Duan C.G., Karelin V.Y. Abrasive Erosion and Corrosion of Hydraulic machinery

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Abrasive Erosion and Corrosion of Hydraulic Machinery

2.2.2 Mechanistic Model Developed by The Erosion/Corrosion

Research Center

In an effort to provide an erosion model that was applicable for a broad range

of production situation, a mechanistic model for abrasion was developed by

The Erosion/Corrosion Research Center, the University of Tulsa. The

mechanistic model accounts for flow velocity, fluid viscosity and density,

sand size and density as well as shape, pipe size and material, and flowing

geometry. Another mechanistic model is being created that will include the

abrasion due to random impingement.

To compute the abrasion ratio, a semi-empirical relation for sand erosion

is used as follows (Ahlert 1994)

[2.8]:

=AV

l73

(2.40)

where B is the Brinell Hardness number of the target material, andfffii) is the

angle function,

is the angle between the impinging velocity of particle to

wall and the tangential of the wall,

and

A = 1.95 x I0~

.f(/3i) is defined as:

/(P,) = [«Pi

+6P

]j:+[Xcos

sin(

) + 7sin

+Z]^

The constants a, b, X, Y and Z have different values for dry and wet

surfaces. These values were given by Ahlert (1994) [2.8] as follows:

Table 2.1 Empirical constants for abrasion

Material

Carbon steel

1.95xlO"

xB-

059

-3.84 x 10"

2.27 x 10'

1.0

3.147 x 10'

3.609 x 10"

2.532 x 10'

Aluminum

2.388 x 10

-34.79

12.3

5.205

0.147

-0.745

1.0

Calculation of Hydraulic Abrasion 85

This abrasion model is used to predict the silt erosion on the blade surface

of hydraulic machinery in the present work by Yulin Wu. In most of other

predictions of erosion, the Eulerian-Lagrangian method is used to calculate

the particle trajectories and velocities. But in the present work, the Eulerian-

Eulerian method of two-fluid model for silt-laden flow in hydraulic turbines

proposed in Chapter 3 is used and the second type of boundary conditions for

particle flow velocities is applied. The parameters of the Francis turbine are

as follows:

Hydraulic runner diameter Dl = 2180 mm

Number of runner blades N= 17

Rotating speed of runner n

450 rpm

Discharge of calculation condition Q

23.08 m

Flow angle at the leading edge of blade

/?/

= 30°

Sand characters of silt phase in silt-laden flow through the runner

Sand diameter d

0.1 mm

Sand density p

2300 kg/m

Silt-phase volumetric concentration Cv

0.032%.

The calculated results of the present computation show the relative

velocity distributions of liquid phase in Figure 2.6 and the velocity

distributions of silt phase in Figure 2.7.

There is a difference between relative velocities of water phase and silt

phase. Near the inlet of runner the two phase's velocities only have a little

difference. On the following areas of runner the particle velocity is smaller

than the water velocity fore large inertia of sands. At the exit of runner, the

velocity of sands increases and has the nearly same value as the water

velocity. Figure 2.8 shows the erosion rate of silt to surfaces of this runner by

using the prediction model. The prediction depth of erosion from the results in

the present computation has indicated the agreement with the date of

prototype turbine observation in Japan.

86 Abrasive Erosion and Corrosion of Hydraulic Machinery

(a) On suction surface (b) On middle surface

(e) On middle surface (f) On band surface

Figure 2.6 Relative velocity distribution of water phase through

turbine runner (Velocity unit: m/s)

Calculation of Hydraulic Abrasion

(a) On suction surface (b) On middle surface

(d) On crown surface

(e) On middle surface

(f) On band surface

Figure 2.7 Relative velocity distribution of silt phase through

turbine runner (Velocity unit: m/s)

Abrasive Erosion and Corrosion of Hydraulic Machinery

(a) On suction side (b) On pressure side

Figure 2.8 Prediction of erosion rate of silt on surfaces of hydraulic runner

2.2.3 Prediction Erosion Model Proposed by McLaury et al

McLaury et al. (1996) [2.10, 2.11] presented several models for the

computation of solid particle erosion. The model equations vary depending

upon the type of material being used. These models are based on direct

impingement tests at various angles and impingement velocities. These

erosion models consist of the following equations, where ER is the erosion

ratio (kg/kg). The erosion ratio is defined as the amount of mass lost by the

pipe wall divided by the mass of particles that cause the erosion. Other

variables involved are the particle impingement angle 9 (radians), the pipe

material Brinell hardness factor B, and the particle impingement velocity V

(m/s).

Erosion equations have been developed for two materials: carbon steel

and aluminum based on existing data in the literature and taken at The

University of Tulsa

[2.9].

Slight modifications to the carbon steel erosion

model are required for the analysis of other steel alloys (e.g., stainless).

Calculation of Hydraulic Abrasion

For carbon steel:

ER =

1559

( V

[.73

0.59

0.3048

f(0)

xlO"

(2.41)

where, for 0< 15°

j\9)

= 2219 -3.846>

for<9> 15°

f{0) = 3.147cos

0sin 0 + 0.3609sin

0 + 2.532

For aluminum:

ER = (2.388 xlO"

)

,1.73

0.3048

f{0)

(2.42)

where, for 6< 10°

/(^) = 12.3(9 -34.79#

for (9>10°

/(6') = l + 0.147cos

6'sin(5.205^)-0.745sin6'

The benchmark case for the erosion prediction method is the aluminum

choke geometry presented by McLaury et al. (1992)

[2.10].

This geometry

consists of a sudden contraction, followed by a short straight throat section,

and a sudden expansion. This geometry was used to verify the integrity of the

erosion model by Jeremy K. Edwards et al [2.12] as shown in Figures 2.9.

In the erosion prediction procedure, the diffuser section (downstream of

the sudden expansion) is sliced into "wafers" that are equally spaced along the

pipe axis. The thickness of each wafer is Ax. Assuming that the mass lost by

the pipe is distributed evenly around the circumference of the pipe wall, and

Abrasive Erosion and Corrosion of Hydraulic Machinery

that the reduction in wall thickness due to erosion is much less than the inside

pipe radius, the penetration rate P is given by:

P =

rtp

dtsx

(3.1536xl0

)

(2.43)

where m

is the pipe wall material mass loss rate (kg/s), p

is the pipe

wall material density (kg/m

), and d is the pipe diameter (m) at the impact

location. Eq. (2.43) gives the penetration rate in millimeters per year (mm/yr)

if the prescribed units are used. Multiplying the result by 39.37 mil/mm

converts the penetration rate to mils per year (mpy).

Pipe wall

cerrterline

Flow

retire ulation

Shearlayer-

reattachment

Figure 2.9 Sudden pipe expansion geometry

Results of the three-dimensional flow model were in close agreement with

the experimental results of Stieghneier et al (1989)

[2.13].

Input data for the

prediction erosion studied is as follows:

Inlet pipe diameter 6.5 mm

Outlet (diffuser) pipe diameter 15.9 mm

Inlet fluid velocity (centerline) 19.82 m/s

Inlet reynolds number 128,830

Entrance length (small diameter) 65 mm

Calculation of Hydraulic Abrasion 91

Diffuser length (large diameter) 240 mm

Sand diameter 150 um

Figure 2.10 (a) shows the variation of penetration rate with axial distance

downstream of the expansion for both the experimental data and the erosion

prediction up to 8 step heights downstream of the expansion. The erosion was

computed based on a wafer thickness Ax = 5 mm. The point x/h = 0

corresponds to the location of the expansion. The erosion profile shows good

agreement in both trend and magnitude with the experimental data for the

steady state penetration rate. Even though experimental data is only available

up to 8 step heights downstream of the expansion, the simulation was

performed up to 30 step heights downstream.

2500

2000

1500

■s

1000

-4—*

500

-t-

Prediction

Exp. (5

hours)

Exp. (10

hours)

□

Exp. (15

hours)

A Exp.(20 hours) + ^X

Exp. (25

hours) X

-t 60

-:20

-:10

0 12 3 4 5 6 7

Dimensionless Axial Distance x/h

Figure 2.10 (a) Erosion profile in choke geometry

The erosion predictions for the entire simulated range are shown in Figure

2.10 (b). These results show a maximum penetration rate at approximately 13

step heights downstream of the expansion. The reattachment location for this

case was determined to be approximately 10.5 step heights from the

expansion. This indicates that the maximum penetration rate for this case

occurs slightly downstream from the reattachment location. Further

experimental investigation is required to verify the predicted results.

Abrasive Erosion and Corrosion of Hydraulic Machinery

0 1 I 1 I I | I I I I—| 1 I I 1 |—I I I I |— I TT V

T'l""

' T"T 0

0 5 10 15 20 25 30

Dimensionless Axial Distance x/h

Figure 2.10 (b) Erosion profile in choke geometry

Calculation of Hydraulic Abrasion 93

References

2.1 Karelin V.Ya, (1983). 'Silt Abrasion of Turbo-pumps', Machinery

Engineering Press, Moscow (in Russian).

2.2 Elkholy A., (1983). 'Prediction of abrasion erosion for slurry pump

materials'. Erosion, Vol. 84, No. 1.

3 Graber P., (1983). 'Solids Handling Pumps'. World Pumps, No. 197.

2.4 Bitter, J. G. A., (1963). 'A study of erosion phenomena (Part I)',

Wear, Vol.6, 5.

5 Bitter, J. G. A., (1963). 'A study of erosion phenomena (Part II)',

Wear, Vol.6, 169.

6 Finnie, I., (1972). 'Some observations on the erosion of ductile metals',

Wear, Vol.19, 81.

7 Takehiko Yokomine, et al, (1997). 'Numerical simulation of erosion of

gas-solid suspension flow in a pipe with a twisted-tape insert', ASME

Fluids Engineering Division Summer Meeting, June 22-26, 1997,

FEDSM97-3638.

2.8 Drtina P. and Krause M., 'Abrasion on a Francis turbine guide

vaneNumerical simulation and field tsts-', Procs. of IAHR 1994,

Beijing, 713-724.

9 Ahlert, K., (1994). 'Effects of Particle Impingement Angle and Surface

Wetting on Solid Particle Erosion of AISI 1018 Steel', M.S. Thesis,

The University of Tulsa.

2.10 McLaury, B.S., (1996). 'Prediction of Solid Particle Erosion Resulting

From Turbulent Fluctuations in Oilfield Geometries', Ph.D. Thesis,

The University of Tulsa.

2.11 McLaury, B.S., Shirazi, S.A., Shadley, J., and Rybicki, E., (1996,).

'Modeling Erosion in Chokes', ASME FED Vol. 236, San Diego, CA,

pp.

773-781.

2.12 Edwards, J.K., McLaury, B.S., and Shirazi S.A., (1998).

'Sopplemeting a CFD Code with Erosion Prediction Capabilities',