A three-phase heat and mass transfer model of a compact mechanical-draft cooling tower with a tubular fill and its adequacy assessment

Abstract

Relevance: cooling towers of circulating water supply systems largely determine the energy efficiency of thermal power plants and of chemical, petrochemical and food industry enterprises. In the hot and dry climate of Uzbekistan, at air temperatures above 40 °C the cooling range drops sharply, which degrades the operating mode of process equipment. For plants with limited floor area, compact mechanical-draft cooling towers are promising, and resolving the contradiction between compactness and energy efficiency is a topical task. The widely used Merkel and Poppe models do not account for the indirect pre-cooling of air inside a tubular fill, so a more accurate calculation model is required.

Aim: to develop a three-phase mathematical model of heat and mass transfer in a compact mechanical-draft cooling tower with a fill made of hollow horizontal tubes, to identify its empirical coefficients from experimental data and to assess the adequacy of the model.

Methods: successive reduction of a three-dimensional multiphase system of equations to a one-dimensional engineering model; solution of the boundary-value problem by the fourth-order collocation method;

Results: the model parameters were identified (C_K = 1.86; K₁ = 700 W/(m³·K); K₂ = 0.624 kg/(m³·s)) and agree within 10 % with β_xv = 0.567 ± 0.019 kg/(m³·s) obtained independently by the Merkel method. The deviation between calculation and experiment is MAPE = 0.8 % for the cooled water temperature and 5.5 % for the heat duty. In 15 tests carried out on the hottest days of 2023–2025 the indirect pre-cooling of air inside the tubes was Δtа = 1.60…2.56 K (2.02 K on average), and its linear dependence on ambient air temperature (R² = 0.989) matched the model parameter within 1.2 %.