RECIPROCATING COMPRESSORS

Q.2) Classify the compressors
(i) On the basis of operations employed
(ii) On the basis of pressure achieved
(iii) On the basis of pressure ratio
(iv) On the basis of capacity of compressors.

A.2) Depending upon different parameters, compressors can be classified on the basis of operations employed, the delivery pressure achieved, pressure ratio and capacity of compressors as follows.

On the basis of operations employed, compressors are classified into two groups:
i) :Reciprocating compressors : It uses piston cylinder arrangement and due to positive displacement of air in the cylinder, the air is compressed and delivered to a vessel called Receiver. These are capable to produce high delivery pressure with low volume flow rate.
ii) Rotary Compressors : These compressors operate at high speeds, therefore, can handle large volume flow rates compared to reciprocating compressors.

In rotary compressors, the dynamic head is imparted to the gas with the help of very high speed impeller rotating at a confined space so that the air is compressed due to centrifugal action.

On the basis of delivery pressure, compressors are classified into three categories
i) Low Pressure Compressors : Delivery pressure upto 1.1 bar
ii) Medium Pressure Compressors : Delivery pressure upto 7 bar
iii) High Pressure Compressors : Delivery pressure between 7 to 10 bar.

On the basis of pressure ratio, we can classify the devices as follows,
Fans : Pressure ratio upto 1.1
Blower : Pressure ratio upto 1.1 to 4.0
Compressors : Pressure ratio above 4.0

On the basis of capacity, compressors can be classified as follows,
Low capacity compressors : Volume flow rate upto 10 m³/min, or less
Medium capacity compressors : Volume flow rate 10 m³/min to 300 m³/min
High capacity compressors : Volume flow rate above 300 m³/min

Q.3) Find an expression for required work done to drive a compressor, when compression is,
adiabatic in nature
isothermal compression
polytropic compression

A.3) During the analysis of the operations of a reciprocating air compressor, we consider some assumptions to simplify the analysis. They are as follows
i) There is no Clearence Volume
ii) Working substance air is an ideal gas
iii) There is no frictional loss.
iv) There is no wire drawing in the valve or pipe lines.

WORK REQUIRED TO DRIVE A COMPRESSOR

Suppose, we are running a single stage air compressor, which draws air at pressure P₁ and temperature T₁ during the suction or induction process. The air thus drawn inside the cylinder then compressed to achieve a delivery pressure, P₂ by adiabatic process. In the adjacent figure, process a - b is the suction process. Process b - c is the adiabatic compression of the air from pressure P₁ to pressure P₂. Process c - d is the delivery stroke, delivering the compressed air at a pressure P₂.

W_ad = P₂V₂ + {( P₂V₂ - P₁V₁)/(γ - 1)} - P₁V₁

=> (P₂V₂ - P₁V₁){1 + 1/(γ - 1)}

=> {γ /(γ - 1)}P₁V₁ {(P₂V₂)/(P₁V₁) - 1}

=> {γ /(γ - 1)}mRT₁{(P₂/P₁)^{{(γ - 1)/γ}} - 1}

POLYTROPIC WORKDONE IN RECIPROCATING COMPRESSORS

W_poly = P₂V₂ + {( P₂V₂ - P₁V₁)/(n - 1)} - P₁V₁

=> (P₂V₂ - P₁V₁){1 + 1/(n - 1)}

=> {n/(n - 1)}P₁V₁ {(P₂V₂)/(P₁V₁) - 1}

=> {n/(n - 1)}mRT₁{(P₂/P₁)^{{(n - 1)/n}} - 1}

ISOTHERMAL WORKDONE REQUIRED TO DRIVE RECIPROCATING COMPRESSOR

W_iso = P₂V₂ + {P₁V₁ln(V₁/V₂)} - P₁V₁

but as the process is isothermal, P₁V₁ = P₂V₂

W_iso = P₁V₁ln(V₁/V₂)

W_iso = mRT₁ln r_p

V₁/V₂ = P₂/P₁ = r_p (pressure ratio)