Fan Curves and System Balance: Where a Cooling Tower Fan Really Operates

A cooling tower fan does not produce a fixed quantity of air. It settles wherever its own pressure-volume curve crosses the resistance of everything downstream of the air inlet, and that intersection — the operating point — is what decides how much air the fill actually sees. This is why replacing a drift eliminator with a tighter one, cleaning a fouled fill, or adding inlet screens can move a tower’s performance without touching the fan at all.

Two curves, one operating point

The fan is characterised by a pressure-volume curve from the manufacturer: at each flow, the pressure the fan can develop. Its shape matters — most curves rise to a peak and then fall, and beyond the peak lies the stall region, where flow becomes unstable and the guarantee on the curve no longer applies.

The tower is characterised by a system resistance curve. For turbulent flow through fill, eliminator and louvres, resistance rises with roughly the square of the flow:

ΔPsystem = K Q²

The fan operates where the two curves cross:

ΔPfan(Q) − ΔPsystem(Q) = 0

Nothing else sets the airflow. If the tower’s resistance rises — a fouled fill, a partially blocked inlet, a scale-loaded eliminator — the intersection slides to a lower flow along the fan curve, and the tower loses air mass flow in proportion.

Every loss coefficient has a reference velocity

The single most common error in assembling an air-side model is comparing pressure drops that were measured at different reference velocities. A vendor’s drift-eliminator pressure drop may be quoted at the eliminator face velocity, a fill pressure drop at its own liquid and gas loading, and an inlet louvre loss at the approach velocity through the louvre. A loss coefficient is only a number relative to the velocity it was defined against — mix two bases and the arithmetic still produces a number, just not a valid one.

Two further points that are easy to lose:

• Velocity is not the same on both sides of the fill. Air enters the fill over the tower’s plan area and leaves at the fan stack, whose area is usually smaller. The stack velocity is higher, and any loss at the stack discharge has to be evaluated there.
• Heat transfer happens over three zones, not one. Spray zone, fill and rain zone each transfer heat and each impose resistance; a model that folds them all into a single fill loss will misplace the pressure drop between the elements.

The affinity laws

To move the operating point deliberately, the fan speed is changed. Around a reference operating point, the affinity laws give the new conditions:

Q2 / Q1 = N2 / N1

ΔP2 / ΔP1 = (ρ2 / ρ1) (N2 / N1)²

with shaft power following the cube of the speed ratio, at equal density and efficiency. The practical reading is brutal: flow is cheap, pressure is dear and power is dearest.

Illustrative example

The following numbers are an illustrative example, not a measured result.

A 10% speed increase buys 10% more flow and costs about 33% more shaft power. Run the same relationship backwards and the energy case for variable speed control appears: dropping to 90% speed gives about 90% of the flow for roughly 73% of the power.

Continuing the example at the original point, with a fan efficiency of 0.70:

Pshaft = Q ΔP / ηfan = (100 × 150) ÷ 0.70 ≈ 21.4 kW

Pelectrical = Pshaft / (ηdrive × ηmotor) = 21.4 ÷ (0.95 × 0.94) ≈ 24.0 kW

The difference between the two figures is not a detail — it is the difference between sizing a motor on its shaft and sizing it on the actual electrical input, which is what the plant pays for.

Density is the quiet variable

Both the fan and the thermal performance depend on air density, and density falls as air gets hotter and more humid. That produces two effects that compound on the hottest, most humid day of the year:

• The fan develops less pressure for the same speed, so it settles at a lower volumetric flow;
• Each cubic metre carries fewer kilograms of dry air, so the mass flow that actually transfers heat falls further.

This is why an air-side model tracked in volumetric flow will over-promise on a design day, and why g in the L/G ratio — dry air mass flow — is the quantity the thermal calculation needs.

From fan power to motor selection

Shaft power is converted to electrical input through the drive and motor efficiencies, and then the motor is selected with margin for what the fan will actually draw across its whole operating range:

• the fan power curve is not flat — the maximum power draw may occur at a flow the plant rarely runs, and the motor must carry it;
• a service factor is applied before the next catalogue size is chosen;
• derating applies at high ambient temperature and at altitude, where cooling is poorer and density is lower;
• stall, blade pitch, tip speed, system effect, noise and vibration all impose limits the curve alone does not show.

Most cooling tower fans are not run at a single fixed speed. Two-speed motors, two-speed gearboxes, variable-frequency drives or pitch control each move the operating point by a different mechanism, and each interacts differently with the tower’s thermal response — because what the fill cares about is air mass flow, not fan revolutions.

Read more

• Overhaul and maintenance service
• Cooling tower capability explained: what 100% really means
• Cooling tower glossary

Sources

• U.S. Department of Energy & AMCA International — Improving Fan System Performance: A Sourcebook for Industry (2003) — the fan laws (flow with speed, pressure with speed squared, power with the cube of speed), the system-resistance curve, the service factor, and the correction of fan performance for air density.
• Hensley, J.C. (ed.) — Cooling Tower Fundamentals, 2nd edition (SPX Cooling Technologies, 2009) — the cooling-tower fan laws — capacity with speed, static pressure with the square of capacity, horsepower with the cube — and their dependence on air density.