## Fluids

#### Temperature divergence at mass transfer location

• andrewcaratenuto
Subscriber

I am simulating water evaporation to still ambient air using species mass transfer. It works fine without the energy equation, but I get strange temperatures when energy is enabled (I need energy on).

The whole domain is initialized at 300 K, pressure inlets/outlets have 300 K specified, and walls have 0 heat flux. Yet, as evaporation occurs, the temperatures near the location of mass transfer start to drop. It starts small, but usually builds to divergence, where I get the "Temperature limited to..." error. These low temperatures actually start to follow the vapor phase as is progresses (see images).

I could understand some evaporative cooling taking place, but I don't think that's what this is (it occurs far too fast, and shows reduced temperatures in the vapor, rather than the liquid).

Images below - Thanks in advance for any suggestions.

• Rob
Ansys Employee

Which multiphase model & phase interaction model(s) are you using?

• andrewcaratenuto
Subscriber

I'm using the Mixture model (explicit). I tried Eulerian first, but I found much more severe divergence issues with Eulerian.

I'm using the species-mass-transfer model for mass transfer. The from-phase and to-phase mass transfer coefficients are both calculated using the ranz-marshall correlation.

Some more info about my model, if needed: realizable k-e, timesteps ~1e-2 - 1e-3, domain is 1m x 1m with uniform 5mm mesh resolution. I've attempted lower timesteps and finer mesh, but it didn't seem to help.

• Rob
Ansys Employee

Is the domain sealed? If you run for a short period before it fails how do the flow and temperature fields look?

• andrewcaratenuto
Subscriber

The top 3 sides are pressure inlets/oulets with 0 gauge pressure specified, and the bottom 3 are all walls. Like a simplified model for a cup of water surrounded by dry air. I've added images of velocity magnitude, temperature, mesh, and steam concentration after 7 s of flowtime below.

The flow and steam concentration after a short time look reasonable. The temperatures maybe aren't diverging so fast, but they are lower in the vapor region where they shouldn't be. The liquid water should be cooling due to evaporation, not the steam.

I also found that it's probably related to enthalpy transfer from phase change. Modifying the standard state enthalpy of the water materials changes the temperature drops accordingly (delta H higher = more T drop in vapor, and vice versa). While I expect to see the effects of evaporative cooling, I feel the trend is opposite what it's supposed to be - steam should not be cooling due to evaporation, the liquid water should be. I'm not sure why it would be reversed like this.

• Rob
Ansys Employee

Odd. Multiphase, multispecies models are usually relatively stable, or fail for a good reason. How is the mass transfer set up?

• andrewcaratenuto
Subscriber

Thanks for your reply, I've attached some pictures of the mass transfer model here. It's species-mass-transfer, constant sat. pressure, both with Ranz-marshall correlation. ia-symmetric is used for interfacial area. "Liquid" contains a mixture just with liquid water in it, and "air-vapor" has a mixture of water vapor and air.

One other behavior I noticed - when I flipped the sign of the standard state enthalpy difference to be negative, temperatures rose in the vapor region instead of falling, with the same magnitude and profile shown above. I suppose a more relevant question might not be about temperature divergence, but more so why the temperature changes are occurring in the vapor phase instead of the liquid phase.

• andrewcaratenuto
Subscriber

Aha, found something else - I'd assumed that only the difference in standard state enthalpy between liquid and vapor matters, so I set water-liquid as 0 and water-vapor as 4.39 E+7 J/kgmol. However, when I revert them back to their default Fluent values (vapor = -2.418 E+8, liquid = -2.858 E+8), the steam becomes hotter, and the liquid becomes cooler - see image below.

This definitely resolves why I was not seeing evaporative cooling. However, I still don't believe the steam should be heating up - shouldn't it have the same temperature as the liquid, as all energy input is used to overcome the vaporization enthalpy?

• Rob
Ansys Employee

Couple of points.

The difference in the formation enthalpy is the latent heat: you add heat to vapourise so get the sign right.  So, water-liquid can be set as zero and vapour then has a value or vice versa. The formation enthalpy in the materials panel also accounts for the chemical energy incase you want to burn the phase too.

What's the specific heat capacity of gas relative to water?

• andrewcaratenuto
Subscriber

Thanks Rob.

I had been using a constant specific heat for the vapor mixture (1100 J/kg K) as a first approximation, which yielded the temp. distribution in my last reply. The liquid water mixture has a constant Cp of 4182 J/kg K.

I just tried switching both mixtures' Cps to "mixing law" after your reply, with water vapor at 2014 J/kg K, air at 1006 J/kg K, and liquid water at 4182 J/kg K. With these settings, only the steam cools, and the liquid water experiences no temperature change. I added a graph of the mass-average temperatures below (Fluid 1 is the bottom air region, Fluid 2 is the top vapor region).

Modifying the standard state enthalpies as you said (water-liquid = 0, vapor = 4.39e+7, and vice versa) does yield the same results, as you mentioned.

It seems to me that the cooling behavior from evaporation is still opposite what it should be

• Rob
Ansys Employee

If the water cp is four times that of vapour and the density is roughly 800 times higher. For every 0.01C change in the air temperature how much would you expect the liquid to change by?

• andrewcaratenuto
Subscriber

Right, I know that based on these properties the air-vapor region will change temperature much faster than the liquid in response to a heat source/sink.

But shouldn't the evaporation process be adding latent heat to the vapor region via the enthalpy change, not sensible heat? The increase in enthalpy in the vapor region should not manifest as a temperature change, because it's consumed in the phase change process.

On top of this, the vapor region is going down in temperature, even though its enthalpy is increasing, which seems incorrect. The liquid region also does not show temperature change even though it's losing enthalpy.

• Rob
Ansys Employee

The temperature will drop as evaporation occurs: but look at the scale of change in your results.

• andrewcaratenuto
Subscriber

Ah right! Okay, I think I understand now - the liquid water experiences a temperature drop right at the interface, but the vapor temperature will also drop at the interface from heat transfer. And since the vapor has a much higher thermal diffusivity, we see it spreading much more in the vapor region than the liquid region.

I generated some new plots (below) and i think it confirms. Thank you very much for helping me understand this!

Liquid temp:

Interface temp:

One last question I do have though - an enthalpy plot shows that the air has an enthalpy of ~1,860. The air's standard state enthalpy is 0, and the reference value for the case is also 0. Shouldn't air's enthalpy be 0?

• Rob
Ansys Employee

Pretty much, the m.cp for water is also a lot higher so for a given amount of energy the dT is much lower than in the gas.

Check the temperature for the enthalpy value - if you're some degrees away from reference that's also reported.

• andrewcaratenuto
Subscriber

Got it, I'll take a look. I think my questions are basically resolved at this point.

Thank you again for all your support Rob! Really appreciate your help.