Implementing Alternative Functions for Erosion Ratio

Erosion equations are often tuned for a particular material/sand combination that are based on experimental testing. In this section, implement the model that was developed by Zhang et al. at the Erosion/Corrosion Research Center in Tulsa as an example.

The model that is given by Zhang et al. ([968]) is:

E R ⁢ =   C ( B H ) − 0.59 F s V p n F ( Θ )

F ( Θ )   =   5.40 Θ ⁢ −   10.11 Θ 2 ⁢ +   10.93 Θ 3 ⁢ −   6.33 Θ 4 ⁢ +   1.42 Θ 5

where:

  • ER is the Erosion Ratio.

  • C and n are empirical constants that are given as 2.17x10-7 and 2.41 respectively.

  • BH is the Brinell hardness of the wall material. For carbon steel, this is taken as 120 after Zhang et al. ([968]).

  • Fs is the particle shape coefficient, which is said to be 0.2 for fully rounded sand particles.

  • Vp is the particle impact velocity.

  • Θ is the particle impact angle in radians.

Implement the angle function in a field function, and reference this angle field function as a field function for erosion ratio:

  1. Right-click the Automation > Field Functions node and select New > Scalar.
  2. Rename the User Field Function 1 node to Zhang Angle Function.
  3. Select the Zhang Angle Function node and set the following properties:
    Property Setting
    Function Name ZhangAngleFunction
    Dimensions Dimensionless
    Definition (5.4 * $ParticleIncidenceAngle) - (10.11 * pow($ParticleIncidenceAngle, 2)) + (10.93 * pow($ParticleIncidenceAngle, 3)) - (6.33 * pow($ParticleIncidenceAngle, 4)) + (1.42 * pow($ParticleIncidenceAngle, 5))

If you insert the numeric constants in the equation:

E R ⁢ =   C ( B H ) − 0.59 F s V p n F ( Θ )

the final equation to be implemented is:

E R ⁢ =   2.17 ⁢ × 10 − 7 ⋅   ( 120 ) − 0.59 ⁢ ⋅   0.2 ⁢ ⋅   V p 2.41 ⁢ F ( Θ )

E R ⁢ =   2.57497 ⁢ ×   10 − 9 ⁢ V p 2.41 ⁢ F ( Θ )

  1. Right-click the Automation > Field Functions node and select New > Scalar.
  2. Rename the User Field Function 1 node to Zhang Erosion Ratio.
  3. Select the Zhang Erosion Ratio node and set the following properties:
    Property Setting
    Function Name ZhangErosionRatio
    Dimensions Dimensionless
    Definition 2.57497E-9 * pow((mag($${ParticleVelocity})), 2.41) * $ZhangAngleFunction

The field function must now be set in the Lagrangian model tree:

  1. Select the Continua > Physics 1 > Models > Lagrangian Multiphase > Lagrangian Phases > Phase 1 > Boundary Conditions > Wall > Physics Values > Impact Wear node and set Method to Field Function.
  2. Set Scalar Function to Zhang Erosion Ratio.

With the new field function in place, it is only necessary to run a single iteration to obtain a further prediction of erosion.

  1. Click (Step) in the Solution toolbar to perform a single iteration. It can take several minutes for the solver to compute all the particle tracks.
  2. Save the simulation.
  3. Run the Overall Erosion Rate report to obtain the mass loss rate from the new result:


    The erosion rate for the whole annulus is four times the predicted amount, which is 0.41 g/hr for the Zhang erosion model.