🌊 Francis & Kaplan Turbine Cavitation Sizer

Calculate Francis and Kaplan reaction turbine cavitation limits: Thoma critical cavitation coefficient sigma, metric specific speed nq, and maximum setting height above tailwater.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 36

⚡ Calculs faits 32

💾 Téléchargements 356 📦 Code Fortran 5.2 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🌊 Reaction Turbine Runner, Draft Tube & Tailwater Elevation

Real-time visual simulation: Runner elevation setting zs relative to tailwater level to avoid cavitation

📝 Configuration & Presets

🏔️ Medium-Head Francis (85m) ⚡ Pumped-Storage (220m) 🏞️ River Kaplan (18m) 🌊 Bulb Tidal Turbine (6.5m)

⚡ Turbine Type & Hydro Duty

Turbine Reaction Architecture:

Net Head H_net [m]:

Water Flow Q [m³/s]:

📐 Generator Speed & Powerhouse Elevation

Rotational Speed N [rpm]:

Altitude above Sea Level [m]:

River Water Temperature [°C]:

Thoma Cavitation & Setting Height Formulation:
• Metric Specific Speed: n_q = N · √Q / H_net^0.75 [rpm]
• Thoma Critical Coeff: σ_c = 0.0437·(n_q/100)^1.64 + 0.015 (Francis)
• Permissible Setting Height: z_s = (H_atm − H_vap) − σ_c·H_net − 0.50 [m]
• If z_s < 0: Powerhouse runner must be submerged below tailwater.

📊 Performance Results

📊 Output Summary
💾 Fortran Source

Max Allowable Setting Height (z_s)

+1.04 m

Power: 70.23 MW | Thoma σ_c: 0.0350

ABOVE TAILWATER (POSITIVE ZS)

Metric Specific Speed (n_q) 62.1 rpm HIGH-HEAD FRANCIS RUNNER

Cavitation Head Drop (σ_c·H) 7.71 m Dynamic pressure drop in runner

Atmospheric Pressure Head 9.39 m w.c. Altitude = 800 m

Shaft Power Generated 70.23 MW η = 93% efficiency

📈 Setting Height zs (m) vs Net Water Head H (m)

📊 Thoma Cavitation Coeff σc vs Specific Speed nq

=================================================================
 THERMOFLUIDCALC — HYDRO TURBINE CAVITATION REPORT
=================================================================
Case Title                 : High-Head Pumped-Storage Francis Runner
Turbine Architecture       : Francis Reaction Runner
Hydro Operating Point      : Hnet = 220.0 m, Q = 35.00 m3/s, N = 600 rpm
Site Conditions            : Altitude = 800 m, Water Temp = 12.0 C (H_atm = 9.39 m w.c.)
-----------------------------------------------------------------
MAX SETTING HEIGHT (zs)    : +1.04 m (ABOVE TAILWATER (POSITIVE ZS))
Thoma Critical Cavitation  : sigma_c = 0.0350 (Cavitation Drop: 7.71 m)
Metric Specific Speed (nq) : 62.1 rpm (HIGH-HEAD FRANCIS RUNNER)
Shaft Power Generated      : 70.23 MW
=================================================================

📘 Calculation Methodology & Hydro Cavitation Standards

Thoma Cavitation Parameter ($\sigma$)

Cavitation occurs when local pressure on the suction side of runner blades drops below vapor pressure $P_v$. The Thoma parameter $\sigma_c$ links dynamic pressure depressions to the net head $H_{net}$.

Setting Height ($z_s$) & Submergence

If $z_s < 0$, the runner must be excavated and placed below the downstream tailwater canal level to provide positive static suction head against cavitation pitting and vibrations.

Key Engineering Assumptions

IEC 60193 / USBR Monograph empirical cavitation coefficients.
Atmospheric barometric pressure correction for powerhouse altitude.
Widely used in hydroelectric dam powerhouse design and pumped storage plants.

ThermoFluidCalc Engineering Report