The primary metric of ejector efficiency is the Entrainment Ratio ( ), defined as:
Steam expands through the motive nozzle supersonically. Assuming isentropic expansion, the critical pressure ratio (
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The entrainment ratio dictates how many kilograms of motive steam are required per kilogram of suction fluid.
): The mass flow rate of entrained vapor divided by the mass flow rate of motive steam. The ratio of discharge pressure ( Pccap P sub c ) to entrained vapor pressure ( Pecap P sub e ). Choked flow is generally defined as Expansion Ratio ( ): The ratio of motive steam pressure ( Ppcap P sub p ) to entrained vapor pressure ( Pecap P sub e Geometry Sizing: Determining the nozzle throat area ( A1cap A sub 1 ), nozzle outlet area ( A2cap A sub 2 ), and diffuser cross-sections. Foundational Research Papers ejector design calculation xls
The motive fluid expands isentropically through a converging-diverging (De Laval) nozzle. The mass flow rate ( ) through the nozzle sonic throat is governed by:
is the diffuser efficiency (typically between 0.75 and 0.85), and is the Mach number of the mixed fluid. 3. Structuring your Excel ( .xls ) Calculation Sheet
Best for (e.g., pumping seawater with a pressurized water jet). Assumes mixing occurs in a constant cross-section throat.
) of . For higher ratios, design a multi-stage system with inter-condensers. The primary metric of ejector efficiency is the
| Pitfall | Solution in .xls | |---------|------------------| | (nozzle area depends on ṁ_s which depends on area) | Enable iterative calculation: File → Options → Formulas → Enable iterative calculation (max 100 iterations). | | Using wrong fluid properties | Always use absolute pressure (bar(a)), not gauge. Add validation rules. | | Neglecting two-phase flow | If motive fluid is saturated steam, check quality at nozzle exit. Use IF condition: if quality < 0.9, warn user. | | Manual lookup errors | Replace all manual chart lookups with FORECAST.LINEAR or VLOOKUP approximate match. | | Unit mix-up (mm vs m) | Use named constants: mm_to_m = 0.001 . Always convert inside formulas. |
To build an accurate calculation spreadsheet, you must define the operational parameters of your system. Organize your Excel sheet to capture these primary inputs: Motive Fluid Properties Motive steam pressure ( Pmcap P sub m , bar a or psia) Motive steam temperature ( Tmcap T sub m , °C or °F) or dryness fraction Motive steam mass flow rate ( , kg/h or lb/h) — if predetermined Suction Fluid Properties Suction pressure ( Pscap P sub s , bar a or Torr) Suction temperature ( Tscap T sub s , °C or °F) Total suction gas mass flow rate ( Average molecular weight of suction gas ( MWscap M cap W sub s Specific heat ratio of suction gas ( Discharge Conditions Discharge/Back pressure ( Pdcap P sub d , bar a or mmHg) 3. Step-by-Step Ejector Design Calculations
Rm=α⋅(PsPd)⋅MsMm−1cap R m equals alpha center dot open paren the fraction with numerator cap P sub s and denominator cap P sub d end-fraction close paren center dot the square root of the fraction with numerator cap M sub s and denominator cap M sub m end-fraction end-root minus 1 (Note:
With the theory established, let's build the spreadsheet. The following section outlines a practical, step-by-step approach to creating an Excel-based design tool. The ratio of discharge pressure ( Pccap P
Motive nozzle conditions
Here are the key equation sets you will implement in Excel. The calculations are typically performed using iterative methods, which Excel's circular reference or iterative calculation features handle well.
Comprehensive Guide to Steam Jet Ejector Design Calculations
[ CR = \fracP_3P_2 \quad \text(absolute pressures) ]