Numerical and Experimental Study of the Heat Pump Water Heater with an Immersed Helical Coil Heat Exchanger

*Sami Missaoui, Zied Driss, Romdhane Ben Slama and Bechir Chaouachi*

## **Abstract**

Traditional water heating and cooling methods consume a significant amount of energy. Heating and cooling were also significant contributors to CO2 emissions. Based on several previous studies, heat pumps are an economical solution because they reduce the energy consumed for water heating and the carbon dioxide emissions compared to conventional electric resistant water heaters, gas boilers, and so on. As a result, this chapter presented research studies on waste heat recovery from heat pumps' immersed helical condenser coils for domestic hot water production. In this work, the three-dimensional geometry of the storage tank with immersed helical pipe heat exchanger was simplified to two-dimensional axisymmetric geometry and the numerical investigation was conducted with using computational fluid dynamics (CFD) commercial software. The variable heat flux from the condenser coil was considered to heat the water in the tank under laminar flow regime. The proposed model was validated with the experimental data and agreed very well. According to the obtained results, the outlet heat flux tended to the decrease with an increase of the heating time. Also, the outcomes indicate that the waste heat can be used for water heating utilized for bathing and cleaning without affecting the heat pumps cycle.

**Keywords:** heat pumps, heating, cooling, thermodynamic parameters, heat recovery, helically coiled pipe

### **1. Introduction**

Energy consumption for domestic hot water production is on the rise in both residential and commercial buildings nowadays. Water heaters have traditionally been equipped with traditional heaters that generate heat by consuming fossil fuels, electricity, wood and oil. All of which are undesirable in terms of greenhouse gas emissions and energy consumption. As a result, the coupling of a heat pump system with a water tank is currently a viable recommended approach for water heating as a

substitute. Because of its excellent energy efficiency, simple operation, low cost, and environmental friendliness, many academics have been interested in heat pump water heaters (HPWH). Missaoui et al. [1] numerically investigate the HPWH with helically coiled tube heat exchanger. The results indicated that when the copper coil pitch is 20 mm, the water velocity increases and reaches its maximum in the middle part of the tank. Qiang and Shuhong et al. [2] carried out a numerical investigation on the performance of HPWH with wrap-around condenser coil. The results indicated that the heat transfer coefficient of variable pitch coil was increased by 21.91% compared with constant-pitch coil. Missaoui et al. [3] conducted an experimental and numerical analysis of a helical coil heat exchanger for domestic refrigerator and water heating. The results indicated that after 5 hours of heating the average coefficient of performance of the refrigerator domestic coupled with water heating process, the variable pitch coil was increased by 16.17% compared with normal coil. Zhou et al. [4] conducted a study on geometric parameter of a wrap-around condenser for a water tank with 200 L capacity. The results indicated that the pipe parameters such as location, turns and spacing have direct effects on the performance of the HPWH. Sami et al. [5] experimentally validated the mathematical model of the domestic refrigerator for water heating. The results indicated that the domestic refrigerator can be used for hot water production without removing its main role.

The goal of this project is to create a device that can take use of the waste heat produced by refrigeration equipment and use it for home functions such as bathing, laundry, and cleaning.

### **2. System description**

A schematic diagram for the water heating system is shown in **Figure 1**. The air conditioning with domestic hot water production is mainly composed of a water heating system and vapor compression cycle, including compressor, water tank with immersed condenser, an expansion valve and evaporator. This system is based on the same principle of vapor compression cycle. But, there is a small change in the condenser. The conventional heat pump was modified to the air conditioner with a domestic hot water supply that is operates in the domestic hot water production and space-cooling. The helically condenser coil was immersed in the water tank of 80 L capacity.

#### **3. Numerical model**

#### **3.1 CFD model**

As shown in **Figure 2**, the three dimensional water tank model was simplified as an axisymmetric two-dimensional model.

#### **3.2 Boundary conditions**

The boundary conditions of the heat transfer between the water and the condenser is illustrated in **Table 1**.

*Numerical and Experimental Study of the Heat Pump Water Heater with an Immersed Helical… DOI: http://dx.doi.org/10.5772/intechopen.105154*

#### **Figure 1.** *Schematic diagram of HPWH system.*

**Figure 2.** *Simplified model. (a) 3D view. (b) 2D view.*


#### **Table 1.**

*Boundary conditions.*

The considered equation was proposed by Dai et al. [6] and it is expressed as follows:

$$q(t) = -0.0000000003t^3 + 0.000032972t^2 - 0.18825t + 4376.4 \tag{1}$$

#### **3.3 Meshing**

As shown in **Figure 3**, the grid near the condenser coil and the tank wall was refined. The mesh was conducted using the commercial computational fluid dynamics

**Figure 3.** *Mesh and boundary conditions.*

*Numerical and Experimental Study of the Heat Pump Water Heater with an Immersed Helical… DOI: http://dx.doi.org/10.5772/intechopen.105154*

#### **Figure 4.** *Model validation results.*

(CFD) package Fluent. In the numerical investigation, the mesh with 40105 cells was adopted for further analysis.

#### **4. Model validation**

In order to validate the accuracy of our numerical method, we have compared our results to those reported by Dai et al. [7]. From these results, it has been observed that the numerical results are in good agreement with the experimental results referring to a HPWH with immersed condenser coil. In these conditions, the maximum absolute error is about 10% as shown in **Figure 4**.

#### **5. Results and discussion**

To calculate the water temperature distribution in each axial location along the height of the tank, the water tank was divided into three layers in the axial direction. Each layer was divided into three points in the radial direction designed by A, B and C. Details for the locations of the different test points are shown in **Figure 5**. In order to calculate the average water temperature in each layer, the Eq. (2) is used:

$$T\_{\mathbf{w},\mathbf{y}}(t) = \frac{\sum\_{\mathbf{x}=1}^{3} \mathbf{T}\_{\mathbf{w},\mathbf{x}}(t)}{3} \tag{2}$$

Where *Tw*,*<sup>x</sup>*ð Þ*t* is the water temperature in each test point.

**Figure 6** shows the average water temperature rising curves of A, B and C in water heating process at three different layers. From these results, it has been observed that the water temperature in the middle and the upper part of the tank was the same. On the other hand, the A water temperature curve rising slowly with slight fluctuations indicating that the hot water in the lower part of the storage tank rises up. This fact is due to the force of gravity (*g*) acting on the fluid density variations. The majority of water liquid in the lower part of storage tank still has not been affected by the


**Figure 5.** *Locations of different test points.*

convective heat transfer, except at the middle and upper part. Thus, this increase in water temperature in the middle and upper part of the storage tank is due to the buoyancy driven flow.

**Figure 7** shows the heat flux distribution of the helical coiled tube heat exchanger. From these results, it is clear that the heat flux decreases with the increase of the

*Numerical and Experimental Study of the Heat Pump Water Heater with an Immersed Helical… DOI: http://dx.doi.org/10.5772/intechopen.105154*

**Figure 6.** *Water temperature distribution in the water tank.*

**Figure 7.** *Heat flux distribution during heating process.*

heating time. Therefore, this result declined to the low convective heat transfers between the water in the tank and the refrigerant in the condenser when the water temperature rises up.

**Figure 8** shows the distribution of the water velocity over 60 min with the initial water temperature equal to 15°C. The zones near the condenser coil and tank wall are zoomed to obtain more detailed information about the water recirculation during heating process. From these results, it has been observed that the velocity distribution is high in the centerline of the vertical direction of the water tank. The high velocity field is accurately visualized near the tank walls and condenser coil. Indeed, a marked higher velocity distribution has been observed in the middle part of the storage tank. From the zoomed regions, the water near the tank wall and condenser coil flowing downward during the heating process. This fact is due to the water recirculation.

**Figure 8.** *Velocity distribution of the water in the storage tank at* t *= 60 min.*
