CN110134980A - The explicit algorithm of solid particle erosion in a kind of liquid phase elbow - Google Patents

Abstract

The invention discloses a kind of explicit algorithm of solid particle erosion in liquid phase elbow, include the following steps: that (1) solves the essential characteristic of pipeline flow field；(2) elbow flow field is solved；(3) drop point of particle is calculated；(4) impact velocity of particle is calculated；(5) collision angle of particle is solved；(6) the material loss ratio at particles collision point is solved；(7) effective silt discharge at particles hit is solved；(8) entrance erosion diffusion coefficient is solved；(9) solid particle erosion on elbow is calculated.The present invention is intended to provide a kind of calculate Particle Trajectory in liquid phase elbow and cause the explicit algorithm of erosion, the approximate flow field in elbow is constructed based on correlation theory, by being simplified the particle equation of motion to obtain the explicit solution of motion profile, material loss caused by particles collision tube wall is tracked.

Description

The explicit algorithm of solid particle erosion in a kind of liquid phase elbow

Technical field

The invention belongs to the explicit algorithm fields of solid particle erosion, in particular in one of field liquid phase elbow The explicit algorithm of solid particle erosion.

Background technique

Solid particle erosion problem in pipeline is widely present in various industrial equipments, such as oil gas pipeline, dredging Hydraulic reclamation equipment, rotary dust wiper, aero-engine etc..Solid particle in pipeline is prominent in flow direction with fluid high-speed motion Inner wall of the pipe can be hit with higher momentum at right change, in turn result in serious material damage.Elbow common changes as a kind of The component of fluid flow direction is easiest to solid particle erosion occur.Pipeline becomes under the action of solid particle erosion Thin, rupture, fluid leakage, will cause serious production accident, endanger personnel safety and periphery ecological environment.Therefore, one is taken The solid particle erosion of kind simple effective method analysis elbow, for instructing equipment Design, the maintenance of many industrial circles Maintenance is of great significance.

There are mainly two types of the methods of existing analysis elbow solid particle erosion.First method is based on many experiments Data fit the experience come or semiempirical algorithm.This method is usually the extension of particle erosion theory, passes through experimental data Fit conveying speed index, angle function and component shape coefficient；Some more fine models can be based on stream in component Field form, provides particle swarm mean collisional speed and mean collisional angle.But the method does not track the movement of particle in elbow Track, can not reflect the complete mechanism of particle erosion in elbow, therefore need to affect this method using a large amount of empirical coefficient The scope of application and computational accuracy.Second method simulates pipeline flow field based on the method for Fluid Mechanics Computation, releases in flow field Amplification quantity discrete particle simultaneously using Lagrangian method track particle swarm, finally by by erosion surface particle impact velocity with touch Breakhead degree substitutes into the elbow erosion of particle erosion theoretical calculation.Since each of detailed analysis elbow particle erosion process is thin Section, complicated operation for this method, generally requires grid division, interative computation, needs to expend biggish meter in calculating process Resource is calculated, therefore is not particularly suited for engineering application.

Summary of the invention

The technical problem to be solved by the invention is to provide a kind of explicit algorithms of solid particle erosion in liquid phase elbow.

The present invention adopts the following technical scheme:

The explicit algorithm of solid particle erosion in a kind of liquid phase elbow, it is improved in that including the following steps:

(1) essential characteristic of pipeline flow field is solved:

The reynolds number Re of turbulent pipeline are as follows:

V in formula_mFor pipe stream average speed, D is pipe diameter, ρ_fFor fluid density, μ_fFor fluid viscosity；

The coefficient of friction resistance f of pipeline are as follows:

The drag velocity v of pipe stream_*Are as follows:

(2) elbow flow field is solved:

If axial velocity profile V in elbow_i ^fAre as follows:

Wherein, V_fFor on elbow in brigade commander's straight pipeline fluid axial velocity, l be elbow in fluid micellar be parallel to it is curved Radial coordinate in the plane of the head plane of symmetry；

R is the center radius of elbow；

(3) drop point of particle is calculated:

Initial radial coordinate of the particle on plane of movement is l₀, the polar coordinates of inlet areThe above coordinate is full It is enough lower relationship:

The then point of impingement coordinate l of particle_hitAre as follows:

Wherein θ_hitFor the point of impingement angular coordinate on particle plane of movement,d_pFor grain diameter, ρ_pFor grain density；

(4) impact velocity of particle is calculated:

Axial direction when particles hit elbow is respectively as follows: with radial velocity

It is axialIt is radial

The then stroke speed of particleAre as follows:WhereinFor the axial direction of elbow Direction,For the radial direction of elbow；

(5) collision angle of particle is solved:

The normal vector of elbow curved surface at particle drop pointAre as follows:

For the angular coordinate of pipeline section upper fluid micelle, θ For the angular coordinate on particle plane of movement；The then collision angle φ of particle are as follows:

(6) it solves the material loss ratio at particles collision point: the impact velocity of particle and collision angle is substituted into lower section Journey:

ER_D=C₂(V_hitsinφ-V_tsh)²

ER=F_s(ER_C+ER_D)

In formula, V_hitFor the impact velocity of particle；ER is Elbow material mass loss caused by unit mass particle；F_SFor Particle shape factor, for sharp particle F_S=1.0, for circular granular F_S=0.2, F when falling between_S=0.5；Formula Middle other parameters value see the table below:

Material

Carbon steel 1018

Carbon steel 4130

Seamless steel 316

Seamless steel 2205

Chromium steel 13

Nickel steel 625

Aluminium alloy 6061

C1

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

C2

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

Vtsh

5.5

3.0

5.8

2.3

5.1

5.5

7.3

(7) effective silt discharge at particles hit is solved:

If elbow upstream line is vertically, the silt discharge c of unit time unit area_pAre as follows:

If elbow upstream line is in the horizontal direction, distribution of particles and uneven on pipeline section, single under the effect of gravity The silt discharge c of position chronomere area_pAre as follows:

In formula, g is acceleration of gravity；H be particle at elbow inlet along the relative coordinate of gravity direction, value is -1 Between 1；w_pFor the sediment transport quality on unit time cross-section of pipeline；I₁For modified 1 rank Bessel function；

(8) entrance erosion diffusion coefficient is solved:

Erosion diffusion coefficient η is the area ratio between effective zone of action of inlet particle and erosion overlay area:

X in formula_hitFor the cartesian coordinate at the particles hit of elbow space, there is following transformational relation between polar coordinates:

x_hit=l_hit cosθ_hit

z_hit=l_hit sinθ_hit

WhereinThe polar coordinates for being particle at elbow inlet；

(9) solid particle erosion on elbow is calculated:

Quality of materials on elbow curved surface on any position unit time unit area loses E_rAre as follows:

E_r=c_pηER。

The beneficial effects of the present invention are:

The present invention is intended to provide a kind of calculate Particle Trajectory in liquid phase elbow and cause the explicit algorithm of erosion, The approximate flow field in elbow is constructed based on correlation theory, obtains the aobvious of motion profile by being simplified the particle equation of motion Formula solution tracks material loss caused by particles collision tube wall.Above procedure can by the microcosmic mechanism of elbow endoparticle erosion with it is macro It sees performance to be closely linked, little flow field element is influenced on particle erosion elbow process due to having ignored, it can be effectively Save computing resource.

Detailed description of the invention

Fig. 1 a is the comparison diagram using the resulting prediction result and experimental data of explicit algorithm disclosed in the embodiment of the present invention 1 a；

Fig. 1 b is the comparison diagram using the resulting prediction result and experimental data of explicit algorithm disclosed in the embodiment of the present invention 1 b。

Specific embodiment

In order to make the objectives, technical solutions, and advantages of the present invention clearer, right below in conjunction with drawings and examples The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.

The object of the present invention is to provide a kind of explicit algorithms of solid particle erosion in calculating liquid phase elbow, based on simplified Elbow flow field derives particle trajectories explicit in liquid phase elbow, and the angle, speed, drop point of particles collision tube wall are substituted into Particle erosion is theoretical, and the explicit solution of solid particle erosion in liquid phase elbow can be obtained.The algorithm is dedicated to a certain extent Reflect the complete mechanism of solid particle erosion in liquid phase elbow, and Simplified analysis and calculation process as far as possible makes that it is suitable for engineerings Using.To reach the above goal of the invention, following theory analysis is first carried out:

(1) the approximate flow field presented in elbow, the prominent flow pattern for influencing particle trajectories.

Flow field characteristic in elbow directly affects the kinetic characteristic, the regularity of distribution of particle in flow field.Mould as accurately as possible Elbow flow field is drawn up, is the basis of accurate analysis elbow endoparticle erosion.The turbulence flow flied of elbow upstream is sufficiently developed, into Enter the essential attributes such as speed, the pressure in flow field after elbow and acute variation occurs, is intended to that all details gesture in elbow flow field are accurately presented Higher computing resource must be expended.Due to the solid particle erosion in elbow only with it is on the outside of the elbow, being capable of impact tube The part particle characteristics of motion of wall is related, there is no need to simulate all Flow details in elbow, is concerned only with and directly affects The flow field characteristic of solid particle erosion in elbow.

On elbow in brigade commander's straight pipeline flow field axial velocity profile are as follows:

In formula, V_mFor fluids within pipes conveying speed；V* is drag velocity in pipeline；D is pipe diameter；R is fluid Radial coordinate.Fluid enters axial velocity acute variation after elbow, and the shearing stress between fluid layer can be ignored.Therefore, fluid is micro- Curvilinear motion is done after entering elbow by group, should meet conservation of angular momentum relationship in motion process.Since fluid is micro- in long straight pipeline Group is almost linear motion, it can be assumed that possesses identical imaginary radius R ' in these fluid micellar motion processes, it may be assumed that

V_i ^fL=V_fR′

In formula, V_i ^fFor the axial velocity of fluid in elbow；L is that fluid micellar is being parallel to the flat of the elbow plane of symmetry in elbow Radial coordinate on face.Fluid in elbow still meets conservation of mass relationship, then:

In formula,For the angular coordinate of pipeline section upper fluid micelle.

(2) movement of the tracking particle in elbow, obtains explicit solution after simplifying the equation of motion.

After solid particle enters elbow, original motion state on the one hand can be kept under inertia, on the one hand will receive stream Body effect of dragging causes motion profile to bend.Since the solid particle on the outside of elbow hardly occurs perpendicular to curved The movement of the head plane of symmetry, therefore only consider curvilinear motion of the solid particle in the plane for being parallel to the elbow plane of symmetry.? In the plane, the equation of motion of particle are as follows:

In formula,Axial direction, radial direction for elbow；m_pFor mass of solid particles；F is fluid to particle Drag；θ is the angular coordinate on particle plane of movement.Drag of the fluid to particle are as follows:

In formula, d_pFor grain diameter；ρ_f、ρ_pRespectively fluid and grain density；C_DTo pull force coefficient；μ_fIt is viscous for fluid Property；v_slipThe speed difference between fluid and particle.The decomposed form of the particle equation of motion can be obtained by formula (2.4)-(2.5c):

After particle enters elbow, axial velocity can gradually level off to fluid velocity under surrounding fluid effect；In addition, formula Centrifugal force item is much larger than percentage speed variation item in (2.6b).Based on conclusions, the particle equation of motion can be simplified into And obtain explicit solution:

(3) particles hit parameter is solved, is distributed in conjunction with particle erosion theoretical calculation elbow erosion.

Based on particle motion trajectory, collision angle, impact velocity and drop point when particles collision tube wall are solved.By particle Relevant to the collision angle substitution particle erosion of impact velocity it is theoretical, calculate the quality of materials loss at corresponding particle drop point Than.Effective zone of action and silt discharge later based on the particle initial position grains of sand calculate the covering of erosion at particle drop point Region and mass loss.The elbow mass loss caused by the particle of arbitrary point from elbow inlet is counted, can be obtained curved Particle erosion distribution outside head.

Embodiment 1, present embodiment discloses a kind of explicit algorithms of solid particle erosion in liquid phase elbow, including walk as follows It is rapid:

(1) essential characteristic of pipeline flow field is solved:

The reynolds number Re of turbulent pipeline are as follows:

V in formula_mFor pipe stream average speed, D is pipe diameter, ρ_fFor fluid density, μ_fFor fluid viscosity；

The coefficient of friction resistance f of pipeline are as follows:

The drag velocity v of pipe stream_*Are as follows:

(2) elbow flow field is solved:

By theory analysis before it is found that axial velocity profile V in elbow_i ^fAre as follows:

Wherein, V_fFor on elbow in brigade commander's straight pipeline fluid axial velocity, l be elbow in fluid micellar be parallel to it is curved Radial coordinate in the plane of the head plane of symmetry；

R is the center radius of elbow；

(3) drop point of particle is calculated:

Initial radial coordinate of the particle on plane of movement is l₀, the polar coordinates of inlet areThe above coordinate is full It is enough lower relationship:

The then point of impingement coordinate l of particle_hitAre as follows:

Wherein θ_hitFor the point of impingement angular coordinate on particle plane of movement,d_pFor grain diameter, ρ_pFor grain density；

(4) impact velocity of particle is calculated:

Axial direction when particles hit elbow is respectively as follows: with radial velocity

It is axialIt is radial

The then stroke speed of particleAre as follows:WhereinFor the axial direction of elbow Direction,For the radial direction of elbow；

(5) collision angle of particle is solved:

The normal vector of elbow curved surface at particle drop pointAre as follows:

For the angular coordinate of pipeline section upper fluid micelle, θ For the angular coordinate on particle plane of movement；The then collision angle φ of particle are as follows:

(6) it solves the material loss ratio at particles collision point: the impact velocity of particle and collision angle is substituted into lower section Journey:

ER_D=C₂(V_hitsinφ-V_tsh)²

ER=F_s(ER_C+ER_D)

In formula, V_hitFor the impact velocity of particle；ER is Elbow material mass loss caused by unit mass particle；F_SFor Particle shape factor, for sharp particle F_S=1.0, for circular granular F_S=0.2, F when falling between_S=0.5；Formula Middle other parameters value see the table below:

Material

Carbon steel 1018

Carbon steel 4130

Seamless steel 316

Seamless steel 2205

Chromium steel 13

Nickel steel 625

Aluminium alloy 6061

C1

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

C2

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

Vtsh

5.5

3.0

5.8

2.3

5.1

5.5

7.3

(7) effective silt discharge at particles hit is solved:

If elbow upstream line is vertically, the silt discharge c of unit time unit area_pAre as follows:

If elbow upstream line is in the horizontal direction, distribution of particles and uneven on pipeline section, single under the effect of gravity The silt discharge c of position chronomere area_pAre as follows:

In formula, g is acceleration of gravity；H be particle at elbow inlet along the relative coordinate of gravity direction, value is -1 Between 1；w_pFor the sediment transport quality on unit time cross-section of pipeline；I₁For modified 1 rank Bessel function；

(8) entrance erosion diffusion coefficient is solved:

Erosion diffusion coefficient η is the area ratio between effective zone of action of inlet particle and erosion overlay area:

Xhit is the cartesian coordinate at the particles hit of elbow space in formula, has following conversion to close between polar coordinates System:

x_hit=l_hit cosθ_hit

z_hit=l_hit sinθ_hit

WhereinThe polar coordinates for being particle at elbow inlet；

(9) solid particle erosion on elbow is calculated:

Quality of materials on elbow curved surface on any position unit time unit area loses E_rAre as follows:

E_r=c_pηER。

The resulting prediction result of explicit algorithm disclosed in the following two groups of experimental datas of selection and the present embodiment carries out verifying pair Than,

(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.

This two groups of experiments have chosen different measurement methods, and the value span of parameter is also larger, the experimental data presented Credibility with higher.Comparison diagram such as Fig. 1 a, shown in 1b, it is seen that the resulting prediction result of explicit algorithm disclosed in the present embodiment Computational accuracy with higher.

Claims (1)

1. the explicit algorithm of solid particle erosion in a kind of liquid phase elbow, which comprises the steps of:

(1) essential characteristic of pipeline flow field is solved:

The reynolds number Re of turbulent pipeline are as follows:

V in formula_mFor pipe stream average speed, D is pipe diameter, ρ_fFor fluid density, μ_fFor fluid viscosity；

The coefficient of friction resistance f of pipeline are as follows:

The drag velocity v of pipe stream_*Are as follows:

(2) elbow flow field is solved:

If axial velocity profile V in elbow_i ^fAre as follows:

Wherein, V_fFor on elbow in brigade commander's straight pipeline fluid axial velocity, l be elbow in fluid micellar be parallel to elbow pair Radial coordinate in the plane in title face；

R is the center radius of elbow；

(3) drop point of particle is calculated:

Initial radial coordinate of the particle on plane of movement is l₀, the polar coordinates of inlet areAbove coordinate meet with Lower relationship:

The then point of impingement coordinate l of particle_hitAre as follows:

Wherein θ_hitFor the point of impingement angular coordinate on particle plane of movement,d_pFor grain diameter, ρ_pFor Grain density；

(4) impact velocity of particle is calculated:

Axial direction when particles hit elbow is respectively as follows: with radial velocity

It is axialIt is radial

The then stroke speed of particleAre as follows:WhereinFor the axial direction of elbow,For the radial direction of elbow；

(5) collision angle of particle is solved:

The normal vector of elbow curved surface at particle drop pointAre as follows:

For the angular coordinate of pipeline section upper fluid micelle, θ is Angular coordinate on grain plane of movement；The then collision angle φ of particle are as follows:

(6) it solves the material loss ratio at particles collision point: the impact velocity of particle and collision angle is substituted into following equation:

ER_D=C₂(V_hitsinφ-V_tsh)²

ER=F_s(ER_C+ER_D)

In formula, V_hitFor the impact velocity of particle；ER is Elbow material mass loss caused by unit mass particle；F_SFor granulated Shape coefficient, for sharp particle F_S=1.0, for circular granular F_S=0.2, F when falling between_S=0.5；Other in formula Parameter value see the table below:

Material Carbon steel 1018 Carbon steel 4130 Seamless steel 316 Seamless steel 2205 Chromium steel 13 Nickel steel 625 Aluminium alloy 6061 C₁ 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 C₂ 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) effective silt discharge at particles hit is solved:

If elbow upstream line is vertically, the silt discharge c of unit time unit area_pAre as follows:

If elbow upstream line is in the horizontal direction, distribution of particles and uneven on pipeline section under the effect of gravity, when unit Between unit area silt discharge c_pAre as follows:

In formula, g is acceleration of gravity；H be particle at elbow inlet along the relative coordinate of gravity direction, value -1 and 1 it Between；w_pFor the sediment transport quality on unit time cross-section of pipeline；I₁For modified 1 rank Bessel function；

(8) entrance erosion diffusion coefficient is solved:

Erosion diffusion coefficient η is the area ratio between effective zone of action of inlet particle and erosion overlay area:

X in formula_hitFor the cartesian coordinate at the particles hit of elbow space, there is following transformational relation between polar coordinates:

x_hit=l_hitcosθ_hit

z_hit=l_hitsinθ_hit

WhereinThe polar coordinates for being particle at elbow inlet；

(9) solid particle erosion on elbow is calculated:

Quality of materials on elbow curved surface on any position unit time unit area loses E_rAre as follows:

E_r=c_pηER。