The Francis Turbine: How Falling Water Becomes Electricity

Reaction, not impulse: where the energy actually lives

A Francis turbine is a reaction turbine, and understanding what that means is the whole game. In an impulse machine like a Pelton wheel, all of the water's pressure energy is first converted to a fast free jet in a nozzle; the runner sits in open air at atmospheric pressure and simply catches the jet's momentum. In a Francis turbine the runner is completely submerged and runs full of pressurized water. The flow still has significant pressure when it reaches the blades, and it gives that pressure up gradually as it passes through — the passages between the curved blades act as a bank of moving nozzles.

The fraction of the total head that is converted to velocity before the runner (versus dropped as pressure inside it) is the degree of reaction, typically around 0.5 for a Francis machine. Because the runner does work on a still-pressurized fluid, the pressure on the upstream face of each blade is genuinely higher than on the downstream face — a real, static force pushing the blade around. That is why it is called a reaction turbine: the water reacts against the blade the way a garden hose kicks back, not merely by slapping into it.

Following one drop of water through the machine

The flow path is a beautifully engineered deceleration and de-swirling of high-pressure water:

• Spiral (scroll) casing. Water arrives from the penstock and is fed into a snail-shell casing whose cross-section shrinks steadily around the circumference. That taper delivers an equal share of flow to every point of the ring, so the runner is loaded symmetrically all the way around.
• Stay vanes + guide vanes (wicket gates). A ring of fixed stay vanes carries structural load, then a ring of pivoting guide vanes aims the water and — critically — sets how much flow enters. Rotating these vanes closed throttles power; this is the turbine's throttle valve.
• Runner. The water enters the runner radially (inward) with a strong tangential swirl and leaves it axially (downward), nearly swirl-free. Twisted blades harvest the change in angular momentum. This inward-then-downward turn is the Francis signature.
• Draft tube. A gently flaring cone below the runner recovers the leftover kinetic energy by slowing the exit flow, converting velocity back into a pressure recovery (suction) that raises the effective head across the runner by 3–10%.

The physics: Euler's turbine equation

All the energy transfer is captured by one relation — the Euler turbomachinery equation, which comes straight from conservation of angular momentum. The specific work extracted per kilogram of water is:

w = U₁⋅Cu₁ − U₂⋅Cu₂

where U is the blade speed at a radius (U = ω⋅r) and Cu is the tangential (swirl) component of the water's absolute velocity, at inlet (1) and outlet (2). The design goal is to inject strong inlet swirl Cu₁ with the guide vanes and then strip almost all of it out by the runner exit, so Cu₂ ≈ 0. The equation says the machine only harvests change in swirl — a drop that enters and leaves with the same spin does zero net work.

The shaft power and torque then follow:

P = ρ⋅Q⋅g⋅H⋅η and τ = P ÷ ω = ρ⋅Q⋅(U₁Cu₁ − U₂Cu₂) ÷ ω

with ρ ≈ 1000 kg/m³, Q the volume flow, H the net head, and η the efficiency. For a 700 MW Three Gorges unit at H ≈ 80 m and η ≈ 0.94, that implies Q = P ÷ (ρ⋅g⋅H⋅η) ≈ 700×10⁶ ÷ (1000⋅9.81⋅80⋅0.94) ≈ 950 m³/s per unit — a small river passing through one runner every second.

Specific speed: why a Francis at all

Engineers don't pick Francis by feel — they compute a dimensionless specific speed that says which turbine family fits a given head and flow. One common form is:

Nq = n⋅√Q ÷ H^0.75 (with n in rpm, Q in m³/s, H in m)

Roughly: Nq ≈ 8–30 → Pelton (high head, low flow), Nq ≈ 40–120 → Francis, Nq ≈ 120–300 → Kaplan (low head, huge flow). Francis owns the enormous middle ground — moderate heads (40–600 m) with moderate-to-large flow — which is exactly the regime most dammed rivers create. That is why it, and not its cousins, is the default for the majority of large plants.

Specific speed also dictates the runner's shape. Low-Nq Francis runners are tall and narrow with a steep radial inflow; high-Nq runners flatten toward a mixed-flow, almost propeller-like geometry as they blend toward the Kaplan regime. A single family thus stretches across a huge span of sites just by re-proportioning the runner.

Cavitation: the failure mode that eats runners

The signature limitation of any reaction turbine is cavitation. As water accelerates over the low-pressure (suction) side of a blade, local static pressure can fall below the vapor pressure of water (≈2.3 kPa at 20°C). Vapor bubbles form, then collapse violently as they sweep into higher-pressure regions downstream. Each implosion sends a micro-jet against the metal at pressures of hundreds of MPa; over months this pits and erodes stainless-steel runners, distorts blade profiles, drops efficiency, and roars audibly.

The design guard is Thoma's cavitation coefficient: σ = (Patm − Pvapor − ρ⋅g⋅Hs) ÷ (ρ⋅g⋅H), where Hs is the suction head — the height of the runner above tailwater. If the plant's σ falls below the runner's critical σ (which rises steeply with specific speed), the machine cavitates. The classic fix is to lower the runner, even below tailwater level, buying pressure margin at the cost of deeper, more expensive civil excavation. A subtler trap is the part-load vortex rope: away from the best efficiency point, residual exit swirl coils into a precessing helical vapor core in the draft tube that can shake the whole powerhouse — a real driver behind the operating-range limits printed on every unit's hill chart.

From runner to the grid — and where you'll find them

The runner is bolted to a vertical shaft that drives a large synchronous generator directly, with no gearbox. To make 50 Hz or 60 Hz grid power, the generator must turn at a synchronous speed n = 120⋅f ÷ p, where p is the number of poles. A slow, big turbine simply gets more poles: a 700 MW Three Gorges generator uses on the order of 80 poles to sit at ≈75 rpm while locked to 50 Hz. A governor continuously trims the guide vanes to match generated power to grid demand and hold speed — the modern electronic descendant of the mechanical centrifugal governor.

Francis machines dominate the real fleet: Three Gorges (China, 32 main units at ≈700–767 MW), Itaipú (Brazil/Paraguay, 700 MW units), Grand Coulee, Hoover Dam, and countless mid-size plants worldwide. Reversible Francis runners also power the majority of pumped-storage plants — the same machine pumps water uphill to store energy, then generates on the way down, forming the grid's largest bulk battery. Physical sizes run from sub-meter runners for a few hundred kW up to runner throats near 10 m diameter and unit masses in the thousands of tonnes for the largest dams.

Francis vs. the other two workhorse hydro turbines — matching machine to head and flow

Property	Francis (reaction)	Pelton (impulse)	Kaplan (reaction)
Best head range	≈40–600 m	≈250–1800 m	≈2–40 m
Flow / discharge	Medium–high	Low, high-velocity jets	Very high
Energy transfer	Pressure drop + swirl in runner	Impulse from free jets	Pressure drop, propeller-like
Runs full of water?	Yes (submerged, pressurized)	No (jets in air, atmospheric)	Yes (submerged)
Blades adjustable?	Fixed runner, adjustable guide vanes	Fixed buckets, needle valve	Both guide vanes & blades pitch
Peak efficiency	90–96%	88–92%	90–95%