Most, if not all, HVAC professionals are confused about Refrigerating Efficiency. For instance, the efficiencies of large industrial air conditioning systems, especially chillers, are given in terms of kW/tonne, to specify the amount of electrical power that is required for a tonne of refrigeration of cooling. In this case, a smaller value represents a more efficient system. However, according to Chapter 2 (Thermodynamics and Refrigeration Cycles) of the 2017 ASHRAE Handbook Fundamentals, the Refrigerating Efficiency has a different formula, which is barely used in the HVAC market. It is simply the ratio between the actual coefficient of performance (COP) and maximum possible COP.

Let’s look at Coefficient of Performance (COP), (COP)rev and Refrigerating Efficiency. Chapter 2 of the ASHRAE Handbook defines the above terms as follows:

COP
Performance of a refrigeration cycle is usually described by a COP, defined as the benefit of the cycle (amount of heat removed) divided by the required energy input to operate the cycle:

COPrev
The ideal reversible cycle (COP)rev is the maximum theoretical COP for an air conditioning system; it is expressed by Carnot’s Theorem, reduced to the following equation:

Where:

The above equation concludes that the COP of the Carnot Cycle is entirely a function of the temperature limits and can vary from zero to infinity.

A low value of TC will make the COP high. A high value of TE increases the numerator and decreases the denominator, both of which increase the COP. The value of TE, therefore, has a more pronounced effect upon the COP than TC.

To summarise, for a high COP, you need to operate with a high TE and a low TC.

REAL WORLD OPERATION OF REFRIGERATION CYCLE

If we left the analysis here, we would leave the false impression that we have complete control over TC and TE. If this were true, TE could simply be set equal to TC, which would make the COP equal to infinity.

A closer study shows that certain temperature requirements are always imposed upon the refrigeration system related to cooling of buildings. For example, if the refrigeration system must maintain a chilled water supply temperature at 8 degrees C and can reject heat to the atmosphere at 15 degrees C during winter operation, these two temperatures are limitations within which the cycle must abide, and as a result, the maximum possible COP would be:

It is important to note here that all the processes in the Carnot Cycle are thermodynamically reversible – that is, all the heat transfers occur at zero temperature difference and zero approaches, and no friction occurs in any of the components.

A Carnot Refrigerator serves as a standard against which actual refrigeration cycles can be compared.

REFRIGERATING EFFICIENCY
Refrigerating Efficiency is the ratio between the actual Coefficient Of Performance COP and the ideal reversible cycle (COP)rev

So, according to the ASHRAE Handbook, the Refrigerating Efficiency is not merely the actual COP, as submitted by the manufacturer, but is the ratio between the actual COP and the maximum possible COP. For instance, the actual COP for a water-cooled centrifugal chiller, operating in accordance with ANSI/AHRI Standard 551/591 (SI) 2018 at full load is 7.2, whereas the maximum possible COP at the same conditions is:

As a result,

is the maximum Refrigerating Efficiency that is currently available in the market for a water-cooled chiller working at full load in accordance with AHRI standard conditions.

It is also important to note here that no refrigeration cycle can be constructed with a full load COP > 10 at the above AHRI temperature limitations without the violation of the second law of thermodynamics.

The table, below, gives the maximum possible COP at various loads, based on their associated AHRI temperature limitations versus the actual COP available in the market at the corresponding load…

The curves in the chart were presented giving correlations of the max COP, actual COP and Refrigerating Efficiency versus the chiller load. These curves confirm that the maximum Refrigerating Efficiency coincides with the chiller full load.

The COP or kW/TR comes from the First Law of Thermodynamics (FLT), hence it fails to identify waste or the effective use of resources. On the other hand, the Refrigerating Efficiency comes from the Second Law of Thermodynamics (SLT), which becomes a logical and meaningful target.

The generality of the SLT gives us a powerful means to understand the thermodynamic aspects of real systems through the usage of ideal systems. What makes this new statement of the SLT valuable as a guide to energy policy is the relationship between entropy and the usefulness of energy.

kW/TR and COP are often misleading in that they do not always provide a measure of how nearly the performance of a system approaches ideality. Further, the thermodynamic losses that occur within a system – that is, those factors that cause performance to deviate from ideality – often are not accurately identified and assessed with energy analysis.

For instance, as indicated in the table and chart, above, the Actual COP of 10 at 50% load may lead you to conclude that the chiller is more efficient at 50% part load than its full load, where the COP equals 7.2. However, we know that the max possible COP at 50% and 100% are 20 and 10, respectively, and as a result, the Refrigerating Efficiency at full load is 7.2 / 10 = 72%, which is higher than the Refrigerating Efficiency at 50% load, which is 10 / 20 = 50%.

CONCLUSION
An HVAC professional designing a system makes trade-offs among competing factors. The designer is expected to aim for the highest reasonable technical efficiency at the lowest reasonable cost under the prevailing technical and economic conditions, and also accounting for ecological and social consequences and objectives. Refrigerating Efficiency is the only tool that provides a measure of how nearly the performance of a system approaches ideality.

References

1. 2017 ASHRAE Handbook Fundamentals

2. Paul de Larminant, “Overview of Fluids for AC Applications”, ASHRAE Journal. February 2017.

Farhan Juratli is District Cooling Project Manager at Nakheel.