[Tonika]

Greetings all,

Context:

I am a student attempting to reproduce experimental results for erosion in pipe elbows caused by liquid-solid mixtures using Fluent. I am currently using the “2021 R1” version of the software and I want to reproduce the results using the “Oka” erosion model which is already available as one of the in-built models. In the process of investigating theoretical details regarding the model, I explored the formula used for the model as provided in the theory guide available by the “Help” section. The guide is for the “2021 R2’ version and the link to the page has been included as Reference 1 along with an attached screenshot for the relevant page. I also accessed the reference corresponding to the formula in the guide, which is a research article cited on the same page as “458”. The DOI for the article has been attached as Reference 3 with the relevant screenshot as well. Reference 2 has also been added, as it is the preceding “Part 1” to Reference 3 and contains relevant equation details.

Reference 1_ Fluent theory guide_link: https://ansyshelp.ansys.com/account/...46062321014024

Reference 1_Fluent theory guide_ screenshot of section 12.10.2, page number 544: Reference 1_Fluent theory guide_ screenshot of section 12.10.2, page number 544.png

Reference 2_Research article (Part 1)_DOI link: https://doi.org/10.1016/j.wear.2005.01.039

Reference 2_Research article (Part 1)_screenshot of page 2: Reference 2_Research article (Part 1)_screenshot of page 2.jpg

Reference 3_Research article (Part 2)_DOI link: https://doi.org/10.1016/j.wear.2005.01.040

Reference 3_Research article (Part 2)_screenshot of page 6: Reference 3_Research article (Part 2)_screenshot of page 6.jpg

Upon inspection of the formulas presented by the theory guide and the article, I discovered the following problems.

Problem 1:

I found a discrepancy between the formula presented by the theory guide and that presented by the cited article. To explain the discrepancy, allow me to organize the formulas, as shown below.

From research article:

Equation 1: g(alpha)=( ( sin(alpha) )^ n1 ) * ( ( 1 + Hv (1 - sin(alpha) ) ) ^ n2 )
Equation 2: E90 =( K * ( ( a* Hv ) ^ ( k1 * b ) ) ) * ( ( v / v’ ) ^ k2 ) * ( ( D / D’ ) ^ k3 )
Equation 3:E(alpha) = g(alpha) * E90
Therefore,
Equation 4:E(alpha) =( ( sin(alpha) )^ n1 ) * ( ( 1 + Hv (1 - sin(alpha) ) ) ^ n2 ) * ( K * ( ( a* Hv ) ^ ( k1 * b ) ) ) * ( ( v / v’ ) ^ k2 ) * ( ( D / D’ ) ^ k3 )

From Fluent guide:

Equation 5: f(gamma) = ( ( sin(gamma) )^ n1 ) * ( ( 1 + Hv (1 - sin(gamma) ) ) ^ n2 )
Equation 6:E = E90 * ( ( V / Vref ) ^ k2 ) ) * ( ( D / Dref ) ^ k3 ) ) * f(gamma)
Therefore,
Equation 7: E =E90 * ( ( V / Vref ) ^ k2 ) ) * ( ( D / Dref ) ^ k3 ) )* ( ( sin(gamma) )^ n1 ) * ( ( 1 + Hv (1 - sin(gamma) ) ) ^ n2 )

Where,

• alphaand gammarefer to impact angle of the particle in degrees
• E(alpha) and E refer to the erosion at an arbitrary angle
• E90refers to the erosion at 90 degrees impact angle
• Hv is the Vickers hardness in GPa of the pipe material
• n1, n2,K , k1, k2 and k3 refer to parameters related to the hardness of the pipe material and characteristics of the particle material and shape
• vand Vrefer to impact velocity of the particle
• v’ and Vrefrefer to reference impact velocity of the particle from the experiment
• D refers to the diameter of the particle
• D’ refers to the reference diameter of the particle from the experiment

We can then compare to find the common terms in the formulas presented by both the sources. The common terms are the greenterms which refer to the impact angle function, pinkterms which refer to the ratio of impact velocity to reference velocity and purpleterms which refer to the ratio of diameter of the particle to reference diameter. However, the orange term seen in the article’s formula is not found in the guide’s formula. Instead, what remains from the guide’s formula is the term E90, which refers to the “reference erosion rate at 90 degrees impact angle (that is, the wall material mass removed per mass of particles). Note that this quantity is usually derived by measurements” as stated by the guide (Reference 1). It has not been elaborated in terms of other parameters, unlike the article.

Problem 2:

The matter is further complicated by the fact that I am unable to confirm the units that Fluent uses for the Oka model.
The final unit of the derived erosion value is determined by the unit of E90 because all the other terms are dimensionless. Fluent presents the unit of E90 as kg/kg because the guide says it is "the wall material mass removed per mass of particles" and so the same unit must apply to the final erosion value E. However, in transient simulations, by default, Fluent presents erosion results with units of (Kg / m^2) regardless of what model has been selected. This raises uncertainty whether Fluent converts the units from kg/kg to (Kg / m^2) and if yes, then how.


Additional note:

If it helps to know, regardless of the above-mentioned dilemma, I had simulated the experimental setup on Fluent and analysed the results using the in-built Oka model that I have been referring to so far. The data, when plotted alongside the experimental curve, shows a considerable similarity in trend and magnitude. However, I am unable to confirm the reliability of the results due to the above explained problems. I have attached the screenshot of these results in Reference 4.

Reference 4_Comparison of experimental erosion data with CFD data based on Oka model_screenshot: Reference 4_Comparison of experimental erosion data with CFD data based on Oka model_screenshot.jpg

Summary:

I want to replicate experimental data for pipe erosion caused by liquid-solid mixture in Fluent using the in-built Oka erosion model. I have attempted to simulate it and found similarity between the CFD and experimental results. However, the formula presented by Fluent for the model in the theory guide does not match the formula presented in the referenced research article. Therefore, I am unable to judge the reliability of the results for further use in my research.
I have not found any relevant post from recent threads regarding this matter yet so, any insight will be appreciated. Thank you for your time.