# Performance Recovery of Natural Draft Dry Cooling Systems by Combined Air Leading Strategies

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## Abstract

**:**

## 1. Introduction

## 2. Modeling and Approaches

#### 2.1. Physical Model

#### 2.2. Mathematical Model

#### 2.2.1. Macro Heat Exchanger Model

_{A}

_{min}are the air density and velocity at the minimum flow area. f is the loss coefficient expressed as follows:

_{min}are areas of the air side surface and minimum cross-section. v

_{i}and v

_{e}are the specific volumes at the inlet and exit, while v

_{m}equals the mean value. K

_{i}and K

_{e}are the inlet and exit loss coefficients set to be 0 because of the core friction factor f

_{c}key role in the loss coefficient:

_{A}

_{min}represents the Reynolds number with the air velocity at the minimum flow section.

_{he}is the heat exchanger effectiveness. (mC

_{p})

_{a}represents the air heat capacity. T

_{in,wa}is the inlet water temperature, while T

_{cell}means the cell temperature. The macro heat flow rate Φ

_{macro}equals the summation of heat rejections from all cells, while the total value Φ

_{total}can be achieved by summing the heat loads of all macros. For the macro heat exchanger model, the pressure loss coefficients and heat transfer effectiveness are listed in Table 2 [27,28].

#### 2.2.2. Conservation Equations and Numerical Approach

_{j}represents the velocity in the x

_{j}direction. φ, Γ

_{φ}and S

_{φ}are the variable, variable diffusivity coefficient and source [3,8,21,29]. For the viscous turbulent flow, the two-equation realizable k-ε model is employed. With the closed numerical equations, the rotation flows, boundary layer flows along with severely adverse pressure gradients which may also incur the recirculation flows, can be accurately predicted for NDDCS.

_{avg}and I are the average velocity and turbulence intensity. The turbulence intensity is typically set 10%. C is the empirical constant with the value of 0.09. μ

_{t}/μ is the turbulent viscosity ratio and assigned 1.1 in this work.

_{wind}takes the power-law equation:

_{w}is the wind speed at the reference height of 10 m with values of 4, 8, 12, 16 and 20 m/s. The exponent e is basically set 0.2 to represent the common ground roughness and atmosphere. The ambient temperature is set as 15 °C for the domain boundaries. The pressure outlet is set for the outlet surface, while symmetry for other planes. When without winds, the pressure inlet is appointed for three domain surfaces, while the pressure outlet for the top one.

^{−4}for all the variable scaled residuals is prescribed. Moreover, the mass flow rate through the dry-cooling tower and the average air temperature at the tower exit are also monitored to ensure the computations are converged to accurate results.

_{B}, and then the condenser heat rejection Φ is obtained according to Equation (11). The inlet water temperature t

_{wa1}of the air-cooled heat exchanger is then assumed and imported to the computational model of NDDCS. By numerical simulations, the heat rejection of air-cooled heat exchanger Φ' is obtained, and the average inlet air temperature t

_{a1}, total air mass flow rate m

_{a}can be obtained as well. If the relative error between Φ and Φ' is within the limit, the condensation temperature t

_{s}can be achieved following Equation (12), therefore the relevant turbine back pressure p

_{B}' can be calculated. If the calculated error between p

_{B}and p

_{B}' satisfies the allowed value, this iterating procedure is converged. Otherwise, re-start the whole process:

_{s}is the steam mass flow rate, h

_{s}and h

_{w}are enthalpies of exhaust steam and condensate. C

_{p,a}represents the air specific heat. K and A equal the overall heat transfer coefficient and total heat exchanger area.

#### 2.3. Experimental Validation

## 3. Results and Discussion

#### 3.1. With No Air Leading

#### 3.1.1. Streamlines

#### 3.1.2. Performances of Cooling Deltas

_{vol,cd}is proposed and defined as follows:

_{w}and V

_{0}are the volumetric flow rates under windy conditions and with no winds.

_{th,cd}, it is defined as follows:

_{w,cd}and Φ

_{0,cd}are the heat rejections of cooling delta in the presence and absence of winds.

#### 3.2. With Air Leading Strategies

#### 3.2.1. Streamlines

#### 3.2.2. Performances of Cooling Deltas

#### 3.3. Overall Performance

_{vol,dct}, average outlet temperature of circulating water t

_{wa2,avg}and turbine back pressure p

_{B}are calculated and compared, as shown in Figure 16.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Schematics of combined air leading strategies. (

**a**) Case A without air leading; (

**b**) Case B with inner air leading baffles and rounded frustum; (

**c**) Case C with outer air leading baffles; (

**d**) Case D with both inner and outer air leading measures; (

**e**) Geometric parameters.

**Figure 7.**Experimental validation for numerical simulation. (

**a**) Measuring points in vertical and horizontal views; (

**b**) Ascending velocity without winds; (

**c**) Ascending velocity at 4 m/s.

**Figure 8.**Streamlines colored by temperature for case A at various wind speeds. (

**a**) at 4 m/s; (

**b**) at 12 m/s; (

**c**) at 20 m/s.

**Figure 9.**Flow and temperature fields through lateral cooling deltas for case A at various wind speeds. (

**a**) at 4 m/s; (

**b**) at 12 m/s; (

**c**) at 20 m/s.

**Figure 10.**Performance distributions for case A. (

**a**) Volume effectiveness; (

**b**) Thermal efficiency; (

**c**) Outlet water temperature.

**Figure 11.**Streamlines colored by temperature for case D at various wind speeds. (

**a**) at 4 m/s; (

**b**) at 12 m/s; (

**c**) at 20 m/s.

**Figure 12.**Flow and temperature fields through lateral cooling deltas of case D at various wind speeds. (

**a**) at 4 m/s; (

**b**) at 12 m/s; (

**c**) at 20 m/s.

**Figure 13.**Performance distributions for case B. (

**a**) Volume effectiveness; (

**b**) Thermal efficiency; (

**c**) Outlet water temperature.

**Figure 14.**Performance distributions for case C. (

**a**) Volume effectiveness; (

**b**) Thermal efficiency; (

**c**) Outlet water temperature.

**Figure 15.**Performance distributions for case D. (

**a**) Volume effectiveness; (

**b**) Thermal efficiency; (

**c**) Outlet water temperature.

**Figure 16.**Overall thermo-flow performances of natural draft dry cooling system with air leading strategies. (

**a**) Overall volume effectiveness; (

**b**) Average outlet water temperature; (

**c**) Turbine back pressure.

Parameters | Symbol | Value |
---|---|---|

Height of tower | H_{t} | 140 m |

Base diameter of tower | d_{b} | 114 m |

Outlet diameter of tower | d_{o} | 78 m |

Throat height of tower | H_{tt} | 110 m |

Throat diameter of tower | d_{tt} | 74 m |

Height of air-cooled heat exchanger | H_{he} | 20 m |

Outlet diameter of heat exchanger | d_{ohe} | 122 m |

Number of cooling deltas | n_{cd} | 136 |

Pressure Loss Coefficients | |||||||||

σ | K_{i} | K_{e} | a | b | |||||

0.492 | 0 | 0 | 0.9255 | −0.34123 | |||||

Effectiveness Versus Velocity | |||||||||

v_{a} (m/s) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 |

ε_{he} | 0.75584 | 0.63524 | 0.55515 | 0.49612 | 0.4501 | 0.41289 | 0.38201 | 0.35588 | 0.33342 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, W.; Chen, L.; Huang, X.; Yang, L.; Du, X.
Performance Recovery of Natural Draft Dry Cooling Systems by Combined Air Leading Strategies. *Energies* **2017**, *10*, 2166.
https://doi.org/10.3390/en10122166

**AMA Style**

Wang W, Chen L, Huang X, Yang L, Du X.
Performance Recovery of Natural Draft Dry Cooling Systems by Combined Air Leading Strategies. *Energies*. 2017; 10(12):2166.
https://doi.org/10.3390/en10122166

**Chicago/Turabian Style**

Wang, Weijia, Lei Chen, Xianwei Huang, Lijun Yang, and Xiaoze Du.
2017. "Performance Recovery of Natural Draft Dry Cooling Systems by Combined Air Leading Strategies" *Energies* 10, no. 12: 2166.
https://doi.org/10.3390/en10122166