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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 127078, 7 pages

http://dx.doi.org/10.1155/2013/127078

## Computer-Aided Simulations of Convective Heat Transfer in a Wedged Channel with Pin-Fins at Various Outlet Arrangements and Nonuniform Diameters

^{1}School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710129, China^{2}School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710129, China

Received 4 June 2013; Accepted 30 September 2013

Academic Editor: Minvydas Ragulskis

Copyright © 2013 Qitao Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The turbine blade works at high thermal loads, especially the trailing edge of the blade due to the hot gas leakage flow. Pin-fins are well recognized as a kind of effective device to augment the convective heat transfer and effectively cool the trailing edge. In this paper, the cooling effectiveness of chordwise outlet pin-fins distance and inner pin fin diameter is, respectively, studied on the heat transfer and flow friction of the trailing edge of the blade with software CFX. A 90 deg turn cooling wedge passage with cylindrical pin-fins is used to model the trailing edge. Results show that the pin-fins distance at the outlet and the arithmetic arrangement of the inner pin-fins diameter both are vital factors to influence the cooling effectiveness in the trailing edge of the blade.

#### 1. Introduction

It is well known that the thermodynamic efficiency of the gas turbines can be highly increased by raising the inlet working temperature, and therefore the highly effective cooling system of turbine blades is indispensable. The trailing edge of the blades has very thin cross-section which makes it very feeble to high temperatures and brings about a particular challenge to cool it. Pin-fin arrays are introduced as appropriate cooling devices to lower down its temperature. Pin-fins increase the internal cooled surface area and produce a high turbulence level to enhance the convective heat transfer performance between the cooling gas and the inner wall of the blade. They can also strengthen the intensity and stiffness of the trailing edge structure.

Lots of work has been performed on the heat transfer and flow characteristics of rectangle channels with the pin-fins. The influence of pin-fin cross-section shapes has been experimentally studied on rectangle channel with elliptic shape by Li et al. [1], with square shape by, respectively, Şara [2] and Jeng and Tzeng [3]. Sahiti et al. [4] numerically simulate the pressure drop and heat transfer of rectangle channels with a NACA profile, a profile having a drop shape, a lancet profile, an elliptic profile cross-section pin-fins. Among all the cross-section shapes, the circular one is the most popular [5–7]. Chang et al. [8] experimentally studied the endwall heat transfer distribution and pressure drop for four rectangular channels with different ratios between clearances from pin tips to the measured endwall and the pin-fin diameter. They found that the area average endwall Nusselt number and the pressure drops both decrease with the increasing ratios. Yu et al. [9] performed experiments on rectangular duct with staggered arrays of pin-fins and found great improvement of an overall thermal performance of their geometrical configuration. The experiments of Lawson et al. [10] on rectangular duct found that spanwise pin spacing affects the pressure loss more greatly than streamwise spacing while the latter had a larger influence on the heat transfer than the former.

The real shape of the trailing edge of the gas-turbine blade is similar to the wedge duct. Hwang and Lui [11] conducted experiments on the heat transfer and pressure drop in the wedge duct pin-fin with the consideration of influence of Reynolds number, outlet flow orientation, and pin configuration. Bianchini et al. [7] investigated the numerical and experimental results of the wedge duct similar to the real trailing of the blade, and two pin-fin arrangements were taken into account as staggered arrays and pentagonal displacements.

In this paper, the connective heat transfer and flow friction of the stagger-arrayed circular pin-fins in the trapezoidal duct are numerically studied. The innovation of the paper is to design new structural styles of pin-fins in the trailing edge of the blade, and then we investigated the influence of the arrangement of distance between each two pin-fins at the chordwise outlet and the arithmetic arrangement of the pin-fins diameter in the inner duct on the cooling effectiveness. This study intends to give instructions on the design of cooling in trailing edge of the turbine blade.

#### 2. Numerical Method

##### 2.1. Geometry

A schematic drawing of a real blade is shown in Figure 1. The trailing edge of the blade is the wedge-shaped gas cooling passage, in which the gas flows from the blade root to the tine, for example, radial direction. The gas flows out from the chordwise outlet. A stagger-arrayed circular pin-fin arranged in the wedged duct is used to model the trailing edge of the turbine blade as shown in Figure 2. Two sets of solid faces, namely, Wall_1 and Wall_2, are indicated in Figure 3 for the use of boundary conditions. Wall_1 includes the top endwall, bottom endwall, and the side face, while Wall_2 is a set of the other outer faces without any inner faces in solid (shown in Figure 2). The cross-section in the cooling passage is given in Figure 3 where the pin-fins in the cooling passage are arranged in nine equidistant and staggered arrays with 13 pin-fins for each array in 2D. Totally, 117 pins span the distance between two principal duct walls. The dimensions of the bottom endwall and the top endwall are 15.5 mm × 30.5 mm and 15.584 mm × 30.5 mm, respectively. The thickness of the walls is 0.5 mm. All pin-fins stand vertically on the bottom endwall. The heights of the duct entrance and straight exit are 3.586 and 2 mm, respectively, forming a wedge angle of about 5.863°. The pin spacings in the same row along the radial (longitude) and chordwise (transverse) directions are 3 mm and 2 mm, respectively, while those in the adjacent row are 1.5 mm and 1 mm, respectively, as shown in Figure 3. Two cases are considered with variable distance between the pins at the chordwise outlet (Case 1) and variable diameter of pin-fins (Case 2), respectively (Figure 3).

In Case 1, the diameter of all the pin-fins is the same value of 1 mm. There are 8 pin-fins with semicircular shape at the whole chordwise outlet location; therefore, these pin-fins partition the outlet to 9 portions denoted by to . The dimension of the 9 portions is geometric-proportioned, and the proportion is set as a parameter :

The variation range of is 11.6. The total length of the outlet section is a fixed value of 30 mm; thus different values of to are derived. Every portion stands for each hole between the two adjacent pin-fins at the chordwise outlet. Particularly when has the value of 1, this represents that the 9 pin-fins are isometrically arranged at the outlet location. In this case, the arrangement of the distances between the outlet pin-fins can influence the mass flow rate of every hole, and then the inner cooling gas flow field will be changed indirectly. Finally, the cooling effectiveness of the blade trailing edge can be altered.

In Case 2, the diameter of the pin-fins in the radial direction (from to ) is set as an arithmetic sequence with the fixed value of 1.2. The difference between each two inner adjacent pin-fins diameter is denoted by a parameter , where the variation range is −0.10.1 mm and the diameter of the middle pin-fins is maintained the same value of 1.0 mm, which are expressed in formula (2). As different as Case 1, the parameter can directly change the inner flow field; thus the cooling effectiveness is also altered:

##### 2.2. Numerical Computation Process

###### 2.2.1. Turbulence Modeling

The numerical calculation uses the realizable model (RKE) of Xie et al. [12] which is proved to be in a good agreement with the experimental data for the case of cylindrical hole. Brief introduction of the main equations is given here. For the details of the model, please refer to [13]. The governing equation for the flow and heat transfer can be expressed as follows [12, 13]:(i) continuity equation: (ii) momentum equations: (iii) energy equation for fluid: (iv) energy equation for solid: (v) turbulent kinetic energy equation:

And in the turbulence model the coefficient .

###### 2.2.2. Boundary Conditions

The static temperature and mass flow rate at the passage inlet are set to 880 K and 20.376 g/s, respectively, while the inlet turbulence level is set to 5% intensity. The average static pressure at the outlet is 0.8 MPa. Wall_1 is set as the adiabatic boundary condition while Wall_2 is the third heat transfer boundary condition in heat conduction within which the heat transfer coefficient is and the outside gas temperature of the blade is 1346 K. The boundary conditions, which are stated in all the computation cases, are shown in Table 1. In this paper, the fluid domain stands for the cooling gas and the solid domain represents the structure of the trailing edge of the blade.

###### 2.2.3. Grid

For all computation models, a kind of unstructured hybrid mesh was generated in both the fluid and solid domains by using the commercial software ICEM CFD. Flow region in the fluid zones near-pin-fins was meshed with denser grids of three prism layers due to the small circular holes produced by the pin-fins of the blade as shown in Figure 4(a). Moreover, in Figure 4(b), three prism layers were also set at the fluid-solid interface in the fluid domain. Three kinds of different amounts of grids about one model with and , namely, 1.77 M, 1.96 M, and 2.27 M cells, were analyzed, and the all-around property parameter (10) was, respectively, 0.147, 0.1426, and 0.151, which showed that the influence of grid amount on the computation results can be neglected when the grids can get to about 2 M cells. Furthermore, the range of the nondimensional wall distances+ of the first nodes near wall is about 20~100.

###### 2.2.4. Solver

In the process of numerical computation, the software CFX is utilized to compute. In pretreatment of CFX, the stated boundary condition of the two computation domains can be set. The minimum convergence criterion is set to with the residual type of RMS in the CFX-Pre. At the fluid-solid interface, an energy balance is satisfied at every iteration, such that the heat flux at the wall on the fluid side is equal in magnitude and opposite in sign to the heat flux on the solid side. The fluid is assumed to be incompressible with constant thermal physical properties and the flow is assumed to be three-dimensional, turbulent, steady, and nonrotating. The working fluid is ideal gas. The blade is chosen as the aluminium material. In this study, the scalable wall functions of the RKE model are applied on the walls for the near wall treatment.

#### 3. Results and Discussion

The study of this paper aims to investigate the best heat transfer and flow friction among all the computation models in the two cases, namely, Case 1 and Case 2. Several parameters are defined before analyzing and comparing the fluid flow characteristic and heat transfer. The friction represents the flow characteristic while the average Nusselt number stands for the heat transfer characteristic. Comparison of each model’s all-around property is denoted by the parameter . Details of the three parameters are listed below.

The friction factor is defined as [12] where is the inlet mean velocity and is the total length of the cooling duct shown in Figure 3.

The average Nusselt number is determined in the following way [12]: where stands for the average temperature of the solid and is the average temperature of the fluid after cooling. is the average wall heat flux which can be obtained by querying the numerical result in the software CFX-POST.

For evaluating the cooling all-around property, the parameter is calculated as [6, 9] where the other two parameters and can be determined by formula (8) and (9) and and are the reference Nusselt number and the reference friction factor [9].

##### 3.1. Case 1

Figure 5 shows the average Nusselt number and flow friction comparison when the outlet hole length proportion changes from 1 to 1.6. With increasing, the average Nusselt number has the increasing trend while the flow friction monotonically increases. When , the average Nusselt number has the highest value and is 16.94 higher than the lowest with . Similarly, the highest is 38.34% more than the lowest.

The distribution curve of all-around property parameter versus the outlet hole length is shown in Figure 6. has the decreasing trend when increases. synthesizes both the average Nusselt number and flow friction , and its change trend is in contrast to the friction . So when increases, the flow friction changes more and is a strong factor to affect the all-around property .

##### 3.2. Case 2

As the analysis of Case 1, we also investigate the fluid flow friction, the average Nusselt number, and the all-around property in this case. Figure 7(a) shows that the average Nusselt number is almost linearly decreasing with the inner pin-fin diameter difference increasing, in which the difference between the highest and lowest value is 46.25. Meanwhile, in Figure 7(b), the friction has the parabola decrease trend when increases. When , has the maximum value and is 6.22 times as much as that when . So it is clear to know that the friction varies distinctly with increasing.

Because of the friction varying distinctly, the all-around property parameter has the opposite change trend of it. As shown in Figure 8, has the parabola increase trend and its maximum value is 2.564 times as much as the minimum value.

#### 4. Conclusion

In this paper, a new structural style of the pin-fins in the wedge duct has been proposed to find the best all-around cooling property through comparison. We studied the array distance of the pin-fins at the chordwise outlet and the arithmetic arrangement of the inner pin-fins diameter in the inner cooling gas passage to improve the cooling performance of the blade trailing edge. From all the foregoing analyses, the main findings can be listed as follows.(1)With the outlet hole length proportion increasing, the average Nusselt number has the increasing trend and the friction monotonically increases. However, the all-around property is almost linearly and inversely proportional to the proportion . In this case, the variation amplitude of these three parameters is small.(2)When the inner and nonuniform pin-fin diameter difference increases, the Nusselt number decreases and the friction has the parabola decrease trend while the all-around property is opposite to the friction . The amplitude of both and varies greatly.(3)In the design process of blade trailing edge, one meaningful suggestion can be concluded. Within the scope of safety design of the blade, the smaller the outlet hole length proportion value and the bigger the inner and nonuniform pin-fin diameter difference are, the better the cooling effectiveness and blade design will be.

#### Nomenclature

Fluid-solid interface surface area | |

: | Volume of the fluid domain |

: | = hydraulic diameter |

Heat transfer coefficient | |

Turbulent kinetic energy | |

Length of the channel in the fluid domain | |

: | Average Nusselt number |

Pressure | |

: | Average heat flux at the interface |

Temperature | |

: | Average temperature = ( is the volume of solid or fluid domain) |

: | Inlet velocity |

All-around property index | |

Pressure drop | |

Prandtl number | |

: | Specific heat at the constant pressure. |

*Greek Symbols*

Rate of energy dissipation | |

Fluid density | |

Fluid dynamic viscosity | |

Fluid-thermal conductivity. |

*Subscripts*

Inlet | |

Solid | |

Fluid | |

Outside. |

#### Acknowledgments

This work was supported by the National Natural Science Fundation of China (51210008, 51205315, and 51375387), Fundamental Research Fundation (JC20120230, JCY20130126, and 13GH014610) at Northwestern Polytechnical University, and 111 Project (B07050).

#### References

- Q. L. Li, Z. Chen, U. Flechtner, and H. J. Warnecke, “Heat transfer and pressure drop characteristics in rectangular channels with elliptic pin fins,”
*International Journal of Heat and Fluid Flow*, vol. 19, no. 3, pp. 245–250, 1998. View at Publisher · View at Google Scholar · View at Scopus - O. N. Şara, “Performance analysis of rectangular ducts with staggered square pin fins,”
*Energy Conversion and Management*, vol. 44, no. 11, pp. 1787–1803, 2003. View at Publisher · View at Google Scholar · View at Scopus - T. M. Jeng and S. C. Tzeng, “Pressure drop and heat transfer of square pin-fin arrays in in-line and staggered arrangements,”
*International Journal of Heat and Mass Transfer*, vol. 50, no. 11-12, pp. 2364–2375, 2007. View at Publisher · View at Google Scholar · View at Scopus - N. Sahiti, A. Lemouedda, D. Stojkovic, F. Durst, and E. Franz, “Performance comparison of pin fin in-duct flow arrays with various pin cross-sections,”
*Applied Thermal Engineering*, vol. 26, no. 11-12, pp. 1176–1192, 2006. View at Publisher · View at Google Scholar · View at Scopus - M. Tahat, Z. H. Kodah, B. A. Jarrah, and S. D. Probert, “Heat transfers from pin-fin arrays experiencing forced convection,”
*Applied Energy*, vol. 67, no. 4, pp. 419–442, 2000. View at Publisher · View at Google Scholar · View at Scopus - E. Galvis, B. A. Jubran, F. Xi, K. Behdinan, and Z. Fawaz, “Numerical modeling of pin-fin micro heat exchangers,”
*Heat and Mass Transfer*, vol. 44, no. 6, pp. 659–666, 2008. View at Publisher · View at Google Scholar · View at Scopus - C. Bianchini, B. Facchini, F. Simonetti, L. Tarchi, and S. Zecchi, “Numerical and experimental investigation of turning flow effects on innovative pin fin arrangements for trailing edge cooling configurations,” in
*Proceedings of the ASME Turbo Expo 2010*, vol. 4, pp. 593–604, ASME, June 2010. View at Scopus - S. W. Chang, T. L. Yang, C. C. Huang, and K. F. Chiang, “Endwall heat transfer and pressure drop in rectangular channels with attached and detached circular pin-fin array,”
*International Journal of Heat and Mass Transfer*, vol. 51, no. 21-22, pp. 5247–5259, 2008. View at Publisher · View at Google Scholar · View at Scopus - R. Yu, W. Chaoyi, and Z. Shusheng, “Transitional flow and heat transfer characteristics in a rectangular duct with stagger-arrayed short pin fins,”
*Chinese Journal of Aeronautics*, vol. 22, no. 3, pp. 237–242, 2009. View at Publisher · View at Google Scholar · View at Scopus - S. A. Lawson, A. A. Thrift, K. A. Thole, and A. Kohli, “Heat transfer from multiple row arrays of low aspect ratio pin fins,”
*International Journal of Heat and Mass Transfer*, vol. 54, no. 17-18, pp. 4099–4109, 2011. View at Publisher · View at Google Scholar · View at Scopus - J. J. Hwang and C. C. Lui, “Measurement of endwall heat transfer and pressure drop in a pin-fin wedge duct,”
*International Journal of Heat and Mass Transfer*, vol. 45, no. 4, pp. 877–889, 2001. View at Publisher · View at Google Scholar · View at Scopus - G. N. Xie, B. Sundén, and W. H. Zhang, “Comparisons of pins/dimples/protrusions cooling concepts for a turbine blade tip-wall at high Reynolds numbers,”
*Journal of Heat Transfer*, vol. 133, no. 6, Article ID 061902, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus - T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, “A new k-
*ε*eddy viscosity model for high reynolds number turbulent flows,”*Computers and Fluids*, vol. 24, no. 3, pp. 227–238, 1995. View at Scopus