A model to predict erosion on mild steel surfaces impacted by boiler fly ash particles

Wear 257 (2004) 612–624

A model to predict erosion on mild steel surfaces impacted by boiler fly ash particles J.G. Mbabazi, T.J. Sheer∗ , R. Shandu School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Private Bag 3, WITS 2050 Johannesburg, South Africa Received 16 June 2003; received in revised form 24 March 2004; accepted 24 March 2004

Abstract Fly ash particles entrained in the flue gas from boiler furnaces in coal-fired power stations can cause serious erosive wear on steel surfaces along the flow path. Such erosion can, as a particular example, reduce significantly the operational life of the mild steel heat transfer plates that are used in rotary regenerative heat exchangers (‘air heaters’) that extract heat from the flue gas and transfer it to the incoming boiler combustion air. This paper describes research into fly ash impingement erosion on such surfaces. The effect of the ash particle impact velocity and impact angle on the erosive wear of mild steel surfaces, using three different power station ash types, was determined through experimental investigations. The experimental data were used to calibrate a fundamentally-derived model for the prediction of erosion rates. The model incorporates the properties of the ash particles and the target metal surface, as well as the characteristics of the ash particle motion in the form of the impingement velocity and the impingement angle. When tested using the three different types of ash, the experimentally-calibrated general model yielded results that generally differed by less than 15% from the values that had been measured experimentally. © 2004 Elsevier B.V. All rights reserved. Keywords: Particle–wall collision; Erosion rate; Relative erosivity; Fly ash impingement

1. Introduction In large coal-fired power stations, pulverised coal is burnt in the burners of the boilers. To improve upon the overall thermal efficiency of the boiler plant, heat exchangers are used to extract residual heat energy from the flue gas before it is released to the atmosphere and to transfer it to the combustion air supplied to the boiler burners. Part of the air supplied, the ‘primary air’, is fed to the coal mills and is used to dry the pulverised coal and to transport the coal to the burners in the furnace. The greater part of the air supplied, the ‘secondary air’, is used in burning the coal. The heat exchangers used for preheating the combustion air are of the rotary regenerative type, commonly referred to as “air heaters”. Air heaters are prone to erosion, corrosion, blocking and fouling, particularly if the coal is of relatively poor quality, as is often the case in large South African power stations (ash content typically above 25%). In coal-fired power stations, about 20% of the ash produced in the boilers is deposited on the boiler walls and superheater tubes. This deposited ash is subsequently dis∗ Corresponding author. Tel.: +27-11-717-7304; fax: +27-11-339-7997. E-mail address: [email protected] (T.J. Sheer).

0043-1648/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.03.007

charged as slag and clinker during the sootblowing process. The rest of the ash is entrained in the stream of flue gas leaving the boiler. The ash-laden flue gas passes through the narrow passages between the corrugated steel plates that constitute the air heater elements. The ash particles collide with the surfaces of the steel air heater elements and material is eroded from the surfaces. In advanced stages of erosion, the plates become perforated. The air heater elements fail once they cannot maintain their structural integrity. Such erosion, together with the processes of blocking, fouling and corrosion, shortens the service life of the air heater elements. Once this happens, the power station unit has to be shut down in order to replace the damaged air heater elements. The resulting penalty is not only the cost of replacing the elements but also the cost of stoppage of power production. It is desirable, therefore, to be able to predict the rate of erosion of the air heater elements in order to plan systematically for the maintenance or replacement of the air heater elements to avoid forced outages. Eskom, South Africa’s leading electric power producer, has undertaken collaborative research with the School of Mechanical, Industrial and Aeronautical Engineering at the University of the Witwatersrand in Johannesburg. Eskom felt the need to improve the operating efficiency and expected

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Nomenclature a c dp E1 E2

constant relating normal force and crater diameter (N m−2 ) particle shape factor (–) ash particle diameter (m) normal component of ash particle’s kinetic energy (J) work done by the normal component of force (J) depth of penetration (m) maximum depth of penetration (m) Vickers hardness number (N m−2 ) erosion index (–)

h hmax Hv Ie K, K1 , K2 , K3 , Kc , Ke , Kp erosion constants (–) m mass of target material eroded by ash particles (kg) mp mass of ash particle (kg) n crater diameter exponent (–) N normal component of force (N) t time (s) V ash particle velocity (m s−1 ) Vref reference velocity (m s−1 ) x mass fraction of silica contained in ash (–) Greek symbols β ash particle impingement angle (◦ ) δ instantaneous crater diameter (m) ε overall erosion rate (mg kg−1 ) εc erosion rate due to cutting wear (mg kg−1 ) εp erosion rate due to plastic deformation (mg kg−1 ) ρm density of mild steel (kg m−3 ) ρp average density of ash particles (kg m−3 ) σy yield stress of mild steel (N m−2 )

service life of the air heaters used in the various coal-fired power stations (amounting to over 30,000 MW of generating capacity). Experimental investigations on the erosion wear by fly ash of air heater plates, which had been carried out by Crookes [1] using a large cold air accelerated erosion test facility at one of Eskom’s power stations (Matimba), required tons of ash. It would be impractical to transport such large quantities of ash from other power stations to Matimba Power Station for erosion tests. A smaller erosion test facility was therefore constructed at the university. The test facility has been used to carry out accelerated erosion tests with a variety of ash types under carefully monitored and controlled conditions, in order to obtain data on the erosion by fly ash of mild steel as used in making air heater

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plates. The test facility used air at speeds of 18–28 m s−1 for conveying ash particles in the size range of 0.2–410 ␮m. 2. Literature review The magnitude and direction of an ash particle’s impact velocity relative to the target metal surface constitute essential data needed for evaluating erosion of the surface due to particle impact. The magnitude and direction of a particle’s rebounding velocity depend upon the conditions at impact and the particular particle–surface material combination. The restitution behaviour is a measure of the momentum lost by the particle at impact and as such, it corresponds with the work done on the target surface and thus the extent of erosive wear suffered by the material of the target surface. The velocity coefficients of restitution depend upon the hardness of the target material, the density of the particle and the velocity at which the particle strikes the target surface. Grant and Tabakoff [2] developed empirical correlations of the velocity restitution coefficients for sand particles impacting 410 stainless steel. Grant and Tabakoff [2] used the correlations in simulating the particle rebounding conditions for solid particles ingested into rotating machinery. It is difficult to specify the values of the velocity restitution coefficients for ash particles bouncing off the surface of a mild steel plate because after an incubation period, the target material becomes pitted with craters and then after a slightly longer period, a regular ripple pattern forms on the eroded surface. Thus, the local impact angle between an ash particle and the eroded surface may deviate considerably from the average. Furthermore, the particles themselves are irregular in shape, with several sharp corners. As the particles approach the target surface, their orientation is random. Thus, some particles strike a surface and do very little work on the target material. On the other hand, other particles impact with a corner orientation in a manner similar to that of a cutting tool. Due to the complex nature of the particle–wall collision process, the model developed in the present study does not account for modification of the mechanical properties of the surface layers by multiple impacts, or by the presence of broken particles of ash. Meng and Ludema [3] have reviewed some of the many erosion models that have been developed since Finnie [4] proposed the first analytical erosion model in 1958. The models include a variety of parameters that influence the amount of material eroded from a target surface and the mechanism of erosion. Bitter [5] developed an erosion model based on repeated plastic deformation of a surface impacted by solid particles. Bitter [6] also developed equations for cutting wear that were based on the energy needed by a particle to scratch a unit volume from a surface. In the models that were developed by Bitter [5,6] the erosion rate depended upon the kinetic energy dissipated by the incident solid particles and was proportional to the square of the average solid particle velocity. After viewing the scanning electron

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micrographs of the metal surfaces that had been impacted obliquely by spherical solid particles, Hutchings and Winter [7] concluded that the mechanism of material removal was one of shearing of the top layers of the target surface in the direction of motion of the projectiles. Winter and Hutchings [8] carried out experimental investigations to determine the effect on the erosion mechanism of particle orientation during oblique impact of angular particles on lead and mild steel targets. The authors noted that for particle incidence angles close to 90◦ , erosion occurred by plastic deformation of the target surface. They also noted that for small impingement angles, erosion occurred by cutting wear or a micromachining action. Levy [9] observed that the models that had been developed based on assuming micromachining of the target metal surface by the tips of eroding solid particles were faulted by not being able to predict several important aspects of measured erosion loss. These included the effect of the particle velocity, or its exponent, the occurrence of considerable mass loss near an impingement angle of 90◦ (the models could not predict the erosion that occurred at 90◦ ), and the impingement angle at which maximum erosion occurred (experimental curves had to be moved to make the measured angle and predicted angle coincide). Levy [9] carried out experimental investigations on eroded metal surfaces using scanning electron microscopy at high magnifications. He observed that the loss of material from an eroded metal surface occurred by a combined extrusion–forging mechanism. Sundararajan [10] developed a compressive theoretical model for erosion. The model, which is valid for all impingement angles and shapes of eroding particles, combines the concept of localisation of plastic deformation leading to lip formation and the generalised energy absorption relations. The experimental and computational investigations carried out by authors such as Jun and Tabakoff [11] and Fan et al. [12] have contributed to understanding the mechanisms of erosion, but the detailed processes leading to material removal are still poorly understood. This means that with a few exceptions, good models for predicting the behaviour of materials during erosion are still not readily available. Gee et al. [13] used the stepwise testing method in determining the mechanisms of gas-borne particulate erosion. Stepwise testing is an approach that has recently been developed as a way of providing information on the build-up of damage in erosion. The essence of the method is to expose a sample to erosion incrementally from small quantities of erodent, and to be able to relocate the test sample accurately in the scanning electron microscope to enable the same area to be examined at high magnification, allowing for the development in damage to be followed at specific points on the sample surface. The ever-increasing capability of computers has led to the development of several numerical models for gas-particle flows. Tu et al. [14] carried out multidimensional computational fluid dynamics (CFD) simulations of flue gas with fly ash to predict erosion of the economisers in coal-fired

boilers. Lee et al. [15] used the Lagrangian approach while carrying out CFD simulations to predict erosion by fly ash of boiler tubes. Molinari and Ortiz [16] modelled particle–wall collisions in a confined gas-particle flow using both Lagrangian and Eulerian approaches. In this paper a model is developed to predict erosion by fly ash impingement on mild steel plates. The model was calibrated using ash from three different power stations.

3. Material removal (erosion) model Erosion is a process by which material is removed from the layers of a surface impacted by a stream of abrasive particles. Erosion is localised in a small volume of the target material that is eventually removed. The magnitude of the wear is quantified by the volume or mass of the material that is removed by the action of the impacting particles. There are two processes by which metal can be removed when an ash particle strikes the surface of an air heater plate: • removal of material due to cutting wear; • removal of material due to repeated plastic deformation. The relative contribution of the two processes is difficult to predict due to the many parameters that are involved, which include impact angle; impact velocity; hardness, shape, and size of the particle; and the hardness and toughness of the target material, to name a few. 3.1. Cutting wear Finnie [17] analysed the motion of a sharp-cornered solid particle as it cuts into the surface of a ductile material. He assumed that the particle would rotate only slightly while in contact with the surface. He predicted the trajectory of the tip of the particle as it ploughed through the material and hence the volume of the material removed by the particle’s machining action. However, this theoretical model was found to overestimate the erosion rates. Finnie et al. [18] carried out experimental investigations to account for particles that do not cut in the idealised manner. These particles impinge upon the surface at low velocities, or at unfavourable incidence angles, or have most of their translational kinetic energy turned into rotational kinetic energy, and hence remove no material. On the other hand, the particles that strike the surface at an acute angle and at a velocity greater than the critical velocity needed for the penetration of the material’s surface do remove some material, in a process similar to the cutting action of a machine tool as shown in Fig. 1. The tool penetrates the surface of the material to a depth of cut f and in the process the tool removes a chip of thickness t. The tool removes the plastically deformed chip along the shear plane that is inclined at an angle φ to the surface of the material being machined. In comparing this model with the erosion of material from the surface of a plate in an air heater by an ash particle, the

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equation is obtained:
9σy h2 dh = ± V 2 sin2 β − dt ρp dp2

The plus sign in Eq. (4) corresponds to an increase in the depth of penetration, and the minus sign corresponds to a decrease in the depth of penetration. The maximum depth of penetration, hmax , occurs when dh/dt = 0, and is given by the following equation:  3/2 dp3 ρp (5) h3max = 3 V 3 sin3 β σy 3

Fig. 1. Surface deformation by a cutting tool [18].

cutting tool is the ash particle and the surface being eroded is the workpiece being machined. The condition for cutting out material as a chip is that the cutting edge of an angular ash particle has to penetrate the surface of the target material. At the impact location the particle loses a fraction of its kinetic energy to the target material in the form of heat and energy for deformation of the surface. Very high levels of shear strain may be induced in the material at the impact location. When the shear strain exceeds the elastic strain limit of the target material, the particle penetrates the surface of the material and ploughs along the surface, removing material in a process similar to the machining action of a cutting tool. During the cutting wear process, it is assumed that the stresses acting at the contact point are constant. The particle penetrating the surface of the material has to overcome the material’s resistance to deformation. The equation of motion for the depth of penetration, h, of a particle of mass mp and diameter dp , as it penetrates through the surface of a material, was developed by Kragelsky et al. [19] and is shown in the following equation: dp d2 h mp 2 = −π hcσy 2 dt

(1)

where t is the time, σ y the yield stress of the target material, and c is a particle shape factor equal to 3 for a sphere. The negative sign in Eq. (1) accounts for the fact that the material resists the penetrating action of the impacting particle. The mass, mp , for a spherical particle is given by the following equation: mp = 16 ρp πdp3

Since the volume of material that is cut away from the target surface by the impacting particle is proportional to h3max , the mass of material removed by a single particle will also be proportional to the value of h3max derived in Eq. (5). The mass of material eroded by a single impacting particle is given by the following equation: 3/2

m=

Kc ρm h3max

=

Kc ρm ρp dp3 V 3 sin3 β 3/2

33 σ y

(6)

where Kc is a constant and ρm the density of the target material. The erosion rate due to cutting wear, defined as the ratio of the mass of the material eroded from the target surface to the mass of the impacting particle, is given by the following equation: 3/2

1/2 Kc ρm ρp dp3 V 3 sin3 β K1 ρm ρp V 3 sin3 β m εc = = = 3/2 3/2 mp 33 σy (πρp dp3 /6) σy

(7) where K1 is a constant. During the impact of the particle with the surface, there are two possibilities for the cutting wear to cease: • the cutting ceases when the particle tip can no longer move forward, that is, when the tangential component of velocity becomes zero; • the cutting may also cease when a release of elastic stresses in the surface of the target material takes place, because of which the particle rebounds off the target surface.

(2)

Substituting for the mass of the spherical particle, Eq. (1) can then be written as follows: 9σy h d2 h =− dt 2 ρp dp2

(4)

(3)

When a particle strikes a surface with a velocity V and at an angle of incidence β, the initial rate at which the particle penetrates into the material is equal to the normal component of the impact velocity. Allowing for the fact that at t = 0, dh/dt = V sin β, and after integrating Eq. (3), the following

3.2. Plastic deformation wear During particle impact, the loss of material from an eroding surface may occur by a combined extrusion–forging mechanism. Platelets are initially extruded from shallow craters made by the impacting particle. Once formed, the platelets are forged into a strained condition, in which they are vulnerable to being knocked off the surface in one or several pieces. Sheldon and Kanhere [20] carried out experimental investigations on impingement erosion. From the appearance of the craters formed on the surface of the eroded

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material, they observed that the surface material was forced to flow from in front and to the sides of the advancing particle, until the material was sufficiently strained so as to fracture, at which time the material loss occurred. Sheldon and Kanhere [20] proposed the following sequence in the erosion process. During the incubation period, platelets are formed, initially without loss of material. Because of the high strain rates, adiabatic shear heating occurs in the surface region immediate to the impact site. Beneath the immediate surface region, a work-hardened zone forms, since the kinetic energy of the impacting particles is enough to result in a considerably greater force being imparted to the metal than is required to generate platelets at the surface. When the surface has been completely converted to platelets and craters and the work-hardened zone has reached its stable hardness and thickness, steady state erosion begins. The reason that the steady state erosion rate is the highest rate is that the subsurface cold-worked zone acts as an anvil, thereby increasing the efficiency of the impacting particles to extrude-forge platelets in the now highly strained, and most deformable, surface region. This cross section of material conditions will move down through the metal as erosion loss occurs. In the platelet mechanism of erosion there is localised sequential extrusion and forging of metal in a ductile manner, leading to removal of the micro segments thus formed. During plastic deformation, the normal component of the particle’s kinetic energy is used to extrude-forge the material. The normal component of the kinetic energy of the particle is given by the following equation: 1 π dp π ρp V 2 sin2 β = ρp dp3 V 2 sin2 β 2 6 12 3

E1 =

(8)

where dp and ρp are the particle diameter and density, respectively, and V and β the particle incident velocity and angle, respectively. The work done by the normal force N of the indenting particle in a direction h normal to the surface from the time of surface contact until penetration stops at a depth hmax is given by the following equation:  hmax E2 = N dh (9)

the following equation:  πHv hmax 2 δ dh E2 = 4 0

(13)

The depth of penetration, h, is related to the instantaneous crater diameter δ and the particle diameter dp by the following equation: h = 21 (dp − (dp2 − δ2 )1/2 )

(14)

Eq. (14) is used to express the particle’s depth of penetration in terms of the instantaneous crater diameter. Eq. (13) is then integrated with respect to the instantaneous crater diameter. Equating the work done during indentation to the normal component of kinetic energy given in Eq. (8), the following equation is obtained:  π 3 δ2 dδ πHv hmax (15) dp ρp V 2 sin2 β = 2 12 8 0 (dp − δ2 )1/2 Evaluating the integral in Eq. (15), the maximum depth of penetration is given by 3/2

h3max =

dp3 V 3 sin3 β ρp

(16)

3/2

Hv

Since the dimensions of the crater formed by the impacting particle are all proportional to h3max , and since the amount of material removed is nearly the full crater size, the mass of material removed by a single particle is proportional to the value of h3max derived in Eq. (16). The mass of material removed by a single particle is given by the following equation: 3 3 3 1/2 dp V sin β 3/2 Hv

m = Kp ρm h3max = Kp ρm ρp

where Kp is a constant and ρm is the density of the target material. The erosion rate, εp , due to plastic deformation is given by the following equation: 1/2

1/2 Kp ρm ρp dp3 V 3 sin3 β K2 ρm ρp V 3 sin3 β m = εp = = 3/2 3/2 mp Hv (ρp πdp3 /6) Hv

0

(18)

Sheldon and Kanhere [20] give the following equation, relating the force N and the diameter δ of the crater formed in the indented surface: N = aδn

(17)

(10)

The empirical constants, a and n, are given by Eqs. (11) and (12): n = 2.0

(11)

a = 41 πHv

(12)

where Hv is the Vickers hardness number of the target surface being eroded. Substituting Eq. (10) into Eq. (9) yields

where K2 is a constant. 3.3. The equation for the overall erosion rate The erosion by fly ash of the plates of air heater elements consists of the wear due to the cutting mechanism plus the wear due to the plastic deformation mechanism. However, it is difficult to predict accurately the proportions contributed by each of the two mechanisms to the overall material loss. Eq. (18), which was derived for the plastic deformation wear, is similar to Eq. (7) for the cutting wear. The yield stress of a metal can be related to the metal’s hardness. Tabor [21]

J.G. Mbabazi et al. / Wear 257 (2004) 612–624 Table 1 Erosion indices of fly ash for various ranges of silica contents [23] Silica (SiO2 ) content of ash (wt.%)

Erosion indices

<40 40–50 50–60

Low, <0.02 Medium, 0.02–0.08 Medium to high, 0.04–0.28

gives the following relationship between the yield stress and the Vickers hardness number: Hv = 2.7σy

(19)

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grains, Raask [23] obtained through experimental investigations the values of the erosion indices shown in Table 1. The erosion indices were based on the percentage by weight of silica contained in ash samples. Using the figures recorded in Table 1, the present authors derived Eq. (22) to relate the erosion index Ie to the mass fraction x of the silica contained in an ash sample: Ie = 3.5x4.95

(22)

After substituting Eq. (22) into Eq. (21), the overall erosion rate is given by 1/2

The overall erosion rate, combining the cutting and plastic deformation wear mechanisms, is then given by the following equation: 1/2

ε=

K3 ρm ρp V 3 sin3 β 3/2

σy

(23)

where K is the overall erosion constant. 4. Experimental erosion wear measurements

1/2

Ke Ie (x)ρm ρp V 3 sin3 β 3/2

σy

3/2

σy

(20)

where K3 is a constant. From the results of the experimental investigations carried out by various authors [11,12,20,22], the erosion rate due to solid particle impact depends upon the particle impingement angle and the characteristics of the particle–wall combination. In modelling the erosion by fly ash of ductile metal surfaces, the constant K3 in Eq. (20) may be replaced by the particle erosion index; the expression for the overall erosion rate is then given by Eq. (21): ε=

ε=

Kx4.95 ρm ρp V 3 sin3 β

(21)

where Ke is a constant, x the mass fraction of silica contained in an ash sample, and Ie the erosion index of the ash, which relates the variation of the erosion rate to the silica content. The two most important constituents of fly ash are, first, silica (SiO2 ) and then alumina (Al2 O3 ). According to Raask [23], “free” crystalline alumina mineral is hard and highly abrasive. However, in the majority of pulverised coal ashes, alumina is present in a softer “combined” form of aluminosilicate glass with some mullite needles dispersed in the glassy matrix. Defining the erosion wear index Ie for mild steel as the ratio of the mass of material eroded by ash particles divided by the mass of material eroded by 100 ␮m quartz

Fig. 2 is a schematic drawing of an erosion test facility at the School of Mechanical, Industrial and Aeronautical Engineering of the University of the Witwatersrand, Johannesburg. The main consideration in designing and operating the test facility was to control the primary variables of air velocity (and therefore ash particle velocity) and ash particle mass flow rate in a representative aerodynamic environment. Provision was made for varying the angle of attack between the impacting ash particles and the target surface of the test specimen. A variable-speed blower delivered air through a pipe incorporating a 32 mm diameter orifice meter, used to measure the volume flow rate of the air being supplied to the test section. Downstream of the orifice meter the pipe incorporated a nozzle that tapered from a diameter of 46.4 mm to a diameter of 16 mm. This reduction in diameter resulted in a sub-atmospheric pressure, to induce the ash particles into the mixing section. A variable-speed screw feeder, mounted on a loss-in-weight electronic balance, delivered ash at a constant rate to the mixing section. The values of the mass of ash in the feed hopper at the beginning and the end of each test period were recorded. After the mixing section the mixture was accelerated through a pipe of 22.4 mm diameter and 1000 mm length. It was assumed that, by the time

Fig. 2. A schematic diagram of the laboratory erosion test facility.

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the ash particles struck the 100 mm ×100 mm mild steel test plate in the test section, the particle velocity was equal to the air velocity. (Using standard relationships for dilute-phase pneumatic conveying given by Dixon [24], the average slip velocity ratio is estimated to be approximately 0.98–0.99, depending on particle size and density.) On striking the surface of the plate the ash particles eroded some material from the surface of the plate; the mass of the test plate was measured before and after the test run. The ash was collected in a bag mounted under the test section and the air was vented to the atmosphere through bag filters. The steel plate specimen for each test was mounted on a lockable transverse shaft. A dial attached to the shaft was used to record the value of the impingement angle. Test runs were conducted with specimens mounted at various impingement angles. The ash for the tests was collected from Eskom’s Lethabo, Matimba, and Matla Power Stations. These three power stations were selected so as to give significant variations in the shape, size distributions and chemical compositions of the ash used.

5. Results and discussion 5.1. The effect of the ash particle impingement angle Fig. 3 shows the erosion rate of mild steel at various ash particle impingement angles, for an ash particle velocity of 24.77 m s−1 . The size of the ash particles in this test using ash from Matimba Power Station varied between 0.2 and 351.48 ␮m, with a mean particle diameter of 57.46 ␮m. Fig. 3 shows that for low impingement angles, the erosion rate increased with an increase in the impingement angle until a maximum value was reached at an angle between 25◦ and 30◦ . Thereafter, the erosion rate fell off rapidly from the peak value. The trend of the curve shown in Fig. 3 is similar to that shown in Fig. 4, which was obtained from experimental investigations carried out by Raask [23] on

Fig. 4. Erosion wear of mild steel at various impaction angles: impact material 125–150 ␮m quartz; impact velocity 27.5 m s−1 [23].

mild steel, using 125–150 ␮m quartz particles conveyed by a stream of air, with a particle impact velocity of 27.5 m s−1 and with impingement angles varying from 15◦ to 90◦ . The values of the erosion rate shown in Fig. 4 are greater than those shown in Fig. 3. The difference may be attributed to the fact that the quartz particles used in the experimental investigations carried out by Raask [23] were harder, bigger, and more sharp-edged compared with the ash particles from the Eskom power stations. 5.2. The ash particle velocity exponents Figs. 5–7 show the experimental results that were obtained by varying the particle impingement velocity, for each of the ash samples from the three power stations. From Fig. 5, Eq. (24) was derived to relate the erosion rate ε to the ash particle velocity V when a mild steel plate was eroded by the ash from Lethabo Power Station. The particle reference velocity Vref was set at 1 m s−1 :   V 2.42 (24) = 0.002V 2.42 ε = 0.002 Vref

Fig. 3. Mild steel erosion rate at various ash particle impingement angles with ash from Matimba: impact velocity 24.77 m s−1 .

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Fig. 5. Mild steel erosion rate at various ash particle impingement velocities with ash from Lethabo: impingement angle 30◦ .

Fig. 6 shows the erosion rate for a mild steel plate with ash from Matimba Power Station. The variation of the erosion rate ε with the ash particle velocity V, for unity particle reference velocity, is represented by the following equation: ε = 0.0004V 3.09

(25)

The variation of the erosion rate with ash from Matla Power Station is shown in Fig. 7. The erosion rate ε and the ash particle velocity V are linked by the following equation, for unity particle reference velocity: ε = 0.00002V 3.64

(26)

It is noted from Eqs. (24)–(26) that for mild steel plate eroded by ash particles the values of the velocity exponents

were 2.42, 3.09 and 3.64 for the ash samples from Lethabo, Matimba and Matla Power Stations, respectively. The different values of the velocity exponent may be explained in terms of variations in the ash particle sizes and shapes. The results of mass spectrometry analysis for the three ash samples yielded particle size ranges of 0.23–409.95, 0.2–351.48, and 0.27–258.95 ␮m for the ash samples from Lethabo, Matimba and Matla, respectively. The big and amorphous ash particles from Lethabo resulted in the lowest value of the velocity exponent, compared with the small and spherical ash particles from Matla that led to the highest value of the velocity exponent. Figs. 8–10 are scanning electron microscopy (SEM) micrographs, showing the shapes and sizes of the ash samples collected from

Fig. 6. Mild steel erosion rate at various ash particle impingement velocities with ash from Matimba: impingement angle 30◦ .

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Fig. 7. Mild steel erosion rate at various ash particle impingement velocities with ash from Matla: impingement angle 30◦ .

Lethabo, Matimba and Matla Power Stations, respectively. The sample obtained from Lethabo had agglomerations of ash particles as shown in Fig. 8. Fig. 9 shows that the sample obtained from Matimba included sharp angular ash particles. Fig. 10 shows the relatively small spherical ash particles in the sample from Matla. SEM micrographs were taken of the eroded steel surface (not reproduced here) and these confirmed that cutting wear took place at low particle impingement angles and deformation wear at high angles. Crookes [1] used experimental results from the accelerated erosion test facility at Matimba Power Station to obtain the velocity exponents shown in Table 2 for various air heater element profiles. With the exception of the plate profile designated as K8G, the velocity exponents are lower than the ones that were obtained in the present work. The lower values of the velocity exponents for the plate profiles designated as KH11, 2.78DU, and H8 may be attributed to Fig. 9. Particles in the ash sample from Matimba.

the enhanced turbulence caused by cross-flows along the twisting-and-turning channels of the corrugated steel surfaces of these plates. Because of the enhanced turbulence, some of the particle kinetic energy is lost through eddy dissipations and the particles strike the surfaces of the plates with velocities that are lower than the air velocity at the inlet to the test section, which was used to compute the exponents. Table 2 Velocity exponents for various air heater element profiles [1]

Fig. 8. Particles in the ash sample from Lethabo.

Air heater element profile type

Velocity exponent

KH11 2.78DU H8 K8G

2.08 1.86 1.95 3.32

± ± ± ±

0.19 0.16 0.02 0.05

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Table 4 Erosion indices for the three ash samples Power station

Erosion index of the ash sample

Matla Lethabo Matimba

0.08 0.18 0.28

Table 5 Maximum erosion rates for the three ash samples: ash particle impingement velocity 27 m s−1 , impingement angle 30◦ Ash sample

Maximum erosion rate (mg kg−1 )

Matla Lethabo Matimba

2.88 5.40 9.37

Fig. 10. Particles in the ash sample from Matla.

On the other hand, the K8G profile, which had straight channels running parallel to the direction of flow, caused less turbulence for the particle–gas flow. The velocity exponent of 3.32 obtained for the K8G profile compares quite well with predicted and laboratory experimental values of 3 and 3.09, respectively. 5.3. The relative erosion potential of the three ash samples Table 3 shows results of chemical analysis carried out on the fly ash samples from the three power stations. Table 4 shows the erosion indices for the three ash samples, which were calculated using Eq. (22) and the values of the silica content recorded in Table 3. In line with the values of the erosion indices shown in Table 4, it was observed that the ash sample from Matla caused the least erosive wear, whereas the ash sample from Matimba caused the highest erosive wear. This trend was confirmed by the experimental results

shown in Table 5 of the maximum erosion rates for the various ash samples for an impingement angle of 30◦ and an impingement velocity of 27 m s−1 . 5.4. The overall erosion constant, K The test specimens for the laboratory investigations were made from commercial grade cold rolled mild steel plates, with density and yield stress of 7860 kg m−3 and 236.1 MN m−2 , respectively. Mass spectrometry analysis was carried out on the fly ash samples, yielding densities of 2460, 2330 and 2130 kg m−3 for the samples from Matimba, Lethabo and Matla, respectively. The theoretical velocity exponent used in the present study, as shown in Eq. (23), is 3. The densities, silica mass fractions and erosion rates were substituted into Eq. (23) to obtain values of the overall erosion constant K at various ash particle impingement velocities. Tables 6–8 show the values of the overall erosion constant for the three ash samples. Due to variations between these values, Eq. (22), which was derived after curve-fitting the data obtained by Raask [23], may be

Table 3 Chemical (elemental) composition of the three ash samples Element

Silicon Aluminium Iron Titanium Phosphorus Calcium Magnesium Sodium Potassium Sulphur Manganese SiO2 + Al2 O3 + Fe2 O3

Compound occurring in ash

Silica (SiO2 ) Aluminium oxide (Al2 O3 ) Iron oxide (Fe2 O3 ) Titanium oxide (TiO2 ) Phosphorus pentoxide (P2 O5 ) Calcium oxide (CaO) Magnesium oxide (MgO) Sodium oxide (Na2 O) Potassium oxide (K2 O) Sulphur (S) Manganese oxide (MnO)

Percentage composition Lethabo

Matimba

Matla

55.20 30.80 3.67 1.61 0.35 5.01 1.40 0.20 0.73 0.20 0.03

60.10 26.50 5.64 1.26 0.31 2.95 0.70 0.10 0.75 0.10 0.06

46.30 29.50 4.55 1.73 1.12 10.70 2.40 0.50 0.88 0.70 0.05

89.67

92.24

80.35

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Table 6 Overall erosion constant for the Matimba ash sample: impingement angle 30◦

Table 9 Experimental and derived erosion rates for the Matimba ash sample: impingement angle 30◦

Ash particle velocity (m s−1 )

Erosion rate (mg kg−1 )

Constant, K

Ash particle velocity (m s−1 )

Experimental erosion rate (mg kg−1 )

Derived erosion rate (mg kg−1 )

19.41 21.86 24.70 25.55 26.59

3.53 5.41 7.59 8.49 9.37

0.45 0.48 0.47 0.47 0.46

19.41 21.86 24.70 25.55 26.59

3.53 5.41 7.59 8.49 9.37

3.71 5.30 7.65 8.47 9.55

± ± ± ± ±

0.03 0.03 0.02 0.03 0.03

Table 7 Overall erosion constant for the Lethabo ash sample: impingement angle 30◦ Ash particle velocity (m s−1 )

Erosion rate (mg kg−1 )

Constant, K

18.49 21.14 23.49 24.62 26.66

2.18 3.38 4.38 4.39 5.40

0.50 0.52 0.49 0.43 0.41

± ± ± ± ±

0.03 0.03 0.03 0.02 0.02

inadequate in determining erosion indices. The authors carried out error analysis to obtain the uncertainties in the overall erosion constant shown in Tables 6–8. An average overall erosion constant of 0.47 with a standard deviation of 0.04 was computed from the figures in Tables 6–8. 5.5. Recommended model to predict the erosion rate for a mild steel surface impacted by fly ash particles When the average value for the overall constant K is substituted into Eq. (23), the resultant expression of Eq. (27) is obtained for predicting the erosion rate for a mild steel surface impacted by ash particles: 1/2

ε=

0.47x4.95 ρm ρp V 3 sin3 β

(27)

3/2

σy

The validity of this general expression in representing the erosion rate of mild steel eroded by the fly ash samples from the three power stations was examined by comparing the values of the erosion rate obtained using the calibrated model against the individual values obtained in the experimental investigations. The authors carried out an error analysis to obtain uncertainties in the predicted erosion Table 8 Overall erosion constant for the Matla ash sample: impingement angle 30◦ Ash particle velocity (m s−1 )

Erosion rate (mg kg−1 )

Constant, K

18.28 20.29 23.15 24.54 27.66

0.60 1.09 1.81 1.84 2.88

0.36 0.47 0.53 0.45 0.49

± ± ± ± ±

0.02 0.03 0.03 0.03 0.03

± ± ± ± ±

0.30 0.44 0.57 0.69 0.78

Table 10 Experimental and derived erosion rates for the Lethabo ash sample: impingement angle 30◦ Ash particle velocity (m s−1 )

Experimental erosion rate (mg kg−1 )

Derived erosion rate (mg kg−1 )

18.49 21.14 23.49 24.62 26.66

2.18 3.38 4.38 4.39 5.40

2.05 3.06 4.20 4.84 6.15

± ± ± ± ±

0.17 0.25 0.33 0.36 0.45

rates. The uncertainties in the predicted erosion rates arise from uncertainties in determining the ash particle velocity, the ash particle impingement angle and the overall erosion constant. Tables 9–11 show the results that were obtained. These results show that the values given by the calibrated model do not differ by more than 15% from those obtained by experiment. The only exception is the erosion rate for the Matla ash sample at an ash particle velocity of 18.28 m s−1 . The discrepancy between the measured and derived values may be attributed to inaccuracies in determining small values of the erosion rate. Fig. 11 shows the variation of the experimental erosion rates with ash particle impingement velocity. There is a notable decrease in the gradients of the curves for the Lethabo and Matla ash samples at ash particle impingement velocities greater than 23 m s−1 . The decrease in the gradients can be attributed to fragmentation of the clusters of spherical ash particles shown in Figs. 8 and 10. Particle fragmentation reduces the kinetic energy of the ash particles striking the mild steel plates. Fig. 12 shows the uncertainty bounds for the predicted erosion rates and ash particle impingement velocities. The error in ash particle velocity was found to be within 1% of the measured values, while the error in erosion rate was found to be within 8% of the measured values. Table 11 Experimental and derived erosion rates for the Matla ash sample: impingement angle 30◦ Ash particle velocity (m s−1 )

Experimental erosion rate (mg kg−1 )

Derived erosion rate (mg kg−1 )

18.28 20.29 23.15 24.54 27.66

0.60 1.09 1.81 1.84 2.88

0.79 1.09 1.61 1.92 2.75

± ± ± ± ±

0.06 0.09 0.14 0.16 0.23

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Fig. 11. Experimental erosion rates on mild steel at various ash particle impingement velocities: impingement angle 30◦ .

Fig. 12. Uncertainty bounds for derived erosion rates and ash particle impingement velocities: impingement angle 30◦ .

623

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6. Conclusions

References

The experimental investigations described here confirm that the erosion rate on a mild steel surface subjected to a stream of fly ash particles varies with the particle impingement angle. For low values of the impingement angle, the erosion rate increases with an increase in impingement angle, with the maximum erosion rate occurring at an impingement angle of about 30◦ . Thereafter the erosion rate decreases with a further increase in impingement angle. The variation of the erosion rate for mild steel follows a power law with the ash particle impact velocity. The value of the velocity exponent appears to be affected by the size and shape of the ash particles. Large, irregularly shaped particles from Lethabo Power Station resulted in a lower velocity exponent of 2.42 compared to 3.64 that was obtained for the small, rounded particles from Matla Power Station. The velocity exponent of 3.09 that was obtained with fly ash from Matimba Power Station compares closely with the value of 3 that was derived in a fundamental model to predict erosion of mild steel. The silica content of the ash particles has a large influence on the erosion rate for mild steel. The results presented here tend to confirm previous findings by Raask [23]. Comparison between the experimental values of the erosion rate for various ash samples with those predicted using a calibrated general model shows that the model yields values of the erosion rate that are generally within 15% of the individual experimental values. The model is being used in ongoing research into air heater erosion, in which computational fluid dynamics software with particle tracking is employed to predict erosion patterns and rates resulting from the flow of ash-laden gas through the complex channels in air heater packs.

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Acknowledgements The authors would like to thank Eskom for permission to publish this paper and the Eskom Resources and Strategy Group Research Division for its support. A research grant for the first author was received from ANSTI (African Network of Scientific and Technological Institutions) through the UNESCO Nairobi Office, which is gratefully acknowledged. The authors would also particularly like to thank Mr. M. Lander of Eskom and Dr. H.H. Jawurek of the University of the Witwatersrand for their ongoing supportive interest in this work.