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

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Abrasive Erosion and Corrosion of Hydraulic Machinery

the flow volume unit; size distribution of particles and their average grain

size;

the incidence angle of impingement as related to the surface; the time

interval of the attack effected by the particles (of specified size and

concentration) on the surface flown about by the fluid; the erosion resistance

of the structural materials used.

There is no comprehensive formula presently capable of evaluating

hydraulic abrasion quantitatively with due consideration of the particular

values characterizing the afore mentioned parameters. There is, however, a

number of theoretical and experimental data enabling to reveal the

relationship mechanism of abrasive erosion or the erosion caused by separate

and interconnected factors.

Specifically, there can be suggested, as applied to hydro-turbines, the

following generalized expression for evaluation of abrasive erosion

[2.1]:

A-p-t-W

J = —

(2.1)

where J is the erosion extent, mm; p is the average annual concentration

of abrasive particles, kg/m

; / is the time interval comprising the period within

a year which the abrasive particles attack the surface, they collide with; W is

the flow velocity, m/s; £ is the erosion resistance of the material used

(equaling the unity for carbon steels); A is the index of the slurry abrasively

depending on shapes of the particles and to be determined experimentally, mm

/year.

In equation (2.1) the numerator defines the abrasive power of the stream

flow, whereas the denominator characterizes the ability of

the

material used to

withstand the abrasive attack exerted by the slurry. However this relationship,

when applied in practice, has certain difficulty, because, as the fluid flow

about curved surfaces, for instance, over the concave and convex sides of a

blade, the erosion level developed will be variable even with the flow

velocities are equal, since the abrasive particles, due to inertial forces arising,

will be pressed to the blade concave side and rejected from the convex one.

Therefore the erosion extent can be evaluated, for instance, by the time

interval required for maintenance-free operation of turbines or by necessity

for repair service to be provided when surveying the impeller and nozzle used

Calculation of Hydraulic Abrasion

as a whole. In this case the flow velocities are calculated, for example, at the

exit from the impeller or nozzle.

The criteria specifying the necessity for performing repair service of an

impeller are mainly as follows: erosion out of trailing edges within a blade, up

to entire disappearance of their thickness, or erosion-and-tear of

the

lower rim

to the extent of up to one third of

its

thickness. In this case the time specifying

the attack period effected by the slurry, f, corresponds to the maintenance

interval.

To determine the erosion extent, or the necessity for performing the

maintenance service of a newly designed turbine, let us consider it together

with one of turbines chosen within an operating hydroelectric plant. The

hydroelectric station is to be selected from among those having a known

slurry mechanism and erosion level; besides, it is better to choose the one with

an annual repair interval t - 1, provided that its components are fabricated

from carbon steel (e - 1). It is essential, in this respect, that the turbines being

compared should be identical or closely similar in their design type.

Consequently, the erosion extent J

for the turbines of an operating

hydroelectric plant introduced as

= A

-p-w

(2.2)

is a known value.

The erosion level J

for the turbines of a newly designed hydroelectric

station will be calculated from

-p-w

. (2.3)

When the standard sizes, of both the operating station and the one being

designed are identical, the necessity for maintenance servicing of the latter

arises when J

= J

; in this case

(2.4)

56 Abrasive Erosion and Corrosion of Hydraulic Machinery

Hence, the servicing time interval expressed in years or the turbine

maintenance-free time, t

, is obtained from

U-^T (2-5)

When comparing the erosion of the turbine being designed with that of the

operating one, their sizes are not taken into account, i.e. the scale factor is

ignored, and this effect manifests itself

the following.

The relative erosion of any component, for instance, that of an impeller

can be evaluated as the ratio of its weight loss to the total component weight.

The weight losses developed are proportional to the surface area being flown

over, that is to the diameter raised to the power two, whereas the weight is

proportional to the impeller diameter cubed. Thus, the erosion of turbines to

be used in the hydroelectric station being worked out, can be obtained from

J,=J?

(26)

whereas the erosion in the operating hydroelectric plant is calculated from

= Jf (2.7)

When comparing the erosion of identical components, used in both the

operating hydroelectric plant and the one being developed, we shall obtain

i.e. the erosion of the components being compared is inversely proportional to

the diameters of the impellers.

With regard to the scale factor, the maintenance-free interval of or a

newly designed hydroelectric plant will be equal to

Calculation of Hydraulic Abrasion

/ •£■ -D

(2.9)

-p-w

-D,

or, if presented as a generalized expression, it will look like

-P„-w'

-D

The maintenance intervals calculated from this formula coincide

adequately with the actual maintenance intervals.

For the calculation of hydraulic abrasion rate one can use the formula

offered by

Prof.

Bovet (Switzerland):

P~P ^

J = /jw

V* (2.11)

R J

where J is the erosion; ju is the friction coefficient between surfaces of a

hydro-turbine impeller blade and slurry abrasive particles; w is the volume of

particles; p is the specific gravity of particles; p

is the specific gravity of

water; R is the radius of an impeller; V is the particle motion velocity. This

formula demonstrates the necessity for taking into account the particle motion

velocity (in the third power).

To evaluate the hydraulic abrasion-out extent within the impellers,

utilized, for instance, as a part of hydraulic turbines, it is possible to make use

of statistical data obtained in the process of their operation. The erosion

index, in this case, will correspond to the weight loss amount of an impeller

blade, as related to the number of working hours consumed during the

maintenance-free operation of the installation.

While selecting the hydro-turbines, in order to restrict the erosion extent

to be developed, the relative water motion velocity within an impeller should

not exceed 15 m/s, which is governed by choosing the hydro-turbine rotational

speed required. In accordance with the admissible limiting rotational speed

range, in this respect, should be within 250 to 350 rev/min. The relationship

between the rotational speed, Q and H, within the relative water motion

velocity equaling 15 m/s, was calculated as well. The maximum rotational

Abrasive Erosion and Corrosion of Hydraulic Machinery

speed is not influenced by H, while it is varied in accordance with Q, m

/s.

The minimum rotational speed grows with a rise of H. when the concentration

of slurry particles suspended in the water is considerable; it is advisable that

an average rotational speed be chosen. For H exceeding 250 m; it is

recommended that active hydro-turbines be employed.

To reduce the erosion extent developed in impellers used in centrifugal

pumps, the relative water velocity in an impeller should not exceed 35 m/s.

For the devices used to pump over the water containing a large amount of

slurry particles the rotational speed to be selected should not exceed 1000

rev/min.

In [2.2] a series of tests were undertaken on different pump materials to

study the effect of slurry properties and pump material on abrasion erosion,

using a test facility, which incorporates most of these parameters. An

analytical model, for hard and brittle materials under different running

conditions was obtained. Experimental and calculated results for cast iron, as

an example of a hard and brittle material, are comparable on a specimen

weight loss basis.

The jet abrasion test facility was designed to evaluate erosion resistance

of different materials that are being subjected to abrasive particles. The main

asset of the test facility is its simple design although each erosion parameter

can be measured.

With a variable speed motor slurry velocities ranging from 5 to 30 m/s at

the nozzle exit can be obtained. Measurement of the slurry velocity is readily

carried out by instantaneously redirecting the flow with a Jaco air-operated

pinch valve through the same nozzle size into a graduated pail. By recording

the time of sampling together with the volume of sample collected by reading

the level from a sight tube on the side of the pail, the nozzle exit velocity is

obtained.

The particle size of the sand sample is determined by selecting one of four

different mesh sizes ranging from 37 to 3.5 or equivalent openings of 0.41 ~

0.50 mm. A particle size range of

0.41

~ 0.50 mm was used for experimental

verification in this study. The impingement angle can be varied from

approximately 15° to 90° by adjusting the specimen holder.

The erosion index is calculated from the following equation:

Calculation of Hydraulic Abrasion

O C T

W=^

" "xlO

(2.12)

loss

where Q is the volume of

sample;

y (g.cm

) is the density of the mixture; C„,is

the concentration; T

(min) is the time (given by time of testing-sample time,

) of erosion and Wi

oss

is the specimen removed per gram of sand. Erosion

can be expressed as an absolute value of

mass

loss or as an erosion index.

By combining all the parameters from the investigations an equation of

the following form is produced:

AW = -KC°/

(ELyd°-

6l6

239

+ sin(-^^-180 - 90)} f(t)g

2 Ti

—

Of |

(2.13)

where C

is the volumetric concentration; H\ is the eroded material hardness;

is the solid particle hardness; n is a function of

H\IH

according to

n = 3.817 if

1.9, and n = 0.268 if

> 1.9; d is the solid particle

size,

mm; Fis the velocity of particles at the nozzle exit and/ft) is an assumed

linear function as suggested by Brauer and Krieger. Here d is the

impingement angle.

The constant K in equation (2.13) was obtained from all the previous

results for velocity, hardness, particle size and concentration and with the help

of the least-squares method. The final equation expressing erosion for cast

iron is

=1.342xl0-

682

(^)V

06,

239

{l + sin(-^^-180-90)}r

90-a,

(2.14)

where n is again a function of

H\IH

From the analytical model, the prediction of erosion resistance for any

sample of cast iron under any running condition can be obtained.

Erosion intensity, as indicated previously, depends on a number of

different factors. With the frictional force involved the erosion rate of an

impeller blade, for instance, when calculated in a slurry pump with reference

60 Abrasive Erosion and Corrosion of Hydraulic Machinery

to the impingement exerted

by a

single abrasive particle,

can be

calculated

from

dA/dA

(2.15)

where K\ is the proportionality coefficient; dA is the work done by an abrasive

particle during its travel over an infinitesimal surface dA;

is the density

this abrasive particle.

The elementary work performed

by the

frictional force during

infinitesimal time period dt will equal to

fN<y,-v

)

where

the

friction coefficient;

N is the

normal component

reaction

acting in

blade; V

and V

are correspondingly the radial and circumferential

velocities of a particle.

The normal component of reaction is calculated from

N =

2mcoV

(2.16)

where

m is the

abrasive particle mass;

is the

angular frequency

the

impeller rotation.

Based on equation (2.16) the elementary work done can be expressed as

2mwf(V

-V

(2.17)

Substituting here

dt by dA and

replacing

the

value

dA in

equation

(2.15) we shall obtain

mcofy

-V

)

(2.18)

where K

is the proportionality coefficient.

The abrasive particles, with respect

the surface

an impeller blade,

can travel with both slip and rolling motion. The blade erosion can take place

Calculation of Hydraulic Abrasion

as the particle travels with slip motion and the particle-to-surface

impingement angle being 45° (intensive erosion).

Using the quantities for values V

and V

, the equation (2.18) can be

presented as:

J = K

mo)

JRy

[s[0Jylb

-1 -0.5(b/R-1)] (2.19)

where R is the radius used when the abrasive particle makes contact with the

blade surface; b is the blade width.

Having differentiated equation (2.16) we shall obtain the maximum

erosion intensity:

ajdb

mco

JRy

[Sjb/[R

(b/R)

-l]-0.5/R]

According to the curves obtained the variations in the impeller blade

erosion intensity, observed within the divergence length corresponding to the

experimental and theoretical data calculated, do not exceed 3 percent. The

erosion intensity of blades increases at small values of ratio b/R. It is

therefore directly proportional to the radius employed.

The erosion of blades depends as well on the amount of particles colliding

with the surface during their travel within the hydro-mixture flow. With

regard to equation (2.16) the erosion to be defined can be expressed in the

following generalized form:

J =

Knco

Rf[s[onJblr-\ - 0.5 -

-1)]

Hence, to decrease the erosion rate to be generated in blades it is necessary to

reduce the rotational speed of the impeller, to decrease the amount of solid

particles in the fluid, which can be accomplished through a more intensive de-

slurring process and, additionally, to make the friction coefficient higher,

specifically, by vulcanizing the working surfaces of impellers.

The erosion level in slurry pumps depends, among other things, on the

grain size used in pulps.

The abrasive particles contained in the pulp have different shapes and the

pump components are worn out under the action effected by faces of these

Abrasive Erosion and Corrosion of Hydraulic Machinery

particles. It is assumed that each of these particles possesses similar faces and

penetrates into the surface with one of its protrusions. Therefore the

penetration force value will depend on diameter d, number n of particles P =

1/n of n = l/d

and consequently, this penetration force of a particle per

area unit can be expressed as

P = kd

(2.20)

where k is the proportionality coefficient.

Assuming that this abrasive particle penetrates into the surface of an

elastic component and possesses the shape of a tough triangle, we shall obtain

P = 2ta[n

l + 24-2a + cos(24 - a) I cos a] (2.21)

where t is the tangential stress exerted by the particle towards the surface; 2a

is the indentation area; a is the angle at the top of a particle's protrusion;/ is

the value defining the friction developed between the particle being forced into

the surface and the metal, f = 0.5 arcsine r

; / is the maximum value of

frictional force.

If the particle travels along the surface of metal having specific gravity

Y , the erosion level per distance unit can be expressed as

AG = Ya

tga (2.22)

Solving equation (2.22) for a, while substituting its values into equation

(2.21) we can obtain

P = 2t[AG(Ytgay

]

]°

\n +1 + 24 + cos(/' - a) I cos a] (2.23)

Taking into account that /' and a are constant quantities, the

relationship given by equation (2.23) can be presented as

P = 2T[TAq(y+tgay']

Calculation of Hydraulic Abrasion

Having substituted P in equation (2.20) by its values, we shall obtain the

erosion level developed:

AG = Kd

qtga(4r

]

(2.24)

The total erosion depends on the amount of particles coming in contact

with the surface, i.e.

<=i

where N

the number of

all

particles.

When expressing the particle size through effective diameter d

, thus

classifying the pulp graininess, the ratio of the number of particles contained

in the fraction used, to their total number can be expressed as d

jfi

where

is the ratio of the particle average diameter size, in the given fraction, to the

effective diameter.

In this case the erosion is calculated from

i=t

= Ad^N^ afi

(2.25)

i=i

Taking into account the relationship between the effective diameter and

the total area of the abrasive medium we can calculate the amount of particles

contained in the specified fraction:

n = 6AQ/mi

where AQ is the total weight of a separate fraction; d is the mean diameter of

a particle present in a separate fraction; y

is the specific gravity of an

abrasive particle.

The total surface of particles contained in a separate fraction will be

presented as AF =6AQ/dya, whereas that of the abrasive medium will

correspond to: