[dlahaye]

Dear reader,

We are looking into the application of ConvergeCFD to the bluff body stabilized flame referred to as HM1. This is a well-known test case of the TNF workshop.

Results are published by Di Mauro e.a. in 2021. The paper can be found at the dropbox link*http://www.dropbox.com/s/9qmm3uln9jb...et-al.pdf?dl=0

The paper and the ConvergeCFD manual do not suffice to fully understand the model equations being used by ConvergeCFD. We in particular have the following two sets of questions.

(1/2) Unsteady Flamelet Generated Manifold (FGM) Model at Non-Unit Lewis Number (differential diffusion) in ConvergeCFD

The HM1 test case is a turbulent premixed test cases that uses as fuel a mixture of 50 percent hydrogen and 50 percent methane (50/50 methane/hydrogen). We thus assume that an unsteady flamelet computation at non-unit Lewis number is indispensable to capture the full complexity of the test case.

Di Mauro e.a., however, presents in Equation 4 (on page 5 of the article) a steady flamelet formulation. Such steady flamelets do not provide data on the range of low progress variable (low CO2, low T). Zones with low progress variable values are present in the HM1 test case. ConvergeCFD has an unsteady flamelets RIF formulation. This formulation, however, seems to be restricted to unit Lewis number.

Our question is thus how to set up a unsteady FGM model at non-unit Lewis number is ConvergeCFD. Does ConvergeCFD provide an extension of RIF for non-unit Lewis number or a formulation that solves the flamelets in physical space? In the latter case, unequal diffusivities can easily be kept.

(2/2) Missing Terms in the Transport Equations for Progress Variable to Account for Strong Gradients in Mixture Fraction at Bluff Body Edges

The HM1 test case is a bluff-body stabilized test case. At the edges of the bluff-body there are strong gradients in mixture fraction. These gradients ought to be taken into account in the modeling procedure.

In the ConvergeCFD manual, Equation 12.40 defines the mixture fraction. In this definition, the linear combination of species mass fraction is normalized by the linear combination of equilibrium values. Equation 12.43 in the same manual is the transport equation for the scaled progress variable. In the case that the equilibrium values depend on the mixture fraction, the equation 12.43 is not correct. Some terms containing spatial gradients of mixture fraction should be added.

The introduction of unscaled progress variable and scaled progress variable and the combined use of them in a lookup procedure (laminar case) are clearly explained in the TU Eindhoven PhD thesis of Giel Ramaekers (in Section*2.3 FGM construction for partially-premixed applications). The relations between mean and variance of unscaled and scaled progress variable are explained in the Appendix B of the MSc thesis of Myra Nelissen http://resolver.tudelft.nl/uuid:45cd...d-3a7e79318dc4
The treatment in that Appendix is not the most general one. But it it should* be sufficient to illustrate the point. The most general case is elaborated in the PhD thesis of Marco Derksen at University*Twente http://ris.utwente.nl/ws/portalfiles...is_Derksen.pdf

Our question is thus how to account for strong gradients in mixture fraction in the transport equation for the progress variable when using ConvergeCFD.

Thanks in advance for sharing your insights.

[Xiao Ren]

Hi Domenico,


Could you send your detailed request to support@convergecfd.com (US); supportEU@convergecfd.com (EU) or support.in@convergecfd.com (India)? If you have other materials like case setup and references, please also share them in your email. Our support team take a look for those details.



Best,

[dlahaye]

Dear Xiao, Thank you. I did send email to support. Kind wishes, Domenico.

[dlahaye]

Dear reader,

We extended our previous discussion taking into account recent insights.

We are looking into the application of ConvergeCFD to the bluff body stabilized flame referred to as HM1. This is a well-known test case of the TNF workshop.

Results are published by Di Mauro e.a. in 2021. The paper can be found at the dropbox link http://www.dropbox.com/s/9qmm3uln9jb...et-al.pdf?dl=0.

The paper and the ConvergeCFD manual do not suffice to fully understand the model equations being used by ConvergeCFD. We in particular have the following two sets of questions.

(1/3) Unsteady Flamelet Generated Manifold (FGM) Model at Non-Unit Lewis Number (differential diffusion) in ConvergeCFD

The HM1 test case is a turbulent non-premixed test cases that uses as fuel a mixture of 50 percent hydrogen and 50 percent methane (50/50 methane/hydrogen). We thus assume that an unsteady flamelet computation at non-unit Lewis number is indispensable to capture the full complexity of the test case.

Di Mauro e.a., however, presents in Equation 4 (on page 5 of the article) a steady flamelet formulation. Such steady flamelets do not provide data on the range of low progress variable (low CO2, low T). Zones with low progress variable values are present in the HM1 test case. ConvergeCFD has an unsteady flamelets RIF formulation. This formulation, however, seems to be restricted to unit Lewis number.

Our question is thus how to set up a unsteady FGM model at non-unit Lewis number is ConvergeCFD. Does ConvergeCFD provide an extension of RIF for non-unit Lewis number or a formulation that solves the flamelets in physical space? In the latter case, unequal diffusivities can easily be kept.

(2/3) Missing Terms in the Transport Equations for Progress Variable to Account for Strong Gradients at Bluff Body Edges

The HM1 test case is a bluff-body stabilized test case. At the edges of the bluff-body there are strong gradients in mixture fraction. These gradients ought to be taken into account in the modeling procedure.

In the ConvergeCFD manual, Equation 12.40 defines the mixture fraction. In this definition, the linear combination of species mass fraction is normalized by the linear combination of equilibrium values. Equation 12.43 in the same manual is the transport equation for the scaled progress variable. In the case that the equilibrium values depend on the mixture fraction, the equation 12.43 is not correct. Some terms containing spatial gradients of mixture fraction should be added.

The introduction of unscaled progress variable and scaled progress variable and the combined use of them in a lookup procedure (laminar case) are clearly explained in the TU Eindhoven PhD thesis of Giel Ramaekers (in Section 2.3 FGM construction for partially-premixed applications). The relations between mean and variance of unscaled and scaled progress variable are explained in the Appendix B of the MSc thesis of Myra Nelissen (http://resolver.tudelft.nl/uuid:45cd...d-3a7e79318dc4). The treatment in that Appendix is not the most general one. But it should be sufficient to illustrate the point. The most general case is elaborated in the PhD thesis of Marco Derksen at University Twente (http://ris.utwente.nl/ws/portalfiles...is_Derksen.pdf).

The strong gradients in mixture fraction close to the bluff body can be partially accounted for by the variance of mixture fraction (ZVAR).

Our question is thus how to account for strong gradients in mixture fraction in the transport equation for the progress variable when using ConvergeCFD.

(3/3) Use of standard and enhanced wall functions

Question: The reason to use both standard and enhance wall functions on the same grid is not clear in DiMauro2021. The results are not really consistent. Standard wall functions give somewhat better velocity field. The enhanced wall function gives better temperature field. This discussion on wall treatment should have been elaborated with information on y+. The suggestion to choose a different model constant Cε1 in the two wall treatment is ad hoc because the term containing this model constant is controlling phenomena far from the wall. One model constant cannot be tuned to optimize predictions both far away and close to the wall.

Partial answer: The main reason for tuning ce1 turbulence constant in this case is that the k-e models are known to wrongly predict the centerline velocity decay of jet flows. So the value chosen is probably done to ensure that the correct velocity profile for the jet is captured.