# Large Eddy Simulation of Flow and Heat Transfer in a Ribbed Channel for the Internal Cooling Passage of a Gas Turbine Blade: A Review

## Abstract

**:**

## 1. Introduction

## 2. Numerical Challenges and Comparative Studies

_{ij}and q

_{j}are the stress and heat flux at the sub-grid scale (SGS), respectively. The parts that need to be modeled in the LES: τ

_{ij}is usually modeled as being proportional to the velocity gradient for which currently, either a constant value is used or it is determined by considering conditions such as the flow or wall [76].

**x**, t) = −βx + p(

**x**, t)

**x**, t) = γx + θ(

**x**, t),

^{2}-f model predicts high TKE of the shear layer to some extent, it predicts the location where the maximum TKE occurs differently than when using LES.

## 3. Instantaneous Flow and Thermal Fields

## 4. Heat Transfer on the Rib

## 5. Conjugate Heat Transfer

## 6. The Effects of Rotating the Gas Turbine Blade

## 7. Geometrical Shapes for Performance Improvement

## 8. Conclusions

## 9. Future Directions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

d | thickness of the channel wall [m] |

D_{h} | hydraulic diameter of the channel [m] |

e | rib height [m] |

f | friction factor |

h | heat transfer coefficient [W/m^{2}K] |

H | channel height [m] |

k_{f} | thermal conductivity of fluid [W/mK] |

Nu | Nusselt number (=h D_{h}/k_{f}) |

p | rib-to-rib pitch [m] |

Pr | Prandtl number (=ν/α) |

Re | bulk Reynolds number (=U_{b} D_{h}/ν) |

Ro | rotation number (=ω D_{h}/U_{b}) |

q | heat transfer rate [W] |

t | time [s] |

T | temperature [K] |

T_{b} | bulk temperature [K] |

T_{w} | wall temperature [K] |

U_{b} | bulk velocity [m/s] |

W | channel width [m] |

Greek symbols | |

α | thermal diffusivity [m^{2}/s] |

ν | kinematic viscosity [m^{2}/s] |

θ | dimensionless temperature (=(T − T_{b})/(T_{w} − T_{b})) |

Θ | time-averaged dimensionless temperature |

Subscripts | |

0 | fully developed value in a smooth pipe |

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**Figure 2.**Modeling and flow patterns of gas turbine internal cooling passages: (

**a**) the ribbed channel modeling cooling passage [11]; (

**b**) streamlines in ribbed channels obtained experimentally [11] and using computational fluid dynamics (CFD) [10,12]. LES: large eddy simulation; p: installation period; e: rib height; U

_{b}: bulk velocity; H: channel height; d: wall thickness; x: streamwise coordinate; y: wall-normal coordinate; SST: shear stress transport model; v

^{:}, the velocity fluctuation normal to the streamlines; f: an elliptic relaxation function; RSM: Reynolds stress model.

**Figure 5.**Instantaneous flow and thermal fields: (

**a**) in the xy plane; (

**b**) in the xz plane at y/e = 0.06.

**Figure 7.**Thermal fields in a ribbed channel with a conducting wall [10]: (

**a**) temperature contours in the xy plane; (

**b**) the temperature around the rib.

**Figure 9.**Heat transfer in the rotating ribbed channel: (

**a**) A typical experimental setup [3]; (

**b**) local heat transfer distributions [3]; (

**c**) the local Nusselt number on the trailing wall; (

**d**) the local Nusselt number on the leading wall. Ro: rotation number (LES data [48,50] compared to experiment [91]).

**Figure 10.**Large eddy simulation of heat transfer in a two-pass rotating ribbed duct [43]: (

**a**) thermal fields in the channel; (

**b**) heat transfer on the channel wall during the first pass; (

**c**) heat transfer on the channel wall during the second pass. Bo: buoyancy number.

**Figure 11.**Geometrical shapes and variables affecting heat transfer in the internal cooling passage of a gas turbine.

**Table 1.**The simulation conditions for performing LES analysis of ribbed channels by research institution.

Institution | Country | Year [Ref] | Software | Reynolds Number | p/e | e/H | Aspect Ratio | Rib Geometry |
---|---|---|---|---|---|---|---|---|

Tokyo Univ. Agriculture and Mechanics | Japan | 2000 [25] | In-house | 4000–9000 | 10 | 0.1 | 1, 2, 4 | 90° |

2001 [26] | In-house | 1000, 4000 | 10 | 0.1 | 1 | 60°, 90° | ||

2001 [27] | In-house | 4000 | 10 | 0.1 | 1 | 60°, 90° | ||

2001 [28] | In-house | 4000 | 10 | 0.1 | 1 | 60°, 90° | ||

2003 [29] | In-house | 4000 | 10 | 0.1 | 0.25, 1, 4 | 60°, 90° | ||

2004 [30] | In-house | 4000 | 10 | 0.1 | 1 | 60°, 90° | ||

2004 [31] | In-house | 4000 | 10 | 0.1 | 1 | 60°, 90° | ||

2008 [32] | In-house | 1000, 4000 | 10 | 0.1 | 1 | 60° | ||

Denken | Japan | 2002 [33] | In-house | 100,000 | 10 | 0.1 | ∞ | 90° |

2005 [34] | In-house | 50,000 | 10 | 0.1 | 2 | 60° | ||

Univ. Iowa | USA | 2003 [35] | In-house | 10,020 | 1, 5, 10 | 0.1 | ∞ | 90° |

Iowa State Univ. | USA | 2004 [36] | In-house | 5600 | 10 | 0.2 | ∞ | 90° |

Virginia Tech | USA | 2004 [37] | In-house | 20,000 | 10 | 0.1 | 1 | 90° |

2005 [38] | In-house | 20,000 | 10 | 0.1 | 1 | 90° | ||

2006 [39] | In-house | 20,000 | 10 | 0.1 | 1 | 90° | ||

2006 [40] | In-house | 20,000 | 10 | 0.1 | 1 | 90° | ||

2006 [41] | In-house | 20,000 | 10 | 0.1 | 1 | 90° | ||

2008 [42] | In-house | 20,000 | 10 | 0.1 | 1 | 90° | ||

2018 [43] | In-house | 100,000 | 10 | 0.1 | 1 | 90° | ||

2021 [44] | In-house | 10,000 | 10 | 0.3 | 90° | |||

2021 [45] | In-house | 20,000 | 10 | 0.1 | 1 | 90°, BS, FS | ||

2022 [46] | In-house | 20,000 | 10 | 0.1 | 1 | 90°, BS, FS | ||

Seoul Nat’l Univ. | Republic of Korea | 2005 [47] | In-house | 30,000 | 10 | 0.1 | ∞ | 90°, semicircle |

2007 [48] | In-house | 30,000 | 10 | 0.1 | ∞ | 90° | ||

2010 [49] | In-house | 30,000 | 10 | 0.1 | ∞ | 90°, detached | ||

Louisiana State Univ. | USA | 2005 [50] | In-house | 12,500 | 10 | 0.1 | 1 | 90° |

2005 [51] | In-house | 25,000 | 10 | 0.1 | 0.25, 1, 4 | 90° | ||

2007 [52] | In-house | 25,000, 100,000 | 10 | 0.1 | 0.25, 1, 4 | 90° | ||

Cambridge | UK | 2005 [53] | In-house | 14,200 | 20 | 0.1 | 1 | 90° |

2015 [54] | In-house | 20,000 | 10 | 0.1 | 1 | 90° | ||

2021 [55] | In-house | 14,200 | 20 | 0.1 | 1 | 90° | ||

Von Karman Institute | Belgium | 2006 [56] | Fluent6.1 | 40,000 | 10 | 0.3 | 1 | 90° |

2015 [57] | In-house | 40,000 | 10 | 0.3 | 1 | 90° | ||

2016 [58] | In-house | 40,000 | 10 | 0.3 | 1 | 90° | ||

IIT | India | 2012 [59] | In-house | 2053 | 10 | 0.1 | 1 | 90° |

Univ. Manchester | UK | 2015 [12] | In-house | 30,000 | 9 | 0.1 | ∞ | 90° |

Sapienza Univ. Roma | Italy | 2015 [60] | In-house | 15,000 | 10 | 0.1 | 1 | 90° |

2017 [61] | In-house | 15,000 | 10 | 0.1 | 1 | 90° | ||

ONERA | France | 2016 [62] | In-house | 40,000 | 10 | 0.3 | 1 | 90° |

Peking Univ. | China | 2016 [63] | In-house | 30,000 | 9 | 0.1 | 1 | 90° |

Univ, Manitoba | Canada | 2015 [64] | PIV | 13,000 | 8 | 0.1 | 1 | 90°, V(30,45,60°) |

2017 [65] | In-house | 5600 | 8 | 0.1 | 1 | 90°, V(45,60°) | ||

2021 [66] | In-house | 5600 | 8 | 0.1 | 1 | 90° | ||

Niigata Univ. | Japan | 2016 [67] | In-house | 5000 | 2, 4, 8, 16 | 0.1 | ∞ | 90° |

2020 [68] | In-house | 5000 | 2, 4, 8, 16 | 0.1 | ∞ | 90° | ||

Kookmin Univ. | Republic of Korea | 2017 [69] | In-house | 30,000 | 10 | 0.1 | ∞ | 90° |

2021 [10] | In-house | 30,000 | 10 | 0.1 | ∞ | 90° | ||

2021 [70] | In-house | 30,000 | 10 | 0.1 | ∞ | 90° | ||

2022 [71] | In-house | 30,000 | 10 | 0.1 | ∞ | 90° | ||

Univ. Stuttgart | Germany | 2018 [72] | o-FOAM | 30,000 | 10 | 0.1 | 1 | |

Karlsruhe Institute of Tech. | Germany | 2018 [73] | Fluent v.15 | 100,000 | 10 | 0.1 | 1 | 90, V(60°) |

CEFRACS | France | 2020 [74] | In-house | 15,000 | 10 | 0.1 | 1 | 90° |

2021 [75] | In-house | 15,000 | 10 | 0.1 | 1 | 90° |

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## Share and Cite

**MDPI and ACS Style**

Ahn, J.
Large Eddy Simulation of Flow and Heat Transfer in a Ribbed Channel for the Internal Cooling Passage of a Gas Turbine Blade: A Review. *Energies* **2023**, *16*, 3656.
https://doi.org/10.3390/en16093656

**AMA Style**

Ahn J.
Large Eddy Simulation of Flow and Heat Transfer in a Ribbed Channel for the Internal Cooling Passage of a Gas Turbine Blade: A Review. *Energies*. 2023; 16(9):3656.
https://doi.org/10.3390/en16093656

**Chicago/Turabian Style**

Ahn, Joon.
2023. "Large Eddy Simulation of Flow and Heat Transfer in a Ribbed Channel for the Internal Cooling Passage of a Gas Turbine Blade: A Review" *Energies* 16, no. 9: 3656.
https://doi.org/10.3390/en16093656