CN110134980B - Explicit algorithm for erosion of solid particles in liquid phase elbow - Google Patents
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Abstract
The invention discloses an explicit algorithm for solid particle erosion in a liquid phase elbow, which comprises the following steps: (1) solving the basic characteristics of a flow field in a pipeline; (2) solving a flow field in the elbow; (3) calculating the drop point of the particles; (4) calculating the collision velocity of the particles; (5) solving the collision angle of the particles; (6) solving for the material loss ratio at the particle impact point; (7) solving the effective sand conveying rate of the impact part of the particles; (8) solving an inlet erosion diffusion coefficient; (9) calculating erosion of solid particles on the elbow. The invention aims to provide an explicit algorithm for calculating the motion trail of solid particles in a liquid-phase elbow and causing erosion, an approximate flow field in the elbow is constructed based on a correlation theory, an explicit solution of the motion trail is obtained by simplifying a particle motion equation, and the material loss caused by the collision of particles with the pipe wall is tracked.
Description
Technical Field
The invention belongs to the field of explicit algorithms for solid particle erosion, and particularly relates to an explicit algorithm for solid particle erosion in a liquid phase elbow in the field.
Background
The problem of erosion of solid particles in pipelines is widespread in various industrial equipment such as oil and gas transfer lines, dredging dredge fill equipment, rotary dust collectors, aeroengines and the like. The solid particles in the pipeline move at high speed along with the fluid, and impact the inner wall of the pipeline with high momentum at the position of abrupt change of the flow direction, thereby causing serious material damage. The elbow is a common component for changing the flow direction of the fluid, and solid particles are most easily eroded. The pipeline becomes thin, breaks and fluid leaks under the effect of solid particle erosion, so that serious production accidents can be caused, and personnel safety and surrounding ecological environment are endangered. Therefore, the method for analyzing the erosion of the solid particles at the elbow by adopting a simple and effective method has important significance for guiding the design, maintenance and the maintenance of equipment in many industrial fields.
The existing methods for analyzing solid particle erosion at the elbow are mainly two. The first method is an empirical or semi-empirical algorithm fitted based on a large amount of experimental data. The method is generally an extension of the particle erosion theory, and the conveying speed index, the angle function and the part shape coefficient are fitted through experimental data; some finer models will give the average collision velocity and average collision angle of the population of particles based on the flow field pattern within the component. However, the method does not track the movement track of the particles in the elbow and can not reflect the complete mechanism of erosion of the particles in the elbow, so that a large amount of experience coefficients are needed to be used, and the application range and calculation accuracy of the method are affected. The second method simulates a flow field in a pipeline based on a computational fluid dynamics method, releases a large amount of discrete particles in the flow field, tracks a particle group by using a Lagrangian method, and finally substitutes the collision speed and the collision angle of the particles on the eroded surface into a particle erosion theory to calculate elbow erosion. Because each detail in the process of erosion of the elbow particles is analyzed in detail, the method is complex in operation, grid division and iterative operation are generally needed, and larger calculation resources are needed in the calculation process, so that the method is not suitable for engineering application.
Disclosure of Invention
The invention aims to solve the technical problem of providing an explicit algorithm for solid particle erosion in a liquid phase elbow.
The invention adopts the following technical scheme:
in the improvement, an explicit algorithm for erosion of solid particles in a liquid phase elbow comprises the following steps:
(1) Solving basic characteristics of a flow field in a pipeline:
the reynolds number Re of the turbulent tube is:
v in m Average velocity of pipe flow, D is pipe diameter, ρ f Is fluid density, mu f Is fluid viscous;
the friction coefficient f of the pipeline is:
friction flow velocity v of pipe flow * The method comprises the following steps:
(2) Solving an elbow inner flow field:
setting the axial velocity distribution V in the elbow i f The method comprises the following steps:
wherein V is f The axial velocity of fluid in a long straight pipe at the upstream of the elbow is l, and the radial coordinate of the fluid micro-mass in the elbow on a plane parallel to the symmetry plane of the elbow is l;
(3) Calculating the drop point of the particles:
the initial radial coordinate of the particles on the movement plane is l 0 Polar coordinates at the entrance are
The above coordinates satisfy the following relationship:
the collision point coordinates of the particles l hit The method comprises the following steps:
wherein θ is hit For the angular position of the collision point on the plane of movement of the particles,
d p is particle size, ρ p Is the particle density;
(4) Calculating the collision velocity of the particles:
the axial and radial speeds of the particles when striking the elbow are respectively:
axial direction
Radial->
The impact velocity of the particles
The method comprises the following steps: />
Wherein->
Is the axial direction of the elbow, is->
Is the radial direction of the elbow;
(5) Solving the collision angle of the particles:
normal vector of elbow curved surface at particle drop point
The method comprises the following steps:
(6) Solving for the material loss ratio at the particle impact point: substituting the collision velocity and the collision angle of the particles into the following equation:
ER D ＝C 2 (V hit sinφ-V tsh ) 2
ER＝F s (ER C +ER D )
wherein V is hit Is the collision velocity of the particles; the ER is the loss of elbow material quality caused by unit mass particles; f (F) S For the sharp particles F, for the particle shape factor S =1.0 for round particles F S =0.2, F when between the two S =0.5; the values of other parameters in the formula are shown in the following table:
| material | Carbon steel 1018 | Carbon steel 4130 | Seamless steel 316 | Seamless steel 2205 | Chrome steel 13 | Nickel steel 625 | Aluminum alloy 6061 |
| C 1 | 5.90×10 -8 | 4.94×10 -8 | 4.58×10 -8 | 3.92×10 -8 | 4.11×10 -8 | 4.58×10 -8 | 3.96×10 -8 |
| C 2 | 4.25×10 -8 | 3.02×10 -8 | 5.56×10 -8 | 2.30×10 -8 | 3.09×10 -8 | 4.22×10 -8 | 3.38×10 -8 |
| κ | 0.5 | 0.4 | 0.4 | 0.4 | 0.5 | 0.4 | 0.4 |
| V tsh | 5.5 | 3.0 | 5.8 | 2.3 | 5.1 | 5.5 | 7.3 |
(7) Solving the effective sand conveying rate at the impact part of the particles:
if the pipeline at the upstream of the elbow is along the vertical direction, the sand conveying rate c of unit area per unit time p The method comprises the following steps:
if the upstream pipeline of the elbow is in the horizontal direction, the particle distribution on the section of the pipeline is not uniform under the action of gravity, and the sand conveying rate c of unit area per unit time p The method comprises the following steps:
wherein g is gravitational acceleration; h is the relative coordinate of the particles at the inlet of the elbow along the gravity direction, and the value is between-1 and 1; w (w) p The sand conveying quality on the cross section of the pipeline in unit time; i 1 Is a modified 1-order Bessel function;
(8) Solving an inlet erosion diffusion coefficient:
the erosion diffusion coefficient eta is the area ratio between the effective active area and the erosion coverage area of the particles at the inlet:
in which x is hit The Cartesian coordinate of the impact position of the elbow space particles has the following conversion relation with the polar coordinate:
x hit ＝l hit cosθ hit
z hit ＝l hit sinθ hit
wherein the method comprises the steps of
The polar coordinates of the particles at the inlet of the elbow;
(9) Calculating erosion of solid particles on a bending head:
loss of material mass per unit area per unit time E at any position on curved surface of elbow r The method comprises the following steps:
E r ＝c p ηER。
the beneficial effects of the invention are as follows:
the invention aims to provide an explicit algorithm for calculating the motion trail of solid particles in a liquid-phase elbow and causing erosion, an approximate flow field in the elbow is constructed based on a correlation theory, an explicit solution of the motion trail is obtained by simplifying a particle motion equation, and the material loss caused by the collision of particles with the pipe wall is tracked. The process can closely relate the microscopic mechanism and macroscopic expression of the particle erosion in the elbow, and the computing resource can be effectively saved because the flow field elements with little influence on the particle erosion elbow process are omitted.
Drawings
FIG. 1a is a graph a comparing the predicted results obtained using the explicit algorithm disclosed in example 1 of the present invention with experimental data;
FIG. 1b is a graph b of the prediction results obtained using the explicit algorithm disclosed in example 1 of the present invention versus experimental data.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The invention aims to provide an explicit algorithm for calculating solid particle erosion in a liquid phase elbow, which is based on a simplified elbow internal flow field, deduces explicit particle tracks in the liquid phase elbow, substitutes angles, speeds and falling points of particles impacting a pipe wall into a particle erosion theory, and can obtain explicit solution of solid particle erosion in the liquid phase elbow. The algorithm aims at reflecting the complete mechanism of erosion of solid particles in the liquid phase elbow to a certain extent, and simplifies the analysis and calculation flow as much as possible, so that the algorithm is suitable for engineering application. To achieve the above object, the following theoretical analysis is performed:
(1) The flow field in the elbow is approximately presented, and the flow field characteristics affecting the particle track are highlighted.
The flow field characteristics in the elbow directly influence the movement characteristics and distribution rules of particles in the flow field. The flow field in the elbow is simulated as accurately as possible, and the method is a basis for accurately analyzing the erosion of particles in the elbow. The turbulent flow field at the upstream of the elbow is fully developed, the basic properties such as speed, pressure and the like of the flow field after entering the elbow are changed drastically, and higher calculation resources are inevitably consumed for accurately presenting all details of the elbow flow field. Because the erosion of the solid particles in the elbow is only related to the movement rule of the part of the particles which are close to the outer side of the elbow and can impact the pipe wall, the flow field characteristics which directly influence the erosion of the solid particles in the elbow are only concerned without simulating all flow field details in the elbow.
The axial velocity distribution of the flow field in the long straight pipe at the upstream of the elbow is as follows:
wherein V is m The fluid conveying speed in the pipeline; v is the friction flow rate in the pipeline; d is the diameter of the pipeline; r is the radial coordinate of the fluid. The axial velocity of the fluid after entering the elbow changes drastically, and the shear stress between the flow layers is negligible. Therefore, the fluid micro-mass enters the elbow to do curve motion, and the angular momentum conservation relation should be satisfied in the motion process. Since the fluid micro-clusters in the long straight pipeline almost all move linearly, the fluid micro-clusters can be assumed to have the same virtual radius R' in the movement process, namely:
V i f l＝V f R′
wherein V is i f Is the axial velocity of the fluid in the elbow; and l is the radial coordinate of the fluid micro-mass in the elbow on a plane parallel to the symmetry plane of the elbow. The fluid in the elbow still satisfies the mass conservation relationship:
in the method, in the process of the invention,
is the angular position of the fluid micro-clusters on the cross section of the pipe.
(2) And tracking the movement of the particles in the elbow, and simplifying the movement equation to obtain an explicit solution.
After the solid particles enter the elbow, the solid particles can keep the original motion state under inertia, and the motion track can be bent under the action of fluid dragging. Since the solid particles near the outside of the bend hardly move perpendicular to the symmetry plane of the bend, only the curved movement of the solid particles in a plane parallel to the symmetry plane of the bend is considered. On this plane, the equation of motion of the particles is:
in the method, in the process of the invention,
is the axial direction and the radial direction of the elbow; m is m p Is the mass of solid particles; f is the drag force of the fluid on the particles; θ is the angular position in the plane of movement of the particles. The drag force of the fluid on the particles is:
wherein d p Is of particle size; ρ f 、ρ p Fluid and particle densities, respectively; c (C) D Is a drag coefficient; mu (mu) f Is fluid viscous; v slip Is the difference in velocity between the fluid and the particles. The decomposed form of the equation of motion of the particles can be obtained from formulas (2.4) - (2.5 c):
after particles enter the elbow, the axial speed gradually approaches to the fluid speed under the action of surrounding fluid; further, the centrifugal force term in the expression (2.6 b) is much larger than the speed change rate term. Based on the above conclusion, the particle motion equation can be simplified to obtain an explicit solution:
(3) And solving the particle impact parameters, and calculating the erosion distribution of the elbow by combining the particle erosion theory.
And solving the collision angle, the collision speed and the falling point when the particles collide with the pipe wall based on the particle motion trail. Substituting the collision speed and the collision angle of the particles into the related particle erosion theory, and calculating the mass loss ratio of the material at the corresponding particle falling point. And then calculating the erosion coverage area and the mass loss at the drop point of the particles based on the effective activity area and the sand conveying rate of the sand particles at the initial position of the particles. And counting the mass loss of the elbow caused by particles at any point from the inlet of the elbow, and obtaining the erosion distribution of the particles outside the elbow.
Embodiment 1, this embodiment discloses an explicit algorithm for erosion of solid particles in a liquid phase elbow, comprising the steps of:
(1) Solving basic characteristics of a flow field in a pipeline:
the reynolds number Re of the turbulent tube is:
v in m Average velocity of pipe flow, D is pipe diameter, ρ f Is fluid density, mu f Is fluid viscous;
the friction coefficient f of the pipeline is:
friction flow of pipe flowSpeed v * The method comprises the following steps:
(2) Solving an elbow inner flow field:
from previous theoretical analysis, the axial velocity profile V in the elbow i f The method comprises the following steps:
wherein V is f The axial velocity of fluid in a long straight pipe at the upstream of the elbow is l, and the radial coordinate of the fluid micro-mass in the elbow on a plane parallel to the symmetry plane of the elbow is l;
(3) Calculating the drop point of the particles:
the initial radial coordinate of the particles on the movement plane is l 0 Polar coordinates at the entrance are
The above coordinates satisfy the following relationship:
the collision point coordinates of the particles l hit The method comprises the following steps:
wherein θ is hit For the angular position of the collision point on the plane of movement of the particles,
d p is particle size, ρ p Is the particle density;
(4) Calculating the collision velocity of the particles:
the axial and radial speeds of the particles when striking the elbow are respectively:
axial direction
Radial->
The impact velocity of the particles
The method comprises the following steps: />
Wherein->
Is the axial direction of the elbow, is->
Is the radial direction of the elbow;
(5) Solving the collision angle of the particles:
normal vector of elbow curved surface at particle drop point
The method comprises the following steps:
(6) Solving for the material loss ratio at the particle impact point: substituting the collision velocity and the collision angle of the particles into the following equation:
ER D ＝C 2 (V hit sinφ-V tsh ) 2
ER＝F s (ER C +ER D )
wherein V is hit Is the collision velocity of the particles; the ER is the loss of elbow material quality caused by unit mass particles; f (F) S For the sharp particles F, for the particle shape factor S =1.0 for round particles F S =0.2, F when between the two S =0.5; the values of other parameters in the formula are shown in the following table:
| material | Carbon steel 1018 | Carbon steel 4130 | Seamless steel 316 | Seamless steel 2205 | Chrome steel 13 | Nickel steel 625 | Aluminum alloy 6061 |
| C 1 | 5.90×10 -8 | 4.94×10 -8 | 4.58×10 -8 | 3.92×10 -8 | 4.11×10 -8 | 4.58×10 -8 | 3.96×10 -8 |
| C 2 | 4.25×10 -8 | 3.02×10 -8 | 5.56×10 -8 | 2.30×10 -8 | 3.09×10 -8 | 4.22×10 -8 | 3.38×10 -8 |
| κ | 0.5 | 0.4 | 0.4 | 0.4 | 0.5 | 0.4 | 0.4 |
| V tsh | 5.5 | 3.0 | 5.8 | 2.3 | 5.1 | 5.5 | 7.3 |
(7) Solving the effective sand conveying rate at the impact part of the particles:
if the pipeline at the upstream of the elbow is along the vertical direction, the sand conveying rate c of unit area per unit time p The method comprises the following steps:
if the upstream pipeline of the elbow is in the horizontal direction, the particle distribution on the section of the pipeline is not uniform under the action of gravity, and the sand conveying rate c of unit area per unit time p The method comprises the following steps:
wherein g is gravitational acceleration; h is the relative coordinate of the particles at the inlet of the elbow along the gravity direction, and the value is between-1 and 1; w (w) p The sand conveying quality on the cross section of the pipeline in unit time; i 1 Is a modified 1-order Bessel function;
(8) Solving an inlet erosion diffusion coefficient:
the erosion diffusion coefficient eta is the area ratio between the effective active area and the erosion coverage area of the particles at the inlet:
wherein xhit is Cartesian coordinates of the impact part of the elbow space particles, and the Cartesian coordinates and the polar coordinates have the following conversion relation:
x hit ＝l hit cosθ hit
z hit ＝l hit sinθ hit
wherein the method comprises the steps of
The polar coordinates of the particles at the inlet of the elbow;
(9) Calculating erosion of solid particles on a bending head:
loss of material mass per unit area per unit time E at any position on curved surface of elbow r The method comprises the following steps:
E r ＝c p ηER。
the following two sets of experimental data were selected for verification comparison with the prediction results obtained by the explicit algorithm disclosed in this example,
(1)P.Frawley,J.Corish,A.Niven,M.Geron,Combination of CFD and DOE to analyse solid particle erosion in elbows,Int.J.Comput.Fluid Dynamics 23(2009)411-426.
(2)L.Zeng,G.A.Zhang,X.P.Guo,Erosion-corrosion at different locations of X65carbon steel elbow,Corros.Sci.85(2014)318-330.
the two groups of experiments select different measuring methods, the span of the values of the parameters is also larger, and the presented experimental data has higher credibility. As shown in fig. 1a and 1b, it can be seen that the prediction result obtained by the explicit algorithm disclosed in the embodiment has higher calculation accuracy.
Claims (1)
1. An explicit method for erosion of solid particles in a liquid phase elbow is characterized by comprising the following steps:
(1) Solving basic characteristics of a flow field in a pipeline:
the reynolds number Re of the turbulent tube is:
v in m Average velocity of pipe flow, D is pipe diameter, ρ f Is fluid density, mu f Is fluid viscous;
the friction coefficient f of the pipeline is:
friction flow velocity v of pipe flow * The method comprises the following steps:
(2) Solving an elbow inner flow field:
setting the axial velocity distribution V in the elbow i f The method comprises the following steps:
wherein V is f The axial velocity of fluid in a long straight pipe at the upstream of the elbow is l, and the radial coordinate of the fluid micro-mass in the elbow on a plane parallel to the symmetry plane of the elbow is l;
(3) Calculating the drop point of the particles:
the initial radial coordinate of the particles on the movement plane is l 0 Polar coordinates at the entrance are
The above coordinates satisfy the following relationship:
the collision point coordinates of the particles l hit The method comprises the following steps:
wherein θ is hit For the angular position of the collision point on the plane of movement of the particles,
d p is particle size, ρ p Is the particle density;
(4) Calculating the collision velocity of the particles:
the axial and radial speeds of the particles when striking the elbow are respectively:
axial direction
Radial direction
The impact velocity of the particles
The method comprises the following steps: />
Wherein->
Is the axial direction of the elbow, is->
Is the radial direction of the elbow;
(5) Solving the collision angle of the particles:
normal vector of elbow curved surface at particle drop point
The method comprises the following steps:
(6) Solving for the material loss ratio at the particle impact point: substituting the collision velocity and the collision angle of the particles into the following equation:
ER D ＝C 2 (V hit sinφ-V tsh ) 2
ER＝F s (ER C +ER D )
wherein V is hit Is the collision velocity of the particles; the ER is the loss of elbow material quality caused by unit mass particles; f (F) S For the sharp particles F, for the particle shape factor S =1.0 for round particles F S =0.2, F when between the two S =0.5; the values of other parameters in the formula are shown in the following table:
(7) Solving the effective sand conveying rate at the impact part of the particles:
if the pipeline at the upstream of the elbow is along the vertical direction, the sand conveying rate c of unit area per unit time p The method comprises the following steps:
if the upstream pipeline of the elbow is in the horizontal direction, the particle distribution on the section of the pipeline is not uniform under the action of gravity, and the sand conveying rate c of unit area per unit time p The method comprises the following steps:
wherein g is gravitational acceleration; h is the relative coordinate of the particles at the inlet of the elbow along the gravity direction, and the value is between-1 and 1; w (w) p The sand conveying quality on the cross section of the pipeline in unit time; i 1 Is a modified 1-order Bessel function;
(8) Solving an inlet erosion diffusion coefficient:
the erosion diffusion coefficient eta is the area ratio between the effective active area and the erosion coverage area of the particles at the inlet:
in which x is hit The Cartesian coordinate of the impact position of the elbow space particles has the following conversion relation with the polar coordinate:
x hit ＝l hit cosθ hit
z hit ＝l hit sinθ hit
wherein the method comprises the steps of
The polar coordinates of the particles at the inlet of the elbow;
(9) Calculating erosion of solid particles on a bending head:
loss of material mass per unit area per unit time E at any position on curved surface of elbow r The method comprises the following steps:
E r ＝c p ηER。
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