Question about One-dimensional energy equation

[Wayne Shen]

Dear, I have a question about One-dimensional energy equation in  https://cantera.org/stable/reference/onedim/governing-equations.html

Imagine the case that a part of O atoms diffuse from one CSTR to anthor CSTR, and they recombine in the current CSTR, does the energy of O atoms count twice by diffusion term j_kh_k and chemical reaction term h_kW_k\omega_k?  

Best,

Wayne

[吳昀叡]

I’m just curious that why the species diffusion flux term is involved in a homogeneous reactor like CSTR? In fact I think multiple connection of CSTRs can be interpreted by m_dot term. 

Wayne Shen <meled...@gmail.com>於 2025年4月22日 週二，下午3:26寫道：

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[Steven DeCaluwe]

Hi Wayne,

The omega_dot term for O would be negative, in that case, I believe, so no, it would not be double counted.

Cheers,

Steven

On Apr 22, 2025, at 1:26 AM, Wayne Shen <meled...@gmail.com> wrote:

Dear, I have a question about One-dimensional energy equation in  https://cantera.org/stable/reference/onedim/governing-equations.html

Imagine the case that a part of O atoms diffuse from one CSTR to anthor CSTR, and they recombine in the current CSTR, does the energy of O atoms count twice by diffusion term j_kh_k and chemical reaction term h_kW_k\omega_k? <Screenshot 2025-04-22 092516.png> 

Best,

Wayne

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<Screenshot 2025-04-22 092516.png>

[Steven DeCaluwe]

Hi, for what it’s worth, the page linked in Wayne’s post was to the documentation for a one-dimensional flow (in this case an axisymmetric stagnation flow).  

The energy equation for a constant volume reactor  is given as:

Oddly, I’ll note that the documentation for a constant pressure reactor appears to have no reaction term at all.  Am I missing something, or does this need to be fixed?

Thanks,

Steven

On Apr 22, 2025, at 6:02 AM, 吳昀叡 <d355...@gmail.com> wrote:

I’m just curious that why the species diffusion flux term is involved in a homogeneous reactor like CSTR? In fact I think multiple connection of CSTRs can be interpreted by m_dot term. 

Wayne Shen <meled...@gmail.com>於 2025年4月22日 週二，下午3:26寫道：

Dear, I have a question about One-dimensional energy equation in  https://cantera.org/stable/reference/onedim/governing-equations.html

Imagine the case that a part of O atoms diffuse from one CSTR to anthor CSTR, and they recombine in the current CSTR, does the energy of O atoms count twice by diffusion term j_kh_k and chemical reaction term h_kW_k\omega_k? <Screenshot 2025-04-22 092516.png> 

Best,

Wayne

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[Ray Speth]

Hi all,

In regards to Wayne's original question about the 1D energy equation: The two terms in question are quite different. As noted, the first term is about diffusion: If you expand the derivative in the case of an ideal gas as dhk/dz = cpk dT/dz, you can see that this term is about the diffusion of sensible enthalpy in cases where species have different heat capacities. The second term is the reaction term, and deals with the enthalpy of reaction. So no, there is no double counting.

In regards to the reactor governing equations that Steven brought up: There is a distinction between the equations used for the generic reactor types like "ConstPressureReactor" which can handle any equation of state and the specializations for ideal gases like "IdealGasReactor". In the former case, the energy equation is written with the total enthalpy (or internal energy) as the state variable. In this case, chemical reactions do not contribute to a change in the total enthalpy, and so there is no reaction-related term in the energy equation. However, when setting the state based on that enthalpy with a changing composition, the temperature will also change.

In the case of the ideal gas reactors, the expression for dH/dt has been expanded so that the temperature appears, which also introduces terms for the rate of change of the species.

Regards,

Ray