Pressure & Heat - Part 4 - Efficient Compression

Hopefully this series of articles about everything you may need to know about PH diagrams but were afraid to ask, has been useful and interesting.

We've gone through:

• The features of a PH diagram.
• How to draw an ideal vapour compression cycle.
• Non-ideal factors of pressure drops, superheat, and subcooling.

And now we get to the point which I was threatening in the last post - isentropic efficiency. Isentropic efficiency is a measure of how efficient the compression is, regardless of where the lines of constant entropy take you. It is independent of how much sub cooling you have, how much useful superheat that CoP relies on - it is a pure measure of compressor efficiency.

Quick note - you are going to see this symbol "~" a lot. It's called a "tilde" and in context means "approximately". I say this upfront, because I didn't know what it meant until I looked it up yesterday. Every day is a school day.

Drawing real world vapour compression cycles

Let us take a "semi-ideal" vapour compression cycle (-10°C evap. / 50°C cond., but with a 20°C Suction Gas Return Temperature), we drew our line of compression to match the nearest line of constant entropy (isentrop).

We can now also a look at what discharge temperature we may get from a typical compressor. From the freely and widely available Bitzer selection software, such a selection is found below.

The simplest way to draw a real-world design is to simply plot the highlighted discharge gas temperature at the relevant point on the PH diagram (i.e. on the isotherm gradient that best represents ~96°C.) and extend your lines of condensation and compression to meet at that point.

Being familiar with compressor selection software (and they're not hard to work), enables you to get representative discharge temperatures very quickly.

We can see that in our semi-ideal cycle, the discharge temperature at the compressor outlet should be 83°C. However, you won't be able to find a single compressor that will have a low discharge temperature as this. Why? Because of the 2nd law of thermodynamics and that is why we can't have nice things (a phrase that can be used for literally anything).

Isentropic Efficiency & how to calculate it.

A compressor must relentlessly live in the real world, and deal with energy losses, thermal inefficiencies, internal pressure drops, leakage etc. All these losses require more energy to be put into the compressor and this will be reflected amongst other things, in an elevated (compared to ideal) discharge temperature, as we've shown.

And this is where we start to talk about Isentropic Efficiency (IE). Sounds complicated, but it's really a simple concept. IE is calculated by dividing the theoretical/isentropic work, by the real work you have to do, and this will return a decimal.

Let's do simple example:

• specific ideal/isentropic compression work is 39.1 kJ/kg
• specific actual compression work is 55.86 kJ/kg

39.1 / 55.86 = 0.7 or 70% Isentropic efficiency.

And it really is that simple.

I didn't arrive at a 70% IE value by accident. ~70% Isentropic Efficiency is particularly good going for a compressor. If you're wondering where the other ~30% has gone, that's a good question. In general, the losses from a hermetic or semi-hermetic compressor could be split to the following proportions.

• Pressure drops, leakage, and related other flow losses. (~10% IE Loss.).
• Friction and parasitic losses like an oil pump (~10% IE Loss).
• Motor losses (~10% IE Loss).

Advances in technology (e.g. BLDC, LSPM motors, new valve plate designs, magnetic bearings) may improve matters now and in the future - but if you assume 70% isentropic efficiency, you will never be too far wrong in what efficient looks like.

Worked Example

Let's take our current example and work out the isentropic efficiency. I'm going to use Coolpack (If you haven't already got a free copy of this excellent software, give your head a wobble) for my values, whereas if you're manually measuring, your values may differ.

We are going to compare ideal/isentropic with a real compressor.

Compressor Work Isentropic (CWI - Green line) is 39.1 kJ/kg.

Compressor Work Real (CWR - Blue line) is 54.4 kJ/kg.

39.1 / 54.4 = 0.718 or 72% Isentropic Efficiency

If you want to go backwards and calculate your work of compression based on a given isentropic efficiency - simply divide your isentropic work by your stated IE. So if we've got a slightly less efficient compressor the example would look like this.

CWI 39.1 / 65% IE 0.65 = 60.2 kJ/kg = CWR Compression Work Real

Use that real compressor work to determine your gradient of the compression line (by drawing a right-angled triangle) and Robert's your father's brother.

Resultingly the discharge temperature can be seen to have increased to 102°C amongst other things.

What affects Isentropic Efficiency?

A compressor's isentropic efficiency is not a constant value, and it will change depending on the compression type and pressure ratio, amongst many other things. I've calculated the isentropic efficiency of three typical compressors of three different types (on R404A) and shown the below isentropic trends. There is a lot of very good work out there already on compressor types, so I won't go over the differences (undoubtedly poorly).

Ignoring the actual efficiency of the lines for a moment (which is why I've removed the values of the axis), we can see the following:

• Reciprocating/Piston compressor has a relatively flat isentropic efficiency curve, with efficiency improving as the pressure ratio increases.
• Scroll compressors tend to have a pronounced sweet spot depending on what part of the pressure ratio that particular scroll set is optimised for and will start to lose isentropic efficiency relatively quickly once out of the optimal area.
• The trend of the Semi-hermetic screw is similar to a scroll, albeit with a flatter curve. A point to note - this trend is for an Un-economised screw, and a economised screw will have a higher isentropic efficiency and capacity.

A compressor that has efficiency advantage at a specific operational point, might not retain that advantage across the entire envelope, or indeed for most of it. In an actual real-world example of the significant differences in isentropic efficiency trend. If one had ever selected a Copeland Scroll compressor, they might have found that the low temperature compressor ZF18K4E-TFD had a significantly better COP than the medium temperature ZB45KCE-TFD at condensing temperatures above 40°C.

Yeah, yeah, but your scientists were so preoccupied with whether or not they could that they didn't stop to think if they should.

Ian Malcolm, Jurassic Park.

And such an observation might (definitely) have resulted in some application engineers (not me on this very one-off occasion in where I reference mistakes) in selecting ZF18 instead of the ZB45 for medium temperature applications. What's the worst that could happen?

We can see the characteristic isentropic curves of a scroll, but more tellingly, we can see that the ZB45 compressor was/is a bit of a beast when it comes to refrigeration in the UK. How much of a beast?

Based on this temperature profile, for 99.9% of the year has a compressor at above 70% isentropic efficiency, is pretty awesome. And we can see that the ZF18 would have been a completely inappropriate substitute for the ZB45.

But... what if we want to recover useful heat on demand and have elevated discharge pressures as a result? We shift more operational hours out of the 15,20,25°C portions of the graph and into the 45-50°C? In such cases there may have been more efficient compressors for the application (such a reciprocating compressor?).

Understanding how compressors perform will enable the most appropriate selection to be made for your application, or indeed the most appropriate system design.

Volumetric Efficiency (VE)

On a related vein - in the same way we can work out the isentropic efficiency of a compressor (i.e. how efficiently it compresses), we can also work out how effectively it uses its displacement to compress suction gas.

And this is fundamentally simple as well.

And much like isentropic efficiency, we will also have losses in volumetric efficiency, such as:

• Suction cooling a motor increases the superheat of the refrigerant, increasing the volume of the refrigerant once past.
• Pressure drops & leakage losses.
• Heat transfer between hot and cold portions of the compressor

Some compressors, particularly scrolls have very high volumetric efficiencies, with very flat curves, where as reciprocating compressors VE curves are almost the reverse of their IE trend (though more steep in gradient).

How do we calculate Volumetric Efficiency?

We know how to calculate our mass flow rate required for a given duty and we also can see the mass flow rate from compressor selection software. In the case of the 4HE-25Y referred to at the start of the article, at our semi-ideal conditions, we have a mass flow of 1108 kg/h. We also know that this compressor has a displacement of 73.7 m^3/h.

To calculate the volume flow rate all we need is the specific volume of the refrigerant gas at the compressor inlet.

And we can either estimate it from the lines of constant volume (isochores), or you can use Coolpack (or similar software) for a more precise value. The precise value, which is 0.05324 cubic metres per kilogram.

Mass flow rate of 1108 kg/h * specific volume of 0.05324 m^3 per kg = a volume flow rate of 59 m3/h.

Now that we have calculated the volume flow, the volumetric efficiency is just a few seconds away.

Volume Flow rate 59 m^3h / Compressor Displacement 73.7 m^3h = 80% VE.

What affects Volumetric Efficiency

Much like isentropic efficiency, VE is affected by both compression type and by pressure ratio. Scrolls have a very high volumetric efficiency. A reciprocating piston compressor has to have a minimum distance between the piston and the valve plate (to avoid mischief). This clearance volume ensures that a progressive degree of re-expansion happens.

We can see below another trend of typical compressor of various types.

• Reciprocating piston compressor volumetric efficiency decreases with an increasing pressure ratio (inversely proportional).
• Scroll compressors as mentioned before have a much higher volumetric efficiency in general, and flatter VE curve as well. Compared to other compressor types - this allows them to do more duty at the edges of the allowable envelope than the equivalent reciprocating piston compressor.
• The trend of this (un-economised) semi-hermetic screw is similar to a piston compressor, with a flatter curve.

What does this mean? Fundamentally it means that a scroll and screw compressor will have less capacity reduction in hot weather than reciprocating compressors. If you've ever wondered why the ZB45KCE-TFD came with a 6 horsepower motor, compared to an equivalent reciprocating 3.5 horsepower reciprocating compressor - it's very likely due to the fact that at the highest compression ratios, it's simply doing much more work, even before you consider how its isentropic efficiency might fall away at these points.

Volumetric efficiency is important in keeping compressors size down, but it doesn't necessarily have to impact on efficiency.

Notes on compressor software

Compressor selection software - it should be noted is an approximation of a compressor's performance. Not every possible operating point in a compressor's envelope is (or even can be) tested by a compressor manufacturer. It takes thousands and thousands of hours to qualify a compressor at a few operational points on the edges of the envelope, so we're not going to have empirical data for every single compressor running at 33 Hz, at a condensing temperature of 18.7°C and an evaporating temperature of -8.3°C.

A compressor polynomial is an approximation of what a compressor will do (potentially with a tolerance of -/+ 5%, any compressor manufacturers reading this, feel free to correct me in the comments or privately!).

There also may be some errors in the software. I was investigating how a compressor may perform at a certain condensing temperature (30.98°C), and the calculated discharge temperature returned was... 31°C. Which if true, is quite the engineering and scientific feat, and Net Zero is indeed solved and we can all go home now (try plotting it on a PH diagram and you'll see what I mean.

I suggest adopting the approach of "trust but verify" when talking compressor software outputs. There maybe be certain points where the software claim things are different to physical reality. And that's fine - just act accordingly.

Fundamentally, don't forget that the most critical thing of all is keeping your suction pressure stable and at the highest practicable value.

Concluding thoughts

Quite a lot to scroll through, and whilst it might seem like a diversion - all of this discussion regarding compression efficiency was enabled by the humble Pressure Enthalpy diagram. And that's why they're great.

To Recap - We've learnt:

• Real world compression has energy losses, and where these losses occur Same for volume.
• How to calculate isentropic efficiency from compressor discharge temperatures.
• How to calculate volumetric efficiency from compressor displacement and your particular cycle.
• How to draw any vapour compression cycle based on the isentropic efficiency you require.
• How different compressor types respond to different pressure ratios.
• Why you should never prefer a ZF18 compressor over a ZB45 compressor in MT conditions.

That's some good going, I think. You now know (if you didn't already) considerably more than most Building Services Engineering graduates when it comes to vapour compression refrigeration cycle.

Next, we are going look at the refrigerants that display a degree of glide and what we need to look for when designing systems that use them (all off the humble Pressure Enthalpy chart again...).