Modelling and calculation of a small-size evaporation cooling apparatus for industrial recirculated water with a heat-and-mass exchange packing based on wastes from metalworking machinery

. The article presents the results of the experiments on fluid and gas dynamics through a layer of packing material S-Aisi304 ε-0,95 ( ε=0,95, σ=160m 2 /m 3 ) suggested for use as packing blocks in small-size evaporation cooling apparatuses for industrial recirculated water. Experimentally confirmed effects are covered that prove the performance efficiency of wastes from metal-working machinery as packing materials for contact evaporation blocks. Results of mathematical modelling and engineering calculation of the main process parameters and dimensions for a small-size evaporation cooling apparatus for industrial recirculated water with use of contact blocks filled with the studied packing material are provided.


Introduction
Low-grade heat transfer from the recirculated water by means of its cooling with atmospheric air is widely used in different technical equipment and process systems. Such recirculated water cooling method is widely used in many industries: chemical, petrochemical, oil-and-gas, nuclear, metallurgical, construction, food processing and many other related fields. Small-size evaporation coolers are widely used in local systems of recycling water supply. Thus, designing of structures for evaporation cooling apparatuses and packing materials (packing elements), which have small dimensions and energy consumption and at the same time a relatively high capacity, is a challenging engineering task. The main structural element in evaporation cooling apparatus ensuring the required efficiency of recirculated water cooling is the heat-and-mass exchange packing .
Operation efficiency of evaporation cooling apparatuses mainly depends on the operation efficiency of their contact packings . Papers [4,9,10,51] demonstrate that spraying units having fibre structure and having high values of porosity and specific surface are very promising in this sphere. An important feature of such fibre structure is that it is simple and easily manufactured [51][52][53]. We regard use of fibre structures, i. e. wastes from metal-working machinery produced in the course of processing of stainless alloyed steels [51][52][53][54][55][56] (that are resistant to weather and aggressive actions), or polymer threads of different thickness and section, i. e. wastes of synthetic fibre manufacturing plants [51], as one of the most promising energy-and resource saving trends for designing and manufacturing of evaporation cooling apparatuses and packing contact blocks. Packing materials in the form of packaged blocks of wastes from metal-working machinery (metal shavings) feature a range of important structural and surface properties [51][52][53][54][55][56], i. e. they have a curly structure with microroughness and chips on the surface. All these structural and surface features result in swirling and purling of the air stream moving through the packing element layer, and liquid in its turn moves in droplet-film flow by the surfaces of the packing elements. Such structural and surface features intensify heat-and-mass exchange processes occurring between recirculated water and upward air stream and meet the requirements for evaporation cooling of industrial recirculated water with regard to the organization of liquid and air (gas) flows with respect to each other. Such materials can be easily used to form cubic or rectangular blocks (cylinder-shaped form of packing blocks is even easier to be created [51][52][53][54][55][56]) with dimensions approximately 200-600 mm that allows visual control of their internal structure. If necessary, the block can have the required stiffness if it is placed in a wire cage. Such blocks can form a packing layer of required size and configuration. Both droplet-film and developed droplet flow mode can be implemented in packing blocks (evaporation cooling blocks) depending on the equivalent diameter value that can range from 5 to 10-12 mm and on air flow velocity. Packing blocks with high equivalent diameter values have high permeability, low resistance to flow and can be larger in height.

Methods and materials
The study considers heat-and-mass exchange process of recirculated water cooling in smallsize apparatuses, where packing blocks (evaporation cooling blocks) are created of wastes from metal-working machinery, i. e. from metal shavings formed during machine processing of stainless allowed steels that are resistant to weather and aggressive actions, and their evaporation packing blocks are working with the development and maintenance of intensive liquid droplet flows. The objective of the study is to prove the application perspectiveness of heat-and-mass exchange blocks with wastes from metal-working machinery and the elaborated method of engineering calculation aimed at determination of the main process parameters and dimensions of small-size evaporation cooling apparatuses for industrial recirculated water (dimensions of evaporation cooling packing block for the pre-set operating conditions of the apparatus with regards to the flow rates of cooled water and air, temperatures of air and water flows in the extreme sections of the packing blocks with known initial parameters of air flow humidity) ensuring developed droplet-film or droplet liquid flows through the evaporation block packing layer. The calculation is based on the determination of phase contact surfaces ensuring the required heat takeoff by means of heat exchange and required moisture exchange (mass exchange) with further agreement of the values of these surfaces. The obtained experimental values of heat-and-mass exchange factors are used in the calculation for the studied packing block and liquid droplet flow retained by the packing. Figure 1 presents the photo of the contact block and experimental plant. Let us consider the obtained experimental data on resistance to flows of the dry and irrigated evaporation cooling packing block based on the wastes from metal-working machines (Packing material S-Aisi304ε-0,95 (ε=0,95m 3    The analysis of the provided experimental data (ref. to Table 1) and comparison with the performance of the packing contact devices that are widely used in the industry [58][59] make it evident that the studied packing material ensures a high permeability of the packing block (Low values of specific flow resistance) and even organization of the liquid flow mode through the layer of the packing materials with different density of irrigation and besides ensures a relatively high liquid retaining capacity [51,52,54]. A rather high efficiency of the studied material with regard to heat-and-mass exchange performance has been experimentally proved (ref. to Table 1). All properties above prove the industrial applicability of the created packing materials based on the wastes from metal-working machines used as evaporation blocks in heat-and-mass exchange evaporation heating apparatuses of recirculated water.
The most important experimentally confirmed property is the capacity of the studied packing material S-Aisi 304ε-0,95 (ε=0,95, σ=160 m 2 /m 3 ) to develop an intensive droplet flow mode by the whole height of the packing block. (Droplet-film flow mode with prevailing droplets) Thus, the method for engineering calculation of heat-and-mass exchange packing blocks in intensive droplet flow modes [51,52,60] that is shown in the block diagram in Figure 4 can be applied for calculation of an industrial evaporation cooling apparatus. The results of calculation of the main process parameters and dimensions of the small-size industrial evaporation cooling apparatus are provided in Table 1. Scheme of the modelled small-size heat-and-mass exchange evaporation cooling apparatus for industrial recirculated water with the studied packing modules represented by formed blocks of metal shavings S-Aisi304ε-0,95 (ε=0,95, σ=160 m 2 /m 3 ) is provided in Figure 3. Start q, t winit , t wf , t airinit, t air f , φ init , сw, ρ w , r v , с v , с air , υ dav , d init , G w init, G airinit, к, п, K t, K m,

Conclusions
The conducted experiments and mathematical modelling of the process demonstrated the advantages and perspectiveness of the use of wastes from metal-working machines as packing materials for the evaporation blocks in small-size evaporation cooling heat-andmass exchange apparatuses for industrial recirculated water. Especially when high-quality from the point of view of resistance to weather and aggressive actions wastes are available like the packing material studied herein S-Aisi304ε-0,95 (ε=0,95, σ=160 m 2 /m 3 ). It is noteworthy that the experiments proved special properties of this packing material, i.e. high permeability of the packing layer and development of an intensive droplet-film flow mode with prevailing droplet mode. High permeability testifies to the energy efficiency of the use of such packing materials, and the development of an intensive droplet flow mode fits the requirements of evaporation cooling process of industrial recirculated water and ensures availability of mathematical modelling of the evaporation cooling process with developed algorithms and software [51,60].
Apart from that, we would like to underscore the fact that many samples of the packing materials represented by the wastes from metal-working machines have significant elastic properties [54,55] (they preserve their elastic properties within a wide range of volumetric deformations of the packing blocks) that enables current automated adjustment of various mass exchange apparatuses operation modes [54][55][56][61][62][63], including evaporation cooling apparatuses for industrial recirculated water [64], thus, self-adaptation of the packing blocks in evaporation cooling apparatuses and shift to energy saving operation modes are available.