Chapter 12
Reciprocating Air Compressors
12.1 ❐ INTRODUCTION
Compressors are mechanical devices used for increasing the pressure of a gas. Compressors used for producing high pressure air are called air compressors. Air is drawn from the atmosphere by suction process, which is then compressed to the required pressure and delivered to the receiver. Air compressors may be classified as shown in Fig. 12.1.
Figure 12.1 Classification of compressors
If compression is done in a conventional cylinder with a closely fitted piston making reciprocating motion, then the compressor is called a reciprocating compressor. External work must be supplied from a prime mover to the compressor to achieve the required compression. The general arrangement of the compressor and prime mover used to run the compressor is shown in Fig. 12.2.
Figure 12.2 Energy flow in an aircompressor
12.2 ❐ USES OF COMPRESSED AIR IN INDUSTRY
The several uses of compressed air are as follows:
 To drive a compressed air engine
 For producing an air blast for a workshop
 For spraying the fuel (atomizing) into a boiler furnace
 For operating pneumatic drills and tools
 For operating pneumatic brakes for locomotives and rolling stock
 Pneumatic conveying and for pumping of water by compressed air
 For working compressed air engines especially in mines
 In gas turbine power plants and airconditioning plants
12.3 ❐ WORKING PRINCIPLE OF SINGLESTAGE RECIPROCATING COMPRESSOR
The schematic arrangement of a singlestage reciprocating compressor is shown in Fig. 12.3. It consists of a cylinder with cooling jacket, piston, connecting rod, crank, suction valve, and delivery valve. The piston will be making toandfro motions through the crankshaft arrangement and generally run by an electric motor, diesel engine, petrol engine, or steam engine. During the outward motion of the piston, the pressure inside the cylinder falls below the atmospheric pressure and the suction valve is opened due to the pressure difference. The atmospheric air is then drawn into the cylinder until the piston reaches the bottom dead centre position.
Figure 12.3 Singlestage reciprocating aircompressor
As the piston starts move inwards, the suction valve gets closed and the pressure starts increasing until the pressure inside the cylinder is more than the pressure of the delivery side. Then the delivery valve opens and high pressure air is delivered to the receiver till the piston reaches the top dead centre. At the end of the delivery stroke, the small volume of high pressure air left in the clearance volume expands as the piston starts moving outwards. Hence, the cycle is repeated.
12.4 ❐ TERMINOLOGY
 Singleacting compressor: If the air admission from the atmosphere is on only one side of the cylinder.
 Doubleacting compressor: When, the air from the atmosphere is drawn on both sides of the piston.
 Singlestage compressor: If the total compression is done fully in one cylinder.
 Multistage compressor: If the compression is carried out in more than one cylinder, and every cylinder carries out a part of the compression.
 Free Air Delivered (FAD): It is the actual volume delivered at the stated pressure, reduced to intake pressure and temperature, and expressed in cubic metre/minute (m3/min). FAD is used to measure the capacity of a compressor.
 Displacement or Swept Volume of the Compressor: The volume displaced by piston movement between two dead centers is called displacement or swept volume. For a single acting compressor, swept volume,
where d = diameter of piston and L = length of stroke
12.5 ❐ TYPES OF COMPRESSION
The theoretical p−V diagram for single acting compressor is shown in Fig.12.4. The line 4–1 represents the suction stroke. The air is then compressed adiabatically as shown by the curve 1–2 in Fig. 12.4. It is then forced out of the cylinder at constant pressure p_{2}, as shown by the line 2–3. The work done is represented by the area 1–2–3–4–1.
Figure 12.4 Theoretical pV diagram for single acting compressor
If the air had been compressed isothermally, as represented by the curve 1–2′, then the work done on the air would be the area 1–2′–3–4–1, which is considerably less than that due to adiabatic compression. However, it is not possible in practice to compress the air isothermally because in that case, the compressor would need to run extremely slow. In practice, the compressors are driven at fairly high speeds in order to compress as much air as possible in a given time. Hence, the compression of air will approximate to an adiabatic. The work saved by compressing isothermally is shown by the shaded area 1–2–2′–1.
12.5.1 Methods for Approximating Compression Process to Isothermal
The following practical methods are used to achieve nearly isothermal compression:
 Cold water spray: In this method, cold water is sprayed onto the cylinder during compression, thus reducing the temperature of the air. Without the cold water spray, the compression would have been adiabatic or pV^{γ} = constant. This effect is shown in Fig. 12.5, where now the compression would be between adiabatic and isothermal or pV^{n} = const., where 1 < n < 1.4. The work saved is represented by 122′′1.
Figure 12.6 Multistage compression
 Water jacketing: The water is circulated around the cylinder through the water jacket to cool the air during compression. This method is commonly used for all types of reciprocating compressors.
 Intercooling by using multistage compression: In a multistage compressor, the air is compressed in several stages. In principle, it is equivalent to number of compressors in series where the air passes from one cylinder to the next and the pressure increases in each cylinder. The p − V diagram for a fourstage compressor is shown in Fig. 12.6. The dotted line 1–4′ is the isothermal. In the first stage, the air is compressed adiabatically to 2′ and cooled at constant pressure to 2′ in the intercooler, possibly to the initial temperature. For complete intercooling, the point 2′ is on the isothermal line 1–4′. The air is then drawn into the second cylinder for the second stage of compression and the process is repeated for the subsequent cylinders. Line 1–a represents the adiabatic compression in a single cylinder. The compressor work saved by intercooling is represented by the area 2–a–4–3′–3–2′–2.
 External fins: Small capacity compressors are provided with fins to increase the heat transfer from the surface of the cylinder.
12.6 ❐ SINGLESTAGE COMPRESSION
12.6.1 Required Work
Without Clearance
Consider the theoretical p−V diagram for a singlestage air compressor as shown in Fig. 12.7. The work done on air per cycle is represented by the area 1–2–3–4–1.
W = area (a − b − 2 − 3 − a) + area (b − c − 1 − 2 − b) − area (a − c − 1 − 4 − a)
where m = mass of air delivered per cycle.
Work done per kg of air
If the compression had followed the law, pV^{n} = c, then
Power required in driving the compressor
where N = number of complete cycles per minute
= rpm, if single acting
= number of strokes per minute, if double acting.
With Clearance Volume
The pV diagram for a singlestage and singleacting air compressor is shown in Fig. 12.8 with clearance volume.
Let V_{c} = clearance volume
V_{s} = swept volume = V_{1} − V_{c}
V_{a} = actual volume = V_{1} − V_{4}
Let the compression and expansion processes follow the same low pV ^{n} = const.
Work done per cycle,
Now, p_{3} = p_{2 }and p_{4} = p_{1}
Figure 12.8 pV diagram with clearance
where m_{1} = actual mass of air delivered per cycle.
12.6.2 Volumetric Efficiency
The volumetric efficiency of a reciprocating compressor is defined as the ratio of the actual free air delivered to the swept volume of the compressor. The free air delivered is (V_{1}–V_{4}), whereas the swept volume is (V_{1}–V_{c}). Thus,
Let clearance ratio
When referred to ambient conditions,
Factors Affecting Volumetric Efficiency
The volumetric efficiency of a compressor can be lowered by any of the following conditions:
 Very high speed
 Leakage through piston seals
 Too large a clearance volume
 Obstruction at inlet valves
 Overheating of air by contact with cylinder walls
 Inertia effect of air
Figure 12.9 shows the variation in volumetric efficiency with clearance ratio (c), and the pressure ratio (p_{2}/p_{1}), and polytropic index of compression (n) (by changing one factor keeping the other two factors constant). The volumetric efficiency decreases with increase in both the clearance ratio (c), and the pressure ratio (p_{2}/p_{1}), whereas it increases with increase in the polytropic index of compression (n).
Figure 12.9 Variation of volumetric efficiency with clearance ratio, pressure ratio and polytropic index of compression
12.6.3 Isothermal Efficiency
The pV and T s diagrams for isothermal and polytropic compression of air in the compressor, respectively, are shown in Fig. 12.10.
Polytropic work done,
Isothermal work done
However, p_{1}v_{1} = p_{2}v_{2′}
Work saved, ∆W = W_{p} − W_{i}
The isothermal efficiency (η_{i})is a measure of the degree to which isothermal compression has been achieved. It is defined as the ratio of isothermal work to that of actual indicated work and is given by
12.6.4 Adiabatic Efficiency
It is defined as the ratio of the work done on the compressor with reversible adiabatic compression to the work done with irreversible polytropic compression.
12.6.5 Calculation of Main Dimensions
The actual volume of air drawn in by the compressor per stroke,
Capacity of a singleacting compressor,
Also,
where d = piston diameter
L = length of stroke
Therefore, L and d can be determined.
12.7 ❐ MULTISTAGE COMPRESSION
Singlestage compression suffers from many disadvantages such as (i) handling of very high pressure range in one cylinder resulting in leakage past the piston, (ii) ineffective cooling of the gas, and (iii) necessitating robust construction of the cylinder to withstand the high delivery pressure.
The volumetric efficiency of a singlestage compressor with fixed clearance decreases with an increase in pressure ratio and thus reduces the capacity. Thus the necessity of of multistage compression with intercooling between stages are listed below:
 The air can be cooled perfectly at pressures intermediate between the suction and delivery pressures resulting in less power required as compared to a singlestage compressor for the same pressure limits and quantity of free air delivered.
 The mechanical balance of the machine is better due to phasing of the operations.
 The pressure range and hence the temperature range in each stage can be kept within desirable limits. This results in:
 Less loss of air due to leakage past the piston.
 More perfect lubrication due to lower temperatures.
 Better volumetric efficiency.
 The lighter construction of the machine that reduces the cost.
12.7.1 Twostage Compressor
The schematic arrangement of twostage compressor with intercooler and p − V diagram are shown in Fig. 12.11. The air is first taken into the low pressure (L.P.) cylinder at pressure p_{1}. After compression to intermediate pressure p_{2}, the air at condition 2 is passed through the intercooler and leaves it at point 3, where its temperature is reduced from T_{2} to T_{3}. The air may be cooled to point 3′ such that T_{3}′ = T_{1}. Finally, the air is compressed in high pressure (H.P.) cylinder from condition 3 to 4 and is discharged to the receiver. Area 2–3–4–6–2 represents the work saved due to intercooling.
Figure 12.12 shows the p − V diagram for twostage compression with perfect intercooling. Process 1–2 represents the polytropic compression in the L.P. cylinder with pV ^{n1} = constant. Process 2–3 represents intercooling from T_{2} to T_{3} = T_{1}. Process 3–4 represents the polytropic compression in the H.P. cylinder with pV ^{n2} = constant. Curve 1–3–4′ represents the isothermal compression.
Total work done on the air,
Let and
Figure 12.11 Two stage compression with intercooling: (a) Schematic arrangement, (b) pV diagram
For p_{1} and p_{3} to be constant, intermediate pressure p_{2} must be determined for minimum work.
Thus,
For n_{1} = n_{2} = n, and a = b.
For perfect intercooling, T_{3} = T_{1}. Thus,
In general, with i number of stages, we have
The minimum indicated powers (I.P.), with imperfect intercooling is:
where m = mass of air delivered in kg per second
The number of stage is decided by the delivery pressure for a given inlet pressure (1 bar) as follows:
 For delivery pressure upto 5 bar: Single stage compressor
 For delivery pressure between 5 to 35 bar: Two stage compressor
 For delivery pressure between 35 to 85 bar: Three stage compressor
 For delivery pressure more than 85 bar: Four stage compressor
12.7.2 Heat Rejected to the Intercooler
Let m = mass of air in the cylinder
Then p_{1}V_{1} = mRT_{1}
or
From the compression 1–2, we have
From the constant pressure line 2–3, we have
12.7.3 Cylinder Dimensions
For steadystate flow, the mass of air passing through each cylinder per stroke must be same.
Let V_{a} = actual volume of air per stroke taken during suction
ρ = density of air
Then, V_{a1} ρ_{1} = V_{a2} ρ_{2} = V_{a3} ρ_{3} = … = const.
For perfect intercooling, T_{1} = T_{2} =T_{3} =…
∴ V_{a1} p_{1} = V_{a3} p_{2} = V_{a3} p_{3} =…
where η_{v} = volumetric efficiency of a cylinder
V_{s} = stroke volume of the cylinder
12.7.4 Intercooler and Aftercooler
Intercooler
An intercooler is a simple heat exchanger in which heat is removed from the air after it has been compressed and its temperature has risen as a result of compression. The intercooler commonly used is of the counter flow type as shown in Fig. 12.13 because it gives high effectiveness.
Effectiveness of intercooler,
A simple section showing the principles of construction of an intercooler is shown in Fig. 12.14. The coolant, which may be water or any other fluid, passes through the tubes secured between two end plates and the air circulates over the tubes through a system of baffles. Two passes are used for water flow and air is made to flow partly parallel and partly cross with the help of baffles. This type of intercooler gives better effectiveness than the ordinary counterflow type. The purpose of the intercooler is to reduce the work done on the air.
Figure 12.13 Counter flow intercooler
Figure 12.14 Principles of construction of intercooler
Aftercooler
An aftercooler is used to cool the air coming out from the compressor before it enters the receiver. The air coming out from the compressor at pressure p_{3} is sufficiently hot at temperature T_{4} (Fig. 12.15). If this air is cooled in the aftercooler, then the pressure will remain p_{3}, but the temperature will fall from T_{4} to T_{4}′′. Therefore, the volume of air leaving the aftercooler will be given by,
However, p_{4}′′ = p_{4}.
As T_{4}′′ < T_{4}, _{}v_{4}′′ < v_{4}
Therefore, the purpose of the aftercooler is to reduce the size of the receiver. The position of the intercooler and aftercooler is shown in Fig. 12.15.
12.8 ❐ INDICATED POWER OF A COMPRESSOR
where A = area of the cylinder, m^{2}
L = length of stroke, m
N = rpm of compressor crank
p_{m} = mean effective pressure of air, P_{a} (N/m^{2})
Theoretically, m.e.p. for a singleacting, singlestage compressor is,
where η_{v} = volumetric efficiency of compressor
Using indicator card, the m.e.p. is:
12.9 ❐ AIR MOTORS
The working of an air motor is similar to that of air compressor. High pressure air is admitted to the motor cylinder through a mechanically operated inlet valve and drives the piston in the forward direction. After a part of the stroke of the piston has been performed, the air supply is cutoff and the stroke is completed after decreasing pressure as the air expands in the cylinder. After the expansion stroke is completed, the air is allowed to escape into the atmosphere through a mechanically operated discharge valve. The return stroke is performed by compressed air acting on the other side of the piston in doubleacting cylinder.
Figure 12.16 shows the p − V diagram for the air motor with clearance. Process 4–1 is the intake with the high pressure p_{2} at cutoff point 1. From 1 to 2, the air expands from higher pressure p_{2} at 1 to atmospheric pressure p_{1} at 2, according to the polytropic law, pV^{n} = c. The process 2–3 represents the exhaust.
Work obtained neglecting clearance,
Work done considering clearance,
where m_{1} = actual mass of air delivered per cycle.
12.10 ❐ INDICATOR DIAGRAM
The theoretical of p − V diagram for the singlestage reciprocating compressor is represented by 1–2–3–4–1 in Fig. 12.17. The actual indicator diagram is 1–2′–3–4′–1. The difference between the actual and theoretical indicator diagrams is due to the intake and discharge losses. The intake losses include the friction losses in pipe, friction loss in inlet valve, and valve inertia loss. Theoretically, the inlet valve should open at 4, but actually, it opens little afterwards at 4′ due to the inertia of the valve, and the pressure inside the cylinder falls below the atmospheric pressure. The oscillating part of the curve indicates valve flutter due to vibration of spring loaded valve. On the delivery side, the discharge valve should open at 2, but actually, it opens little afterwards at 2′ due to the inertia of the spring loaded discharge valve. The effect of these losses is to increase the work required by the compressor.
Figure 12.17 Actual p−V diagram for single stage compressor
Figure 12.18 Actual p−V diagram for twostage compressor
The actual indicator diagram for twostage compressor with intercooler is shown in Fig. 12.18.
12.11 ❐ HEAT REJECTED
If the air is cooled to the initial temperature, then there is no change in internal energy per kg mass of air, and all the work done is rejected to the cooling medium party during the compression process and the remaining after compression at constant pressure.
Now, q_{1–2} = du + w_{1–2}
However, du = 0
For a singlestage compressor, the heat rejected is given by work done  ∫ vdp.
12.12 ❐ CONTROL OF COMPRESSOR
In order to balance the demand and supply of air, it is necessary to incorporate devices for the compressor control. The common methods of control are as follows:
 Throttle control: When the demand is less, there is buildup of pressure in the receiver, and the high pressure air from the receiver is led to piston and cylinder. The movement of piston is resisted by a spring. However, with excessive pressure, the piston depresses the spring, thus closing partly the suction valve. Therefore, during the suction stroke, the air intake is partly throttled. The reverse action takes place when the pressure in the receiver drops due to increase in demand.
 Clearance control: In this method, clearance pockets are provided for increasing or decreasing clearance. Therefore, the volumetric efficiency is reduced in proper proportion to control output.
 Blowing air to waste: In case of excessive pressure builtup in the receiver due to decrease in demand, a bypass valve from the high pressure cylinder delivers air directly to atmosphere. When the pressure in the receiver drops, the relay piston closes the valve.
Example 12.1
A singlestage reciprocating air compressor is required to compress 72 m^{3} of air per minute from 15°C and 1.0 bar to 8 bar pressure. Find the temperature at the end of compression, work done, power, and heat rejected during each of the following processes: (a) isothermal, (b) adiabatic, and (c) polytropic compression following the law pV^{1.25} = constant.
Solution
Note: Example 9.1 illustrates that isothermal compression requires the minimum compression work, while isentropic compression requires the maximum for the same suction and delivery pressure.
Example 12.2
A doubleacting reciprocating compressor with a piston displacement of 0.05 m^{3} per stroke operates at 500 rpm. The clearance is 5 per cent and it receives air at 100 kPa, discharges it at 600 kPa. The compression is polytropic, pV^{1.35} = c. Determine the power required and the air discharged in m^{3}/s.
Solution
The p–V diagram for the compressor is shown in Fig. 12.19.
Example 12.3
A doubleacting reciprocating compressor with complete intercooling delivers air to the main at a pressure of 30 atm, the suction condition being 1 atm and 27°C. If both cylinders have the same stroke, then find the ratio of the diameters of the cylinders for the efficiency of compression to be a maximum. Assume the index of compression to be 1.3.
Solution
Volume of L.P. cylinder = V_{1}
Volume of H.P. cylinder = V_{3}
L_{1} = L_{3}
From constant pressure process 2–3: (see Fig. 12.12)
Example 12.4
A doubleacting reciprocating compressor with perfect intercooling takes in air at 1 bar and 27°C. The law of compression in both the stages is pV^{1.3} = constant. The compressed air is delivered at 9 bar from the H.P. cylinder to an air receiver. Calculate per kg of air (a) the minimum work done, (b) the heat rejected to the intercooler, and (c) the minimum work done in a threestage compressor working under the same conditions. Take c_{p} = 1.005 kJ/kg.K.
For 1 kg of air, p_{1}v_{1} = RT_{1},
or v_{1} = 0.861 m^{3}/kg
 The minimum work required in twostage compressor with perfect intercooling is,
The intermediate pressure is found to be

Heat rejected to intercooler,
q = c_{p} (T_{2} − T_{3}) = cp (T2_{} − T_{1}) [∴T_{2} = T_{3}]= 1.005(386.6 − 300) = 87 kJ/kg of air  The least work done in case of threestage air compressor working between the same pressure limits is given by,
Example 12.5
A singlestage, singleacting reciprocating compressor delivers 15 m^{3}/min of free air from 1 bar to 8 bar at 300 rpm. The clearance volume is 6% of the stroke volume, and compression and expansion follow the law pV^{1.3} = constant. Calculate the diameter and stroke of the compressor. Take L = 1.5 D. The temperature and pressure of air at suction are the same as atmospheric air.
Clearance ratio, c = 0.06
Volumetric efficiency,
Example 12.6
A twocylinder, singleacting reciprocating air compressor is to deliver 15 kg of air per minute at 6.5 bar from suction conditions 1 bar and 13°C. Clearance may be taken as 4 per cent of stroke volume and the index for both compression and reexpansion as 1.3. The compressor is directly coupled to a fourcylinder, fourstroke petrol engine that runs at 1800 rpm with b.m.e.p. of 6 bar. Assuming a stroke–bore ratio of 1.1 for both engine and compressor and a mechanical efficiency of 85% for the compressor, calculate the required cylinder dimensions. Take R = 287 J/kgK.
Solution
The p−V diagram for the compressor is shown in Fig. 12.20.
Amount of air delivered per cylinder
Now, p_{1}(V_{1} − V_{4}) = mRT_{1}
From the expansion curve, we have
Now, V_{1} = V_{3} + V_{s} = 0.04 V_{s} + V_{s} = 1.04 V_{s}
Figure 12.20 pV diagram
Example 12.7
A multistage reciprocating compressor has to be designed to supply air at 135 bar, while atmospheric condition is 1.03 bar and 15°C. The value of compression index may be assumed as 1.35. Due to practical reasons, the intercoolers are not able to cool the air below 45°C, while the maximum temperature allowable in the system is 120°C. Calculate the number of stages that are necessary in the compression and the rate of cooling water circulated per kg of air. Take c_{p} = 1 kJ/kg. K.
Solution
The p−V diagram for the compressor is shown in Fig. 12.21.
T_{1} = 273 +15 = 288 K, p_{1 }= 1.03 bar, n =1.35
Since the maximum allowable temperature is 120°C, the temperature after first stage of compression,
The intercoolers cool the air from T_{2} = 393 K to T_{3} = 273 + 45 =318 K. For the second stage, the inlet temperature is T_{3} = 318 K and outlet temperature is T_{4} = 393 K (see Fig. 12.10b).
Figure 12.21 pV diagram
The pressure ratio is same for all the subsequent stage till the pressure reaches 135 bar. Hence, the number of stage i can be calculated from,
Therefore, the minimum number of stages required including the first stage
Heat received by stage coolers per kg of air compressed
Cooling water circulated per kg of air
Example 12.8
A singleacting, twostage reciprocating compressor with complete intercooling delivers 10 kg/min of air at 16 bar. The suction occurs at 1 bar and 27°C. The compression and expansion processes are reversible with polytropic index n = 1.3. The compressor runs at 450 rpm. Calculate the following:
 The power required to drive the compressor.
 The isothermal efficiency.
 The free air delivered.
 The heat transferred in intercooler.
 The swept and clearance volumes for each cylinder if the clearance ratios for L.P. and H.P. cylinders are 0.04 and 0.06, respectively.
Solution
The p − V diagram is shown in Fig. 12.22.
p_{1} = bar, p_{3} = 16 bar, T_{1} = 273 + 27 = 300 K, N = 450 rpm, n = 1.3, c_{1} = 0.04, and c_{2} = 0.06
For perfect intercooling,
Figure 12.22 p − V diagram for twostage compressor
 Work done in two stages with perfect intercooling,
 Isothermal power,
 Free air delivered

Heat transferred in intercooler with perfect intercooling

Clearance volume = c_{1} (V_{1} − V_{3}) = c_{1}V_{s} = 0.04 × 0.0207
= 8.285 × 10^{−4} m^{3}  H.P. stage:
Clearance volume = c_{2}V_{s} = 0.06 × 5.4 × 10^{−3} = 3.24 × 10^{−4} m^{3}
Example 12.9
A reciprocating compressor is to be designed to deliver 4.5 kg/min of air from 100 kPa and 27°C to compress through an overall pressure ratio of 9. The law of compression is pV^{1.3} = constant. Calculate the saving in power consumption and gain in isothermal efficiency, when a twostage compressor with complete intercooling is used in place of a singlestage compressor. Assume equal pressure ratio in both the stages of the twostage compressor. Take R = 0.287 kJ/kg K.
Solution
Given: m = 4.5 kg/min, p_{1} = 100 kPa, T_{1} = 273 + 27 = 300 K, r_{p} = 9, n = 1.3
Rate of work required in singlestage compression
Rate of work required in twostage compression
Saving in power = 5.54 − 4.84 = 0.70 kW
Example 12.10
A doubleacting, singlecylinder reciprocating air compressor has a piston displacement of 0.015 m^{3 }per revolution, operates at 500 rpm, and has 5% clearance ratio. The air is received at 1 bar and delivered at 6 bar. The compression and expansion are polytropic with n = 1.3. If the inlet temperature of air is 20°C, determine (a) the volumetric efficiency, (b) the power required and (c) the heat transferred and its direction, during compression.
Solution
Given that V_{s} = 0.015 m^{3}/rev, N = 500 rpm, c = V_{c}/V_{s} = 0.05
p_{1} = 1 bar, p_{2} = 6 bar, n = 1.3, T_{1} = 273 + 20 = 293 K
Example 12.11
Find the optimum intermediate pressure of a twostage reciprocating compressor, if intercooling is done up to a temperature , which is greater than the inlet temperature.
Solution
Work done in the L.P. cylinder (Fig. 12.23)
Work done in the H.P. cylinder,
Total work done, W = W_{1} + W_{2}
Figure 12.23 p − V diagram for twostage compressor
Example 12.12
A twostage reciprocating air compressor takes in air at 1.013 bar and 15°C and delivers at 43.4 bar. The intercooler pressure is 7.56 bar. The intercooling is perfect and the index of compression is 1.3. Calculate the work done in compressing 1 kg of air. If both cylinders have the same stroke and the piston diameters are 9 cm and 3 cm and the volumetric efficiency of the compressor is 90%, will the intercooler pressure be steady or will rise or fall as the compressor continues working?
Solution
Given that p_{1} = 1.013 bar, T_{1} = 273 + 15 = 288 K
p_{3} = 43.4 bar, p_{2} = 7.56 bar, n = 1.3,
m = 1 kg, d_{1} = 9cm, d_{2} = 3 cm, η_{v} = 0.9
Input work per kg for perfect intercooling T_{3} = T_{1},
Compression in L.P. cylinder:
For constant pressure in the intercooler, the volume of air leaving the intercooler and entering the H.P. cylinder,
Ratio of effective cylinder volumes,
As more air is supplied to H.P. cylinder than it can hold and consequently the pressure in the intercooler will rise.
Example 12.13
Find the percentage saving in work done by compressing air in two stages from 1 bar to 7 bar instead of one stage. Assume compression index 1.35 in both the cases and optimum pressure and complete intercooling in twostage compression.
Solution
Given that p_{1} = 1 bar, p_{3} = 7 bar, n_{1} = n_{2} = 1.35
For perfect intercooling, = 2.646 bar and T_{3} = T_{1}
With compression in one stage (see Fig. 12.7) without clearance, work done per kg of air is given by,
Work done with perfect intercooling,
Example 12.14
A singlestage, doubleacting reciprocating air compressor delivers 3 m^{3} of free air/min at 1.013 bar and 20°C to 8 bar with the following data:
Rotational speed = 300 rpm, mechanical efficiency η_{mech} = 0.9, pressure loss in passing through intake valve = 0.04 bar, temperature rise of air during suction stroke = 12°C, clearance volume = 5% of stroke volume. Index of compression and expression = 1.35, and length of stroke = 1.2 times of the cylinder diameter. Calculate: (a) volumetric efficiency, (b) cylinder dimension, (c) indicated power, and (d) isothermal efficiency of the compressor, take for air, R = 0.287 kJ/kg K.
Solution
Given that V_{a} = 3 m^{3}/min, p_{a} = 1.013 bar, T_{a} = 273 + 20 = 293 K, p_{1} = 1.013 − 0.04 = 0.973 bar, T_{1} = T_{a} + 12 = 293 + 12 = 305 K, V_{c} = 0.05V_{s}, n = 1.35, L = 1.2D, R = 0.287 kJ/kg K, N = 300 rpm
The p − V diagram is shown in Fig 12.24.
Mass of free air delivered,
Compression process 1–2:
Figure 12.24 p − V diagram for single stage compressor
Corresponding value of F.A.D. per cycle,
 Volumetric efficiency,
 Volume of air inhaled per cycle,
Stroke volume, V_{s} = = 0.94248D^{3} m^{3}/cycle
Also stroke volume = = 6.6756 ×10^{−3} m^{3}/cycle
∴ 0.94248D^{3} = 6.6756 × 10^{−}^{3}
D = 0.192 m or 192 mm
L = 1.2 × 192 = 230.4 mm
 Indicated power, I.P. = ṁR (T_{2} − T_{1})
 Isothermal indicated power,
Isothermal efficiency,
Example 12.15
The following data were obtained from a performance test of a 14 cm × 10 cm single stage reciprocating air compressor having 3 percent clearance: barometer 77 cm Hg, suction pressure 0 bar gauge, suction temperature 22°C, discharge pressure 4.05 bar gauge, discharge temperature 174°C, shaft rpm 1160, shaft power 350 kW, mass of air delivered per minute 1.75 kg. Determine (a) the actual volumetric efficiency; (b) the approximate indicated power; (c) the isothermal compression efficiency; (d) the mechanical efficiency and (e) the overall efficiency of the unit. Take p_{atm} = 1.031 bar.
Solution
Atmospheric pressure corresponding to 77 cm Hg
∴ p_{1} = 0 + 1.0447 = 1.0447 bar
and p_{2} = 4.05 + 1.0447465 = 5.0947 bar
Air entering the cylinder
Piston displacement
 Volumetric efficiency

∴ Compression index n = 1.353
 Isothermal power
 Compressor mechanical efficiency
 Overall efficiency = isothermal efficiency × mechanical efficiency
= 0.8023 × 0.836 = 67.07%
Example 12.16
A twostage reciprocating compressor is used to compress from 1.0 bar to 16 bar. The compression is as per the law pV^{1.25 }= const. The temperature of air at inlet of compressor is 300 K. Neglecting the clearance and assuming perfect intercooling find out the minimum indicated power to deliver 5 m^{3}/min air measured at inlet conditions and find the intermediate pressure also.
Solution
Given: p_{1} = 1 bar v_{1} = 5m^{3}/min = 0.083 m^{3}/s, p_{3} = 16 bar, n = 1.25, T_{1} = 300 K
For complete intercooling, the intercooler pressure,
Work done in compressing the air,
Power required to drive the compressor is 26.519 kW.
Summary for Quick Revision
 A reciprocating compressor is a device in which air is compressed in a conventional cylinder with a closely fitted piston making reciprocating motion.
 Free air delivered (FAD) is the actual volume delivered by the compressor at the stated pressure, reduced to intake pressure and temperature and expressed in m^{3}/min.
 The work done on the compressor to compress a given volume of air at a given pressure shall be the least when the compression process is isothermal.
 Approximation to isothermal compression can be achieved by spraying cold water on the cylinder, water jacketing the cylinder, intercooling by using multistage compression and by using external fins of the cylinder surface.
 Single stage compression:
 Twostage compression:
 For perfect intercooling,
 Minimum compression work, (W_{t})_{min}
 In general, with i number of stages,
 Minimum shaft work,
 Minimum indicated power with imperfect intercooling,
 Heat rejected to intercooler = mc_{p} (T_{2 }− T_{3})
 Cylinder dimensions:
 Effectiveness of intercooler,
 Indicated power,
 Mechanical efficiency,
 Heat rejected per kg of air,
 A compressor can be controlled by: Throttle control, clearance control or by blowing air to waste.
Multiplechoice Questions
 Which one of the following statements is correct? In reciprocating compressors, one should aim at compressing the air
 adiabatically
 isentropically
 isothermally
 polytropically
 Consider the following statements:
 Reciprocating compressors are best suited for high pressure and low volume capacity.
 The effect of clearance volume on power consumption is negligible of the same volume of discharge.
 iii. While the compressor is idling, the delivery value is kept open by the control circuit.
 Intercooling of air between the stages of compression helps to minimize losses. Of these statements
 i and ii are correct
 i and iii are correct
 ii and iv are correct
 iii alone is correct
 For twostage compressor in which index of compression for low pressure stage is m and for high pressure stage in n. The load sharing with perfect intercooling in expressed as:
 For a twostage reciprocating compressor, compression from pressure p_{1} to p_{3} is with perfect intercooling and no pressure losses. If compression in both cylinders follows the same polytropic process and the atmospheric pressure is p_{a} then the intermediate pressure p_{2} is given by
 p_{2} = (p_{1} + p_{3})/2
 A large clearance volume in reciprocating compressor results in
 reduced volume flow rate
 increased volume flow rate
 lower suction pressure
 lower delivery pressure
 In a reciprocating air compressor, the compression work per kg of air
 increases as clearance volume increases
 decreases as clearance volume increases
 is independent of clearance volume
 increases with clearance volume only of multistage compressor
 Consider the following statements:
When air is to be compressed to reasonably high pressure, it is usually carried out by multistage compressor with an intercooler between the stages because
 work supplied is saved.
 weight of compressor is reduced.
 more uniform torque is obtained leading to the reduction in the size of flywheel.
 volumetric efficiency is increased.
Of the four statements listed above
 1 alone is correct
 2 and 4 are correct
 1, 2 and 3 are correct
 1, 2, 3 and 4 are correct
 Consider the following statements:
The volumetric efficiency of a compressor depends upon
 clearance volume
 pressure ratio
 index of expansion
Of these statements:
 1 and 2 are correct
 1 and 3 are correct
 2 and 3 are correct
 1, 2 and 3 are correct
 The heat rejection by a reciprocating air compressor during the reversible compression process AB, shown in the temperatureentropy diagram, is represented by the area:
 A 3stage reciprocating compressor has suction pressure of 1 bar and delivery pressure of 27 bar. For minimum work of compression, the delivery pressure of 1st stage is
 14 bar
 9 bar
 5.196 bar
 3 bar
 Consider the following factors:
 Cylinder size
 Clearance ratio
 Delivery pressure
 Compressor shaft power
The factors which affect the volumetric efficiency of a singlestage reciprocating air compressor would include
 1 and 2
 3 and 4
 2 and 3
 1 and 4
 A fourstage compressor with perfect intercooling between stages, compresses air from 1 bar to 16 bar. The optimum pressure in the last intercooler will be
 6 bar
 8 bar
 10 bar
 12 bar
 The clearance volume of a reciprocating compressor directly affects
 piston speed
 noise level
 volumetric efficiency
 temperature of air after compression
 The capacity of an air compressor is specified as 3m^{3}/min. It means that the compressor is capable of
 supplying 3 m^{3} of compressed air per minute
 compressing 3 m^{3} of free air per minute
 supplying 3 m^{3} of compressed air at NTP
 compressing 3 m^{3} of standard air per minute
 A twostage compressor takes in air at 1.1 bars and discharges at 20 bars. For minimum work input, the intermediate pressure is
 10.55 bars
 7.33 bars
 5.5 bars
 4.7 bars
 Consider the following statements:
The volumetric efficiency of a reciprocating compressor can be enhanced by
 heating the intake air
 decreasing the clearance volume
 cooling the intake air
Which of these statements is/are correct?
 1 alone
 1 and 2
 2 and 3
 3 alone
 Reciprocating compressors are provided with
 simple disc/plate valve
 poppet valve
 springloaded disc value
 solenoid valve
 If n is the polytropic index of compression and is the pressure ratio for a threestage compressor with ideal intercooling, the expression for total work of three stage is
 Consider the following statements:
Volumetric efficiency of a reciprocating air compressor increases with
 increase in clearance ratio
 decrease in delivery pressure
 multistaging
Which of the statements given above is/are correct?
 What is the preferred intercooler pressure for a two stage air compressor working between the suction pressure p_{s} and the delivery pressure p_{d}?
 Which of the following statements are correct for multistaging in a reciprocating air compressor?
 It decreases the volumetric efficiency
 The work done can be reduced
 A small highpressure cylinder is required.
 The size of flywheel is reduced.
Select the correct answer using the code given below:
 1, 2 and 3
 2, 3 and 4
 1, 3 and 4
 1, 2 and 4
 For a twostage reciprocating air compressor, the suction pressure is 1.5 bar and the delivery pressure is 54 bar. What is the value of the ideal intercooler pressure?
 6 bar
 9 bar
 27.75 bar
 Consider the following statements:
In a reciprocating compressor, clearance volume is provided
 so that piston does not hit and damage the valves
 to account for differential thermal expansion of piston and cylinder
 to account for machining tolerances
 to achieve isentropic compression
Which of these statements are correct?
 1, 2 and 3
 1, 2 and 4
 1, 3 and 4
 2, 3 and 4
 Which of the following can be the cause/causes of an aircooled compressor getting overheated during operation?
 Insufficient lubricating oil.
 Broken valve strip.
 Clogged intake filter.
Select the correct answer using the code given below:
 Only 3
 Only 1 and 2
 Only 2 and 3
 1, 2 and 3
 Performance of a reciprocating compressor is expressed by
Explanatory Notes
 10. (d)
 12. (b) Optimum pressure in the last intercooler
 15. (d)
 22. (b)
Review Questions
 List at least six uses of compressed air in industry.
 Explain the working of a single stage reciprocating air compressor.
 What do you mean by free air delivered (FAD)?
 Define volumetric efficiency.
 What are the factors on which volumetric efficiency depends?
 What are the methods generally adopted for approximating the compression process of a reciprocating air compressor as isothermal one?
 Define clearance ratio. How the volumetric efficiency is dependent on clearance ratio?
 Define isothermal efficiency and compressor efficiency.
 Differentiate between isothermal power and indicated power.
 Define adiabatic efficiency.
 What are the advantages of multistage compression?
 What is the condition for minimum compressor work with perfect intercooling for a multistage reciprocating air compressor?
 Distinguish between the function of intercooler and aftercooler.
 What is an air motor?
 How heat is rejected in air compressor?
Exercises
12.1 A singlestage singleacting reciprocating air compressor delivers 15 m^{3} of free air per minute from 1 bar to 8 bar at 300 rpm.The index of both compression and expansion is n = 1.3 for and clearance of swept volume, find the diameter and stroke of the compressor. Take L = 1.5 D.
[Ans. 383 mm, 587.5 mm]
12.2 A singlestage doubleacting reciprocating air compressor delivers air at 7 bar. The pressure and temperature at the end of suction stroke are 1 bar and 27°C. It delivers 2 m^{3} of free air per minute when the compressor is running at 300 rpm. The clearance volume is 5% of the stroke volume. The ambient pressure and temperature are 1.03 bar and 20°C. Index of compression and expansion is 1.30 and 1.35 respectively. Calculate (a) the volumetric efficiency, (b) indicated power and brake power if mechanical efficiency is 80%, and (c) diameter and stroke of the cylinder if both are equal.
[Ans. 83.9%, 8.5 kW, 10.64 kW, 174.6 mm]
12.3 A twostage singleacting reciprocating air compressor delivers air at 20 bar. The pressure and temperature of air before compression in L.P. cylinder are 1 bar and 27°C. The discharge pressure of L.P. cylinder is 4.7 bar. The pressure of air leaving the intercooler is 4.5 bar and the air is cooled to 27°C. The diameter and stroke of L.P. cylinder are 0.4 m and 0.5 m respectively. The clearance volume is 4% of stroke in both cylinders. The speed of compressor is 200 rpm. The index of compression and reexpansion in both cylinders is 1.3. Determine (a) the indicated power to run the compressor, and (b) the heat rejected to intercooler per minute.
[Ans. 68.9 kW, 1716 kJ/min]
12.4 A singlestage, doubleacting reciprocating air compressor delivers 15 m^{3} of air per minute measured at 1.013 bar, 27°C and delivers at 7 bar. At the end of the suction stroke the pressure and temperature are 0.98 bar and 40°C. The clearance volume is 4% of the swept volume and the stroke is 1.3 times the bore. The compressor runs at 300 rpm. Calculate (a) the volumetric efficiency, (b) cylinder dimensions, (c) indicated power and (d) isothermal efficiency. n = 1.3 for both compression and expansion. Take R = 0.287 kJ/kg.K
[Ans. 79.6%; 313.3 mm, 407.3 mm; 65.83 kW; 78.92%]
12.5 A singlestage, double acting air reciprocating compressor takes air at 0.98 bar and 32°C and delivers at 6.32 bar. The clearance is 5% of the stroke volume. The compression and expansion follow the law pV^{1.32} = c. The air handled by the compressor is 17 m^{3}/min when measured at 1 bar and 15°C. Determine the temperature of air delivered, the stroke volume and the indicated power of compressor if it turns at 500 rpm. Neglect the area of piston and take R = 0.287 kJ/kg.K.
12.6 The free air delivered of a single cylinder single stage reciprocating air compressor is 2.5 m^{3}/min. The ambient air is at 0°C and 1.013 bar and delivery pressure is 7 bar. The clearance ratio is 5% and law of compression and expansion is pv^{1.25} = c. If L =1.2 D and the compressor runs at 150 rpm, determine the size of the cylinder.
[Ans. 275.5 mm, 330 mm]
12.7 A single stage double acting reciprocating air compressor delivers air at 7 bar. The amount of free air delivered is 2 m^{3} at 300 rpm. The pressure and temperature at the end of suction stroke are 1 bar and 27°C. The ambient conditions are 1.03 bar and 20°C. The clearance is 5% stroke. The compression and reexpansion follow the law pV^{1.3} = const. Determine the brake power required to run the compressor if the mechanical efficiency is 80%, and the diameter and stroke of the cylinder if both are equal.
[Ans. 10.8kW, 179.5 mm]
12.8 A twostage double acting reciprocating air compressor delivers air at the rate of 1.35 kg/s. The suction pressure is 1 bar and interstage pressure is 7 bar and delivery pressure 42 bar. Air enters the L.P. cylinder at 17°C and cooled in the intercooler to 32°C. The clearances in L.P. and H.P. cylinders are 6% and 8% of respective strokes. The law of compression and reexpansion is pV^{1.21} = c in both cylinders. The compressor runs at 500 rpm. Calculate the amount of cooling water required per minute in intercooler, if rise in temperature of water is limited to 20°C, power required, and size of cylinder if length of stroke and bore are equal.
[Ans. 2259 kg/min, 1068 kW, 483 mm]
12.9 Determine the size of a cylinder for a double acting reciprocating air compressor of 37 kW, in which air is drawn in at 1 bar, 15°C and compressed according to the law pV^{1.2} = const. to 6 bar. The compressor runs at 100 rpm with average piston speed of 152.5 m/min. Neglect clearance.
[Ans. 298.5 mm, 762.5 mm]
12.10 A single stage double acting reciprocating air compressor running at 500 rpm handles 17 m^{3}/min of air, measured at 1 bar and 15°C. The pressure and temperature at the end of suction are 0.98 bar and 32°C. The air is delivered at 6.325 bar. Assuming a clearance factor of 5% and the compression and expansion processes to follow the law pV^{1.32} = const, determine the stroke volume of the compressor. Also calculate the indicated power of the compressor. Take R = 0.287 kJ/kg.K
[Ans. 0.2175 m^{3}, 70.73 kW]
12.11 A single acting compressed air motor works on compressed air at 10.5 bar and 37°C supplied at the rate of 1 kg/min. Cutoff takes place at 25% of the stroke and the expansion follows the adiabatic frictionless law down to 1.0135 bar. Determine the mean effective pressure, the indicated power and the cylinder volume if the motor runs at 250 rpm. Neglect clearance.
[Ans. 3.37 bar, 1.94 kW, 0.001383 m^{3}]
12.12 The cylinder of an air motor has a bore of 63.5 mm and a stroke of 114 mm. The supply pressure and temperature are 6.3 bar and 24°C and exhaust pressure is 1.013 bar. The clearance volume is 5% of the swept volume and the cutoff ratio is 0.5. The air is compressed by the returning piston after it has travelled through 0.95 of its stroke. The law of compression and expansion is pV^{1.3} = const. Calculate the temperature at the end of expansion and the indicated power of the motor which runs at 300 rpm. Also calculate the air supplied per minute. Take R = 0.287 kJ/kgK.
[Ans. 244.4 K, 0.746 kW, 0.418 kg/min]
12.13 A water cooled air compressor requires a work input of 200 kJ/kg of air delivered. The enthalpy of air leaving the compressor is 75 kJ/kg greater than that entering. Heat lost to the cooling water is 105 kJ/kg. From the first law analysis estimate the heat lost by compressor to atmosphere.
12.14 A twostage single acting air reciprocating compressor equipped with an intercooler draws air at 1.013 bar and 30°C and delivers it at 20 bar. The mass of air delivered by the compressor is 10 kg/min. The ratio of clearance volume to swept volume in the low pressure and high pressure cylinders is 0.03 and 0.04 respectively. If the compressor has a mechanical efficiency of 82% and it operates under most efficient conditions, determine:
 power supplied at the shaft of the compressor;
 isothermal efficiency;
 ratio of cylinder diameters for identical stroke length; and
 heat rejected in the intercooler.
Take R = 0.287 kJ/kg.K, c_{p} = 1.005 kJ/kgK and γ = 1.4.
12.15 A single acting twostage reciprocating air compressor is to compress air from 1 bar and 30°C to 12 bar. The base of the low pressure cylinder is 30 cm. The stroke length of both the low and the high pressure cylinders is the same and is equal to 40 cm. The compressor runs at 180 rpm. The clearance volume in both the cylinders is 3% of the stroke volume. Index of compression and expansion is 1.3 in both the cylinders. Determine the shaft power required to drive the compressor when (a) the air is cooled to its original temperature before entering the H.P. cylinder, (ii) when the air is cooled to 45°C in the intercooler. Assume mechanical efficiency to be 85% in both cases. Take R = 0.287 kJ/kg.K.
12.16 A multistage reciprocating compressor has to be designed to supply air at 135 bar, while atmospheric condition is 1.03 bar and 15°C. The value of compression index may be assumed as 1.35. Due to practical reasons the intercoolers are not able to cool the air below 45°C, while the maximum temperature allowable in the system is 120°C. Calculate the number of stages that are necessary in the compression and the rate of cooling water circulated per kg of air. Take c_{p} = 1 kJ/kgK.
ANSWERS TO MULTIPLECHOICE QUESTIONS
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