CN117787142B - Method for constructing erosion and abrasion model of ore pulp pipeline based on energy method - Google Patents

Abstract

The invention relates to the technical field of mine pipeline abrasion detection, and discloses an ore pulp pipeline erosion abrasion model construction method based on an energy method. According to the method for constructing the erosion and abrasion model of the ore pulp pipeline based on the energy method, through a control equation and a turbulence model, input data are read, a solid-liquid two-phase flow field is calculated, V _s,C_s,τ_s data are extracted from flow field solution, near-wall flow field information is extracted, according to the calculated impact angle alpha, the impact angle alpha is obtained to be within the range of 0-8 degrees, the erosion and abrasion model is utilized to calculate the extracted data, and the erosion rate is obtained.

Description

A method for constructing erosion and wear model of slurry pipeline based on energy method

Technical Field

The invention relates to the technical field of mine pipeline wear detection, and in particular to a method for constructing an erosion and wear model of a slurry pipeline based on an energy method.

Background technique

Pipeline transportation has become the fifth largest mode of transportation after highway, railway, water transportation and aviation, which has played a huge role in promoting the development of the transportation industry, especially providing a scientific and feasible solution for the transportation of mine concentrates in remote mountainous areas with complex terrain, which is of great significance to the development and comprehensive utilization of mineral resources. As one of the common components in the slurry pipeline transportation process, the slurry pipeline carries a large amount of solid particles (such as iron ore concentrate) during the transportation process, which easily causes erosion and wear of the outer wall of the pipeline, thereby causing problems such as reduced pressure reduction capacity and shortened service life of the pipeline, affecting the normal operation of slurry transportation, and thus causing serious economic losses. The erosion and wear models widely used at present mainly include: the E/CRC model proposed by the University of Tulsa in the United States, as well as the Finnie model, Oka model, McLaury model, DNV model, etc. However, due to the complex solid-liquid flow inside the slurry pipeline, and the erosion and wear of the slurry pipeline is affected by many factors (such as impact velocity, impact angle, particle properties, slurry concentration, wall material, etc.), the calculation accuracy of the above erosion and wear models is low.

Summary of the invention

1. Technical issues to be solved

In view of the shortcomings of the prior art, the present invention provides a method for constructing a slurry pipeline erosion and wear model based on an energy method, which has the advantages of accurate calculation of the constructed slurry pipeline erosion and wear model, and solves the above-mentioned technical problems.

(II) Technical solution

To achieve the above object, the present invention provides the following technical solution: a method for constructing an erosion and wear model of a slurry pipeline based on an energy method, comprising the following steps:

S1. Establish the control equations, including the mass continuity equation and momentum equation for solid-liquid two-phase flow passing through the elbow;

S2. Construct a turbulence model to calculate the transport equations controlling the turbulent kinetic energy k and the turbulent dissipation rate ε in the pipeline;

S3, constructing an erosion wear model, including impact wear rate and sliding wear rate;

S4. Perform erosion wear calculations.

As a preferred technical solution of the present invention, the expressions of the continuity equation and momentum equation in step S1 are as follows:

Continuity equation:

Momentum equation:

Where C _k is the volume concentration of phase k, which includes liquid phase L and solid phase S, and ρ _k and are the density and velocity of the k phase, represents the stress-strain tensor of the k phase, represents the gradient of a scalar field, is the divergence operation of the vector field, represents the acceleration due to gravity, is the interaction force between the two phases, represents the force due to lift and turbulent diffusion, Represents the gradient of the k-phase pressure.

As a preferred technical solution of the present invention, the stress-strain tensor includes a liquid phase and a solid phase, and the stress tensor expressions of the liquid phase and the solid phase are as follows:

Liquid phase stress-strain tensor:

Stress-strain tensor of the solid phase:

in, and denote the stress-strain tensor of the liquid phase and the solid phase, _CL and _CS denote the volume concentration of the liquid phase and the solid phase, respectively. and represent the velocities of the liquid and solid phases, respectively, and They represent the velocity tensor of the liquid phase and the solid phase respectively, μ _L and μ _S represent the shear viscosity of the liquid phase and the solid phase respectively, λ _S represents the solid volume viscosity, which is the solid's ability to resist compression and expansion. Representing the unit tensor, the expression of solid volume viscosity λ _S is as follows:

Among them, θ _S represents the particle temperature, ρ _S represents the solid phase density, represents the diffusion coefficient, represents the collision dissipation of energy, represents the energy exchange between the liquid phase and the solid phase, _dS represents the solid particle size, _eS represents the solid particle collision coefficient, and _g0 represents the radial distribution function of the solid, which is expressed as follows:

Here, the volume concentration of the _CS solid phase, CS _,max, represents the maximum filling limit.

As a preferred technical solution of the present invention, the interaction force between the two phases is The expression is as follows:

Where _βj represents the interphase momentum exchange coefficient between the liquid phase and the solid phase, and represent the velocities of the liquid and solid phases respectively.

As a preferred technical solution of the present invention, The lift expression affected is as follows:

in, and represent the velocity of the liquid phase and the solid phase respectively, F _lift represents the lift, f _lift is the lift coefficient, and the turbulent dispersion force The expression is as follows:

Wherein, C _TD = 1, K _LS represents the turbulent kinetic energy between the liquid and solid phases, σ _SL = 0.9, _DS represents the diffusion scalar, _CS is the solid phase volume concentration, and _CL is the liquid phase volume concentration.

As a preferred technical solution of the present invention, the expression of the turbulence model is as follows:

Where t is time, ρ is the mixed phase fluid density, _xj is the coordinate component, _uj is the velocity component, k is the turbulent kinetic energy, ε is the dissipation rate, _Gk and _Gb represent the turbulent kinetic energy generation terms caused by the average velocity gradient and lift, respectively, _Sk and _Sε are custom source phases, _YM is the contribution of wave expansion in compressible turbulence to the total dissipation rate, _C1ε ＝1.44, _C2 ＝1.9, _C3ε ＝0.9, _σk and _σε are the turbulent Prandtl numbers of turbulent kinetic energy k and dissipation rate ε, _σk ＝1.0, _σε ＝1.2, μ is the fluid viscosity, v is the mixed phase velocity, _μt is the mixed phase turbulent viscosity coefficient, _C1 represents the maximum function, _C2 represents the input parameter, η represents the relative strain parameter, and max{*} represents the maximum value of the internal data.

As a preferred technical solution of the present invention, the impact wear rate calculation expression is as follows:

Where α represents the impact angle of the particle on the wall, ER _imp represents the impact wear rate, ρ _S C _S V _S ³ represents the impact energy flux of the solid, and ER _I (α) represents the impact erosion specific energy.

As a preferred technical solution of the present invention, the sliding wear rate ER _sl is expressed as follows:

Among them, _Esp represents the sliding erosion specific energy, _Psl is the friction power when the solid particles slide, and the expression of the total erosion wear rate ER is as follows:

ER＝ER _imp +ER _sl

As a preferred technical solution of the present invention, the friction power _Psl of the solid particles during sliding is expressed as follows:

_{Psl = τsUst}

Among them, _τs represents the solid shear stress, and _Ust represents the solid velocity tangent to the erosion surface.

As a preferred technical solution of the present invention, the erosion wear calculation in step S4 is combined with the control equation in step S1 and the turbulence model in step S2, and the input data is read to calculate the solid-liquid two-phase flow field and obtain the erosion rate.

Compared with the prior art, the present invention provides a method for constructing a slurry pipeline erosion and wear model based on an energy method, which has the following beneficial effects:

The present invention calculates the solid-liquid two-phase flow field through control equations and turbulence models and reads input data, extracts _Vs , _Cs , and _τs data from the flow field solution, extracts near-wall flow field information, calculates the impact angle α, obtains the impact angle α is in the range of 0° to 8°, calculates the extracted data using the erosion wear model, and obtains the erosion rate, thereby ensuring the improvement of calculation accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow diagram of a slurry pipeline erosion and wear model of the present invention;

FIG2 is a schematic diagram showing a comparison between experimental and calculated values of erosion wear rate according to the present invention;

FIG3 is a schematic diagram of the overall process of the present invention;

FIG. 4 is a schematic diagram of input data of the present invention.

Detailed ways

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Please refer to Figures 1-4, a method for constructing a slurry pipeline erosion and wear model based on an energy method, comprising the following steps:

S1. Establish the control equations, including the mass continuity equation and momentum equation when the solid-liquid two-phase flow passes through the elbow. The expressions of the continuity equation and momentum equation are as follows:

Continuity equation:

Momentum equation:

Where C _k is the volume concentration of phase k (L is liquid phase and S is solid phase), ρ _k and are the density and velocity of the k phase, represents the stress-strain tensor of the k phase, represents the gradient of the scalar field, is the divergence operation of the vector field, represents the acceleration due to gravity, represents the gradient of the k-phase pressure, is the interaction force between the two phases, Represents the force caused by lift and turbulent diffusion. The stress-strain tensor includes the liquid phase and the solid phase. The stress tensor expressions of the liquid phase and the solid phase are as follows:

Liquid phase stress-strain tensor:

Stress-strain tensor of the solid phase:

in, and denote the stress-strain tensor of the liquid phase and the solid phase, _CL and _CS denote the volume concentration of the liquid phase and the solid phase, respectively. and represent the velocities of the liquid and solid phases, respectively, and They represent the velocity tensors of the liquid phase and the solid phase, μ _L and μ _S represent the shear viscosity of the liquid phase and the solid phase, respectively. The expression of the shear viscosity μ _S of the solid is as follows:

Wherein, μ _S,kin is the dynamic solid shear viscosity; μ _S,col is the collision solid shear viscosity; μ _S,fr is the friction solid shear viscosity; d _S is the solid particle size; ρ _S is the solid phase density; e _S is the solid particle collision coefficient, which is taken as 0.9; φ is the friction angle, which is taken as 30°; I _2D is the second invariant of the deviatoric stress; P _S is the solid phase pressure; θ _S is the particle temperature; g ₀ is the radial distribution function of the solid, which represents the dimensionless distance between solid (spherical) particles, expressed as:

Where, _{CS is} the volume concentration of the solid phase, and CS _,max represents the maximum filling limit.

λ _S represents the solid volume viscosity, which is the solid's ability to resist compression and expansion. Representing the unit tensor, the expression of solid volume viscosity λ _S is as follows:

Among them, θ _S represents the particle temperature, ρ _S represents the solid phase density, represents the diffusion coefficient, represents the collision dissipation of energy, represents the energy exchange between the liquid phase and the solid phase, d _S represents the solid particle size, and e _{S represents} the solid particle collision coefficient;

The interaction between the two phases The expression is as follows:

Where _βj represents the interphase momentum exchange coefficient between the liquid phase and the solid phase, and denote the velocities of the liquid phase and the solid phase respectively, and the expression of _βj is as follows:

Among them, ρ _L is the liquid density, μ _L represents the shear viscosity of the liquid, d _S represents the particle size of the solid particles, and _CD is the drag coefficient. The expression is as follows:

Where Re _S is the particle Reynolds number;

The solid-solid momentum exchange coefficient between any two solid particles S1 and S2 is expressed as:

Where _β0 is the solid-solid exchange coefficient; and are the densities of any two solid particles S ₁ and S ₂ respectively; and are the velocities of any two solid particles S ₁ and S ₂ respectively; and are the volume concentrations of any two solid particles S ₁ and S ₂ respectively; and are the particle sizes of any two solid particles S ₁ and S ₂ respectively; C _fr is the friction coefficient between solids, which is set to 0;

Regarding the The lift expression affected is as follows:

in, and represent the velocity of the liquid phase and the solid phase respectively, F _lift represents the lift, f _lift is the lift coefficient, and the turbulent dispersion force The expression is as follows:

Where, C _TD = 1, K _LS represents the turbulent kinetic energy between the liquid phase and the solid phase, σ _SL = 0.9, _DS represents the diffusion scalar, _CS is the solid phase volume concentration, _CL is the liquid phase volume concentration, and the diffusion scalars _DS and _DL are given by _DS = _DL = μt _,L / _ρL , which are calculated based on the turbulent viscosity of the liquid phase μt _,L and the density of the liquid phase _ρL . When using the k-ε mixed turbulence model, the mixed diffusion scalar _Dm is given by _Dm = μt _,m / _ρm ;

S2. Construct a turbulence model to calculate the transport equation that controls the turbulent kinetic energy k and the turbulent dissipation rate ε in the pipeline. The expression of the turbulence model is as follows:

Where t is time, ρ is the mixed phase fluid density, _xj is the coordinate component, _uj is the velocity component, k is the turbulent kinetic energy, ε is the dissipation rate, _Gk and _Gb represent the turbulent kinetic energy generation terms caused by the average velocity gradient and lift, respectively, _Sk and _Sε are custom source phases, _YM is the contribution of wave expansion in compressible turbulence to the total dissipation rate, _C1ε ＝1.44, _C2 ＝1.9, _C3ε ＝0.9, _σk and _σε are the turbulent Prandtl numbers of turbulent kinetic energy k and dissipation rate ε, _σk ＝1.0, _σε ＝1.2, μ is the fluid viscosity, v is the mixed phase velocity, _μt is the mixed phase turbulent viscosity coefficient, _C1 represents the maximum function, _C2 represents the input parameter, η represents the relative strain parameter, and max{*} represents the maximum value of the internal data

C _μ is taken as 0.09, η is the relative strain parameter, which can be expressed as S represents the modulus of the mean strain rate tensor, defined as The shear rate tensor S _ij can be expressed as:

Among them, x _i and x _j are coordinate components;

S3. Construct an erosion wear model, including impact wear rate and sliding wear rate. The impact wear rate calculation expression is as follows:

Where α represents the impact angle of the particle on the wall, ER _imp represents the impact wear rate, ρ _S C _S V _S ³ represents the impact energy flux of the solid, and ER _I (α) represents the impact erosion specific energy, which is the impact erosion specific energy, and is a function of the impact angle α.

The method to obtain the particle collision angle α from the Euler-Euler flow field is: extract the near-wall flow field data, convert the calculated overall velocity field near the wall into the wall normal coordinate system or local coordinate system, where the overall flow direction is the axial flow direction, the tangential flow is the velocity tangent to the circumference, and the third direction is the radial flow away from the center of the circle. Then calculate the impact angle α:

Therefore, the particle collision angle is calculated based on the local particle velocity extracted from the near-wall flow field.

The sliding wear rate is related to the specific energy or (for solid particles) energy required to remove a unit volume of material. By introducing the empirically determined sliding wear rate ER _sl :

Where, E _sp represents the sliding erosion specific energy, E _sp is taken as 7.2×10 ¹¹ J/m ³ , P _sl is the friction power when the solid particles slide, and the expression of the total erosion wear rate ER is as follows:

ER＝ER _imp +ER _sl

S4. Perform erosion wear calculation, combine the control equation in step S1 and the turbulence model in step S2, read the input data, calculate the solid-liquid two-phase flow field, extract _Vs , _Cs , _τs data from the flow field solution, extract the near-wall flow field information, calculate the impact angle α, obtain the impact angle α is between 0° and 8°, use the erosion wear model based on the energy method to calculate the extracted data, and obtain the erosion rate.

Please refer to Figure 4 for the input data of this paper. According to Figure 2, the horizontal axis is the different bending angles of the slurry pipeline elbow, and the vertical axis is the normalized erosion wear rate. As can be seen from Figure 2, the erosion wear rate calculated by the slurry pipeline erosion wear model based on the energy method is compared with the actual data, which shows good consistency.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims (6)

1. The method for constructing the erosion and abrasion model of the ore pulp pipeline based on the energy method is characterized by comprising the following steps of: the method comprises the following steps:

S1, establishing a control equation, wherein the control equation comprises a mass continuity equation and a momentum equation when a solid-liquid two-phase flow passes through a bent pipe;

the expression of the continuity equation and the momentum equation in the step S1 is as follows:

Continuity equation:

momentum equation:

Wherein C _k is the volume concentration of k phases including a liquid phase L and a solid phase S, ρ _k and The density and velocity of the k-phase, respectively, τk represents the stress-strain tensor of the k-phase,Representing the gradient of the scalar field,For the divergence operation of the vector field,Indicating the acceleration of gravity and,Is the interaction force between the two phases,Representing forces caused by lift and turbulence diffusion,Representing the gradient of k-phase pressure;

S2, constructing a turbulence model for calculating a transportation equation and a turbulence dissipation rate epsilon for controlling turbulence kinetic energy k in the pipeline;

The expression of the turbulence model is as follows:

Where t is time, ρ is the mixed phase fluid density, x _j is the coordinate component, u _j is the velocity component, k is the turbulent kinetic energy, ε is the dissipation rate, G _k and G _b represent the turbulent kinetic energy generation terms caused by the average velocity gradient and lift respectively, S _k and S _ε are the custom source phases, Y _M is the contribution of the fluctuating expansion in compressible turbulence to the total dissipation rate, C _1ε＝1.44,C₂＝1.9,C_3ε＝0.9,σ_k and σ _ε are the turbulent planets of the turbulent energy k and dissipation rate ε, σ _k＝1.0,σ_ε =1.2, μ is the fluid viscosity, v is the mixed phase velocity, μ _t is the mixed phase turbulent viscosity coefficient, C ₁ represents the maximum function, C ₂ represents the input parameter, η represents the relative strain parameter, max { x } represents the maximum value for the internal data;

s3, constructing an erosion wear model, wherein the erosion wear model comprises an impact wear rate and a sliding wear rate;

The impact wear rate calculation expression is as follows:

Where α represents the angle of impact of the particle on the wall, ER _imp represents the impact wear rate, ρ _SC_SV_S ³ represents the impact energy flux of the solid, ER _I (α) represents the impact erosion specific energy;

The sliding wear rate ER _sl is expressed as follows:

Wherein E _sp represents the slip erosion specific energy, P _sl is the friction power at the time of solid particle slip action, and the total erosive wear rate ER is expressed as follows:

ER＝ER_imp+ER_sl

S4, performing erosion and abrasion calculation.

2. The method for constructing the erosion and abrasion model of the ore pulp pipeline based on the energy method according to claim 1, which is characterized by comprising the following steps of: the stress-strain tensors include a liquidus stress-strain tensor and a solidus stress-strain tensor, and the liquidus and solidus stress-strain tensors are expressed as follows:

Liquid phase stress-strain tensor:

Stress-strain tensor for solid phase:

Wherein, AndRepresenting the stress-strain tensor of the liquid and solid phases, respectively, C _L and C _S representing the volume concentrations of the liquid and solid phases, respectively,AndThe velocities of the liquid and solid phases are indicated separately,AndRepresents velocity tensors of the liquid phase and the solid phase respectively, mu _L and mu _S represent shear viscosity of the liquid phase and the solid phase respectively, lambda _S represents solid volume viscosity, is the compression resistance and expansion resistance of the solid,The expression for the solid volume viscosity lambda _S, representing the unit tensor, is as follows:

Wherein Θ _S represents the particle temperature, ρ _S represents the solid phase density, The diffusion coefficient is indicated as such,Representing the collision dissipation of energy,Representing the energy exchange between the liquid and solid phases, P _S is the solid phase pressure, d _S represents the solid particle size, e _S the solid particle collision coefficient, g ₀ represents the radial distribution function of the solid, expressed as follows:

Wherein, the volume concentration of C _S solid phase, C _S,max represents the maximum filling limit.

3. The method for constructing the erosion and abrasion model of the ore pulp pipeline based on the energy method according to claim 2, which is characterized by comprising the following steps of: interaction force between the two phasesThe expression of (2) is as follows:

wherein beta _j represents the inter-phase momentum exchange coefficient between the liquid phase and the solid phase, AndThe velocities of the liquid and solid phases are indicated, respectively.

4. The method for constructing the erosion and abrasion model of the ore pulp pipeline based on the energy method according to claim 2, which is characterized by comprising the following steps of: for the saidThe lift of the effect is expressed as follows:

Wherein, AndRespectively representing the speeds of liquid phase and solid phase, F _lift represents lift force, F _lift represents lift force coefficient, ρ _L represents liquid phase density, and the dispersion force of turbulent flowThe expression is as follows:

Wherein C _TD＝1,K_LS represents turbulent kinetic energy between the liquid phase and the solid phase, σ _SL＝0.9,D_S represents diffusion scalar, C _S is solid phase volume concentration, and C _L is liquid phase volume concentration.

5. The method for constructing the erosion and abrasion model of the ore pulp pipeline based on the energy method according to claim 1, which is characterized by comprising the following steps of: the expression of the friction power P _sl during the sliding action of the solid particles is as follows:

P_sl＝τ_sU_st

Where τ _s represents the solid shear stress and U _st represents the solid velocity tangential to the erosion surface.

6. The method for constructing the erosion and abrasion model of the ore pulp pipeline based on the energy method according to claim 1, which is characterized by comprising the following steps of: and the erosion and abrasion calculation in the step S4 is combined with the control equation in the step S1 and the turbulence model in the step S2, input data are read, and the flow field of the solid-liquid two-phase flow is calculated to obtain the erosion rate.