Efficiency - Working with the Refrigerant Circuit

To measure what is happening the first thing to do is to find the temperatures and pressures at key points in the circuit.
Measurement points for Temperature **T** and Pressure **P **can be used to
define the process.

Once the points 1,2,3,4 in the P-h diagram have been defined, the cycle can be plotted
on a P-h chart. P-h charts for all common working fluids (refrigerants) are available.
In these charts the pressure and enthalpy values are shown to scale. In the old days
large charts were used, and refrigeration engineers would plot
the circuit diagram on the chart, allowing various parameters
at each point in the circuit to be read. The pressure level
before and after compression determines the position of the horizontal lines. These pressure
levels define the
evaporating and condensing temperature and this
can be read off the chart by finding which temperature line intersects the saturation curve.
The measured temperatures determine the end points of the lines, using the contour lines of
temperature shown on the chart.

Today, refrigerant properties are readily available on the computer, and so working
with charts has come to be a thing of the past. The computer method is very much faster.
Information on all parameters such as
evaporating temperature, condensing temperature,
superheat, subcooling, and COP is instantly
available from the pressure and temperature sensor inputs which feed the data directly
in to the computer. .

An explanation of the P-h diagram, Practical Refrigeration Cycle,
Evaporation and Condensation is in the
the Understanding Refrigeration pages.

Efficiency or COP

The conventional way to express the effectiveness of refrigeration is Coefficient of Performance
(COP). This is the ratio of heat extraction to energy input. Both are expressed in the same units,
normally kilowatt (kW). For a system in which the mass flow rate is constant, COP becomes equal to the
ratio of ratio of enthalpy change in the evaporator and enthalpy increase during compression. i.e.
**dh1/dh2**. On the pH chart, enthalpy is shown as enthalpy per
per unit mass, or specific enthalpy. The ratio dh1/dh2 is the rate of transfer of energy
in the evaporator divided by the rate of transfer of energy in the compressor.

In an actual system pressure drops are bound to occur in the heat exchangers and connecting
pipes. Sloping lines are shown to indicate this. A downward slope indicates
that the pressure is reducing. Provided the pressures are measured at the
inlet and outlet of the compressor, and the temperatures are measured in the appropriate places,
the COP of the system can be found.

Suction Line Losses

The astute reader will have noticed that in the event of a long connecting line between the evaporator and the compressor
the condition of the refrigerant at the compressor inlet could differ from that at the evaporator outlet.
Between these two points there could be a pressure drop and an increase in enthalpy. The pressure drop
would arise from the flow losses in the line. The enthalpy increase would be due to heat gain by
the refrigerant on its journey from the evaporator to the compressor. In the diagram this additional
pressure drop is shown by **dP** and the increase in enthalpy is denoted by the gap
between **dh1** and **dh2**.

In most systems both of these effects are very small. In the diagram they are much enlarged
for clarity. For practical purposes they only arise in systems where
the evaporator or cooler is a long way away from the compressor. In this event the accuracy
of COP may be improved by measuring the temperature at the evaporator outlet, and using this
value to determine dh1, while at the same time using the compressor inlet temperature
to determine dh2. Note that for perfection, the pressure at the evaporator outlet
should also be measured, but this is not necessary in practice because the enthalpy
effect of the
pressure change in pressure, dP, is normally very small in this situation . The
enthalpy, h, of the vapour is primarily temperature dependent.

Compressor Efficiency

Accurate measurement of the pressures and temperatures at the positions shown above allows the efficiency of the
compressor to be found. How? Read off the enthalpy at point **2** where the vapour
enters the compressor, and at point **3** where the vapour
leaves the compressor to find the enthalpy change **dh2**. The increase in enthalpy arises because work is done on the vapour
in order to raise its pressure. The ideal (minimum) amount of work is known. It is the work which
would need to be done in the case of an ideal or reversible compression process. The enthalpy
increase for such a process can be read off the chart (or calculated by the computer). This is
done by finding the point on the chart at the high pressure which has the same **entropy**
as point **2**. This "ideal" or "mimimum" enthalpy
difference is shown as **Ideal dh2** in the diagram. Entropy is the property which remains constant for reversible processes.
Contours of constant entropy are shown on the chart.

Compressor efficiency can be defined as the ratio between this enthalpy increase and the actual
measured enthalpy increase, i.e. **(Ideal dh2/dh2)**. It is called the isentropic efficiency of the compressor.

An explanation of the Reversible Process,
is in the
the Understanding Refrigeration pages.

Compressor Heat Loss

In the above method for finding COP the enthalpy increase dh2 is determined by measurement
of the temperature and pressure at the end of the compression process. Measurement immediately
before and after compressor allows points 2 and 3
to be plotted on the chart, so that dh2 can be read off. However, a compressor gives off heat to the atmosphere.
It becomes warm. Heat leaving the
compressor and dissipating into the surrounding air results in correspondingly less heat leaving in the refrigerant vapour stream.
The consequence
is that the enthalpy at point 3, taken from discharge line temperature
measurement, will tend to be too low, and dh2 is then smaller than it should
be. The COP will be too high. For an accurate assessment of COP this heat loss **H** needs to be
accounted.

The compressor heat loss is usually expressed as a percentage
of the electrical power input. The net energy input becomes the electrical
energy input **E **less the heat loss **H** , and this quantity **(E-H)**
is equal to
energy gain represented by dh2. For example if it is known that 5% of the electrical
power input is heat loss, then 5% should be added to the value of dh2 found from
the measured temperature values. The correct dh2 and hence the correct efficiency
can then be found. For most compressors the heat loss is between 5 and 7%, and an error
in this value has only a very small effect on the final result in most cases.

Sounds Very Complicated?

The calculations maybe, but the computer will do all the work, and it will do it almost instantly!

An explanation of the P-h diagram, Practical Refrigeration Cycle, Evaporation and Condensation is in the the Understanding Refrigeration pages.

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