Brent Cullimore

It might be apparent by now that I get bothered by silly or strange things. But what’s the point of even having a pet peeve if you can’t enjoy it?

Thermally stratified tanks bother me.  Fill a tank partially full of cryogenic liquid, leave it alone for a few hours … maybe even days. Even with great insulation, you’ll have a heat leak into the tank. The liquid will boil at the wall perhaps, and may also vaporize at the surface. The pressure will build slowly.

Why does this bother me? Because this scenario seems so simple compared to all the other wild thermal/fluid problems I have dealt with. After all, the fluid just sits there, doesn’t it? Yet this situation defies modern simulation methods. You will have a hard time even predicting the pressure inside the tank, which means it is hard to predict how many hours or days it will be until a vent valve opens, or how that venting affects the tank contents, or how much cryogen you’ll lose while you wait for a need to drain the tank.

Who even lets cryogens sit around like this? People storing liquefied gases (including LNG) while waiting for their ship (or train) to come in. People filling rocket fuel and oxidizer tanks and topping them off while waiting for their launch window to open. People who fill dewars with liquid helium to cool MRI magnets (so that when I’m told that I should have my head examined, I know just where to go).

You might wonder why this is even an issue. For cryostats and dewars, isn’t the heat leak pretty insensitive to the temperature inside, so that you can just estimate the average boil-off rate using a first-order closed-form back-of-the-envelope front-of-the-bar-napkin calculation?

Sure, but that is only good for preliminary sizing. Complex flow patterns form inside the tank. Here are a few cartoons of the highly-simplified patterns that can occur. (You’ll just have to imagine the increased complexity due to domes, anti-slosh or anti-swirl baffles, internal structures, isogrids or orthogrids on the straight sections of the walls, and so forth.)

Mostly-vertical temperature gradients will form in both the liquid and vapor (ullage, perhaps with pressurant gases) portions of the tank. This is why it is called a “stratified tank” in the first place.

Stratification makes it hard to predict the liquid surface temperature, which is what is needed to estimate the saturation pressure. A tank with enough pressure will suppress nucleate boiling in the liquid phase as that portion of the tank subcools. (That phrasing makes it sound like it is cooling down, when in fact it is really pressurizing faster than it is warming up.) The ullage will superheat, which can mean it is condensing in the cold section of the wall near the liquid. And that superheat just ruined your first-order heat leak calculation, BTW. It is also is creating gradients within the structures that carry heat to the liquid.

The kicker is that the degree of stratification itself is something you need to determine, not just the pressure and boil-off rate. Why would you care? Well, if you are pulling out the liquid using the pump end of a high-speed turbopump, the degree of subcooling (related to the NPSH) that is arriving at your pump’s inducer can mean the difference between succeeding and failing.

If you are a salesperson for a CFD program, you haven’t read this far. You’ve already decided that your program can do this, so you stopped reading because surely I’m an ignorant crank. Or a git, depending on which country you are from. If you’re right, please educate me. I could use a good gob-smacking, and you’re just the salesperson to do it!

But I’m not worried about getting any calls (or smacks), because you didn’t read this far, remember? Sheesh, keep up!

OK, you can mesh the bejesus out of the ribs and baffles and the fluid cells near those, and you can exploit your latest VOF improvement or your other free-surface tracking technology, and you can turn on all the two-phase physics, complete with phase change in all the right places (don’t forget diffusion-blocked condensation!). Hopefully you can get away with axisymmetry, and hopefully you have a spare cluster that is being underutilized for a week or two, because you have to run a transient for days of real time with simulations of discrete venting events. Then do it a few more times to characterize uncertainties, OK? Oh, and sometimes the tanks move around if they're on a ship, train, or truck.

The thermal event is arduously slow, so even calling it an ‘event’ is a stretch. But you can’t do a good job without resolving all the slow-moving and often unstable natural convection motions, usually augmented by a little nucleate boiling at the wall, especially near the liquid surface.

I’m not dissing CFD codes. They will be the ultimate solution, after all. Someday in the future my gob will get a well-deserved smacking, and I will welcome that day. We’re just not there yet; my face is safe for the foreseeable future.

How do I know? Because people keep coming to us asking for help modeling thermally stratified cryogenic vessels, even though I’m not thrilled with the progress we’ve made so far in our 3D-thermal plus less-than-3D fluid world.

What progress and I talking about? Some “bring-your-own boundary layer and mixing estimate” methods that apply to pancake-stacked control volumes. Some “bulk-ullage meets bulk-liquid” Compartments (see fuel tanks, or LNG rail cars) that include orientation factors for localized augmentation and degradation of heat transfer (for example, plumes  near the bottom). Pretty good for pressure estimates. Not so much for predicting the temperature profiles of the out-flowing liquid.

We’re still working madly to improve the state-of-the-art in stratified tank modeling, and are currently chasing down various strategies. While the salesperson gave up reading long ago, if you are a researcher who understands the difficulty of this problem, and you’d like to work together on this, please contact us.

I’d love nothing more than to shed this pet peeve, so I can move on to the next one.

For an update (August 2019), see A Compartment and a Pipe walk into a bar ...