Method Article – Title PageTitle Computational tools for a new hybrid air conditioning system in hot-dry climate

Authors Yang Yang, Chengqin Ren*, Zhao Wang, Baojun Luo

AffiliationsState Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China

Corresponding Author’s email address renchengqin@163.com

KeywordsHeat exchanger net; Distributed-parameter method; Evaporative cooling; Mechanical vapor compression cycle; MATLAB/SIMULINK

Direct Submission or Co-Submission

Co-submissions are papers that have been submitted alongside an original research paper accepted for publication by another Elsevier journal

Co-Submission

Theoretical performance analysis of a new hybrid air conditioning system in hot-dry climate, International Journal of Refrigeration (2020), DOI: https://doi.org/10.1016/j.ijrefrig.2020.03.015. [21]

ABSTRACTWith the shortage of fossil energy and the intensification of environmental pollution, building energy conservation has received more and more attention, especially HVAC. From the perspective of energy saving, the new air-conditioning system concept tends to complicate the structure and heat exchangers network. Traditional experimental researches are time-consuming and costly, thus, it is necessary to develop corresponding computational tools for the hybrid air-conditioning system. Ren proposed a patented hybrid air-conditioning system based on two patents (CN201310055011, CN201710082365). In order to quickly and detailedly analyze the conceptual design of the hybrid system, a complete computer model was established in MATLAB/SIMULINK. The computational program has the following characteristics:

It reflects the coupled relationship of the complex heat exchangers network in the hybrid air-conditioning system in hot-dry climates. It involves two typical and common cooling cycles: a mechanical vapor compression cycle and an external cooling dew-point evaporative

cooling cycle. It contains the distributed-parameter sub-model of all heat exchangers with maximum experimental deviation of 7.5%, and the sub-models

can be used alone or in other hybrid air-conditioning systems with complex heat-exchanger networks.

SPECIFICATIONS TABLE

Subject Area Engineering

More specific subject area Heating, Ventilation and Air Conditioning (HVAC)

Method name Distributed-parameter-method-based global solution method (DPGSM) for heat exchanger network of hybrid air-conditioning system

Name and reference of original method

Distributed parameter method: C.Q. Ren. An Analytical Approach to the Heat and Mass Transfer Processes in Counterflow Cooling Towers. Journal of Heat Transfer 128 (2006) 1142-1148 [17] and C.Q. Ren, H.X. Yang. An analytical model for the heat and mass transfer processes in indirect evaporative cooling with parallel/counter flow configurations. International journal of heat and mass transfer 49 (3-4) (2006) 617-627[19]

Resource availability Please see the model verification section in this paper

Method details

Overview of method

Conventional AC system performance simulation involves the modeling of the compressor, evaporator, condenser and expansion devices. Usually, expansion devices and compressors are modeled [1-4] based on empirical correlations. However, different methods have been proposed to simulate the heat and fluid flow in heat exchangers in the AC systems. LMTD or effectiveness-NTU method is used for some simplified models [5,6]. In order to improve the simplified model accuracy, it is suggested to divide the exchangers into different phase regions [7]. But their prediction accuracy are still compromised due to the coexistence of sensible and latent heat transfers, non-uniformity of heat transfer coefficient and partially wetted coils. For more accurate predictions, the distributed parameter method is preferred in either dynamic [8-10] or steady-state [11-13] processes, in which the entire heat exchanger are divided into a number of (finite) control volumes (CVs) and the reasonable number of the CVs can be between 20 and 40 [14].

Different models were also developed by many researchers for evaporative coolers, including the Merkel method, the effectiveness-NTU method and the distributed parameter method. The earliest Merkel method applied to the prediction of the overall thermal performance of cooling towers [15]. It is based on the assumptions of unit Lewis number; fully saturated air at tower exit; neglecting the reduction of water flow rate due to evaporation; and assuming the specific heat capacity of the air-vapor mixture is the same as that of the dry air. Jaber and Webb [16] applied the effectiveness-NTU method for evaluation of the performance of counter flow or cross flow cooling towers. This method relies on the same simplifying assumptions as mentioned in the Merkel method. Some researchers [15,17,18] proposed a few modifications for the Merkel assumptions and the effectiveness-NTU method to improve the prediction accuracy. For details of heat and mass transfer process and better prediction accuracy, distributed parameter method [13,19,20] is also preferred not only for cooling towers but also for other types of evaporative cooling heat exchangers, including direct and indirect evaporative coolers.

Recently, Ren proposed a patented design of a hybrid air conditioning (HAC) system (CN201710082365, CN201310055011) as shown in Fig. 1 in order to synergically incorporate external cooling dew-point evaporative cooling technologies with mechanical vapor compression system. The hybrid air-conditioning system has a complex heat-exchanger network, which involves three types of heat/mass exchange equipment: air-to-water heat exchange finned coils, packed bed heat exchanger, and air-to-refrigerant heat exchange finned coils. By the way, also in HAC, two cooling cycles are formed: water cycle and refrigerant cycle. In hot-dry climate conditions, the hybrid air-conditioning system can realize parallel or serial treatment for fresh air by switching the heat-exchanger network. The computational tools of the two treatment modes of HAC, parallel (HAC-P) and serial (HAC-S), are completed in MATLAB/SIMULINK, which is to perform the theoretical performance research in a fast and detailed way. In the computational tools, all heat exchanger sub-models are modeled using the distributed-parameter method and individually packaged in SIMULINK, which is conducive to building other complex heat exchanger networks.

Brief description of the hybrid air-conditioning system

As is seen from Fig. 1a, the HAC system has a compressor, an outdoor heat exchanger unit (OHU), and two parallel-connected refrigerant evaporators, i.e., an indoor air-handling unit (IAU) and a heat exchanger HE5 installed in FAC. By referring to Fig. 1b, it can be further seen that the FAC contains two boxes, one is the exhaust air box and another is the fresh air box. Both boxes are connected by cycling water pipes. Two heat exchangers (HE1 and HE3) are placed in the exhaust air box. HE1 is the packed bed heat exchanger, where circulation water is in direct contact with the exhaust air. HE3 is a fin-tube coil type air-to-water heat exchanger. In the fresh air box, there are three heat exchangers, two fin-tube coil type air-to-water heat exchangers (HE2 and HE4) and a refrigerant coil heat exchanger HE5. A high-pressure sprayer is placed before the HE2 and HE4 for humidifying the fresh air. In addition, a bypass controlled by the air valve AV3 is designed for handling fresh air in two parallel passages. In real equipment design, the HE2 and HE4 channels can be simply separated by a flat plate and there is no real horizontal ducts on both sides of the AV3. Under hot-dry climates, the sprayer system is ON and the HE5 is OFF. HAC has two operation modes for treating fresh air, a series mode (HAC-S) and a parallel mode (HAC-P). Table 1 shows the different component status for the two modes. Fig. 2 illustrates the equivalent system structure and the psychometric diagram of air handling processes in HAC-S and HAC-P. The components and connecting pipes shown in gray dotted lines are inactive. For a detailed introduction, please refer to our other work [21].

TV1-TV2—Throttle valve; RV1,RV2—Reversing valve; L1-L6—Refrigerant pipelines; OHU—Outdoor heat exchanging unit; IAU—Indoor air-handling unit

HE1 Packed bed cooling tower V1,V2 Water valveHE2,HE3,HE4 Air-to-water coils MV1-MV3 Three-way water valveHE5 Air-refrigerant coils AV1-AV3 Air valveP1-P3 Water pump RA,R2,EA States of exhaust airFA,FS,F2,SA1,SA2 States of fresh air A,B,C,D Water flow nodes

Fig. 1: (a) The overall structure of the hybrid air conditioning system (HAC) [CN201710082365], (b) The design of hybrid fresh air conditioner (FAC) [CN201310055011].

Table 1: Component status information of HAC-S and HAC-PComponent HAC-S HAC-P Componen

tHAC-S HAC-P

AV1 OFF ON MV1 a3→a1 a2→a3AV2 ON OFF MV2 a2→a3 a3→a1AV3 OFF ON MV3 a1/a2→a3 a1/a2→a3P1 ON ON V1 ON ONP2 OFF OFF V2 OFF ONP3 ON ON

Fig. 2: The equivalent system structure and air-path psychometric diagram of the HAC-S and HAC-P under hot-dry climates

Mathematical model

Assumptions

The basic assumptions for the modelling of the air-to-refrigerant coils, the packed bed and the air-to-water coils can be referenced to the literatures of Jia et al.[9], Ren [17] and Ren and Yang [19] respectively. Additionally, the following assumptions are made as well:

(1) Superheat (SH) and subcooling (SC) of refrigerant in mechanical compression refrigeration cycle are fixed.(2) Pressure drop of the refrigerant inside all heat exchangers is neglected.(3) Heat transfer process only occurs in heat exchanges.(4) Neglect heat transfer resistance of the metal tube walls, condensate water films and the air-water interfaces in the heat exchangers.(5) Lewis number is equal to unit.(6) Process for refrigerant in the electronic expansion valve are isenthalpic.

Air-to-refrigerant colis (evaporator and condenser)

The model presented in literature [9] is adapted in its steady-state form for the evaporators and condensers based on the same mass and energy conservation principles as follow:

mr d hr=U r d A i (t r−ttw ) (1)

ma c pad t a=U a d Ao (t a−t tw ) (2)

ma d wa=U a

C pad Ao ( wa−w tw )

(3)

mr d hr=mac pa d t a+ma hfg d wa (4)

Where, Ai , Ao are the heat exchange area of the tube- and fin-side of the finned coils (m2) respectively. mr , ma are refrigerant and air flowrate

(kg s-1) respectively. U r ,U a are the convective heat transfer coefficient (W m-2 K-1) in refrigerant- and air-side respectively. c pa is the specific

heat for air at constant pressure (J kg-1 K-1). t a ,wa are the air temperature (℃) and humidity (g kg-1). hr is the specific enthalpy of refrigerant (J

kg-1). h fg is the specific enthalpy of water evaporation (h fg=2501−2.32 t aJ kg-1). The saturation humidity ratio of air at tube wall

temperature w tw is a monotonic function of the tube wall temperatures t tw and function w tw(t tw) can be fitted as polynomial function before simulation based on water properties, the refrigerant-side (tube-side) heat transfer coefficient is calculated based on the correlations of Dittus and Boeler [22], Gungor and Winterton [23] and Shah [24] for single-phase flow, boiling evaporation and condensation respectively. On the air side, the heat transfer coefficient correlation presented by Wang et al. [25] is used. The above four equations control the variations of the four free model parameters hr , t a, wa and t tw.

Packed cooling tower

For the counter-flow packed cooling tower, it is divided into several equal-volume control volumes (CVs) in the vertical direction. For both air and water in each CV, the energy and mass conservation differential equations presented by Ren [17] are used.

d t a=−d NTU m¿ (5)

d wa=−d NTU m¿ (6)

d mw=ma d wa (7)

ma d ha=c pw d ( mw tw ) (8)

Where, mw is the water flowrate (kg s-1). c pw is the specific heat for water at constant pressure (J kg-1 K-1). The saturation humidity ratio of air

at the interface w∫¿¿ (g kg-1)is also a monotonic function of the interface temperatures t∫¿¿ (℃) and the function is the same as w tw (t tw). The

dimensionless parameter NTU m (=Um α Lp

ρa ua) is the number of mass transfer units in packed tower, in which, Um is convective mass transfer

coefficient (kg m-2 s-1), α is the specific surface area of the packed material (m2 m-3), Lp is the thickness of packing (m), ρa is the air density (kg

m-3) and ua is the frontal velocity (m s-1) of the packed tower. The above four equations control the variations of the four free model parameters:

t a,wa, mw, tw.

Air-to-water coils

For the air-water coils, the energy and mass conservation equations for air and water presented in literature [19] are adapted as follow:

d t a=−d NTU (t tw−t a) (9)

d wa=−d NTU (wtw−wa ) (10)

d tw=d NTU w (t tw−tw ) (11)

mw c pw d tw=mac pa d t a+ma hfg d wa (12)

Where, w tw is also determined by the fitted equation w tw (t tw ) as mentioned above. The dimensionless parameters NTU (¿U a Ao

mac pa) and

NTU w (¿Uw A i

mwc pw) are the numbers of air and water side heat transfer units respectively for the fin-coil heat exchangers. The above four

equations control the variations of the four free model parameters t a, wa, tw and t tw.

Compressor

The power consumption of the compressor is given by:

W c=mc,∈¿ ¿¿¿ (13)

Where, the total mechanical and electrical drive efficiency of the compressor ηc , t, often being expressed as the product of the inverter efficiency, motor efficiency, mechanical transmission efficiency, and friction efficiency, is taken as 0.85 here. The isentropic compression efficiencyηc , is can be calculated by following empirical correlation [26]:

ηc , is=0.991−0.112( Pout

P¿)

0.714

(14)

Fan and pump

Fan and pump power consumptions can be calculated by the following equations:

W fan=ma ∆ pa

ρa ηfan,W pump=

mw ∆ pw

ρwη pump

(15)

Where, the efficiencies of fan and pump (η fan , ηpump) are taken as 0.25 and 0.3 respectively. In addition, the power consumption of the spray system pump in FAC can be neglected.

For refrigerant evaporator and condenser, fin-side pressure drops are evaluated based on the correlation of Wang et al. [25]. For the packed-bed and air-side of the air-to-water coils, Chilton-Colburn analogy and Darcy equation are used to obtain the relation between the numbers of the heat/mass transfer units (NTU , NTU w, NTU m) and the pressure drops (Δ𝑝). The relevant equations are listed in Table 2. In addition, In FAC, considering all the additional pressure drops caused by ducts, valves or air vent residual pressures, the fan or pump head is taken as 1.2 times the total pressure drop caused by the heat exchangers along the air or water flow path.

Table 2: Correlations of pressure drop based on Chilton-Colburn analogy and Darcy equationItems Equations No.

Chilton-Colburn analogy [27]C f

2= jH= jm (16)

Darcy equation ∆ p=4C fld

ρu2

2 (17)

Packed-bed ∆ pa=kap NTU m Pra

23 ρaua

2 (18)

Air-side of air-to-water coils ∆ pa=kac NTU Pra

23 ρa umax

2 (19)

Water-side of air-to-water coils ∆ pw=kwc NTU w Prw

23 ρw uw

2 (20)

Note: Coefficients (k ac , kwc) are fitted as 2.3 and 2.5 respectively based on some literature [25] data for

different geometric sizes. Coefficient k ap is fitted as 6.5 based on manufacturer data of CELdek with different geometric sizes.

In Table 2, the equs. (18)-(20) are derived from the Chilton-Colburn analogy (Equ. (16)) and Darcy equation (Equ. (17)). Since the derivation process are similar, only the equation of the air-side of the air-to-water coils (Equ. (19)) is given as an example.

According to Colburn analogy and Darcy equation:

jH=St ×Pr23= U

ρ umax CpPr

23

(21)

∆ pa=4C fLdh

ρ umax2

2

(22)

Where, C f is Fanning friction coefficient, jH is Colburn j factors for heat transfer respectively, St is Stanton number, Pr is Prandtl number,

Sc is Schmidt number, U is Heat and mass transfer coefficient respectively, umax is the maximum air velocity of finned tube. ∆ pa is air flow

pressure drop, L is length, dh is the hydraulic diameter.

The Stanton number St also can be written:

St= hρ umax C p

A tot

Ah

Ah

A tot=

h A tot

ma Cp

Ah

Atot=NTU

Ah

Atot

(23)

Where, Atot is total heat exchange area of the finned coils, Ah is the minimum flow cross-sectional area corresponding to the maximum air

velocity umax .

It is assumed that the air flow is a tube-type flow. Therefore, the hydraulic diameter dh of the flow channel can be written as:

dh=4 Ah

Ch=

4 Ah LCh L

=4 Ah L

A tot

(24)

Where, Ch is the circumference.

Then:

Ah

A tot=

dh

4 L

(25)

Substituting Equs. (23) and (25) into Equ. (16) to get:

C f

2= jH=St × Pr

23=NTU

dh

4 LPr

23

(26)

Then, substituting Equs. (26) into Equ. (22) to get:

∆ pa=4C fLdh

ρ u2

2=4× 2NTU

dh

4 LPr

23 L

dh

ρu2

2=NTU Pr

23 ρu2

(27)

Finally, considering the errors caused by the assumption of tube-type flow, a correction factor is introduced:

∆ pa=kac NTU Pr23 ρ u2

(28)

The coefficient k ac can be fitted based on the experimental data/correlations of some common heat exchangers.

Model solution

For all heat exchangers, including the packed bed (HE1), air-water coils (HE2, HE3, HE4) and air-refrigerant coils (HE5, IAU, OHU), solution schemes of the distributed parameter models described in literatures [17,19] are applied. All heat exchangers are discretized into at least 30 control volumes. Thermo-physical properties for the working refrigerant, R410a, are obtained using REFPROP [28] subroutines from NIST.

For air-refrigerant coils, Equs. (1)-(4) are the control equations and mr .∈¿ ,ma .∈¿ , ta.∈ ¿ ,wa.∈¿ ,hr .∈¿ , p¿ ¿¿¿¿ are input parameters, while hr , t a, wa and t tw

distributions and their outlet values are determined through iteration. For the packed-bed, Equs. (5)-(8) are the control equations and ma .∈¿¿,

mw .∈¿¿, t a .∈¿¿, wa .∈¿¿, tw .∈¿¿, NTU m are input parameters, while t a, wa, mw and tw distribution and their outlet values are determined

through iteration. For air-water coils, Equs. (9)-(12)are the control equations and ma .∈¿¿, mw .∈¿¿, t a .∈¿¿, wa .∈¿¿, tw .∈¿¿, NTU , NTU w

are input parameters, while t a, wa, tw and t tw distributions and their outlet values are determined through iteration. In solution for compressor outlet parameters, its inlet pressure, enthalpy, mass flow rate, and outlet pressure are taken as the corresponding outlet or inlet parameters of the adjacently connected parts.

Overall solution procedure for the whole air conditioning system is shown in Fig. 3. In Fig. 3, the input parameters for the computational tools include operating parameters and design parameters of the hybrid air conditioning system. The operating parameters include ambient temperature t am and humidity wam, air-conditioned room information (including the heat transfer coefficient of envelope structure, indoor heat

load density, and set values of room temperature tRA and humidity wRA), and air and water flowrate of each heat exchanger in FAC. The

design parameters involve three dimensionless parameters (NTU , NTU w ,NTU m) and the structural parameters of the air-to-refrigerant

coils. Another thing to note is that the IAU Load (Q IAU) in MVC system can be calculated by the equation of

Q IAU=QAC .sen−mFA c pa (tFA−t SA ), in which, the QAC . sen is the total sensible heat load of hybrid air-conditioning system (W), and the

mFA c pa ( tFA−t SA ) is the sensible cooling load handled by FAC.

Fig. 3. The solution flow chart of the HAC

Model validation

According to Fig. 1, the hybrid air-conditioning system (HAC) can be clearly divided into three parts (mechanical compression cycle, packed bed and air-to-water finned coils), which indicates that the overall system verification can be also divided into the three parts. In other words, all local characteristics of the HAC can also reflect its overall characteristics.

Simulated mechanical compression cycle (MVC) performances based on the general model and the simulation program developed for HAC in this article are compared with experimental data [29]. Both simulated and experimental data of evaporating and condensing temperatures and COP for MVC are shown in Fig. 4. The model input parameters of the cases for simulation and comparison not shown in Fig. 4 are as follow: the evaporator and condenser inlet temperatures are 27℃ and 35℃ respectively; the air velocities flowing through the evaporator and the condenser are 1.14 (m s-1) and 1.35 (m s-1) respectively; both the superheat and subcooled degrees of the refrigerant are 2K; and the system cooling capacity varies between 0.5 KW and 4 KW for a rated cooling capacity of 3.5 KW. The relative error is calculated as

e (%)=|exp−¿|exp

×100 %. It is evident from Fig. 4a that the discrepancy between the predicted and experimental values for both the

evaporation and condensation temperatures are less than 5%. From Fig. 4b, it can be see that the discrepancy between the predicted and experimental values for COP are less than 7% except for the cases with the cooling capacity less than 1.2kW. The discrepancy for exceptional cases with low compression ratio may be caused by the deteriorated lubrication conditions and the aggravated friction losses in the experimental

setup and so the total compressor efficiency ηc , t in this article can be corrected by an additional fitted coefficient (2.67pout

p¿−3.1), in which,

p¿ , pout are the compressor suction and discharge pressure respectively.

Fig. 4. Comparison between the simulated results and experimental data: (a) Evaporation and Evaporation and condensation temperature (b) COP

For the experimental verification of packed-bed cooling tower, the experimental data of R-1 type cooling tower (CT) [30] is used. The

number of mass transfer unit of R-1 type CT can be calculated by fitted equation of NTU m=1.6( mw

ma)−0.341

[30] (mw , ma are the mass

flow of water and air respectively). The test range of water inlet and air inlet temperature are 28.72-47.78℃ and 28.83-37.06℃ respectively, which means that the experimental data can fully reflect the performance of the cooling tower under hot and humid conditions. As seen from Fig. 5a and Fig. 5b, the temperature error of water outlet and air outlet are both less than 7.5%. Considering the error of the experiment itself and correlation of NTU m, ± 7.5% is an acceptable error range.

(a) (b)

Fig. 5. The experimental verification of packed bed cooling towerWater outlet temperature, (b) Air outlet temperature

For the experimental verification of air-to-water heat exchanger finned coils, the experimental data, structure and ambience parameters are come from the literature [31], and the test experiment includes both the wet condition and dry condition. In addition, the heat transfer coefficient of the air-side and water-side in this paper are calculated respectively by the correlations of [25] and [32], which are used to calculate the number of heat or mass transfer unit (NTU , NTU w). As seen from Fig. 6a and Fig. 6b, the temperature error of water outlet and air outlet are less

than 5% and 7.5% respectively. Considering the error of the experiment itself and heat exchange correlations, both of the ±5% and ± 7.5% are the acceptable error range.

Fig. 6. The experimental verification of outlet air temperature of air-water surface type heat exchangeroutlet air temperature, (b) outlet water temperature

Declaration of interests:

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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