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# Calculate Stagnation Conditions In Hne-Models

stagantion condition; hne-model

10 replies to this topic
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### #1 KingKoch3000

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Posted 24 June 2020 - 08:41 AM

Hello,

I'm looking for ideas to calculate stagnation conditions in a two-phase flow in a HNE-Model to design a two phase nozzle.

Homogeneous Non Equilibrium models often rely on stagnation conditions, such as pressure and quality.

I'd like to calculate the pressure drop in a two phase nozzle. And use the HNE-CSE model. But it shouldn't matter which kind of HNE model to use..like HNE-DSE or the American API RP 520 model

I'd like to take a closer look and divide the nozzle into sections. To use a HNE-Model I'd have to calculate the stagnation conditions at the entrance of every segment.

The objective is to calculate stagnation conditions via an isentropic flash. But I didn't find any useful information on how to do this.

Maybe someone here can help me with this ?

Thanks a lot

### #2 PaoloPemi

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Posted 24 June 2020 - 02:57 PM

HNE-CSE is based on Leung Omega method, which adopts a simplified correlation for phase equilibria and fluid properties, see

https://www.cheresou...g-omega-method/

many HNE models proposed in literature are derived from Leung Omega (HEM) including empirical corrections for boiling delay, slip, degassing,

some (for example the HNE model in Prode Properties) adopts formulations similar to rigorous HEM (meaning rigorous phase equilibria and fluid properties ) but including some non-equilibrium and slip factors.

The usual procedure allows to estimate a critical flow , do you wish to estimate a pressure drop with subcritical flow ?

### #3 KingKoch3000

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Posted 25 June 2020 - 03:21 AM

Hello Paolo,

Yes, I'm aware that the HNE-Models originate from Leung model.

My nozzle flow includes a initially subcooled mixture of ammonia/water, with a required pressure drop which is resulting in a pressure of the mixture to be beneath saturation conditions. Which is why I'm going for the HNE-CSE model.

So the thermal non-equilibrium or boiling delay should be of special interest to this application.

The flow should be subcritical. I've already looked into PRODE Properties, but only the freeware version.

But I'd like to take a detailed look at the changing conditions over the nozzle, which is why I'm going for a segmented approach.

There's an example for such an approach to calculate a pressure drop in a pipe with the HNE-CSE model by Prof Schmidt in the recent release of the german version of the "VDI-Heat-Atlas"

In this segmented approach, the author is calculating the stagnation conditions (pressure and quality) at the entrance of every segment.

But the only information given on how to do this is via isentropic flash.

So far, I've not been able to recreate this example, since all my efforts to calculate this isentropic flash yielded quite a lot of different results.

So, I'd like to ask I've someone could give me a hint on how to do this the right way

Edited by KingKoch3000, 25 June 2020 - 04:01 AM.

### #4 breizh

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Posted 25 June 2020 - 04:05 AM

Hi,

http://www.engsoft.c...team_flow_e.htm

In case ,you will find some print out from Chemical engineering journal.

Hope this is helping you

Breizh

#### Attached Files

Edited by breizh, 25 June 2020 - 04:36 AM.

### #5 PaoloPemi

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Posted 25 June 2020 - 07:56 AM

My knowledge of HNE-CSE is limited to Sizing of rupture disks for two-phase gas/liquid flow according to HNE-CSE-model by Jürgen Schmidt and Sara Claramunt , this document

https://indico.cern....enf_Handout.pdf

and a few other papers,

the segmental solution you mentioned may recall the direct integration method (HEM) but I  have not the german version of the "VDI-Heat-Atlas" to verify,

may I suggest to contact the author, Dr. JÜRGEN SCHMIDT ?

### #6 KingKoch3000

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Posted 25 June 2020 - 12:08 PM

Hi,

http://www.engsoft.c...team_flow_e.htm

In case ,you will find some print out from Chemical engineering journal.

Hope this is helping you

Breizh

Hi Breizh,

and thanks a lot for your contribution.

But I don't think that those calculations mentioned can sufficiently describe my application.
Since they take an approach at thermodynamic equilibrium ? and the discussed equations are mostly for ideal gases and steam applications.

In my case one of the main problems is calculating the specific volume of my mixture once it's pressure is beneath saturation condition.
When I calculate this volume in accordance with classical equilibrium thermodynamics the changes in density / specific volume are with an factor of around 1000.
Which means, if I use the continuity equation in accordance with equilibrium approach, the velocity will suddenly skyrocket. I've already calculated a maximum velocity which should occur at isentropic nozzle flow via h_0 = h + v^2/2 (like in PRV sizing for 2 phase flow.pdf). But the velocity with equilibrium calculations and occuring phase change is bigger than this max velocity.

But considering boiling delay, the mixture should stay in a liquid phase for much longer. Maybe even not flash at all during the flow through the nozzle.

My knowledge of HNE-CSE is limited to Sizing of rupture disks for two-phase gas/liquid flow according to HNE-CSE-model by Jürgen Schmidt and Sara Claramunt , this document

https://indico.cern....enf_Handout.pdf

and a few other papers,

the segmental solution you mentioned may recall the direct integration method (HEM) but I  have not the german version of the "VDI-Heat-Atlas" to verify,

may I suggest to contact the author, Dr. JÜRGEN SCHMIDT ?

Hey Paolo,

yes, I've read those paper and the hand out as well. I don't think it has anything to do with the HEM, since it's clearly an application of the HNE-CSE Model. Unfortunately the segmental approach seems only to be found in the "VDI-Heat-Atlas"

Stagnation conditions are mentioned in most articles related to this topic. But mostly the entrance speed to the orifice is assumed to be negligable and thus stagnation conditions won't differ from the actual conditions. And I've found no way to calculate them.

I've already contacted Prof Schmidt and his suggestion to do the isentropic flash and obtain the stagnation condition was to use  the first law, the continuity eq. and if neccessary the perfect gas relation p*v**kappa = const. but I wasn't able to solve it with this information.

The thing is that I really need to know whats happening in the nozzle and at its exit, since it should be used as an motive nozzle for an jet ejector.

### #7 PaoloPemi

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Posted 25 June 2020 - 01:29 PM

I do not undestand if you wish to design  a isentropic nozzle or a ejector, the mentioned methods are for isentropic nozzles, meaning you solve single and two-phase critical (choked) flow with a simplified equation (Omega) or a rigorous methods,

The simplified (one or more parameters) Omega model allows to estimate phase equilibria and fluid properties.

With ejectors you can still assume isentropic flow but the procedure is different, the models which I know (Munday and Bagster, Huang etc.) can adopt simplified models (for example ideal gas law) for solving local conditions as local pressures, ideally you should be able to replace the ideal model with some variation of Omega model (which is a one parameter equation of state as described by Leung) but I do not know if that is the scope of your work, if you wish to design an ejector there are good books and papers discussing the details...

### #8 latexman

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Posted 25 June 2020 - 01:32 PM

This is just my opinion.  I see the practicality of a simple, discrete flow nozzle calculation, when the calculations align fairly closely to reality.  When one has to divide that flow nozzle up into segments, couple it with a complex vapor/liquid equilibrium model to represent ammonia/water, and further couple that with delayed equilibrium*, I think it may be time to solve the problem with CFD.  My \$0.02.

* How do you determine how much to delay the equilibrium without experimentation anyway?

Edited by latexman, 25 June 2020 - 02:03 PM.

### #9 KingKoch3000

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Posted 26 June 2020 - 02:07 AM

I do not undestand if you wish to design  a isentropic nozzle or a ejector, the mentioned methods are for isentropic nozzles, meaning you solve single and two-phase critical (choked) flow with a simplified equation (Omega) or a rigorous methods,

The simplified (one or more parameters) Omega model allows to estimate phase equilibria and fluid properties.

With ejectors you can still assume isentropic flow but the procedure is different, the models which I know (Munday and Bagster, Huang etc.) can adopt simplified models (for example ideal gas law) for solving local conditions as local pressures, ideally you should be able to replace the ideal model with some variation of Omega model (which is a one parameter equation of state as described by Leung) but I do not know if that is the scope of your work, if you wish to design an ejector there are good books and papers discussing the details...

Hello Paolo,

I'm quite new to this specific topic. The isentropic flash is just referring to the calculation of said stagnation conditions.

And the results I've gotten so far exceed the isentropic expectations for example in terms of velocity.
I've read quite a lot about ejector design, but haven't seen a comparable case so far. But I'll look into your mentioned models. Thanks for your help.

This is just my opinion.  I see the practicality of a simple, discrete flow nozzle calculation, when the calculations align fairly closely to reality.  When one has to divide that flow nozzle up into segments, couple it with a complex vapor/liquid equilibrium model to represent ammonia/water, and further couple that with delayed equilibrium*, I think it may be time to solve the problem with CFD.  My \$0.02.

* How do you determine how much to delay the equilibrium without experimentation anyway?

Hello Latexman,

experimental investigation of said nozzle is planned as well. And you're probably right to call for an CFD simulation. This may be done depending on experimental investigations.

### #10 PaoloPemi

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Posted 26 June 2020 - 03:32 AM

probably your best resource to understand that model is the author itself,

anyway, if you plan to calculate in sequence the different sections note that stagnation properties are constant throughout a steady, isentropic flow field, hence you can derive local properties solving (depending from adopted model) with ideal gas law or a equation of state as Omega etc.

the solution shouldn't be too difficult with HEM (where you can replace the ideal gas density with mixed vapor+liquid density and presume the same speed)  but HNE can be very different, there the author can help providing the required details which we do not know.

### #11 KingKoch3000

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Posted 26 June 2020 - 04:09 AM

Hey Paolo,

anyway, if you plan to calculate in sequence the different sections note that stagnation properties are constant throughout a steady, isentropic flow field, hence you can derive local properties solving (depending from adopted model) with ideal gas law or a equation of state as Omega etc.

in the CSE Model there's also wall friction included, so there's no assumption of an isentropic flow - hence the change in stagnaton conditions. But you're right, maybe thats the best way to go, when designing the nozzle

the solution shouldn't be too difficult with HEM (where you can replace the ideal gas density with mixed vapor+liquid density and presume the same speed)

This was my first approach and I've tried this a couple of times with equilibrium assumptions in different ways. Result were never satisfying. As soon as mixture drops below saturation conditions and starts flashing, the calculation of mixture density/volume becomes a mess (and everything corresponding with it). I think this wouldn't be this much of a problem if the entrance steam to the nozzle would be already in two-phase-conditions.

So I'm quite sure I've got to adress the boiling delay. And that this has a big impact on the calculations. Which is why I was quite happy when I discovered the HNE models.