- Email: [email protected]
Investigation on the performance and optimization of heat pump water heater with wrap-around condenser coil
International Journal of Heat and Mass Transfer 143 (2019) 118556
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Investigation on the performance and optimization of heat pump water heater with wrap-around condenser coil Qiang Ye, Shuhong Li ⇑ School of Energy and Environment, Southeast University, Nanjing 210096, China
a r t i c l e
i n f o
Article history: Received 17 February 2019 Received in revised form 6 August 2019 Accepted 9 August 2019
Keywords: Heat pump water heater Heat transfer Optimization Coupled model Variable/constant-pitch coil Heat flux
a b s t r a c t A numerical investigation on the performance of heat pump water heater (HPWH) with wrap-around condenser coil was carried out. In this study, a coupled model was developed to simulate the static energy storage process of HPWH, which consisted of a multi-heat flux CFD model to describe the flow and heat transfer in water tank and a vapor-compression system model established in MATLAB to simulate the system operation characteristics. Heat flux in superheated steam, two-phase flow, and subcooled liquid regions of the condenser was obtained from the system model as boundary conditions of water tank model. The simulation results of the coupled model were in good agreement with experimental results. Heat transfer coefficient, COP and water temperature distribution of variable-pitch and constant-pitch coil were obtained by simulation. The results indicated that the heat transfer coefficient and average COP of variable-pitch coil were increased by 21.91% and 10.75% respectively, compared with constant-pitch coil. In addition, it was found that by appropriately reducing spiral pitch and coil diameter, average water temperature was increased by about 1 °C and maximum temperature difference in the vertical direction was no more than 7.50 °C. This work provides meaningful guidance for performance optimization of heat pump water heater. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Water heating accounts for a significant part of buildings energy consumption [1,2]. Heat pump water heater (HPWH) has outstanding advantages in energy saving, and many countries attach great importance to its promotion and application [3,4]. Investigating and optimizing the heat transfer process between condenser and water is conducive to improving the thermal stratification within the water tank [5]. According to the heat transfer between condenser coil and water, the condenser can be divided into wrap-around coil and immersed coil [6]. Compared with the immersed coil, the wrap-around coil has no direct contact with water, so it has no scaling and corrosion problems. Therefore, the wrap-around coil is mostly used in the current HPWH products in the market. At present, the research on HPWH mainly involves system cycle, working fluid, component design, control and operation optimization, etc [7–11]. For component design, condenser coil and water tank are the research focus. For HPWH with the wrap-wound coil, optimizing the coil structure and the wrap-around form is important for improving the
⇑ Corresponding author. E-mail address: [email protected] (S. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118556 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
temperature stratification in the tank and the system performance. Park and Hrnjak [12] experimentally investigated the performance of a microchannel condenser and a round-tube condenser, and the results showed that the COP and heat flux of the microchannel condenser were higher than those of the round-tube condenser. Wang [13] found by simulation that reducing the condenser coil diameter and increasing the spiral diameter could improve the system performance. Yang, Shao and Zhang [14] found that the heat transfer performance of refrigerant in condenser coil could be slightly improved by changing the coil sectional structure. However, although the condenser coil structure is changed, the heat transfer resistance is not effectively reduced, and the temperature stratification in water tank temperature is still obvious. Therefore, the coil wrap-around form should be further optimized. In order to research the thermal performance of water tank, the simulation method is often used to study the temperature distribution in water tank [15–17]. When using computational fluid dynamics (CFD) software package to establish water tank model, reasonable boundary conditions are set to obtain accurate simulation results. In general, the boundary conditions such as constant wall temperature or constant heat flux are adopted [18,19]. Jayakumar et al. [20] suggested that more reasonable boundary conditions should be adopted, such as those that vary with heating time or water temperature. Lv et al. [21] considered
2
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Nomenclature A Cp,w Dt dc g Hc Ht h hc Lc m N Nu P Q q Ra R T t U u Vt Vh
vs
W x y
area, m2 specific heat of water, J/(kgK) diameter of water tank, m diameter of condenser tube, m gravitational acceleration, m/s2 coil height, m height of water tank, m refrigerant enthalpy, J/kg coil pitch, mm total length of condenser coil, m mass flow rate, kg/s number of turns Nusselt number pressure, Pa heat energy, W heat flux, W/m2 Rayleigh number thermal resistance temperature, °C time, min overall heat transfer coefficient, W/(m2K) velocity, m/s volume of water tank, L theoretical displacement volume, m3/h suction specific volume, m3/kg input power of compressor, W horizontal direction in master coordinate vertical direction in master coordinate
that the condensation temperature was constantly changing, so the boundary condition was set as variable wall temperature. Dai and Li [22] fitted the polynomial of the average heat flux of the condenser coil varying with heating time as the boundary condition. However, there are superheated steam, two-phase flow and subcooled liquid regions in the condenser, so the heat flux between the upper and lower parts of the condenser coil is not equal. Therefore, it is necessary to divide the heat transfer boundary condition into three parts to set for optimizing the CFD model of water tank, so that the model can accurately simulate the actual heating process of water tank. Coupling heat pump system model with water tank CFD model is a new simulation method [22–24]. Dai and Li [22] established a coupled model including heat pump system model and water tank model for domestic HPWH, and simulated the heating process of water tank. Shah and Hrnjak [23] also established a coupled model, which well simulated the system operation process and the transient heating process in water tank. Therefore, specific attention is attached to the development of a coupled model consisting of a multi-heat flux CFD model of water tank to capture the heat transfer in tank and a vapor-compression system model established in MATLAB to obtain the system operating parameters. Heat flux in the superheated steam, two-phase flow, and subcooled liquid regions of the condenser is obtained from the system model as boundary conditions. Then the heat transfer coefficient, COP and water temperature distribution are obtained by simulation. The coupled model is used to investigate the influence of different wrap-around condenser coil structure designs on the operating performance of HPWH, so as to obtain the optimum coil structure to improve the heat transfer process between condenser and water, and the system performance.
Greek symbols heat transfer coefficient, W/(m2K) b thermal expansion coefficient, 1/K g efficiency k thermal conductivity, W/(mk) l viscosity, kg/(ms) m kinematic viscosity, m2/s q variable density of water, kg/m3 qw0 constant density of water, kg/m3
a
Subscripts a air c condenser co compressor e evaporator ev expansion valve i inlet o outlet r refrigerant sc subcooled sh superheated t tank tp two phase w water Abbreviations CFD computational fluid dynamics COP coefficient of performance HPWH heat pump water heater
2. System description HPWH system mainly consists of a vapor-compression system and a water heating system, including compressor, water tank with wrap-around condenser, expansion valve and evaporator. The condenser coil is wound around the tank wall, and the condensation heat is transferred from the tube to the tank for heating water. The structure schematic diagram of water tank with wraparound constant/variable-pitch coil is shown in Fig. 1. And the main structural parameters are illustrated in Table 1. The rationale for determining hc,i is as follows: First, ensure that the variable-pitch coil structure and the constant-pitch coil have the same number of turns, coil height, total length, and tube diameter. Then, in order to regularly change the coil pitch, a linear equation (y = a + bx) is used to express hc,i. Finally, based on the above basic principles, several groups of numerical combinations of a and b are selected to simulate and output the temperature distribution of the water tank. Through comparison and analysis, the optimal numerical combination is determined to obtain the equation of hc,i. 3. Coupled method During the energy storage process of HPWH, the water temperature distribution parameters and the system operating parameters interact with each other. The system performance is affected by water temperature and refrigerant distribution in the condenser. As shown in Fig. 2, through the heat transfer process between the condenser coil and the water tank, heat is transferred from the condenser to the tank to heat water. The heat transfer performance of the condenser affects the heating process on the
3
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Dt
Dc
Ht
Hc
hc,i hc
Fig. 1. Structure of water tank with wrap-around constant/variable-pitch coil.
Table 1 Main structural parameters of water tank with constant/variable-pitch coil. Component
a
Structural parameter
Symbol
Value Constant-pitch
Variable-pitch 0.010 0.012 hc,ia 28 0.70 35
Condenser coil
Inner diameter of tube (m) Outer diameter of tube (m) Coil pitch (m) Number of turns Coil height (m) Total length (m)
dc,i dc,o hc N Hc Lc
0.010 0.012 0.01 28 0.70 35
Water tank
Volume of tank (L) Diameter of tank (m) Height of tank (m)
Vt Dt Ht
150 0.40 1.20
hc,i = 0.015 + nd0,(d0 = 0.0003, 0 n 27).
water side. At the same time, the water temperature distribution in turn affects the convective heat transfer process of the refrigerant in the condenser. The CFD model of water tank can simulate the flow and heat transfer process of water tank, but only reflects water temperature and velocity distribution in the tank. The MATLAB model of HPWH can simulate the vapor-compression system, but only outputs the system operating parameters. In order to analyze the characteristics of water temperature distribution and the system performance in the heating process, it is necessary to establish the system model and the water tank model respectively. Through the heat transfer process between the refrigerant in the condenser and the hot water in the water tank, the coupled model based on the heat pump cycle and the heat transfer of the condenser coil is established. There are superheated steam, two-phase flow and subcooled liquid regions in the condenser as shown in Fig. 3, so the heat flux between the upper and lower parts of the wrap-around condenser coil could not be equal. Therefore, it is necessary to fit the law of heat flux variation with heating time in the three regions of condenser coil, and divide the heat transfer boundary conditions into three parts for setting. Coupled algorithm divided the whole heating process into several steady-state heating time intervals for simulation. In the initialization, the initial heat flux values qsh(t)0, qtp(t)0, qsc(t)0 in three regions of condenser coil were assumed. The heating process of water tank was simulated by CFD model
of water tank, and the parameters of water temperature and velocity distribution in water tank were obtained. Then these new parameters were substituted into the MATLAB model of HPWH for numerical calculation, and the heat flux values qsh(t)i, qtp(t)i, qsc(t)i in the three regions of the condenser coil were output, which were used as the boundary conditions of the CFD model in the new round of simulation. The iterative simulation was carried out until the iteration error meets the requirements (variation between iterations <1%), and then the next time interval was simulated. 4. Model development The coupled model included a vapor-compression system model established by MATLAB and a water tank with wraparound condenser coil model established by CFD. The boundary condition of the water tank CFD model was divided into three regions (superheated steam, two-phase flow and subcooled liquid), so the multi-heat flux coupled model was obtained. 4.1. Vapor-compression system model 4.1.1. Compressor model The compressor model is performed using lumped parameter method [25], and the pressure loss during suction and exhaust is
4
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
dc,o
Q
dc,i
Water Tube
Waater tank Water n thickness
(a)
(b)
Fig. 2. Heat transfer process from condenser side to water side.
x=1
La (Superheat)
x=0
Lb (Two-phase)
Lc (Subcool)
Fig. 3. Schematic diagram of condenser with three fluid regions.
negligible. The mass flow of refrigerant mr and input power of the compressor Wco are calculated as:
Vh mr ¼ gv 3600v s Wco ¼
mr hco;r;o hco;r;i
gco
ð1Þ
ð2Þ
where gv, gco are volumetric efficiency and total efficiency of compressor respectively, ms is suction specific volume, Vh is theoretical displacement volume, and hco,r,o, hco,r,i are refrigerant enthalpy at the inlet and outlet of compressor respectively. 4.1.2. Condenser model According to the phase of refrigerant, the condenser is divided into three regions (superheated steam, two-phase flow and subcooled liquid) where the length of each region is different [26]. The condenser model is described by multi-zone moving boundary approach [27]. In each region of the condenser, the energy conservation equation is given as:
Q c ¼ mr hc;r;i hc;r;o The heat transferred to the water is:
ð3Þ
Q w ¼ C P;w mw T w;o T w;i
ð4Þ
The heat flux between the condenser coil and the water is:
q ¼ U c DT c;w
ð5Þ
where hc,r,i, hc,r,o are refrigerant enthalpy at the inlet and outlet of condenser respectively, Cp,w, mw are heat capacity and mass flow of water respectively, Tw,o, Tw,i are water temperature at the inlet and outlet of water tank respectively, Uc are total heat transfer coefficient, DTc,w are heat transfer temperature difference between the condenser and the water. Generally speaking, the threedimensional heat transfer process between the condenser coil and the water tank can be deeply studied by the ANSYS program. However, in order to obtain the heat flux boundary conditions of the water tank model, only the numerical model of heat transfer between the condenser and the water needs to be established by MATLAB in this paper. The heat flux can be accurately and conveniently calculated by Eq. (5) in this study. Generally, in the experimental equipment or the market products, the thermal silica gel is applied to the wall of the water tank in order to solve the problem of contact thermal resistance. Therefore, the contact thermal resistance between condenser coil and water tank is neglected in this study. For the overall heat transfer process of one segment, the resistance network diagram between wrap-around condenser coil and water [6] is shown in Fig. 4. Since
5
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Rr
Rtube
Rtank
Rw
Tr
Tw Refrigerant side heat transfer resistance
Tube wall Tank wall Water tank side heat thermal resistance thermal resistance transfer resistance
Fig. 4. Thermal resistance network diagram of water tank.
there are three phase regions in the condenser, the convective heat transfer coefficient ac is different in each region and should be divided into ash,c, atp,c, asc,c, respectively [28]. Therefore, the total heat transfer coefficient Uc also needs to be divided into heat transfer coefficient Ush,c, Utp,c, Usc,c in superheated steam, two-phase flow and subcooled liquid regions respectively. The specific calculations are as follows: The convective heat transfer coefficients in single phase flow regions (ash,c, asc,c): 0:4 0:1 Nuc;r ¼ 0:023Re0:8 c;r Pr c;r d
ð6Þ
ash;c ¼
Nush;c;r ksh;c;r dc;i
ð7Þ
asc;c ¼
Nusc;c;r ksc;c;r dc;i
ð8Þ
atp;c ¼ 1:3asc;c ð1 xÞ0:8 þ
3:8x0:76 ð1 xÞ0:04 Pr0:38 tp;c;r
#
U sh;c Ash;c þ U tp;c Atp;c þ U sc;c Asc;c Ac
ð9Þ
Xin and Ebadian [31] have proposed the Nusselt number using the coil vertical height Hc as characteristic length, and Nu is calculated by [32]:
Nu ¼ 0:590Ra0:293 ; 4 103 6 RaH 6 1 105 H RaH ¼
gbDT w H3c mw aw
ð10Þ ð11Þ
Therefore, the convective heat transfer coefficient aw at water side is:
aw ¼
Nukw Hc
ð12Þ
In addition, the coefficient of performance of HPWH system is calculated as:
COP ¼
Qw W co
ð13Þ
And the average COPave over the time interval Dt is:
P Q ðtÞ COP av e ¼ P w W co ðtÞ
ð15Þ
where hev,r,i, hev,r,o are refrigerant enthalpy at the inlet and outlet of expansion valve respectively. 4.1.4. Evaporator model Similar to the condenser, the evaporator is divided, by the phase of refrigerant, into two regions (superheated steam and two-phase flow), and modeled using multi-zone moving boundary approach. In each region of the evaporator, the total heat transfer and energy conservation equation is:
ð16Þ
where Ue is overall heat transfer coefficient, and Ae, DTe are heat transfer area and temperature difference between air and refrigerant respectively. 4.2. Water tank model
Compared with the straight tube, the convective heat transfer coefficient of refrigerant in the two-phase flow region in the spiral coil is 1.16–1.43 times more than that in the straight tube. This paper chooses 1.3 [29]. Meanwhile, the average dryness x of refrigerant is used to modify the Nusselt number of forced convection in single phase [30]. And the total heat transfer coefficient Uc is:
Uc ¼
hev ;r;i ¼ hev ;r;o
Q a ¼ Q e ¼ U e A e DT e
The convective heat transfer coefficient in two-phase flow region (atp,c):
"
4.1.3. Thermostatic expansion valve model Since the thermostatic expansion valve is assumed to be isenthalpic, the enthalpy of refrigerant at the inlet and outlet of expansion valve is considered to be equal. The energy balance equation is:
ð14Þ
4.2.1. Modelling assumptions In order to simplify practical problems and facilitate numerical calculation, the following assumptions were adopted: (1) The three-dimensional water tank with wrap-around condenser coil model was simplified to a two-dimensional axisymmetric model by replacing spiral coil with annular layer-by-layer coil as shown in Fig. 5. In order to simplify the setting of boundary conditions, annular coil could be simplified to rectangular coil [23]. CFD was used to establish the two-dimensional axisymmetric water tank model to simulate the heating process in water tank. (2) The outer wall of the water tank was assumed adiabatic. (3) The wrap-around coil was regarded as variable external heat source, which is equivalent to 28 discrete line heat sources. According to the three regions of the condenser, the line heat sources were divided into three parts, and the multi-heat flux boundary conditions were set. (4) Laminar flow was assumed to simulate the buoyancy driven flow and SIMPLEC scheme is selected for pressure-velocity coupling [24]. (5) Since the driving force of water flow was the density difference caused by temperature difference, the Boussinesq approximation was adopted for considering the water density variation during CFD simulation [33]. In the Boussinesq approximation, fluid density was treated as a constant value in all solved equations, except for the buoyancy term in the momentum equation:
ðq q0 Þg ffi q0 bðT T 0 Þg
ð17Þ
6
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Fig. 5. Two-dimensional simplified model of water tank.
where q0, T0 are the reference density and temperature respectively, and b is the thermal expansion coefficient. 4.2.2. Governing equation Since the CFD model of water tank adopts two-dimensional axisymmetric model, the governing equations, including mass, momentum and energy conservation equations, are given by Eqs. (18)–(21). Mass conservation equation:
@ux @uy þ ¼0 @x @y
ð18Þ
Momentum conservation equation:
" # @ux @ux @ux 1 @P @ 2 ux @ 2 ux þ mw þ þ ux þ uy ¼ @t @x @y qw0 @x @x2 @y2
ð19Þ
" # @uy @uy @uy 1 @P @ 2 uy @ 2 uy þm þ þ ux þ uy ¼ @t @x @y qw0 @y w @x2 @y2 gbðT w T w0 Þ
In order to validate the accuracy of the coupled model, this paper simulated three different initial water temperature conditions and output the water temperature distribution parameters in the tank. The model validation was performed by comparing the simulated average water temperature with experimental measurements reported by Dai, Li and Ye [34]. The volume of the water tank is 150L in the experimental setup. The structural parameters of the water tank model and the operating conditions of simulated calculation are consistent with the experimental setup. As shown in Fig. 6, the maximum average water temperature deviation between the simulated values and the experimental results was within 8%, 6% and 4% at working conditions 10 ± 0.5 °C, 15 ± 0.5 °C, 20 ± 0.5 °C respectively. Since the deviation was within a reasonable range, the simulated values were in good agreement with the experimental results. The coupled model could further simulate the heating process of the water tank.
6. Results and discussion
ð20Þ
Energy conservation equation:
" # @T @T @T @2T @2T þ ux þ uy ¼ kw þ @t @x @y @x2 @y2
5. Model validation
ð21Þ
4.2.3. Mesh generation Structured quadrilateral mesh was used for meshing CFD model of water tank. In order to better reflect the flow and heat transfer relationship between tank wall and water, boundary layer grids were used to intense the grid density near the tank wall. 4.2.4. Boundary condition Non-slip condition was adopted for wall velocity of water tank. The boundary conditions of heat transfer process between the condenser and water were set as multi-heat flux boundary conditions according to the three regions in condenser. And the heat flux of the three regions was fitted by the system model and input by Fluent’s User Defined Function (UDF) feature. In addition, the initial water temperature T0 of the tank was natural temperature as the initial condition.
6.1. Performance comparison between variable-pitch coil and constant-pitch coil In this section, the length and height of coils of the two structures are equal, and the volume of water tank is 150L. The structure parameters can be referred to Table 1. Fig. 7 shows the temperature distribution in the water tank with wrap-around variable-pitch coil and constant-pitch coil at different heating time. At t = 60 min, the average water temperature is 26.90 °C and 27.51 °C, respectively, and the maximum temperature difference in the vertical direction of the tank center is 15.86 °C and 16.37 °C, respectively, for the constant-pitch coil and variable-pitch coil. With the process of heating, the average water temperature is gradually increased, and the maximum temperature difference in the tank vertical direction is gradually decreased. At t = 240 min, the average water temperatures were 47.46 °C and 49.13 °C while the maximum temperature difference is 10.77 °C and 8.68 °C, in addition, the maximum temperature difference is 6.21 °C and 4.11 °C at Ht > 0.2 m for the constant-pitch coil and variable-pitch coil respectively. From the results, the average water temperature under the variable-pitch coil structure is higher, and the maximum temperature difference is smaller, compared with the constant-pitch coil. The temperature contours of
7
60
60
50
50
50
40
+8% 30
-8%
20
Initial water temperature 10 0.5 C
10 10
20
30
40
50
40
+6% 30
-6%
20
Initial water temperature 15 0.5 C
10 10
60
20
30
40
50
Calculated data ( C)
Calculated data ( C)
60
Experimental data ( C)
60
Experimental data ( C)
Experimental data ( C)
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
40
+4% 30
-4%
20
Initial water temperature 20 0.5 C
10 10
20
30
40
50
60
Calculated data ( C)
Fig. 6. Simulated average water temperature vs experimental measurements at three conditions.
1.4
constant-pitch 60min variable-pitch
1.2
120min 180min 240min
height of tank (m)
1.0 0.8 0.6 0.4 0.2 0.0 15
20
25
30
35
40
45
50
55
water temperature ( C) Fig. 7. Variation of water temperature vs the height of water tank at various heating times.
constant-pitch coil and variable-pitch coil after heating for 240 min are demonstrated in Fig. 8. It is obvious that the variable-pitch coil structure can significantly improve the temperature stratification in the tank. The Nusselt number of the water tank under the two coil structures at different heating times is shown in Fig. 9. During the whole heating process, the average Nu of constant-pitch coil and variablepitch coil is 31.66 and 32.76 respectively, which is 3.48% higher than that of constant-pitch coil. For constant-pitch coil, lower temperature water flow downwards and higher temperature water flow upwards, resulting in significant temperature stratification. However, compared with the constant-pitch coil, the effective heat exchange area at the bottom of the variable-pitch coil is larger than that of the upper part, so the increase of the bottom heat flux can accelerate the increase of the bottom water temperature and improve the flow and thermal performance of the tank. In addition, several physical parameters and water temperature values are involved in the equation for calculating Nusselt number. During the whole heating process, the water temperature increases gradually and the flow of the water tank is gradually enhanced, but the comprehensive change of parameters is more complex. Therefore, the curve of Nusselt number changing with heating time does not show a regular increasing rate.
For the constant-pitch coil and variable-pitch coil, the heat transfer coefficient Uc and COP at different heating time are shown in Fig. 10. During the whole heating process from 15 °C to 50 °C, the average Uc of constant-pitch coil and variable-pitch coil are 261.92 W/(m2K) and 319.31 W/(m2K), respectively, and the average Uc of variable-pitch coil is 21.91% higher than that of constantpitch coil. COP of constant-pitch coil and variable-pitch coil are 4.72 and 5.18 at the beginning, and 3.63, 4.05 at the end of heating, respectively. The average COP of the two coil structures is 4.10 and 4.54, respectively. Therefore, the average COP is increased by 10.75% by using variable-pitch coil structure. This is because the convective heat transfer coefficient increases and the heat transfer resistance decreases under the variable-pitch coil structure. At the same time, the heat transfer performance is improved, resulting in reducing the condensing temperature. Therefore, the compressor power consumption is reduced, and the operation performance of HPWH is improved. It can be concluded that the variable-pitch coil is superior to the constant-pitch coil in the flow and heat transfer process of water tank and the system operation performance. Fig. 11 shows the variation of the qsh, qtp, qsc in three fluid regions at various heating time. During the whole heating process, the heat flux in the superheated steam and two-phase flow regions tend to decrease gradually, while the heat flux values in the subcooled liquid region decrease slightly and rise slightly, fluctuating in a relatively stable range. Before t = 80 min, the qtp is greater than the qsh and the qsc. Since the water temperature and velocity in the water tank area corresponding to the two-phase flow region change rapidly, the qtp decreases faster than the qsh, and the qtp is gradually lower than the qsh. It can be seen that the heat fluxes in three fluid regions of the variable-pitch coil is higher than that of the constant-pitch coil, This is because the variable-pitch coil adopts gradually changing helical pitch, which strengthens the secondary circulation in the tube, improves the convective heat transfer coefficient, enlarges the heat transfer coefficient and increases the heat flux. 6.2. Effect of coil pitch on thermal performance of water tank In order to investigate the influence of different coil pitch on the thermal performance of the water tank under the variable-pitch coil structure, the water temperature distribution and flow characteristics were simulated. The total length of the condenser coil was equal, while the initial spiral pitch hc,0 was 14 mm, 15 mm, 16 mm respectively. Fig. 12 shows the water temperature distribution in the tank at t = 60 min, 120 min, 180 min and 240 min, respectively. At t = 60 min, the temperature stratification at the bottom of the tank
8
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
(a) t = 240 min
(b) t = 240 min
Fig. 8. (a) Temperature contours (°C) of constant-pitch. (b) Temperature contours (°C) of variable-pitch.
4500
38
36
variable-pitch constant-pitch
variable-pitch (superheated steam) variable-pitch (two-phase flow) variable-pitch (subcooled liquid) constant-pitch (superheated steam) constant-pitch (two-phase flow) constant-pitch (subcooled liquid)
4000
Heat flux (W/m2)
3500
Nu
34
32
30
3000 2500 2000 1500 1000
28
500 0
26 30
60
90
120
150
180
210
heating time (min)
20
40
60
80
100
120
140
160
180
200
Heating time (min) Fig. 11. Variation of heat fluxes in three fluid regions at various heating time.
Fig. 9. Nusselt number of constant/variable-pitch coil water tank vs heating time.
600
6
constant-pitch (COP) variable-pitch (COP)
550
COP
450 400
4
350 300
3
250
constant-pitch (Uc)
2
200
variable-pitch (Uc) 0
50
100
150
200
150 250
heating time (min) Fig. 10. COP and Uc of constant/variable-pitch coils vs heating time.
Uc(W m-2 K-1)
500
5
is more obvious and the average water temperature under the three structures is 27.99 °C, 27.51 °C and 27.14 °C, respectively. With the heating process, the temperature difference is gradually decreased, and the temperature stratification phenomenon is gradually improved. At t = 240 min, the maximum temperature difference in the vertical direction of the tank center under the three structures is 7.40 °C, 8.68 °C, 8.98 °C, respectively. During the whole heating process, the average water temperature of hc,0 = 14 mm is higher than the other two coil structures, and water temperature distribution of hc,0 = 14 mm is also more uniform. Nu is increased with heating time during the whole heating process as shown in Fig. 13. The average Nu of three coil structures was 33.44, 32.76 and 32.36, respectively. Among them, the average Nu of hc,0 = 14 mm was the largest, which is 3.36% higher than that of hc,0 = 16 mm. With the decrease of coil pitch, the natural convection of water tank is promoted, and the mixing process between different temperature layers is accelerated. At the same time, the effective heat transfer area at the bottom of the water tank is increased, which can increase the heat flux at the bottom and improve the thermal performance of the water tank.
9
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
1.4
1.4 60min
hc,0=14mm
1.2
120min
dc=8mm
180min 240min
1.2
hc,0=16mm
0.8 0.6 0.4
0.8 0.6 0.4
0.2 0.0 15
120min 180min 240min
dc=12mm
1.0
height of tank (m)
height of tank (m)
1.0
60min
dc=10mm
hc,0=15mm
0.2
20
25
30
35
40
45
0.0 15
50
water temperature ( C)
20
25
30
35
40
45
50
55
water temperature ( C) Fig. 12. Variation of water temperature vs the height of water tank under different coil pitch.
Fig. 14. Variation of water temperature vs the height of water tank under different coil diameter.
38
38 36
36
34
32
Nu
Nu
34
30
32
hc,0=14mm
dc=8mm
hc,0=15mm
28
30
hc,0=16mm 26 30
dc=10mm dc=12mm
60
90
120
150
180
210
heating time (min) Fig. 13. Nusselt number of variable-pitch coil water tank vs heating time.
28 30
60
90
120
150
180
210
heating time (min) Fig. 15. Nusselt number of variable-pitch coil water tank vs heating time under different coil diameter.
Table 2 Structure parameters of three variable-pitch coils with different diameters. Type
dc (mm)
N
hc,0 (m)
d0 (m)
1 2 3
8 10 12
35 28 23
0.013 0.014 0.015
0.0002 0.0003 0.00045
6.3. Effect of coil diameter on thermal performance of water tank In this section, the water temperature distribution and flow characteristics were simulated to investigate the influence of different coil diameter on the thermal performance of the water tank. The total heat transfer area of the condenser was equal, and the coil height Hc remained unchanged. And detailed structural parameters of different coil diameter structures are shown in Table 2. The water temperature distribution in the vertical direction of the tank center under the three coil structures is presented in Fig. 14. The temperature stratification at the bottom of the water tank is obvious. With the heating process, the average water
temperature is gradually increased. When t = 240 min, the maximum temperature difference in the vertical direction of the tank center under the three coil diameter structures is 7.38 °C, 7.40 °C and 7.47 °C, respectively, and the average water temperature is 50.79 °C, 49.73 °C, 49.33 °C respectively. During the whole heating process, the water temperature at dc = 8 mm is higher than that of the other two coil diameter structures, and the water temperature is more uniform. During the whole heating process, Nu is increased with heating time as presented in Fig. 15. The average Nu of three coil diameter structures are 33.83, 33.44, 32.79, respectively. The Nu of dc = 8 mm is the largest and thus 3.18% higher than that of dc = 12 mm. It can be concluded that the flow and heat transfer characteristics of water tank can be improved by appropriately reducing the coil diameter. This is because the improvement of the heat transfer performance promotes the flow and heat transfer process in the tank, and the natural convection in the tank is enhanced, which improves the thermal performance of the water tank and thus improves the temperature stratification in the tank.
10
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
7. Conclusions In this study, a coupled model was established to investigate the performance of HPWH with wrap-around variable-pitch coil and constant-pitch coil. The system performance could be improved by optimizing the wrap-around forms and structural parameters of the coil. In addition, our experimental study on HPWH with variable-pitch coil is still in progress. The conclusions are as follows: (1) Heat flux of three regions (superheated steam, two-phase flow and subcooled liquid) of the condenser was fitted as a function of heating time as boundary conditions of the tank model. The multi-heat flux coupled model could be used as an effective research method to accurately simulate the dynamic heating process of the water tank and the operating characteristics of the system. (2) During the whole heating process, the temperature stratification of the water tank in the variable-pitch coil structure was improved. The average heat transfer coefficient and COP of variable-pitch coil were 319.31 W/(m2K) and 4.54, respectively, which increased by 21.91% and 10.75%, compared with the constant-pitch coil. Therefore, the variablepitch coil structure is beneficial to improve the operating performance of HPWH. (3) In the energy storage process of HPWP, the system performance was influenced by water temperature in the tank and refrigerant distribution in the condenser. Therefore, a comprehensive understanding of heat transfer and flow characteristics in the tank is helpful to the design of the condenser. As can be seen in this paper, appropriately reducing the spiral pitch and coil diameter is beneficial to improve the thermal performance of water tank. (4) In the future, we can use the ANSYS program to simulate the heat transfer process between the condenser and the water tank. Through the simulation method, the heat transfer characteristics of the heat transfer process can be investigated and a new method can be proposed to calculate Uc.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51876033). References [1] W. Chen, S.Q. Liang, Y.X. Guo, K.Y. Cheng, X.H. Gui, D.W. Tang, Investigation on the thermal performance and optimization of a heat pump water heater assisted by shower waste water, Energy Build. 64 (2013) 172–181. [2] H. Willem, Y. Lin, A. Lekov, Review of energy efficiency and system performance of residential heat pump water heaters, Energy Build. 143 (2017) 191–201. [3] A. Hepbasli, Y. Kalinci, A review of heat pump water heating systems, Renew. Sustain. Energy Rev. 13 (2009) 1211–1229. [4] K.J. Chua, S.K. Chou, W.M. Yang, Advances in heat pump systems: a review, Appl. Energy 87 (2010) 3611–3624. [5] Y.M. Han, R.Z. Wang, Y.J. Dai, Thermal stratification within the water tank, Renew. Sustain. Energy Rev. 13 (2009) 1014–1026. [6] B. Shen, K. Nawaz, V. Baxter, A. Elatar, Development and validation of quasisteady-state heat pump water heater model having stratified water tank and wrapped-tank condenser, Int. J. Refrig. 87 (2018) 78–90.
[7] X. Liu, L. Ni, S.K. Lau, H. Li, Performance analysis of a multi-functional Heat pump system in heating mode, Appl. Therm. Eng. 51 (2013) 698–710. [8] A.S. Vieira, R.A. Stewart, C.D. Beal, Air source heat pump water heaters in residential buildings in Australia: identification of key performance parameters, Energy Build. 91 (2015) 148–162. [9] W. Wu, X.L. Zhang, X.T. Li, W.X. Shi, B.L. Wang, Comparisons of different working pairs and cycles on the performance of absorption heat pump for heating and domestic hot water in cold regions, Appl. Therm. Eng. 48 (2012) 349–358. [10] F.H. Wang, Z.H. Wang, Y.X. Zheng, Z. Lin, P.F. Hao, C. Huan, T. Wang, Performance investigation of a novel frost-free air-source heat pump water heater combined with energy storage and dehumidification, Appl. Energy 139 (2015) 212–219. [11] Y. Chen, L. Lan, A fault detection technique for air-source heat pump water chiller/heaters, Energy Build. 41 (2009) 881–887. [12] C.Y. Park, P. Hrnjak, Experimental and numerical study on microchannel and round-tube condensers in a R410A residential air-conditioning system, Int. J. Refrig. 31 (2008) 822–831. [13] D.D. Wang, Research on Temperature Field and Flow Field in Tank of ASHPWH, Beijing Institute of Civil Engineering and Architecture Doctor of Philosophy, 2006. [14] L. Yang, L.L. Shao, Z.C. Zhang, Modeling and optimization of air source heat pump water heaters using wrap-around micro-channel condenser, J. Refrig. 35 (2014) 66–70. [15] H. Mirgolbabaei, H. Taherian, G. Domairry, N. Ghorbani, Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers, Int. J. Numer. Meth. Fluids 66 (2011) 805–819. [16] J. Fernández-Seara, C. Piñeiro-Pontevedra, J.A. Dopazo, On the performance of a vertical helical coil heat exchanger. Numerical model and experimental validation, Appl. Therm. Eng. 62 (2014) 680–689. [17] M.S. Shin, H.S. Kim, D.S. Jang, S.N. Lee, Y.S. Lee, H.G. Yoon, Numerical and experimental study on the design of a stratified thermal storage system, Appl. Therm. Eng. 24 (2004) 17–27. [18] D.G. Prabhanjan, T.J. Rennie, G.S.V. Raghavan, Natural convection heat transfer from helical coiled tubes, Int. J. Therm. Sci. 43 (2004) 359–365. [19] K. Nandakumar, J.H. Masliyah, Bifurcation in steady laminar flow through curved tubes, J. Fluid Mech. 119 (2006) 475–490. [20] J.S. Jayakumar, S.M. Mahajani, J.C. Mandal, P.K. Vijayan, B. Rohidas, Experimental and CFD estimation of heat transfer in helically coiled heat exchangers, Chem. Eng. Res. Des. 86 (2008) 221–232. [21] C.C. Lv, Y. Li, Y. Liu, R. Wang, X.X. E, F. Yan, Numerical simulation and configuration optimization of a hot water storage tank of heat pump water heater, Fluid Mach. 42 (2014) 76–80. [22] N.N. Dai, S.H. Li, Simulation and performance analysis on condenser coil in household heat pump water heater, Sustain. Cit. Soc. 36 (2018) 176–184. [23] T. Shah, P. Hrnjak, Linked modelling of heat pump water heater vapor compression system and water tank, International Refrigeration and Air Conditioning Conference, 2014. [24] W. Li, P. Hrnjak, Experimentally validated model of heat pump water heater with a water tank in heating-up transients, Int. J. Refrig. 88 (2018) 420–431. [25] J.W. Choi, G. Lee, M.S. Kim, Numerical study on the steady state and transient performance of a multi-type heat pump system, Int. J. Refrig. 34 (2011) 429– 443. [26] O. Ibrahim, F. Fardoun, R. Younes, H. Louahlia-Gualous, Air source heat pump water heater: dynamic modeling, optimal energy management and mini-tubes condensers, Energy 64 (2014) 1102–1116. [27] M. Chamoun, R. Rulliere, P. Haberschill, J.F. Berail, Dynamic model of an industrial heat pump using water as refrigerant, Int. J. Refrig. 35 (2012) 1080– 1091. [28] J.J. Guo, J.Y. Wu, R.Z. Wang, S. Li, Experimental research and operation optimization of an air-source heat pump water heater, Appl. Energy 88 (2011) 4128–4138. [29] D.G. Prabhanjan, G.S.V. Raghavan, T.J. Rennie, Comparison of heat transfer rates between a straight tube heat exchanger and a helically coiled heat exchanger, Int. Commun. Heat Mass Transfer 29 (2002) 185–191. [30] M.M. Shah, A general correlation for heat transfer during film condensation inside pipes, Int. J. Heat Mass Transf. 22 (1979) 547–556. [31] R.C. Xin, M.A. Ebadian, Natural convection heat transfer from helicoidal pipes, J. Thermophys. Heat Transfer 10 (1995) 297–302. [32] S.M. Yang, W.Q. Tao, Heat Transfer, fourth ed., Higher Education Press, Beijing, 2006. [33] Z. Gao, V.C. Mei, F.C. Chen, CFD Solution and experimental testing of buoyancydriven convection caused by condensers immersed in a water tank of HPWH, ASME 2003 International Mechanical Engineering Congress and Exposition, 2003. [34] N.N. Dai, S.H. Li, Q. Ye, Performance analysis on the charging and discharging process of a household heat pump water heater, Int. J. Refrig. 98 (2019) 266– 273.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Investigation on the performance and optimization of heat pump water heater with wrap-around condenser coil Qiang Ye, Shuhong Li ⇑ School of Energy and Environment, Southeast University, Nanjing 210096, China
a r t i c l e
i n f o
Article history: Received 17 February 2019 Received in revised form 6 August 2019 Accepted 9 August 2019
Keywords: Heat pump water heater Heat transfer Optimization Coupled model Variable/constant-pitch coil Heat flux
a b s t r a c t A numerical investigation on the performance of heat pump water heater (HPWH) with wrap-around condenser coil was carried out. In this study, a coupled model was developed to simulate the static energy storage process of HPWH, which consisted of a multi-heat flux CFD model to describe the flow and heat transfer in water tank and a vapor-compression system model established in MATLAB to simulate the system operation characteristics. Heat flux in superheated steam, two-phase flow, and subcooled liquid regions of the condenser was obtained from the system model as boundary conditions of water tank model. The simulation results of the coupled model were in good agreement with experimental results. Heat transfer coefficient, COP and water temperature distribution of variable-pitch and constant-pitch coil were obtained by simulation. The results indicated that the heat transfer coefficient and average COP of variable-pitch coil were increased by 21.91% and 10.75% respectively, compared with constant-pitch coil. In addition, it was found that by appropriately reducing spiral pitch and coil diameter, average water temperature was increased by about 1 °C and maximum temperature difference in the vertical direction was no more than 7.50 °C. This work provides meaningful guidance for performance optimization of heat pump water heater. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Water heating accounts for a significant part of buildings energy consumption [1,2]. Heat pump water heater (HPWH) has outstanding advantages in energy saving, and many countries attach great importance to its promotion and application [3,4]. Investigating and optimizing the heat transfer process between condenser and water is conducive to improving the thermal stratification within the water tank [5]. According to the heat transfer between condenser coil and water, the condenser can be divided into wrap-around coil and immersed coil [6]. Compared with the immersed coil, the wrap-around coil has no direct contact with water, so it has no scaling and corrosion problems. Therefore, the wrap-around coil is mostly used in the current HPWH products in the market. At present, the research on HPWH mainly involves system cycle, working fluid, component design, control and operation optimization, etc [7–11]. For component design, condenser coil and water tank are the research focus. For HPWH with the wrap-wound coil, optimizing the coil structure and the wrap-around form is important for improving the
⇑ Corresponding author. E-mail address: [email protected] (S. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118556 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
temperature stratification in the tank and the system performance. Park and Hrnjak [12] experimentally investigated the performance of a microchannel condenser and a round-tube condenser, and the results showed that the COP and heat flux of the microchannel condenser were higher than those of the round-tube condenser. Wang [13] found by simulation that reducing the condenser coil diameter and increasing the spiral diameter could improve the system performance. Yang, Shao and Zhang [14] found that the heat transfer performance of refrigerant in condenser coil could be slightly improved by changing the coil sectional structure. However, although the condenser coil structure is changed, the heat transfer resistance is not effectively reduced, and the temperature stratification in water tank temperature is still obvious. Therefore, the coil wrap-around form should be further optimized. In order to research the thermal performance of water tank, the simulation method is often used to study the temperature distribution in water tank [15–17]. When using computational fluid dynamics (CFD) software package to establish water tank model, reasonable boundary conditions are set to obtain accurate simulation results. In general, the boundary conditions such as constant wall temperature or constant heat flux are adopted [18,19]. Jayakumar et al. [20] suggested that more reasonable boundary conditions should be adopted, such as those that vary with heating time or water temperature. Lv et al. [21] considered
2
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Nomenclature A Cp,w Dt dc g Hc Ht h hc Lc m N Nu P Q q Ra R T t U u Vt Vh
vs
W x y
area, m2 specific heat of water, J/(kgK) diameter of water tank, m diameter of condenser tube, m gravitational acceleration, m/s2 coil height, m height of water tank, m refrigerant enthalpy, J/kg coil pitch, mm total length of condenser coil, m mass flow rate, kg/s number of turns Nusselt number pressure, Pa heat energy, W heat flux, W/m2 Rayleigh number thermal resistance temperature, °C time, min overall heat transfer coefficient, W/(m2K) velocity, m/s volume of water tank, L theoretical displacement volume, m3/h suction specific volume, m3/kg input power of compressor, W horizontal direction in master coordinate vertical direction in master coordinate
that the condensation temperature was constantly changing, so the boundary condition was set as variable wall temperature. Dai and Li [22] fitted the polynomial of the average heat flux of the condenser coil varying with heating time as the boundary condition. However, there are superheated steam, two-phase flow and subcooled liquid regions in the condenser, so the heat flux between the upper and lower parts of the condenser coil is not equal. Therefore, it is necessary to divide the heat transfer boundary condition into three parts to set for optimizing the CFD model of water tank, so that the model can accurately simulate the actual heating process of water tank. Coupling heat pump system model with water tank CFD model is a new simulation method [22–24]. Dai and Li [22] established a coupled model including heat pump system model and water tank model for domestic HPWH, and simulated the heating process of water tank. Shah and Hrnjak [23] also established a coupled model, which well simulated the system operation process and the transient heating process in water tank. Therefore, specific attention is attached to the development of a coupled model consisting of a multi-heat flux CFD model of water tank to capture the heat transfer in tank and a vapor-compression system model established in MATLAB to obtain the system operating parameters. Heat flux in the superheated steam, two-phase flow, and subcooled liquid regions of the condenser is obtained from the system model as boundary conditions. Then the heat transfer coefficient, COP and water temperature distribution are obtained by simulation. The coupled model is used to investigate the influence of different wrap-around condenser coil structure designs on the operating performance of HPWH, so as to obtain the optimum coil structure to improve the heat transfer process between condenser and water, and the system performance.
Greek symbols heat transfer coefficient, W/(m2K) b thermal expansion coefficient, 1/K g efficiency k thermal conductivity, W/(mk) l viscosity, kg/(ms) m kinematic viscosity, m2/s q variable density of water, kg/m3 qw0 constant density of water, kg/m3
a
Subscripts a air c condenser co compressor e evaporator ev expansion valve i inlet o outlet r refrigerant sc subcooled sh superheated t tank tp two phase w water Abbreviations CFD computational fluid dynamics COP coefficient of performance HPWH heat pump water heater
2. System description HPWH system mainly consists of a vapor-compression system and a water heating system, including compressor, water tank with wrap-around condenser, expansion valve and evaporator. The condenser coil is wound around the tank wall, and the condensation heat is transferred from the tube to the tank for heating water. The structure schematic diagram of water tank with wraparound constant/variable-pitch coil is shown in Fig. 1. And the main structural parameters are illustrated in Table 1. The rationale for determining hc,i is as follows: First, ensure that the variable-pitch coil structure and the constant-pitch coil have the same number of turns, coil height, total length, and tube diameter. Then, in order to regularly change the coil pitch, a linear equation (y = a + bx) is used to express hc,i. Finally, based on the above basic principles, several groups of numerical combinations of a and b are selected to simulate and output the temperature distribution of the water tank. Through comparison and analysis, the optimal numerical combination is determined to obtain the equation of hc,i. 3. Coupled method During the energy storage process of HPWH, the water temperature distribution parameters and the system operating parameters interact with each other. The system performance is affected by water temperature and refrigerant distribution in the condenser. As shown in Fig. 2, through the heat transfer process between the condenser coil and the water tank, heat is transferred from the condenser to the tank to heat water. The heat transfer performance of the condenser affects the heating process on the
3
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Dt
Dc
Ht
Hc
hc,i hc
Fig. 1. Structure of water tank with wrap-around constant/variable-pitch coil.
Table 1 Main structural parameters of water tank with constant/variable-pitch coil. Component
a
Structural parameter
Symbol
Value Constant-pitch
Variable-pitch 0.010 0.012 hc,ia 28 0.70 35
Condenser coil
Inner diameter of tube (m) Outer diameter of tube (m) Coil pitch (m) Number of turns Coil height (m) Total length (m)
dc,i dc,o hc N Hc Lc
0.010 0.012 0.01 28 0.70 35
Water tank
Volume of tank (L) Diameter of tank (m) Height of tank (m)
Vt Dt Ht
150 0.40 1.20
hc,i = 0.015 + nd0,(d0 = 0.0003, 0 n 27).
water side. At the same time, the water temperature distribution in turn affects the convective heat transfer process of the refrigerant in the condenser. The CFD model of water tank can simulate the flow and heat transfer process of water tank, but only reflects water temperature and velocity distribution in the tank. The MATLAB model of HPWH can simulate the vapor-compression system, but only outputs the system operating parameters. In order to analyze the characteristics of water temperature distribution and the system performance in the heating process, it is necessary to establish the system model and the water tank model respectively. Through the heat transfer process between the refrigerant in the condenser and the hot water in the water tank, the coupled model based on the heat pump cycle and the heat transfer of the condenser coil is established. There are superheated steam, two-phase flow and subcooled liquid regions in the condenser as shown in Fig. 3, so the heat flux between the upper and lower parts of the wrap-around condenser coil could not be equal. Therefore, it is necessary to fit the law of heat flux variation with heating time in the three regions of condenser coil, and divide the heat transfer boundary conditions into three parts for setting. Coupled algorithm divided the whole heating process into several steady-state heating time intervals for simulation. In the initialization, the initial heat flux values qsh(t)0, qtp(t)0, qsc(t)0 in three regions of condenser coil were assumed. The heating process of water tank was simulated by CFD model
of water tank, and the parameters of water temperature and velocity distribution in water tank were obtained. Then these new parameters were substituted into the MATLAB model of HPWH for numerical calculation, and the heat flux values qsh(t)i, qtp(t)i, qsc(t)i in the three regions of the condenser coil were output, which were used as the boundary conditions of the CFD model in the new round of simulation. The iterative simulation was carried out until the iteration error meets the requirements (variation between iterations <1%), and then the next time interval was simulated. 4. Model development The coupled model included a vapor-compression system model established by MATLAB and a water tank with wraparound condenser coil model established by CFD. The boundary condition of the water tank CFD model was divided into three regions (superheated steam, two-phase flow and subcooled liquid), so the multi-heat flux coupled model was obtained. 4.1. Vapor-compression system model 4.1.1. Compressor model The compressor model is performed using lumped parameter method [25], and the pressure loss during suction and exhaust is
4
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
dc,o
Q
dc,i
Water Tube
Waater tank Water n thickness
(a)
(b)
Fig. 2. Heat transfer process from condenser side to water side.
x=1
La (Superheat)
x=0
Lb (Two-phase)
Lc (Subcool)
Fig. 3. Schematic diagram of condenser with three fluid regions.
negligible. The mass flow of refrigerant mr and input power of the compressor Wco are calculated as:
Vh mr ¼ gv 3600v s Wco ¼
mr hco;r;o hco;r;i
gco
ð1Þ
ð2Þ
where gv, gco are volumetric efficiency and total efficiency of compressor respectively, ms is suction specific volume, Vh is theoretical displacement volume, and hco,r,o, hco,r,i are refrigerant enthalpy at the inlet and outlet of compressor respectively. 4.1.2. Condenser model According to the phase of refrigerant, the condenser is divided into three regions (superheated steam, two-phase flow and subcooled liquid) where the length of each region is different [26]. The condenser model is described by multi-zone moving boundary approach [27]. In each region of the condenser, the energy conservation equation is given as:
Q c ¼ mr hc;r;i hc;r;o The heat transferred to the water is:
ð3Þ
Q w ¼ C P;w mw T w;o T w;i
ð4Þ
The heat flux between the condenser coil and the water is:
q ¼ U c DT c;w
ð5Þ
where hc,r,i, hc,r,o are refrigerant enthalpy at the inlet and outlet of condenser respectively, Cp,w, mw are heat capacity and mass flow of water respectively, Tw,o, Tw,i are water temperature at the inlet and outlet of water tank respectively, Uc are total heat transfer coefficient, DTc,w are heat transfer temperature difference between the condenser and the water. Generally speaking, the threedimensional heat transfer process between the condenser coil and the water tank can be deeply studied by the ANSYS program. However, in order to obtain the heat flux boundary conditions of the water tank model, only the numerical model of heat transfer between the condenser and the water needs to be established by MATLAB in this paper. The heat flux can be accurately and conveniently calculated by Eq. (5) in this study. Generally, in the experimental equipment or the market products, the thermal silica gel is applied to the wall of the water tank in order to solve the problem of contact thermal resistance. Therefore, the contact thermal resistance between condenser coil and water tank is neglected in this study. For the overall heat transfer process of one segment, the resistance network diagram between wrap-around condenser coil and water [6] is shown in Fig. 4. Since
5
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Rr
Rtube
Rtank
Rw
Tr
Tw Refrigerant side heat transfer resistance
Tube wall Tank wall Water tank side heat thermal resistance thermal resistance transfer resistance
Fig. 4. Thermal resistance network diagram of water tank.
there are three phase regions in the condenser, the convective heat transfer coefficient ac is different in each region and should be divided into ash,c, atp,c, asc,c, respectively [28]. Therefore, the total heat transfer coefficient Uc also needs to be divided into heat transfer coefficient Ush,c, Utp,c, Usc,c in superheated steam, two-phase flow and subcooled liquid regions respectively. The specific calculations are as follows: The convective heat transfer coefficients in single phase flow regions (ash,c, asc,c): 0:4 0:1 Nuc;r ¼ 0:023Re0:8 c;r Pr c;r d
ð6Þ
ash;c ¼
Nush;c;r ksh;c;r dc;i
ð7Þ
asc;c ¼
Nusc;c;r ksc;c;r dc;i
ð8Þ
atp;c ¼ 1:3asc;c ð1 xÞ0:8 þ
3:8x0:76 ð1 xÞ0:04 Pr0:38 tp;c;r
#
U sh;c Ash;c þ U tp;c Atp;c þ U sc;c Asc;c Ac
ð9Þ
Xin and Ebadian [31] have proposed the Nusselt number using the coil vertical height Hc as characteristic length, and Nu is calculated by [32]:
Nu ¼ 0:590Ra0:293 ; 4 103 6 RaH 6 1 105 H RaH ¼
gbDT w H3c mw aw
ð10Þ ð11Þ
Therefore, the convective heat transfer coefficient aw at water side is:
aw ¼
Nukw Hc
ð12Þ
In addition, the coefficient of performance of HPWH system is calculated as:
COP ¼
Qw W co
ð13Þ
And the average COPave over the time interval Dt is:
P Q ðtÞ COP av e ¼ P w W co ðtÞ
ð15Þ
where hev,r,i, hev,r,o are refrigerant enthalpy at the inlet and outlet of expansion valve respectively. 4.1.4. Evaporator model Similar to the condenser, the evaporator is divided, by the phase of refrigerant, into two regions (superheated steam and two-phase flow), and modeled using multi-zone moving boundary approach. In each region of the evaporator, the total heat transfer and energy conservation equation is:
ð16Þ
where Ue is overall heat transfer coefficient, and Ae, DTe are heat transfer area and temperature difference between air and refrigerant respectively. 4.2. Water tank model
Compared with the straight tube, the convective heat transfer coefficient of refrigerant in the two-phase flow region in the spiral coil is 1.16–1.43 times more than that in the straight tube. This paper chooses 1.3 [29]. Meanwhile, the average dryness x of refrigerant is used to modify the Nusselt number of forced convection in single phase [30]. And the total heat transfer coefficient Uc is:
Uc ¼
hev ;r;i ¼ hev ;r;o
Q a ¼ Q e ¼ U e A e DT e
The convective heat transfer coefficient in two-phase flow region (atp,c):
"
4.1.3. Thermostatic expansion valve model Since the thermostatic expansion valve is assumed to be isenthalpic, the enthalpy of refrigerant at the inlet and outlet of expansion valve is considered to be equal. The energy balance equation is:
ð14Þ
4.2.1. Modelling assumptions In order to simplify practical problems and facilitate numerical calculation, the following assumptions were adopted: (1) The three-dimensional water tank with wrap-around condenser coil model was simplified to a two-dimensional axisymmetric model by replacing spiral coil with annular layer-by-layer coil as shown in Fig. 5. In order to simplify the setting of boundary conditions, annular coil could be simplified to rectangular coil [23]. CFD was used to establish the two-dimensional axisymmetric water tank model to simulate the heating process in water tank. (2) The outer wall of the water tank was assumed adiabatic. (3) The wrap-around coil was regarded as variable external heat source, which is equivalent to 28 discrete line heat sources. According to the three regions of the condenser, the line heat sources were divided into three parts, and the multi-heat flux boundary conditions were set. (4) Laminar flow was assumed to simulate the buoyancy driven flow and SIMPLEC scheme is selected for pressure-velocity coupling [24]. (5) Since the driving force of water flow was the density difference caused by temperature difference, the Boussinesq approximation was adopted for considering the water density variation during CFD simulation [33]. In the Boussinesq approximation, fluid density was treated as a constant value in all solved equations, except for the buoyancy term in the momentum equation:
ðq q0 Þg ffi q0 bðT T 0 Þg
ð17Þ
6
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
Fig. 5. Two-dimensional simplified model of water tank.
where q0, T0 are the reference density and temperature respectively, and b is the thermal expansion coefficient. 4.2.2. Governing equation Since the CFD model of water tank adopts two-dimensional axisymmetric model, the governing equations, including mass, momentum and energy conservation equations, are given by Eqs. (18)–(21). Mass conservation equation:
@ux @uy þ ¼0 @x @y
ð18Þ
Momentum conservation equation:
" # @ux @ux @ux 1 @P @ 2 ux @ 2 ux þ mw þ þ ux þ uy ¼ @t @x @y qw0 @x @x2 @y2
ð19Þ
" # @uy @uy @uy 1 @P @ 2 uy @ 2 uy þm þ þ ux þ uy ¼ @t @x @y qw0 @y w @x2 @y2 gbðT w T w0 Þ
In order to validate the accuracy of the coupled model, this paper simulated three different initial water temperature conditions and output the water temperature distribution parameters in the tank. The model validation was performed by comparing the simulated average water temperature with experimental measurements reported by Dai, Li and Ye [34]. The volume of the water tank is 150L in the experimental setup. The structural parameters of the water tank model and the operating conditions of simulated calculation are consistent with the experimental setup. As shown in Fig. 6, the maximum average water temperature deviation between the simulated values and the experimental results was within 8%, 6% and 4% at working conditions 10 ± 0.5 °C, 15 ± 0.5 °C, 20 ± 0.5 °C respectively. Since the deviation was within a reasonable range, the simulated values were in good agreement with the experimental results. The coupled model could further simulate the heating process of the water tank.
6. Results and discussion
ð20Þ
Energy conservation equation:
" # @T @T @T @2T @2T þ ux þ uy ¼ kw þ @t @x @y @x2 @y2
5. Model validation
ð21Þ
4.2.3. Mesh generation Structured quadrilateral mesh was used for meshing CFD model of water tank. In order to better reflect the flow and heat transfer relationship between tank wall and water, boundary layer grids were used to intense the grid density near the tank wall. 4.2.4. Boundary condition Non-slip condition was adopted for wall velocity of water tank. The boundary conditions of heat transfer process between the condenser and water were set as multi-heat flux boundary conditions according to the three regions in condenser. And the heat flux of the three regions was fitted by the system model and input by Fluent’s User Defined Function (UDF) feature. In addition, the initial water temperature T0 of the tank was natural temperature as the initial condition.
6.1. Performance comparison between variable-pitch coil and constant-pitch coil In this section, the length and height of coils of the two structures are equal, and the volume of water tank is 150L. The structure parameters can be referred to Table 1. Fig. 7 shows the temperature distribution in the water tank with wrap-around variable-pitch coil and constant-pitch coil at different heating time. At t = 60 min, the average water temperature is 26.90 °C and 27.51 °C, respectively, and the maximum temperature difference in the vertical direction of the tank center is 15.86 °C and 16.37 °C, respectively, for the constant-pitch coil and variable-pitch coil. With the process of heating, the average water temperature is gradually increased, and the maximum temperature difference in the tank vertical direction is gradually decreased. At t = 240 min, the average water temperatures were 47.46 °C and 49.13 °C while the maximum temperature difference is 10.77 °C and 8.68 °C, in addition, the maximum temperature difference is 6.21 °C and 4.11 °C at Ht > 0.2 m for the constant-pitch coil and variable-pitch coil respectively. From the results, the average water temperature under the variable-pitch coil structure is higher, and the maximum temperature difference is smaller, compared with the constant-pitch coil. The temperature contours of
7
60
60
50
50
50
40
+8% 30
-8%
20
Initial water temperature 10 0.5 C
10 10
20
30
40
50
40
+6% 30
-6%
20
Initial water temperature 15 0.5 C
10 10
60
20
30
40
50
Calculated data ( C)
Calculated data ( C)
60
Experimental data ( C)
60
Experimental data ( C)
Experimental data ( C)
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
40
+4% 30
-4%
20
Initial water temperature 20 0.5 C
10 10
20
30
40
50
60
Calculated data ( C)
Fig. 6. Simulated average water temperature vs experimental measurements at three conditions.
1.4
constant-pitch 60min variable-pitch
1.2
120min 180min 240min
height of tank (m)
1.0 0.8 0.6 0.4 0.2 0.0 15
20
25
30
35
40
45
50
55
water temperature ( C) Fig. 7. Variation of water temperature vs the height of water tank at various heating times.
constant-pitch coil and variable-pitch coil after heating for 240 min are demonstrated in Fig. 8. It is obvious that the variable-pitch coil structure can significantly improve the temperature stratification in the tank. The Nusselt number of the water tank under the two coil structures at different heating times is shown in Fig. 9. During the whole heating process, the average Nu of constant-pitch coil and variablepitch coil is 31.66 and 32.76 respectively, which is 3.48% higher than that of constant-pitch coil. For constant-pitch coil, lower temperature water flow downwards and higher temperature water flow upwards, resulting in significant temperature stratification. However, compared with the constant-pitch coil, the effective heat exchange area at the bottom of the variable-pitch coil is larger than that of the upper part, so the increase of the bottom heat flux can accelerate the increase of the bottom water temperature and improve the flow and thermal performance of the tank. In addition, several physical parameters and water temperature values are involved in the equation for calculating Nusselt number. During the whole heating process, the water temperature increases gradually and the flow of the water tank is gradually enhanced, but the comprehensive change of parameters is more complex. Therefore, the curve of Nusselt number changing with heating time does not show a regular increasing rate.
For the constant-pitch coil and variable-pitch coil, the heat transfer coefficient Uc and COP at different heating time are shown in Fig. 10. During the whole heating process from 15 °C to 50 °C, the average Uc of constant-pitch coil and variable-pitch coil are 261.92 W/(m2K) and 319.31 W/(m2K), respectively, and the average Uc of variable-pitch coil is 21.91% higher than that of constantpitch coil. COP of constant-pitch coil and variable-pitch coil are 4.72 and 5.18 at the beginning, and 3.63, 4.05 at the end of heating, respectively. The average COP of the two coil structures is 4.10 and 4.54, respectively. Therefore, the average COP is increased by 10.75% by using variable-pitch coil structure. This is because the convective heat transfer coefficient increases and the heat transfer resistance decreases under the variable-pitch coil structure. At the same time, the heat transfer performance is improved, resulting in reducing the condensing temperature. Therefore, the compressor power consumption is reduced, and the operation performance of HPWH is improved. It can be concluded that the variable-pitch coil is superior to the constant-pitch coil in the flow and heat transfer process of water tank and the system operation performance. Fig. 11 shows the variation of the qsh, qtp, qsc in three fluid regions at various heating time. During the whole heating process, the heat flux in the superheated steam and two-phase flow regions tend to decrease gradually, while the heat flux values in the subcooled liquid region decrease slightly and rise slightly, fluctuating in a relatively stable range. Before t = 80 min, the qtp is greater than the qsh and the qsc. Since the water temperature and velocity in the water tank area corresponding to the two-phase flow region change rapidly, the qtp decreases faster than the qsh, and the qtp is gradually lower than the qsh. It can be seen that the heat fluxes in three fluid regions of the variable-pitch coil is higher than that of the constant-pitch coil, This is because the variable-pitch coil adopts gradually changing helical pitch, which strengthens the secondary circulation in the tube, improves the convective heat transfer coefficient, enlarges the heat transfer coefficient and increases the heat flux. 6.2. Effect of coil pitch on thermal performance of water tank In order to investigate the influence of different coil pitch on the thermal performance of the water tank under the variable-pitch coil structure, the water temperature distribution and flow characteristics were simulated. The total length of the condenser coil was equal, while the initial spiral pitch hc,0 was 14 mm, 15 mm, 16 mm respectively. Fig. 12 shows the water temperature distribution in the tank at t = 60 min, 120 min, 180 min and 240 min, respectively. At t = 60 min, the temperature stratification at the bottom of the tank
8
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
(a) t = 240 min
(b) t = 240 min
Fig. 8. (a) Temperature contours (°C) of constant-pitch. (b) Temperature contours (°C) of variable-pitch.
4500
38
36
variable-pitch constant-pitch
variable-pitch (superheated steam) variable-pitch (two-phase flow) variable-pitch (subcooled liquid) constant-pitch (superheated steam) constant-pitch (two-phase flow) constant-pitch (subcooled liquid)
4000
Heat flux (W/m2)
3500
Nu
34
32
30
3000 2500 2000 1500 1000
28
500 0
26 30
60
90
120
150
180
210
heating time (min)
20
40
60
80
100
120
140
160
180
200
Heating time (min) Fig. 11. Variation of heat fluxes in three fluid regions at various heating time.
Fig. 9. Nusselt number of constant/variable-pitch coil water tank vs heating time.
600
6
constant-pitch (COP) variable-pitch (COP)
550
COP
450 400
4
350 300
3
250
constant-pitch (Uc)
2
200
variable-pitch (Uc) 0
50
100
150
200
150 250
heating time (min) Fig. 10. COP and Uc of constant/variable-pitch coils vs heating time.
Uc(W m-2 K-1)
500
5
is more obvious and the average water temperature under the three structures is 27.99 °C, 27.51 °C and 27.14 °C, respectively. With the heating process, the temperature difference is gradually decreased, and the temperature stratification phenomenon is gradually improved. At t = 240 min, the maximum temperature difference in the vertical direction of the tank center under the three structures is 7.40 °C, 8.68 °C, 8.98 °C, respectively. During the whole heating process, the average water temperature of hc,0 = 14 mm is higher than the other two coil structures, and water temperature distribution of hc,0 = 14 mm is also more uniform. Nu is increased with heating time during the whole heating process as shown in Fig. 13. The average Nu of three coil structures was 33.44, 32.76 and 32.36, respectively. Among them, the average Nu of hc,0 = 14 mm was the largest, which is 3.36% higher than that of hc,0 = 16 mm. With the decrease of coil pitch, the natural convection of water tank is promoted, and the mixing process between different temperature layers is accelerated. At the same time, the effective heat transfer area at the bottom of the water tank is increased, which can increase the heat flux at the bottom and improve the thermal performance of the water tank.
9
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
1.4
1.4 60min
hc,0=14mm
1.2
120min
dc=8mm
180min 240min
1.2
hc,0=16mm
0.8 0.6 0.4
0.8 0.6 0.4
0.2 0.0 15
120min 180min 240min
dc=12mm
1.0
height of tank (m)
height of tank (m)
1.0
60min
dc=10mm
hc,0=15mm
0.2
20
25
30
35
40
45
0.0 15
50
water temperature ( C)
20
25
30
35
40
45
50
55
water temperature ( C) Fig. 12. Variation of water temperature vs the height of water tank under different coil pitch.
Fig. 14. Variation of water temperature vs the height of water tank under different coil diameter.
38
38 36
36
34
32
Nu
Nu
34
30
32
hc,0=14mm
dc=8mm
hc,0=15mm
28
30
hc,0=16mm 26 30
dc=10mm dc=12mm
60
90
120
150
180
210
heating time (min) Fig. 13. Nusselt number of variable-pitch coil water tank vs heating time.
28 30
60
90
120
150
180
210
heating time (min) Fig. 15. Nusselt number of variable-pitch coil water tank vs heating time under different coil diameter.
Table 2 Structure parameters of three variable-pitch coils with different diameters. Type
dc (mm)
N
hc,0 (m)
d0 (m)
1 2 3
8 10 12
35 28 23
0.013 0.014 0.015
0.0002 0.0003 0.00045
6.3. Effect of coil diameter on thermal performance of water tank In this section, the water temperature distribution and flow characteristics were simulated to investigate the influence of different coil diameter on the thermal performance of the water tank. The total heat transfer area of the condenser was equal, and the coil height Hc remained unchanged. And detailed structural parameters of different coil diameter structures are shown in Table 2. The water temperature distribution in the vertical direction of the tank center under the three coil structures is presented in Fig. 14. The temperature stratification at the bottom of the water tank is obvious. With the heating process, the average water
temperature is gradually increased. When t = 240 min, the maximum temperature difference in the vertical direction of the tank center under the three coil diameter structures is 7.38 °C, 7.40 °C and 7.47 °C, respectively, and the average water temperature is 50.79 °C, 49.73 °C, 49.33 °C respectively. During the whole heating process, the water temperature at dc = 8 mm is higher than that of the other two coil diameter structures, and the water temperature is more uniform. During the whole heating process, Nu is increased with heating time as presented in Fig. 15. The average Nu of three coil diameter structures are 33.83, 33.44, 32.79, respectively. The Nu of dc = 8 mm is the largest and thus 3.18% higher than that of dc = 12 mm. It can be concluded that the flow and heat transfer characteristics of water tank can be improved by appropriately reducing the coil diameter. This is because the improvement of the heat transfer performance promotes the flow and heat transfer process in the tank, and the natural convection in the tank is enhanced, which improves the thermal performance of the water tank and thus improves the temperature stratification in the tank.
10
Q. Ye, S. Li / International Journal of Heat and Mass Transfer 143 (2019) 118556
7. Conclusions In this study, a coupled model was established to investigate the performance of HPWH with wrap-around variable-pitch coil and constant-pitch coil. The system performance could be improved by optimizing the wrap-around forms and structural parameters of the coil. In addition, our experimental study on HPWH with variable-pitch coil is still in progress. The conclusions are as follows: (1) Heat flux of three regions (superheated steam, two-phase flow and subcooled liquid) of the condenser was fitted as a function of heating time as boundary conditions of the tank model. The multi-heat flux coupled model could be used as an effective research method to accurately simulate the dynamic heating process of the water tank and the operating characteristics of the system. (2) During the whole heating process, the temperature stratification of the water tank in the variable-pitch coil structure was improved. The average heat transfer coefficient and COP of variable-pitch coil were 319.31 W/(m2K) and 4.54, respectively, which increased by 21.91% and 10.75%, compared with the constant-pitch coil. Therefore, the variablepitch coil structure is beneficial to improve the operating performance of HPWH. (3) In the energy storage process of HPWP, the system performance was influenced by water temperature in the tank and refrigerant distribution in the condenser. Therefore, a comprehensive understanding of heat transfer and flow characteristics in the tank is helpful to the design of the condenser. As can be seen in this paper, appropriately reducing the spiral pitch and coil diameter is beneficial to improve the thermal performance of water tank. (4) In the future, we can use the ANSYS program to simulate the heat transfer process between the condenser and the water tank. Through the simulation method, the heat transfer characteristics of the heat transfer process can be investigated and a new method can be proposed to calculate Uc.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51876033). References [1] W. Chen, S.Q. Liang, Y.X. Guo, K.Y. Cheng, X.H. Gui, D.W. Tang, Investigation on the thermal performance and optimization of a heat pump water heater assisted by shower waste water, Energy Build. 64 (2013) 172–181. [2] H. Willem, Y. Lin, A. Lekov, Review of energy efficiency and system performance of residential heat pump water heaters, Energy Build. 143 (2017) 191–201. [3] A. Hepbasli, Y. Kalinci, A review of heat pump water heating systems, Renew. Sustain. Energy Rev. 13 (2009) 1211–1229. [4] K.J. Chua, S.K. Chou, W.M. Yang, Advances in heat pump systems: a review, Appl. Energy 87 (2010) 3611–3624. [5] Y.M. Han, R.Z. Wang, Y.J. Dai, Thermal stratification within the water tank, Renew. Sustain. Energy Rev. 13 (2009) 1014–1026. [6] B. Shen, K. Nawaz, V. Baxter, A. Elatar, Development and validation of quasisteady-state heat pump water heater model having stratified water tank and wrapped-tank condenser, Int. J. Refrig. 87 (2018) 78–90.
[7] X. Liu, L. Ni, S.K. Lau, H. Li, Performance analysis of a multi-functional Heat pump system in heating mode, Appl. Therm. Eng. 51 (2013) 698–710. [8] A.S. Vieira, R.A. Stewart, C.D. Beal, Air source heat pump water heaters in residential buildings in Australia: identification of key performance parameters, Energy Build. 91 (2015) 148–162. [9] W. Wu, X.L. Zhang, X.T. Li, W.X. Shi, B.L. Wang, Comparisons of different working pairs and cycles on the performance of absorption heat pump for heating and domestic hot water in cold regions, Appl. Therm. Eng. 48 (2012) 349–358. [10] F.H. Wang, Z.H. Wang, Y.X. Zheng, Z. Lin, P.F. Hao, C. Huan, T. Wang, Performance investigation of a novel frost-free air-source heat pump water heater combined with energy storage and dehumidification, Appl. Energy 139 (2015) 212–219. [11] Y. Chen, L. Lan, A fault detection technique for air-source heat pump water chiller/heaters, Energy Build. 41 (2009) 881–887. [12] C.Y. Park, P. Hrnjak, Experimental and numerical study on microchannel and round-tube condensers in a R410A residential air-conditioning system, Int. J. Refrig. 31 (2008) 822–831. [13] D.D. Wang, Research on Temperature Field and Flow Field in Tank of ASHPWH, Beijing Institute of Civil Engineering and Architecture Doctor of Philosophy, 2006. [14] L. Yang, L.L. Shao, Z.C. Zhang, Modeling and optimization of air source heat pump water heaters using wrap-around micro-channel condenser, J. Refrig. 35 (2014) 66–70. [15] H. Mirgolbabaei, H. Taherian, G. Domairry, N. Ghorbani, Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers, Int. J. Numer. Meth. Fluids 66 (2011) 805–819. [16] J. Fernández-Seara, C. Piñeiro-Pontevedra, J.A. Dopazo, On the performance of a vertical helical coil heat exchanger. Numerical model and experimental validation, Appl. Therm. Eng. 62 (2014) 680–689. [17] M.S. Shin, H.S. Kim, D.S. Jang, S.N. Lee, Y.S. Lee, H.G. Yoon, Numerical and experimental study on the design of a stratified thermal storage system, Appl. Therm. Eng. 24 (2004) 17–27. [18] D.G. Prabhanjan, T.J. Rennie, G.S.V. Raghavan, Natural convection heat transfer from helical coiled tubes, Int. J. Therm. Sci. 43 (2004) 359–365. [19] K. Nandakumar, J.H. Masliyah, Bifurcation in steady laminar flow through curved tubes, J. Fluid Mech. 119 (2006) 475–490. [20] J.S. Jayakumar, S.M. Mahajani, J.C. Mandal, P.K. Vijayan, B. Rohidas, Experimental and CFD estimation of heat transfer in helically coiled heat exchangers, Chem. Eng. Res. Des. 86 (2008) 221–232. [21] C.C. Lv, Y. Li, Y. Liu, R. Wang, X.X. E, F. Yan, Numerical simulation and configuration optimization of a hot water storage tank of heat pump water heater, Fluid Mach. 42 (2014) 76–80. [22] N.N. Dai, S.H. Li, Simulation and performance analysis on condenser coil in household heat pump water heater, Sustain. Cit. Soc. 36 (2018) 176–184. [23] T. Shah, P. Hrnjak, Linked modelling of heat pump water heater vapor compression system and water tank, International Refrigeration and Air Conditioning Conference, 2014. [24] W. Li, P. Hrnjak, Experimentally validated model of heat pump water heater with a water tank in heating-up transients, Int. J. Refrig. 88 (2018) 420–431. [25] J.W. Choi, G. Lee, M.S. Kim, Numerical study on the steady state and transient performance of a multi-type heat pump system, Int. J. Refrig. 34 (2011) 429– 443. [26] O. Ibrahim, F. Fardoun, R. Younes, H. Louahlia-Gualous, Air source heat pump water heater: dynamic modeling, optimal energy management and mini-tubes condensers, Energy 64 (2014) 1102–1116. [27] M. Chamoun, R. Rulliere, P. Haberschill, J.F. Berail, Dynamic model of an industrial heat pump using water as refrigerant, Int. J. Refrig. 35 (2012) 1080– 1091. [28] J.J. Guo, J.Y. Wu, R.Z. Wang, S. Li, Experimental research and operation optimization of an air-source heat pump water heater, Appl. Energy 88 (2011) 4128–4138. [29] D.G. Prabhanjan, G.S.V. Raghavan, T.J. Rennie, Comparison of heat transfer rates between a straight tube heat exchanger and a helically coiled heat exchanger, Int. Commun. Heat Mass Transfer 29 (2002) 185–191. [30] M.M. Shah, A general correlation for heat transfer during film condensation inside pipes, Int. J. Heat Mass Transf. 22 (1979) 547–556. [31] R.C. Xin, M.A. Ebadian, Natural convection heat transfer from helicoidal pipes, J. Thermophys. Heat Transfer 10 (1995) 297–302. [32] S.M. Yang, W.Q. Tao, Heat Transfer, fourth ed., Higher Education Press, Beijing, 2006. [33] Z. Gao, V.C. Mei, F.C. Chen, CFD Solution and experimental testing of buoyancydriven convection caused by condensers immersed in a water tank of HPWH, ASME 2003 International Mechanical Engineering Congress and Exposition, 2003. [34] N.N. Dai, S.H. Li, Q. Ye, Performance analysis on the charging and discharging process of a household heat pump water heater, Int. J. Refrig. 98 (2019) 266– 273.