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Article

Advanced Method of Variable Refrigerant Flow (VRF) Systems Designing to Forecast Onsite Operation—Part 2: Phenomenological Simulation to Recoup Refrigeration Energy

by
Mykola Radchenko
1,
Andrii Radchenko
1,
Eugeniy Trushliakov
2,
Hanna Koshlak
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 Sanitary Engineering, Kielce University of Technology, Al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland
*
Author to whom correspondence should be addressed.
Energies 2023, 16(4), 1922; https://doi.org/10.3390/en16041922
Submission received: 26 December 2022 / Revised: 31 January 2023 / Accepted: 11 February 2023 / Published: 15 February 2023
(This article belongs to the Special Issue Latest Research of Building Heat and Mass Transfer)
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Abstract

:
This paper focuses on the application of speed-regulated compressors (SRCs) to cover changeable heat loads with high efficiency in conventional air conditioning systems (ACS) as well as in the more advanced variable refrigerant flow (VRF)-type outdoor and indoor ACS. In reality, an SRC is an oversized compressor, although it can operate efficiently at part loads. The higher the level of regulated loads (LRL) of the SRC, the more the compressor is oversized. It is preferable to reduce the size of the SRC by covering the peak loads and recouping the excessive refrigeration energy reserved at decreased actual loads within the range of regulated loads. Therefore, the range of changeable loads is chosen as the object to be narrowed by using the reserved refrigeration capacity. Thus, the general fundamental approach of dividing the overall heat load range of the ACS into the ranges with changeable and unchangeable loads, as previously developed by the authors, is applied for the range of primary changeable loads. Due to this innovative step, the principle of two-stage outdoor air conditioning according to changeable and unchangeable loads, also proposed by the authors, has been extended over the range of primary changeable loads to reduce the level of refrigeration capacity regulation and SRC size. To realize this, part of the changeable load range is offset by the reserved refrigeration capacity, leading to a reduction in the changeable load range and the SRC size by approximately 20% for temperate climatic conditions.

1. Introduction

Air conditioning systems (ACSs) are the most widespread systems applied in buildings to maintain comfort parameters [1,2] and in engine rooms to support low-intake air temperatures, enabling the efficient operation of engines [3,4]. Their widespread application in the conditioning of cyclic air in combustion engines, particularly in internal combustion engines [5,6] and gas turbines [7,8], has led to the requirement for the development of ACSs as subsystems of trigeneration plants [9,10] for the combined cooling, heating, and power (CCHP) supply of districts [11,12]. Such a wide use of ACSs in energetic applications, including stationary [13,14] and transport power plants [15,16], is a result of the significant exhaust heat potential available for conversion to refrigeration by chillers [17,18] due to the application of highly efficient economizers and low-temperature heating surfaces [19,20]. This excessive refrigeration led to the widening of its application in traditional building and engine-sucked air conditioning [21,22].
The changeable loads on the ACS and heat exchangers accordingly lead to falling heat fluxes and require the application of highly efficient heat exchangers and working fluid circulation circuits. The application of advanced heat exchangers [23,24], initially by compact evaporators [25,26] and minichannel-type condensers [27,28], led to an increased interest in research focused on intensifying heat transfer [29,30] and hydrodynamics [31,32] under conditions of unstable two-phase flows [33,34], uneven refrigerant [35,36], and airflow distribution [37,38]. A considerable number of innovative air conditioning and refrigerant supply [39,40] circuits have been proposed, particularly with the application of ejectors [41,42] and thermopressors [43,44] as circulation devices using the potential energy of high-pressure fluids [45,46].
The performance of energy conversion systems [47,48], including ACSs, is characterized by off-design modes [49,50] especially evident in mild and off-season climatic conditions.
Various thermal demand and primary energy-saving (TDM and PES) management methods [51,52], criteria [53,54], and indicators [55,56] were proposed for providing a high level of loading [57,58] and estimating the effect gained due to the application of combined energy systems [59,60] performance efficiency, including ACSs as subsystems [61,62] or autonomic variable refrigerant flow (VRF)-type ACSs with SRCs [63,64].
The VRF systems are considered the most efficient for off-season operation [65,66]. Their combined version includes two subsystems for outdoor and indoor air processing [67,68]. The outdoor system treats the outdoor air and offsets fluctuated heat loads in order to avoid overloading the indoor system [69,70]. The VRF system provides an energy saving of more than 20% compared to the variable air volume ACS [71,72,73,74].
The method used to estimate the performance efficiency of SRCs through imposing the load ranges, regulated by the SRC, on the ranges of changeable and unchangeable loads within the overall range of actual loading was previously developed by the authors. With this, the efficiency of SRC operation is estimated by the rate of loading the unregulated range assumed as the object of investigation [75].
In reality, the SRC is an oversized compressor, although it operates efficiently at part loads. The higher the level of regulated loads (LRL) of the SRC, the more oversized the compressor. It is preferable to reduce its size through the application of the SRC with LRL = 0.5 instead of LRL = 0.7. This might be possible by reducing the range of fluctuating loads and increasing its level of loading (LL). The latter is possible by covering the peak loads using the exceeding refrigeration energy reserved at lowered actual loads. Thus, the enhancement of the operation efficiency of the advanced VRF system with a modern SRC and reduced size may be achieved by recouping the refrigeration energy excess.
The aim of the research is to enhance the operation efficiency of VRF systems with SRCs by recouping the refrigeration energy reserved at lowered loading to reduce the range of outdoor air preconditioning at changeable heat loads and the level of regulated load (LRL) and SRC sizes as a result.

2. Methods

The following approaches and assumptions have been accepted in the design methodology of advanced ACSs to simplify quantifying the analysis results.
In order to obtain a direct and a simple tool and a more precise method for minimizing the errors caused by the approximation of the actual primary data, the fluctuations of data on actual refrigeration energy consumption Q0·τ is considered by the rate of the summarized annual values versus the refrigeration capacity Q0:
Σ(Q0·τ) = f(Q0).
Such an approach enables the treatment of the annual refrigeration energy cumulative characteristic (1) independent of the rate of annual refrigeration energy increment and allows the determination of the optimal value of refrigeration capacity Q0.opt, associated with the maximum rate of cumulative curve Σ(Q0·τ) = f(Q0), and a precise value of rational refrigeration capacity Q0.rat, avoiding its overestimation accompanied by a negligible increment of annual output.
Thus, the annual refrigeration energy consumption Σ(Q0·τ) is considered a primary criterion to design the refrigeration capacity of an ACS.
The next stage of ACS designing focuses on the rational distribution of the overall design refrigeration capacity according to the peculiarities of heat loading in response to current climatic conditions. The distribution of the total design refrigeration capacity between the range of changeable loads, affected by outdoor air parameter variations and covered by the speed-regulated compressor (SRC) and the range of unchangeable loads of further subconditioned air to the set temperature, is the result of the second stage of ACS designing.
The method for shearing the overall range of actual thermal loads on the ACS into the ranges of changeable loads for ambient air precooling and the unchangeable load for further air subcooling to the target temperature ta2, accordingly, was developed for adopting the designed refrigeration capacity to cover both of them [75].
The value of the threshold temperature tthr to share the overall range of the designed thermal load q0.10rat into the ranges with different characters of loading is first determined by stabilizing the loads below its magnitude. Thus, the threshold temperature tthr is used as an indicator for sharing the overall load range of outdoor air conditioning into the ranges with different characters of loading.
The method for the distribution of the overall design heat load (design refrigeration capacity) developed by the authors [75] is expanded to narrow the range of changeable loads through recouping the excessive refrigeration energy obtained at lower current loads to cover peak loads within the additional range of an artificially stabilized heat load. As a result, the residual part of the range with initially changeable loads becomes considerably narrower than the primary load, leading to a reduction in 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).
Based on the fact that any heat loading influenced by current climatic conditions has changeable behavior, inevitably accompanied by the formation of refrigeration energy excesses, the next step of the analysis is focused on realizing these reserves through the recoup of the increased heat loads.
Thus, the concept of two-stage outdoor air conditioning [75] has received renewed interest in terms of broadening its application within the primary range of changeable loads; it can be narrowed using the excessive refrigeration energy obtained at lowered current loads to cover the peak loads. This leads to a reduction in the ratio of the changeable load range, covered by the RSC, to the overall load range including the unchangeable loads.
The specific refrigeration capacity q0 as the total value of the refrigeration capacity Q0, referred to as unit air mass flow rate (Ga = 1 kg/s), i.e., q0 = Q0/Ga, is used in the following calculations:
q0 = ξ·ca·(ta − ta2), kW/(kg/s),
where ta—initial or ambient tamb air temperature, K or °C; ta2—a set air temperature, accepted as an example in the investigation equal to ta2 = 10 °C; ξ—relative heat ratio as the total heat, removed from the air, related to its sensible heat; and ca—air-specific heat, kJ/(kg·K).
Specific annual and monthly refrigeration energy consumption is calculated as:
Σ(q0·τ) = Σξca·(ta − ta2)·τ·10−3, kWh/(kg/s).
Accordingly, the specific values of refrigeration capacity q0.10 and refrigeration energy consumption q0.10·τ are needed for cooling air to ta2 = 10 °C.
This enables the generalization of the results and their widespread application for any value of air mass flow rate Ga and total refrigeration capacity Q0 = q0 Ga as a result.
According to the proposed method, the changes in the actual specific refrigeration energy consumption q0·τ are taken into account by the rate of their annual summation ∑(q0·τ) increment. With this, a cumulative energetic characteristic of the ACS as a dependence of specific annual refrigeration energy consumption Σ(q0·τ) on the design (installed) specific refrigeration capacity q0 is used as a basic factor to determine a rational q0.rat design value: Σ(q0·τ) = f(q0) (Figure 1) [75].
The values of rational q0.rat specific refrigeration capacities when conditioning outdoor air were calculated for temperate climatic conditions in southern Ukraine (the Mykolayiv region) in 2017 (Figure 1).
The rational value q0.rat of the design refrigeration capacity is able to offset the annual refrigeration consumption ∑(q0τ)rat = 48 MWh/(kg/s) close to its maximum value of 50 MWh/(kg/s), but at a reduced design refrigeration capacity q0.10rat = 35 kW/(kg/s) less than q0.10max = 42 kW/(kg/s) (Figure 1).
Further development of the methodology for the rational design of an ACS that regulates the refrigeration capacity aims to develop the method for shearing the total design refrigeration capacity according to current heat loads into ranges with different change behaviors. The range of fluctuations of the heat load requires the application of a speed-regulated compressor (SRC). The range of a relatively stable heat load for deeper air cooling to the final temperature, for example ta2 = 10 °C, can be covered by a conventional compressor without refrigeration capacity regulation.
In order to apply the compressor with refrigeration capacity regulation to offset both loading ranges, it is necessary to analyze the ratio between both ranges and compare it to the level of refrigeration capacity regulation by the SRC, id est, the load regulation level (LRL).
The SRC with LRL = 0.5 is assumed to simplify the analyses at the initial step of approximation. Accordingly, the changeable load range, from LRL·q0.10rat = 0.5q0.10rat up to q0.10rat, is considered the level of regulated load covered by the SRC, whereas a range of load below (outside) the SRC-regulated range, from 1–LRL q0.10rat = 0.5 q0.10rat or q0.10rat/2 = 0.5 q0.10rat down to q0 = 0, designed as the stable range, must be analyzed by the level of loading for the estimation of the SRC’s operation efficiency.
It should be noted that fluctuations (drops) of heat load in the range q0.10-15 = q0.10 − q0.15 of further deeper air conditioning below the threshold temperature tthr = 15 °C indicate the excess of the designed refrigeration capacity q0.15rat over its current values q0.15. The latter is revealed at the booster stage of preconditioning the outdoor air to tthr = 15 °C, calculated on the residual principle as q0.b10-15rat = q0.10 − q0.10-15 (Figure 2).

3. Results and Discussion

The total values of the specific refrigeration capacities q0.10, needed for conditioning outdoor air to 10 °C, can be sheared into the range of changeable values q0.15, needed for preconditioning outdoor air to 15 °C, and practically unchangeable refrigeration capacities q0.10-15 for the subsequent conditioning of air from 15 °C to 10 °C. The calculation results for July 2017 in climatic conditions in the Mykolayiv region, southern Ukraine, as example of a temperate climate, are presented in Figure 2.
As Figure 2 shows, the current total fluctuated heat load q0.10 for conditioning outdoor air to 10 °C can be shared in the range of the fluctuated load for preconditioning outdoor air to 15 °C, and the range of practically unchangeable heat load q0.10-15 for subsequent air conditioning from 15 °C to 10 °C. Accordingly, the latter is to be 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 remainder of the rational design value q0.10rat, might be used as the residual booster q0.b10-15 = q0.10rat − q0.10-15 available for preconditioning outdoor air to 15 °C.
Basing on the above, the intermediate temperature of 15 °C might be accepted as the threshold tthr, stabilizing the heat loads in the further conditioning of outdoor air below tthr = 15 °C, and as an indicator to share the overall range of the design heat load q0.10rat (Figure 1) in two ranges according to the different loading characteristics.
In terms of the changeable loading characteristics, accompanied by the inevitable excesses of the designed refrigeration capacity q0.10rat over the actual loads q0.10, reflected in the booster refrigeration capacity q0.b10-15 = q0.10rat − q0.10-15 available for preconditioning outdoor air to 15 °C, the latter is accepted as the object for analysis to use the excess refrigeration capacity for covering the peak loads.
The range of load, regulated by the SRC, is characterized by the level of regulated load as a ratio of the load regulated to the overall load q0.10, including the unregulated load.
The operation efficiency of the SRC with a definite design LRL (LRL = 0.5, for example) is at its maximum when the loads q0.10<0.5 are within a range from q0 = 0 to q0.10rat/2, equal to q0.10rat/2 (Figure 3).
The consumption of refrigeration capacity q0.10<0.5 within a range without its regulation (from 0 to q0.10rat/2) is marked as q0.10<0.5.
A lack of loads within its unregulated range q0.10 < q0.10rat/2 is considered to exceed q0.10rat/2ex<0.5 = q0.10rat/2 − q0.10<0.5 of the rational design value of the refrigeration capacity q0.10rat/2 over the actual loads q0.10<0.5 (Figure 3).
The monthly summarized values of the designed refrigeration energy generation exceedance ∑(q0.10rat/2τ)ex<0.5 of the refrigeration energy ∑(q0.10rat/2τ), generated according to the design value q0.10rat/2 above the consumed values ∑(q0.10<0.5τ), reflect the trend in the ratio of reserved and consumed refrigeration energy under onsite climatic conditions.
The continuously growing character of the curve of the monthly summarized refrigeration energy exceedance ∑(q0.10rat/2τ)ex<0.5 (Figure 3) exposes the refrigeration reserve for partly covering the daily fluctuated heat loads when preconditioning outdoor air to 15 °C. This leads to a narrowing of the range of the changeable load and the value of the LRL.
The relative values of the summarized consumed refrigeration energy ∑(q0.10<0.5τ)<0.5/∑(q0.10rat/2τ) characterize the level of loading in the range of the unregulated load, LL = ∑(q0.10<0.5τ)<0.5/∑(q0.10rat/2τ) (Figure 4).
Accordingly, the lack of heat loading in the range of the unregulated load, considered as the exceedance q0.10rat/2ex<0.5 of the design load (refrigeration capacity) q0.10rat above the actual heat loads (refrigeration consumption) q0.10<0.5, can be characterized by the relative values of the summarized excess of the refrigeration energy ∑(q0.10rat/2τ)ex<0.5/∑(q0.10rat/2τ) generated according to the design value q0.10rat/2. In reality, these relative values characterize the reduction of the load level LLred = ∑(q0.10rat/2τ)ex<0.5/∑(q0.10rat/2τ) and, accordingly, can be calculated by the correlation LLred = 1 − LL (Figure 4). This will be used in further analyses.
The following correlations are used: ∑(q0.10rat/2τ)ex<0.5 = ∑(q0.10rat/2τ − q0.10<0.5τ)ex<0.5; q0.10rat/2ex<0.5 = q0.10rat/2 − q0.10<0.5; ∑(q0.10rat/2τ)ex<0.5/∑(q0.10rat/2τ); and the criteria developed are: LL = ∑(q0.10τ)<0.5/∑(q0.10rat/2τ), LLred = ∑(q0.10rat/2τ)ex<0.5/∑(q0.10rat/2τ), LL = 1 − LLred.
Thus, the character of the summarized refrigeration energy exceedance curve ∑(q0.10rat/2exτ)<0.5 can serve as the indicator for its recoup to cover the peak loads and to reduce the installed refrigeration capacity as a result (Figure 3 and Figure 4).
In addition, the relative summarized refrigeration energy exceedance ∑(q0.10rat/2exτ)<0.5/∑(q0.10rat/2τ), characterizing the level of loading in the unregulated load range, indirectly indicates the potential reduction in the LRL of the SRC.
The exceedance of the design refrigeration capacity q0.10rat over the actual loads q0.10 is reflected in the booster refrigeration capacity q0.b10-15 available for preconditioning outdoor air to 15 °C. Therefore, this is accepted as the object for the next step of the analysis aimed at partly stabilizing the heat load, leading to a reduction in the booster load range from q0.b10-15 to q0.b10-20 as the regulated load range and the LRL of the SRC by recouping the refrigeration energy exceedance.
In the approach to partly offset the current heat load fluctuations due to the reduction in the refrigeration capacity q0.15, the value q0.20rat required for conditioning air to 20 °C might be accepted as the artificial threshold temperature tthr = 20 °C and the range of heat loads q0.10-20 as an artificially (relatively) stable range in the initial approximation (Figure 5).
The extended artificially (relatively) stable heat load q0.10-20 might be considered an increased basic design value q0.10-20 compared to its initial value of q0.10-15. Such an approach, as the initial step in the approximation (based on initial, not reduced, value q0.10rat and LRL = 0.5), is approved by the calculation results in Figure 6.
The following correlations are used: q0.10-15,20 = q0.10 − q0.15,20, q0.b10-15,20 = q0.10rat − q0.10-15,20; and the correlations for the developed criteria are: LRL = ∑(q0.b10-15,20τ)/∑(q0.10ratτ), 1 − LRL = ∑(q0.10-15,20τ)/∑(q0.10ratτ).
As previously established, at the same value of LRL (LRL = 0.5 in our example), the higher the value of the intermediate threshold temperature tthr, id est, the larger the range of artificially unchangeable load, q0.10-20 compared to q0.10-15, and the more efficient the performance of the SRC with an LRL of 50%; the value of q0.10-20 is closer to q0.10rat/2 compared to q0.10-15 at LRL = 0.5 (Figure 6a). This is also supported by the values of the relative summarized refrigeration energy consumed ∑(q0.10-20τ)/∑(q0.10ratτ) and the corresponding available relative summarized booster refrigeration energy ∑(q0.b10-20τ)/∑(q0.10ratτ) closer to q0.10rat/2 compared to ∑(q0.10-15τ)/∑(q0.10ratτ) and ∑(q0.b10-15τ)/∑(q0.10ratτ) (Figure 6).
As a result, due to the recouping of the refrigeration energy exceedance ∑(q0.10rat/2exτ)<0.5 (Figure 4), the fluctuations of the current subconditioning heat loads (refrigeration capacities) q0.10-20/q0.10rat and corresponding booster preconditioning heat loads (refrigeration capacities) q0.b10-20/q0.10rat, initially characterized by significant deviations (amplitudes), are narrowed by about 1.5 to 2.0 times according to the ratios q0.10-15/q0.10-20 and q0.b10-15/q0.b10-20, respectively. They follow the trend of the relative summarized refrigeration energy consumed ∑(q0.10-20τ)/∑(q0.10ratτ) and q0.b10-20/q0.10rat, but with considerably fewer deviations (amplitudes), similar to those for q0.10-15/q0.10rat and q0.b10-15/q0.10rat (Figure 6).
The results of the refrigeration energy exceedance recuperation for covering the booster preconditioning load q0.20 and q0.15 using the reduced rational refrigeration capacity q0.20rat are presented in Figure 7 and Figure 8.
The following correlations are used: q0.20rat.ex15 = q0.20rat − q0.15, q0.20rat.def15 = q0.15 − q0.20rat, ∑q0.20rat.ex20τ = ∑(q0.20rat − q0.20)τ′, ∑q0.20rat.ex15τ = ∑(q0.20rat − q0.15)τ.
As Figure 7 shows, the rising character of the available summarized exceedance of the refrigeration energy curve ∑(q0.20rat − q0.20)τ ‘ indicates that a design refrigeration capacity of q0.20rat is sufficient not only to offset its actual deficit q0.20 − q0.20rat, but also to enable the deeper cooling of outdoor air to 15 °C from 20 °C by recouping the reserved refrigeration energy ∑(q0.20rat − q0.15)τ at lowered actual heat loads q0.15.
As observed, the actual values of the available exceedance q0.20rat − q0.15 of the rational refrigeration capacity q0.20rat above q0.15 dominate their deficit (lack) q0.15 − q0.20rat.
The practically constant values ∑(q0.20rat − q0.15)τ between 10…13 and 20…26 July demonstrate that the daily values of deficit ∑(q0.15 − q0.20rat)τ are compensated by their values of reserved refrigeration energy ∑(q0.20rat − q0.15)τ. However, the short time-lowering values ∑(q0.20rat − q0.15 )τ during 27 and 28 July reveal the presence of a small daily refrigeration capacity deficit of q0.20rat.
In order to avoid a daily refrigeration capacity deficit of q0.20rat, it is necessary to increase the design refrigeration capacity, for instance, to q0.10rat/2 = 17.5 kW/(kg/s) instead of q0.20rat = 15 kW/(kg/s) (Figure 8).
The following correlations are used: q0.10rat/2.ex15 = q0.10rat/2 − q0.15, q0.10rat/2def15 = q0.15 − q0.10rat/2, ∑q0.10rat/2ex15τ = ∑(q0.10rat/2 − q0.15)τ, ∑q0.20rat.ex15τ = ∑(q0.20rat − q0.15)τ.
The continuously rising character of the available summarized exceedance of the refrigeration energy curve ∑(q0.10rat/2 − q0.15)τ demonstrates that the increased refrigeration capacity q0.10rat/2 compared to q0.20rat is able to cover its actual deficit q0.15 − q0.10rat/2 by the daily recouping of the reserved refrigeration energy ∑(q0.10rat/2 − q0.15)τ at lowered current heat loads q0.10, as well as with a significant monthly exceedance of 5600 kWh/(kg/s) (Figure 8).
Meanwhile, proceeding from the use of q0.20rat as the design refrigeration capacity for conditioning outdoor air to 15 °C instead of q0.15rat (Figure 7), the overall design refrigeration capacity for conditioning outdoor air to 10 °C can be reduced to q0.10red = 25 kW/(kg/s) against q0.10rat = 35 kW/(kg/s), that is, by the value of the difference q0.15rat − q0.20rat = 10 kW/(kg/s) according to Figure 1. In reality, we can use q0.10red = q0.15rat. The results of the calculations are presented in Figure 9.
The following correlations are used: q0.10red = q0.15rat, q0.15rat/2.ex15 = q0.15rat/2 − q0.15, q0.15rat/2def15 = q0.15 − q0.15rat/2, ∑q0.15rat/2ex15τ = ∑(q0.15rat/2 − q0.15)τ, ∑q0.20rat.ex15τ = ∑(q0.20rat − q0.15)τ.
As Figure 9 shows, in the case of applying the value of the refrigeration capacity q0.10/2red = q0.15rat/2 instead of q0.10rat/2, id est, q0.15rat instead of q0.10rat as a design value, within nearly half of a month, the current values of deficit q0.15 − q0.15rat/2 are not covered by the actual values of the available exceedance q0.15rat/2 − q0.15 of the rational refrigeration capacity q0.15rat/2 above q0.15, leading to a reduction in the summarized curve ∑(q0.15rat/2 − q0.15)τ. However, the monthly exceedance of the refrigeration energy ∑(q0.15rat/2 − q0.15)τ = 2000 kWh/(kg/s) is much less than ∑(q0.20rat − q0.15)τ = 3500 kWh/(kg/s) (Figure 9).
The increase in the available summarized exceedance of the refrigeration energy curve ∑(q0.20rat − q0.15)τ indicates that a design refrigeration capacity of q0.20rat is sufficient to cover its actual deficit q0.15 − q0.20rat, even for deeper cooling of outdoor air to 15 °C instead of 20 °C by recouping the reserved refrigeration energy ∑(q0.20rat − q0.15)τ at lowered current heat loads q0.20.
The generalized results on the values of the summarized monthly refrigeration energy exceedance ∑(q0.10rat/2 − q0.15)τ, ∑(q0.20rat − q0.15)τ, and ∑(q0.15rat/2 − q0.15)τ over q0.15 are presented in Figure 10.
The following correlations are used: ∑q0.10rat/2ex15τ = ∑(q0.10rat/2 − q0.15)τ, ∑q0.20rat.ex15τ = ∑(q0.20rat − q0.15)τ, ∑q0.15rat/2ex15τ = ∑(q0.15rat/2 − q0.15)τ.
As Figure 10 shows, in the case of applying the value of the reduced refrigeration capacity q0.10/2red = q0.15rat/2 instead of q0.10rat/2, id est, q0.15rat instead of q0.10rat as a design value, within nearly half of the month, the current values of deficit q0.15 − q0.15rat/2 are not covered by the actual values of the available exceedance q0.15rat/2 − q0.15 of the rational refrigeration capacity q0.15rat/2 above q0.15, and is accompanied by a reduction in the summarized curve ∑(q0.15rat/2 − q0.15)τ. However, with this, the monthly exceedance of the refrigeration energy is the lowest ∑(q0.15rat/2 − q0.15)τ = 2000 kWh/(kg/s) and the lowest value of the level of regulated loading is expected.
The application of the reduced refrigeration capacity q0.20rat for conditioning air to 15 °C instead of q0.15rat 20 °C by recouping the reserved refrigeration energy ∑(q0.20rat − q0.15)τ generally covers the deficit, and is accompanied by the increase in the available summarized exceedance of the refrigeration energy curve ∑(q0.20rat − q0.15)τ, excluding two days (27 and 28 July). With this, the monthly exceedance of the refrigeration energy is ∑(q0.20rat − q0.15)τ = 3500 kWh/(kg/s) and a higher LRL value is expected.
The largest value of the monthly exceedance of refrigeration energy ∑(q0.10rat/2 − q0.15)τ = 5500 kWh/(kg/s) takes place without recouping the reserved refrigeration energy, providing a continuous increase in the summarized curve ∑(q0.10rat/2 − q0.15)τ.
The following correlations are used: q0.10red = q0.15rat, ∑(q0.b10-15ratτ)/∑(q0.15ratτ), ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ), q0.b10-15,20 = q0.10rat − q0.10-15,20; q0.b10-15,20.rat15 = q0.15rat − q0.10-15,20; and the correlations for the developed criteria are: LRL10-15,20 =∑(q0.b10-15,20τ)/∑(q0.10ratτ), LRL10-15,20red = ∑(q0.b10-15,20.rat15τ)/∑(q0.15ratτ).
Figure 11 shows the values of the reduced relative summarized booster refrigeration energy ∑(q0.b10-15ratτ)/∑(q0.15ratτ) ≈ 0.65 at reduced design refrigeration capacity q0.15red =q0.15rat, gained due to recuperation, against their values ∑(q0.b10-15τ)/∑(q0.10ratτ) ≈ 0.75 at q0.10rat without recuperation for tthr = 15 °C and ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ)≈ 0.4 against ∑(q0.b10-20ratτ)/∑(q0.10ratτ) ≈ 0.55 at q0.10rat without recuperation for the artificial air threshold temperature tthr = 20 °C. Thus, due to reserved refrigeration energy recuperation, the design refrigeration capacity is reduced to q0.10red = q0.15rat = 25 kW/(kg/s) against the initial value of q0.10rat = 35 kW/(kg/s), id est, by about 30%.
Furthermore, according to the rising air threshold temperature from the initial value of tthr = 15 °C at q0.10rat without recuperation to the artificial increased value of tthr = 20 °C at reduced design refrigeration capacity q0.10red = q0.15rat with recuperation, the LRL value for the SRC reduces from an initial LRL10-15 = ∑(q0.b10-15τ)/∑(q0.10ratτ) of about 0.75 to LRL10-20red = ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ) of about 0.4.
This conclusion is also supported by the results of the calculation of the current LRL10-15,20red.cur as current relative values of reduced residual booster refrigeration capacities LRL10-15red.cur = q0.b10-15rat/q0.15rat and LRL10-20red.cur = q0.b10-20.rat15/q0.15rat available for conditioning air to 10 °C at tthr = 15 °C and 20 °C, referring to the reduced design refrigeration capacity q0.15rat and the corresponding summarized LRL10-15,20red as reduced summarized refrigeration energy LRL10-15red = ∑(q0.b10-15ratτ)/∑(q0.15ratτ) and ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ), generated according to the reduced value of the design refrigeration capacity q0.15rat (Figure 12).
The following correlations are used: q0.10red = q0.15rat, q0.b10-15rat/q0.15rat, q0.b10-20.rat15/q0.15rat, q0.b10-15rat = q0.15rat − q0.10-15, q0.b10-20.rat15 = q0.15rat − q0.10-20, ∑(q0.b10-15ratτ)/∑(q0.15ratτ), ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ); and the correlations for the developed criteria are: LRL10-15red =∑(q0.b10-15ratτ)/∑(q0.15ratτ); LRL10-20red =∑(q0.b10-20.rat15τ)/∑(q0.15ratτ); LRL10-15red.cur = q0.b10-15rat/q0.15rat; LRL10-20red.cur = q0.b10-20.rat15/q0.15rat.
As Figure 12 shows, the values of the summarized LRL10-15,20red, affected by the current LRL10-15,20red.cur, strictly follow the latter, justifying all of the methodological innovative approaches and revealing the technical solutions, resulting in the enhancement of the obtained output.
Thus, an advanced reserved refrigeration energy recuperation approach to reduce the design refrigeration capacity for a VRF-type ACS and the level of regulated load, id est, SRC operation efficiency, has been developed.

4. Conclusions

An advanced methodology of designing VRF systems with SRCs has been developed to distribute heat flows proceeding from the peculiarities of the different characteristics of heat loads while processing outdoor air, involving changeable loads for the preconditioning of outdoor air to a definite threshold temperature and practically unchangeable loads for further conditioning of the air to a set temperature value.
The methodology makes it possible to reveal the reserves for the enhancement of the SRCs and the operational efficiency of the whole VRF system by recouping the refrigeration energy, reserved at lowered heat loads, to match the current refrigeration consumption at reduced refrigeration capacities.
The methodology helps to determine the values of reduced design refrigeration capacities to provide a continuously increasing growth of the monthly summarized refrigeration energy, reserved at reduced loading.
The recuperation of the reserved refrigeration energy helps to reduce the design refrigeration capacity of the VRF system using SRCs by about 20% for temperate climatic conditions.
Furthermore, under increasing air temperature conditions, limiting the range of the regulated fluctuated loads and narrowing this range through reserved refrigeration recuperation reduces the LRL value of the SRC by almost half.
All of the methodological innovative approaches aimed to enhance the obtained output are justified by the calculations of the current refrigeration capacities and the summarized refrigeration energy characterized the operation efficiency of the VRF systems with SRCs.
It should be noted that all quantitative results were obtained for the specific climatic conditions of the object with minimal assumptions and limitations. Methodological innovative approaches, which are implemented in this work through phenomenological modeling, can be extended and applied to any particular case.
Thus, an advanced approach to reserved refrigeration energy recuperation to reduce the design refrigeration capacity of VRF-type ACSs and the required level of the regulated load, id est, SRC operation efficiency, has been developed.
Further investigations are required to reveal the methodological peculiarities of ACS design to determine the rational refrigeration capacities to avoid oversizing in different climates (European temperate, Mediterranean, Middle East, subtropical, tropical, and other climatic regions) as well as for railway ACSs and engine-intake air cooling including driving engines in trigeneration and marine power plants.

Author Contributions

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

Funding

The project is supported by the program of the Minister of Science and Higher Education under the name: “Regional Initiative of Excellence” in 2019–2023 project number 025/RID/2018/19 financing amount PLN 12,000,000.

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)
dambabsolute humidityg/kg
Gaair mass flow ratekg/s
Q0total refrigeration capacitykW
q0specific refrigeration capacity (per unit air mass flow rate)kW/(kg/s)
q0τspecific refrigeration energy (per unit air mass flow rate)kW/(kg/s)
tambambient (outdoor) air temperatureK, °C
ta2target air temperature K, °C
ξspecific heat ratio of the total heat (latent and sensible) removed from air to sensible heat
τtime intervalh
φambrelative humidity %
Δttemperature decrease K, °C
∑(q0τ)annual (monthly) specific refrigeration energy consumption (per unit air mass rate)kWh/(kg/s)
Subscripts
10, 15, 20air temperatureK, °C
aair
ambambient
bbooster
maxmaximum
ratrational

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Energies 16 01922 g001 550
Figure 1. Specific annual refrigeration energy consumption ∑(q0·τ) and the rational values q0.rat when conditioning air to ta2 = 10, 15 °C, and 20 °C.
Figure 1. Specific annual refrigeration energy consumption ∑(q0·τ) and the rational values q0.rat when conditioning air to ta2 = 10, 15 °C, and 20 °C.
Energies 16 01922 g001
Energies 16 01922 g002 550
Figure 2. 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, and 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. 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, and 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.
Energies 16 01922 g002
Energies 16 01922 g003 550
Figure 3. Actual values of refrigeration capacity consumption q0.10<0.5 and exceedance of rational refrigeration capacity q0.10rat/2ex<0.5 within a range without regulation (q0.10 < q0.10rat/2), monthly summarized values of exceedance ∑(q0.10rat/2τ)ex<0.5: q0.10rat/2ex<0.5 = q0.10rat/2 − q0.10<0.5; ∑(q0.10rat/2τ)ex<0.5 = ∑(q0.10rat/2τ − q0.10<0.5τ)ex<0.5; q0.10rat/2 = 0.5q0.10rat; q0.10<0.5—marked for q0.10 < 0.5q0.10rat.
Figure 3. Actual values of refrigeration capacity consumption q0.10<0.5 and exceedance of rational refrigeration capacity q0.10rat/2ex<0.5 within a range without regulation (q0.10 < q0.10rat/2), monthly summarized values of exceedance ∑(q0.10rat/2τ)ex<0.5: q0.10rat/2ex<0.5 = q0.10rat/2 − q0.10<0.5; ∑(q0.10rat/2τ)ex<0.5 = ∑(q0.10rat/2τ − q0.10<0.5τ)ex<0.5; q0.10rat/2 = 0.5q0.10rat; q0.10<0.5—marked for q0.10 < 0.5q0.10rat.
Energies 16 01922 g003
Energies 16 01922 g004 550
Figure 4. Monthly summarized values of design refrigeration energy exceedance ∑(q0.10rat/2τ)ex<0.5 above consumed values ∑(q0.10<0.5τ) within q0.10 < q0.10rat/2, relative values of summarized exceedance ∑(q0.10rat/2τ)ex<0.5/∑(q0.10rat/2τ), and summarized refrigeration energy consumed ∑(q0.10τ)<0.5/∑(q0.10rat/2τ).
Figure 4. Monthly summarized values of design refrigeration energy exceedance ∑(q0.10rat/2τ)ex<0.5 above consumed values ∑(q0.10<0.5τ) within q0.10 < q0.10rat/2, relative values of summarized exceedance ∑(q0.10rat/2τ)ex<0.5/∑(q0.10rat/2τ), and summarized refrigeration energy consumed ∑(q0.10τ)<0.5/∑(q0.10rat/2τ).
Energies 16 01922 g004
Energies 16 01922 g005 550
Figure 5. Actual values of refrigeration capacities q0.10-15,20 for further conditioning of air from 15 °C and 20 °C to 10 °C and residual booster values q0.b10-15,20 for preconditioning ambient air to 15 °C and 20 °C: q0.10-15,20 = q0.10 − q0.15,20, q0.b10-15,20 = q0.10rat − q0.10-15,20.
Figure 5. Actual values of refrigeration capacities q0.10-15,20 for further conditioning of air from 15 °C and 20 °C to 10 °C and residual booster values q0.b10-15,20 for preconditioning ambient air to 15 °C and 20 °C: q0.10-15,20 = q0.10 − q0.15,20, q0.b10-15,20 = q0.10rat − q0.10-15,20.
Energies 16 01922 g005
Energies 16 01922 g006 550
Figure 6. Relative values of refrigeration capacities q0.10-15,20/q0.10rat for further conditioning of air from 15 °C and 20 °C to 10 °C, and corresponding relative summarized refrigeration energy consumed ∑(q0.10-15,20τ)/∑(q0.10ratτ) (a), relative residual booster refrigeration capacities q0.b10-15,20/q0.10rat and corresponding relative summarized booster refrigeration energy ∑(q0.b10-15,20τ)/∑(q0.10ratτ) (b): (a)—q0.10-15,20; (b)—q0.b10-15,20.
Figure 6. Relative values of refrigeration capacities q0.10-15,20/q0.10rat for further conditioning of air from 15 °C and 20 °C to 10 °C, and corresponding relative summarized refrigeration energy consumed ∑(q0.10-15,20τ)/∑(q0.10ratτ) (a), relative residual booster refrigeration capacities q0.b10-15,20/q0.10rat and corresponding relative summarized booster refrigeration energy ∑(q0.b10-15,20τ)/∑(q0.10ratτ) (b): (a)—q0.10-15,20; (b)—q0.b10-15,20.
Energies 16 01922 g006
Energies 16 01922 g007 550
Figure 7. Actual values of rational refrigeration capacity q0.20rat exceedance q0.20rat − q0.15 above q0.15 and its deficit q0.15 − q0.20rat, and summarized monthly refrigeration energy exceedance ∑(q0.20rat − q0.20 )τ over q0.20 and ∑(q0.20rat − q0.15 )τ over q0.15.
Figure 7. Actual values of rational refrigeration capacity q0.20rat exceedance q0.20rat − q0.15 above q0.15 and its deficit q0.15 − q0.20rat, and summarized monthly refrigeration energy exceedance ∑(q0.20rat − q0.20 )τ over q0.20 and ∑(q0.20rat − q0.15 )τ over q0.15.
Energies 16 01922 g007
Energies 16 01922 g008 550
Figure 8. Actual values of rational refrigeration capacity q0.10rat/2 exceedance q0.10rat/2 − q0.15 above q0.15 and its deficit q0.15 − q0.10rat/2, summarized monthly refrigeration energy ∑q0.10rat/2τ exceedance ∑(q0.10rat/2 − q0.15)τ over q0.15, and summarized refrigeration ∑q0.20ratτ exceedance ∑q0.20rat.ex15τ = ∑(q0.20rat − q0.15)τ over q0.15.
Figure 8. Actual values of rational refrigeration capacity q0.10rat/2 exceedance q0.10rat/2 − q0.15 above q0.15 and its deficit q0.15 − q0.10rat/2, summarized monthly refrigeration energy ∑q0.10rat/2τ exceedance ∑(q0.10rat/2 − q0.15)τ over q0.15, and summarized refrigeration ∑q0.20ratτ exceedance ∑q0.20rat.ex15τ = ∑(q0.20rat − q0.15)τ over q0.15.
Energies 16 01922 g008
Energies 16 01922 g009 550
Figure 9. Reduced rational value q0.10red = q0.15rat for conditioning outdoor air to 10 °C using reserved refrigeration energy, actual refrigeration capacities q0.15 needed for conditioning outdoor air to 15 °C, reduced refrigeration capacity q0.15rat/2 exceedance q0.15rat/2 − q0.15 above q0.15 and its deficit q0.15 − q0.15rat/2, summarized monthly refrigeration energy exceedance ∑(q0.15rat/2 − q0.15)τ and ∑(q0.20rat − q0.15)τ over q0.15.
Figure 9. Reduced rational value q0.10red = q0.15rat for conditioning outdoor air to 10 °C using reserved refrigeration energy, actual refrigeration capacities q0.15 needed for conditioning outdoor air to 15 °C, reduced refrigeration capacity q0.15rat/2 exceedance q0.15rat/2 − q0.15 above q0.15 and its deficit q0.15 − q0.15rat/2, summarized monthly refrigeration energy exceedance ∑(q0.15rat/2 − q0.15)τ and ∑(q0.20rat − q0.15)τ over q0.15.
Energies 16 01922 g009
Energies 16 01922 g010 550
Figure 10. Rational values of refrigeration capacities q0.10rat, q0.15rat, and q0.20rat for conditioning outdoor air to 10 °C, 15 °C, and 20 °C, respectively, and summarized monthly refrigeration energy exceedance ∑(q0.10rat/2 − q0.15)τ, ∑(q0.20rat − q0.15)τ, and ∑(q0.15rat/2 − q0.15)τ over q0.15.
Figure 10. Rational values of refrigeration capacities q0.10rat, q0.15rat, and q0.20rat for conditioning outdoor air to 10 °C, 15 °C, and 20 °C, respectively, and summarized monthly refrigeration energy exceedance ∑(q0.10rat/2 − q0.15)τ, ∑(q0.20rat − q0.15)τ, and ∑(q0.15rat/2 − q0.15)τ over q0.15.
Energies 16 01922 g010
Energies 16 01922 g011 550
Figure 11. Values of relative summarized booster refrigeration energy ∑(q0.b10-15τ)/∑(q0.10ratτ) and ∑(q0.b10-20τ)/∑(q0.10ratτ) available for conditioning air to 15 °C and 20 °C, reduced summarized refrigeration energy ∑(q0.b10-15ratτ)/∑(q0.15ratτ) and ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ), generated according to reduced value of design refrigeration capacity q0.15red = q0.15rat.
Figure 11. Values of relative summarized booster refrigeration energy ∑(q0.b10-15τ)/∑(q0.10ratτ) and ∑(q0.b10-20τ)/∑(q0.10ratτ) available for conditioning air to 15 °C and 20 °C, reduced summarized refrigeration energy ∑(q0.b10-15ratτ)/∑(q0.15ratτ) and ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ), generated according to reduced value of design refrigeration capacity q0.15red = q0.15rat.
Energies 16 01922 g011
Energies 16 01922 g012 550
Figure 12. Actual relative reduced booster refrigeration capacities q0.b10-15rat/q0.15rat and q0.b10-20.rat15/q0.15rat available for conditioning air to 10 °C at threshold temperatures of tthr = 15 °C and 20 °C and corresponding reduced summarized refrigeration energy ∑(q0.b10-15ratτ)/∑(q0.15ratτ) and ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ), generated according to reduced design refrigeration capacity q0.10red = q0.15rat.
Figure 12. Actual relative reduced booster refrigeration capacities q0.b10-15rat/q0.15rat and q0.b10-20.rat15/q0.15rat available for conditioning air to 10 °C at threshold temperatures of tthr = 15 °C and 20 °C and corresponding reduced summarized refrigeration energy ∑(q0.b10-15ratτ)/∑(q0.15ratτ) and ∑(q0.b10-20.rat15τ)/∑(q0.15ratτ), generated according to reduced design refrigeration capacity q0.10red = q0.15rat.
Energies 16 01922 g012
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MDPI and ACS Style

Radchenko, M.; Radchenko, A.; Trushliakov, E.; Koshlak, H.; Radchenko, R. Advanced Method of Variable Refrigerant Flow (VRF) Systems Designing to Forecast Onsite Operation—Part 2: Phenomenological Simulation to Recoup Refrigeration Energy. Energies 2023, 16, 1922. https://doi.org/10.3390/en16041922

AMA Style

Radchenko M, Radchenko A, Trushliakov E, Koshlak H, Radchenko R. Advanced Method of Variable Refrigerant Flow (VRF) Systems Designing to Forecast Onsite Operation—Part 2: Phenomenological Simulation to Recoup Refrigeration Energy. Energies. 2023; 16(4):1922. https://doi.org/10.3390/en16041922

Chicago/Turabian Style

Radchenko, Mykola, Andrii Radchenko, Eugeniy Trushliakov, Hanna Koshlak, and Roman Radchenko. 2023. "Advanced Method of Variable Refrigerant Flow (VRF) Systems Designing to Forecast Onsite Operation—Part 2: Phenomenological Simulation to Recoup Refrigeration Energy" Energies 16, no. 4: 1922. https://doi.org/10.3390/en16041922

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