Roots Blower – Quick thermodynamics-based explanation

 A Roots blower is a positive displacement machine that delivers a nearly constant volumetric flow rate per revolution.

From a thermodynamic perspective, it is not a true compressor, because no significant pressure rise occurs inside the casing. Compression occurs externally, after discharge.

2. Operating Principle

The Roots blower consists of two counter-rotating lobed rotors synchronized by external gears.

Flow process:

1- Suction phase
Air at inlet pressure $P_1$ and temperature $T_1$ fills the cavities between the lobes and casing.

2- Transfer phase (constant volume)

The trapped air is carried from inlet to outlet without change in volume.

3- Discharge phase (sudden pressure rise)

When the trapped air opens to the outlet manifold at pressure 

$P_2$, backflow occurs, raising the pressure of the trapped air instantaneously.

🔑 Key thermodynamic point:
The blower itself does no internal compression → compression is caused by pressure equalization at the outlet.

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3. Thermodynamic Model

Control volume analysis

The Roots blower is analyzed as an open system operating at steady state.

Assumptions:

• Ideal gas behavior
• Negligible kinetic and potential energy changes
• Adiabatic casing (approximate)
• No internal pressure rise

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4. Pressure–Volume (P–V) Diagram

The thermodynamic cycle of a Roots blower differs from conventional compressors.

Process description:

1 → 2: Constant pressure suction at $P_1$

2 → 3: Constant volume transfer (no compression)

3 → 4: Sudden pressure rise from $P_1$ to $P_2$ at constant volume

4 → 1: Discharge at pressure $P_2$​

This results in shock-like compression losses, increasing entropy.

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5. Temperature Rise

Since compression is non-isentropic:

$$T_2 > T_1$$

The temperature rise is mainly due to:

• Backflow mixing
• Irreversibility
• Mechanical losses

Approximate outlet temperature:

$$T_2 = T_1 \left( \frac{P_2}{P_1} \right)^{(\gamma -1)/\gamma} \cdot \eta_c^{-1}$$

Where:

• $\gamma$ = specific heat ratio

• $\eta_c$ = compressor efficiency (low for Roots blowers)

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6. Work and Power Requirement

Ideal power:

$$\dot{W}_{ideal} = \dot{V} (P_2 - P_1)$$

Actual power:

$$\dot{W}_{actual} = \frac{\dot{W}_{ideal}}{\eta_m}$$

Where:

• $\dot{V}$ = volumetric flow rate

• $\eta_m$ = mechanical efficiency

Roots blowers require higher power than internal compression machines for the same pressure ratio.

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7. Efficiency Considerations

Volumetric efficiency

$$\eta_v = \frac{\dot{V}_{actual}}{\dot{V}_{theoretical}}$$

Leakage and backflow reduce volumetric efficiency at higher pressure ratios.

Isentropic efficiency

Low due to:

• No internal compression
• High entropy generation
• Pressure shock losses

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8. Comparison with Isentropic Compression

Feature	Roots Blower	Isentropic Compressor
Internal compression	❌ No	✅ Yes
Entropy change	High	Minimal
Temperature rise	High	Lower
Efficiency	Low–moderate	High

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9. Applications (Thermodynamic Justification)

Roots blowers are used where:

• Low pressure ratios

 ($P_2\mathrm{/}{P}_1<2$)

• High mass flow
• Instant response required

Examples:

• Supercharging IC engines
• Scavenging in two-stroke engines
• Pneumatic conveying

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10. Key Academic Takeaway

• The Roots blower is a positive displacement air mover, not a true compressor.
• Its thermodynamic inefficiency arises from constant-volume transfer followed by irreversible pressure equalization, resulting in high entropy generation and temperature rise.