DEVELOPMENT OF STRAIN IN OXIDES GROWN IN STEAM TUBES

I.G. Wrighta, A.S. Sabaub, and R.B. Dooley*c Oak Ridge National Laboratory, 1, Bethel Valley Road, Oak Ridge, TN 37831, USA *Structural Integrity Associates, Inc., Oakville, Toronto L6J 7L7, Ontario, Canada

awrightig@ornl.gov, bsabaua@ornl.gov, cbdooley@structint.com

Keywords: exfoliation; steam oxidation; computation of strains in oxides

Abstract. In this study, the foundation is being developed for the numerical simulation of the

processes that determine the oxide scale exfoliation behavior of the steam-side surfaces of

superheater and reheater tubes in a steam boiler. Initially, the assumptions concerning the base state

for calculating oxide strains also were critically examined. The state of stress-strain of an oxide

growing on the inside surface of an externally-heated tube was considered for the conditions

experienced in a boiler during transition from full- to partial-load operation. Since the rate at which

the oxide grows is an important consideration, it was necessary to determine the appropriate

temperature to use in the oxidation rate calculations. The existence of a temperature gradient

through the tube, and the cyclic nature of the boiler operation (temperature and pressure) were

considered; the growth temperature of the oxide was taken to be the oxide surface temperature. It

was determined that the commonly-used approach for accounting for geometrical effects when

calculating stress-strain development in a growing oxide scale of using the analogy of an infinitely-

long flat plate gave sufficiently different results than when using a cylindrical geometry, that the

latter was adopted as the preferred calculation procedure. Preliminary calculation of strains

developed in multilayered oxides formed on alloy T22 as a function of boiler operating conditions

indicated the magnitude of the strains in each layer; the large strain gradients between the layers

inferred the importance of the detailed scale morphology in determining the mode of exfoliation.

Introduction

A major concern resulting from the growth of oxide on the inside surfaces of steam tubes is

that, as the oxide scales become thicker, there is a reduction in the ability to accommodate stresses

resulting from the growth process (volume change) and from thermal transients (especially upon

cool down). Accommodating these stresses leads to modification of the scale morphology, the

development of flaws, and the eventual exfoliation of the oxide from the tube surface into the steam

flow. Factors such as the extent and frequency of exfoliation, the size and shape of the oxide

particles lost, the location in the boiler where exfoliation occurs, and boiler operating parameters

determine the subsequent fate of the exfoliant, but in extreme cases blocking of tube bends and/or

erosion of the steam turbine can result [1-3].

In order to anticipate the occurrence of scale exfoliation, it is necessary to develop a

quantitative understanding of contributions from all sources to the stress accumulated in the scale,

the interactions among these stresses, and of the processes by which such stress is accommodated.

There has been a considerable amount of pioneering work conducted in this area by several

research groups [3-13], and the intent of this effort is to build on that foundation. Common

assumptions used in the estimation of stresses and strains in oxide scales include: (a) uniform

temperature/no temperature gradient through the oxide scale; (b) semi-infinite, thick, flat plate

geometry; (c) isothermal conditions, or temperature cycling quite unrepresentative of boiler

operation; and (d) no effects of steam pressure. Laboratory oxidation experiments often are

performed using specimen geometries quite different from those experienced on the inside of tubes.

The intent of this study is to attempt to incorporate a proper accounting of these factors into a

computational methodology that provides a realistic basis for modeling of the exfoliation process.

The approaches used for addressing the issues listed above are discussed in the following.

Effect Typical of Steam Boiler Operating Cycles on Steam-Side Oxide Growth

An example of the thermal cycle associated with standard steam boiler operation is shown

schematically in Fig. 1. The load of the boiler follows demand, so that periods of full load are

followed by period when the boiler operates at partial load. In order to calculate the oxide growth

associated with the conditions experienced during a boiler operating cycle, it is necessary to

explicitly specify the parameters associated with that cycle. Since actual boiler operating schedules

can vary significantly, and details usually are not readily available, the values used (shown in Table

I) were based on plant experience for a ‘typical’ boiler schedule, and are similar to those discussed

in Gonzales et al. [14] and Zarrabi and Rose [15]. In Table 1, Tst and Tg are the internal (steam) and

external (combustion gas) gas temperatures, respectively, and Pst and Pg are the pressures of the

steam and combustion gas, respectively. It is assumed that the boiler is shut down only at scheduled

maintenance intervals (in this case, every four years). The time taken to change from partial-to-full

load, or vice versa, is taken as one hour.

Figure 1. Assumed Temperature Cycle.

Table 1. Assumed Boiler Operating Conditions.

Load Duration

(hrs)

Tg

(°C)

Tst

(°C)

Pg

(bar)

Pst

(bar)

Full 14 1 200 550 2 170

Partial 8 550 460 1 100

Thus, the oxide thickness (dox), at a given time (tk) is given by:

!

dox.(k)

2 = dox,(k"1)

2 + d dox2( ) . (1)

!

where : d dox2( ) = 2"t kp Tgr tk( )( ), denoting that the usual parabolic oxidation relationship (dox

2 = 2 kp

!t) now takes account of the periods of scale growth under the conditions associated with full load

and partial load; and

!

kp T( ) = A e"Q RT , indicating that the parabolic rate constant (kp) corresponds to

the prevailing oxide growth temperature (Tgr), and where t is time; A is the Arrhenius constant, Q is

the activation energy for the rate-controlling process; and R is the Universal Gas Constant.

Oxide Growth in Under a Thermal Gradient Typical of a Boiler Steam Tube

A schematic representation of a cross section through an idealized boiler tube wall is shown in

Fig. 2, which suggests the form of the temperature gradient resulting from the fact that the heat

transfer path is from the combustion gas to the steam. Thus, the temperature of the alloy will be

higher than that of the steam-side oxide which, in turn, will be higher than that of the steam.

Further, as the oxide thickens, the thermal resistivity through the tube assembly will be increased,

leading to a higher metal temperature and an increased rate of oxide growth. For the purposes of

calculation, the various layers considered to represent the tube configuration are shown in Fig. 3.

Layer 0 is a layer of oxide and/or slag on the fireside of the tube; Layer 1 is the thickness of the

alloy tube, while Layers 2 to N are the multiple layers of steam-side oxide. The location of each

boundary is identified by its radial distance from the tube centerline (rbi, etc). Here, the tube was

assumed to have an outer diameter of 50 mm (rb1 = 25 mm), and a wall thickness of 5 mm (rb2 =

20 mm). The alloy was assumed to be T22 (nominally Fe-2.25Cr-1Mo wt%, a ferritic steel

commonly used for boiler tubes), which forms an oxide scale in steam that typically consists of two

main layers, starting with Fe-Cr spinel [(Fe,Cr)3O4] next to the alloy, and magnetite (Fe3O4), which

are essentially uniform in thickness and approximately equally thick. Often, a thin, outermost layer

of haematite (Fe2O3) also is present [3].

Figure 2. Schematic representation of the thermal gradient through the wall of a steam tube.

Figure 3. Schematic representation of the tube configuration with oxide layers growth on the

fireside and steam side.

The thermal properties of the individual oxides and their temperature dependencies were taken

from Schütze [11]. Within each layer defined in Fig. 3, the temperature was computed at several

points uniformly distributed in the radial direction. For the ith layer, the total number of points at

which the temperature was computed was Mi. Thus, the equation for the temperature profile in the

ith layer is given by:

!

Ti, j = Ti rj( ) = ai + bi ln rj . (2)

where j ranges from 1 to Mi. The coefficients ai and bi were determined through the continuity of

temperature and heat flux in the radial direction at boundary radii (rb) between adjacent layers, and

the heat transfer boundary conditions on the flue gas side and steam side were calculated from

appropriate temperature-dependent relationships [16]. The following values were used in this

study: gas-side (hg) and steam-side (hst) heat transfer coefficients of 100 and 2 800 W/m2K,

respectively, based on the ranges listed by French [17]. These HTC values incorporate the effects

of convection and thermal radiation in the system. The thermal conductivity of each of the three

oxide types was evaluated over the temperature range of 400 to 600°C, (based on the expressions

given by Armitt, et al. [1]). Over that temperature range, the thermal conductivity values (k) were 3

W/mK for all three oxide types, and 30 W/mK for alloy T22 [18]. The oxidation-specific

parameters used for alloy T22 were: A = 6.22 x 1020 µm2/hr and Q = 326 kJ/mole [3].

If the oxide is assumed to grow predominantly at the oxide-steam interface, the oxidation

temperature can be taken as that of the oxide surface (Tos), i.e., Tgr = Tos. In that case, a few iterative

steps are required to obtain the oxide thickness (dox) grown during the thermal cycle. The iterations

end when the difference between the old and new oxide surface temperature is smaller than the

acceptable error (taken as 0.1°C). Otherwise, a new growth temperature is assigned and a new

iteration is conducted. Thus, for an arbitrarily-chosen oxide growth period of four years (35 040 h),

when the oxidation temperature was taken as the steam temperature (Tgr=Tst), the calculated total

oxide thickness was approximately 240 µm whereas, where Tgr=Tos the thickness was 480 µm. The

large difference between the two cases is illustrated in Fig. 4a. The oxide surface temperature was

approximately 26°C higher than the steam temperature at full load, and 3°C at partial load (Fig.

4b). In the remainder of this paper, the results shown are only for the case where Tgr= Tos.

(a) (b)

Figure 4. Difference in total oxide thickness on alloy T22 for assumption that the oxidation

temperature (Tgr) is Tst or Tos: (a) differences in thickness for oxide growth (at full load conditions);

(b) temperature differences during cooling from full to partial load.

Comparison Stress-Strain Development on the Inside of a Tube vs. a Flat Plate

Before proceeding to calculate the stresses and strains associated with oxide grown in steam

tubes, it was necessary to evaluate the magnitude of differences that would result from considering

the oxide to grow on a flat plate compared to the inside of a tube. For a flat-plate geometry

involving a thin oxide on a thick substrate, the strain and stresses normal to the plate surface may

be estimated using a relationship involving temperature-dependent thermal expansion

coefficients[8]:

strain:

!

"#th

= #th,met

T,TR( ) $#th,ox T,TR( ) . (3)

and stress:

!

"FP

=Eox#$

th

1%&. (4)

where E is the Young’s modulus and " is the Poisson’s ratio. Other expressions for the flat-plate

configuration also have been developed to take into account the oxide thickness [19]. The materials

properties used were close to those for alloy T22, and the oxide scale had properties of a composite

of the actually-expected oxide layers. Also, it is usual to assume that the scale is stress-free at

temperature, so that the reference state for stress generation in the oxide was taken to be the full-

load regime. Following Noda et al. [16], the reference temperature at each location (full-load state)

was taken to be

!

Ti, jR = Ti rj( ), and the current temperature was given by

!

Ti, j = Ti rj( ). Values were

calculated for the hoop stress developed in the overall oxide scale as a result of the temperature

variation between the various layers (defined in the previous section). As shown in Fig. 5a, the

oxide scale is in tension at all times. As the oxide thickens with time, the maximum hoop stress

increases, while the minimum hoop stress decreases, that is, the stress range experienced by the

oxide increases with increasing thickness. Scale failure would be expected when these maximum

values exceed some criterion.

(a) (b)

Figure 5. Hoop strains developed in an oxide under partial load conditions calculated for

(a) flat plate geometry and (b) hollow tube geometry

The methodology used to calculate the stresses and strains associated with the oxide grown on

the inside surfaces of a tube was based on formulations presented by Noda et al. [16], Davies and

Bruce [20], and Ackay and Kaynak [21], extended to include temperature- and spatial-dependent

thermal strains. As a first approximation, plasticity and creep effects were neglected in both the

oxide scale and metal. Also, the time-dependence was neglected, since the time scale between the

full- and partial-load regimes was very large (i.e., one hour) for transient phenomena to be

considered implicitly. Details of the computational methodology are reported elsewhere [22].

In addition to thermal stresses and strains, the contribution from the system pressures were

considered. The pressure conditions on the hot gas side and steam side of a steam tube are given

by:

!

" r,1,1 = #pg ,

!

" r,N ,M N= #pst . (5)

where pg and pst are the pressures of the flue gas and steam, respectively, and the axial force

equation was used to solve for model constants. The stress-strain equations were solved for both

the full- and partial-load regimes by considering the free thermal expansion (

!

"th,i

) given by the

temperature distribution within the oxide and metal. The stress strain fields were computed at 7 and

5 points within the tube and oxide, respectively.

A test case run to assess the accuracy of this methodology used a configuration of two hollow

cylinders (representing a tube with a single layer of oxide scale on its inner surface) that undergo

elastic deformation upon cooling from full load to partial load. Temperature gradient effects were

neglected, and a uniform temperature was assumed for both the reference (full load, 550°C) and

current state (partial load, 460°C). Also, pressure effects on the inner and outer surfaces were

neglected, so that the same pressure was used on both surfaces in both states. The tube was

assumed to have an outer diameter of 60 mm and a wall thickness of 5 mm, with a 200 mm-thick

oxide on its inside surface (after cooling to room temperature). The same materials properties were

used as for the flat plat case.

In any comparison of stresses and strains in flat-plate and cylindrical geometries, care is required

to ensure that the parameters involved are directly equivalent. The results for the test case are

shown in Table 2, and indicate that the free thermal strain (

!

"#th

) for the flat plate case is lower than

that the equivalent parameter (

!

"#s ) for cylindrical geometry (which involves only the hoop strain

component that generates stress), and that both are positive. However, the total hoop strain (

!

"# ) for

cylindrical geometry, which includes the effects of the thermal strains, is larger and negative.

Table 2. Average Strain in the Oxide Scale for the Test Case.

Assumption

Free Thermal

Strain

!

"#th

x103

Hoop Strain Component

that Generates Stress

!

"#s x103

Hoop

Strain

!

"# x103

Flat plate 0.91 0.91 (shear) 0.91 (shear)

Cylindrical (tube) 0.91 1.14 -1.86

The calculated hoop stresses for the cylindrical case at partial load as a function of oxide

thickness (including the loading due to the steam pressure) are shown in Fig. 5b which indicates

that, while the oxide always was in tension, the hoop strain in the oxide was significantly greater

than for the flat plate case (and more than twice that at full load). Also, the strain variation

experienced by the oxide (maximum to minimum) as it thickened from 12 to 400 µm, was slightly

larger for the cylindrical case (and much larger for the partial-load than the full-load condition).

Based on these results for the tube/oxide dimensions considered, the errors associated with the use

of a flat-plate assumption were approximately 25% for the hoop strain (and 4% for the hoop stress).

Strain Evolution During Transition From Full- to Partial-Load Regimes

In order to understand the evolution of strain in the oxide scale during transition from the full-

to partial-load regimes specified earlier, calculations were made of the hoop stress in a single-

layered (composite) oxide due to pressure loading only; to thermal expansion only; and to a

combination of pressure loading and thermal expansion, and the results are shown in Fig. 6. The

effect of the pressure change during the transition period was to decrease the strain in the oxide

(Fig. 6a), whereas the effect of the !CTE was to increase oxide strain (the reference/zero strain

state is the full-load regime). Figure 6c shows a net increase in strain due to the combined effects of

pressure and !CTE loading during transition from full to partial load.

Figure 6. Hoop strain (

!

"#s ) as function of time during the transition from the full to partial load, due

to: (a) pressure loading only; (b) thermal expansion only; (c) pressure and thermal expansion.

Stress-strain development in real oxide scales often requires consideration of interaction

among different oxide layers; in the case of alloy T22, two- and sometimes three-layered scales are

formed in steam [3] (Fig. 7a). The temperature-dependence of the CTE of the major oxide layers,

(a) (b)

Figure 7. Schematic diagram of the oxide layers formed on T22 (a); and (b) temperature-

dependence of the CTE of the alloy and oxides (after Osgerby and McCartney [23]).

(a) (b)

Figure 8. Calculated hoop strains developed in the oxide layers formed on the steam-side of a T22

tube during transition from full to partial load: (a) Fe-Cr spinel layer; and (b) magnetite layer.

shown in Fig. 7b, is such that both experience significantly greater change in volume than the alloy

over the temperature range of interest in the boiler operating cycle [23]. By inspection of Fig. 7b,

cooling from 550 to 460°C would be expected to result in both oxide layers being in tension. The

calculated values for the hoop strain developed in the Fe-Cr spinel and Fe3O4 during load

transitioning are shown in Fig. 8, and indicate that the tensile strain developed in the magnetite

layer is approximately twice that in the spinel. As the oxide thickens, the absolute value of the

strain developed decreases slightly, but the range between minimum and maximum strain

increases, particularly for the spinel. These calculations also show that the strain rate varied from

1.2 x 10-7 s-1 at an oxide thickness of 12 µm, to 1.0 x 10-7 s-1 for a 400 µm-thick oxide, during the 1-

hour cooling ramp from full- to partial-load conditions.

In Fig. 9, the calculated strain profiles through a tube wall with a 400 µm-thick scale illustrate

the very large strain gradients that develop along the various interfaces on cooling from the

thermally unstressed state (full load) to the partial load condition. The implication for scale failure

at such interfaces is obvious, and suggests that the details of the scale morphology will be very

important in determining the location and mode of failure.

Figure 9. Calculated strains profiles though the wall of a steam tube (T22 with a 400 µm-thick

scale) as a function of distance.

Summary and Conclusions

The results described indicated that calculations using a flat plate geometry sufficiently under-

estimate the strain developed in oxide formed on the inside surface of a tube that the use of a

cylindrical geometry should be adopted as the preferred calculation procedure. Consideration of the

prevailing temperature gradient through a steam tube showed, for the specific boiler operating

conditions assumed, that the outer surface of the oxide was up to 26°C hotter than the steam, and

that such a difference in temperature could result in a doubling of the oxide thickness over four

years of boiler operation. When considering the oxides formed in steam on a ferritic steel such as

T22, the temperature-dependence of the CTE of the individual layers was of particular importance

in the development of strain, since the boiler operating cycle traversed the maximum differences in

CTE among the oxide layers and the alloy. Preliminary calculation of strains developed in

multilayered oxides formed on alloy T22 as a function of boiler operating conditions (including

temperature and pressure cycling) indicated large differences between the layers. It is suggested

that the routes taken to accommodate such large strain gradients between the layers will depend

heavily on details of the scale morphology, so that the evolution of scale morphology assumes a

most important role in determining scale exfoliation behavior.

Acknowledgements

This research was sponsored by EPRI, Charlotte, North Carolina under a Work for Others

program (agreement No. EP-P18842/C9306) with the U.S. Department of Energy, Office of Fossil

Energy, Advanced Research Materials Program, under Contract DE-AC05-00OR22725 with UT-

Battelle, LLC. We also express our thanks to Bruce Pint and Peter Tortorelli for reviewing the

manuscript.

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