# Replace the rho(T,P) with rho(h,P) method.

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 June 5, 2022, 11:50 Replace the rho(T,P) with rho(h,P) method. #1 New Member   Zhiyuan Liu Join Date: Oct 2018 Location: China Posts: 26 Rep Power: 7 By default, RGP file of CFX uses temperature and pressure as the EoS basic variables to calculate enthalpy and entropy. However, the calculation result of the energy equation is indeed enthalpy. This is unfavorable to the accuracy and robustness of the calculation. Is there any possibility of replacing the rho(T,P) with rho(h,P) method. I found that Fluent could replace the temperature-based energy equation with an enthalpy-based formulation. Moreover, density, viscosity, diffusion coefficient etc.. could be expressed as functions of pressure and specific enthalpy.

June 6, 2022, 09:36
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Quote:
 Originally Posted by Saeef By default, RGP file of CFX uses temperature and pressure as the EoS basic variables to calculate enthalpy and entropy. However, the calculation result of the energy equation is indeed enthalpy. This is unfavorable to the accuracy and robustness of the calculation.

In the general CFD literature, the most common solution variable for the compressible (ideal and real gas) form of the energy equation is Total Enthalpy. It is not Temperature, nor Static Enthalpy.
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June 6, 2022, 21:44
#3
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Zhiyuan Liu
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Quote:
 Originally Posted by Opaque May I ask what is the source of such conclusions? Is there a paper or reference which I can read about this? In the general CFD literature, the most common solution variable for the compressible (ideal and real gas) form of the energy equation is Total Enthalpy. It is not Temperature, nor Static Enthalpy.
reference:Evaporation in supersonic CO2 ejectors: analysis of theoretical and numerical models

Based on the mass/momentum/energy equations, CFX can obtain local velocity/pressure/enthalpy (h_tot-V^2/2).

However, CFX needs to first calculate h (T, P) and s (T, P) according to EoS rho (T, P) + Cp (T, P), and then obtain T= (h, P), rho (h, P) and s (h, P).

This means that CFX needs to perform a reverse lookup on the physical property table, which may lead to deviations in physical properties. Especially when the physical properties are sensitive to temperature and pressure.

 June 7, 2022, 09:55 #4 Senior Member   Join Date: Jun 2009 Posts: 1,775 Rep Power: 31 I see what you are referring to; however, there is confusion on where the errors are coming from. Let us assume the thermodynamic state is analytical and non-linear, i.e. no table lookup. That means we can compute the sequence you describe - calculate h (T, P) and s (T, P) - according to EoS rho (T, P) and Cp (T, P), - and then obtain T= (h, P) exactly. Corrrect? A root-finder must be used since the equations are likely non-linear (say Newton method). The above proves there is no need for an alternative formulation. The source of error is not in the formulation but in the quality of how obtain the remaining thermodynamic quantities. When CFX uses property tables, there is an inherent assumption that some error is introduced, and that error comes in from the creation of those tables. If you want to reduce the error, you generate better tables. The formulation is correct already. If you change the formulation, you still have to do a reverse lookup, either analytical or via numerical interpolation. You will be moving the "concern" to another variable, but fixing nothing. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

 June 8, 2022, 18:28 #5 Senior Member   Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 1,161 Rep Power: 23 Any general advice on "Generating better tables"? More data points? But can you make them too large where truncation with too fine of points becomes a problem?

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