# Modelling the Steady-State Performance of Coiled Falling-Film Drain Water Heat Recovery Systems Using Rated Data

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## Abstract

**:**

## 1. Introduction

_{2}emissions [13,14]. Other studies conducted in Canada and the Netherlands support these results [15,16].

## 2. Method

## 3. Model Development

#### 3.1. Estimating the Rated Equal Flow Effectiveness Curve

- The user may have access to CSA test data from a system manufacturer, or from CSA reports. If available, these data would contain the equal flow effectiveness curve fit in the form of Equation (3);
- The user may have equal flow effectiveness measurements taken at the CSA test flow rates of 5.5, 7, 9, 10, 12 and 14 L/min, or similar data produced from other sources. The equal flow effectiveness curve can be developed by fitting Equation (3) to these data. Care must be taken when doing this. At low flow rates, the falling film on the drain side becomes unstable and, as a result, the steady-state performance varies between DWHR systems. Therefore, when generating the curve fit, the user is advised not to use any data obtained at flow rates below 5.5 L/min, or below 7 L/min for DWHR systems with diameters of 10.2 cm or larger.

#### 3.2. Temperature Adjustment of the Equal Flow Effectiveness Curve

#### 3.3. Performance at Unequal Flow Conditions

## 4. Overall Model

- Obtain the equal flow effectiveness curve. The curve may be directly available from CSA reports. If not, fit a curve of best fit in the form of Equation (3) to the equal flow data from CSA or an equivalent rating process. The user is advised not to use any data obtained at flow rates below 7 L/min for DWHR systems with diameters of 10.2 cm or larger, or flow rates below 5.5 L/min for DWHR systems with smaller diameters. Use this curve fit to calculate the equal flow effectiveness at the desired mains-side flow rate;
- Adjust the calculated effectiveness to represent the input temperatures being considered using Equation (4). This is a two-stage process. If the effectiveness curves determined in step (1) are not taken from the reference condition of ${T}_{h,i}$ = 40 °C and ${T}_{c,i}$ = 10 °C, then Equation (4) must first be used to determine ${\epsilon}_{ref}$. Following this, Equation (4) is used again to calculate $\epsilon $ at the inlet temperatures of interest;
- A conversion from effectiveness to heat transfer rate is required. Make the conversion using Equation (6), where $\dot{V}$ is the flow rate in L/min, the heat transfer rate, q, is in kW, and temperatures are in °C. The numbers in Equation (6) assume constant fluid density ($\rho $ = 1000 kg/m
^{3}) and specific heat (${C}_{p}$ = 4.18 kJ/kg°C) for water. The 60,000 in the denominator is to convert $\dot{V}$ from L/min into m^{3}/s.$$\begin{array}{c}q=\epsilon \times {q}_{max}=\epsilon {C}_{min}\left({T}_{h,i}-{T}_{c,i}\right)=\epsilon {\left(\rho \dot{V}{C}_{p}\right)}_{min}\left({T}_{h,i}-{T}_{c,i}\right)=\frac{4180\times \dot{V}\times \epsilon \times \left({T}_{h,i}-{T}_{c,i}\right)}{60000}\end{array}.\text{}$$ - If required, find the unequal flow heat transfer rate using Equation (5).

#### 4.1. Model Limitations

#### 4.2. Model Validation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Simplified schematic of the test apparatus during operation, where the blue and red branches allow variation in flow rates on the cold and hot side of the DWHR unit respectively.

**Figure 5.**Possible plumbing setups for DWHR systems in a residential building. In the figure, (

**A**) depicts a system where all preheated water from the DWHR pipe is fed to the water heater, (

**B**) depicts a system where all preheated water is fed to the mixing valve at the showerhead, and (

**C**) is a combination of (

**A**,

**B**).

**Figure 6.**Mains water flow rate through the DWHR system as a function of shower temperature for a 9.5-L/min showerhead, for constant mains water temperatures of 5, 10 and 15 °C.

System | Diameter | Length |
---|---|---|

# | cm | cm |

1 | 5.1 | 91 |

2 | 5.1 | 152 |

3 | 7.6 | 91 |

4 | 7.6 | 107 |

5 | 7.6 | 152 |

6 | 7.6 | 244 |

7 | 10.2 | 122 |

8 | 10.2 | 152 |

$\dot{\mathit{V}}$ (L/min) | $\mathit{\epsilon}$ | ${\mathit{q}}_{\mathit{c}}$ (kW) |
---|---|---|

5.49 | 39.2% | 4.06 |

12.11 | 27.6% | 4.80 |

7.00 | 35.2% | 5.36 |

8.94 | 31.5% | 5.88 |

9.99 | 30.0% | 6.57 |

14.11 | 25.7% | 6.94 |

Data Set | Number of Tests | Mean Absolute Percentage Error | Maximum Percentage Error |
---|---|---|---|

CSA flow rates | 42 | 1.8% | 7.9% |

Non-CSA flow rates | 93 | 3.5% | 9.7% |

All Test Points | 135 | 3.0% |

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**MDPI and ACS Style**

Manouchehri, R.; Collins, M.R. Modelling the Steady-State Performance of Coiled Falling-Film Drain Water Heat Recovery Systems Using Rated Data. *Resources* **2020**, *9*, 69.
https://doi.org/10.3390/resources9060069

**AMA Style**

Manouchehri R, Collins MR. Modelling the Steady-State Performance of Coiled Falling-Film Drain Water Heat Recovery Systems Using Rated Data. *Resources*. 2020; 9(6):69.
https://doi.org/10.3390/resources9060069

**Chicago/Turabian Style**

Manouchehri, Ramin, and Michael R. Collins. 2020. "Modelling the Steady-State Performance of Coiled Falling-Film Drain Water Heat Recovery Systems Using Rated Data" *Resources* 9, no. 6: 69.
https://doi.org/10.3390/resources9060069