Cooling Tower Fill Characteristics: KaV/L against L/G (and Why Twice the Depth Is Not Twice the Cooling)

Fill performance is quoted as two curves, and both matter. The thermal curve says how much heat transfer the fill can deliver; the wet pressure-drop curve says what it costs in air pressure to push the air through it. A fill selection that reads only the first curve will produce a cooling tower that cannot get the air flow its own rating assumed.

Two curves, and neither stands alone

The thermal characteristic is the Merkel number the fill can deliver at a given water-to-air ratio:

KaV/L = C (L/G)^m

The coefficient C and the exponent m come from the fill’s tested characteristic — normally measured on a test stand, then normalised per unit fill height so that a tower of any depth can be evaluated. The wet pressure drop is a separate curve, expressed against the liquid and gas loadings, and it rises steeply with both: more water film thickness and more air velocity each cost pressure.

Both curves carry valid loading ranges. Outside the tested range — very high water loading, very low air flow, or the opposite — the curves are extrapolations, and extrapolating a fill characteristic is how designs acquire performance that the fill will not actually deliver.

Why the exponent is negative

For most film fill, m is negative. The reason is in the operating line: at a fixed air flow, more water means a higher L/G, which makes the air’s enthalpy rise faster as it crosses the fill. The air reaches a state close to saturation sooner, the enthalpy gap hs(Tw) − ha(Tw) closes earlier, and each cubic metre of fill does less useful work. A KaV/L that falls as L/G rises is the arithmetic expression of that.

Illustrative arithmetic

The following is an illustrative example, not a measured result. It uses a coefficient of 1.9 and an exponent of −0.6 purely to show the shape of the relationship.

Raising the water-to-air ratio from 1.2 to 1.5 costs about 12.5% of the available characteristic at the same air flow. The real coefficients and exponents come from the fill’s tested data, and different fill types — film, splash, and the various flute geometries within film — have materially different shapes.

Depth is not proportional to cooling

Since KaV/L contains the fill volume, doubling the depth roughly doubles the characteristic the fill can offer at the same loadings. That sounds like a doubling of performance, and it is not.

The reason is that the integral is a cost integral against a shrinking potential. The top of the fill sees hot water against relatively dry air, so the enthalpy gap is wide and transfer is cheap. By the time the water has cooled, the same fill is working against an enthalpy gap that has narrowed — and the bottom of a deeper fill is working against a narrower gap still than the bottom of a shallower one would. Every additional metre of fill adds less cooling than the metre above it, because the potential it works against is smaller.

Three effects reinforce the point:

• Pressure drop is cumulative. The deeper fill raises air-side resistance, and the fan responds by moving less air — which reduces L/G and shifts the operating point in a direction that partly offsets the extra fill.
• Distribution quality matters more as depth grows. An uneven water distribution that a shallow fill tolerates can starve the lower passages of a deep fill, and the area that is starved contributes pressure drop without contributing transfer.
• The spray and rain zones already transfer heat. The distribution spray zone above the fill and the rain zone below it are both transfer surfaces. In a shallow-fill tower they are a meaningful fraction of the total, so the marginal value of extra fill is smaller than the fill-only analysis suggests.

This is why fill depth is a design variable with an optimum, not a dial that goes to “more is better”.

What degrades a fill over time

Fill loses performance in four ways, and they are distinguishable because they move the two curves differently:

• Scale and hardness deposits coat the transfer surfaces and thicken with water loading. Thermal characteristic falls; wet pressure drop rises; the fill’s weight and structural load rise too.
• Biofilm and biological fouling have the same signature as scale but respond to a different treatment and inspection method.
• Mechanical deformation, collapse or passage blockage reduce effective surface area and can locally close passages. Pressure drop rises sharply for a given loading, sometimes with a visible channel of air bypass.
• Chemical attack — from aggressive water chemistry or over-dosing — degrades the material itself, embrittling or dissolving the fill until it no longer holds its shape.

In every case the tower-side symptom is usually small: a fraction of a degree of approach, a slightly higher fan power. That is precisely why performance evaluation has to compare curves at the same L/G rather than just compare temperatures, and why the performance test and the physical inspection belong in the same visit.

What this means for a fill replacement decision

A fill replacement is often proposed on the basis of a temperature that “used to be lower”. The stronger case is built from the curves:

1. Measure the tower’s current characteristic, and measure it at a documented L/G — with the water flow and the air flow both known.
2. Compare it with the fill’s own characteristic at that same L/G, including the wet pressure drop at the measured loadings.
3. Decide which degradation mechanism the evidence points to, because scale calls for cleaning and water treatment while deformation calls for replacement.
4. If replacement is chosen, expect the gain to follow from the restored characteristic — and be sceptical of a predicted gain that assumed depth and cooling scale linearly, because they do not.

Read more

• Parts replacement and spare parts service
• The Merkel number and the entering-air convention
• Fan curves and system balance
• Cooling tower fill replacement: how it saves energy and reduces operating costs
• Cooling tower glossary

Sources

• Kloppers & Kröger — Cooling tower performance: a critical evaluation of the Merkel assumptions (SAIMechE, 2004) — the Merkel number KaV/L the fill’s thermal characteristic is written in, and the operating-line treatment behind this article’s explanation of the negative exponent.
• Hensley, J.C. (ed.) — Cooling Tower Fundamentals, 2nd edition (SPX Cooling Technologies, 2009) — the film and splash fill types and the behaviour this article’s condition list follows — cooling capacity within the same space, air pressure loss, and sensitivity to water distribution and support.