Ejector Design

Engineering fundamentals for vacuum and compression systems

Contents

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1. Operating Principles

Ejectors use a high-pressure motive fluid to entrain and compress a lower-pressure suction fluid. They have no moving parts, providing reliable operation for vacuum generation and gas compression.

Basic Components

Operating Mechanism

Energy conversion sequence: 1. Motive fluid: Pressure energy → Kinetic energy (nozzle) 2. Mixing: Momentum transfer from motive to suction 3. Diffuser: Kinetic energy → Pressure energy Conservation of momentum: ṁ_m × V_m + ṁ_s × V_s = (ṁ_m + ṁ_s) × V_mix

Key Terminology

Term Symbol Definition
Motive pressure P_m Driving fluid inlet pressure
Suction pressure P_s Entrained fluid inlet pressure
Discharge pressure P_d Mixed fluid outlet pressure
Entrainment ratio ω ṁ_s / ṁ_m (mass basis)
Compression ratio CR P_d / P_s
Expansion ratio ER P_m / P_d
Design trade-off: Higher compression ratios require lower entrainment ratios. A single ejector stage typically achieves compression ratios of 6:1 to 10:1. Multi-stage systems are used for higher ratios.

2. Design Equations

Ejector design involves sizing the nozzle throat, mixing section, and diffuser based on the required entrainment and compression ratios.

Motive Nozzle Flow

Critical (choked) flow through nozzle: ṁ_m = C_d × A_t × P_m × √(k × M / (R × T_m)) × [2/(k+1)]^[(k+1)/(2(k-1))] Simplified for steam (k=1.3): ṁ_m = 0.0165 × A_t × P_m / √T_m Where: A_t = Nozzle throat area (in²) P_m = Motive pressure (psia) T_m = Motive temperature (°R) ṁ_m = Motive flow (lb/hr) C_d = Discharge coefficient (0.95-0.98)

Entrainment Ratio

Approximate entrainment ratio: ω = ṁ_s / ṁ_m ≈ K × √[(P_m - P_d)/(P_d - P_s)] × √(MW_m/MW_s) × √(T_s/T_m) Where K depends on ejector geometry (typically 0.2-0.4) For steam ejecting air: ω ≈ 0.3 × √[(P_m - P_d)/(P_d - P_s)]

Area Ratios

Ratio Typical Range Effect
A_mixing / A_throat 4-12 Higher = more entrainment, less compression
A_diffuser_exit / A_mixing 3-8 Higher = more pressure recovery
L_mixing / D_mixing 5-10 Adequate mixing length
Diffuser half-angle 3-5° Prevents flow separation

Example: Steam Ejector Sizing

Given: 100 lb/hr air at 1 psia suction, 150 psig steam, discharge to atmosphere (14.7 psia)

Compression ratio = 14.7 / 1.0 = 14.7:1
(May require 2 stages for this ratio)

Single stage estimate:
Expansion ratio = 164.7 / 14.7 = 11.2
ω ≈ 0.3 × √[(164.7-14.7)/(14.7-1.0)]
ω ≈ 0.3 × √(150/13.7) = 0.3 × 3.31 = 0.99

Steam required ≈ 100 / 0.99 = 101 lb/hr steam
(Actual will be higher due to efficiency losses)

3. Performance Characteristics

Ejector performance is characterized by operating curves showing the relationship between suction pressure, discharge pressure, and entrainment capacity.

Operating Curves

Performance Factors

Parameter Change Effect on Capacity Effect on Compression
↑ Motive pressure ↑ Increases ↑ Increases
↑ Motive temperature ↓ Decreases ↓ Decreases
↑ Suction temperature ↓ Decreases (mass) Slight decrease
↑ Discharge pressure ↓ Decreases N/A (fixed by system)
↑ Suction MW ↓ Decreases (molar) Slight increase

Efficiency

Ejector efficiency: η = (Ideal compression work) / (Motive fluid energy) η = [ṁ_s × c_p × T_s × ((P_d/P_s)^((k-1)/k) - 1)] / [ṁ_m × Δh_motive] Typical efficiencies: Single stage: 10-30% Multi-stage with intercooling: 15-35% (Lower than mechanical compressors but no moving parts)

⚠ Backflow condition: If discharge pressure exceeds the break point, the ejector can reverse flow, potentially causing dangerous conditions. Install check valves and pressure relief on suction systems.

4. Applications

Ejectors are widely used in oil and gas, refining, and chemical industries for vacuum generation and gas handling.

Common Applications

Application Motive Fluid Typical Suction
Vacuum distillation Steam 10-100 mmHg abs
Condenser air removal Steam 1-5 psia
Flare gas recovery Natural gas, N₂ 0-5 psig
Tank vapor recovery Natural gas Atmospheric
Gas lift High-pressure gas Well casing
Glycol dehydration Natural gas Flash tank vapor

Midstream Applications

Multi-Stage Systems

For compression ratios exceeding 10:1, multiple ejector stages with intercondensers are used:

5. Sizing Guidelines

Ejector sizing requires balancing motive consumption against required capacity and compression ratio.

Design Parameters

Parameter Typical Range Notes
Steam pressure 50-200 psig Higher = more capacity
Steam quality >98% dry Wet steam erodes nozzle
Single stage CR 6:1 to 10:1 Practical maximum
Entrainment ratio 0.1 to 2.0 Depends on pressures
Nozzle velocity Mach 2-4 Supersonic at throat exit

Steam Consumption Estimates

Rule of thumb for steam ejectors: Steam (lb/hr) ≈ Air equivalent (lb/hr) × Steam ratio Steam ratios (100 psig steam, atmospheric discharge): Suction 100 mmHg: ~3 lb steam/lb air Suction 50 mmHg: ~5 lb steam/lb air Suction 25 mmHg: ~10 lb steam/lb air Suction 10 mmHg: ~20 lb steam/lb air Air equivalent: W_eq = W_actual × √(MW/29) × √(T_std/T_actual)

Gas Ejector Sizing

For gas-driven ejectors: ṁ_motive / ṁ_suction ≈ (1/K) × √[(P_d - P_s)/(P_m - P_d)] × √(MW_s/MW_m) Where K = 0.25-0.35 depending on design Motive gas consumption: Higher motive pressure = less gas required Typical motive: 2-4× discharge pressure

Selection Considerations

References

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