MULTI-STAGE COMPRESSION

Single-stage 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 single-stage compressor with fixed clearance decreases with an increase in pressure ratio and thus reduces the capacity. Thus the necessity of of multi-stage compression with intercooling between stages are listed below:

1. The air can be cooled perfectly at pressures intermediate between the suction and delivery pressures resulting in less power required as compared to a single-stage compressor for the same pressure limits and quantity of free air delivered.
2. The mechanical balance of the machine is better due to phasing of the operations.
3. The pressure range and hence the temperature range in each stage can be kept within desirable limits. This results in:
   1. Less loss of air due to leakage past the piston.
   2. More perfect lubrication due to lower temperatures.
   3. Better volumetric efficiency.
   4. The lighter construction of the machine that reduces the cost.

1 Two-stage Compressor

The schematic arrangement of two-stage 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 p₁. After compression to intermediate pressure p₂, the air at condition 2 is passed through the intercooler and leaves it at point 3, where its temperature is reduced from T₂ to T₃. The air may be cooled to point 3′ such that T₃′ = T₁. 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 two-stage 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 T₂ to T₃ = T₁. 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) p-V diagram

Figure 12.12 Two stage compression with perfect intercooling

For p₁ and p₃ to be constant, intermediate pressure p₂ must be determined for minimum work.

Thus,

For n₁ = n₂ = n, and a = b.

For perfect intercooling, T₃ = T₁. 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:

1. For delivery pressure upto 5 bar: Single stage compressor
2. For delivery pressure between 5 to 35 bar: Two stage compressor
3. For delivery pressure between 35 to 85 bar: Three stage compressor
4. For delivery pressure more than 85 bar: Four stage compressor

2 Heat Rejected to the Intercooler

Let m = mass of air in the cylinder

Then p₁V₁ = mRT₁

or 

From the compression 1–2, we have

From the constant pressure line 2–3, we have

3 Cylinder Dimensions

For steady-state 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 ρ₁ = V_a2 ρ₂ = V_a3 ρ₃ = … = const.

For perfect intercooling, T₁ = T₂ =T₃ =…

∴ V_a1 p₁ = V_a3 p₂ = V_a3 p₃ =…

V_s1 η_v1 p₁ = V_s2 η_v2 p₂ = V_s3 η_v3 p₃ =…

where η_v = volumetric efficiency of a cylinder

V_s = stroke volume of the cylinder

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 counter-flow 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 inter-cooler