Steam Jet Ejector & Multi-Stage Vacuum System Sizing Calculator
Perform industrial sizing of steam jet vacuum ejectors and inter-condenser stages based on Heat Exchange Institute (HEI) standards. Calculate motive steam consumption, entrainment ratio (Rm), compression ratio, Equivalent Dry Air (EDA), and condenser cooling water demand.
1. Suction Load & Steam Operating Inputs
2. Vacuum Performance & Steam Consumption
First-Principles Mathematical Derivation of Supersonic Ejector Systems
Steam jet vacuum ejectors utilize compressible gas dynamics to transfer momentum from a high-pressure motive steam jet to a low-pressure suction stream.
1. Motive Steam Isentropic Expansion & Throat Area
For choked critical flow through the motive De Laval nozzle ($P_{mot} / P_s > 2$), the throat mass flux is given by Fliegner's formula for superheated steam ($\gamma = 1.3$):
2. HEI Equivalent Dry Air (EDA) Conversion
Per Heat Exchange Institute (HEI) standards, process suction loads are normalized to Equivalent Dry Air at 70°F (21.1°C):
3. Multi-Stage Compression Ratio & Steam Sizing
The overall compression ratio $CR = P_d / P_s$ is split geometrically across $N$ stages: $CR_{stage} = (P_d / P_s)^{1/N}$. The mass entrainment ratio $R_m = \dot{m}_{EDA} / \dot{m}_{mot}$ is correlated empirically against $CR_{stage}$ and expansion ratio ($P_{mot} / P_s$).
5 Fatal Traps & Engineering Pitfalls in Steam Ejector Design
1. Wet Motive Steam Droplet Erosion & Supersonic Shock Stall
Supplying wet motive steam ($< 99.5\%$ quality) allows liquid water droplets to accelerate to Mach 3. High-velocity droplet impact erodes stainless steel nozzle throats within months, enlarging the throat and cutting exit velocity. Wet steam also causes premature shock wave collapse, triggering sudden loss of vacuum.
2. Discharge Backpressure Exceeding Break Pressure
If downstream condenser cooling water warms up or barometric vent piping suffers excessive friction loss, discharge backpressure exceeds the critical break pressure ($P_{break}$). The internal supersonic shock wave pops out of the diffuser throat into the suction head, causing suction pressure to spike by 500% within seconds.
3. Over-Pressure Motive Steam Choking
Operating with motive steam pressure $> 20\%$ above design is just as hazardous as under-pressure. Excessively high steam pressure causes severe nozzle over-expansion; the expanding steam jet plumes outward and physically chokes the suction annular clearance, reducing suction gas capacity by 40%.
4. Inter-Condenser Air-Locking & Water Siphon Surge
If the barometric drain leg from the inter-condenser lacks sufficient vertical drop height ($< 10.5\,\text{m}$) or the seal pot overflows, condensate backs up into the condenser shell. Liquid water slugs are drawn directly into the secondary ejector suction nozzle, shattering the diffuser body.
5. Sub-Triple Point Ice Freezing in Deep Vacuum ($P_s < 4.5\,\text{mbar}$)
In high-vacuum booster ejectors operating below the triple point of water ($6.1\,\text{mbar}$, $0.01^\circ\text{C}$), isentropic expansion drops stream temperatures below $-15^\circ\text{C}$. Sublimated ice crystals coat the diffuser throat walls, constricting gas flow until steam jackets are energized to melt the ice glaze.