(i) What are the advantages of using an expansion valve instead of an expander in a vapour compression refrigeration cycle ? (ii) Give a comparison between centrifugal and reciprocating compressors. (iii) An ice-making machine operates on ideal vapour compression refrigeration

Question

(i) What are the advantages of using an expansion valve instead of an expander in a vapour compression refrigeration cycle ?
(ii) Give a comparison between centrifugal and reciprocating compressors.
(iii) An ice-making machine operates on ideal vapour compression refrigeration cycle using refrigerant R-12. The refrigerant enters the compressor as dry saturated vapour at – 15°C and leaves the condenser as saturated liquid at 30°C. Water enters the machine at 15°C and leaves as ice at – 5°C. For an ice production rate of 2400 kg in a day, determine the power required to run the unit. Find also the C.O.P. of the machine. Use refrigerant table only to solve the problem. Take the latent heat of fusion for water as 335 kJ/kg.

Accepted Answer

(i) If an expansion cylinder is used in a vapour compression system, the work recovered would be extremely small, in fact not even sufficient to overcome the mechanical friction. It will not be possible to gain any work. Further, the expansion cylinder is bulky. On the other hand the expansion valve is a very simple and handy device, much cheaper than the expansion cylinder. It does not need installation, lubrication or maintenance.
The expansion valve also controls the refrigerant flow rate according to the requirement, in addition to serving the function of reducting the pressure of the refrigerant.

(ii) The comparison between centrifugal and reciprocating compressors :
The comparison between centrifugal and reciprocating compressors is given in the table below:

S. No.

Particulars

Centrifugal compressor

Reciprocating compressor

1.

2.
3.
4.
5.

6.

7.
8.
9.
10.
11.

Suitability

Operational speeds
Air supply
Balancing
Lubrication system

Quality of air delivered

Air compressor size
Free air handled
Delivery pressure
Usual standard of compression
Action of compressor

Suitable for handling large
volumes of air at low pressures
Usually high
Continuous
Less vibrations
Generally simple lubrication
systems are required.
Air delivered is relatively
more clean
Small for given discharge
2000–3000 m³/min
Normally below 10 bar
Isentropic compression
Dynamic action

Suitable for low discharges
of air at high pressure.
Low
Pulsating
Cyclic vibrations occur
Generally complicatedGenerally contaminated
with oil.
Large for same discharge
250–300 m³/min
500 to 800 bar
Isothermal compression
Positive displacement.

(iii) Using property table of R-12 :

[latex]h_{2} [/latex] = 344.927 kJ/kg
[latex]h_{4} = h_{1} [/latex] = 228.538 kJ/kg
[latex](c_{p})_{v} = 0.611 [/latex] kJ/kg°C
[latex]s_{2} = s_{3} [/latex]

or 1.56323 = 1.5434 + 0.611 [latex] log_{e} [\frac{t_{3} + 273}{30 + 273} ] [/latex]

or [latex] t_{3} [/latex] = 39.995°C
[latex] h_{3} [/latex] = 363.575 + 0.611(39.995 – 30)
= 369.68 kJ/kg.
[latex] R_{n} /kg = h_{2} – h_{1} [/latex] = 344.927 – 228.538
= 116.389 kJ/kg
[latex] W/kg = h_{3} – h_{2} [/latex] = 369.68 – 344.927 = 24.753

C.O.P. = [latex] \frac{R_{n}}{W} = \frac{116.389}{24.753} [/latex] = 4.702.

Assuming [latex] c_{p} [/latex] for ice = 2.0935 kJ/kg°C
Heat to be removed to produce ice

= [latex] \frac{2400}{24 × 3600} [/latex] [4.187(15 – 0) + 335 + 2.0935(0 – (– 5))]

= 11.3409 kJ/s = Work required, kJ/s (kW) × C.O.P.

∴ Work required (Power) = [latex] \frac{11.3409}{4.702} [/latex] = 2.4 kW.

Question 12.16: (i) What are the advantages of using an expansion valve inst...

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