Keywords

1 Introduction

Energy consumption for the processing of ambient air in air conditioning systems (ACS) depends on the ambient air temperature ta and relative humidity φa, which changes significantly during the day. It is obvious that the production of refrigeration by refrigeration machine (RM) according to air conditioning duties over a certain period of time, for example a year (annual refrigeration production) ∑(Q0⋅τ), [kWh], where: Q0 – is the current refrigeration capacity of RM (thermal load on the ACS), [kW]; τ – is the duration of the ACS operation in hours, is chosen as a criterion to estimate the efficiency of using the installed refrigeration capacities of the RM. Since the amount of refrigeration capacity spent on ambient air processing in the ACS depends on the current ambient air parameters and the duration of the ACS operation, the efficiency of using the installed refrigeration capacity of ACS can be estimated by comparing its value spent for air conditioning over a certain period of the operation and potentially possible refrigeration production due to operation of RM on full, nominal, load.

2 Literature Review

Many publications are devoted to improving air processing in ACS by intensification of heat transfer processes in air coolers [1, 2], evaporators [3, 4] and condensers [5], application of various refrigerant circulation contours [6, 7], alternate safe refrigerants [8, 9], waste heat recovery technics, including combined cooling, heating and power generation [10, 11], modelling [12, 13], optimization [14, 15], experimental and monitoring [16, 17] methods to match current cooling demands. Some of principal technical innovations and methodological approaches in waste heat recovery refrigeration [2, 18] might be successfully applied for air conditioning [19], in particular, evaporative cooling [20, 21], two-stage air cooling [22, 23].

Numerous researchers have studied the energy efficiency of the Variable Refrigerant Flow (VRF) systems [24, 25] and proposed some practical recommendations. Most of the studies have been conducted on solutions of efficient operation of the VRF system in buildings and control strategies of the systems [26]. A control algorithm of the supply air temperature as a threshold temperature in the outdoor air processing (OAP) unit to run the VRF‐OAP system more efficiently for buildings was developed [27]. The control algorithm was conducted to adjust the refrigerant flow supply to the OAP and the indoor unit appropriately through supporting the supply air temperature. Results [28] show that ACS have a great potential for energy saving and the adjustability of VRF.

The VRF system with heat recuperative ventilation [29] and a dedicated outdoor ACS was introduced [30]. The evaluation of indoor thermal-humidity environments and energy consumption of the VRF system [31] with a heat pump was conducted [32].

The author [33] proposes the method to calculate thermal load of building. The VRF systems operate with high part-load efficiency [34], 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 [35].

The majority of ACS designing methods issue from the assumption to cover the maximum current cooling needs or with some limitation [34,35,36] or annual maximum cooling consumption [37,38,39,40]. Such approach inevitable leads to considerable overestimation of design cooling capacities and systems oversizing. So, the problem to determine a rational design cooling capacity without ACS oversizing needs further solution.

The aim of the study is to develop an approach to analyzing the efficiency of using the installed refrigeration capacity of ACS and method to determine a rational design (installed) refrigeration capacity value and its distribution according to the current climatic conditions to avoid oversizing a refrigeration machine and its enlarged cost.

3 Methodology

The efficiency of ACS and their RM performance depends on their loading and a duration of their yearly operation. Therefore, the annual refrigeration production in response to air conditioning duties is considered as a primary criterion for the choice of a rational design overall thermal load of ACS. For this the current refrigeration capacities, generated by RM at any time period in response to the air conditioning duties for ambient air conditioning down to the target leaving air temperature, have been summarized over the year to determine the rational design overall refrigeration capacity of ACS.

In order to conduct this procedure the authors develop a method of rational designing based on the yearly loading characteristic curve of annual summarized refrigeration production dependence on the design specific refrigeration capacity of the RM to choose its value, that provides closed to maximum annual production of refrigeration.

The specific annual production of refrigeration:

$$ \sum \left( {q_{0} \cdot \tau } \right) = \sum ( \, \xi \cdot c_{ma} \cdot (t_{amb} {-} t_{{a{2}}} ) \cdot \tau ) $$
(1)

where: ∑(q0⋅τ) – specific annual production of refrigeration [kg⋅h/kW]; ξ – specific heat ratio; ta – ambient air temperature [°C]; ta2 – air temperature at the air cooler outlet [°C]; cma –specific heat of moist air [kJ/(kg·K)]; τ – time interval [h].

The specific refrigeration capacity is calculated as:

$$ q_{0} = \xi \cdot c_{ma} \cdot (t_{a} {-} t_{a2} ) $$
(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 production of refrigeration ∑(q0⋅τ), that was limited by the value of (0.95…0.97)∑(q0⋅τ) to choose corresponding rational specific refrigeration capacity q0.rat.

Proceeding from a different behavior of current thermal loads, the ambient air treatment in the ACS is considered as a two-stage processing and includes a range of hermal load fluctuation as the first (high-temperature) stage and a range of comparatively stable thermal load as the second (low-temperature) stage. The threshold air temperature is determined to provide a rational distribution of design overall cooling capacity of ACS between two stages with different thermal load behaviors.

Taking into account a relatively stable behavior of the specific thermal (cooling) load on the air cooler (AC) of the ACS within the range q0.10–15 = q0.10 –q0.15 (or q0.10–17 = q0.10 – q0.17) when the air is cooled from the temperature ta2 = 15 (or 17)°C to ta2 = 10 ℃ compared to the ambient air cooling from tato ta2 = 15 (or 17)°C the first thermal load range is taken as a basic design (installed) for deep cooling of air from ta2 = 15 (or 17)°C to ta2 = 10 ℃. Accordingly, a design refrigeration capacity for precooling the ambient air from the current temperature tato ta2 = 15 (or 17)°C, 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 tato ta2 = 10 ℃ and its stable component q010–15: q0.b10–15 = q0.10rat – q010–15 (or q0.b10–17 = q0.10rat – q010–17).

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 (or q0.17), which corresponds to precooling the ambient air from ta to ta2 = 15 (or 17)°C, at elevated current thermal loads q0.15 there is some deficit of the installed booster component q0.b10–15 (q0.b10–17) of refrigeration capacity q0.b10–15 (q0.b10–17), calculated by the residual principle, whereas at reduced current thermal loads q0.15 (or q0.17), on the contrary, its excess q0.bex10–15 = q0.10rat – q0.b10–15 = q0.10rat – q0.15 compared to the current specific thermal loads q0.15 and in according q0.bex10–17.

How efficiently the installed booster component of the refrigeration capacity of the ACS is spent on precooling the ambient air from its current temperature ta to ta2 = 15 ℃ (or 17 ℃) with the change of current thermal loads according to the actual climatic conditions can be judged by comparing the total monthly summarized specific refrigeration consumption to cover the current thermal loads ∑(q0.15⋅τ) (or ∑(q0.17⋅τ)) for cooling the ambient air from the current ta to ta2 = 15 ℃ (or 17 ℃) with potentially possible refrigeration production by a booster stage with design specific refrigeration capacity calculated on the residual basis, ∑(q0.b10–15⋅τ) (or ∑(q0.b10–17⋅τ)), on the other hand.

4 Results

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, but in relative (specific) values per unit air mass flow rate (Ga = 1 kg/s) – in the form of specific refrigeration (cooling) 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 = tamb – ta2 – decrease in air temperature.

To justify the approach to the analysis of the efficiency of using the installed (design) refrigeration capacities of ACS chillers taking into account the change in thermal loads according to the current 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, 15 and 17 ℃, respectively q0.10, q0.15 and q0.17 for July of 2017 year, Nikolaev region, Ukraine (Fig. 1) have been considered.

As can be seen, when the ambient air is cooled from its current temperatures ta to ta2, the thermal load fluctuations of q0.10, q0.15 and q0.17 are very significant. The almost equidistant trend lines of the specific thermal load q0.10, q0.15 and q0.17 indicate that these fluctuations are due primarily to changes in the specific thermal load q0.15 and q0.17 for precooling the ambient air to the temperatures ta2 = 15, 17 ℃, within which there is practically damping of the fluctuations of the current thermal load.

Fig. 1.
figure 1

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 and q0.17, needed for cooling ambient air from ta to various intermediate temperatures ta2 = 15 ℃ and ta2 = 17 ℃: a – q0.15 for ta2 = 15 ℃; b – q0.17 for ta2 = 17 ℃

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At the same time, with the further cooling of the air from the intermediate temperature ta2 = 15 ℃ to ta2 = 10 ℃ the fluctuations of the specific thermal loads on the ACS q0.10–15 = q0.10 – q0.15 are relatively small, 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. 2, a).

Obviously, the higher the value of the precooling temperature of the ambient air (intermediate temperature ta2), i. e., the narrower the range of fluctuations of thermal (cooling) loads, the longer the operating life of the refrigeration machine for booster precooling ambient air during the year at current thermal loads.

Fig. 2.
figure 2

Current values of booster specific refrigeration capacity q0.b10–15 = q0.10rat – q0.10–15 with basic specific refrigeration capacity q0.10–15 = q0.10 – q0.15, needed for subcooling air from 15 ℃ to ta2 = 10 ℃ (a) and booster specific refrigeration capacity q0.b10–17 = q0.10rat – q0.10–17 with basic specific refrigeration capacity q0.10–17 = q0.10 – q0.17, needed for subcooling air from 17 ℃ to ta2 = 10 ℃ (b) with rational design overall (for two-stage ambient air cooling) specific refrigeration capacity q0.10rat = 35 kJ/kg

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In order to determine the upper threshold temperature for precooling ambient air, the calculations of the processes of cooling the ambient air from current ta to a higher intermediate temperature ta2 = 17 ℃ were made and the corresponding specific refrigeration capacity for the subsequent subcooling the air q0.10–17 = q0.10 – q0.17 from ta2 = 17 ℃ to ta2 = 10 ℃ was determined (Fig. 2, b).

As can be seen, the specific refrigeration capacity q0.10–17 = q0.10 – q0.17 for subcooling the air from the intermediate temperature ta2 = 17 ℃ to ta2 = 10 ℃ becomes very unstable compared to the lower intermediate temperature ta2 = 15 ℃ (Fig. 2, a). This is caused by an earlier (at ta2 = 17 ℃) fall to zero of the specific refrigeration capacity q0.17 for precooling the ambient air due to the narrowing of the temperature range Δt17 = ta – 17 ℃ of cooling the ambient air at an elevated intermediate temperature ta2 = 17 ℃ (compared to Δt15 = ta – 15 ℃ at ta2 = 15 ℃), that results in replacing the fluctuations of specific refrigeration capacity, previously damped when cooling the ambient air to the temperature ta2 = 15 ℃, with corresponding increase in specific refrigeration capacity q0.10–17 = q0.10 – q0.17 for further subcooling air from the temperature ta2 = 17 ℃ to ta2 = 10 ℃.

Taking into account a relatively stable behavior of the specific thermal load on the air cooler of the ACS within the range q0.10–15 = q0.10 – q0.15 when the air is subcooled from ta2 = 15 ℃ to ta2 = 10 ℃ (Fig. 2,a) compared to large fluctuations of refrigeration capacity q0.15 within the range of ambient air precooling from ta to ta2 = 15 ℃ (Fig. 1,a), the first thermal load q0.10–15 is taken as a design stable component of refrigeration capacity for deep cooling of air from ta2 = 15 ℃ to ta2 = 10 ℃.

Accordingly, a design refrigeration capacity q0.b10–15 for booster precooling the ambient air from the current temperatures ta to ta2 = 15 ℃ is determined by a residual principle as the difference between a design specific refrigeration capacity q0.10rat for the entire process of cooling the ambient air from the current temperatures ta to ta2 = 10 ℃ and its stable component q010–15: q0.b10–15 = q0.10rat –q010–15.

With this a rational design refrigeration capacity q0.10rat = 35 kJ/kg for the entire process of cooling the ambient air from the current temperatures ta to 10 ℃ is assumed to provide closed to a maximum annual refrigeration production ∑(q0⋅τ) (Fig. 3).

Fig. 3.
figure 3

Specific annual refrigeration production ∑(q0⋅τ) required for cooling the ambient air to the temperatures ta2 = 10, 15 and 17 ℃ against a design specific refrigeration capacity q0

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As can be seen, for the considered climatic conditions when the air is cooled to the temperature of ta2 = 10 ℃ in the ACS with installed (design) specific (at Ga = 1 kg/s) refrigeration capacity of RM q0.10rat = 35 kJ/kg, which provides close to the maximum annual refrigeration production ∑(q0⋅τ) ≈ 48⋅103 kWh/(kg/s), while maintaining its increment with a noticeable high rate. Similarly, for cooling ambient air to the temperature of ta2 = 15 ℃ the rational value of specific refrigeration capacity of RM q0.15rat = 25 kJ/kg, and to ta2 = 17 ℃ – the value of q0.17rat = 22⋅kJ/kg.

Current values of booster specific refrigeration capacity q0.b10–15 = q0.10rat – q0.10–15 and q0.b10–17 = q0.10rat – q0.10–17 and booster specific refrigeration capacity excess q0.bex10–15 = q0.b10–15 – q0.15 and q0.bex10–17 = q0.b10–17 – q0.17 with subcooling air from ta2 = 15 ℃ and ta2 = 17 ℃ accordingly to ta2 = 10 ℃ with rational design overall (for two-stage ambient air cooling) specific refrigeration capacity q0.10rat = 35 kJ/kg (according to Fig. 3) are presented in Fig. 4.

Fig. 4.
figure 4

Current values of ambient air temperature ta, booster specific refrigeration capacity q0.b10–15 = q0.10rat – q0.10–15 and booster specific refrigeration capacity excess q0.bex10–15 = q0.b10–15 – q0.15 with subcooling air from ta2 = 15 ℃ to ta2 = 10 ℃ (a) and booster specific refrigeration capacity q0.b10–17 = q0.10rat – q0.10–17 and booster specific refrigeration capacity excess q0.bex10–17 = q0.b10–17 – q0.17 with subcooling air from ta2 = 17 ℃ to ta2 = 10 ℃ (b) with rational design overall specific refrigeration capacity q0.10rat = 35 kJ/kg according to Fig. 3

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As Fig. 4 shows, the excess of the current values of the specific refrigeration capacity q0.b10–15 = 35 – q010–15 for precooling the ambient air from its current temperature ta to ta2 = 15 ℃ above its design value drops from the current specific refrigeration capacity q0.15 to zero, and the fact that the excess of the current values of the specific refrigeration capacity q0.b10–15 in some days (4, 6, 7, 14 and 17.07.2017) exceeds the design value, is explained by the reduction of refrigeration capacity q0.10–15 for deep cooling the air while reducing the current ambient air temperature ta below 15 ℃.

Potentially possible monthly summarised refrigeration production for precooling the ambient air to the intermediate temperature ta2 = 15 ℃ in a booster stage of two-stage air cooler available in accordance with its design specific refrigeration calculated on a residual basis, ∑(q0.b10–15⋅τ), its potential excess ∑(q0.bexc10–15⋅τ) = ∑(q0.b10–15⋅τ)–∑(q0.15⋅τ) over the current values of the specific refrigeration spent for precooling the ambient air to ta2 = 15 ℃ in a booster stage (refrigeration consumption) monthly summarised ∑(q0.15⋅τ) and monthly summarised refrigeration consumption ∑(q0.10–15⋅τ) for deep subcooling the air from ta2 = 15 ℃ to ta2 = 10 ℃ is plotted in Fig. 5, a, as well as their values for precooling the ambient air to an increased intermediate temperature ta2 = 17 ℃ are presented in Fig. 5, b.

Fig. 5.
figure 5

Current values of total summarized per month specific refrigeration consumption ∑(q0.15⋅τ) for precooling the ambient air to 15 ℃, refrigeration spent for subcooling air from 15 ℃ to 10 ℃, ∑(q0.10–17⋅τ), potentially possible refrigeration production for precooling ambient air ∑(q0.b10–15⋅τ) according to a design refrigeration capacity of booster stage, potentially possible excess of refrigeration production for precooling ambient air in a booster stage ∑(q0.bexc10–15⋅τ) = ∑(q0.b10–15⋅τ) – ∑(q0.15⋅τ) (a) and total monthly summarized specific refrigeration consumption ∑(q0.17⋅τ) for precooling the ambient air to the intermediate temperature 17 ℃, refrigeration spent for subcooling air from 17 ℃ to 10 ℃, ∑(q0.10–17⋅τ), potentially possible refrigeration production for precooling ambient air ∑(q0.b10–17⋅τ) according to a design refrigeration capacity of booster stage, potentially possible excess of refrigeration production for precooling ambient air in a booster stage ∑(q0.bexc10–17⋅τ) = ∑(q0.b10–17⋅τ) – ∑(q0.17⋅τ) and ∑(q0exc10–17⋅τ) = ∑(q0.10rat⋅τ) – ∑(q0.17rat⋅τ) – ∑(q0.10–17⋅τ)

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An elevated intermediate temperature ta2 = 17 ℃ of ambient air precooling does not provide stabilization of thermal loading of subsequent subcooling the air from increased intermediate temperature ta2 = 17 ℃ down to the target temperature ta2 = 10 ℃ that leads to arising an excess of refrigeration production ∑(q0.bexc10–17⋅τ) = ∑(q0.b10–17⋅τ) – ∑(q0.17⋅τ) compared to its consumption ∑(q0.10–17⋅τ) q0.10–17 = q0.10–17 = q0.10 – q0.17 when cooling the air from ta2 = 17 ℃ to ta2 = 10 ℃ (Fig. 5, b).

As can be seen, the specific refrigeration capacity q0.10–17 = q0.10 – q0.17 for subcooling the air from the increased intermediate temperature ta2 = 17 ℃ to the target ta2 = 10 ℃ becomes very unstable compared to the lower intermediate temperature ta2 = 15 ℃ (Fig. 2, a). This is caused by an earlier (at ta2 = 17 ℃) fall to zero of the refrigeration capacity q0.17 for precooling the ambient air due to the narrowing of the temperature range Δt17 = ta – 17 ℃ of cooling the ambient air at an elevated intermediate temperature ta2 = 17 ℃ (compared to Δt15 = ta – 15 ℃ at ta2 = 15 ℃), that results in replacing the fluctuations of specific refrigeration capacity, previously damped when cooling the ambient air to the temperature ta2 = 15 ℃, with corresponding increase in specific refrigeration capacity q0.10–17 = q0.10 – q0.17 for further subcooling air from the temperature ta2 = 17 ℃ to ta2 = 10 ℃.

Comparison of refrigeration capacity of air subcooling q0.10–15 = q0.10 – q0.15 and q0.10–17 = q0.10 – q0.17 shows that the stabilization of thermal load occurs as a result of precooling the ambient air to the lower intermediate temperature ta2 = 15 ℃ compared to ta2 = 17 ℃. Therefore, the intermediate temperature ta2 = 15 ℃ is assumed as a threshold value and specific refrigeration capacity q0.10–15 = q0.10 – q0.15 is taken as the base, which ensures the effective operation of the RM in the mode close to the nominal.

As can be seen, the total consumption of the specific refrigeration generation per month ∑(q0.15⋅τ) for cooling the ambient air to ta2 = 15 ℃ is ∑(q0.15⋅τ) ≈ 7 kW⋅h/(kg/s), which is less than the excess of the potential refrigeration production for a precooling of the ambient air (to ta2 = 15 ℃) ∑(q0.bexc10–15⋅τ) ≈ 11 kW⋅h/(kg/s) and is less 40% of the potential refrigeration output of booster stage ∑(q0.b10–15⋅τ) ≈ 19 kW⋅h/(kg/s).

In the first approximation, we can assume that the total per month consumption of the specific refrigeration is ∑(q0.15⋅τ) ≈ 7 kW⋅h/(kg/s), which is 40% of the potentially possible refrigeration production of booster stage ∑(q0b10–15⋅τ) ≈ 19 kW⋅h/(kg/s), corresponds to the required refrigeration capacity range from 100% to 40% of nominal. Based on this hypothesis, the use of refrigeration compressors with a frequency regulation to 40% could be considered as a way of energy-efficient operation for precooling ambient air to ta2 = 15 ℃.

At the same time, the total per month consumption of specific refrigeration ∑(q0.17⋅τ) for cooling the ambient air to ta2 = 17 ℃ is about ∑(q0.17⋅τ) ≈ 5 kW⋅h/(kg/s), which is much less than the excess of the potential refrigeration production according to a design refrigeration capacity of a booster stage for precooling the ambient air (to ta2 = 17 ℃) ∑(q0bexc10–17⋅τ) ≈ 11,5 kW⋅h/(kg/s) over the actual refrigeration needed for precooling the ambient air to ta2 = 17 ℃.

Insufficient damping of the drop in the current thermal load within precooling the ambient air to ta2 = 17 ℃ (compared to ta2 = 15 ℃) leads to arising the excess of design refrigeration production ∑(q0exc10–17⋅τ) ≈ 1 kW⋅h/(kg/s), though insignificant in comparison with its consumption ∑(q010–17⋅τ) ≈ 9 kW⋅h/(kg/s) within further subcooling the air from the temperature ta2 = 17 ℃ to ta2 = 10 ℃. Obviously, the use of compressors with frequency regulation of refrigeration capacity can be effective in the range of thermal loads q010–17 for subcooling the air to ta2 = 10 ℃, whereas the damping of booster refrigeration capacity q0b10–17 for precooling the ambient air to ta2 = 17 ℃ their application is possible only in conjunction with the accumulation of excessive refrigeration.

Thus, the proposed approach to analyzing the efficiency of using the installed refrigeration capacity of the ACS can be applied both to choose its rational distribution depending on the character of the change in actual thermal load, and to determine the ranges of thermal loads for the effective application of different methods of managing the ambient air processing in the ACS.

5 Conclusions

A novel method to determine a rational design refrigeration capacity to provide a closed to maximum annual refrigeration production according to conditioning duties at reduced by about 20% design refrigeration capacity compared with traditional designing assumption to cover the maximum current cooling needs has been developed.

Proceeding from a different behavior of current thermal loads, the ambient air processing in ACS is proposed to consider as a two-stage process that includes a range of thermal load fluctuation as the first (high-temperature) stage and a range of comparatively stable thermal load as the second (low-temperature) stage.

The method of rational design refrigeration capacity and its distribution is quite useful for a comfort air conditioning, as well as for cooling air at the inlet of combustion engines to enhance their power output (electricity production) in trigeneration systems. It provides the effective application of energy saving methods, in particular, to cover increased thermal loads by accumulated excessive refrigeration and by application of compressors with variable refrigeration capacity to cover changeable loads.