Crossflow against counterflow: the same fill, two arrangements

The driving force along the fill in both arrangements, and the extra fill a crossflow needs.

The driving force hs(Tw) − ha along the fill for the same fill in both arrangements, from the water inlet to the water outlet — counterflow as the one-dimensional demand, crossflow as a two-dimensional marching solution in which the air crosses water already at other temperatures.

Reference conditions: water entering at 42 °C, air at 27 °C wet bulb, L/G 1.50, same fill KaV/L 1.52 for both curves; the crossflow leaves the water 0.86 K warmer and needs 1.47 times the fill for the same duty.

Formula: the counterflow curve is the one-dimensional Merkel demand KaV/L = ∫ cp,w dTw / (hs(Tw) − ha(Tw)); the crossflow curve is the two-dimensional marching solution over the same fill.

Crossflow against counterflow: driving force in kJ/kg along the fill, from the water inlet at the left to the water outlet at the right. Both profiles start at their highest at the inlet and fall toward the outlet; the crossflow profile collapses faster because the air has already crossed water at other temperatures by the time it reaches the later strips. At the same fill the crossflow leaves the water 0.86 K warmer and needs 1.47 times the fill for the same duty (illustrative)Illustrative crossflow-versus-counterflow chart. Both curves are the same fill (merkel number KaV/L 1.52) with water entering at 42 °C, air at 27 °C wet bulb and L/G 1.50, and both plot the driving force hs(Tw) − ha in kJ/kg against fraction of fill height measured from the water inlet (x = 0) to the water outlet (x = 1). The counterflow curve is the one-dimensional demand: its height axis is the cumulative Merkel integral from the inlet, and its driving force falls from 35.88 kJ/kg at the inlet to 25.60 kJ/kg at the outlet. The crossflow curve is a two-dimensional marching solution (80 × 80 cells): the air crosses the falling water, so by the time it reaches the far strips it has already taken up heat and the potential there is narrower — the profile falls from 38.64 to 15.08 kJ/kg. At the same fill the crossflow arrangement leaves the water at 32.86 °C instead of 32.00 °C, and reaching 32.00 °C in crossflow needs 1.47 times the fill (KaV/L 2.23 against 1.52); the grid refinement 20 / 40 / 80 gives 2.235 / 2.234 / 2.234, so the reported number is converged to about 0.1 %. Values are computed from the model, not measured; no tower, no rating. (chart-flow-arrangement)Flow arrangement — Illustrative — not a measurementWhere the potential goes0.000.250.500.751.00010203040Fraction of fill height (0 = water in, 1 = water out)Driving force hs − ha (kJ/kg)38.6435.8825.60counterflow (1-D demand)crossflow (2-D model)Reference: water in 42 °C · air 27 °C wb · L/G 1.50 · cp,w 4.18 kJ/kg·KSame fill for both arrangements · crossflow: 2-D marching solution, 80 × 80 cellsfill KaV/L (same for both)1.52counterflow CWT (°C)32.00crossflow CWT, same fill (°C)32.86crossflow fill for CWT 32 °C (×)1.47grid refinement 20/40/802.235 / 2.234 / 2.234penalty at the same fill (K)+0.86Computed from the formula — not field data.
Illustrative, computed from the model above — not a measurement. Both curves are the same fill; the x axis runs from the water inlet to the water outlet, and the crossflow profile collapses toward the outlet because its air has already met water at other temperatures.

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