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Minimum Fluid Depth/Slug Flow Two-Phase Steam

Minimum Fluid Depth/Slug Flow Two-Phase Steam

At what depth does the fluid level in a pipe produce waves resulting in slug flow?  It seems to me that a thin film of fluid on the bottom of a pipe can not result in wave formation.  But for a given high velocity at some point there is enough fluid (liquid hold-up, void fraction) to produce a "dangerous wave".  Can a fluid depth of 1/4 inch produce a wave higher that twice that depth?  Does the fluid depth, need to approach 1/2 the pipe diameter for slug flow to be a possibility?

Example 1:  Steam distribution pipeline, 12 inch S40 pipe, with 125 psig saturated steam, good quality (above 90%), pipe sloped 1" in 20 ft down in the direction of flow (co-current two-phase flow), drips spaced every 500 ft (on the long side, but not uncommon), during warm-up the condensate rate is about 4.1 gpm (~60 fpm) at the dripleg, the condensate depth is about 1/2 inch, the steam flow is near maximum and at 12-15,000 fpm velocity.  At running load about 0.08 gpm (17 fpm) and condensate depth of 3/32 inch.

Will slug flow be a possibility?  What height waves could be generated?  Will the outcome be some small waves which crest and disperse more moisture into the steam?

Example 2:  Same as above, but now the slope is up in the direction of flow and we have counter-current flow.  What happens in terms of slugging, waves, moisure level?

My understanding is that the flow regime is not annular given the low fluid volume and the relatively low velocity for multiphase flow.  So, we are probably dealing with stratified smooth, stratified wavy, slug, and dispersed regimes and transitions.

I've been chewing on these nuts for a while, and would like to get them as digested as possible...

RE: Minimum Fluid Depth/Slug Flow Two-Phase Steam

A real understanding of two phase flow needs a lot of partial differential equations which make my brain hurt.
Do search for Aziz and Govier on the web.
My limited knowledge of this suggests that the vapor velocity (200 fps +) is much too high to even think about slug flow and that the friction will generate vapor borne droplets in the mist flow region.  The liquid you collect is also probably traveling with the vapor flow in both of your cases.
Even in a vertical pipe, once the vapor velocity exceeds (say 80 fps) my information says that everything is going upwards.
I don't pretent to be an expert in this but I do have a couple of text book graphics which I could make into pdf form if you're interested.
email me at

RE: Minimum Fluid Depth/Slug Flow Two-Phase Steam

He he he.  The answer to your question could take up pages.  And pages.  And pages . . .

The two-minute answer is - the prediction of flow regime for horizontal flow (slug vs. wavy in your first example) depends on whose model you use: Taitel-Dukler, Chien, Baker, Mukherjee-Brill, etc.  Most folks in the two-phase steam flow business use Mukherjee-Brill as a first approximation; however, the usual software used for this type of work (Pipephase) uses Taitel-Dukler.  This is not a trivial question, as you have discovered, and if you design right on the edge of the transitional region between flow regimes, in practice you do not know what you will get.  For design purposes, it is best to design well away from the suspected slug region, if at all possible.  If you can't, then beef up your pipe supports.

In example 2, you do not know a priori if you have countercurrnet flow unless you have some other way of determing it (mass balance, for example, from liquid removed in traps vs. the balance coming out of the spearator overhead downstrea, for example).

I have the Lockhart-Martinelli (air-water) method programmed into a spreadsheet if you want it (  You use this one with the oft-published Baker plot.  Use at your own risk...

I will run your case in Pipephase and see what we get.  Who sez you don't get something for nuthin'?!?!?!


RE: Minimum Fluid Depth/Slug Flow Two-Phase Steam

Flareman -

I would prefer to avoid the diffy q's, partial or otherwise.  But I am interested in a working understanding and the capability to predict the flow dynamics in steam systems as best possible at this point.  

I've collected 200 references to try to get at these issues: read/reviewed ~75%, understand ~20%.  I'll look more closely at the two Aziz/Govier (& Mandhane) references I have on-hand for more application.

Your comments help me position and focus my understanding in this hugh area of study.  One mechanical engineering society (ASHRAE) sponsored some related research in 1966 and again in late 1970's.  The 1966 research was for low pressure steam, small pipes, and assumed equal countercurrent steam & condensate mass flows.  The 1970's research was primarily for condensate flows with flash steam.  What I gathered from that research, in a very generalized interpretation, is that velocities around 70 fps in cocurrent flow and around 40 fps in countercurrent flow can present slugging problems in (horizontal) steam/condenstate flows.  

The velocity I stated in the examples is for peak flow.  The off-peak loads are much lower and would occur most of the operating hours.  So, if there is enough fluid present, and the pipe run is long enough, and if a lower than peak velocity can elicit slug flow, then I would like to know what combinations could result in slug flow.

I'll contact you for the graphics you have suggested may be helpful.  Thanks for your input.


RE: Minimum Fluid Depth/Slug Flow Two-Phase Steam


If I might make a suggestion, based on a lot of hard knocks in this area, I would suggest you be judicious in your review and application of any multiphase fluid flow reference to your particular application.  Most of the two-phase flow research papers that have been done out there only apply to very specific applications and the vast majority, if not all of them, do not apply to steam systems at all.  

Extrapolation of anyone's correlations to any particular situation, if that situation lies outside of the range of applicability of the research, is an educated guess at best.  I have been doing two-phase steam distribution for about 15 years now so I can tell you that the above is based on a lot of experience and a lot of mistakes made in the field.  I have spent many hours retrofitting existing steam distribution systems that did not work as originally designed because the designers were not aware of the issues.

The majority of the regime prediction methods are empirically-based using flow visualization data from air-water flow in clear pipe.  The flow data are visually classified into flow patterns and then used to construct flow regime maps.  Unfortunately, there are currently no published flow regime data available for two-phase steam.  Thus, the existing air-water maps must be used until something else is developed.

An outstanding reference on this topic is "Steam Distribution and Metering" by S. G. Castrup (Integrated Sciences Group, 2002),, (661) 872-1683.  I have attended several schools by the author and I can assure you they are on top of the 2Ø steam flow issue.  They have done a ton of their own research most notably in the area of flowsplitting of 2Ø steam at impacting and side-branching tees.  I would highly recommend this reference.  It compiles all the wheat and chaff of the bazillions of 2Ø papers out there and presents the material in a clear concise manner (only a few PDEs) with recommendations for the correlations that you can use on a daily basis.

I have not had a chance to run your cases in Pipephase.  I should get to it this afternoon.

P. J. (Pete) Chandler, PE
Principal Engineer
Mechanical, piping, thermal/hydraulics
Processes Unlimited International, Inc.
Bakersfield, California USA


RE: Minimum Fluid Depth/Slug Flow Two-Phase Steam

Pete -

Is it generally acknowledged that all the models vary in a significant way, including for steam/water?  Why is Mukherjee-Brill used as a first approximation, but Taitel-Dukler used in the modeling software?  Is M-B more proven for steam but T-D more broadly applicable and easier to program?  I don't have access to any of the multiphase modeling software, so would greatly appreciate knowing what a run from such software would indicate.  I appreciate you offering access to the L-M spreadsheet and I'll see what I can learn from it (disclaimers understood).

Is the Chien model by Sze-Foo Chien?  I bought two papers from SPE by S-F Chien which were very helpful, and to-date, Chien's work comes closest to addressing the steam flows in which I'm interested.  However, Chien's work does not adress low moisture saturated steam.  So close...but yet so elusive...

Who are the folks that you know that do a lot of two-phase steam work?  I'm thinking of process engineers in process equipment design, power engineers in steam/turbine stations (esp. nuclear), petroleum engineers with steamflood EOR projects, marine engineers with ships/submarines (changing pipe slopes - cocurrent & countercurrent flows in the same pipe perhaps).  Others?

Regarding Example 2 (countercurrent flow):  The intent would be to design and size the piping to ensure countercurrent flow where a positive slope is absolutely necessary to meet elevation requirements.  My assumption in this case is that if the piping is sized for countercurrent flow a peak flow, then countercurrent flow will be maintained at lower flows and without slugging.

Thank you,

RE: Minimum Fluid Depth/Slug Flow Two-Phase Steam

Pete -

I talked to Ms. Castrup about the notebook she published.  She recommended that I not consider purchasing it as the subject matter is wet steam and will not address the conditions in steam heating mains where steam quality is typically high.

Ms. Castrup was so helpful as to forward a copy of her spreadsheet which looks at flow regimes for a set of flow conditions in three different models, one is Mukherjee-Brill.  The pressure assumed in her spreadsheet is several times higher than I used in my example, but all three models indicate annular flow predominately for greater than about 85% quality.  This is quite interesting as the heat distribution industry typically conceptualizes condensate flow in mains as stratified for condensate removal and dripleg design.  (The models indicate that slug flow is unlikely).  I understand that the transition lines are actually quite wide and the regime distinctions are not, therefore, clearcut.

Would be very interested in what the PipePhase model indicates.

Hope you can address my questions in my 9/24 posting.

Thanks for your input...Ken

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