Keywords

1 Introduction

Energy consumption for treating the ambient air in air conditioning systems (ACS) depends on the ambient air temperature ta and relative humidity φa, which changes considerably during the day. It is obvious that the production of refrigeration by refrigeration machine (RM) according to ambient air conditioning duties over a certain period of time, for instance a year (annual refrigeration) ∑(Q0·τ), depends on the current thermal loading Q0, caused by ambient air processing, as well as on the hour duration τ of the ACS operation. Issuing from this the efficiency of using the refrigeration capacity for ambient air processing in ACS can be estimated by annual refrigeration ∑(Q0·τ) as a primary criterion in further complex thermal and economical optimization of the whole ACS, including indoor air processing about actual cooling loads of building and indoor thermal-humidity environments in targeted climatic conditions.

The existing approaches to improve the efficiency of ambient air processing in ACS are aimed at determining a design refrigeration capacity to cover the maximum yearly cooling load, which leads to oversizing the RM and other equipment and enlarged their cost as a consequence. The application of various controlling systems and variable speed compressors provides lowering energy consumption, but the problem of determining a rational design refrigeration capacity, providing closed to maximum annual effect without overestimating the installed refrigeration capacity, needs further solving.

2 Literature Review

Many publications are devoted to improving air processing in ACS by the intensification of heat transfer processes in air coolers [1, 2], evaporators [3, 4], alternate safe refrigerants [5, 6], application of various refrigerant circulation contours [7, 8], waste heat recovery technics, including combined cooling, heating and power generation [9, 10], modeling [11, 12], analysis [13, 14], optimization [15, 16], experimental and monitoring [17, 18] methods to match current cooling demands. Some of the principal technical innovations and methodological approaches in waste heat recovery refrigeration might be successfully applied for air conditioning, in particular, two-stage air cooling [19], evaporative cooling [20].

Numerous researchers have studied the energy efficiency of the Variable Refrigerant Flow (VRF) systems [21, 22] and proposed some practical recommendations. Mainly the studies have been conducted on solutions of efficient operation of the VRF system in buildings and control strategies of the systems [23]. A control algorithm of the supply air temperature as a set temperature in the outdoor air processing (OAP) unit to run the VRF–OAP system more efficiently for buildings was developed in [24]. The control algorithm was conducted with adjusting the refrigerant flow supply to the OAP and the indoor unit appropriately through supporting the supply air temperature according to the outdoor ambient and indoor temperature and humidity conditions. Results [25] show that ACS have a great potential for energy saving, and the adjustability of the VRF system is better than of centralized ACS.

The VRF system with heat recuperative ventilation [26] and outdoor ACS was introduced [27]. The evaluation of indoor thermal-humidity environments and energy consumption of the VRF system with a heat pump desiccant was conducted [28].

The author [29] proposes the method of calculating the thermal load of the building. The VRF systems operate with high part-load efficiency, that results into high daily and seasonal energy efficiency, so as ACS typically spend most of their operating hours within the range of 40% to 80% of maximum cooling capacity [30].

Despite the existence of a lot of control algorithms and devices to minimize the power consumption and provide indoor thermal-humidity environments in all the central ACS, the problem of choosing a rational design cooling capacity to provide annually efficient operation at changeable current loadings and to exclude oversizing RM and cooling equipment and its cost as a consequence needs a solution.

The study aims to develop an approach to improve the efficiency of utilizing the refrigeration capacity of ACS and method to determine a rational design cooling capacity that provides closed to maximum annual effect without oversizing and its distribution concerning current climatic conditions.

3 Research Methodology

The efficiency of ACS and their RM performance depends on their current loading Q0 and an hour duration τ of yearly operation. The efficiency of using the refrigeration capacity for covering the ambient air processing needs is estimated by annual refrigeration energy production ∑(Q0·τ) as a primary criterion to determine a rational design refrigeration capacity.

The proposed method to determine the rational design refrigeration capacity is based on the yearly loading characteristic cumulative curve of annual refrigeration production dependence on the design refrigeration capacity of the RM. The current refrigeration, generated by RM at any time period for ambient air cooling down to the target temperature ta2 = 10 ℃, has been summarized over the year. The rational design refrigeration capacity is selected according to the yearly loading characteristic cumulative curve to provide closed to maximum annual refrigeration production.

In order to generalize the results and simplify calculations for any total refrigeration capacities Q0, it is convenient to present the refrigeration capacity of the RM ACS, not in absolute Q0. However, in relative (specific) values per unit airflow rate (Ga = 1 kg/s) – in the form of specific refrigeration capacity, q0 = Q0/Ga, kW/(kg/s), or kJ/kg, where Q0 is the total refrigeration capacity when cooling the air with the flow rate Ga: Q0 = (ca ξ·Δta)Ga, where Δta = ta − ta2 – decrease in air temperature.

The specific annual production of refrigeration:

$$ \sum {\left( {q_{0} \, \cdot \,\uptau } \right)} = \sum {\left( {\upxi c_{ma} \left( {t_{a} - t_{a2} } \right)\uptau } \right)} $$
(1)

where: q0 – specific refrigeration capacity [kJ/kg] or [kW/(kg/s)]; ∑(q0·τ) – specific annual production of refrigeration [kJ/(kg/h)] or [kW∙h/(kg/s)]; ξ – specific heat ratio of total heat, including sensible and latent heat, to sensible heat of humid air; ta – ambient air temperature [℃]; ta2 – air temperature at the air cooler outlet [℃]; cma – specific heat of moist air [kJ/(kg·K)]; τ – time interval [h].

The specific refrigeration capacity is calculated as:

$$ q_{0} \, = \,\upxi c_{ma} \left( {t_{a} - t_{a2} } \right) $$
(2)

A rational specific refrigeration capacity q0.rat is determined to exclude unproductive expenses of refrigeration capacity q0 caused by oversizing RM without obtaining a noticeable effect in increasing the annual refrigeration production ∑(q0·τ).

The further improved approach to enhance the efficiency of utilizing the ACS refrigeration capacity is based on shearing the overall refrigeration capacity, spent for ambient air processing, in two ranges with regard to current cooling loads. The first, booster, range of ambient air precooling to a certain intermediate threshold temperature, is characterized by considerable fluctuations in cooling load, whereas the second range of subsequent subcooling air to a target leaving temperature is characterized by the comparatively stable cooling load. The first booster range of cooling load requires regulation of the cooling capacity by the application of a variable speed compressor, whereas the second range of subsequent subcooling air can be covered by the operation of a conventional compressor in a mode closed to a nominal value.

Nomenclature

Δta

Ambient air temperature reduction

∑(q0·τ)

Specific annual production of refrigeration energy, ∑(q0·τ) = ∑(Q0·τ)/Ga

φa

Ambient air relative humidity

AC

Air cooler

cma

Specific heat of moist air

ACS

Air conditioning system

Subscripts

c

Specific heat of the air

10, 15

Parameters of air-cooled to temperatures 10 ℃ and 15 ℃

Ga

Air mass flow rate

10–15

The difference in the parameters of air-cooled from 10 ℃ to 15 ℃

OAP

Outdoor air processing

a

Ambient air at the inlet of cooler

q0

Specific refrigeration capacity, q0 = Q0/Ga

a2

Cooled air at the outlet of the cooler

Q0

Refrigeration capacity

b

Booster stage of air cooler

q0.10, q0.15

Specific refrigeration capacity for cooling ambient air to 10 ℃ and 15 ℃

def

Deficit

q0.10–15

Specific refrigeration capacity for cooling air from 10 ℃ to 15 ℃

ma

Moist air

q0.b

Booster stage specific refrigeration capacity

rat

Rational

q0.bdef

Booster stage specific refrigeration capacity deficit

Greek letters

q0.rat

Rational specific refrigeration capacity

Δ

Difference

RM

Refrigeration machine

ξ

Specific heat ratio of total heat (sensible and latent) to sensible heat of moist air

t

Temperature

Σ

Sum

ta

Ambient air temperature

τ

Time interval

ta2

Air temperature at the air cooler outlet

φ

Relative humidity

VRF

Variable refrigerant flow

  

4 Results

Specific annual refrigeration energy production ∑(q0·τ) required for cooling the ambient air to ta2 = 10 and 15 ℃ against a design specific refrigeration capacity q0, calculated for 2017 and 2019 in Mykolaiv region, south of Ukraine, is presented in Fig. 1.

Fig. 1.
figure 1

Specific annual refrigeration energy production ∑(q0·τ) required for cooling the ambient air to ta2 = 10 and 15 ℃ against a design specific refrigeration capacity q0 for 2017 (a) and 2019 (b).

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For the considered climatic conditions when the ambient air is cooled to the temperature ta2 = 10 °C a design specific (at Ga = 1 kg/s) refrigeration capacity of RM q0.10rat = 35 kJ/kg provides close to the maximum annual refrigeration production ∑(q0·τ) ≈ 48∙103 kW·h/(kg/s) while maintaining its increment with a noticeable high rate. A design specific refrigeration capacity q0.10rat = 35 kJ/kg for cooling the ambient air to ta2 = 10 °C is assumed as rational one to provide closed to a maximum annual refrigeration production ∑(q0·τ). However, with decreased specific refrigeration capacity q0.10rat = 35 kJ/kg versus its maximum value q0.10 = 42 kJ/kg, id est. by more than 15%. Similarly, for cooling ambient air to ta2 = 15 °C the rational value of specific refrigeration capacity is q0.15rat = 25 kJ/kg is lower than its maximum value q0.15 = 32 kJ/kg by about 20% with the corresponding reduction in sizes of RM and other equipment.

In order to prove the approach to the analysis of the efficiency of using design refrigeration capacities of ACS chillers, taking into account the change in cooling loads by actual climatic conditions, the current values of specific refrigeration capacity q0 of RM ACS when cooling the ambient air from the current temperature ta to ta2 = 10 and 15 ℃, respectively q0.10 and q0.15 for July of 2017 and 2019 year, Mykolaiv region, south of Ukraine, have been considered (Fig. 2).

As calculation results in Fig. 1 shows, when the ambient air is cooled from its current temperatures ta to ta2, the cooling load fluctuations of q0.10 and q0.15 are very significant. The almost equidistant trend lines of the specific cooling load q0.10 and q0.15 indicate that these fluctuations are caused primarily by changes in the specific cooling load q0.15 for precooling the ambient air to the temperature ta2 = 15 ℃, within which there is practically damping of the fluctuations of the current cooling load. The intermediate temperature ta2 = 15 ℃ is assumed as threshold temperature for the rational distribution of design overall cooling capacity of ACS between two ranges with different characters of cooling load behavior.

Fig. 2.
figure 2

Current values of ambient air temperature ta, specific refrigeration capacity q0.10, needed for cooling ambient air from ta to ta2 = 10 ℃, specific refrigeration capacity q0.15, needed for cooling ambient air from ta to intermediate temperature ta2 = 15 ℃ for July 2017 (a) and 2019 (b).

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At the same time, within further cooling of the air from the intermediate temperature ta2 = 15 ℃ to ta2 = 10 ℃ the fluctuations of the specific cooling loads on the ACS q0.10–15 = q0.10 − q0.15 are comparatively small (within a range of 6–10 kJ/kg in Fig. 3a versus 24–2 kJ/kg for q0.15 in Fig. 2a and within a range of 4–10 kJ/kg in Fig. 3b versus 24–0 kJ/kg for q0.15 in Fig. 2b for a bit lower monthly ambient air temperature) without taking into account 3–5 short-term bursts-drops, caused by a decrease in the current values of the ambient air temperature below 15 ℃ (Fig. 3).

Fig. 3.
figure 3

Current values of ambient air temperature ta, specific refrigeration capacity q0.10–15 = q0.10 − q0.15, needed for subcooling air from ta2 = 15 ℃ to ta2 = 10 ℃ for July 2017 (a) and 2019 (b).

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Proceeding from a different behavior of current cooling loads, the ambient air treatment in the ACS is considered as two-stage processing and includes a range of cooling load fluctuation as the first booster stage ambient air precooling and a range of comparatively stable cooling load as the second air subcooling stage.

Accordingly, a design refrigeration capacity for precooling the ambient air from the current temperature ta to ta2 = 15 ℃, as booster component, is determined by the residual principle as the difference between the design specific refrigeration capacity q0.10rat for the entire process of cooling the ambient air from the current temperature ta to ta2 = 10 ℃ according to Fig. 1, and its stable component q0.10–15 for further subcooling air: q0b = q0.10rat − q0.10–15 (Fig. 4).

Fig. 4.
figure 4

Current values of ambient air temperature ta, specific refrigeration capacity q0.15, needed for cooling ambient air from ta to intermediate temperature ta2 = 15 ℃, booster specific refrigeration capacity q0b = q0.10rat − q0.10–15 and booster specific refrigeration capacity deficit q0bdef = q0.15 − q0b within subcooling air from ta2 = 15 ℃ to ta2 = 10 ℃ for July 2017 (a) and 2019 (b).

Full size image

Since the fluctuations of the current refrigeration capacity, spent for cooling the ambient air from ta to ta2 = 10 ℃, are caused mainly by its booster part q0.15, which corresponds to precooling the ambient air from ta to ta2 = 15 ℃, at elevated current cooling loads q0.15 there is some deficit of the booster component q0bdef of refrigeration capacity calculated by the residual principle, q0bdef = q0b − q0.15, compared to the current specific thermal loads q0.15. However, the booster refrigeration capacity deficit q0bdef occurs very seldom 1, 27, 28 July of 2017 (Fig. 4a) and 2 and 29 July of 2019 (Fig. 4b). It proves the appropriate results of the application of the proposed method for analyzing the efficiency and rational distribution of a design refrigeration capacity used for ambient air processing in ACS according to current cooling loading.

5 Conclusions

The approach to analyzing the efficiency of utilizing a refrigeration capacity used for ambient air processing in ACS and method of determining its rational values and their distribution during the operation in actual changeable current climatic conditions is presented. The annual refrigeration production is assumed as a primary criterion for estimation of utilizing a refrigeration capacity, and its dependence on a design refrigeration capacity is used as a basic yearly loading characteristic curve for determining a rational design refrigeration capacity.

The method to determine a rational design cooling capacity to provide a closed to maximum annual refrigeration production and, at the same time, to avoid oversizing a refrigeration machine and its enlarged cost has been developed.

The ambient air treatment in ACS is proposed to consider as two-stage processing, which includes a range of cooling load fluctuation as the first booster stage of air cooler for ambient air precooling and a range of comparatively stable cooling load as the second stage for further air deep cooling. The first booster range of cooling load requires regulation of the cooling capacity, for instance, by the application of a variable speed compressor, whereas the second range of subsequent subcooling air can be covered by the operation of a conventional compressor in a mode closed to a nominal value.