Condenser-Tank Interaction in a Heat Pump Water Heater with a Wraparound Condenser T.N.Anderson and G.L. Morrison School of Mechanical and Manufacturing Engineering University of New South Wales, Sydney, 2052, Australia
[email protected] ABSTRACT An experimental study was conducted to determine the overall heat transfer coefficient of a wrap around coil condenser soldered to the exterior surface of a water tank in a heat pump water heater (HPWH). The experimental data showed that the heat transfer coefficient did not significantly vary during the heat pump’s operation. Numerical and computational fluid dynamics models were developed to examine this phenomenon further. The modelling found that the tank water side heat transfer coefficient was the controlling thermal resistance in the condenser, and that reducing the coil pitch could improve the heat transfer coefficient.
1.
INTRODUCTION
Heat pumps have a long history of being utilised for water heating; an early example was cited by Sumner (1953) of the Norwich Corporation Electricity Department. In their water source system, heat was provided by a local river and delivered heat to a circulating hot water system. Although the heated water was used to provide space heating, Sumner suggested that such systems could be used for domestic water heating. An advantage of heat pump water heaters is the reduction in electrical power consumption compared to an electric resistance element heater. Anderson, Bradford and Carrington (1985) showed that by installing an air-source heat pump water heater in a New Zealand home, annual average energy savings of between 50 and 58% could be achieved compared to an electric water heater. Solar energy can also be used as a heating source for heat pumps. Charters, De Forest, Dixon and Taylor (1980) presented one of the pioneering bodies of research in the field of solar boosted heat pumps. In this Charters et al. discussed the development of a solar boosted HPWH that achieved a COP of 2.5. Further work by Charters, de Forest and Taylor (1984) showed that the solar boosted system could achieve a COP approaching 5 in favourable conditions. One important factor in determining the performance of HPWH’s is the temperature of the water to which the condenser is exposed. Huang and Chyng (2001) and Ito et. al. (1999) have shown that the COP of these systems can be correlated with water temperature. Given the relationship that has been shown to exist between COP and condenser temperature this study was undertaken to examine the interaction between a wrap around condenser and water tank in a typical HPWH system.
2.
EXPERIMENTAL SETUP AND ANALYSIS
The system examined, comprised a heat pump unit delivering energy to a 270 L (1300 x ∅550) storage tank. The tank was of a 2.5mm mild steel construction with a 0.25mm thick vitreous enamel glass liner to prevent corrosion and was insulated with 50mm of polyurethane foam; thus ensuring that heat loss from the tank was minimal.
Although some HPWHs, such as that developed by Charters et. al. (1980), use an external heat exchanger and pump to transfer heat from the refrigerant to the water, the system studied herein had the condenser coil wrapped around and soldered to the exterior surface of the storage tank surface, as shown in Figure 1. This transferred the heat from the condenser directly to the water, thus negating the need for a water pump to circulate water through a separate condenser. To ensure good thermal contact between the condenser coil and the tank wall, the condenser tubing was rolled to produce a “D” shaped cross-section before being soldered to the tank. This resulted in an increase in the contact area between the coil and the tank wall. The coil around the tank was 10mm in diameter, 33m long and was wrapped in 18 coils with a pitch of 53mm, however only 17 of these were in good contact with the wall.
Figure 1: Wrap around condenser and water tank In order to gather temperature data relating to the system, nine T-type thermocouples were soldered to the condenser coil. These thermocouples allowed the temperature of the refrigerant from the heat pump to be measured as it condensed. Additionally the tank water temperature was measured using a series of T-type thermocouples inserted along the axis of the tank. This allowed the water temperature at known heights within the tank to be determined. A custom data acquisition program was written to collect 16 temperature readings per minute and to average these on a minute by minute basis. This allowed the heat transfer from the condenser to the water in the tank to be determined. In order to determine the heat transferred to the water a modified first law analysis was implemented, as shown in Eqn 1. Using the rate of change of the temperature of the water in the tank over a seven minute period to a closed system, less the heat loss to the surrounding environment it was possible to ascertain the heat transferred to the water in the tank.
QWater = MC p
dTWater + U external A(TWater − TAmbient ) dt
(1)
By knowing the heat transfer to the water tank it was possible to calculate the overall heat transfer coefficient for the wrap around condenser used in the system. Because both the tank wall area and temperature and the water temperature were known, an overall heat transfer coefficient could be calculated using Eqn 2.
U=
QWater A(TWall − TWater )
(2)
During operation of the heat pump mixing in the tank produces an approximately uniform water temperature over the depth of the condenser coil hence a linear temperature difference has been used in Eqn 2.
3.
NUMERICAL THERMAL RESISTANCE MODEL
When developing the thermal resistance network for the condenser the analysis was divided into two distinct sections, the fin and the flat region. The fin region including the unbonded section of the tube, the soldered bond and the extended surface of the water tank between adjacent coils was treated as one region. In addition the area where the coil was bonded to the water tank was treated as a separate heat transfer path, as shown in Figure 2.
Figure 2: Resistance elements showing fin and flat region Having designated the two regions, a resistance circuit diagram as shown in Figure 3, was developed. This analysis accounted for the thermal resistance within each of the condensertank elements.
Rwall-fin
Rtube-fin
Rglass-fin
Rbond
Rrefrigerant
Rwater Rtube-flat
Rwall-flat
Rglass-flat
Figure 3: Thermal resistance network diagram Using the methodology described by Morrison (1994) it was possible to determine the magnitude of the thermal resistance in the fin and flat region, as well as the bond resistance. As such the thermal resistance (R1) of the flat region was given by Eqn 3.
R1 =
1 4tt kt ht L2 tanh(m1πD / 2)
(3)
ht is the condensing refrigerant film coefficient, L the coil length, D the coil diameter, tt the tube wall thickness, kt the tube thermal conductivity and m1 given by m1=√ (ht/kttt).
Similarly the thermal resistance in the finned area (R2), between adjacent coils was determined using Eqn 4.
R2 =
1 4t w k w hw L2 tanh(m2 S / 2)
(4)
hw is the water side heat transfer coefficient, L the coil length, S the coil pitch, tw the tube wall thickness, kw the tube thermal conductivity and m2 given by m2=√ (hw/kwtw). These equations were used in conjunction with the standard formulae for calculating thermal resistance both by conduction and convection to quantify all the thermal resistance elements.
4.
COMPUTATIONAL FLUID DYNAMICS MODEL
In the experimental component of this work the wrap around condenser coil design studied was fixed at a given pitch. As such to examine to examine alternative designs experimentally would require significant expense. Thus the use of computational fluid dynamics (CFD) modelling allowed coil pitch effects to be investigated before going to production. 4.1
Development of the CFD Model
Perhaps the most fundamental step of ensuring a CFD analysis is successful is the selection of boundary conditions that are an exact match or realistic approximation of the conditions likely to be encountered in an experimental situation. Because a significant portion of experimental work had been undertaken before the CFD model was developed, it was possible to use some of the experimental data to define the boundary conditions of the initial model. Although this may seem unusual it was done in this manner so that optimisation of the system could be undertaken in a realistic manner. From the experimental analysis and data supplied by the tank manufacturer, the dimensions of the tank and its material properties were known. Using this information a spatial mesh was generated using the program Gambit. In the generation of the mesh, it was assumed that the tank was axi-symmetric. This assumption, although not exactly the same as the experiment, allowed the analysis to be significantly simplified. By assuming that the tank was axi-symmetric this meant that the condenser coil was treated as a series of toroidal heating rings mounted to the surface of the tank. In addition to this it was assumed that instead of modelling the tube, it would be adequate to model it as discrete heat sources acting directly on the tanks outer wall but with the tank wall modelled to account for conduction between adjacent coils. Although there were 17 ½ tube coils in contact with the wall, only 17 were actually included in the model. From the experimental analysis that had been conducted on the system it was found that the heat transfer rate to the water did not vary significantly over a single heat up cycle. Therefore it was assumed that it would be adequate to apply a constant heat flux source as the heating elements for the transient CFD analysis. Additionally, it was assumed that the area between the heating rings was adiabatic, while the top and bottom surface of the tank were assumed to be insulated with 20mm of foam. All analyses were conducted using the commercial CFD package Fluent. Fluent is able to solve the governing equations of continuity, momentum and energy by discretising them for a specified grid or mesh. The equations are discretised for the mesh using the finite volume
method and for this study the QUICK discretisation scheme was used. Additionally the Boussinesq approximation was used to simplify the governing equations. Rosengarten (2000) had shown that the Boussinesq approximation was applicable to natural convection in horizontal cylinders containing water and therefore it was applied to all the situations. Although numerous authors have discussed the advantages of using low Reynolds number turbulence models for natural convection, such as that inside the water tank, it was decided that as a starting point the problem should be examined using the two-layer k-ε turbulence model. This route was chosen since the k-ε is the simplest of the turbulence models and has also been widely validated (Versteeg and Malalasekera, 1995). In using two-layer k-ε model, however the mesh had to be made fine near the walls so that the laminar sub layer could be accurately resolved, this technique was used by Rosengarten (2000) and is also recommended by Fluent (2001). In order to satisfy the criterion used by Fluent for determining the use of the two layer model that y+
