[LiamH]

Hey CFD experts,

I have a question that I was hoping you guys could help me out with.

I am doing some sand erosion bench-marking to the "Oka" paper where they compare the E/CRC & Oka erosion equations (through CFD) to experimental data.

I have wrote a UDF for the Oka model according to the paper which is modeling for a sand called "OK#1" which I believe is SiO2-1.

The objective is to match my CFD model to the CFD simulations completed in the paper but my % error is >60% when comparing the results. Assuming that my UDF is correct, I would like to ask you guys for some input on the wall boundary conditions. More specifically, the "Diameter Function" and how it relates to the Oka model.

The equation for the oka model is:

E(theta) = g(theta)*E90
where:
E90 = K[(HV)^k1]*[(V_p/V')^k_2]*[(D_p/D')^k_3]

the value of k2 represents the velocity exponent in the boundary conditions. But I am confused as to what the diameter function value will be? I have a feeling that the % error I am getting is directly associated with this.

Paper Reference:
https://www.google.com/url?sa=t&rct=...lnnoqw&cad=rja

Cheers!

[carlos_antonio]

Dear LiamH,

Nice question. Recently I published two articles showing the strength of the Oka's erosion model on elbow erosion, extending the application to one, two and four-way coupling simulations (Interesting results were achieved). The power of this model resides on the capability of return the erosion patterns by means of more fundamental coefficients (Hv, impact velocity, particle diameter, type of particle, etc.).

So, let's try to answer your question:

1) Check both eroding (particles) and eroded (wall) material properties used in your simulations. Oka's model works for a range of materials (see Ref. 3, page 97). Be sure to work in this range to validate your cfd model.

2) Before talk about the "diameter function" you mentioned let's briefly remind the erosion model equations:

"E(theta) = g(theta)*E90" is correct. Don't forget that g(theta) is defined by (sin(theta)^n1 * (1 + Hv (1 - sin(theta))^n2)) where n1 and n2 are constants defined by the eroded material hardness number (Hv) (see Ref. 3, pag. 100, table 3).

Second, "E90 = K[(HV)^k1]*[(V_p/V')^k_2]*[(D_p/D')^k_3]" is also correct, but this equation requires a little bit more attention. The first constant K[(HV)^k1] is not that simple as it seems. If you read carefully the Oka publication (Ref. 4, page 107, equation 4) you notice that your K[(HV)^k1] is equal to K(aHv)^k1b and this function can be obtained from the curve fitting of Fig. 11 from Ref. 4 for your simulated conditions. For the case of Si02-1 and aluminum, the function obtained is K(aHv)^k1b = 81.714(Hv)^(-0.79) (see Ref. 1, equation 43 or Ref. 2, equation 14 for details). With this function well-defined, you need to feed your E90 with: eroded Vickers hardness (Hv), particle impact velocity (V_p) and particle diameter (D_p). The others constants (k2, k3) are function of Vickers hardness (Ref. 2, equation 13) and an arbitrary unit that is determined by the properties of the particles, respectively (for all pairs of Oka's paper, k3 is equal to 0.19).

So, the "Diameter function" you mentioned is not a function is just the actual particle diameter that collides with the wall boundary. If you are simulating different particle sizes, this erosion model takes this into account. Computationally, every time a particle hit the wall you need to call your UDF script to compute the erosion based on the impact velocity and particle diameter. In fact, in real word situations, particles with different sizes shows different erosion patterns.

3) Be careful with the output units, as stated by Oka's paper, the E90 unit is mm^3/kg.

I hope this helps. If you are interested in elbow erosion mitigation I suggest my recent publication (Ref. 2).

Cheers!

References:

Ref. 1: Numerical investigation of mass loading effects on elbow erosion
http://www.sciencedirect.com/science...32591015004763

Ref. 2: Mitigating elbow erosion with a vortex chamber
http://www.sciencedirect.com/science...32591015301200

Ref. 3: Practical estimation of erosion damage caused by solid particle impact: Part 1: Effects of impact parameters on a predictive equation
http://www.sciencedirect.com/science...43164805000979

Ref. 4: Practical estimation of erosion damage caused by solid particle impact: Part 2: Mechanical properties of materials directly associated with erosion damage
http://www.sciencedirect.com/science...4316480500102X

[LiamH]

Thanks for the papers Carlos, it took me this long to re-investigate the oka model but now I am thankful for your reply.

My new concern is testing out a comparison between SiO2-1 & SiC and which one causes a higher erosion rate. My prediction is that SiC would have a higher erosion rate due to the increased hardness of the particle but this doesn't seem to be the case with modeling the Oka model. In fact, SiO2 is nearly 4 times more erosive!!! Why?

I assume this is because of the E90 value = K(hv)^k1 and this value is always higher for the SiO2 particles. This doesn't seem correct to me...but I will have to investigate it further.

I am going to read your papers to get more insight on these models and then email you. Hopefully you are still around since it has been almost a year!

Cheers,

Liam

[LiamH]

Good afternoon Carlos,

I have a question for you regarding how to determined the E90 value as 84.714(Hv)^-0.79 in your paper.

I can see that you chose to run SiO2-1 particles in your model and that you used Aluminum (6061-T6) as your target material but I cannot see how you determined your "a" & "b" values from figure #11 in the paper. I understand that if I am using Tungsten Carbide (Hv=13.8GPa) as my target material and comparing two different particles (SiC and SiO2-1) that I will also develop separate equations. Can you please guide me as to how you developed these constants?

At this point, I am finding that SiC has a lower ER compared to SiO2 which I assume is incorrect since harder sands should cause a higher rate of erosion. Either the Oka model is unable to capture this particular type of physics or there is a serious problem with how I am using the Erosion module as well as my UDF.

Cheers,

Liam

[carlos_antonio]

Dear LiamH

Thank you very much for your reply. Regarding your posts:

If you read carefully my last post you will see:

""E90 = K[(HV)^k1]*[(V_p/V')^k_2]*[(D_p/D')^k_3]" is also correct, but this equation requires a little bit more attention. The first constant K[(HV)^k1] is not that simple as it seems. If you read carefully the Oka publication (Ref. 4, page 107, equation 4) you notice that your K[(HV)^k1] is equal to K(aHv)^k1b and this function can be obtained from the curve fitting of Fig. 11 from Ref. 4 for your simulated conditions. For the case of Si02-1 and aluminum, the function obtained is K(aHv)^k1b = 81.714(Hv)^(-0.79) (see Ref. 1, equation 43 or Ref. 2, equation 14 for details)."


So, E90 is not only 84.714(Hv)^-0.79. E90 is equal to 84.714(Hv)^-0.79 * [(V_p/V')^k_2]*[(D_p/D')^k_3] and the former is obtained by curve fitting of Fig. 11 from Ref. 1. But here, you will have a problem. Fig. 11 of Ref. 1 only give the experimental results from Si02 and as you said, your target material is Tungsten Carbide which is not available from Oka's experiment. If you take a look at Fig. 11 of Ref. 1 you will see the results of Aluminum, Stainless Steel, Carbon and Cooper against Si02 particles. You can try to extrapolate to your material to obtain the "K(aHv)^k1b = ???" for your Tungsten. Constants a and b are in this curve fitting. Both papers from Oka did not show the exact values of a and b but from Fig. 11 of Ref. 1 you can obtain the exponential "K(aHv)^k1b".

If you are using the same fitting (K(aHv)^k1b = 81.714(Hv)^(-0.79)) for SiC, this probably explains such difference in your results. I recommend you to careffully read both papers from Oka to obtain such curve for your target material.

Recently I published another paper on a device called twisted tape which is used to reduce erosion in elbows. Again, we used the Oka's model for particles of Si02 hitting on Aluminum. You can find more here:

Reducing bend erosion with a twisted tape insert:
http://www.sciencedirect.com/science...32591016304144


I hope this can help you!


References:
Ref. 4: Practical estimation of erosion damage caused by solid particle impact: Part 2: Mechanical properties of materials directly associated with erosion damage
http://www.sciencedirect.com/science...4316480500102X

I also have the following videos that might help you understand some erosion mechanisms:

Mitigating elbow erosion with a vortex chamber:
https://www.youtube.com/watch?v=gBQbwNcnZ1c

Reducing bend erosion with a twisted tape insert:
https://www.youtube.com/watch?v=QIrTjAQ8-ok

[Lubo]

Originally Posted by carlos_antonio

Dear LiamH

Thank you very much for your reply. Regarding your posts:

If you read carefully my last post you will see:

""E90 = K[(HV)^k1]*[(V_p/V')^k_2]*[(D_p/D')^k_3]" is also correct, but this equation requires a little bit more attention. The first constant K[(HV)^k1] is not that simple as it seems. If you read carefully the Oka publication (Ref. 4, page 107, equation 4) you notice that your K[(HV)^k1] is equal to K(aHv)^k1b and this function can be obtained from the curve fitting of Fig. 11 from Ref. 4 for your simulated conditions. For the case of Si02-1 and aluminum, the function obtained is K(aHv)^k1b = 81.714(Hv)^(-0.79) (see Ref. 1, equation 43 or Ref. 2, equation 14 for details)."


So, E90 is not only 84.714(Hv)^-0.79. E90 is equal to 84.714(Hv)^-0.79 * [(V_p/V')^k_2]*[(D_p/D')^k_3] and the former is obtained by curve fitting of Fig. 11 from Ref. 1. But here, you will have a problem. Fig. 11 of Ref. 1 only give the experimental results from Si02 and as you said, your target material is Tungsten Carbide which is not available from Oka's experiment. If you take a look at Fig. 11 of Ref. 1 you will see the results of Aluminum, Stainless Steel, Carbon and Cooper against Si02 particles. You can try to extrapolate to your material to obtain the "K(aHv)^k1b = ???" for your Tungsten. Constants a and b are in this curve fitting. Both papers from Oka did not show the exact values of a and b but from Fig. 11 of Ref. 1 you can obtain the exponential "K(aHv)^k1b".

If you are using the same fitting (K(aHv)^k1b = 81.714(Hv)^(-0.79)) for SiC, this probably explains such difference in your results. I recommend you to careffully read both papers from Oka to obtain such curve for your target material.

Recently I published another paper on a device called twisted tape which is used to reduce erosion in elbows. Again, we used the Oka's model for particles of Si02 hitting on Aluminum. You can find more here:

Reducing bend erosion with a twisted tape insert:
http://www.sciencedirect.com/science...32591016304144


I hope this can help you!


References:
Ref. 4: Practical estimation of erosion damage caused by solid particle impact: Part 2: Mechanical properties of materials directly associated with erosion damage
http://www.sciencedirect.com/science...4316480500102X

I also have the following videos that might help you understand some erosion mechanisms:

Mitigating elbow erosion with a vortex chamber:
https://www.youtube.com/watch?v=gBQbwNcnZ1c

Reducing bend erosion with a twisted tape insert:
https://www.youtube.com/watch?v=QIrTjAQ8-ok

Hi dear friends
I want to calculate default reference erosion value in fluent, the 0.000615 （E90）, but the problem is that Up cannot calculate.

Because the velocity（Vp） at which the particles hit the wall is different from the initial velocity (boundary condition) at which the particles just entered the fluid domain.

So I am very confused how the value of 0.00615 is calculated.

Moreover, I guess E90（Refenence Erosion Rate） in Fluent is different from that in the paper and I would like to know his formula very much.

I am looking forward to your help, thank you！

[gimson]

The E90 in terms of mm3/kg seems to be the volume loss of steel in mm3 divided by the mass of erodent. Thus to achieve the kg/kg units, we have to multiply by the density of steel 84.714*(1.8)^-0.79*(7890[kg/m3]/1000000000[mm3/m3]) this nets u around 0.000420 which is within the same order of magnitude used by Fluent's 0.000615