Air-driven evaporators - stability issues

[Chef]

Chef will know it well. It represents a bifurcation curve generated for a particular case of this same evap. The two branches you see represent two 'stable' modes of evap operation, as a function of the heat-transfer governing equations. The test points are always found to be on one of the branches, even though, in practice, the curves morph slightly with change in evap conditions.

Evaps are non-linear in their nature & hence present some quite extraordinary complications in their control.

If the process ends up on the 'wrong' branch, bad things happen - unstable process (stable evap). If it ends up on the 'other' branch, the process (& evap) is/are stable.

The dTlm='0/0' point is at the bifurcation point i.e. where the single line splits into two (a fork).

It is now fairly clear for 'one' (not all) of the underlying reasons for TXV hunting - the system tries to jump between the two branches on offer...

(A lot of this is pretty much 'hot-off-the-press' as I've been burning the midnight oil developing the theory - in order to best understand the system dynamics).

desA your coming up with some dramatic new revelations in heat transfer and fluid flow!

First is it possible you can explain the two axis on your graph, as they are calculated you should also include the original formulae. You have previously introduced the alpha and beta coefficients but are they the same in the plot you have posted.

I have not come across a curve like this but have seen heat transfer coefficients change during changes in the flow regime, these are almost parrallel but offset and can cause jumps in the evap condition. These curves are always sloping in the same direction leading to stabliity assuming all alse is industry standard. The flow can jump from one line to another but they always have a positive slope.

Many years ago there was a paper that purported a mythical negative pressure slope where an increase in flow reduced the pressure drop, an interesting concept but it has never been shown in experimental data.

You also mention that evaps are non linear in their behaviour, well condensers, compressors, pressure drops in pipes and TXV's are all non linear but it does not mean they can't be modelled or understood.

Looking forward to graph details.

Chef

[desA]

desA your coming up with some dramatic new revelations in heat transfer and fluid flow!

Yes, I know this...

The idea is intrinsic in every heat-exchanger in existence!!! It is, however, accentuated in a system where a change between flow regimes occurs - such as in an evaporator.

Heat-exchanger design theory has a fundamental flaw - at the dTlm=0/0 point. Even if you look into the derivation of NTU-effectiveness method, it conveniently skips over the dTlm=0/0 point, or even ()/0 for that matter. There are two natures at work.

I first observed this in automotive cross-flow radiators.

First is it possible you can explain the two axis on your graph, as they are calculated you should also include the original formulae. You have previously introduced the alpha and beta coefficients but are they the same in the plot you have posted.

The theory to derive this curve is, in essence, very simple - incredibly simple. I'll have to write it up in a decent note & post it up for us to discuss. The recent incarnation of this Beta theory came out a study in trying to confirm the Magoo rule. You could imagine my dismay, when it produced two answers - every time - sometimes very close to each other - at other times far apart.

It was only when I plotted the curves a few days ago, that the nature of the bifurcation became clearly evident.

The alfa stands for the degree of temperature cross between the air-leaving temp & the refrigerant leaving temp. The beta values come from the Magoo rule:
SH=beta*TD.

There are TWO suitable beta values for every alfa!!! In other words, there are two possible SH values for the evaporator.

If the wrong beta is used, the system, as a whole is unstable - leading to Te,sat drift.

I have not come across a curve like this but have seen heat transfer coefficients change during changes in the flow regime, these are almost parrallel but offset and can cause jumps in the evap condition. These curves are always sloping in the same direction leading to stabliity assuming all alse is industry standard. The flow can jump from one line to another but they always have a positive slope.

I am able to demonstrate the movement between the beta1 (bottom one) & beta2 curves (top one) - experimentally, at will.

You also mention that evaps are non linear in their behaviour, well condensers, compressors, pressure drops in pipes and TXV's are all non linear but it does not mean they can't be modelled or understood.

Looking forward to graph details.

I'm currently developing the condenser instability theory. This is going to be a few levels tougher, in that there are more degrees of freedom.

Non-linear science is fascinating & I'm so stunned that it can evidence itself in a simple HFC-based cycle - & in stable solutions at that.

CO2 trans-critical systems suffer from bi-stability, & this can produce low COP, & high COP cycles, on an apparent
whim. The maths used there is transient in nature & obviously far more complex. This is generally really not necessary, however, as the transient 'stable' states often have a way of dissipating as thermodynamic 'equilibrium' is approached - sometimes not...

[desA]

Condenser multi-stability bifurcation theory now complete - turned out to be easier than I'd first thought.

I'll work on how to get that to make sense experimentally & we'll open another thread later on that...

[Gary]

If the compressor can not suck all the vapor the pressure would rise reducing the pressure differential across the expansion device and reducing the LMTD of the evap thus reducing transfer energy. Equalibrium reached.

At the same time, that same pressure rise would increase the density of the vapor entering the compressor, causing the compressor to pump more vapor.

[desA]

^ It is the evap moving towards its stable point, by raising Te,sat (in order to reduce TD) & the compressor's apparent willingness to move along with it towards higher & higher output power, that is the mechanism at work here.

This mechanism has no self-limiting step (danger lies ahead for high TD's) - unless mechanical blocks, or throttles are put in place to limit the flows. Hence the success of the CPR & valve, on the previous thread - each with it's own 'issues'.

Under the unrestricted scenario, the evap seems to follow the Beta1 curve (the lower one), if fan-controlled (so far this seems to hold), or climb up to the bifurcation point at dTlm=0/0. I have loosely termed this the 'dither point'.

If the throttle is installed, the evaporator is free to float on its own path to limit TD. It then seems to be able to push itself up onto the Beta2 (top curve).

The Magoo Rule firmly places the evaporator on the Beta2 curve!!!

http://www.kueba.de/en-us/Tools/K%C3...s/default.aspx

It seems that Kuba has some hidden depth in their products...

I'll continue to explore further & report back on the experimental evidence & how these bifurcation curves shift slightly to match the circumstances. At each & every experimental test point computed thus far, at the combination of (alfa, beta), the data WILL lie on either the Beta1, or Beta2 line. A very, very interesting topic.

[Gary]

Ta,in (close to evap face)
Ta,out (rear of evap)
va,in (average over face)
RH%
A,face known

Q'e=m'aw*Cpaw*(Ta,i - Ta,o)

Obviously an amount for water condensed should be brought into the calc, to be tight about it.

The thing that gets to me is that using this method & balancing it against refrigerant loop:

Q'e = m'g*[(1-x)*hfg + Cpv*SH]

provides a mass balance within 1% of the compressor requirement, under stable system conditions.

Under Te,sat drift conditions, the difference can be as much as +50%... go figure where the heat, or mass went to.

I'm not sure where specific heat factors into these equations, but as I recall specific heat is extremely complex and non-linear as well.

[desA]

Originally Posted by desA
Ta,in (close to evap face)
Ta,out (rear of evap)
va,in (average over face)
RH%
A,face known

Q'e=m'aw*Cpaw*(Ta,i - Ta,o)

Obviously an amount for water condensed should be brought into the calc, to be tight about it.

The thing that gets to me is that using this method & balancing it against refrigerant loop:

Q'e = m'g*[(1-x)*hfg + Cpv*SH]

provides a mass balance within 1% of the compressor requirement, under stable system conditions.

Under Te,sat drift conditions, the difference can be as much as +50%... go figure where the heat, or mass went to.

Gary:
I'm not sure where specific heat factors into these equations, but as I recall specific heat is extremely complex and non-linear as well.

I never knew that, thanks so much for that input. The Cp values are highlighted in the above eqns.

Cp, eh... well, I never. Ok, for moist air - there will be some trading between the air & water vapour. I wonder what gives in the refrigerant vapour? I'll look into this.

The other thing to remember is that there are a number of transient 'stable' states in complex systems, but these are often (should be) damped out by the more stable parts of the system, as it moves towards thermodynamic steady-state... or, do they?

[Gary]

Some years back, I attempted to devise a simple table plotting inlet superheat vs discharge temp in order to judge the relative efficiency of compressors, the theory being that inefficiency shows up as excess discharge temp.

The complexity of specific heat caused the idea to be scrapped. It became way too complex to be a useful troubleshooting tool.

[desA]

^ Do you perhaps have any links to the specific heat information that you were using? This would be very interesting.

[Gary]

^ Do you perhaps have any links to the specific heat information that you were using? This would be very interesting.

It's been a very long time, but I'll see if I can find something.

[desA]

^ Thanks very much for that...

[Gary]

I haven't been able to find my notes yet, but perhaps this may get you started:

http://hyperphysics.phy-astr.gsu.edu...rmo/debye.html

http://hyperphysics.phy-astr.gsu.edu...o/spht.html#c1

[Gary]

This mechanism has no self-limiting step (danger lies ahead for high TD's) - unless mechanical blocks, or throttles are put in place to limit the flows. Hence the success of the CPR & valve, on the previous thread - each with it's own 'issues'.

Under the unrestricted scenario, the evap seems to follow the Beta1 curve (the lower one), if fan-controlled (so far this seems to hold), or climb up to the bifurcation point at dTlm=0/0. I have loosely termed this the 'dither point'.

If the throttle is installed, the evaporator is free to float on its own path to limit TD. It then seems to be able to push itself up onto the Beta2 (top curve).

The Magoo Rule firmly places the evaporator on the Beta2 curve!!!

http://www.kueba.de/en-us/Tools/K%C3...s/default.aspx

It seems that Kuba has some hidden depth in their products...

I'll continue to explore further & report back on the experimental evidence & how these bifurcation curves shift slightly to match the circumstances. At each & every experimental test point computed thus far, at the combination of (alfa, beta), the data WILL lie on either the Beta1, or Beta2 line. A very, very interesting topic.

Actually, the Kuba rule calls for .5*TD to .7*TD.

For rock stable operation, I would suggest using an AEV. However, changes in heat load will result in changes in superheat. Possibly this can be counteracted by fan control, the control points coinciding with .5*TD and .7*TD... although I suspect that lower SH would be entirely acceptable with an AEV in control.

[desA]

I haven't been able to find my notes yet, but perhaps this may get you started:

http://hyperphysics.phy-astr.gsu.edu...rmo/debye.html

http://hyperphysics.phy-astr.gsu.edu...o/spht.html#c1

These refer to essentially metallic specific heats. I've not yet been able to locate suitable references on liquid/2-phase/gaseous specific heats for refrigerants.

Never fear, at some point, I'll check in the Chemstations database, but that would, in all likelihood be a simple polynomial expansion expression.

[desA]

Actually, the Kuba rule calls for .5*TD to .7*TD.

Kuba call for a Beta=0.65 setting, as their standard.



The Beta2 curve corresponds to Beta > 0.48, climbing up to slightly in excess of 0.78.

For rock stable operation, I would suggest using an AEV. However, changes in heat load will result in changes in superheat. Possibly this can be counteracted by fan control, the control points coinciding with .5*TD and .7*TD... although I suspect that lower SH would be entirely acceptable with an AEV in control.

The lower SH (Beta1) curve leads to Te,sat drift - although the fan control will help track on this curve.

[Gary]

Kuba call for a Beta=0.65 setting, as their standard.

With .5 to .7 as their "ok" range.

[desA]

With .5 to .7 as their "ok" range.

What you will find is the following:
1. The bifurcation curves tend to 'slide' along the linear part slightly (back, or forth), with system changes, cycle heat-soak & so forth.
2. The bifurcation point is reasonably close to Beta = 0.5, or there-abouts.
3. To set a safe operating point, it would be wise to be some 'distance' away from Beta=0.5.

Kueba seem to be happy at 0.65. Magoo has good experience in the range 0.6 - 0.7.

I would say that both have a solid theoretical, as well as practical basis for their usage. I would stay some distance away from Beta=0.5 as this means a potential constant flipping between two modes of operation - hence system instability.

[Gary]

Then every A/C system I have ever seen, heard of, or worked on is... wrong.

It is going to take a lot more than bifurcation curves to convince me that a typical A/C coil with 20K/36F TD should have 13K/23.4F superheat.

[desA]

It is the > 20K, off a small dTlm coil, that I would be concerned about.

In other words, if you operate in a region where TD < 20K, you may not experience excessive temp drift - or at least enough to worry te compressor. Of course, the 'distance' between operating Te,sat & the compressor window limit will also come into play.

If you are going to use low SH, but have a Te,sat initial of say 4.4'C, & final Te,sat of 9K - this will be of little, or no concern.

Remember, too - & this is the nut-cracker - aircon & refrigeration systems are self-governing in terms of the evaporator, in that TD lowers as the cooled space gets colder. The system moves into a 'safe region' as a function of operation.

For an air-driven heat-pump, the external air is outside your control & this is precisely where hot Asian conditions prove to be the 'compressor killers'. These are different beasts & deserve to be treated with some respect.

For the record, I will tell you that this evaporator under study now experiences an initial temperature drift of no more than 1K on the first heat-up run - moves up to around 12-12.5K after extensive heat-cycling & is rock solid thereafter. No tricks, or special requirements, other than correct tuning. The system even sounds 'smooth'.

This has been tested repeatably over many days, under varying TD's. It remains sweet & well-behaved, with no Te,sat drift.

The tuning was driven off the back of the knowledge of the evap bifurcation characteristics. The previous Te,sat control strategies have also been tested against this new concept, & mapped. They are beginning to make sense.

To fully tune the system to where I would like it to remain, will require some innovation from certain equipment manufacturers, with whom I'm now working closely. Once this is place, I'll be more comfortable to begin attempting TD's up to around 35K. This makes for a fairly safe AWHP & opens up new markets.

[Gary]

Are you still testing with the same system?... the one where the condenser is piped wrong?

[desA]

Yep...

We can discuss the condenser matters on another thread, in a few weeks. I have to be abroad for a round 10 days & will begin developing alfa-beta-delta curves for the condenser.

The bifuraction theory is complete, but the condenser is a bit more complex to explore practically, since 3 possible pinch points occur. This makes for many more operational options.

[Chef]

The theory to derive this curve is, in essence, very simple - incredibly simple. I'll have to write it up in a decent note & post it up for us to discuss. The recent incarnation of this Beta theory came out a study in trying to confirm the Magoo rule. You could imagine my dismay, when it produced two answers - every time - sometimes very close to each other - at other times far apart.
..

How are you doing with the write up? Would be interesting to see the methodology you have used.

Chef

[Gary]

With an AEV holding Te,sat steady, it would be possible to hold SH=.65*TD by controlling fan speed off Tair,in.

[desA]

How are you doing with the write up? Would be interesting to see the methodology you have used.

Working on it. I'll be abroad for around 10 days, but plan to write up along the way - time permitting.

The concept is growing each day.

[desA]

With an AEV holding Te,sat steady, it would be possible to hold SH=.65*TD by controlling fan speed off Tair,in.

This is a good idea. I'll continue working up the technology & see how exactly fan speed co-operates under each mode of operation.

In the Beta2 mode, I found fan roll-off to produce some interesting results, as the evaporator held itself steady. Te,sat, of course, drops lower with lower fan speed.

[sterl]

The original Coil Loading shows a sensible heat ratio of about 62% and a pretty large Delta-T at a high laent....i haven't run the psychormetircs, but with a constant-speed compressor: this thing is going to respond drastically to a small decrease in air flow...Initially TXV is going to undershoot as Suction pressure drops with reduced air flow; then overshoot as refrigerant-dry section of coil becomes incapable of maintaining a temperature below the Dew Point of the air...THIS REALLY NOTICEABLE when a fairly high capacity single coil is working on a fairly small room, that is, volume of air...

As to Flow Regimes:

Suggest you look up articles (multiple) by Mr. Bruce Nelson of Colmac on DX coils....With R-134 at these temperature, you can eliminate about 50% of the phase-momentum regimes unless you have a lot of subcooling at the TXV Inlet.

And a one on one, hermetic or semi-hermetic circuit will quite easily accomodate some short term excess flow of liquid to the evaporator...The motor cools off very quickly.

[desA]

^ Thanks for your input, Sterl.

Do you perhaps have an idea of the SH/TD ratio recommended by Colmac Coil? (SH = superheat; TD = temperature difference)

[Joey.zhang]

Ta,in (close to evap face)
Ta,out (rear of evap)
va,in (average over face)
RH%
A,face known

Q'e=m'aw*Cpaw*(Ta,i - Ta,o)

Obviously an amount for water condensed should be brought into the calc, to be tight about it.

The thing that gets to me is that using this method & balancing it against refrigerant loop:

Q'e = m'g*[(1-x)*hfg + Cpv*SH]

provides a mass balance within 1% of the compressor requirement, under stable system conditions.

Under Te,sat drift conditions, the difference can be as much as +50%... go figure where the heat, or mass went to.

I think for this instability issue we need pay attention on
1. TXV. Check its performance, its bulb
As you know, TXV, NOT EEV, operates and controls the refrigerant flow depending on SH (including SS). Its response time will effect the system stability directly.
2. Evaporator performance.
--Uneven liquid to the circuits of the Evap. It will also effect the actual SH.

--Heat transfer coefficient. Check if Heat transfer coefficient has been change during the period.
a. Air side, Water drop on the evap.
b. Refrigerant side, mass flow changes, but it affects slight on experience.
3. Liquid return. The chiller will be instable if liquid return happens to compressors.
Other opinion
4. Mass flow exiting the evap must be same to that entering the compressors. It is subject to the suction pressure, that is, SX minus pressues drop, due to the constant suction volume for compressors.
5.I don't think there will be vapour re-condense in the Evaporator per 1st and 2nd law of thermodinamics.

[Joey.zhang]

I never knew that, thanks so much for that input. The Cp values are highlighted in the above eqns.

Cp, eh... well, I never. Ok, for moist air - there will be some trading between the air & water vapour. I wonder what gives in the refrigerant vapour? I'll look into this.

The other thing to remember is that there are a number of transient 'stable' states in complex systems, but these are often (should be) damped out by the more stable parts of the system, as it moves towards thermodynamic steady-state... or, do they?

I think you need to calculate the enthalpy differece of air in/out instand of their specfic heat.

Q=m*(h'a,out - h' a,in)

On the other hand, it's difficult to test the temperature of air in/out exactly as the air flow or velocity. They will affect enthalpy and mass flow of the air.

[desA]

^ Thanks Joey, for your excellent input. Much obliged.

[desA]

Originally Posted by Chef
How are you doing with the write up? Would be interesting to see the methodology you have used.

desA:
Working on it. I'll be abroad for around 10 days, but plan to write up along the way - time permitting.

The concept is growing each day.

A brief update on the stable bifurcation theory.

The theory has actually become pretty advanced, now - with refinement to dimensionless parameters which apply to ANY heat-exchanger. To do the concept justice, I think that it would be preferable to expand the findings into a decent journal publication, or conference proceeding.

Each evap, or condenser I've tested thus far, falls onto an appropriate bifurcation curve - it's becoming pretty interesting.

[desA]

A challenge

If anyone would like to participate in some research into evap bi-stable phenomena (bifurcation), please pm me the following information (minimum):
1. Te,sat (evap temp at LP - inside evap);
2. Te,sup (evap superheat temp at TXV bulb);
3. Ta,in (air inlet temp to evap);
4. Ta,out (air outlet temp - at evap exit - just behind unit).

Additional information will also be useful in tuning your evap:
a. Evap inlet face area [m2];
b. Evap air inlet velocity [m/s];
c. TXV, capillary, or EEV?

Based on the information received, I'll plot the bi-stability curves for the evap & note where your current system setting lies. We can then discuss ways to improve, or otherwise, the evap performance.

Please note - this information must be extracted from experimental, measured information - not from an evap designer's concept - they must be actual, hard measurements. The evap can come from ANY refrigeration, aircon, or heat-pump circuit - please state, though, which one, with your information.

You can elect to keep the information private & confidential, or to publish the results to this thread. The choice is entirely yours & will be honoured at all times. There is no cost for this service...