# Thermal CFD Analysis of Tubular Light Guides

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## Abstract

**:**

## 1. Introduction

## 2. CFD Model

**Figure 2.**Result of the CFD simulation of a tubular light guide [23].

- Simulation of thermal profile and determination of heat loss through tubular light guides;
- Specification of potential condensation risks on internal surface of the light guide tube at the interface between the tube and the roof construction;
- Simulation of air flow within tubular light guides under specified boundary conditions.

- Outdoor temperature interval is set to −15 °C and +15 °C to correspond with the winter and spring/autumn seasons of the temperate climate of the Central Europe region;
- Indoor temperature +20 °C and relative humidity of indoor air 50%.

#### 2.1. Physical Models

^{9}. The laminar model was created in accordance with the already published articles focused on the laminar convection in air cavities [26,27].

#### 2.2. Geometric Models

**Figure 3.**The 3D model, geometry, materials and boundary conditions [23].

**Figure 5.**Meshes and geometric types: (

**a**) Initial-structured 3D mesh; (

**b**) boundary adapted 3D mesh; (

**c**) Very fine structural 3D comparative mesh; (

**d**) Non structured 2D rotation symmetrical mesh. Scheme of the geometric models considered; (

**e**) 3D-cylinder; (

**f**) 3D/4-quadrant; (

**g**) 2D rotation symmetrical segment.

- The mesh adaptation on the internal surfaces of the light guide serves for the fine discretisation of boundary layers. It is essential for the simulation model accuracy;
- Widening of the horizontal mesh distances in the detail of the roof construction connected with the light guide tube is useful for reduction of the simulation time;
- 3D model discretisation of very thin metal tube (thickness 1 mm) needs the discretisation of millimetre fractions in the tube and also in the part of the roof construction that is in contact with the tube. The very fine discretisation extends the simulation time;
- The simplified model was created on the “shell conduction” method. In this model the light guide tube is substituted with a virtual layer of cells for simulation of heat transfer along the model its surface;
- The 2D rotation symmetrical model with unstructured mesh gives results that are comparable to the 3D models. The simple model offers possibility of more calculation results and geometric variations at a given simulation time;
- Performed mesh variants serve to show that the mesh independence of the geometric model is achieved.

#### 2.3. The Final 2D Simplified Model

^{−1}·K

^{−1}) of the model materials and heat transfer coefficients h (W·m

^{−2}·K

^{−1}) and indoor and outdoor temperatures are defined in accordance with standard values [29].

**Figure 6.**The 2D rotation symmetrical model—thermally insulated roof segment with the studied tubular light guide.

## 3. Results and Discussion

**Figure 7.**Comparison of temperature distribution profiles in the flat roof segment with the tubular light guide of diameter 0.6 m, length 0.56 m, emissivity of internal surface of the tube ε = 0.1: (

**a**) k-ω SST model; (

**b**) laminar model.

- Average temperature in the tubular light guide—difference about 7% (for temperatures in °C) and max difference 0.35% (compared temperatures in K);
- Minimal internal surface temperatures—difference max 6% (compared temperatures in °C) and max difference 0.30% (compared temperatures in K);
- Total heat flux and heat loss—difference to 7%;
- Maximal accessible velocity of air flow in the whole domain—to 50% (max. velocity is lower than 0.15 m·s
^{−1});

**Figure 8.**Example of the 2D model of the tubular light guide thermal profile (

**a**) and air flow pattern (

**b**), light guide of diameter d = 0.30 m; length l = 0.56 m, emissivity of internal surface of the pipe ε = 0.10.

**Figure 9.**Example of the 2D model of the tubular light guide thermal profile and air flow pattern, light guide of diameter d = 0.60 m; length l = 0.56 m, emissivity of internal surface of the pipe ε = 0.10. (

**a**) Temperature profile; (

**b**) air flow vectors; (

**c**) air flow pattern.

**Figure 10.**Example of the 2D model of the tubular light guide thermal profile (

**a**) and air flow pattern (

**b**), light guide of diameter d = 0.60 m and length l = 9.0, emissivity of internal surface of the pipe ε = 0.10.

**Figure 11.**Mean temperature in tubes of diameters d = 0.3 m (Tmean_0.3), 0.6 m (Tmean_0.6) and 0.9 m (Tmean_0.9) and lengths l = 0.56 m to 9 m.

**Figure 12.**Heat losses of tubes of diameters d = 0.3 m (Q_tot_0.3), 0.6 m (Q_tot_0.6) and 0.9 m (Q_tot_0.9) and lengths l = 0.56 m to 9 m.

- L
^{3D}is thermal coupling coefficient (W·K^{−1}). - U
_{j}is thermal transmittance of the j element in the studied detail (W·m^{−2}·K^{−1}). - A
_{j}is area of the j element in the studied detail (m^{2}). - Ψ is linear thermal transmittance (W·m
^{−1}·K^{−1}). - b is length of the linear thermal bridge (m).

**Figure 13.**Point thermal transmittance in dependence on the tubular light guide aspect ratio (length/diameter); the tubular light guides of diameters d = 0.3 m—TT3D (0.3), d = 0.6 m—TT3D (0.6) and d = 0.9 m—TT3D (0.9).

**Figure 14.**Point thermal transmittance of the tubular light guides of diameter d = 0.6 m, length l = 0.56 m—TT3D (0.56) and length l = 9 m—TT3D (9.0), dependence on outdoor temperature between −15 °C and +15 °C.

^{−1}and 0.20 m·s

^{−1}.

**Figure 15.**Maximal air flow velocity in tubular light guides d = 0.6 m, l = 9 m (Vel_max_l0.56) and d = 0.6 m, l = 0.56 m (Vel_max_l9), dependence on the outdoor temperature between −15 °C and +15 °C.

**Figure 16.**Mean temperatures (Tmean) in the light guides and minimal surface temperatures (Tmin_int), light guides of diameter d = 0.6 m, lengths l = 0.56 m (Tmean_l0.56 and Tmin_int_l0.56) and l = 9 m (Tmean_l9 and Tmin_int_l9).

**Figure 17.**Temperature profile—simulation result for outdoor temperature θ

_{e}= +15 °C, length 9 m, diameter 0.6 m.

#### Example of the Real Evaluation of Tubular Light Guides

_{T}is specular reflectance of mirrored inner surface of the tube.

_{r}= 0.95 (reflectance of internal surface of the light guide).

Length | Tubular light guide diameter | ||||||||
---|---|---|---|---|---|---|---|---|---|

d = 0.30 m | d = 0.60 m | d = 0.90 m | |||||||

L (m) | TTE (-) | TT3D (W/K) | Q (W) | TTE (-) | TT3D (W/K) | Q (W) | TTE (-) | TT3D (W/K) | Q (W) |

0.56 | 0.9648 | −0.1391 | 39.5 | 0.9822 | 1.6885 | 70.3 | 0.9881 | 2.9965 | 116.1 |

1.00 | 0.9381 | 0.0544 | 43.2 | 0.9685 | 2.0055 | 81.4 | 0.9788 | 3.5365 | 135.0 |

9.00 | 0.5775 | 0.3172 | 45.3 | 0.7549 | 2.4250 | 96.1 | 0.8277 | 4.5864 | 171.8 |

- Variation I: 1 × TLG, d = 0.60 m, length 1.0 m: Total heat loss by TLG = 70 W—the tubular light guide increases the heat transmission loss by 74%.
- Variation II: 2 × TLG, d = 0.30 m, length 1.0 m: Total heat loss by TLG = 3.8 W—the tubular light guide increases heat transmission loss by 4%.

## 4. Conclusions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

d | diameter (m) |

l | length (m) |

L^{3D} | thermal coupling coefficient (W·K ^{−1}) |

A | area (m ^{2}) |

b | length of the linear thermal bridge(m) |

Ψ | linear thermal transmittance (W·m ^{−1}·K^{−1}) |

Q | heat loss (W) |

k | thermal conductivity (W·m ^{−1}·K^{−1}) |

ε | emissivity (-) |

h | heat loss coefficient (W·m ^{−2}·K^{−1}) |

T | local temperature (K) |

U | thermal transmittance (W·m ^{−2}·K^{−1}) |

TT3D | point thermal transmittance (W·K ^{−1}) |

TTE | Tube transmission efficiency |

t | an exponent in TTE (-) |

ρ_{r} | specular reflectance (-) |

Z | portion of the zenithal sky (°) |

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**MDPI and ACS Style**

Šikula, O.; Mohelníková, J.; Plášek, J. Thermal CFD Analysis of Tubular Light Guides. *Energies* **2013**, *6*, 6304-6321.
https://doi.org/10.3390/en6126304

**AMA Style**

Šikula O, Mohelníková J, Plášek J. Thermal CFD Analysis of Tubular Light Guides. *Energies*. 2013; 6(12):6304-6321.
https://doi.org/10.3390/en6126304

**Chicago/Turabian Style**

Šikula, Ondřej, Jitka Mohelníková, and Josef Plášek. 2013. "Thermal CFD Analysis of Tubular Light Guides" *Energies* 6, no. 12: 6304-6321.
https://doi.org/10.3390/en6126304