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  1. #101
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    Re: AWHP superheat & sub-cooling



    Quote Originally Posted by desA View Post
    Basically, since the hot water is generally blended with cold water by the end user, the terminal tank temperature can undershoot, or even overshoot a little, without much problem - in general.
    Our strategy being to fully heat the feed water before sending it to the storage vessel, we would not want the hot water to be blended with cold water in the storage vessel.



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    Re: AWHP superheat & sub-cooling

    ^^ Thanks for the pic.

    That would be fairly easy to implement. Install valve on water ?exit? line - install bulb in discharge line prior to condenser, or at entry.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by Gary View Post
    Our strategy being to fully heat the feed water before sending it to the storage vessel, we would not want the hot water to be blended with cold water in the storage vessel.
    What I was aiming at is that for many hot water applications - at least for hotels, is that the hot water from the storage vessel (sat 60-65'C) is piped into a blender/mixer head in the shower, where it is blended with cold water.

    So, the storage tank temperature could actually be acceptable at an upper temp of 63-65'C say, with little noticeable difference to the person taking a shower.
    Last edited by desA; 29-07-2009 at 04:31 PM.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    ^^ Thanks for the pic.

    That would be fairly easy to implement. Install valve on water ?exit? line - install bulb in discharge line prior to condenser, or at entry.
    Yes, the valve would be installed at the water exit.

    On the end of that cap tube in the picture there is a 1/4 inch flare nut, which would be connected to a standard 1/4 inch access fitting, preferably in the discharge line prior to the condenser. It might be a good idea to also install a small shutoff valve between the access fitting and the flare nut, in case the valve may someday need to be replaced.
    Last edited by Gary; 29-07-2009 at 04:36 PM.

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    Re: AWHP superheat & sub-cooling

    ^ Thanks, Gary. I'm very happy with using the water flow-control concept via a capillary tube. I loathe too much reliance on electronics, if at all possible.

    Next on the list:

    At startup temperatures, with a Tc,sat temperature of around 35'C, say, the required refrigerant mass charge could be around 1200g, for instance. At Tc,sat of around 70'C, the required mass charge would only be 1020g - per calculation.

    The required mass charges for the cold & hot condition are different. How to set up a suitable refrigerant loop such that the charge difference doesn't end up swamping the condenser in the hot condition?

    The mass charge in the evaporator seems to decrease as the cycle moves upwards towards Tc,sat=70/75'C, since the quality moves from around x=0.12 to around 0.4. The excess refrigerant then needs to move to the condenser, where it holds up.
    Last edited by desA; 29-07-2009 at 05:05 PM.
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    Re: AWHP superheat & sub-cooling

    The refrigerant charge should be suitable for the hot condition, not the cold condition... and given the water regulating valve that hot condition would be very quickly reached.
    Last edited by Gary; 29-07-2009 at 05:23 PM.

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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by Gary View Post
    The refrigerant charge should be suitable for the hot condition, not the cold condition... and given the water regulating valve that hot condition would be very quickly reached.
    Perhaps this answer is too simplistic. To elaborate:

    A TXV system requires surplus refrigerant in order to respond to variations in heat load. That surplus is stored in a receiver, or takes up valuable space in the condenser if there is no receiver. In addition there is excessive liquid pressure at the TXV due to the desired high side temperature, requiring a PRV to reduce the liquid pressure.

    In adding the fan control we eliminate the heat load variations and stabilize the low side pressure... and in adding the water regulating valve we stabilize the high side pressure. Thus we ride the upper limits of the compressor (Te,sat 15C, Tc,sat 75C) throughout the cycle.

    Having stabilized the heat load as well as both low and high side pressures, the system is now ideal for a cap tube as the metering device, thus eliminating the TXV, PRV, receiver... and the surplus refrigerant.
    Last edited by Gary; 29-07-2009 at 07:33 PM.

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    Re: AWHP superheat & sub-cooling

    The required mass charges for the cold & hot condition are different. How to set up a suitable refrigerant loop such that the charge difference doesn't end up swamping the condenser in the hot condition?
    A few thoughts on this - let's say for a typical, unoptimized, low-cost circuit (open to critical review):
    1. Set system charge at start-up temp mass requirements - to optimize start-up heat-performance;
    2. Oversize condenser suitably such that its internal storage provides sufficient space to store the excess refrigerant for the high-temp end point.

    At this point, the condenser acts as a receiver.

    The refrigerant excess at hot condition is around (1200-1020)/1020*100 = +17.6%. For most condensers, the design oversurface is in excess of this value & so the condenser provides a natural mass storage receiver, at little additional on-cost.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    A few thoughts on this - let's say for a typical, unoptimized, low-cost circuit (open to critical review):
    1. Set system charge at start-up temp mass requirements - to optimize start-up heat-performance;
    2. Oversize condenser suitably such that its internal storage provides sufficient space to store the excess refrigerant for the high-temp end point.

    At this point, the condenser acts as a receiver.

    The refrigerant excess at hot condition is around (1200-1020)/1020*100 = +17.6%. For most condensers, the design oversurface is in excess of this value & so the condenser provides a natural mass storage receiver, at little additional on-cost.
    You forgot to add:

    3. TXV

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    Re: AWHP superheat & sub-cooling

    I'm not sure if there was a question in your last post.

    TXV's excell at handling variable loads... and for this they need surplus refrigerant.

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    Re: AWHP superheat & sub-cooling

    ^ I'd imagine that a TXV would have to be in that kind of circuit, due to the mass charge migration issues.

    What I was thinking through is the case of some of the typical lowish-cost systems I've come across, where no liquid receiver, or suction accumulators are present in the system.

    In academic literature, the mass migration effect is known & some have even talked about the idea of storing the excess refrigerant outside the main circuit, until required. All kinds of ideas. The idea of using the heat-exchanger as a storage device probably allows this to be done, at low cost - although the TXV comes at a price.

    --------
    Cap-tube system (open to review):
    So, for a cap-tube system, the main idea would then be to rather size the refrigerant mass charge for hot-load condition (not start-up) & run a little low on start-up heat-performance, knowing that most of the run time will be spent at the hot condition anyway.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by Gary View Post
    I'm not sure if there was a question in your last post.
    More of thinking out aloud.

    TXV's excell at handling variable loads... and for this they need surplus refrigerant.
    Fair-enough.

    To extend the condenser storage idea & TXV a little further, on such systems. Would it be feasible to further over-size the condenser so that it sub-cools beyond the typical ~8K amount?

    For example, to try & force a larger sub-cooling in the condenser through a combination of design over-surface & liquid-line design.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    More of thinking out aloud.



    Fair-enough.

    To extend the condenser storage idea & TXV a little further, on such systems. Would it be feasible to further over-size the condenser so that it sub-cools beyond the typical ~8K amount?

    For example, to try & force a larger sub-cooling in the condenser through a combination of design over-surface & liquid-line design.
    How does this benefit the system?

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    Re: AWHP superheat & sub-cooling

    The basic idea is as follows:

    Increasing the sub-cooling in the condenser will allow additional heat to the water stream. This will increase COP,hp slightly for very little on-cost.

    Essentially, this is integrating the sub-cooler into the condenser through designed over-surface. As long as the amount of over-surface doesn't wreak havoc with the de-superheating & condensing operation, then it should, in principle, be possible.

    I'm not sure just how far this can be pushed - I'd estimate that the 20-30% range would be within normal design limits. For ultra-compact condenser designs, the increase in condenser volume is marginal, although for concentric tube condensers, the impact could be much larger.
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    Re: AWHP superheat & sub-cooling

    I am getting a tad confused here, generall parallel flow has a heat transfer lose, but are you using that to maintain higher condensing/ SDT. I would tend to go counter flow with water and control water outlet temp., with a variable water flow to acheive same result.
    Years ago I was involved with the developemnt of a HW heat pump as at the experimental stage on R12 [ OK years ago ]. tube and tube counter flow. Had to be tube soldered to tube, due to health regs of double wall separation. Fractional HP compressor as a pre-heater for general electric hot water heating system [ domestic ]. ran like a dream cut hot water heating costs by around 50%.
    Carrier Inc.. also then marketed a system called a "hot shot "as and add on to existing air con system. Acted as a de-superheater on discharge.
    Both systems probably way ahead of there time as and energy saver. Now everyone wants to save costs. Strange how things turn out.

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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    The basic idea is as follows:

    Increasing the sub-cooling in the condenser will allow additional heat to the water stream. This will increase COP,hp slightly for very little on-cost.
    The cooling would be limited to the temp of the entering water. I'm thinking there would be little if any gain and in fact I would bet there would be a loss as compared to using that same oversized condenser without the excess subcooling... but I could be wrong.
    Last edited by Gary; 30-07-2009 at 04:47 AM.

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    Re: AWHP superheat & sub-cooling

    ^^ For heat-pumps, the condenser is typically either a tube-in-tube, or plate. The piping is usually run in a counterflow direction.

    Sidebar:
    Practically though, if the condensing part carries most of the load, then even a parallel flow condition (via water connections), will not make a huge difference - theorectically, at least. Reason is that the de-superheating & sub-cooling parts of the condenser typically take up around 15-20% of the heat-load. If all is well, then the volume used by de-superheating & sub-cooling will be close to the heat-load fraction, although this is not actually always the case (needs to be checked carefully).

    ------------
    With a need to push up the sub-cooling portion of the condenser, it will occupy additional space, which will need to be carefully managed. Normally, liquid-liquid (sub-cooler) heat-exchange does not require much surface area, compared to say vapour-liquid (de-superheater), so the additional space required is not that large, in practice.

    Some tricks may have to be played on the liquid-line pipework to hold back the liquid in the condenser a tad, to force the volume retention, for instance.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by Gary View Post
    The cooling would be limited to the temp of the entering water.
    This is very true - it is. The entry temperature is critical, in how far the sub-cooling can be pushed.

    I'm thinking there would be little if any gain and in fact I would bet there would be a loss as compared to using that same oversized condenser without the excess subcooling... but I could be wrong.
    Where would the loss come from, though?
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    Re: AWHP superheat & sub-cooling

    I've put up a link to the TXV rule Magoo mentioned earlier. (I hope this is ok).

    http://pdf.directindustry.com/pdf/ge...57696-_27.html
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    Where would the loss come from, though?
    I'm thinking there would be more gain from using the extra condenser area to lower the approach temp, therefore a loss by comparison.

    There is very little heat transfer involved in subcooling a liquid.
    Last edited by Gary; 30-07-2009 at 05:11 AM.

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    Re: AWHP superheat & sub-cooling

    ^ Fair-enough - good thought.

    What I'll do is to have a set of ratings done by my condenser supplier, for various combinations of water entry temp & Tc,sat. From that data we should have a more clear idea of the system trade-offs.

    I've already done this for a fixed Tc,sat & variable water inlet temp, but will extend the study to see where the sensitivities lie. Good one...

    ------
    During operation with a pump-around system, the water flow-rate setting will determine the number of water passes (times) through the condenser, & hence the dTw across the condenser.

    If the condenser is sized to cope with the hot-condition such that the condensing area is sufficient for this, any additional over-surface can then be put to good use, without disrupting the condensing section.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    I've put up a link to the TXV rule Magoo mentioned earlier. (I hope this is ok).

    http://pdf.directindustry.com/pdf/ge...57696-_27.html
    I haven't tested the Magoo Method (superheat 60-70% of TD), but it makes good sense. It should work very well over a wide range of conditions.

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    Re: AWHP superheat & sub-cooling

    Experimental feedback - AWHP test system - 30.07.09

    Evaporator:
    Te,sat = 13'C (sat temp)
    Te,sup = 20.8'C (vapour exit temp)
    Ta,in = 24.9'C (air inlet temp)
    va,in = 3.5 m/s (air inlet face velocity to evap face)
    Ta,out = 21.5'C (air outlet temp)
    va,out = 9.5 m/s (air outlet velocity - fan discharge)

    Condenser:
    Tc,sup = 64.3'C (superheated vapour inlet to condenser)
    Tc,sat = 50'C (condenser sat temp)
    Tc,sc = 43.7'C (liquid exit temp)
    Tw,out = 39.8'C (water outlet temp)

    Other:
    Tw,tank = 38.9'C (water storage tank temp - mixed, half-height)
    Tcomp,base = 41.1'C (compressor base temp)

    Electrical:
    Current = 6.1 A
    Voltage = 223V (single phase, ~50Hz)
    This run was performed at a mass charge calculated from the internal volume at operating conditions - internal software. The cold start-up mass was used in this trial.

    I'm very interested in hearing your comments on this unit.

    The particular test unit is undersized on the condenser, in my view. It is an early test machine, using a tube-in-tube condenser, TXV & scroll compressor. Typically, under a dynamic heat-ramp test, the heat-up power to raise the storage tank water temp from ambient to hot temp temp is slightly lower than the compressor performance tables would predict. I have always suspected that this stemmed from a slightly under-sized condenser. The low sub-cooling value seems to bear this out.
    Last edited by desA; 30-07-2009 at 04:44 PM.
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    Re: AWHP superheat & sub-cooling

    Evaporator:
    Te,sat = 13'C (sat temp)
    Te,sup = 20.8'C (vapour exit temp)
    Ta,in = 24.9'C (air inlet temp)
    va,in = 3.5 m/s (air inlet face velocity to evap face)
    Ta,out = 21.5'C (air outlet temp)
    va,out = 9.5 m/s (air outlet velocity - fan discharge)

    Condenser:
    Tc,sup = 64.3'C (superheated vapour inlet to condenser)
    Tc,sat = 50'C (condenser sat temp)
    Tc,sc = 43.7'C (liquid exit temp)
    Tw,out = 39.8'C (water outlet temp)

    Other:
    Tw,tank = 38.9'C (water storage tank temp - mixed, half-height)
    Tcomp,base = 41.1'C (compressor base temp)

    Electrical:
    Current = 6.1 A
    Voltage = 223V (single phase, ~50Hz)
    Evaporator:

    dT = 24.9-21.5 = 3.4K/6.1F
    TD = 24.9-13 = 11.9K/21.4F
    SH = 20.8-13 = 7.8K/14F
    Appr = 21.5-13 = 8.5K/15.3F

    Condenser:

    dT = 39.8-38.9 = 0.9K/1.6F
    TD = 50-38.9 = 11.1K/20F
    SC = 50-43.7 = 6.3K/11.3F
    Appr = 50-39.8 = 10.2K/18.4F

    I am assuming that the Tw,tank is the same as the cond entering water temp, although this may not be the case.

    The subcooling at 6.3K is well within what I would consider to be a normal range (5.5-8.5K). This is largely a matter of refrigerant charge.

    As to undersize/oversize, these are terms that are relative to accepted standards. Are there in fact any accepted standards for this type of system?

    All seems to be working well at this point. It will be interesting to see how these numbers compare with (all else being equal) a much hotter incoming water temp, as will be seen at the end of the heating cycle.

    An additional temp which should be monitored/recorded would be the discharge line temp near the compressor.
    Last edited by Gary; 30-07-2009 at 07:54 PM.

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    Re: AWHP superheat & sub-cooling

    Thanks so much for your comments.

    I am assuming that the Tw,tank is the same as the cond entering water temp, although this may not be the case.
    This is a close-enough approximation & within the range of experimental measurement uncertainty.

    The subcooling at 6.3K is well within what I would consider to be a normal range (5.5-8.5K). This is largely a matter of refrigerant charge.
    The current test point (Tc,sat=50'C) is around mid-range for the current designs. The amount of sub-cooling increases as the heating cycle advances. Towards the point Tc,sat~70-75'C, the sub-cooling effect is far more pronounced - in excess of 10-12K. This is what makes me think that the condenser is under-size.

    As to undersize/oversize, these are terms that are relative to accepted standards. Are there in fact any accepted standards for this type of system?
    To be honest, the standards that seem to be out there, for this kind of machine, seem to be locally-applied, rather than an industry-wide standard. Most of it seems to be still manufacturer-specific, as far as I can determine.

    All seems to be working well at this point. It will be interesting to see how these numbers compare with (all else being equal) a much hotter incoming water temp, as will be seen at the end of the heating cycle.
    Ok - good. What I'll do next is to do a set of tests at fixed points across the whole heating cycle & feed back. This will allow a more clear picture of the overall performance.

    An additional temp which should be monitored/recorded would be the discharge line temp near the compressor.
    The Tc,sup = 64.3'C (superheated vapour inlet to condenser) should be re-named as 'superheated vapour exit from compressor', as this is the point where it is physically measured. I'm used to using the figure for condenser performance checks & so lumped it there. Apologies.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    Ok - good. What I'll do next is to do a set of tests at fixed points across the whole heating cycle & feed back. This will allow a more clear picture of the overall performance.
    Excellent. Then we can see the changes throughout the system that occur due to the incoming water temperature rising.

    There should also be a similar set of tests (start of cycle/end of cycle) with the incoming air at 35C, as this is the other design extreme.

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    Re: AWHP superheat & sub-cooling

    There should also be a similar set of tests (start of cycle/end of cycle) with the incoming air at 35C, as this is the other design extreme.
    May have to wait a while for that - we're in the rainy season at present. Probably get up to ~30'C in the next few days, with lots of humidity. (Fill up water buckets from the evap drain - lol)
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    May have to wait a while for that - we're in the rainy season at present. Probably get up to ~30'C in the next few days, with lots of humidity. (Fill up water buckets from the evap drain - lol)
    I recall the weather extremes in that area of the world. When I was over there, people were shooting at me, so that made it even more uncomfortable... lol

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    Re: AWHP superheat & sub-cooling

    You really should have some means of regulating the intake air temp to simulate the two extremes that you are designing for.

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    Re: AWHP superheat & sub-cooling

    That's true.

    I'm presently planning to relocate from SEA back to my homeland. Once settled, I plan to set up the lab with some level of environmental control - it has to be done. To add hot air is not a problem, it's more when you want to cool the air to just above 0'C, that it gets a little more costly.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    That's true.

    I'm presently planning to relocate from SEA back to my homeland. Once settled, I plan to set up the lab with some level of environmental control - it has to be done. To add hot air is not a problem, it's more when you want to cool the air to just above 0'C, that it gets a little more costly.
    What you need is a good heat pump.

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    Re: AWHP superheat & sub-cooling

    ^ Hahaha... got 4 of those already. Point taken...
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    Re: AWHP superheat & sub-cooling

    A few thoughts on using only AWHP's to create a hot/cold test capability.

    Air cooling
    Using a air-source AWHP, where the output air-stream is partially re-circulated back to the evap inlet would bring the air temp down. I wonder how far this could go, though - if ducted properly?

    Air heating
    Use the hot water storage to pre-heat the incoming air-stream, or use a bank of direct-element heaters to raise the incoming air stream. Ducted flow.

    Any thoughts?
    Last edited by desA; 31-07-2009 at 05:59 AM.
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    A few thoughts on using only AWHP's to create a hot/cold test capability.

    Air cooling
    Using a air-source AWHP, where the output air-stream is partially re-circulated back to the evap inlet would bring the air temp down. I wonder how far this could go, though - if ducted properly?
    Aside from the obvious coil freezing problems:

    As the temp drops the heat load drops, so eventually the TXV would start hunting and then uncontrolled flooding.

    The orifice could be downsized, but the smaller the orifice the slower the pulldown.

    The temp could theoretically keep dropping until the compressor reached its lower limit, where it just can't pull a deeper vacuum or the liquid temp coming back from the condenser engages the entire coil in flashing.

    If you have a target temp you want to stop at you could do this with an evaporator pressure regulator (EPR) valve.

    Quote Originally Posted by desA View Post
    Air heating
    Use the hot water storage to pre-heat the incoming air-stream, or use a bank of direct-element heaters to raise the incoming air stream. Ducted flow.
    A hot water coil could be used easily enough.

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    Re: AWHP superheat & sub-cooling

    Actually, nothing so exotic is needed. I'm thinking a cheap window A/C could be modified to provide the heating and/or cooling.
    Last edited by Gary; 31-07-2009 at 06:59 AM.

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    Re: AWHP superheat & sub-cooling

    Good idea. A window-rattler.

    Isn't this the beauty of being in the HVAC&R game... lol...
    Last edited by desA; 31-07-2009 at 02:48 PM.
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    Re: AWHP superheat & sub-cooling

    The performance tests from Tc,sat = 40'C through 75'C, in steps of 5'C, are done. I need to tabulate & graph the results. Hope to have these out this weekend.

    At Tc,sat=40'C, the condenser sub-cooling is 3.8K & goes up to 15.2K at Tc,sat=75'C !!!
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    The performance tests from Tc,sat = 40'C through 75'C, in steps of 5'C, are done. I need to tabulate & graph the results. Hope to have these out this weekend.

    At Tc,sat=40'C, the condenser sub-cooling is 3.8K & goes up to 15.2K at Tc,sat=75'C !!!
    Now you know what receivers are for.

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    Re: AWHP superheat & sub-cooling

    What was the leaving water temp at Tc,sat=75C?
    Last edited by Gary; 31-07-2009 at 04:48 PM.

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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by Gary View Post
    What was the leaving water temp at Tc,sat=75C?
    Tw,out = 60.9'C @ Tc,sat=75'C
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    Re: AWHP superheat & sub-cooling

    Quote Originally Posted by desA View Post
    At Tc,sat=40'C, the condenser sub-cooling is 3.8K & goes up to 15.2K at Tc,sat=75'C !!!
    Quote Originally Posted by desA View Post
    Tw,out = 60.9'C @ Tc,sat=75'C
    Hmmm... 15.2K subcooling with 14.1K approach.

    This would seem like an opportune moment to test the excess subcooling theory. You could remove refrigerant until the subcooling is 8.5K and see if the approach increases or decreases.

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    Re: AWHP superheat & sub-cooling

    ^ Can you explain a little further on this, please?
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    Re: AWHP superheat & sub-cooling

    You were speculating earlier about using part of the condenser for excess subcooling. You now have excess subcooling backing up into the condenser.

    If that excess subcooling is beneficial, then removing it would increase the approach temp at Tc,sat=75C.

    If that excess subcooling is not beneficial, then removing it would decrease the approach temp at Tc,sat=75C.

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    Re: AWHP superheat & sub-cooling

    Ok, fair-enough.

    Let me finish the full test table & put it up (wip). We can then see the progression the whole way through the heat-up cycle. I also have the dynamic ramp test from the previous day, to measure overall (average) heating rate under that mass condition.

    We can then make a solid decision on how much charge to remove.

    I value your input greatly - it is an extremely valuable exercise for me.
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    Re: AWHP superheat & sub-cooling

    Sorry, I don't mean to rush you. You will of course, need a full spectrum of test tables for a base, in order to quantify the value of improvements.

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    Re: AWHP superheat & sub-cooling



    http://tinypic.com/r/34dn8gi/3

    That's the recent raw data.
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    Re: AWHP superheat & sub-cooling



    http://tinypic.com/r/21c7ame/3

    Correction... @ Tc,sat=75'C swapped Tc,exit & Tw,out data.
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    Re: AWHP superheat & sub-cooling

    We can be as critical of this design as we like.

    It is a machine I bartered in trade for consulting work performed for a now defunct heat-pump builder. It is not my design, I've just fine-tuned its performance a little & tested its robustness under 3rd world conditions. I use it as my test basis on which to benchmark my next machine, which is almost complete.
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    Re: AWHP superheat & sub-cooling

    Note that the data speaks with a forked tongue...

    You will observe that the Tw,out & T,tank values cross at some point. This should be non-physical & will definitely affect the condenser Approach calculation.

    It is something I've observed in earlier trials at one of my clients. In my view the temp probe for the water outlet from the condenser, although insulated, is losing accuracy as temp increases, whereas the storage water temp is mixed & therefore more representative.

    I will upload a plot showing both the conventional (Approach=Tc,sat-Tw,out) & modified (Approach'=Tc,sat-T,tank), for clarity. It makes a huge difference in interpretation.
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    Re: AWHP superheat & sub-cooling



    http://tinypic.com/r/2hi3r6o/3

    The value (-Cross)=Tc,exit-Tw,out. This is a critical parameter for heat-exchanger design purposes.

    (-Cross)'=Tc,exit-T,tank
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