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Article

Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes

by
Mykola Radchenko
1,
Andrii Radchenko
1,
Eugeniy Trushliakov
2,
Anatoliy Pavlenko
3,* and
Roman Radchenko
1
1
Machinebuilding Institute, Admiral Makarov National University of Shipbuilding, Heroes of Ukraine Avenue 9, 54025 Mykolayiv, Ukraine
2
Department of Air Conditioning and Refrigeration, Admiral Makarov National University of Shipbuilding, Heroes of Ukraine Avenue 9, 54025 Mykolayiv, Ukraine
3
Department of Building Physics and Renewable Energy, Kielce University of Technology, Avenue of 1000 Years of the Polish State, 7, 25-314 Kielce, Poland
*
Author to whom correspondence should be addressed.
Energies 2023, 16(5), 2417; https://doi.org/10.3390/en16052417
Submission received: 18 February 2023 / Accepted: 28 February 2023 / Published: 3 March 2023
(This article belongs to the Special Issue Latest Research of Building Heat and Mass Transfer)
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Versions Notes

Abstract

:
Outdoor air conditioning systems (ACS) are used as autonomic systems as well as in combined outdoor and indoor ACS of the variable refrigerant flow (VRF) type, with variable speed compressors (VSC) as their advanced version. Methods for determining the optimal value of refrigeration capacity and providing the maximum rate of the summarized annual refrigeration energy generation increment, according to its needs at minimum compressor sizes and rational values, are applied to reveal the reserves for reducing the designed (installed) refrigeration capacity, thus enabling us to practically achieve maximum annual refrigeration energy generation as the primary criterion at the second stage of the general design methodology previously developed by the authors. The principle of sharing the total thermal load on the ACS between the ranges of changeable loads for outdoor air precooling, and a relatively stable load range for further processing air are used as its basis. According to this principle, the changeable thermal load range is chosen as the object for energy saving by recuperating the excessive refrigeration generated at lowered loading in order to compensate for the increased loads, thereby matching actual duties at a reduced designed refrigeration capacity. The method allows us to determine the corresponding level of regulated loads (LRL) of SRC and the load range of compressor operation to minimize sizes.

1. Introduction

Ambient air conditioning systems (ACS) are desired to provide comfortable environments in buildings [1,2] and other stationary objects [3,4]. They are widespread in transport application, in particular in railways [5,6] and ships [7,8]. As the air is a working fluid (cyclic air) for combustion, ACS are used for cooling air sucked out of combustion engines, these being internal combustion engines [9,10], gas turbines [11,12] and gas engines [13,14]. The latter are effective in the development of engine intake air conditioning systems as subsystems of trigeneration (in-cycle trigeneration) [15,16] and integrated power plants [17,18] for combined cooling, heat and power (CCHP) generation [19,20]. In these cases, the ACS function as waste heat recovery systems [21,22] and their cooling potential depends on a depth of engine exhaust heat utilization [23,24]; the deeper the exhaust heat utilization, the higher the thermal (refrigeration) potential of the ACS.
Such mutual penetration of ACS into power plants and, conversely, the use of energy heat exhausts as a thermal source for ACS reveal the potential for application of the principal findings gained in energetic application to ACS. Therefore, evaporative cooling [25,26], two-stage cooling air [27,28] by chilled water and refrigerants coolants [29,30] in hybrid coolers [31,32] and combined chillers of different types [33,34], including absorption [35,36] and refrigerant [37,38] chillers as cascade chillers [39,40], and excessive heat recuperation to cover peak loads [41,42] were implemented into ACS as two-stage outdoor air conditioning systems that use refrigeration recuperation [43,44]; they are especially efficient for combined outdoor and indoor air-processing unites [45,46].
The outdoor unit is desired for conditioning the ambient air in order to avoid fluctuated heat loads and overloading the indoor unit [47,48]. The VRF systems save more than 20% energy compared to the variable air volume ACS [49,50].
A performance of ACS is characterized by off-design modes which are especially evident in temperate climatic conditions and off-season operation. Therefore, the VRF systems are the most well adapted to cover efficient off-season operation [51,52].
The varying heat loads on ACS and heat exchangers accordingly are accompanied by heat flux drops which require application of efficient heat exchangers and working fluid circulation circuits. The application of high-efficiency heat exchangers [53,54], in particular compact evaporators [55,56] and condensers [57,58], accelerates research focused on intensifying heat transfer [59,60] and hydrodynamics [61,62] to mitigate the instabilities of two-phase refrigerant flows [63,64] and uneven refrigerant [65,66] and air [67,68] distribution. Advanced air conditioning, refrigerant feeding and exhaust heat recovery circuits, in particular with the application of ejectors [69,70] and thermopressors [71,72], as circulation devices which use potential energy and exhaust heat [73,74], were developed.
In reality, all the management methods [75,76], criteria [77,78] and indicators [79,80] are required in order to cover varying loads without considerable oversizing.
Methods for determining the rational value of the design refrigeration capacity enable us to achieve practically maximum annual fuel saving [81,82] as well as refrigeration energy generation according to current need, as the primary criterion and its optimal value, providing the maximum rate of the summarized annual refrigeration energy generation increment at minimum compressor sizes, was previously developed by the authors [83,84]. The general methodology of rational designing also includes the rational distribution of the overall current thermal loads in the ranges of changeable loads for ambient air preconditioning, and a relatively stable load range for further air subcooling from a threshold temperature to the set value.
The method for estimating the SRC compressors performance efficiency by comparing the load ranges of regulated and unregulated by SRC with the ranges of changeable and unchangeable loads was developed by the authors earlier. With this, the efficiency of SCR operation is estimated by the loading rate of the unregulated (stable) range assumed as the object of investigation [84].
It is quite evident that the range of unstable (regulated) loads can be accepted as the object for the recuperation of excessive refrigeration to cover the current increased loads that result in the reduction of the range needed for load regulation.
In reality, the SRC is the oversized (underloaded) compressor that operates efficiently at part loads. With a higher level of regulated (changeable) loads (LRL) of the SRC, there is more oversizing of the compressor. It is quite preferable to reduce the SCR sizes through narrowing the range of changeable thermal loads, leading to a decrease in the LRL of the SRC applied. In its turn, in concrete site climatic conditions, the magnitude of the changeable thermal load range depends on the exceedance of the design refrigeration capacity over current loads.
The lesser the exceedance of the design refrigeration capacity (the higher the level of loading LL), the narrower the changeable (booster) thermal load range.
Thus, reduction in the SCR size may be possible due to reduction in the exceedance (excess) of the design refrigeration capacity through its use to cover the pick loads that leads to shortening of the changeable load range due to its part-stabilization [85].
The level of loading LL is a criterion for shearing the total range of loading q0 to the ranges of changeable (1 − LL) q0, and unchangeable LL q0 loads, and is calculated as the ratio of unchangeable load LL q0 to the total load q0.
The enhancement of the ACS operation efficiency is focused on raising the level of load LL followed by reducing the range of changeable load (1 − LL)q0 while correspondingly growing the range of unchangeable load LL q0.
The maximum rate of the summarized annual refrigeration energy generation increment according to its consumption (as the maximum level of loading LL) is associated with a threshold (optimal) value of refrigeration capacity as the minimum permissible value of the design refrigeration capacity [84].
The further reduction of the design refrigeration capacity to less than its threshold (optimal) value at the maximum rate of the annual refrigeration increment is unreasonable, because it propagates an unchangeable (stable) load range. The operation in the unchangeable load range is characterized by full loading of the compressor and the ACS as a whole (LL = 1).
The rational value that enables us to achieve close to maximum annual refrigeration energy generation as a primary criterion is determined at the second stage of the general design methodology developed by the authors [84].
It is quite evident that an increase in the design refrigeration capacity from its optimal value as a minimum to the rational value, providing maximum refrigeration energy generation in response to current need, is accompanied by widening the changeable (requiring the regulation by SCR) load range and an increase in the exceedance (excess) of the design refrigeration capacity available for recuperation leading to part-stabilization of initially changeable load range for outdoor air preconditioning [85].
Thus, it is quite reasonable to assess the application of both methods to reveal the reserves for reducing the design (installed) refrigeration capacity of ACS and the level of regulated loads (LRL) of SRC, as well as the load range of compressor operation. These reserves can be evaluated by comparing the exceedance of the installed (design) refrigeration energy determined according to both methods and conserved at lowered actual loads with current need. Their realization is made possible by recuperating the excess refrigeration energy to enhance the operation efficiency of the advanced VRF system with modern SRC to minimize the oversizing.
The object of the research is the range of unstable (regulated) loads within the overall range of actual loading as the source of exceedance (excess) of refrigeration to cover the current increased loads, resulting in a reduction in the range of necessary load regulation.
The aim of the research is to reveal the reserves for reducing the design (installed) refrigeration capacity of ACS, determined by different methods, to provide maximum annual refrigeration energy generation or a maximum rate of its increment (rational and optimal values), and to realize them through recuperation of the excessive refrigeration to cover the current increased loads, resulting in a reduction in the range of unstable (regulated) loads, the level of regulated loads (LRL) of SRC and the load range of compressor operation.
The following tasks are to be solved to reach these aims:
-
Determine the ranges of changeable thermal loads for optimal and rational refrigeration capacities of ACS, calculated according two methods of providing the maximum rate of the summarized annual refrigeration energy generation increment, or providing close to maximum refrigeration energy generation;
-
Develop a method to determine the range of artificially stabilized loads due to recuperation of excessive refrigeration energy, reserved at lowered current loads, to cover peak loads and the rest of the range of unstable loads regulated by SRC, thereby defining the level of regulated loads (LRL) of SRC and the load range of compressor operation.
These reserves are evaluated by comparing the exceedance of the installed (design) refrigeration energy conserved at lowered actual loads, according to both methods with current need.

2. Methods

In order to generalize the results and adopt their application for ACS of any sizes (refrigeration capacity Q0 according to air mass flow rate Ga), they are presented in relative values as specific refrigeration capacity q0, id est, referred to in the unit of air mass flow rate (Ga = 1 kg/s):
q0 = Q0/Ga,
and calculated as
q0 = ξ∙ca∙(ta − ta2), kW/(kg/s),
where ta—initial or ambient tamb air temperature, K or °C;
  • ta2—a set air temperature;
  • ξ—relative heat ratio as the total heat, removed from the air, related to its sensible heat;
  • ca—air specific heat, kJ/(kg·K).
The summarized annual refrigeration energy generation in response to consumption is accepted as a primary criterion. The corresponding specific annual energy generation is calculated as
Σ(q0∙τ) = Σξca∙(ta − ta2)∙τ∙10−3, MWh/(kg/s).
In order to avoid the errors of about 20% caused by approximation of the actual changeable thermal loads and corresponding required refrigeration capacities, their fluctuations are considered by the rate of their summarized annual value increment versus the refrigeration capacity q0 used as a cumulative annual refrigeration energy characteristic:
Σ(q0∙τ) = f(q0).
Such an approach allows us to use the rate of their summarized annual values increment in response to refrigeration capacity q0 as the indicative criterion Σ(q0∙τ)/q0 to choose the optimal value of refrigeration capacity q0.opt corresponding to its maximum.
The same indicative criterion is applied to determine the precise value of rational refrigeration capacity q0.rat within the range of cumulative annual refrigeration energy characteristics above the optimal value q0.opt to avoid the overestimation of refrigeration capacity accompanied by a negligible increment of annual output.
The values of rational q0.rat’s specific refrigeration capacities while conditioning outdoor air were calculated for temperate climatic conditions in southern Ukraine (Mykolayiv region), 2017 (Figure 1).
The rational value q0.rat of the design refrigeration capacity enables us to offset the annual refrigeration consumption ∑(q0∙τ)rat = 48 MWh/(kg/s) that is close to its maximum value 50 MWh/(kg/s) but is also achieved at reduced design refrigeration capacity q0.10rat = 35 kW/(kg/s), which is less than q0.10max = 42 kW/(kg/s) (Figure 1).
The level of load (LL) on ACS proceeding from the summarized annual refrigeration energy can be applied as a modified criterion in contrast to the current level of load LLcur used in conventional practice: LL10rat = (q0.10rat − q0.15rat)/q0.10rat ≈ 0.3, where q0.10rat − q0.15rat is the range of stable thermal load and q0.15rat is the range of changeable thermal loads.
The maximum value of the indicative criterion Σ(q0∙τ)/q0 reflects the maximum rate of the summarized annual refrigeration energy increment, and naturally, the minimum deviation of the optimal value of refrigeration capacity q0.opt from the current loads q0, followed by minimum exceedances of q0.opt over q0. Therefore, the rational value of refrigeration capacity q0.rat, being higher than q0.opt, is characterized by larger deviation from the current loads q0 and exceedances (excesses) of q0.rat over q0. The latter are considered the reserves for refrigeration exceedances (excesses)’ recuperation to cover peak loads and reduce a design refrigeration capacity less than q0.rat. The refrigeration exceedances (excesses) are associated with changeable load range of the total one. Therefore, the range of changeable loads is considered the object for partly stabilizing due to refrigeration exceedances (excesses) recuperation that leads to a reduction in its value and the total design refrigeration capacity q0.rat as result.
The residual part of the range with initially changeable loads becomes considerably narrower than the primary one that leads to reducing the ratio of the changeable load range, covered by the RSC, to the overall load range, id est. the required level of regulated loads (LRL).

3. Results and Discussion

According to the aim of the research, the range of changeable loads is considered as the object for partly stabilizing due to refrigeration exceedances (excesses)’ recuperation in order to reduce its value and the total design refrigeration capacity q0.rat as result. Such an approach, substantiated by the results of calculation of the summarized annual refrigeration energy generation Σ(q0∙τ) and optimal q0.opt and rational q0.rat refrigeration capacities (Figure 1), should be proven by the exceedances (excesses) of design refrigeration capacities q0.opt and q0.opt over current loads q0, and corresponding monthly summarized values of the refrigeration energy exceedances Σ(q0∙τ) within initial changeable load range q0.15 reduced by its partially stabilization due to refrigeration energy exceedance’s recuperation in the range to q0.20.
The total values of specific refrigeration capacities q0.10 needed for conditioning outdoor air to 10 °C can be sheared into the range of changeable values q0.15, which are needed for preconditioning outdoor air to 15 °C. Practically unchangeable refrigeration capacities q0.10-15 are needed for subsequent conditioning of air from 15 °C to 10 °C. The calculation results for July 2017 in climatic conditions in southern Ukraine, Mykolayiv region, as example of temperate climate, are presented in Figure 2.
As Figure 2 shows, the current total changeable heat load q0.10 for conditioning outdoor air to 10 °C can be shared in the range of changeable load for preconditioning outdoor air to 15 °C, and in the range of practically unchangeable heat load q0.10-15 for subsequent conditioning air from 15 °C to 10 °C. Accordingly, the latter is accepted as the basic practically unchangeable part, q0.10-15 ≈ q0.10rat − q0.15rat, of the total rational design value q0.10rat, whereas the rest, as a remainder of the rational design value q0.10rat, might be used as the residual booster one q0.b10-15 = q0.10rat − q0.10-15, available for preconditioning outdoor air to 15 °C. It is chosen as the object for reduction through refrigeration exceedances (excesses)’ recuperation.
Based on the above, the intermediate temperature 15 °C is accepted as a threshold one tthr, stabilizing the heat loads for further conditioning outdoor air below tthr = 15 °C, and as an indicator to share the overall range of design heat load q0.10rat (Figure 1) in two ranges according to different character of the loading.
Issuing from a changeable character of loading and accompanied by inevitable excesses of design refrigeration capacity q0.10rat over actual loads q0.10, reflected in the booster refrigeration capacity q0.b10-15 = q0.10rat − q0.10-15 and available for preconditioning outdoor air to 15 °C, the latter is accepted as the object for analyses in order to use the excess refrigeration capacity for covering the peak loads. Therefore, the next step of the analyses aims to partly stabilize the initially changeable heat loads q0.15, which would lead to reduce the booster load range from q0.b10-15 to q0.b10-20, as the regulated load range and the LRL of SRC compressor recuperate the refrigeration energy exceedance.
Proceeding from the approach to partly offset the current heat load fluctuations due to a reduction in the refrigeration capacity q0.15 by using the value q0.20rat to condition air to 20 °C, the latter might be accepted as the artificial threshold temperature tthr = 20 °C, and the range of heat loads q0.10-20 as the artificially stable range in the initial approximation (Figure 3).
The results of the refrigeration energy exceedance recuperation for covering the booster preconditioning load q0.15 using the reduced rational refrigeration capacity q0.20rat are presented in Figure 3.
The following correlations are used: q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20rat.ex = q0.b10-20rat − q0.15, q0.b10-20rat.def = q0.15 − q0.b10-20rat, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15 )τ.
As can be seen, the actual values of available booster refrigeration capacities q0.b10-20rat are mostly higher than the current requirement of q0.15 for preconditioning outdoor air to 15 °C (Figure 3a). Accordingly, the current exceedances of the booster refrigeration capacities, q0.b10-20rat.ex, in the majority offset the current deficit, q0.b10-20rat.def, which is proven by the dominant rise in the summarized exceedance of booster refrigeration energy values ∑q0.b10-20rat.exτ, except on a couple of days at the end of July (Figure 3b).
The practically constant summarized exceedance of the booster refrigeration energy values ∑q0.b10-20rat.exτ between the 10–13th and 20–26th July justifies that the daily values of deficit ∑q0.b10-20rat.defτ are compensated by their values of reserved refrigeration energy ∑q0.b10-20rat.exτ. However, the briefly lowering values ∑q0.b10-20rat.exτ within the 27–28th July indicate the presence of small daily refrigeration capacity deficit of q0.20rat.
The continuously rising character of the available summarized exceedance of the booster refrigeration energy curve ∑q0.b10-20rat.ex confirms that the booster refrigeration energy enables it to cover the current need q0.15 for preconditioning outdoor air to 15 °C instead of 20 °C, and to offset the actual deficit q0.b10-20rat.def by recuperating the daily excess of refrigeration energy ∑q0.b10-20rat.ex reserved at lowered current heat loads q0.15, with a significant monthly exceedance of 6600 kWh/(kg/s) (Figure 3). The latter indicates the refrigeration energy reserve for reducing the installed booster refrigeration capacity from q0.15rat to q0.20rat, and the total q0.10rat by the value of their difference q0.15rat − q0.20rat = 10 kW/(kg/s) according to Figure 1.
Meanwhile, the booster refrigeration capacities q0.b10-20opt, based on the optimal design value q0.10opt, are not able to offset the current need q0.15 for preconditioning outdoor air to 15 °C (Figure 4).
The following correlations are used: q0.b10-20opt = q0.10opt − q0.10-20, q0.b10-20opt.ex = q0.b10-20opt − q0.15, q0.b10-20opt.def = q0.15 − q0.b10-20opt, ∑q0.b10-20opt.ex = ∑(q0.b10-20opt − q0.15)τ.
As can be seen, the actual values of available booster refrigeration capacities q0.b10-20opt are lower than the current need q0.15 within 10–13th and later 20th of July, which leads to considerable values of the current deficit q0.b10-20opt.def (Figure 4a). Accordingly, the current deficits q0.b10-20opt.def are comparable with the current exceedance of booster refrigeration capacities q0.b10-20opt.ex that is proven by alternating the rising and falling of the summarized exceedance of booster refrigeration energy values ∑q0.b10-20opt.exτ during July (Figure 4b).
Thus, in contrast to the rational value q0.20rat, the optimal value q0.20opt is lower than the current need q0.15 to be covered by daily reserved refrigeration energy ∑q0.b10-20opt.exτ.
In order to approve such a preliminary conclusion, calculations of the current values of the available booster optimal refrigeration capacities q0.b10-20opt and corresponding summarized monthly refrigeration energy values Σq0.b10-20optτ = Σ(q0.10opt − q0.10-20)τ, compared with the current exceedances of booster rational refrigeration capacities q0.b10-20rat.ex = q0.b10-20rat − q0.15, and corresponding summarized data on refrigeration energy Σq0.b10-20rat.exτ = Σ(q0.b10-20rat − q0.15)τ, are performed (Figure 5).
The following correlations are used: q0.b10-20opt = q0.10opt − q0.10-20, q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20opt.ex = q0.b10-20opt − q0.15, q0.b10-20opt.def = q0.15 − q0.b10-20opt, q0.b10-20rat.ex = q0.b10-20rat − q0.15, Σq0.b10-20optτ= Σ(q0.10opt − q0.10-20)τ, ∑q0.b10-20opt.exτ = ∑(q0.b10-20opt − q0.15 )τ, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15)τ.
As Figure 5a shows, the values of available summarized monthly booster optimal refrigeration energy values Σq0.b10-20optτ = Σ(q0.10opt − q0.10-20)τ are quite close to the summarized exceedances of the booster rational refrigeration energy Σq0.b10-20rat.exτ = Σ(q0.b10-20rat − q0.15)τ which remain from the excessive refrigeration recuperation and are unavailable for further reducing the booster rational refrigeration energy. Proceeding from this data, we can conclude that in the general sense, the booster optimal refrigeration energy exceedance ∑q0.b10-20opt.ex = ∑(q0.b10-20opt − q0.15)τ is not enough to precondition outdoor air lower than 20 °C down to 15 °C; this is in contrast with the excessive booster rational refrigeration energy ∑q0.b10-20rat, which is able to cover q0.15, even with the rest ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15 )τ.
The booster refrigeration capacities q0.b10-20opt/rat = q0.10opt/rat − q0.10-20 and the values of their refrigeration capacity exceedance q0.b10-20opt/rat.ex = q0.b10-20opt/rat − q0.15 over q0.15 were calculated to approve this assumption (Figure 6 and Figure 7).
As may be seen, the actual values of available booster refrigeration capacities q0.b10-20opt are lower than the current need q0.15 from 10–13th and later 20th of July, which leads to considerable current deficit values of q0.b10-20opt.def (Figure 7a). Accordingly, the current deficits q0.b10-20opt.def are comparable with the current exceedances of the booster refrigeration capacities q0.b10-20opt.ex that are proven by alternating the rising and falling of the summarized exceedance of booster refrigeration energy values ∑q0.b10-20opt.exτ during July (Figure 7b).
Thus, in contrast to the rational value q0.20rat, the optimal value q0.20opt is lower than the current need q0.15 to be covered by the daily reserved refrigeration energy ∑q0.b10-20opt.exτ.
As Figure 8 shows, the current values of required level of regulated load (LRL) of SRC in the ratio q0.b10-20opt/q0.10-20rat fluctuate within the range of the required design nominal value LRLnom = q0.15rat/q0.10rat, of about 0.7 to 0.3–0.2. The range of load, regulated by an SCR compressor, is characterized by the level of regulated load LRL as a ratio of the regulated load to the overall load q0.10, including the unregulated load.
Thus, the developed two methods of determining the optimal refrigeration capacity q0.10opt and its rational value q0.10rat as the second stage in the generalized designing methodology [84,85] make it possible to define not only the value of LRLnom, but the range of the current values of LRLcur fluctuation too.
As Figure 9 shows, the booster optimal refrigeration capacities q0.b10-20opt of q0.10opt are enough to cover current need q0.20 for cooling air to 20 °C with considerable exceedance q0.b10-20opt.ex20, but sometimes less than the current need q0.15 for cooling air to 15 °C (Figure 8), when corresponding exceedance q0.b10-20opt.ex15 drops to zero (Figure 9). The latter is also proven by the alternating the rising and falling of the summarized available exceedance of the booster optimal refrigeration energy values ∑q0.b10-20opt.exτ = Σ(q0.b10-20opt − q0.15)τ during July (Figure 9). There are opposite results for the summarized available exceedance of the booster rational refrigeration energy values ∑q0.b10-20rat.exτ = Σ(q0.b10-20rat − q0.15 )τ, characterized by a continuous rise that demonstrates that the booster rational refrigeration energy is able to cover the current need q0.15 for preconditioning outdoor air to 15 °C instead of 20 °C; this is achieved by recuperating the daily excess of refrigeration energy ∑q0.b10-20rat.ex reserved at lower current heat loads q0.15.
The practically constant summarized exceedance of the booster rational refrigeration energy values ∑q0.b10-20rat.exτ = Σ(q0.b10-20rat − q0.15)τ between 10–13th and 20–26th July justifies that daily values of the deficit are compensated by the values of reserved refrigeration energy ∑q0.b10-20rat.exτ.
The similar character of the summarized exceedance of the booster optimal refrigeration energy values ∑q0.b10-20opt.ex20τ = Σ(q0.b10-20opt − q0.20)τ indicates that operation of the compressor at optimal loads also requires refrigeration energy exceedance recuperation for booster air to be preconditioned to 20 °C.
The results of reduction in installed (design) refrigeration capacities through refrigeration energy exceedance recuperation, proceeding from optimal q0.10opt and rational q0.10orat values calculated for temperate climatic conditions in southern Ukraine, 2017, are presented in Figure 10.
As may be seen, the values of reduction in initial rational design specific refrigeration capacity due to optimal design Δq0.10opt and by refrigeration energy exceedance recuperation in booster air preconditioning to 15 °C Δq0.15-20rat, resulting in reducing the rational value of design refrigeration capacity from q0.15rat to q0.20rat, are nearly the same. However, the annual refrigeration energy generation according to current consumption ∑(q0∙τ)10opt at the optimal refrigeration capacity q0.10opt is considerably lower than ∑(q0∙τ)10rat at the rational refrigeration capacity q0.10rat. In order to increase the annual refrigeration energy generation, as the primary criterion for the effect gained at optimal refrigeration capacity q0.10opt, the refrigeration energy exceedance Σq0.b10-20optτ = Σ(q0.10opt -q0.10-20)τ (Figure 8) has to be recuperated.

4. Conclusions

The methods earlier developed by authors and aimed at determining the rational refrigeration capacity of ACS, providing the maximum annual refrigeration energy generation according to its consumption and its optimal value at the maximum rate of annual refrigeration energy increment, are adopted to reveal reserves for reducing the design refrigeration capacity of ACS through recuperation of the excessive refrigeration reserved at lowered loads to cover the current increased loads.
The modified methods of rational and optimal design of the ACS allow us to determine the initial ranges of changeable and unchangeable thermal loads, subsequently allowing us to partly stabilize the changeable load range through covering it with recuperated excessive refrigeration.
The artificial threshold air temperature, limiting the range of initially changeable loads stabilized through excessive refrigeration recuperation, is determined and proceeds from the rising character of the monthly summarized available exceedance of the refrigeration energy beyond its needs.
Such artificial thermal load stabilization through excessive refrigeration recuperation leads to a narrowed range of changeable loads and a reduction in the level of the regulated loads (LRL) of the SRC compressor.
Thus, the modified methods of rational and optimal design of the ACS allow us to determine the level of regulated loads (LRL) of the SRC, thus the load range of the compressor’s operation was reduced more than 1.5 times. It has been shown that for temperate climatic conditions, the required LRL is about 0.5 with excessive refrigeration recuperation, versus 0.7 without refrigeration recuperation.
The further investigation is focused on the application of the approaches to designing two-stage outdoor ACS and the methods of defying the rational and optimal refrigeration capacities, developed initially for outdoor air conditioning, to realize two-stage principal in indoor subsystem with using the refrigeration excess gained in outdoor subsystem to reduce installed refrigeration capacity of indoor one.

Author Contributions

Conceptualization, M.R. (30%), A.R. (25%), E.T. (15%), A.P. (10%) and R.R. (20%); methodology, M.R. (30%), A.R. (25%), E.T. (15%), A.P. (10%) and R.R. (20%); software, M.R. (25%), A.R. (30%), E.T. (10%), A.P. (10%) and R.R. (25%); validation, M.R. (25%), A.R. (30%), E.T. (10%), A.P. (15%) and R.R. (20%); a formal analysis, M.R. (30%), A.R. (25%), E.T. (10%), A.P. (15%) and R.R. (20%); writing—original draft preparation, M.R. (30%), A.R. (25%), E.T. (10%), A.P. (15%) and R.R. (20%); writing—review and editing, M.R. (30%), A.R. (25%), E.T. (15%), A.P. (10%) and R.R. (20%). All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature and Units

ACSAir conditioning system
LLLevel of load
LRLLevel of regulated load
SRCSpeed regulated compressor
VRFVariable refrigerant flow
Symbols and units
bBooster
caSpecific heat of humid air kJ/(kg·K)
GaAir mass flow ratekg/s
Q0Total refrigeration capacitykW
q0Specific refrigeration capacity (per unit air mass flow rate)kW/(kg/s)
q0 τSpecific refrigeration energy (per unit air mass flow rate)kW/(kg/s)
tAir temperatureK, °C
ξSpecific heat ratio of the total heat (latent and sensible) removed from air to sensible heat
τTime intervalh
ΔtTemperature decrease K, °C
∑(q0 τ)Annual (monthly) specific refrigeration energy consumption (per unit air mass rate)kWh/(kg/s)
Subscripts
10, 15, 20Air temperatureK, °C
aAir
ambAmbient
bBooster
maxMaximum
optOptimal
ratRational

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Energies 16 02417 g001 550
Figure 1. Specific annual refrigeration energy consumption ∑(q0∙τ), rational q0.rat and optimal q0.opt refrigeration capacities while conditioning air to ta2 = 10, 15 °C and 20 °C: LL10rat = (q0.10rat − q0.15rat)/q0.10rat.
Figure 1. Specific annual refrigeration energy consumption ∑(q0∙τ), rational q0.rat and optimal q0.opt refrigeration capacities while conditioning air to ta2 = 10, 15 °C and 20 °C: LL10rat = (q0.10rat − q0.15rat)/q0.10rat.
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Figure 2. The current values of specific refrigeration capacities q0.10 required for outdoor air conditioning to 10 °C; refrigeration capacities q0.10-15 for subsequent air conditioning from 15 °C to 10 °C; available booster values q0.b10-15 remained for outdoor air conditioning to 15 °C: q0.10-15 = q0.10 − q0.15; q0.b10-15 = q0.10 − q0.10-15.
Figure 2. The current values of specific refrigeration capacities q0.10 required for outdoor air conditioning to 10 °C; refrigeration capacities q0.10-15 for subsequent air conditioning from 15 °C to 10 °C; available booster values q0.b10-15 remained for outdoor air conditioning to 15 °C: q0.10-15 = q0.10 − q0.15; q0.b10-15 = q0.10 − q0.10-15.
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Figure 3. Rational values of refrigeration capacities q0.10rat, q0.15rat and q0.20rat for conditioning outdoor air to 10 °C, 15 °C and 20 °C accordingly; actual refrigeration capacities q0.15 needed for preconditioning air to 15 °C, and available booster refrigeration capacity q0.b10-20rat for preconditioning air and booster refrigeration capacity exceedance q0.b10-20rat.ex over q0.15 (a), and its deficit q0.b10-20rat.def, summarized monthly refrigeration energy exceedance ∑q0.b10-20rat.ex over q0.15 (b): q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20rat.ex = q0.b10-20rat − q0.15, q0.b10-20rat.def = q0.15 − q0.b10-20rat, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15 )τ.
Figure 3. Rational values of refrigeration capacities q0.10rat, q0.15rat and q0.20rat for conditioning outdoor air to 10 °C, 15 °C and 20 °C accordingly; actual refrigeration capacities q0.15 needed for preconditioning air to 15 °C, and available booster refrigeration capacity q0.b10-20rat for preconditioning air and booster refrigeration capacity exceedance q0.b10-20rat.ex over q0.15 (a), and its deficit q0.b10-20rat.def, summarized monthly refrigeration energy exceedance ∑q0.b10-20rat.ex over q0.15 (b): q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20rat.ex = q0.b10-20rat − q0.15, q0.b10-20rat.def = q0.15 − q0.b10-20rat, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15 )τ.
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Energies 16 02417 g004 550
Figure 4. Optimal values of refrigeration capacities q0.10opt, q0.15opt and q0.20opt for conditioning outdoor air to 10 °C, 15 °C and 20 °C accordingly; actual refrigeration capacities q0.15 needed for preconditioning outdoor air to 15 °C; booster refrigeration capacity q0.b10-20opt and its deficit q0.b10-20opt.def compared to needed q0.15 (a), booster refrigeration capacity exceedance q0.b10-20opt.ex over q0.15 and summarized monthly refrigeration energy exceedance ∑q0.b10-20opt.ex (b).
Figure 4. Optimal values of refrigeration capacities q0.10opt, q0.15opt and q0.20opt for conditioning outdoor air to 10 °C, 15 °C and 20 °C accordingly; actual refrigeration capacities q0.15 needed for preconditioning outdoor air to 15 °C; booster refrigeration capacity q0.b10-20opt and its deficit q0.b10-20opt.def compared to needed q0.15 (a), booster refrigeration capacity exceedance q0.b10-20opt.ex over q0.15 and summarized monthly refrigeration energy exceedance ∑q0.b10-20opt.ex (b).
Energies 16 02417 g004
Energies 16 02417 g005 550
Figure 5. Current values of refrigeration capacities q0.15 needed for preconditioning outdoor air to 15 °C; booster optimal refrigeration capacity q0.b10-20opt and corresponding summarized monthly refrigeration energy values Σq0.b10-20optτ, current exceedances of booster rational refrigeration capacities q0.b10-20rat.ex and corresponding summarized data Σq0.b10-20rat.exτ (a), current booster optimal refrigeration capacity exceedance q0.b10-20opt.ex and its deficit q0.b10-20opt.def, summarized booster refrigeration energy exceedance for optimal ∑q0.b10-20opt.ex and rational data ∑q0.b10-20rat.ex (b).
Figure 5. Current values of refrigeration capacities q0.15 needed for preconditioning outdoor air to 15 °C; booster optimal refrigeration capacity q0.b10-20opt and corresponding summarized monthly refrigeration energy values Σq0.b10-20optτ, current exceedances of booster rational refrigeration capacities q0.b10-20rat.ex and corresponding summarized data Σq0.b10-20rat.exτ (a), current booster optimal refrigeration capacity exceedance q0.b10-20opt.ex and its deficit q0.b10-20opt.def, summarized booster refrigeration energy exceedance for optimal ∑q0.b10-20opt.ex and rational data ∑q0.b10-20rat.ex (b).
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Energies 16 02417 g006 550
Figure 6. Actual values of refrigeration capacities q0.15 needed for conditioning outdoor air to 15 °C, and booster refrigeration capacities q0.b10-20opt and q0.b10-20rat based on the optimal and rational design values q0.10opt and q0.10rat for conditioning outdoor air to 10 °C: q0.b10-20opt = q0.10opt − q0.10-20; q0.b10-20rat = q0.10rat − q0.10-20.
Figure 6. Actual values of refrigeration capacities q0.15 needed for conditioning outdoor air to 15 °C, and booster refrigeration capacities q0.b10-20opt and q0.b10-20rat based on the optimal and rational design values q0.10opt and q0.10rat for conditioning outdoor air to 10 °C: q0.b10-20opt = q0.10opt − q0.10-20; q0.b10-20rat = q0.10rat − q0.10-20.
Energies 16 02417 g006
Energies 16 02417 g007a 550Energies 16 02417 g007b 550
Figure 7. Actual values of booster refrigeration capacity exceedance q0.b10-20opt.ex and q0.b10-20rat.ex over q0.15 (a) and its deficit q0.b10-20opt.def and q0.b10-20rat.def based on the optimal and rational design values q0.10opt and q0.10rat for conditioning outdoor air to 10 °C; summarized monthly refrigeration energy exceedance ∑q0.b10-20opt.ex over q0.15; (b): q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20rat.ex = q0.b10-20rat − q0.15, q0.b10-20opt.def = q0.15 − q0.b10-20opt, q0.b10-20rat.def = q0.15 − q0.b10-20rat, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15)τ, ∑q0.b10-20opt.ex = ∑(q0.b10-20opt − q0.15)τ.
Figure 7. Actual values of booster refrigeration capacity exceedance q0.b10-20opt.ex and q0.b10-20rat.ex over q0.15 (a) and its deficit q0.b10-20opt.def and q0.b10-20rat.def based on the optimal and rational design values q0.10opt and q0.10rat for conditioning outdoor air to 10 °C; summarized monthly refrigeration energy exceedance ∑q0.b10-20opt.ex over q0.15; (b): q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20rat.ex = q0.b10-20rat − q0.15, q0.b10-20opt.def = q0.15 − q0.b10-20opt, q0.b10-20rat.def = q0.15 − q0.b10-20rat, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15)τ, ∑q0.b10-20opt.ex = ∑(q0.b10-20opt − q0.15)τ.
Energies 16 02417 g007aEnergies 16 02417 g007b
Energies 16 02417 g008 550
Figure 8. Actual refrigeration capacities q0.15 needed for preconditioning outdoor air to 15 °C, booster refrigeration capacity q0.b10-20opt and q0.b10-20rat based on q0.10opt and q0.10rat, the difference q0.b10-20rat − q0.b10-20opt = q0.10rat − q0.10opt, current LRLcur and nominal LRLnom: q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20opt = q0.10opt − q0.10-20 q0.b10-20rat.ex = q0.b10-20rat − q0.15, q0.b10-20rat.def = q0.15 − q0.b10-20rat, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15)τ; LRLnom = q0.15rat/q0.10rat; LRLcur = q0.b10-20opt/q0.10-20rat; q0.b10-20rat − q0.b10-20opt = q0.10rat − q0.10opt.
Figure 8. Actual refrigeration capacities q0.15 needed for preconditioning outdoor air to 15 °C, booster refrigeration capacity q0.b10-20opt and q0.b10-20rat based on q0.10opt and q0.10rat, the difference q0.b10-20rat − q0.b10-20opt = q0.10rat − q0.10opt, current LRLcur and nominal LRLnom: q0.b10-20rat = q0.10rat − q0.10-20, q0.b10-20opt = q0.10opt − q0.10-20 q0.b10-20rat.ex = q0.b10-20rat − q0.15, q0.b10-20rat.def = q0.15 − q0.b10-20rat, ∑q0.b10-20rat.ex = ∑(q0.b10-20rat − q0.15)τ; LRLnom = q0.15rat/q0.10rat; LRLcur = q0.b10-20opt/q0.10-20rat; q0.b10-20rat − q0.b10-20opt = q0.10rat − q0.10opt.
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Energies 16 02417 g009 550
Figure 9. Actual values of booster optimal refrigeration capacity exceedance q0.b10-20opt.ex over q0.15 and q0.b10-20opt.ex20 over q0.20; summarized monthly booster optimal refrigeration energy exceedances Σq0.b10-20opt.exτ over q0.15 and Σq0.b10-20opt.exτ over q0.20; summarized data on booster rational refrigeration energy Σq0.b10-20rat.exτ over q0.15 and Σq0.b10-20rat.ex20τ over q0.20: q0.b10-20opt.ex = q0.b10-20opt − q0.15; q0.b10-20opt.ex20 = q0.b10-20opt − q0.20; Σq0.b10-20opt.exτ = Σ(q0.b10-20opt − q0.15)τ; Σq0.b10-20opt.exτ= Σ(q0.b10-20opt − q0.20 )τ; Σq0.b10-20rat.exτ= Σ(q0.b10-20rat − q0.15)τ; Σq0.b10-20rat.ex20τ = Σ(q0.b10-20rat − q0.20 )τ.
Figure 9. Actual values of booster optimal refrigeration capacity exceedance q0.b10-20opt.ex over q0.15 and q0.b10-20opt.ex20 over q0.20; summarized monthly booster optimal refrigeration energy exceedances Σq0.b10-20opt.exτ over q0.15 and Σq0.b10-20opt.exτ over q0.20; summarized data on booster rational refrigeration energy Σq0.b10-20rat.exτ over q0.15 and Σq0.b10-20rat.ex20τ over q0.20: q0.b10-20opt.ex = q0.b10-20opt − q0.15; q0.b10-20opt.ex20 = q0.b10-20opt − q0.20; Σq0.b10-20opt.exτ = Σ(q0.b10-20opt − q0.15)τ; Σq0.b10-20opt.exτ= Σ(q0.b10-20opt − q0.20 )τ; Σq0.b10-20rat.exτ= Σ(q0.b10-20rat − q0.15)τ; Σq0.b10-20rat.ex20τ = Σ(q0.b10-20rat − q0.20 )τ.
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Energies 16 02417 g010 550
Figure 10. Specific annual refrigeration energy consumption ∑(q0∙τ); the rational q0.10,15,20rat and optimal q0.10,15,20opt values of design specific refrigeration capacity and their reductions Δq0.10,15,20rat/opt due to rational and optimal designing and refrigeration energy exceedance recuperation while conditioning air to ta2 = 10, 15 and 20 °C: Δq0.10,15,20rat = q0.10,15,20max − q0.10,15,20rat; Δq0.10opt = q0.10rat − q0.10opt; Δq0.15-20rat = q0.15rat − q0.20rat.
Figure 10. Specific annual refrigeration energy consumption ∑(q0∙τ); the rational q0.10,15,20rat and optimal q0.10,15,20opt values of design specific refrigeration capacity and their reductions Δq0.10,15,20rat/opt due to rational and optimal designing and refrigeration energy exceedance recuperation while conditioning air to ta2 = 10, 15 and 20 °C: Δq0.10,15,20rat = q0.10,15,20max − q0.10,15,20rat; Δq0.10opt = q0.10rat − q0.10opt; Δq0.15-20rat = q0.15rat − q0.20rat.
Energies 16 02417 g010
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Radchenko, M.; Radchenko, A.; Trushliakov, E.; Pavlenko, A.; Radchenko, R. Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes. Energies 2023, 16, 2417. https://doi.org/10.3390/en16052417

AMA Style

Radchenko M, Radchenko A, Trushliakov E, Pavlenko A, Radchenko R. Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes. Energies. 2023; 16(5):2417. https://doi.org/10.3390/en16052417

Chicago/Turabian Style

Radchenko, Mykola, Andrii Radchenko, Eugeniy Trushliakov, Anatoliy Pavlenko, and Roman Radchenko. 2023. "Advanced Method of Variable Refrigerant Flow (VRF) System Design to Forecast on Site Operation—Part 3: Optimal Solutions to Minimize Sizes" Energies 16, no. 5: 2417. https://doi.org/10.3390/en16052417

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