Pneumatic transport of bulk materials in construction of composite floating docks

Abstract

Investigations of pneumatic transport of bulk materials used in shipbuilding have carried out. Their abrasiveness, wear of straight and curved sections of pipelines were investigated. Theoretically, the dependences of the amount of wear on various factors were defined: abrasiveness and concentration of transported particles, flow rate, pipe diameter and wear resistance of its material, structural and operational features of the transport system, etc. Formulas for determining the maximum useful life of straight and curved sections of pipelines are obtained. Theoretical results confirmed experimentally.

Keywords

Pneumatic transport bulk materials composite floating docks flow rate wear resistance

Abbreviations

particle volume, m³;

d_{c p}

average size of an abrasive particle, m;

A_{m}

coefficient of the transported material abrasiveness;

the angle of attack, rad.;

constant of friction;

wear of the pipe wall, mm;

ρ_{m}

weight density of abrasive particles, kgf · sec²/m⁴;

size of abrasive particles, m;

two-phase flow velocity, m/s;

weight density of the two-phase flow, kgf · sec ²/m⁴;

concentration of transported particles in the stream, kg/kg;

inner diameter of the pipeline, m;

wear resistance of the pipe material;

transportation time of abrasive particles, hours;

k_{e}

coefficient which takes into account design and operational factors;

k_{1}

coefficient of proportionality;

\bar{u}

average speed of an abrasive particle, m/s;

u_{N}

normal component of the average particle velocity, m/s;

u_{τ}

tangent component of the average particle velocity, m/s;

H_{din}

dynamic hardness of metal, kgf/mm;

mass of abrasive particles, kg

consumption of transported material, kg/s;

weight concentration of the mixture, kg/kg;

\overline{υ}

average speed of a two-phase flow, m/s

maximum overpressure in the pipeline, MPa;

σ_{p}

allowable stresses in the pipe wall, MPa; $σ_{p} = 0.46 σ_{в}$ .;

weight wear of the pipe, g/m²;

thinning of the pipe wall, mm;

β_{μ}

coefficient which takes into account the uneven concentration of particles in the stream;

β_{υ}

coefficient which takes into account the unevenness of the flow velocity over the pipe cross section;

k, ξ

constant values for a given material;

length of removed chips, m;

γ_{m}

mass density of an abrasive particle, kg/m³;

k_{c}

slip coefficient of the pipe material;

coefficient which takes into account the probability of particles hit on the pipe;

radius of curvature of the outer wall of the curved section of the pipe, m;

inner radius of the curved section of the pipe, m;

γ_{m p}

mass density of the pipe metal, kg/m³;

angle between the two radii of the curved section of the pipe, rad;

coefficient characterizing the abrasive properties of the transported materials

Target setting. Floating docks of a ∐-shaped form are widely used in launching ships from horizontal construction sites and repairing ships. All-metal multi-pontoon and composite floating docks are in use for these purposes. Floating docks of great lifting force are increasingly coming into use due to the growth of the deadweight and dimensions of marine vessels. The service life of all-metal docks does not exceed 25 … 30 years due to corrosion. With certain regularity, they repair their pontoons, during which the dock is not used for docking ships. In this regard, the metal dock is decommissioned for self-docking for approximately 5 years during the full service life [9].

The most popular modern type of dock is a composite floating dock of high lift, consisting of a reinforced concrete monolithic pontoon and two solid steel towers. Composite docks are more economical than all-metal ones, reinforced concrete pontoon practically does not corrode in sea water, which significantly increases its operation time and reduces the cost of maintaining the dock and its repair [7]. The use of reinforced concrete pontoon makes possible to eliminate the decommissioning of the dock for repair of its hull, as a result, the operating costs of the composite dock are approximately lower on 70% than that of the all-metal one.

During the construction of a floating dock with a large lifting force for the manufacture of reinforced concrete pontoons with a length of 250 m, a width of 50 m, a height of 6 … 7 m, with a thickness of the outer shell and internal structures of 100 … 120 mm, are used a large number of different bulk materials [6,10,13] (Table 1).

Table 1
The average consumption of bulk materials during the construction of composite floating docks at the Kherson plant “Pallada”

Item of bulk material Consumption per 1 ton of dock lifting force, kg Consumption per 1 dock with a lifting force of 8500 tons, t Consumption per 1 dock with a lifting force of 25,000 tons, t

Cement 233 1980 5825

Sand 245 2082 6125

Crushed stone 452 3842 11300

Per one dock pontoon 930 7905 23250

For the annual program (with the release of 1.85 docks) 14624 43012

Item of bulk material	Consumption per 1 ton of dock lifting force, kg	Consumption per 1 dock with a lifting force of 8500 tons, t	Consumption per 1 dock with a lifting force of 25,000 tons, t
Cement	233	1980	5825
Sand	245	2082	6125
Crushed stone	452	3842	11300
Per one dock pontoon	930	7905	23250
For the annual program (with the release of 1.85 docks)		14624	43012

The most progressive method of delivering various bulk materials to the place of manufacture of reinforced concrete structures is their pneumatic transportation through steel pipes [8,11,12]. Due to the formability of the transported particles, the pipelines often wear out and go out of service. One of the important tasks is to determine the service life of pneumatic conveying pipelines.

The purpose of the article is to study the wear of pneumatic conveying pipelines under the influence of transported abrasive bulk materials and to obtain dependencies for determining the service life of pipelines depending on various flow characteristics.

The statement of basic materials. Transportation of solid bulk materials by pipeline has become widespread in various industries during loading, unloading works, transportation and storage. One of the pipeline transport varietiesis pneumatic transportation (pneumotransport) of bulk materials [11,12].

Pneumatic transportation is the process of solid particles moving in a mixture with air, carried out through pipes under the influence of a differential pressure. The principle of operation of pneumatic devices of pipeline transport is based on the transfer of energy of the carrier medium to solid particles of bulk materials for a moving them through transport communications with relatively high speeds reaching 40 … 50 m/s in systems.

Bulk materials are characterized by variety of properties: strength, hardness, shape, grain size, density, etc. The combination of these properties of bulk material can be combined into the concept of abrasiveness – the ability of solid particles to affect other solids with different mechanical strength (steel pipelines, various equipment).

One of the tasks is to find the connection between the abrasive properties of transported particles and the mechanical characteristics of the interacting materials.

The destruction of the metal in the flow of abrasive particles has much in common with the destruction of the metal when concentrated to the point of impact of another, more solid body. Therefore, the strength and hardness of an abrasive particle are its most important characteristics. The hardness of the material determines the amount of mutual penetration of the contacting bodies. The area of actual contact of surfaces and the volume of material drawn into the deformation depend on the value of hardness.

During pneumatic transportation of a material of heterogeneous size, its natural classification occurs in the cross section of the flow. Smaller fractions are located in the middle part of the stream closer to the axis of the pipe, and larger particles are closer to its lower solid boundary. To characterize the properties of the materials being moved are essential their fractional composition, as well as the shape of the particles.

All investigated non-metallic bulk materials are not monodisperse and do not have spherical particles. Particles differ from each other in size and weight. Therefore, for their characterization, it is introduced the concept of an equivalent sphere, the volume and mass of which are respectively equal to the volume and mass of spherical: particles with $d_{c p}$ . The size that characterizes this bulk material should be considered the equivalent diameter $d_{e}$ , determined from the formula $\begin{matrix} (1) & d_{e} = \sqrt[3]{\frac{6 V}{π}} . \end{matrix}$

Conducted studies and comparison of the results with the properties of other abrasive materials allowed us to build a diagram on which various bulk materials could be arranged in a row according to their abrasive ability. The abrasiveness of bulk materials can be characterized by the coefficient of abrasiveness $A_{m}$ . In Fig. 1 is a diagram of the abrasiveness of some bulk materials used in shipbuilding.

Fig. 1.

Chart of abrasiveness of a variety of bulk materials, used in shipbuilding 1 – Portland cement; 2 – dolomite; 3 – magnesite; 4 – expanded clay gravel; 5 – sand; 6 – crushed granite.

The wear of the elements of pneumatic conveying installations depends on many factors: concentration and angle of attack of abrasive particles, physicomechanical properties of the wearing materials, design features of the pneumatic conveying system, the duration of the installation, the abrasiveness of the transported particles, flow rate, etc. The pneumatic conveying pipelines are subject to the most intense wear. Therefore, from the point of view of wear, they are of the greatest interest.

During the movement of a two-phase flow the gas – solid particle through the pipeline, occurs the random impact of abrasive particles on the pipe walls at different angles of attack and with different impact forces. Upon impact of the transported particles on the walls of the pipeline happens sliding friction takes, as a result of – a shift adds to plastic compression caused by the friction force. In this case, plastic deformation differs in that a temperature increase occurs on the friction surface and a large amount of heat develops. The temperature of the chipped and cuted particles of the pipe material which have the ability to reflowing [3,4].

All these circumstances create considerable difficulties in studying the process of pipeline wear, which is a complex phenomenon and depends on many factors.

It was explored the mechanism of wear of the inner surface of a direct pneumatic pipeline. During the moving abrasive particles hit the walls of the pipe, which leads to its wear due to the breaking of the material particles or the removal of the smallest chips. In this case, the wear depends on the angle of attack α, the energy and the abrasiveness of the particles. At the moment of the particle’s hit on the pipe wall, the impact force P decomposes into two components – normal $P_{N}$ and tangent $P_{τ}$ (Fig. 2). The particle has a shock effect ( $P_{y}$ ) on the surface of the pipe and is introduced into it by the action of $P_{N}$ force, and it moves along the surface and cuts off the smallest chips of pipe material ( $P_{c}$ ) by the action of force $P_{τ}$ . In such a case, in contrast to the $P_{N}$ force, a $P_{R}$ reaction force arises, which tries to push the particle away from the surface. The force $P_{τ}$ can cause slipping if the friction force T is overcome.

Most abrasive particles have some deviations from the spherical shape, small projections, sharp edges [5]. Therefore, each moving particle is a cutting element that carries out scratching action and participates in the process of mass removal of the smallest chips from the inner surface of the pipeline.

Fig. 2.

The scheme of forces which effect on the wall of the pipeline on impact with an abrasive particle.

Based on the conditions of the forces equilibrium and tension of the metal layer shear of the pipe with a thickness Δ in the scratching action of the circular particle, in [11] it was obtained the dependence, which can be represented for the considered case as follows: $\begin{matrix} (2) & \frac{P_{y}}{P_{c}} = \frac{sin α + f cos α}{cos α - f sin α} . \end{matrix}$

Graphs (Fig. 3), which are constructed using an equation (2) show that the relation $\frac{P_{y}}{P_{c}}$ increases rapidly with the increase of the angle of attack α, and at certain values α and f becomes equal to infinity. Consequently, the scratching of the inner surface of the pipeline occurs only at certain ratios $P_{y}$ and $P_{c}$ , depending on α and f, i.e. from contact conditions of abrasive particles with a wearing surface. With an increase in the angle of attack α, and, consequently, the force $P_{y}$ , the value of the impact of particles also increases. At values of $\frac{P_{y}}{P_{c}} = \infty$ the wear occurs only as a result of the impact of abrasive particles. Thus, the wear of pneumatic conveying pipelines occurs mainly due to the impact-scratching action of abrasive particles.

Fig. 3.

Dependances of $\frac{P_{y}}{P_{c}}$ on α and f.

The boundary separating both types of wear is a certain (critical) angle of attack, depending on the nature of the contact of the abrasive particles with the wear surface and the coefficient of friction between the particle and the pipe wall.

It is difficult to establish sufficiently accurate mathematical relationships due to the large number of factors affecting the wear of pneumatic conveying pipelines. However, the method of studying wear that we adopted with the addition of its experimental determination of the coefficients allows us to obtain calculation formulas for various cases of pipelines wear during pneumatic transportation of abrasive bulk materials.

The rate of pipe wear can be symbolically express in terms of a function of a number of independent variables, which characterize properties of the transported particles, two-phase flow, pipeline material and operational factors: $\begin{matrix} (3) & Δ = f (A_{m}, ρ_{m}, d, υ, ρ, α, μ, D, N, τ, k_{e}) . \end{matrix}$

We accept a number of assumptions during the deriving of determining wear formula:

transported abrasive particles have the same size, shape and weight;

particles are not subjected to deformation and destruction during an impact and are considered as impact-scratching elements;

the angle of impact on the pipe wall is the same for all particles;

particles are located evenly over the cross section of the pipe;

the shape of the scratch, which is formed by the particle, is rectangular.

In accordance with the adopted above hypothesis about the impact-scratching effect of abrasive particles on the walls of the pipeline, we assume that the indentation of the pipe wall occurs from the normal component of the force, and a metal cut occurs from the tangent component. We accept an abrasive particle for an elementary cutter.

We use the well-known formula [4] to determine the cutting force (scratching), and we determine the volume of metal removed from the pipe surface during a single impact of an abrasive particle on the basis of the assumption made on the rectangular shape of the scratch. We use the theory of shot peening of metals to determine the thickness of chips.

If we conditionally assume that the chip thickness s will be average and the same cross-section, then in order to determine it, you can use the formula obtained in [4] for the depth of the dent: $\begin{matrix} (4) & s = k_{1} \frac{d u_{N}}{\sqrt{H_{din}}} = k_{1} \frac{d \bar{u} sin α}{\sqrt{H_{din}}} . \end{matrix}$

The impact energy per shear can be foormulated by the following relation: $\begin{matrix} (5) & A = \frac{m u_{τ}^{2}}{2} = \frac{m {\overline{u}}^{2} {cos}^{2} α}{2} . \end{matrix}$ We determine the length of the chip, solving simultaneously a series of equations. The number of particles passing through the cross section of the pipe per one second can be determined by the formula: $\begin{matrix} (6) & n_{1} = \frac{Q}{m q} = \frac{μ ρ \overline{υ} π D^{2}}{4 m} . \end{matrix}$

Not all abrasive particles hit the pipe wall during transportation. Some of them move with the flow, another part does not reach the walls due to the shielding effect of the bounced particles. Therefore, a coefficient is introduced in the formula for determining the number of particles in contact with the walls of the pipe, which takes into account the probability of particle impacts on the pipe. During pneumatic conveying of bulk materials particles lag behind the air flow. This lag depends on their fractional composition and increases sharply with flow rate increasing [3].

An expression for determining the volume of metal removed from the inner surface of the pipe was obtained; $\begin{matrix} (7) & V = \int_{0}^{2 π} η \frac{k_{c}^{3 - ξ}}{2 k} \sqrt{{(\frac{ρ_{T}}{6 H_{din}})}^{1 - ξ}} μ ρ {\overline{υ}}^{4 - ξ} d^{1 - ξ} τ L r {sin}^{2 - ξ} α \times {cos}^{2} α \cdot d β . \end{matrix}$

However, operating experience of pneumatic conveying installations [8] and investigational study show that the wear of direct horizontal pipelines flows in the lower part, about at half of its inner perimeter. Therefore, it can be assumed that, the entire volume V of metal is removed from 1/2 of the inner surface of the pipe upon the wearing.

Then, after a series of transformations, the weight of the metal removed from a unit of the pipe’s inner surface during time τ with the mass density of the pipe metal $γ_{m p}$ can be determined by $\begin{matrix} (8) & G = η \frac{k_{c}^{3 - ξ}}{k} \sqrt{{(\frac{ρ_{m}}{6 H_{din}})}^{1 - ξ}} γ_{m p} μ ρ {\overline{υ}}^{4 - ξ} d^{1 - ξ} τ r {sin}^{2 - ξ} α \times {cos}^{2} α . \end{matrix}$

The obtained dependence (8) reflects the influence of various factors on the wear of direct steel pneumatic conveying pipelines: angle of attack α, density ρ and flow rate $\overline{υ}$ , concentration μ, density $ρ_{m}$ and size d of abrasive particles, pipe metal density $γ_{m p}$ , transport time τ, and coefficient of particle impacts probability on the pipe η, mechanical properties of the wear material, both during cutting, sliding (k, $k_{c}$ , ξ), and upon impact ( $H_{din}$ ). However, it is difficult for practical use. An analysis of formula (8) allows us to highlight a value that includes the mechanical properties of the pipeline metal and the angle of attack of abrasive particles. We introduce into it the coefficient $k_{e}$ , taking into account structural and operational factors. Then $\begin{matrix} (9) & M = \frac{k_{e} {sin}^{2 - ξ} α \times {cos}^{2} α}{k \sqrt{{(6 H_{din})}^{2 - ξ}}} . \end{matrix}$

All materials have various abrasive properties. While calculating the wear, this can be taken into account by the proportionality coefficient C. We introduce into it values related to abrasive particles: coefficients of slip $k_{c}$ and abrasiveness $A_{m}$ , density $ρ_{m}$ of particles. Then the coefficient C will characterize the abrasive properties of various transported materials of the same fractional composition. Therefore, the value of $d^{1 - ξ}$ we will separate by a special multiplier.

The derivation of formula (8) was built from the accepted assumption about the equilibrium distribution of abrasive particles over the pipe section. However, during transportation, the particles are distributed unevenly over the cross section of the pipe. In addition, the non-uniformity of the flow velocity over the pipe cross section should be taken into account. Therefore, the coefficients of non-uniformity of particle concentration $β_{μ}$ and non-uniformity of airflow rate $β_{υ}$ along the pipeline cross section are introduced in the obtained formula (8). Taking into account all of the above factors (9), the formula for determining the weight wear of horizontal metal pneumatic conveying pipelines in the place of maximum thinning of the pipe wall will take the form $\begin{matrix} (10) & G_{max} = η C M γ_{m p} β_{μ} μ ρ {(β_{υ} \overline{υ})}^{4 - ξ} d^{1 - ξ} τ . \end{matrix}$

The thinning of the pipe wall in the place of maximum wear can be determined with the formula $\begin{matrix} (11) & h_{max} = \frac{G_{max}}{γ_{m p}} = η C M β_{μ} μ ρ {(β_{υ} \overline{υ})}^{4 - ξ} d^{1 - ξ} τ . \end{matrix}$

It should to multiply the right side of the obtained formula (11) by $10^{- 3}$ in order to obtain the thinning of the pipe wall $h_{max}$ in mm. The time τ expressed in seconds in (11). We should to introduce the multiplier $2.78 \cdot 10^{- 4}$ for an opportunity of substitution of τ in hours (11). We introduce both of these factors in C. Then $\begin{matrix} (12) & C = 2.78 \cdot 10^{- 7} A_{m} k_{C}^{3 - ξ} \sqrt{ρ_{m}^{1 - ξ}} \end{matrix}$

The obtained dependences (10) and (11) are in good agreement with the experimental results of the wear of the samples by the flow of abrasive particles. However, they do not reflect the influence on the wear of certain factors: the design features of the pipeline and its position in space, the entire complex of abrasive properties of the transported material, etc. The degree of their influence is determined experimentally.

For most metals the value of ξ is at the limits of 0.6 … 0.9. It is defined the value for carbon steels $ξ = 0.75$ , which is well within the experimental data of the work [1]. With this value of ξ, the maximum wear of horizontal steel pneumatic conveying pipelines occurs at an angle of attack of $α = 38.3$ °. Experimental studies conducted on flat steel samples confirm that the most intense wear is observed at angles of attack of 33 … 40°. As far as the distribution of impacts of abrasive particles along the perimeter of the pipe obeys the sin law, the influence of the angle of attack on the wear rate can be represented by the ${sin}^{2 - ξ} α \times {cos}^{2} α$ curve depending on α (Fig. 4). The maximum of this curve corresponds to $α = 38.3$ °.

Fig. 4.

Change in wear intensity of horizontal pipelines from the angle of attack α of abrasive particles.

Particles are affected by centrifugal force directed perpendicular to their movement in curvilinear sections of pipelines. This force presses the particles against the outer wall of the curved section and makes them slide along it [11].

Based on the theory of the motion of an ideal fluid [2], it is generally accepted that in the initial section of the pipeline rotation, the velocity distribution over the cross section of the curved section corresponds to the law of areas. Using the well-known equation of impact of a solid particle on an obstacle, in [2] the average value of the reflection angle = 88.5° was established for various particle sizes, different diameters of the pipeline and the radii of curvature of the curved sections. It was also established that after hitting the pipe wall, the particles do not bounce, but move along it. Based on the literature data [11], the wear mechanism can be represented as follows.

While entering a curved section, abrasive particles are discarded to its outer wall under the action of centrifugal forces, and then move along it in the form of a jet pressed against this wall. Their speed decreases due to the particles’ friction on the wall. It follows from [11] that the particle velocity in the curved sections of pipelines depends on its input velocity, the coefficient of friction of the material on the wall, the location of the particle, and the radius of curvature of the pipe. Upon exiting the curvilinear section, the particle flow constantly changes to the state that is appropriate of the rectilinear section.

When deriving the wear formula for curved sections, we use the assumptions and methodology adopted for straight sections of the pipeline, but taking into account the nature of the distribution of particles in the curved part.

Then, to determine the weight of the metal $G_{1}$ , striped from a unit of the inner surface of the curvilinear section during the time $τ_{1}$ , we multiply the resulting expression by the density of the pipe metal $γ_{m p}$ and divide by one quarter of the inner surface of the pipe. After simple transformations we will get $\begin{array}{rcl} G_{1} & = & η \frac{2 k_{n} \cdot k_{c}^{3 - ξ}}{k} \sqrt{{(\frac{ρ_{m}}{6 H_{din}})}^{1 - ξ}} γ_{m p} μ ρ {(\frac{\overline{R}}{\overline{R} + r})}^{3 - ξ} \\ (13) & \times {\overline{υ}}_{1}^{4 - ξ} d^{1 - ξ} τ_{1} {sin}^{2 - ξ} α \times {cos}^{2} α . \end{array}$

The obtained dependence (13) reflects the influence of various factors on the wear of curved sections of metal pneumatic conveying pipelines. Formula (13) reflects the effect on the wear of structural elements of curved sections ( $\overline{R}$ and r), compared with the similar dependence (8) for straight pipelines.

The angle of attack α of the abrasive particles depends on the ratio $\frac{\overline{R}}{r}$ . In practical conditions, curved section, which have a large value of the relative radius, i.e. for which $\frac{\overline{R}}{r} \to max$ . In such pipelines the angle of impact of particles on the wall decreases, which entails a decrease in wear and its approximation to the wear of straight sections.

The value of the angle α at the moment the particles entering into curved section of the pipe with an average distance from the center of curvature can be determined by the formula $\begin{matrix} (14) & cos α \approx \frac{\overline{R}}{\overline{R} + r} \end{matrix}$

Then formula (13) takes the form $\begin{array}{rcl} G_{1} & = & η \frac{2 k_{n} \cdot k_{c}^{3 - ξ}}{k} \sqrt{{(\frac{ρ_{m}}{6 H_{din}})}^{1 - ξ}} \\ (15) & \times γ_{m p} μ ρ {\overline{υ}}_{1}^{4 - ξ} d^{1 - ξ} τ_{1} {sin}^{2 - ξ} α \times {cos}^{5 - ξ} α \end{array}$

In view of this, the formula for determining the weight wear of curved sections of steel pneumatic conveying pipelines in the place of maximum thinning of the pipe wall takes the form $\begin{matrix} (16) & G_{1 max} = η C M_{1} γ_{m p} β_{μ} μ ρ {(β_{υ} {\overline{υ}}_{1})}^{4 - ξ} d^{1 - ξ} τ_{1} \end{matrix}$

The thinning of the wall of the curved section of the pipeline in the place of maximum wear can be determined by the formula $\begin{matrix} (17) & h_{1 max} = η C M_{1} β_{μ} μ ρ {(β_{υ} {\overline{υ}}_{1})}^{4 - ξ} d^{1 - ξ} τ_{1} \end{matrix}$

At a previously determined value $ξ = 0.75$ for most steels the maximum wear of the curved sections occurs at an angle of attack of $α = 28.5$ °. This is confirmed by the constructed curve of the influence of the angle of attack on the wear rate in coordinates ${sin}^{2 - ξ} α \times {cos}^{5 - ξ} α - α$ .

Thus, obtained formulas (11) and (17) for determining the thinning of the pipe wall in the bridge of maximum wear are quite simple and reduced in appearance to (2).

During operating pneumatic conveying pipelines, the maximum allowable wear of the pipes should be such as the residual wall thickness $h_{min}$ provides sufficient strength at a working pressure in the pipeline. This thickness will be equal to $\begin{matrix} (18) & h_{min} = h - h_{max} \end{matrix}$

The minimum pipe wall thickness can be determined by the formula $\begin{array}{l} (19) & h_{min} = \frac{p D}{2 σ_{p}} . \end{array}$

Based on this condition, it is determined one of the most important characteristics – the maximum life of pneumatic conveying pipelines. Solving together (11) and (18) for straight pipelines, (17) and (18) for curved sections with respect to τ and assuming $h_{min} = 1.0$ mm, we obtain $\begin{array}{l} (20) & τ_{max} = \frac{h - 1}{η C M β_{μ} μ ρ {(β_{υ} \overline{υ})}^{4 - ξ} d^{1 - ξ}}, \\ (21) & τ_{1 max} = \frac{h - 1}{η C M_{1} β_{μ} μ ρ {(β_{υ} {\overline{υ}}_{1})}^{4 - ξ} d^{1 - ξ}} . \end{array}$

Numerous conducted experiments for determining the maximum life of pneumatic conveying pipelines show satisfactory convergence of theoretical and experimental results at $\frac{d_{c p}}{D} ⩽ 0.1$ . The discrepancy between results obtained theoretically and experimentally for straight sections of pipelines does not exceed 8.7%, for curvilinear – 12.2%.

1. Conclusions

The abrasiveness of bulk materials used in shipbuilding, the wear of streight pneumatic conveying pipelines and their curved sections are investigated. Theoretically, the dependences of the amount of wear on various factors were established: the density of abrasiveness and concentration of transported particles, flow rate, diameter and wear resistance of the pipeline material, structural and operational features of the transport system, etc. Formulas for determining the maximum service life of straight and curved sections of the pipeline are obtained.

Experimental research made it possible to determine the value of a number of coefficients included in the calculation formulas and to confirm obtained dependences theoretically. Good convergence of theoretical and experimental results was achieved: the discrepancy between results obtained theoretically and experimentally for straight sections of pipelines does not exceed 8.7%, for curvilinear – 12.2%.

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