 ## Fluids

#### Model description for heat transfer coefficient between the two phases with thermal phase change

• khbang1958
Subscriber

Hi.

My question seems regarding one of the basic physics in interfacial heat transfer, but somehow I can not find a description of mathematical model in Fluent documents such as Fluent Theory or Model.

The right hand side of multiphase energy equations (Euler) contains the term of convective heat transfer between the phases, H _pq (T_p - T_q). Also if thermal phase change is involved, the term (phase change rate) * enthalpy of p.

Here, I am concerned with the model for H_pq when there is thermal phase change.

If there is no phase change, it is simple such as two-resistance model between the phases. But when there is phase change, the two-resistance model is no longer valid, I think, because of phase change at the interface. In this case, how is the H_pq modelled? I can not find any comments on this in any of Fluid documents. The documents have descriptions for only the case of no phase change.

Can anyone give me a clue or guide to this matter?

Kwan.

• Karthik R
Hello:
It gets added as a source term when you invoke mass transfer.
14.7.1. Source Terms due to Mass Transfer (ansys.com)
I hope this helps.
Karthik
• Karthik R
Hello:
Regarding your comment, I'm not sure I'm able to follow the term you have highlighted. If you are referring to Equation 14-179 (energy equation in Eulerian model), h_pq is referring to enthalpy and not heat transfer coefficient.
14.5.4. Conservation Equations (ansys.com)
If I'm not addressing the correct question, you could please take a screenshot of the equation you are referring to and add it to this post and I'll help you.
Thank you.
Karthik
• khbang1958
Subscriber The above is a screen shot of the energy equation for Euler multiphase model (Ansys v. 2019)
I marked a red circle on Q_pq, which is heat transfer between phase p and q.
Q_pq can be written as a form like Q_pq = H_pq * (T_p -T_q). It is given in the Theory doc., but I can not locate it at the moment.
Here H_pq is overall heat transfer coefficient between p and q phases.
Without mass transfer, H_pq can be simply defined by two-resistance model.
With mass transfer, however, the phase change rate can be determined by the net heat transfer rate to the interface of p and q.
And H_pq must be defined with consideration of mass transfer at the interface.
My question was that the Fluent manual does not provide the expression for H_pq for the case of mass transfer.

Thank you very much for your kind support and hope to hear more from you.
• khbang1958
Subscriber
Referring to Fluent Theory Guide (2019 version), the formulation of two-resistance model is given only for no mass transfer case (Eqs. 18.354, 18.355).
Then follow-up model in the next page introduces "fixed-to-sat-temp" model.
In this model, the temperature of the phase to which mass is added is set equal to saturation temperature.
For example, T_v = T_sat when evaporation, and T_l = T_sat when condensation.
If you do these assumption, the conservation of energy is violated because the temperature is forced to set to saturation temperature without proper calculation of energy.
I am curious in what kind of problems the fixed-to-sat-temp model can be a good approximation.
• Rob
Ansys Employee
• khbang1958
Subscriber
Dear Rob:
Thank you very much for your advise. I looked at the recent Fluent Theory Guide of 2022/R1, but still the answer to my question is up air.
Let me please summarize my question based on the 2022/R1 Theory Guide.
My task is that I have a pool containing a mixture of 120C liquid and 110C steam at 1 atmospheric pressure (T_sat = 100C).
I want to calculate transient behavior of this pool using Fluent's Eulerian multiphase flow model. The energy equation is Here, my question is what is the model for Q_pq (red circle) when mass transfer is modelled.
In the 14.5.17 Description of Heat Transfer, the Q_pq is defined as I chose thermal phase change model. So I must select two-resistance model for h_l and h_v for heat transfer to work with thermal phase change model.
Now I am interested in how h_pq is calculated in this case. The Theory Guide only tells the case for no mass transfer as below. My question is how to model h_pq when there is mass transfer.
Thank you.

• Rob
Ansys Employee
I can't discuss beyond what's written in the documentation as the Forum is considered to be public domain, but looking at the wording I wonder if it's dealing with the heat transfer between phases ONLY. Ie it's separate from when mass transfer occurs. All the other options are for a HTC, with no reference to any mass transfer.
• DrAmine
Ansys Employee
If thermal phase change is used heat transfer and mass transfer are coupled and in balance. Same heat transfer correlations still apply.
• khbang1958
Subscriber
Thank you for the comments. Let me take a simple example with a hope to clarify my question.
If I have a mixture of 120C water and 90C steam (metastable) at one atmospheric pressure, the heat transfers from liquid to interface (100C) and also from interface to steam.
(I think the Eulerian multiphase model should allow the metastable state of any phase.)
If I choose two-resistance model and thermal phase change model, the evaporation rate is computed by the net energy (heat from liquid to interface minus heat from interface to steam).
Then, what should be the heat transfer coefficient "between the liquid and vapor," h_pq, which is included in the energy equation of Eulerian model?
I think the zero-resistance of one phase or fixted-to-sat-temp model can be an option but it violates energy conservation because it forces to set the phase temperature to saturation temperature.
As Rob said, if my question is beyond the matter that can be discussed in this public domain, I will stop, but hope to continue to exchange comments on this matter in alternative way if possible.
Thank you.
• DrAmine
Ansys Employee
h_pq is the overall heat transfer coefficient which is not used if you are using thermal phase change model / two-resistance model.
• khbang1958
Subscriber
Thank you very much for your comment.
That is true if the heat flows toward the interface from both phases (evaporation) or out of the interface to both phases (condensation)
But if heat flows from one phase to the interface and also from the interface to the other phase, the net heat at the interface is used for phase change
and the convective heat from the interface to colder phase is not zero, thus h_pq is not zero, but must be some value.
My question is what is the expression for h_pq in this case.
Thank you.
• khbang1958
Subscriber
This could be an example for what I said in the previous message.
I have water drops of 80 C in 120 C steam in atmospheric pressure. Heat flows from steam to water droplets and evaporation or condensation occurs depending on the net energy at the interface. If I want to use Eulerian model and thermal phase change model, which heat transfer option in the two-resistance model should I choose for each phase?
Thank you.
• DrAmine
Ansys Employee
I wrote it is not used I didn't write that it's zero
• DrAmine
Ansys Employee
Typically you will assume less resistance on the diserpsed side . In your scenario as it seems you cannot assume droplets to be at saturated conditions you might assume a constant small nusselt number or use same resistance formulation as on the steam side.
• khbang1958
Subscriber
Now let's say I choose h_p for p phase and h_q for q phase as you suggested.
Then what is the expression for h_pq, which appears in the energy equation.
As you know, 1/h_pq = 1/h_p + 1/h_q is valid only for no mass transfer.
You mentioned earlier that h_pq is not used, but I think it should be defined if T_p, T_q, T_sat are different each other.
Thank you.
• DrAmine
Ansys Employee
Sometimes writing documentations one should stick to very general/multipurpose formulation is not always simple to fulfil all model variants.
For every phase energy Equation we have a Q_alpha which is the heat transfer to that phase. That Q_alpha is equal to Gamma*Latent_Heat+h_alpha(T_alpha-T_sat) when using Thermal Phase Change Model.
• khbang1958
Subscriber
Thank you very much for the comment. I guess this is what I have been looking for.
My original question arose when I was wondering about the expression of h_pq in case of phase change.
Sometimes it is easier way to write h_p*(T_p - T_sat) instead of h_pq*(T_p - T_q) when thermal phase change must be considered.
But the solution procedure could be quite different because the earlier has only one unknown T_p in the source term part, but the later has two unknown, T_p and T_q.
I think I get the answer so I will stop hear.
• DrAmine 