Unit - 5
Reciprocating Air Compressors
Compressed air is carried, from the air compressor, to the air motor. Sometimes, air compressor and air motor are installed as two separate units. But sometimes they are installed as one unit. A little consideration will show, that if the air compressor and air motor are installed at some distance apart, the hot* compressed air, flowing through the duct, will get cooled to some extent. But if they are installed as one unit, there is no time for the air to get cooled. In such a case, some cooling arrangement is provided between the two units. i.e., after the air compressor or in other words before the motor. Such a system is known as compressed air system. In a compressed air system, the air is first compressed in an air compressor from pressure p1 top2 with a corresponding rise in its temperature. The hot air, leaving the compressor, is now cooled to the initial compressor temperature. The air is then made to expand in the air motor cylinder from pressure p2 top1 with a corresponding fall in its temperature. Thus, the temperature of air discharged from the air motor is less than the initial compressor intake temperature.
Efficiency of Compressed Air
The theoretical indicator diagram of a compressed air system is shown in Fig. The compression of air, in a compressor cylinder from pressure p 1 to p2 is represented by the curve 1-2. The hot air leaving the compressor is cooled down in an air cooler to original compressor intake temperature.
The air now enters the air motor cylinder, and expands from pressure p. to p 1 as shown by the curve 3-4 in Fig. 31.2. Now let us assume the compression and expansion according to pu = constant and neglect clearance. Work done on the air compressor
And work done by the air in the motor
Now, let 
Efficiency of the air motor, and
Efficiency of the compressor
Shaft output of the air motor=work done by the air × m
And shaft input to the compressor
The overall efficiency of the compressed air system is the ratio of the shaft output of the air motor to the shaft input to the compressor. Mathematically, overall efficiency of the compressed air system,
Equation (iii) may also be written as 
We know that 
and 
We have assumed that there is no clearance volume in the compressor cylinder. In other words, the entire volume of air, in the compressor cylinder, is compressed by the inward stroke of the piston. But in actual practice, it is not possible to reduce the clearance volume to zero, for mechanical reasons. Moreover, it is not desirable to allow the piston head to come in contact with the cylinder head. In addition to this, the passage leading to the inlet and outlet valves always contribute to clearance volume. In general, the clearance volume is expressed as some percentage of the piston displacement.
Now consider a reciprocating air compressor with clearance volume, as shown in Fig.
Let p1 = Initial pressure of air (before compression)
v 1 = Initial volume of air (before compression).
T1= Initial temperature of air (before compression),
P2' V2 T2 = Corresponding values for the final conditions (i.e., at the delivery points).
r= Pressure ratio (i.e., pp1),
Vc = Clearance volume (i.e., volume at point 3).
Vs = Stroke volume= Vi-Vc, and
n = Polytropic index for compression and expansion.
The p-v diagram of a single stage single acting reciprocating air compressor with clearance major part i.e., compression stroke 1-2. This compression continues, till the pressure p2 in the cylinder is sufficient to force open the delivery valve at 2. After that, no more '3 2 compression takes place with the inward movement of f 2 the piston. Now during the remaining part of compress- pva " Cision stroke, compressed air is delivered till the piston reaches at 3. At this stage, there will be some air (equal to clearance volume) left in the clearance space of the cylinder at pressure p2. After that air in the clearance space will expand during some part of outward stroke of the piston i.e., expansion stroke 3-4. This expansion continues till the pressure p1 in the cylinder is sufficient to force open the inlet valve at 4. After that the air is sucked from the atmosphere during the suction stoke 4-1 pressure p1. volume.
Though the compression and expansion of air may be isothermal, isentropic or polytropic, yet for all calculation purposes, it is assumed to be polytropic. We know that work done by the compressor per cycle
Area 1-2-3-4=Area A-1-2-B – Area A-4-3-B
where (v 1 - v4) and m is equal to the actual volume and mass of air sucked by the piston per cycle respectively. We see that the clearance volume does not affect the work done on the air and the power required for compressing the air. This is due to the reason that the work requlre6 to compress the clearance volume air is theoretically regained during its expansion from 3 to 4. Note The terms v4 and (v 1 - v) are known as expanded clearance volume and effective swept volume respectively
Volumetric efficiency.
It is the ratio of actual volume of charge admitted during the suction stroke at N.T.P. to the swept volume of the piston. Mathematically, volumetric efficiency
Note: The volumetric efficiency may also be defined as the ratio of the mass of actual charge admitted to the swept mass of the charge at N.T.P.
Multistage compression
1.Intercooler required in multistage compressor so construction of multistage compressor is difficult.
2. In multistage compressor intercooler is used and two compressor is required so cost is high required.
INTERCOOLERS
Limitation of these intercoolers is that their efficiency depends on both the ambient temperature and the road speed of the vehicle if the airflow through the intercooler's core is not fan-assisted.
It is the most widely used compressor with cooling capacities ranging from a few Watts to hundreds of kilowatts. Modern day reciprocating compressors are high speed (≈ 3000 to 3600 rpm), single acting, single or multi-cylinder (up to 16 cylinders) type
Figure shows the schematic of a reciprocating compressor. Reciprocating compressors consist of a piston moving back and forth in a cylinder, with suction and discharge valves to achieve suction and compression of the refrigerant vapor. Its construction and working are somewhat similar to a two-stroke engine, as suction and compression of the refrigerant vapor are completed in one revolution of the crank. The suction side of the compressor is connected to the exit of the evaporator, while the discharge side of the compressor is connected to the condenser inlet. The suction (inlet) and the discharge (outlet) valves open and close due to pressure differences between the cylinder and inlet or outlet manifolds respectively. The pressure in the inlet manifold is equal to or slightly less than the evaporator pressure. Similarly, the pressure in the outlet manifold is equal to or slightly greater than the condenser pressure. The purpose of the manifolds is to provide stable inlet and outlet pressures for the smooth operation of the valves and also provide a space for mounting the valves
The valves used are of reed or plate type, which are either floating or clamped. Usually, backstops are provided to limit the valve displacement and springs may be provided for smooth return after opening or closing. The piston speed is decided by valve type. Too high a speed will give excessive vapor velocities that will decrease the volumetric efficiency and the throttling loss will decrease the compression efficiency
Performance of reciprocating compressors
For a given evaporator and condenser pressures, the important performance parameters of a refrigerant compressor are:
a) The mass flow rate (m) of the compressor for a given displacement rate
b) Power consumption of the compressor (Wc)
c) Temperature of the refrigerant at compressor exit, Td, and
d) Performance under part load conditions.
The mass flow rate decides the refrigeration capacity of the system and for a given compressor inlet condition, it depends on the volumetric efficiency of the compressor. The volumetric efficiency, ηV is defined as the ratio of volumetric flow rate of refrigerant to the maximum possible volumetric flow rate, which is equal to the compressor displacement rate, i.e.,
where are the mass flow rate of refrigerant (kg/s) and compressor displacement rate (m SW, V and m3 /s) respectively, and v is the specific volume (m3 i /kg) of the refrigerant at compressor inlet.
For a given evaporator and condenser temperatures, one can also use the volumetric refrigeration capacity (kW/m3) to indicate the volumetric efficiency of the compressor. The actual volumetric efficiency (or volumetric capacity) of the compressor depends on the operating conditions and the design of the compressor.
The power consumption (kW) or alternately the power input per unit refrigeration capacity (kW/kW) depends on the compressor efficiency (ηC), efficiency of the mechanical drive (ηmech) and the motor efficiency (ηmotor). For a refrigerant compressor, the power input (Wc) is given by:
where Wideal is the power input to an ideal compressor. The temperature at the exit of the compressor (discharge compressor) depends on the type of refrigerant used and the type of compressor cooling. This parameter has a bearing on the life of the compressor. The performance of the compressor under part load conditions depends on the type and design of the compressor.
a) Ideal reciprocating compressor: An ideal reciprocating compressor is one in which:
i. The clearance volume is zero, i.e., at the end of discharge process, the volume of refrigerant inside the cylinder is zero.
ii. No pressure drops during suction and compression.
iii. Suction, compression and discharge are reversible and adiabatic.
Ideal reciprocating compressor on P-V and P-θ diagrams
Process D-A: This is an isobaric suction process, during which the piston moves from the Inner Dead Centre (IDC) to the Outer Dead Centre (ODC). The suction valve remains open during this process and refrigerant at a constant pressure Pe flows into the cylinder.
Process A-B: This is an isentropic compression process. During this process, the piston moves from ODC towards IDC. Both the suction and discharge valves remain closed during the process and the pressure of refrigerant increases from Pe to Pc.
Process B-C: This is an isobaric discharge process. During this process, the suction valve remains closed and the discharge valve opens. Refrigerant at a constant Pc is expelled from the compressor as the piston moves to IDC.
Since the clearance volume is zero for an ideal compressor, no gas is left in the compressor at the end of the discharge stroke, as a result the suction process D-A starts as soon as the piston starts moving again towards ODC. The volumetric flow rate of refrigerant at suction conditions is equal to the compressor displacement rate hence, the volumetric efficiency of the ideal compressor is 100 percent. The mass flow rate of refrigerant of an ideal compressor is given by:
Thus, for a given refrigeration capacity, the required size of the compressor will be minimum if the compressor behaves as an ideal compressor. The swept volume Vsw of the compressor is given by:
where n = Number of cylinders
N = Rotational speed of compressor, revolutions per second
D = Bore of the cylinder, m
L = Stroke length, m
As a matter of fact, the compressed air (from an air compressor) is made to enter the cylinder of an air motor which pushes its piston forward in the same way as of a reciprocating steam engine. Now the actual work is done by the movement of the piston. Now consider an air motor working with the help of compressed air
P1 = Pressure of the compressed air,
V1 = Volume of the compressed air.
The theoretical indicator diagram of a reciprocating air motor without clearance, compression and pressure drop at release is shown in Fig. 31.1. The compressed air from the compressor is admitted into an air motor at A with pressure p1. It drives the piston forward. But after a part stroke is performed, the air supply is cut-off at B and the expansion occurs from B to C. After the stroke is completed, the air which has done some work is exhausted into the atmosphere at a constant pressure p2. We know that work done by the air per cycle.
References:
1. Engineering Thermodynamics by P. K. Nag, Publisher: TMH
2. Engineering Thermodynamics by P. Chattopadhyay, OXFORD
3. Fundamentals of Thermodynamics by Sonntag, Borgnakke, Van Wylen, John Wiley & Sons
4. Thermodynamics An Engineering Approach by Yunus A. Cingel and Michale A. Boles, TMH
5. Engineering Thermodynamics by M. Achyuthan, PHI
