# Optimum Design and Operation of an HVAC Cooling Tower for Energy and Water Conservation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. General Description of the Model

#### 2.2. Component Models

#### 2.2.1. Cooling Tower (type51b)

#### Cooling Tower Water Output Temperature (${T}_{w2}$) Prediction

- Heat and mass transfer in a direction normal to the flows only.
- Negligible heat and mass transfer through the tower to/from the surroundings.
- Constant water and dry air specific heats.
- Uniform temperature throughout the water stream at any cross-section.
- Uniform cross-sectional area of the tower.

**Effectiveness Model**Type51b uses the effectiveness model for cooling towers developed by Braun et al. [29] to predict the cooling tower performance. This model is based on the well-known Merkel [30] model, which relies on two key assumptions: Le = 1 and negligible water loss due to evaporation in the energy balance. According to these simplifications, the equations for the cooling tower may be reduced to:

#### Cooling Tower Power Consumption Prediction

#### Cooling Tower Water Consumption Prediction

#### Validation of Cooling Tower Model

#### 2.2.2. Reference Building (type56a)

#### 2.2.3. Chiller (type666)

#### 2.2.4. Control Strategies

- Fan cycling control (FCC).
- Multiple-speed fan motor control in 3 stages of velocity (MSC).
- Frequency-modulating control via VFD (FMC).
- Optimum control (OC).

## 3. Results and Discussion

#### 3.1. Influence of the Optimizing Control Strategy

#### 3.2. Components Influence

## 4. Conclusions

- A new method to control HVAC systems was developed. Compared to the traditional control methods used in practice (fan cycling, multiple-speed fan motors or frequency-modulating controls), significant savings in the overall operation costs can be achieved (up to 0.7% depending on the cooling tower configuration). The usual ${T}_{w2}$-based controls provided the worst results related to energy consumption and cost in all of the scenarios considered in the simulations (even worse than the simplest FCC method). This fact has been assessed by the influence of the water temperature on the compressor consumption. An appropriate operation criterion should take into account the relative influence of the fan frequency on the cooling tower output water temperature alongside the power absorbed by the fans. A higher temperature can result in a major cost in the system because of the compressor consumption of the chiller.
- The cooling tower configuration has a direct influence on the energy and water consumption of the air conditioning system. Both the water distribution device and drift eliminator affect the thermal behavior of the cooling tower, working as an additional surface of mass and energy exchange. Changing the combination of these two elements can result in an improvement of 10.2% in energy savings between Drift Eliminator E and GWDS and Drift Eliminator A with PWDS. The water consumption can be reduced to 4.8%, from Drift Eliminator A and PWDS to Drift Eliminator F and PWDS. In economic terms, costs can be reduced to 8.2%, from the configuration with GWDS and Drift Eliminator E to PWDS with Drift Eliminator C.
- Taking into account the maximum saving achievable considering the four control systems presented and the twelve configurations of the cooling tower, it is possible to achieve a savings of 212.25 € per story (6.30 €·kW${}_{\mathrm{installed}}$${}^{-1}$) between the optimization system with Drift Eliminator C and PWDS and the water temperature control with VFD (FMC) using Drift Eliminator E and GWDS.
- Considering an average hotel with 300 rooms in the southeast region of Spain, energy costs can be reduced to 3240 € per year by using the proposed capacity control method. This scenario corresponds to the operation with minimum costs. This value can increase to 36% in oversized systems, according to the research carried out in this study (9.28 €·kW${}_{\mathrm{installed}}$${}^{-1}$, 312.87 € per story, 4382 € per year in the reference hotel).
- The results presented in this paper could eventually assist engineers to select the suitable equipment and system control of an HVAC system. The selection of the components and the control method described above was based on economic parameters. However, the results provided in this work may also be used to define additional criteria based on specific situations.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

${A}_{V}$ | Surface area of water droplets per tower cell exchange volume (m${}^{2}$·m${}^{-3}$) |

c | Tower characteristic constant |

${C}_{p}$ | Specific heat at constant pressure (kJ·kg${}^{-1}$·K${}^{-1}$) |

${C}_{c}$ | Cycles of concentration |

${C}_{s}$ | Average derivative of saturation air enthalpy with respect to temperature |

$\dot{Q}$ | Heat transferred (kW) |

${\dot{Q}}_{ch}$ | Capacity of the chiller (kW) |

COP | Coefficient of performance |

D | Drift losses |

f | Fan frequency (Hz) |

g-value | Solar heat gain |

h | Enthalpy (kJ·kg${}^{-1}$) |

${h}_{C}$ | Convective heat transfer coefficient of air (W·m${}^{-2}$·K${}^{-1}$) |

${h}_{D}$ | Convective mass transfer coefficient (kg${}_{a}$·m${}^{2}$·s${}^{-1}$) |

${h}_{g,w}$ | Specific enthalpy of saturated water vapor at Tw (kJ·kg·${}^{-1}$·w${}^{-1}$) |

${h}_{s,w,e}$ | Effective saturation enthalpy (kJ·kg${}^{-1}$) |

Le | Lewis number Le = h${}_{C}$·h${}_{D}$${}^{-1}$·C${}_{pa}$${}^{-1}$ |

$\dot{m}$ | Mass flow rate (kg·h${}^{-1}$) |

${\dot{m}}_{b}$ | Blowdown losses (kg·h${}^{-1}$) |

${\dot{m}}_{d}$ | Water escaping from the cooling tower (kg·h${}^{-1}$) |

${\dot{m}}_{r}$ | Mass flow recirculated by the tower (kg·h${}^{-1}$) |

n | Tower characteristic exponent |

${\dot{W}}_{\mathrm{comp}}$ | Chiller’s compressor power (kW) |

${\dot{W}}_{\mathrm{fan}}$ | Cooling tower’s fan power (kW) |

$\dot{Q}$ | Capacity of the chiller (kW) |

T | Temperature (${}^{\circ}$C) |

${U}_{\mathrm{mean}}$ | Wall heat transfer coefficient (W·m${}^{-2}$·K${}^{-1}$) |

u-value | Glass heat transfer coefficient (W·m${}^{-2}$) |

${V}_{T}$ | Volume of the cooling tower (m${}^{3}$) |

${W}_{T}$ | Total energy consumption (kWh·year${}^{-1}$) |

$x,{x}^{\prime},{x}^{\u2033},y,{y}^{\prime},{y}^{\u2033},z,{z}^{\prime},{z}^{\u2033}$ | Constants in ${\dot{m}}_{a}$ calculation |

## Abbreviations

config | Configuration |

DE | Drift eliminator |

DoE | United States Department of Energy |

EPBD | European Energy Performance of Buildings Directive |

EU | European Union |

NTU | Number of transfer units |

FCC | Fan cycling control |

PLR | Chiller part load ratio (the ratio of the current load to the rated load) |

FFLC | Fraction of full load capacity |

FMC | Frequency-modulating control via VFD |

IEA | International Energy Agency |

HVAC | Heating, ventilation and air conditioning |

MSC | Multiple-speed fan motor control in three stages of velocity |

GWDS | Gravity water distribution system |

OC | Optimum control |

PWDS | Pressure water distribution system |

TMY | Typical meteorological year file |

VFD | Variable frequency drive |

## Greek Symbols

$\alpha ,\beta ,\gamma ,\delta $ | Constants in ${\dot{W}}_{\mathrm{fan}}$ calculation |

${\omega}_{a}$ | humidity ratio of moist air (kgw·kga${}^{-1}$) |

${\omega}_{s}$ | humidity of saturated air (kgw·kga${}^{-1}$) |

${\omega}_{s,w,e}$ | effective saturation humidity (kgw·kga${}^{-1}$) |

${\epsilon}_{a}$ | air-side heat transfer effectiveness |

## Subscripts

1 | inlet |

2 | outlet |

a | air |

max | maximum |

met | outlet |

nom | nominal |

w | water |

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**Figure 4.**Experimental results for the power consumption of the fan as a function of f. Type51b prediction and proposed correlation. (

**a**) Splash (pressure) water distribution system (PWDS) and (

**b**) film flow (gravity) water distribution system (GWDS).

**Figure 5.**Cooling tower validation configured with PWDS system and Drift Eliminator D, regarding water outlet temperature (

**a**) and air mass flow rate (

**b**).

**Figure 8.**Coefficient of performance (COP) versus condenser water inlet temperature (range of 5 ${}^{\circ}$C). Airwell CWP 09 CO.

**Figure 9.**Behavior of the capacity control methods (FCC, MSC, FMC and OC from left to right and top to bottom) during a day, regarding the power consumption (fan and compressor), the frequency of the fan and the outlet water temperature of the cooling tower and the temperature of the hotel.

**Figure 11.**Interaction between the power consumption of the cooling tower fan and chiller compressor.

**Table 1.**Constants for Equation (17).

Configuration | α | β | γ | δ |
---|---|---|---|---|

[W·Hz${}^{-3}$] | [W·Hz${}^{-2}$] | [W·Hz${}^{-1}$] | [W] | |

PWDS-A | 0.00704 | −0.34459 | 11.54566 | 4.64615 |

PWDS-B | 0.00626 | −0.29466 | 10.90257 | 3.66853 |

PWDS-C | 0.00628 | −0.29149 | 10.78880 | 3.88112 |

PWDS-D | 0.00650 | −0.29934 | 10.82658 | 3.95944 |

PWDS-E | 0.00661 | −0.30910 | 10.99469 | 3.50420 |

PWDS-F | 0.00626 | −0.29325 | 10.83723 | 3.71678 |

GWDS-A | 0.00655 | −0.31012 | 11.01327 | 3.68462 |

GWDS-B | 0.00688 | −0.33929 | 11.61161 | 2.05175 |

GWDS-C | 0.00652 | −0.30857 | 11.01921 | 3.67483 |

GWDS-D | 0.00635 | −0.30900 | 11.08539 | 3.53916 |

GWDS-E | 0.00635 | −0.30136 | 11.05990 | 3.26014 |

GWDS-F | 0.00585 | −0.27771 | 10.68402 | 3.98112 |

**Table 2.**Constants for Equation (18).

Configuration | ${\dot{\mathit{m}}}_{\mathit{a},\mathbf{max}}$ | $\mathit{x}\times {10}^{9}$ | $\mathit{y}\times {10}^{7}$ | $\mathit{z}\times {10}^{7}$ | ${\mathit{x}}^{\prime}\times {10}^{6}$ | ${\mathit{y}}^{\prime}\times {10}^{4}$ | ${\mathit{z}}^{\prime}\times {10}^{2}$ | ${\mathit{x}}^{\prime \prime}\times {10}^{2}$ | ${\mathit{y}}^{\prime \prime}\times {10}^{1}$ | ${\mathit{z}}^{\prime \prime}\times {10}^{0}$ |
---|---|---|---|---|---|---|---|---|---|---|

[kg· h${}^{-1}$] | [h${}^{-2}$·kg${}^{-2}$·Hz${}^{-2}$] | [h${}^{-2}$·kg${}^{-2}$·Hz${}^{-1}$] | [h${}^{-2}$·kg${}^{-2}$] | [h${}^{-1}$·kg${}^{-1}$·Hz${}^{-2}$] | [h${}^{-1}$·kg${}^{-1}$·Hz${}^{-1}$] | [h${}^{-1}$·kg${}^{-1}$] | [Hz${}^{-2}$] | [Hz${}^{-1}$] | [-] | |

PWDS-A | 3148.18 | 0.09460 | −0.05048 | 0.37426 | −0.67950 | 0.34870 | −0.01952 | 0.09413 | −0.24351 | 0.05077 |

PWDS-B | 3947.54 | 0.21874 | −0.15843 | 2.65464 | −1.81739 | 1.31301 | −0.21864 | 0.35127 | −2.31797 | 4.11900 |

PWDS-C | 4132.97 | −0.20945 | 0.16038 | −2.58101 | 1.75825 | −1.34302 | 0.21220 | −0.34058 | 2.80877 | −4.11206 |

PWDS-D | 3770.53 | 0.02849 | −0.04030 | 0.99325 | −0.19989 | 0.29741 | −0.07719 | 0.02015 | −0.22406 | 1.24783 |

PWDS-E | 3059.00 | −0.11425 | 0.07863 | −1.31778 | 0.81994 | −0.55919 | 0.09099 | −0.13032 | 1.07447 | −1.38599 |

PWDS-F | 3142.05 | 0.45753 | −0.34221 | 6.03667 | −3.68569 | 2.74174 | −0.48699 | 0.68581 | −4.88648 | 9.09243 |

GWDS-A | 4402.98 | 0.00217 | −0.03071 | 0.83499 | 0.32532 | 0.02083 | −0.03215 | −0.10400 | 0.43010 | 0.10470 |

GWDS-B | 3469.25 | −0.08375 | 0.05941 | −1.10113 | 0.50596 | −0.36311 | 0.07121 | −0.04455 | 0.53083 | −0.82314 |

GWDS-C | 4171.26 | 0.02978 | −0.01378 | −0.08302 | −0.50219 | 0.30391 | −0.02564 | 0.15544 | −0.80898 | 1.09495 |

GWDS-D | 3741.09 | 0.34067 | −0.22908 | 3.45193 | −2.69013 | 1.79803 | −0.26871 | 0.49231 | −3.08144 | 4.85449 |

GWDS-E | 2330.40 | 0.07389 | −0.04520 | 0.41255 | −0.63511 | 0.39548 | −0.03896 | 0.09702 | −0.38986 | 0.52379 |

GWDS-F | 2438.36 | 0.03954 | −0.02633 | 0.32788 | −0.35884 | 0.24167 | −0.03113 | 0.04567 | −0.09154 | 0.31584 |

Building Properties | |
---|---|

Area [m${}^{2}$] | 642.6 |

Wall U${}_{\mathrm{mean}}$ [W·m${}^{-2}$·K${}^{-1}$] | 0.24 |

Wall thickness [m] | 0.16 |

Window u-value [W·m${}^{-2}$·K${}^{-1}$] | 1.0 |

Window g-value | 0.58 |

Solar shading | 0.8 |

Infiltration constant [h${}^{-1}$] | 0.5 |

Volume of air change [m${}^{3}$·h${}^{-1}$] | 900 |

Room temperature set-point [${}^{\circ}$C] | 24 |

Configuration | Value | Schedule |
---|---|---|

Laptop [W] | 80 | 9:00–11:00 |

TV [W] | 250 | 17:00–22:00 |

Refrigerator [W] | 100 | 00:00–24:00 |

Lightning [W·m${}^{-2}$] | 13 | 17:00–22:00 |

Guests [W] [sensible/latent] | [65/55] × 19 | 00:00–11:00/14:00–24:00 |

Employees [W] [sensible/latent] | [65/55] × 2 | 11:00–14:00 |

Measure | Range | Cost | Unit |
---|---|---|---|

Energy | - | 0.224 | €· kWh${}^{-1}$ |

Water | 9 $\ge {V}_{\mathrm{m}}$ | 0.962 | €·m${}^{-3}$ |

32 $\ge {V}_{\mathrm{m}}>$ 9 | 1.578 | ||

60 $\ge {V}_{\mathrm{m}}>$ 32 | 2.695 | ||

${V}_{\mathrm{m}}>$ 60 | 4.520 |

Test | Config | ${\dot{\mathit{W}}}_{\mathbf{fan},\mathbf{FCC}}$ | ${\dot{\mathit{W}}}_{\mathbf{comp},\mathbf{FCC}}$ | V${}_{\mathbf{tot},\mathbf{FCC}}$ | ${\dot{\mathit{W}}}_{\mathbf{fan},\mathbf{MSC}}$ | ${\dot{\mathit{W}}}_{\mathbf{comp},\mathbf{MSC}}$ | V${}_{\mathbf{tot},\mathbf{MSC}}$ | ${\dot{\mathit{W}}}_{\mathbf{fan},\mathbf{FMC}}$ | ${\dot{\mathit{W}}}_{\mathbf{comp},\mathbf{FMC}}$ | V${}_{\mathbf{tot},\mathbf{FMC}}$ | ${\dot{\mathit{W}}}_{\mathbf{fan},\mathbf{OC}}$ | ${\dot{\mathit{W}}}_{\mathbf{comp},\mathbf{OC}}$ | V${}_{\mathbf{tot},\mathbf{OC}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Run | [kWh] | [kWh] | [m${}^{3}$] | [kWh] | [kWh] | [m${}^{3}$] | [kWh] | [kWh] | [m${}^{3}$] | [kWh] | [kWh] | [m${}^{3}$] | |

1 | PWDS-A | 914.31 | 7868.83 | 179.03 | 734.43 | 8115.69 | 179.02 | 610.70 | 8324.59 | 178.57 | 780.72 | 7984.65 | 178.90 |

2 | PWDS-B | 905.90 | 7925.09 | 172.60 | 714.88 | 8170.18 | 173.04 | 607.93 | 8336.06 | 172.92 | 730.77 | 8061.45 | 172.65 |

3 | PWDS-C | 913.21 | 7908.48 | 171.43 | 729.32 | 8144.71 | 171.44 | 613.20 | 8334.73 | 171.17 | 750.70 | 8032.97 | 170.94 |

4 | PWDS-D | 928.00 | 7992.24 | 171.08 | 731.76 | 8217.39 | 171.36 | 630.60 | 8355.53 | 171.13 | 689.93 | 8169.51 | 171.09 |

5 | PWDS-E | 923.10 | 8019.19 | 170.69 | 758.59 | 8201.77 | 170.85 | 652.43 | 8378.02 | 170.86 | 724.55 | 8174.35 | 170.74 |

6 | PWDS-F | 906.54 | 8117.43 | 170.66 | 766.80 | 8293.39 | 170.95 | 680.87 | 8421.47 | 170.79 | 777.32 | 8230.28 | 170.69 |

7 | GWDS-A | 909.60 | 8094.18 | 171.12 | 844.19 | 8217.73 | 171.36 | 740.35 | 8410.87 | 171.14 | 902.81 | 8106.35 | 171.32 |

8 | GWDS-B | 906.32 | 8311.25 | 171.07 | 794.99 | 8427.69 | 171.20 | 723.71 | 8533.06 | 171.24 | 740.26 | 8438.89 | 171.13 |

9 | GWDS-C | 911.72 | 8310.46 | 171.10 | 794.25 | 8423.79 | 171.26 | 722.28 | 8530.97 | 171.18 | 703.29 | 8457.54 | 171.24 |

10 | GWDS-D | 881.64 | 8285.69 | 170.99 | 804.23 | 8396.14 | 171.20 | 727.15 | 8514.00 | 171.04 | 860.61 | 8306.49 | 171.12 |

11 | GWDS-E | 907.91 | 8796.20 | 171.80 | 868.15 | 8843.78 | 172.28 | 822.36 | 8888.53 | 172.21 | 737.77 | 8924.19 | 172.45 |

12 | GWDS-F | 876.79 | 8602.50 | 171.29 | 812.34 | 8672.32 | 171.71 | 758.69 | 8736.19 | 171.65 | 701.31 | 8731.29 | 171.82 |

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## Share and Cite

**MDPI and ACS Style**

García Cutillas, C.; Ruiz Ramírez, J.; Lucas Miralles, M.
Optimum Design and Operation of an HVAC Cooling Tower for Energy and Water Conservation. *Energies* **2017**, *10*, 299.
https://doi.org/10.3390/en10030299

**AMA Style**

García Cutillas C, Ruiz Ramírez J, Lucas Miralles M.
Optimum Design and Operation of an HVAC Cooling Tower for Energy and Water Conservation. *Energies*. 2017; 10(3):299.
https://doi.org/10.3390/en10030299

**Chicago/Turabian Style**

García Cutillas, Clemente, Javier Ruiz Ramírez, and Manuel Lucas Miralles.
2017. "Optimum Design and Operation of an HVAC Cooling Tower for Energy and Water Conservation" *Energies* 10, no. 3: 299.
https://doi.org/10.3390/en10030299