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A three-stage compressor receives 500 liters per second of air at 101 kPa and 27ºC and discharges at 750 kPa. Determine:

a) The power required.

b) The pressure at each intercooler.

c) The maximum temperature.

d) The heat transferred in each intercooler.

e) What is the discharge temperature of a single-stage compressor operating at the same intake and discharge pressures?

Answer :

a) Power required: 139.6 kW

b) Intercooler pressures: 198 kPa and 388 kPa

c) Maximum temperature: 95.5°C

d) Heat transferred per intercooler: 40.3 kW

e) Single-stage discharge temperature: 293.7°C

1) Basic principles:

  • - Equal pressure ratio for each stage for maximum efficiency
  • - Air cooled to initial temperature after each stage
  • - Air assumed as ideal gas with γ = 1.4 and R = 0.287 kJ/kg·K

2) Overall pressure ratio:

750 kPa / 101 kPa = 7.426

3) Each stage pressure ratio:

³√7.426 = 1.96

a) Power required:

Work per stage = (γ/(γ-1)) · R · T · [(P₂/P₁)⁽ᵞ⁻¹⁾ᐟᵞ - 1]

= (1.4/0.4) · 0.287 · 300 · (1.96⁽⁰·⁴⁾ᐟ¹·⁴ - 1)

= 79.3 kJ/kg

Total work = 3 · 79.3 = 237.9 kJ/kg

Mass flow rate = (101 kPa · 0.5 m³/s) / (0.287 kJ/kg·K · 300 K) = 0.587 kg/s

Power = 237.9 kJ/kg · 0.587 kg/s = 139.6 kW

b) Intercooler pressures:

1ˢᵗ stage: 101 · 1.96 = 198 kPa

2ⁿᵈ stage: 198 · 1.96 = 388 kPa

c) Maximum temperature:

T₂ = T₁ · (P₂/P₁)⁽ᵞ⁻¹⁾ᐟᵞ = 300 · (1.96)⁽⁰·⁴⁾ᐟ¹·⁴ = 368.5 K = 95.5°C

d) Heat transferred per intercooler:

Q = m · cₚ · ΔT = 0.587 · 1.005 · (95.5 - 27) = 40.3 kW

e) Single-stage discharge temperature:

T₂ = T₁ · (P₂/P₁)⁽ᵞ⁻¹⁾ᐟᵞ = 300 · (7.426)⁽⁰·⁴⁾ᐟ¹·⁴ = 566.7 K = 293.7°C

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