Elsevier

Applied Energy

Volume 78, Issue 4, August 2004, Pages 433-451
Applied Energy

Simplified model for indirect-contact evaporative cooling-tower behaviour

https://doi.org/10.1016/j.apenergy.2003.09.004Get rights and content

Abstract

A simplified model for indirect cooling towers behaviour is presented. The model is devoted to building simulation tools and fulfils several criteria such as simplicity of parameterisation, accuracy, possibility to model the equipment under various operation conditions and short computation time. On the basis of Merkel's theory, the model is described by using the Effectiveness-NTU method. The model introduces only two parameters, air-side and water-side heat-transfer coefficients which can be identified from only two rating points, data easily available in manufacturers' catalogues. Thus, the model allows one to estimate energy and water consumptions under different operating conditions such as variable wet-bulb temperatures or variable airflow rates.

Introduction

Indirect cooling towers are commonly used in industrial processes and in air-conditioning systems to reject heat to the atmosphere. An indirect cooling tower is a device which uses heat and mass transfer to cool water from a process. The hot water goes through serpentine tubes arranged in rows, whereas the air passes on the external side of this coil. An additional circuit sprays water to cool further the coil by evaporation (Fig. 1). The main advantage of this system compared with an open cooling-tower is that the contamination risks with airborne dusts and corrosion are limited since the process water never contacts the outside air. The main drawback compared to an open cooling-tower is that the cost and the size are increased since a larger heat-exchange surface is required to reach the same heat transfer. In order to reduce water consumption, some closed cooling towers can operate in a dry regime when the outdoor conditions are favourable and the cooling demand is low.

We will focus on modelling of this equipment's behaviour. The aim is to determine its performance and its energy and water consumptions in order to assess its advantages in operation. The model should fulfil several requirements identified for building simulation tools devoted to HVAC designers:

  • Simplicity of parameterisation; the information available for HVAC designers and researchers is often limited to that contained in manufacturer's catalogues. Unfortunately, it is scarce to find the coil characteristics, one can only find performance data under different inlet conditions. The parameterisation should be based on a minimum of rating points:

  • Short computation time;

  • Model under different operational conditions;

  • High accuracy.

In the literature, several models fulfil the requirement of accuracy and running time. Facão [1] compared simplified models [2], [3] with detailed models such as numerical models [4], [5] and noticed that simplified models based on an overall approach provide as good or even better results as those based on finite differences. Notice that other simplified models have been developed such as the unified model for evaporative cooling devices [6]. Most of the simplified models are built on the basis of Merkel's theory assuming a Lewis number equal to unity and neglecting the losses due to water evaporation. Additional hypothesis are often taken into account such as:

  • the spray enthalpy is neglected;

  • the water film temperature is assumed to be constant along the whole coil;

  • the enthalpy is expressed by a linear function of the wet bulb temperature only.

The aim of this paper is to adapt a simplified model for analysing the combined heat-and-mass transfers in indirect cooling towers which can (i) be easily parameterised through performance data available in manufacturer's catalogues, (ii) evaluate the tower performance under different operating conditions, notably variable airflow rate and (iii) assess the water consumption.

Section snippets

Heat and mass transfer equations

In this section of the paper, the basic equations of the mass and heat transfer which occurs in the systems using evaporative cooling are stated. The main assumptions are:

  • The heat exchange between the cooling tower and the surroundings is negligible.

  • The specific heats of the fluids are assumed to be constant.

  • The mass and heat transfers take place only in the direction normal to the flow.

  • The fluids at entry are uniformly distributed in the plane perpendicular to the flow.

  • The water film covers

Air side heat-transfer coefficient

The closed cooling tower coils are generally staggered rows of finned or unfinned circular tubes. The finned tubes are used for cooling towers which can operate in a dry regime. First, one considers staggered tubes without fins. In the literature, many correlations have been established [1], [10], [11], [12] for mass transfer coefficient. Misushina and Miyashita [12] proposed a correlation for 1200⩽Rea ⩽14,000, 50⩽Respray ⩽240 and 12⩽dext ⩽40 mm :h̄ma=5.028×10−8Rea0.9Respray0.15dext−2.6When Ġ

Validation data

The model has been compared to manufacturers' data [17], [18]. Three closed cooling towers from two manufacturers have been studied (Table 3). The three coils are unfinned and with staggered tube ranks. The first one is equipped with a centrifugal fan placed under the coil, the second one with a centrifugal fan located on the side of the coil. In this last case, the arrangement aims to limit the height of the cooling tower. The air is still extracted at the top of the cooling tower and one

Water consumption

The cooling in the tower is mainly due to the evaporation of the water spray on the tubes. The water losses represent about 1–4% of the spray-water-flow rate. The drift losses can be neglected since they represent generally less than 0.2%. Since one part of the water evaporates, it is necessary to bleed the tower in order to limit the concentrations of impurities. The waste of a small percentage of circulating water is expressed by the concentration ratio:concentrationratio=evaporation+blowdown

Conclusions

A model for the behaviour of a closed cooling-tower, adapted from building energy simulation programs, has been developed. It is based on effectiveness models by simplification of heat and mass balance and transfer equations.

One need not assume that the water-film temperature is constant along the coil. Moreover, it allows one to estimate the cooling-tower's performance at variable air flow rates and to calculate the water consumption. The parameterisation is obtained from two rating points at

References (18)

  • Facão J, Oliveira AC. Thermal behaviour of closed wet cooling-towers for use with chilled ceilings. Applied Thermal...
  • J.L. Peterson

    An effectiveness model for indirect evaporative coolers

    ASHRAE Transactions

    (1993)
  • R.I.T. Mizushina et al.

    Experimental study of an evaporative cooler

    International Chemical Engineering

    (1967)
  • R.I.T. Mizushina et al.

    Characteristics and methods of thermal design of evaporative coolers

    International Chemical Engineering

    (1968)
  • W.A. Kals

    Wet-surfaces air coolers

    Chemical Engineering

    (1971)
  • Lebrun J, Aparecida Silva C, Trebilcock F, Winandy E. Simplified models for direct and indirect contact cooling-towers...
  • J.L. Threlkeld

    Thermal environmental engineering

    (1970)
  • Bourdouxhe P, Grodent M, Lebrun J. Cooling-tower model developed in a toolkit for primary HVAC system energy...
  • J.E. Braun et al.

    Effectiveness models for cooling towers and cooling coils

    ASHRAE Transactions

    (1989)
There are more references available in the full text version of this article.

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