Compressors

Compressors are turbomachines or positive-displacement devices that increase the pressure of a working fluid (usually a gas). They are classified broadly into positive-displacement compressors (reciprocating, rotary screw, vane) that trap a fixed mass and reduce its volume, and dynamic compressors (centrifugal, axial) that convert kinetic energy to pressure via diffusers. Important practical issues include isentropic (ideal) vs. polytropic and isothermal models of compression, compressor efficiencies (isentropic/compression efficiency), volumetric efficiency for reciprocating machines (affected by clearance volume and re-expansion of trapped gas), interstage cooling and optimal pressure split in multistage machines, surge and stall phenomena in axial/centrifugal compressors, and power requirements related to mass flow and specific work. Common engineering assumptions are ideal gas behavior, constant specific heats for isentropic relations, and steady operation.

Governing FormulaKey relations (ideal gas, SI units): - Isentropic compression work (specific) per kg: Ws = (k/(k-1)) R T1 [ (P2/P1)^{(k-1)/k} - 1 ] - Isothermal compression work (specific) per kg: Wiso = R T1 ln(P2/P1) - Polytropic compression (exponent n) work per kg: Wp = (n/(n-1)) R T1 [ (P2/P1)^{(n-1)/n} - 1 ] - Compressor (isentropic) efficiency: eta_c = W_ideal / W_actual (so W_actual = W_ideal / eta_c) - Volumetric efficiency (reciprocating with clearance ratio C, approximate polytropic re-expansion): eta_v = 1 + C - C (P_discharge / P_suction)^{1/k} - For minimum work in m equal stages (perfect intercooling to inlet temperature), equal pressure ratio per stage: (P2/P1)^{1/m} Where: k = cp/cv (ratio of specific heats), R = specific gas constant (J kg^{-1} K^{-1}), T1 = inlet temperature (K), P1, P2 = inlet and discharge pressures (Pa).

Knowledge Check

10 Questions

1.Which compressor type principally increases gas pressure by first increasing velocity and then converting kinetic energy to static pressure in a diffuser?

2.Calculate the specific isentropic work (J/kg) required to compress air (ideal gas, k = 1.4, R = 287 J kg^-1 K^-1) from P1 = 100 kPa, T1 = 300 K to P2 = 800 kPa.

3.For the same inlet conditions (P1 = 100 kPa, T1 = 300 K) and discharge P2 = 800 kPa, what is the specific isothermal compression work (J/kg) for an ideal gas (R = 287 J kg^-1 K^-1)?

4.A compressor compresses air from 100 kPa to 700 kPa with inlet temperature 300 K (k = 1.4, R = 287 J kg^-1 K^-1). The mass flow is 0.40 kg/s and the isentropic efficiency is 78%. Estimate the electrical power input (W) required.

5.A single-stage reciprocating compressor has clearance ratio C = 0.05, suction pressure 100 kPa and discharge pressure 600 kPa. Assuming adiabatic re-expansion of the clearance gas with k = 1.4, what is the approximate volumetric efficiency (eta_v)?

6.For a two-stage compressor with perfect intercooling to the inlet temperature between stages and an overall pressure ratio P2/P1 = 16, what should the intermediate (interstage) pressure be (if P1 = 100 kPa) to minimize total compression work?

7.Which statement correctly describes 'surge' in an axial or centrifugal compressor?

8.Calculate the specific polytropic work (J/kg) for compression with polytropic exponent n = 1.25 of an ideal gas (R = 287 J kg^-1 K^-1) from P1 = 100 kPa, T1 = 290 K to P2 = 500 kPa.

9.A three-stage compressor with perfect intercooling must achieve an overall pressure ratio of 27. What is the optimal (equal) pressure ratio per stage?

10.A single-cylinder reciprocating compressor has clearance ratio C = 0.03. Suction pressure is 100 kPa, discharge is 500 kPa, and k = 1.4. Using the approximate clearance re-expansion formula, what is the volumetric efficiency (eta_v)?