OpenFOAM's Energy Equation 'h' Form: Replacing 'Fourie' with Gradient of 'hk/cp'

ztdep · January 27, 2024, 21:01

In the "h" form of the energy equation, OpenFOAM has replaced the "Fourier Law" with the gradient of "h" multiplied with "k/cp". I want to know what kind of assumptions should be satisfied to validate this. I think Cp must be a constant value, but in reality , most fluids don't satisfy this condition.

fvm::laplacian(turbulence->alphaEff(), he)

$\frac{\partial h}{\partial x} = \frac{\partial h}{\partial T} \frac{\partial T}{\partial x} = C_p \frac{\partial T}{\partial x}$

Tobermory · January 29, 2024, 10:09

No - I don't believe so. You have written out the chain rule which demonstrates that grad T can be replaced with grad h divided by Cp ... there is no need for Cp to be constant. However, note that:

$C_p \equiv (\frac{\partial h}{\partial T})_p$

and this provides you your assumption ... the equivalence holds for constant pressure, which is generally acceptable for many flows but may prove problematic for strongly compressible flows.

January 27, 2024, 21:01	OpenFOAM's Energy Equation 'h' Form: Replacing 'Fourie' with Gradient of 'hk/cp'	#1
ztdep Senior Member p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19	In the "h" form of the energy equation, OpenFOAM has replaced the "Fourier Law" with the gradient of "h" multiplied with "k/cp". I want to know what kind of assumptions should be satisfied to validate this. I think Cp must be a constant value, but in reality , most fluids don't satisfy this condition. fvm::laplacian(turbulence->alphaEff(), he) $\frac{\partial h}{\partial x} = \frac{\partial h}{\partial T} \frac{\partial T}{\partial x} = C_p \frac{\partial T}{\partial x}$

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Regarding the energy equation(Internal energy equation) in the sonicFoam solver.	applekiller	OpenFOAM Programming & Development	4	May 16, 2023 10:52
Turbulence dissipation vs Viscous dissipation	granzer	Main CFD Forum	18	January 10, 2022 01:27
OpenFOAM Training Jan-Jul 2017, Virtual, London, Houston, Berlin	CFDFoundation	OpenFOAM Announcements from Other Sources	0	January 4, 2017 07:15
OpenFOAM v3.0+ ??	SBusch	OpenFOAM	22	December 26, 2016 15:24
Calculation of the Governing Equations	Mihail	CFX	7	September 7, 2014 07:27

January 29, 2024, 10:09		#2
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 747 Rep Power: 14	No - I don't believe so. You have written out the chain rule which demonstrates that grad T can be replaced with grad h divided by Cp ... there is no need for Cp to be constant. However, note that: $C_p \equiv (\frac{\partial h}{\partial T})_p$ and this provides you your assumption ... the equivalence holds for constant pressure, which is generally acceptable for many flows but may prove problematic for strongly compressible flows.