D (D = 25.4 mm) and a total length of 65D. The flow field is divided into two sections of length 25D upstream and 40D downstream an orifice plate. These lengths are selected to ensure fully developed flow on either sides of the orifice. The upstream wall is made of non-water soluble acrylic material while the downstream wall is made of hydrocal (CaSO4 ·½H2 O) that is sparingly soluble in water. The inlet velocity, UO , is selected to represent a Reynolds number (Re) of 20,000, while its profile is assumed to be fully developed turbulent profile. Hence, turbulence intensity, I, and hydraulic diameter are specified to account for this assumption. Mass fraction for the hydrocal, Yi , is specified at both inlet and exit sections. The exit section is open to ambient with reference gauge pressure, PO . The conservation

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W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

Fig. 10. Numerical results for the flow downstream orifice.

equations are integrated over each control volume in the flow field. The Reynolds Average Navier–Stokes equations were solved using the K–ε (RNG) differential viscosity turbulence model to account for low-Reynolds-number (LRN) effects. It should be noted that the solution convergence is greatly improved by using extremely fine near-wall grids as shown in Fig. 7. Also, the computational mesh was refined where high velocity and species concentration gradients were expected. Due to the high Schmidt numbers encountered in mass transfer problems, Nesic et al. (1993) suggested that the maximum value of Y+ should not exceed 0.1. The Reynolds average mass transport equation was also solved for determining the concentration field of the dissolved wall species.

A mixture of hydrocal and water is selected as the material for the wall species in order to compare the results with the experiments. Convergence is considered when the maximum of the summation of the residuals of all the elements for velocity components and pressure correction equations is less than 1 × 10−5 . A grid independence tests were performed by increasing the number of control volumes from 104,903 to 327,000. The effect of mesh refinement on the variation of the velocity and mass transfer coefficient found to be negligible beyond 205,475 grid points. The grid independence test resulted in a maximum difference of less than ±2% in the axial velocity downstream the orifice as the number of finite volumes increased from 104,903 to 327,000. Fully developed turbulent velocity profile is selected as the entrance condition for the inlet pipe. Assumption such as no-slip condition at the walls, steady, viscous, incompressible liquid and fully turbulent with constant transport properties are also used in the present analysis.

Fig. 11. Surface pressure coefficient along the pipe wall downstream the orifice for different orifice diameters.

Fig. 12. Skin friction coefficient along the pipe wall downstream the orifice for different orifice diameters.

W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

61

Fig. 13. (a) Contours of normalized turbulent kinetic energy downstream the orifice, for d/D = 0.5 and Re = 20,000 and (b) radial profiles of normalized turbulent kinetic energy at Re = 20,000 and d/D = 0.25, 0.5 and 0.74.

Fig. 14. Normalized turbulent kinetic energy distribution downstream the orifice, for different orifice diameters and Re = 20,000.

The mass concentration of the mixture species along the walls are adjusted to unity. Also, the solubility (Cw ) of species in water is set to 0.275 g/100 g as specified by the manufacturer’s properties table for hydrocal-X21 (USG Corporations). Numerical simulations were performed at Reynolds number, Re = 20,000 and orifice-to-pipe diameter ratios of d/D = 0.25, 0.5 and 0.74. Prior to the commencement of the simulations, a sensitivity study of three different grid numbers was performed, using axial velocity distributions as shown in Fig. 8a–c. The results indicate that deviations in flow characteristics within the flow domains are minor (±2%) when one-half or one-and-a-half number of grids were used. The model for the present study was validated by running the work of Smith et al. (2008). The results of centreline axial velocity distributions and wall static pressure distributions shown, respectively, in Fig. 9a and b agree very well with those obtained by Smith et al. (2008). The flow characteristics for the three orifice geometries are found to be qualitatively similar. Therefore, only representative

Fig. 15. Radial profiles of normalized concentration (Re = 20,000).

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W.H. Ahmed et al. / Nuclear Engineering and Design 252 (2012) 52–67

Fig. 16. Mass transfer coefficient distributions downstream the orifice, for different orifice diameters, and Re = 20,000.

vector and contour plots for d/D = 0.5 are presented here. In addition, relevant profiles for the three geometries are also presented. Fig. 10a shows the mean velocity vectors, normalized by the averaged inlet velocity (UO ) within the flow domain. It can be seen that the flow accelerates as it approaches the orifice then separates at the orifice sharp edges, forming large vortices behind the device. These vortices sustain the reduction in the flow cross-sectional area further downstream up to the minimum obtainable for the given orifice diameter, known as the vena contracta, after which the flow decelerates towards the flow reattachment point. This is the cause of the high velocity central region observed just downstream the orifice which changes to lower velocity region as the

Fig. 17. (a) Sherwood number distributions downstream the orifice, for different orifice diameters, and Re = 20,000 and (b) enhancement of mass transfer downstream the orifice, for different orifice diameters, and Re = 20,000.

Fig. 18. FAC wear rate downstream the orifice, for different orifice diameters, and Re = 20,000.

flow develops further downstream. Fig. 10b shows the profiles of the mean horizontal velocity for the three geometries at different axial locations. The ordinate r/D is measured from the centreline of the pipe while Z/D is measured from the orifice. The maximum centreline velocity increases within the circulation zone as the orifice diameter decreases. The relative reductions in the centreline velocity at Z/D = 1 through Z/D = 4 are about 93%, 92%, 75% and 5.7%, respectively, as d/D increases from 0.25 to 0.74. From Z/D = 5 upwards, the velocity profiles are almost similar for the three

Fig. 19. Variation of hydrocal concentration.

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geometries, with the flow returning to fully developed turbulent flow at Z/D ∼ = 30. The flow reattachment locations from the orifice also increases as the orifice diameter decreases, with the closest at Z/D ∼ = 3 for d/D = 0.5 and Z/D ∼ =4 = 2 for d/D = 0.74, followed by Z/D ∼ for d/D = 0.25. Fig. 11 shows the surface pressure distribution along the pipe walls, which is expressed as a pressure coefficient CP , defined as CP = (P − PO )/(1/2UO2 ), where P is the static pressure and PO is a reference pressure taken at the outflow, for the three d/D. Variation of CP is similar for the three d/D, but it decreases as d/D decreases within the circulation zone (Z/D ∼ = 0–2) up to the vena contracta. There is a decrease in CP immediately downstream the orifice, due to the suction pressure produced by the circulating vortices, until it reaches the minimum value at Z/D ∼ = 0.3, 0.7 and 1.5, for d/D = 0.74, 0.5 and 0.25, respectively. It then increases and reaches a maximum value within the flow reattachment region before decreasing slowly further downstream. The most appreciable decrease in CP is from d/D = 0.25 while the least is from d/D = 0.74. The relative change in the minimum value of CP is about 98% as d/D increases from 0.25 to 0.74. The skin friction coefficient Cf distribution downstream the orifice, which is defined as Cf = W /(1/2UO2 ), where  W is the wall shear stress, for the three d/D is illustrated in Fig. 12. Variation of Cf is similar for the three d/D; it increases steeply downstream the orifice, as a result of the reversed flow generated by the separating vortices, and reaches a maximum value at Z/D ∼ = 0.4, 1.3 and 2.3, for d/D = 0.74, 0.5 and 0.25, respectively. It then decreases steeply and reaches a minimum value at Z/D ∼ = 1.4, 3.4 and 3.7, for d/D = 0.74, 0.5 and 0.25, respectively, within the flow re-attachment region. As the flow progresses downstream, the surface shear stress increases due to the boundary layer developed by the reattached flow, and reaches the second local peak between Z/D = 4 and 5. These local peak values of Cf decrease as d/D increases; the first value decreases by about 92% as d/D increases from 0.25 to 0.74, while the second value decreases just marginally. The shear stress decreases as the boundary layer thickness increases with axial distance afterwards. Fig. 13a shows the contours of normalized turbulent kinetic energy (TKE) within the flow domain for d/D = 0.5. TKE increases appreciably within the flow separation zone due to the high velocity gradients within the region. Fig. 13b shows the profiles of the normalized TKE for the three d/D at different axial locations. The profiles are qualitatively similar for all the three d/D; within the circulation region (Z/D = 0–2), normalized TKE value increases from zero at the wall to a maximum value at a radial distance towards

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the centreline. It then decreases steeply to a value slightly above zero at the centreline. These local peak values of TKE, as well as its radial location from the wall, increase as d/D decreases. All the profiles however collapse to a single line at Z/D = 8. The axial distribution of normalized TKE downstream the orifice is shown in Fig. 14 for the three d/D. There is a steep increase in the TKE immediately downstream the orifice, to a peak value at Z/D ∼ = 0.4, 0.9 and 1.2, for d/D = 0.74, 0.5 and 0.25, respectively. It then decreases as the flow develops further downstream. The peak value of TKE decreases by about 96% as d/D increases from 0.25 to 0.74. The normalized concentration profiles shown in Fig. 15 are qualitatively similar for all the three d/D. For each of the d/D, the wall species concentration decreases and reaches a minimum within the flow reversal region of Z/D = 1–2, resulting in reduction in the diffusive boundary layer thickness. The wall species concentration however increases after Z/D = 2, becoming almost homogeneous within the pipe as the flow develops further downstream. On the effect of geometry on mass transfer, the diffusive boundary layer thickness increases while the concentration gradient at the wall decreases as d/D increases. The predictions of the present model for MTC distributions downstream the orifice for all the three d/D is shown in Fig. 16. This parameter increases steeply downstream the orifice and reaches the peak at Z/D ∼ = 1, 4 and 3, for d/D = 0.74, 0.5 and 0.25, respectively, after which it decreases steeply further downstream as the flow develops. The MTC distributions correlate only approximately with the TKE, Fig. 14, because the location of its peak value lags that for the TKE. Fig. 17a and b respectively show the predictions of the model for the distributions of Sherwood number Sh and the mass transfer enhancement ShZ Shfd downstream the orifice for the three d/D. The peak value of Sh, as well as ShZ Shfd , decreases by about 63% and 42% when d/D increases from 0.25 to 0.5 and from 0.5 to 0.74, respectively. The axial locations of the peak values however move downstream from Z/D ∼ = 1 to 4 when d/D decreases from 0.74 to 0.5, while the peak locations move upstream from Z/D ∼ =4 to 3 when d/D decreases from 0.5 to 0.25. FAC rate downstream the orifice is shown in Fig. 18 for the three d/D. The peak value of FAC increases as d/D decreases. Its peak value increases by about 23% and 90% when d/D decreases from 0.74 to 0.5 and from 0.5 to 0.25 respectively. The axial locations of the peak values however progressively move downstream from Z/D ∼ = 1 to 3 as d/D decreases from 0.74 to 0.25. The location of FAC peak values correlate very well with the location of the peak TKE. The hydrocal test section wear rates downstream the orifice for the sets of 1-h, 2-h and 3-h experiments have similar trend, hence,

Fig. 20. The surface wear morphology for the hydrocal test sections.

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the representative plot for the 2-h experiment for the three d/D is shown in Fig. 19a. It can be seen that the gradients of the dissolution rate lines increases as d/D decreases. That is, the wear rate downstream the orifice increases as the orifice diameter decreases. Fig. 19b shows the test section wear rates downstream the orifice for d/D = 0.5 for the three experiments. As expected, the three lines are parallel, meaning that the dissolution rate is constant regardless of the duration of the experiment, provided that the saturation concentration for the hydrocal is not exceeded. The surface wear morphology for the hydrocal test section after the sets of 1-h, 2-h and 3-h experiments for d/D of 0.25, and 0.74 is shown in Fig. 20. The figure shows qualitatively that the maximum wear occur within the range Z/D ∼ = 2 to Z/D ∼ = 5 downstream the orifice. Moreover, the wear rate decreases as d/D ratio increases. For the same operating conditions and after the same elapsed time, the area downstream of the orifice with d/D ratio of 0.25 shows higher wear than for d/D ratio of 0.74. 5. Validation of results The numerical results for the wear enhancement profiles downstream each of the orifices are compared with Coney (1980) correlation as shown in Fig. 21. The qualitative evaluation of Fig. 21 reveals similar trend of ShZ Shfd −1 profile downstream of all the orifices. The wear found to increase steeply downstream the orifice and reaches a maximum value within the flow recirculation region and then decreases as the flow progresses far downstream. For d/D = 0.25 in Fig. 21a, the wear peak value obtained from the numerical simulation is about 60% higher than the value obtained from Coney (1980) correlation while the simulation under predicts the maximum wear for d/D = 0.74 by 23% as shown in Fig. 21c. However, the simulation tend to agree well with Coney (1980) within ±7% for d/D = 0.5 as shown in Fig. 21b. This can be attributed to the extreme d/D ratio presented in this study for large contraction (d/D = 0.25) or very small contraction presented by d/D = 0.74. The FAC distributions along the pipe surface downstream the orifice for d/D = 0.25 and 0.5, and Re = 20,000 are plotted in Fig. 22. The experimental results for the same operating conditions are also plotted on the figure. The figure shows a good agreement between the numerical and experimental results of FAC wear rate. Similar to the MTC profiles, the FAC wear rate increases steeply downstream of the orifice and reaches a maximum value within the flow recirculation region (z/D = 2–5), and then decreases as the flow develops downstream. For d/D = 0.25, the maximum value of the wear is under predicted by about 26% while its location is exactly predicted at Z/D ∼ = 2.8. For d/D = 0.5, the peak value is over predicted by about 5% while its location is under predicted by about 36%. In general, the FAC wear rate profile found to be strongly correlated with both MTC and TKE profiles. Moreover, the location of the maximum FAC wear rate found to be within 5D downstream of the orifice as commonly found in practice. 6. Power plants inspection data Ultrasonic techniques (UT) measurements are commonly used to determine the wall thinning measurement in nearly all power plants and to provide more accurate data for measuring the remaining wall thickness in piping system. The UT inspection data were obtained at grid intersection points marked on the piping component. The data are usually stored in a data logger and transferred to a PC for further processing using appropriate software. The wall thickness data were obtained at different grid point on the piping as shown in Fig. 23. For each band, the difference between the measured wall thickness and the nominal pipe wall thickness is calculated and considered to be the wear at this axial location

Fig. 21. (a) Enhancement of mass transfer downstream an orifice empirical constants by Tagg et al. (1979) (TPW) (d/D = 0.25). (b) Enhancement of mass transfer downstream an orifice: comparison of numerical data with Coney correlation using the empirical constants by Tagg et al. (1979) (TPW) (d/D = 0.5). (c) Enhancement of mass transfer downstream an orifice: comparison of numerical data with Coney correlation using the empirical constants by Tagg et al. (1979) (TPW) (d/D = 0.74).

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Fig. 22. Comparison between experimental and numerical FAC wear rate.

along the pipe. Sometimes, scanning within grids and recording the minimum found within each grid square is an acceptable alternative to the above method. However, it should also be noted that scanning within grids and the minimum wall thickness recorded can affect the accuracy of the data if point-to-point comparison between two consecutive inspections times. The inspection data are used to determine whether the component has experienced wear and to identify the location of maximum wall thinning as well

as to evaluate the wear rate and identify wear pattern in piping component. In the present study, 132 inspection data collected from 5 nuclear power plants and 3 fossil power plants for piping downstream an orifice were analyzed. The data of very high and low values of wear are compared to adjacent inspection readings in order to remove data outliers. Once the data set for each inspection location is verified, the wear is identified at each band along

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the orifice and the value of the maximum FAC wear rate increases as the orifices diameter reduces.

Acknowledgements The support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through the project No. IN090038, is gratefully acknowledged. The authors thank Dr. Mohamed El-Gammal and Dr. Chan Ching for their valuable input into this work. Special thanks to Mr. Hassan Iqbal for performing the laser scanning, at the Rapid Prototyping Laboratory, and to Mr. Ahmed Abdel Rehim for fabricating the hydrocal test sections.

References Fig. 23. Inspection grids downstream of the orifice.

Measured Wear Rate (mm/year) x 10

Maximum FAC rate 7 Condensate System

6

Moisture Separator Drain System

5

Reheat Supply System Reheat Drain System

4 3 2 1 0

0

1

2

3

4

5

6

7

8

L/D Fig. 24. Measured wear rate downstream orifices at different power plants.

the pipe axis. The measured wear data at different location from the orifice were presented for different piping systems as shown in Fig. 24. 7. Conclusion Numerical and experimental simulations were performed to determine the wall mass transfer rate downstream orifices. Three different cases with orifice to pipe diameter ratios of d/D = 0.25, 0.5 and 0.74, were investigated at Re of 20,000. The Reynolds averaged mass, momentum and concentration conservation equations were solved using the K–ε differential viscosity turbulence model, to account for low-Reynolds-number effects close to the wall. The simulation results of Sh distribution downstream were obtained and found to be in good agreement with both the present experiments and also with Coney experiments. Also, the results obtained from the numerical simulation for the Sh in the fully developed region downstream of the orifice were in good agreement with the FAC wear values obtained from the correlation of Coney (1980) correlation and for fully developed pipe flow. The effect of geometry found to strongly affect the FAC wear rate downstream of the orifice. The maximum value of the wear found to be located within 5D downstream of the orifice. Also, the hydrodynamic profiles such as TKE and MTC found to characterize the FAC wear rate downstream

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