# A Comparative Study of CFD Models of a Real Wind Turbine in Solar Chimney Power Plants

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Methodologies

#### 2.1. Modelling the Fluid Flow and Heat Transfer Inside the System

^{10}, which shows that the airflow should be modelled as a turbulent flow. Guo et al. and Ming et al. used the standard k-ε turbulence closure, while Gholamalizadeh et al. employed the Renormalization-group (RNG) turbulence closure, in which the full buoyancy effect was activated. Scalable wall function is adopted to model the near wall treatment of the turbulent airflow. The simulations conducted in this study used the RNG turbulence closure, which is able to employ the scalable wall functions to capture the boundary layer. The main reason for selecting this method was to reduce the mesh resolution since the computational cost of simulations is high. A multi-block mesh was used to discrete the computational domain consisting of three parts. Unstructured mesh was adopted for the turbine zone, including prismatic inflation layers on the turbine surface, which captured the boundary layer. The meshes of the domains before and after the turbine zone were structural. Three mesh sizes were adopted for the computational domain to obtain a mesh independent solution. Temperature increase inside of the collector and the mass flow rate were captured to obtain the fine mesh. A mesh sensitivity study indicated that attempts to refine the mesh further never achieved more than a relative difference of 1.5%, while it increased the computational cost considerably. Therefore, for the fine mesh, insensitivity of the solution to the mesh was verified. For the fine mesh, numbers of the structural mesh and unstructured mesh were about 2,280,000 and 5,200,000, respectively. Using the fine mesh, simulations were validated by comparing the numerical results with the experimental data of the Manzanares SCPP [3]. At a solar irradiance of 850 W/m

^{2}, the simulation predicted a pressure drop of 81.5 Pa across the turbine, the inlet chimney velocity of 9 m/s, and the collector temperature increase of 17.2 K, while, according to the measured data, those reached 80 Pa, 8.8 m/s and 17.5 K, respectively.

#### 2.2. Turbine Zone

#### 2.3. System Performance Calculation

## 3. Results and Discussion

^{2}.

^{2}, respectively. In [27], Gholamalizadeh et al.’s model predicted a turbine pressure drop of 81.5 Pa for the same conditions, which was in a good agreement with the measured data. According to simulations conducted in this study, the model predicted a turbine pressure drop of about 74.9 Pa at a solar irradiance of 800 W/m

^{2}. Ming et al.’s model predicted a pressure drop of about 79 Pa, and this pressure drop value is close to that of Gholamalizadeh et al.’s model. However, the turbine in Ming et al.’s model had three blades and therefore, it should be noted that, in Ming et al.’s model, the pressure would drop to a higher value if a 4-bladed turbine had been modelled. Consequently, considering number of blades, this model overestimated the pressure drop.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

a_{λ} | spectral absorption coefficient |

E | energy (J) |

${G}_{b}$ | generation of turbulence kinetic energy due to buoyancy |

${G}_{k}$ | generation of turbulence kinetic energy due to the mean velocity gradients |

g | gravitational acceleration (m/s^{2}) |

H | total enthalpy (J) |

h | species enthalpy(energy/mass) |

I | radiation intensity (W/m^{2}), unit matrix |

J | diffusion flux (kg/m^{2}s) |

k | thermal conductivity (W/m∙K) |

n | refractive index, turbine speed (rpm) |

P | power (W) |

p | pressure (Pa) |

p_{0} | operating pressure (Pa) |

Q | heat transfer rate (W), volume flow rate (m^{3}/s) |

R | rotor radius (m) |

r | radial coordinate (m) |

$\overrightarrow{r}$ | position |

$\overrightarrow{s}$ | direction |

S_{h} | heat source term |

T | temperature (K), torque (N∙m) |

T_{0} | operating temperature (K) |

u | velocity magnitude (m/s) |

$\overrightarrow{v}$ | overall velocity vector (m/s) |

ν | velocity (m/s) |

x | axial coordinate (m) |

${Y}_{M}$ | contribution of the fluctuating dilatation in compressible turbulence to overall dissipation rate |

Greek Symbols | |

α | thermal diffusivity (m^{2}/s) |

${\alpha}_{k}$ | inverse effective Prandtl numbers for k |

${\alpha}_{\epsilon}$ | inverse effective Prandtl numbers for ε |

β | thermal expansion coefficient (1/K) |

Δ | differential |

η | efficiency |

λ | wavelength (μm) |

θ | incident angle |

μ | dynamic viscosity (Pa-s) |

ρ | density (kg/m^{3}) |

σ | stefan-Boltzmann constant (5.67 × 10^{−8} W/m^{2} K^{4}) |

σ_{S} | scattering coefficient (1/m) |

$\stackrel{=}{\tau}$ | stress tensor (Pa) |

$\phi $ | phase function |

${\mathsf{\Omega}}^{\prime}$ | solid angle (radians) |

$\overrightarrow{\omega}$ | angular velocity (1/s) |

Subscripts | |

0 | reference |

b | black body |

c | cover |

eff | effective |

r | relative |

rev | reversible |

SCPP | solar chimney power plant |

s | surface |

t | turbine |

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Parameters | Values |
---|---|

Chimney height | 194.6 m |

Chimney diameter | 10.16 m |

Collector radius | 122 m |

Mean collector height | 1.85 m |

Number of turbine blades | 4 |

Turbine blade profile | FX W-151-A |

Parameters | Values |
---|---|

Ambient pressure | 101,325 Pa |

Ambient temperature | 302 K |

Thermal expansion coefficient | 0.00331 (1/K) |

Solar irradiance | 800 W/m^{2} |

Equation | Gholamalizadeh et al. | Guo et al. | Ming et al. | |
---|---|---|---|---|

Continuity | $\frac{\partial}{\partial {x}_{i}}\left(\rho {u}_{i}\right)=0$ | (1) | ||

Momentum | $\frac{\partial}{\partial {x}_{j}}\left(\rho {u}_{i}{u}_{j}\right)=-\frac{\partial p}{\partial {x}_{i}}+\frac{\partial}{\partial {x}_{j}}\left[\mu \left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {x}_{i}}-\frac{2}{3}{\delta}_{ij}\frac{\partial {u}_{l}}{\partial {x}_{l}}\right)\right]+\frac{\partial}{\partial {x}_{j}}(-\rho \overline{{u}_{i}^{\prime}{u}_{j}^{\prime}})+\rho \overrightarrow{g}$ | (2) | ||

Energy | $\nabla \xb7\left(\overrightarrow{v}\left(\rho E+p\right)\right)=\nabla \xb7\left({\mathrm{k}}_{eff}\nabla \mathrm{T}-\sum _{j}{h}_{j}\overrightarrow{{J}_{j}}+\left({\stackrel{=}{\tau}}_{eff}\xb7\overrightarrow{v}\right)\right)+{S}_{h}$ | (3) | ||

Radiative Transfer Equation | $\nabla \xb7({I}_{\lambda}(\overrightarrow{r},\overrightarrow{s})\overrightarrow{s})+\left({a}_{\lambda}+{\sigma}_{s}\right){I}_{\lambda}(\overrightarrow{r},\overrightarrow{s})={a}_{\lambda}{n}^{2}{I}_{b\lambda}+\frac{{\sigma}_{s}}{4\pi}{\int}_{0}^{4\pi}{I}_{\lambda}\left(\overrightarrow{r},{\overrightarrow{s}}^{\prime}\right)\phi \left(\overrightarrow{s}\xb7{\overrightarrow{s}}^{\prime}\right)d\mathsf{\Omega}\prime $ | Not Solved | (4) |

Place | Gholamalizadeh et al. | Guo et al. | Ming et al. |
---|---|---|---|

Collector inlet | Pressure inlet (p_{gage,in} = 0) | ||

Chimney outlet | Pressure outlet (p_{gage,out} = 0) | ||

Collector cover | Convection, Solar Irradiation | Convection, Solar Irradiation | T_{C} = f(x, y, z) K |

Surface of chimney | Adiabatic (Q = 0) | Undefined | Adiabatic (Q = 0) |

Ground-Air interface | Coupled | Coupled | T_{S} = f(x, y, z) K |

Bottom of the ground | Constant Temperature T = constant (K) | Constant Temperature T = constant (K) | Undefined |

Equation | Gholamalizadeh et al. | Guo et al. | Ming et al. | |
---|---|---|---|---|

Relative velocity | ${\overrightarrow{v}}_{r}=\overrightarrow{v}-\overrightarrow{\omega}\times \overrightarrow{r}$ | (5) | ||

Continuity | $\nabla \xb7\rho {\overrightarrow{v}}_{r}=0$ | (6) | ||

Momentum | $\nabla \xb7\left(\rho {\overrightarrow{v}}_{r}{\overrightarrow{v}}_{r}\right)+\rho \left(2\overrightarrow{\omega}\times {\overrightarrow{v}}_{r}+\overrightarrow{\omega}\times \overrightarrow{\omega}\times \overrightarrow{r}\right)=-\nabla \mathrm{p}+\nabla \xb7{\stackrel{=}{\tau}}_{r}$ | (7) | ||

Energy | $\nabla \xb7\left(\rho {\overrightarrow{v}}_{r}{H}_{r}\right)=\nabla \xb7\left(\mathrm{k}\nabla \mathrm{T}+{\stackrel{=}{\tau}}_{r}\xb7{\overrightarrow{v}}_{r}\right)$ | (8) |

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**MDPI and ACS Style**

Gholamalizadeh, E.; Chung, J.D.
A Comparative Study of CFD Models of a Real Wind Turbine in Solar Chimney Power Plants. *Energies* **2017**, *10*, 1674.
https://doi.org/10.3390/en10101674

**AMA Style**

Gholamalizadeh E, Chung JD.
A Comparative Study of CFD Models of a Real Wind Turbine in Solar Chimney Power Plants. *Energies*. 2017; 10(10):1674.
https://doi.org/10.3390/en10101674

**Chicago/Turabian Style**

Gholamalizadeh, Ehsan, and Jae Dong Chung.
2017. "A Comparative Study of CFD Models of a Real Wind Turbine in Solar Chimney Power Plants" *Energies* 10, no. 10: 1674.
https://doi.org/10.3390/en10101674