`Advances in Mechanical EngineeringVolume 2014 (2014), Article ID 569243, 9 pageshttp://dx.doi.org/10.1155/2014/569243`
Research Article

## Computational Study of Air/Mist Impinging Jets Cooling Effectiveness under Various Curvature Models

1College of Mechanical Science & Engineering, Jilin University, Changchun 130025, China
2Department of Aviation Theory, Air Force Aviation University, Changchun 130022, China

Received 21 September 2013; Revised 17 December 2013; Accepted 2 January 2014; Published 11 February 2014

Copyright © 2014 Peng Cheng 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

Efficiency is one of the most important parameters in evaluating the performance of a gas turbine engine by increasing the turbine inlet temperature, which could increase the gas turbine cycle’s efficiency. In order to increase the turbine inlet temperature significantly, an advanced cooling system needs to be researched and developed. This paper will establish a double chamber model simulating mist impingement cooling under typical gas turbine operating conditions of high temperature and pressure. Numerical simulations are examined to investigate the curvature and mist effect of air impingement cooling. The air impingement cooling can be significantly affected by the curvature which is measured by central angle. The 30° central angle model has a better cooling effectiveness than the flat surface model, while the 90° central angle model has the lowest cooling performance. Under real gas turbine operating conditions at high temperature, pressure, and velocity, comparing with the 90° central angle model, the 30° central angle model air impingement cooling’s enhancement could be better than 98% and provides a wall cooling of approximately 175 K. By adding mist, impingement cooling effectiveness can be enhanced approximately by 64% on the 90° central angle model and by 6–10% on the other models.

#### 1. Introduction

As modern gas turbine operating temperature increased continually for the sake of increasing the efficiency and power, turbines’ inlet temperature has been already far beyond the material acceptable level. Hence, there is always demand for continuously developing new advanced cooling technologies to cool the hot components in high-performance gas turbines. Cooling technology has been successfully applied in protecting turbine airfoils from high temperature since the last half-century [13] and there were continuous researches striving to make cooling more effective. As one of most important cooling technologies, impingement cooling has been studied on the transform piece cooling [4].

Impingement cooling has been studied mainly on a flat plate, while relatively a few studies focus on the curved surface. The numerical investigations on the flow and heat transfer of impingement cooling on concave surfaces were first conducted by Kayansayan and Küçüka [5]. They compared the numerical results with experimental data, and their findings showed that the variation of the channel radius ratio could not affect the Nusselt number of the stagnation region, which is not in accordance with the results obtained by Choi et al. [6]. Choi investigated impingement cooling on a semicircular concave surface. They measured the distributions of mean velocity and velocity fluctuation on concave surface in free, impinging and wall jet flow regions and local Nusselt numbers variation with Reynolds numbers, jet spacing, and spacing between the nozzle exit and the target surface. Taslim and Bethka [7] investigated heat transfer of impingement cooling on concave surface under the influence of smooth and roughness wall, horseshoe ribs, jet to target wall spacing, with and without showerhead and gill film holes exit flow schemes, and crossflow. Their results indicated that heat transfer is enhanced by roughness target surface, notched horseshoe, horseshoe geometries, and the showerhead film holes, but reduced by the external crossflow. Rhee et al. [8] showed a 50% improvement in jet array average transfer rate at by adding effusion holes but noted minimal influence for . Souris et al. [9] studied impinging cooling on a semicircular concave surface and compared their numerical results with those from Choi et al. [6]. Kumar and Prasad [10] studied the flow and heat transfer of a row of circular jets impinging on a concave surface. Zhao and Feng [11] investigated the impingement cooling on internal leading edge region which was stretched by the middle cross-section of the first stage rotor blade of GE engine high pressure gas turbine. Yu et al. [12] studied the effects of impingement cooling for the different turbulence models and the aerodynamic behavior of a simplified transition piece model. Wei et al. [13] investigated impingement and serpentine convection cooling under the effect of rotation. Their results suggested that rotation effects increase the serpentine cooling, and reduce the jet impingement cooling.

Cooling of high heat flux microprocessors has become a critical limitation in the future development of high-performance integrated circuits. A promising technology to enhance impingement cooling is to inject mist (small water droplet) into the coolant flow. Each droplet acts as a cooling sink and flies over a distance before it completely vaporizes. Based on the aforementioned heat transfer mechanisms, mist can be used in gas turbine systems in different ways, including gas turbine inlet air fog cooling, overspray cooling through wet compression in the compressor [14], and airfoils (vanes and blades) internal cooling [15, 16]. Li and Wang [17] studied the curvature effect on mist film cooling in 2D cases as well. They found that the magnitude of the mist cooling enhancement is ordered as follows: flat surface > pressure surface > suction surface > leading edge. Recently, Dhanasekaran and Wang [18] simulated the mist/air film cooling enhancement over a rotating blade under gas turbine working conditions with elevated pressure, heat flux, and Reynolds number. They predicted an average of 35% mist cooling enhancement with an equivalent blade surface temperature reduction of 100–125 K.

From the foregoing discussion, it is clear that almost all these studies concentrated on blade shower head mist/air film cooling [1318]; however, less attention was given to the transform piece (TP) mist/air impingement cooling. Due to the limit of jet flow structure and stagnation region area, surface curvature of the double chamber model has a more significant influence on mist/air impingement cooling. Therefore, the main objective of this thesis is to elucidate how the curvature and mist affect the transform piece models, which look like a quarter torus with the curved double chambers. The effects of curvature (0°, 30°, 60°, and 90° of central angles) on the flow physics and heat transfer in the double chamber model are investigated. Finally, the mist cooling enhancement is simulated using the validated computational model.

#### 2. Numerical Model

##### 2.1. Test Model Configurations

The discrete coolant jets, forming a protective film chamber on the side of transition piece, are drawn from the upstream compressor in an operational gas turbine engine. The coolant flows are fed through internal passages with surface holes. From the supply plenum, the coolants are ejected through several rows of discrete-holes over the external boundary layer against the local high thermal conduction on the other side of the TP.

This study builds four models, a flat plate and three curve surface cylinders, which could simulate the TP’s structure and performance, to discuss the impingement cooling effectiveness over different curvatures shown in Figure 1. The arc length and area of the outer surface are same in the four models. We simulated different curvatures conduction with 0°, 30°, 60°, and 90° central angle (Figures 1(a), 1(b), 1(c), and 1(d)).

Figure 1: Four different curvature double chamber models and boundary conditions: (a) flat model, (b) 30° central angle model, (c) 60° central angle model, and (d) 90° central angle model.

As shown in the picture, all models have two layers of chambers with length of 1050 mm, and the outer and inner height are 200 mm and 162 mm, respectively. In each model, there are 18 holes distributed uniformly in three rows on the surface of the outer wall that the distance between the two rows is 68 mm and the size of all the holes is about 10.26 mm. But the holes on curved surface are not circular.

##### 2.2. Numerical Methods

To simulate impingement cooling with mist, it is feasible to consider the droplets as a discrete phase since the volume fraction of the liquid is usually small (less than 1%). The droplets are tracked in a Lagrangian frame of reference, and the mass, momentum, and heat transfer are computed between the discrete phase and the continuous flow. The effect of droplets on the continuous phase is incorporated as a source term to the governing equations [19, 20].

To apply the discrete phase model to mist film cooling, the time-averaged steady-state Navier-Stokes equations, as well as equations for mass, energy, and species transport, are solved. Therefore, a turbulence model has to be considered. In this study, the realizable model is employed. This model proposed by Shih et al. [21] was intended to address these deficiencies of standard models by adopting the following: (1) model contains a new formulation for the turbulent viscosity and (2) a new transport equation for the dissipation rate, , is derived from an exact equation for the transport of the mean square vorticity fluctuation.

The realizable turbulence model is based on the time-averaged equations. Using this flow velocity to trace the droplet will result in an averaged trajectory. In the real flow, the instantaneous velocity fluctuation would make the droplet dance around this average track. However, the instantaneous velocity is not calculated in the current approach as the time-averaged Navier-Stokes equations are solved. One way to simulate the effect of instantaneous turbulence on droplet dispersion is to use the stochastic tracking scheme [22]. This method has also been used in the studies of mist/air impingement cooling with a flat surface by the authors [13].

##### 2.3. Boundary Condition Setup

A schematic of the flow domain along with boundary conditions and dimensions is given in Figure 2 [4, 12]. In the diagram, one side of the outer chamber called the coolant chamber is closed; contrarily, both sides of the mainstream chamber as the inner chamber are unfolding in which gas could flow through from one side to the other.

Figure 2: Computational domain showing boundary conditions.
###### 2.3.1. Coolant Flow

The coolant flow is assigned as saturated air. The jet inlet pressure is 1.4552 MPa, and the coolant outlet pressure recovery coefficient is 0.95. The inlet temperature, hydraulic diameter, and turbulent intensity are 300 K, 0.01026 m, and 5%, respectively.

###### 2.3.2. Mainstream

In the gas chamber it is assumed that the mainstream is a mixture of O2, H2O, CO2, N2, and some rare gases. The main flow in this case has a temperature of 1300 K and a mass flux rate of 31.46 kg/s. The operational pressure of flow outlet is 1.512 MPa. The inlet condition of the turbulence is specified by the turbulence intensity (5%) and the hydraulic diameter (0.324 m) to calculate the turbulence length scale. The convection coefficient of gas is 10 W/m2 K. These settings are not selected to match any specific commercial model but they are a realistic representation of typical gas turbine operating conditions [4].

###### 2.3.3. Droplet Injection

The droplet is uniformly given as 5 μm in diameter. The mass ratio of mist over the cooling airflow is 1% for lower operating conditions, which is about 3E-3 kg/s. The uniform velocity (0 m/s) is assigned to droplet injection. The boundary condition of droplets at walls is assigned as “reflect,” which means the droplets elastically rebound off once reaching the wall. At the outlet, the droplets just simply flee/escape from the computational domain.

In gas chamber, egress of the mainstream was fixed and export free expansion. The assumption of the solid wall of the quarter torus is modeled with a hypothesis of negligible thermal resistance by conduction, the thermal properties of the material were considered by Nimonic263. The coefficient of Near-Wall treatment uses the “Standard Wall Functions” in FLUENT (version 12.0.6).

##### 2.4. Meshing and Simulation Procedures

To conduct numerical simulation, the computational domain is meshed with a proper setup on the boundary conditions. As shown in Figure 3, the HEXA mesh in the ICEM/CFD software is used to generate the structured multiblock and the body-fitted grid system. In this study, the grid system associated with the parts of the mainstream and the coolant supply plenum is H-type. The total number of the cells for the four models are 390000, 1251980, 1410544, and 1100478, respectively. The local grid refinement is used near the hole regions. All the grid dependencies of four models are more than 0.5.

Figure 3: Meshes of four models.

The commercial software package FLUENT from Ansys, Inc. is adopted. At the same time, the drag, heat, and mass transfer between the droplets and the airflow are calculated. Iteration proceeds alternatively between the continuous and discrete phases. Converged results are obtained after the residuals are less than the specified values. A converged result renders a mass residual of 10−4, an energy residual of 10−6, and momentum and turbulence kinetic energy residuals of 10−5. These residuals are the summation of the imbalance for each cell, scaled by a representative of the flow rate. All runs were made on a PC cluster with four Pentium-4 2.8 GHz personal computers. The convergence criteria of the steady-state solution are judged by the reduction in the mass residual by a factor of 6, typically, in 2000 iterations.

#### 3. Results and Discussion

The gas turbine operating conditions selected in this study are featured by high temperature, high pressure, and high velocity of typical high-efficient commercial gas turbines, although not for any specific model. In this section the results obtained with different curvature are presented in order to validate the CFD model so that the air and mist/air impingement cooling physics would be investigated.

##### 3.1. Inner Wall Temperature

The temperature results of all the four curvature cases (0°, 30°, 60°, and 90° central angle) are compared in Figure 4. The regions shown in the picture are the main areas of concern in this study. From all the models we can illustrate that the temperature at the starting point is cooled by the coolant holes at the curve  mm on the outer wall while temperature remains the same throughout the coolant holes. The delicate color regions are approximately where the coolant strikes the inner wall after being reflected by the coolant holes. The temperature distribution shows strong diffusion in this region, correspondingly.

Figure 4: Comparative analysis of temperature in air/mist impingement jets with different curvature (0°, 30°, 60°, and 90° central angle): (a) without mist; (b) with mist.

From the figure it is seen that three rows of jet can protect the inner wall from overheating. From the simulations, the lowest temperature in the four models is 975, 953, 989, and 1128 K, respectively. The coldest parts of all models are at the center of the domain ( mm). The 30° central angle model has the coolest effect, and the flat model is secondly. When the surface curvature increasing, the temperature distribution is higher than flat model. In flat and 30° central angle models, the color of coolant effectiveness distribution in the same region is deeper than others, and the surface has been better protected by the coolant flow. Both phenomena are different from film-cooling mechanism over a flat surface.

In order to be acquainted with the reason why the droplet advanced impingement effectiveness, a sequence of instantaneous images of the temperature contours along the axis at various locations in the size 5 μm with 3E-3 kg/s droplets mass is presented in Figure 4(b). Compared with the coolant air (Figure 3(a)), the color of temperature distribution in the same region is becoming lighter. In the mist cooling cases, the phenomena of using mist cooling are obvious when the curvature (central angle) increases. From Figure 4(b), the 90° central angle model with the water droplets performs better than without mist case.

##### 3.2. Cooling Effectiveness

The adiabatic cooling effectiveness () is used to examine the performance of cooling effectiveness. The definition of is where is the mainstream hot gas inlet temperature, which is a fixed value for calculation of the adiabatic cooling effectiveness of any location, is the temperature of the coolant, which is assigned as a constant of 300 K in this issue and is the adiabatic wall temperature.

The average cooling effectiveness on the coolant chamber is calculated by the weighted method of cooling effectiveness on the part of inner wall area: where is the area of the inner wall, is the area of element, is the adiabatic cooling effectiveness, and is the finite element numbers.

The effects of curvature are studied with both air and mist/air impingement cooling. Figure 5 presents the contours of the local cooling effectiveness of the adiabatic film with and without mist under elevated operating conditions. In Figures 5(a) and 5(b), it is observed that the cooling effectiveness of the inner wall with the different curvature in both air and mist/air cases remains the same trend. And the arrangement order of cooling effectiveness of mist cases is the same between 300 and 700 mm along the axis. Mist/air impingement cooling of the double chamber model is also affected significantly by the curvature. The 30° central angle model case has lower temperature and higher cooling effectiveness, which is increased by 8% and 33.3% compared to the 90° central angle model.

Figure 5: Distributions of averaged cooling effectiveness with and without mist in the four curvature models: (a) air only; (b) with mist.

The cooling effectiveness is defined the same as it was in the previous section. To evaluate the cooling enhancement of adding mist into the air film, the net enhancement is plotted in Figure 6. The net enhancement is defined as follows:

Figure 6: Distributions of net enhancement comparing air and mist/air impingement cooling.

The subscript “” means mist is added. Without any subscript, it means air-only film is used. From the definition, net enhancement is zero if the mist cooling effectiveness is the same as the air-only cooling effectiveness.

This could be contributed by the computational certainty among different curvature models between the two-phase mist/air calculation and the single air phase calculation near the holes region. The net enhancement distribution between air and mist/air effect in the four curvature models is shown in Figure 6. The cooling enhancement, approximately 6–10% point, can be seen in 0°, 30°, and 60° central angel models from  mm to 675 mm. However, compared with air impingement cooling in the 90° central angel model, the mist/air case is enhanced almost 64%.

##### 3.3. Characteristics of the Droplet Particle Track and Flow Field (Amend)

Figures 7 and 8 show the droplet particle track and the velocity magnitude contours in the four curvature models, to evaluate how the droplet wall boundary conditions affect the mist cooling simulation. This mechanism of water droplets moving further away from the wall contributes to ineffectiveness of producing film-cooling protection of the inner wall even though the latent heat absorption can reduce the coolant chamber temperature. In Figure 8, to represent velocity magnitude contours we cut out the center line plane. In the sections of models, cooling jet impinges onto the target surface directly, and 30° central angle model typical vortexes of impinging jets are generated towards the target surface. For a curved suction side surface, the Coanda Effect makes the jets flow move to the pressure side, and the typical vortex on the suction side becomes stronger and larger than the one on the pressure side through all sections. For the 90° central angle model, because of the high speed flow and the large curvature of the surface, the droplets deviate from the inner wall and then reattach to the outer wall near the apex. The small size droplets jet is formed as the impinging jet turning parallel to the surface from the stagnation region and then it is further advantageous to complete evaporation adjacent to the wall.

Figure 7: Distributions of droplet particle track in the four curvature models with mist/air impingement cooling.
Figure 8: Velocity magnitude contours in the four curvature models with mist/air impingement cooling.

#### 4. Conclusion

A numerical simulation has been performed to study the flow and heat transfer of air and mist/air impinging cooling on the double chamber model. The influences of the surface curvature and mist have been analyzed respectively. However injection of mist into the coolant flow can increase the adiabatic cooling effectiveness on the four curved surfaces. The major findings are as follows.(1)In the different curvature double chamber models with only air impingement jets of this study, the adiabatic cooling effectiveness () degrades under the effect of curvature in the following descending order: 30° central angle model > flat model > 60°central angle model > 90° central angle model. During this investigation, the 30° central angle model case has lower temperature and higher cooling effectiveness, which is increased by 98.6% compared to the 90° central angle model.(2)The liquid droplets in the film provide a more extended impingement cooling coverage effect than the air impingement cooling. Compared with air-only case in each model, the maximum enhancement of adiabatic cooling effectiveness is about 64% in the 90° central angel model and corresponding to an additional adiabatic wall temperature reduction of 108 K. The cooling enhancement, approximately 6–10%, can be seen in 0°, 30°, and 60° central angel models.(3)Curvature of the model also influences the mist/air impingement cooling. The descending order of the cooling effectiveness () is in accord with air-only cases.

Mist/air impingement cooling keeps all the merits of air impingement cooling while being more effective. Therefore, retrofitting the old air impingement cooling systems with mist cooling seems attractive.

#### Nomenclature

 : Diameter of coolant chamber : Diameter of mainstream chamber : Length of the model : Absolute static temperature : Nondimensional coordinates in diameter, spanwise, and mainstream directions.
Greek Symbols
 : Cooling effectiveness.
Suffixes
 : Mainstraim flow : Coolant flow aw: Adiabatic wall : Mist/air : Size.

#### Conflict of Interests

The authors declare no conflict of interests.

#### Acknowledgment

This research is supported by the Technology Development of Jilin Province (no. 20126001).

#### References

1. R. J. Goldstein, Advances in Heat Transfer, Academic Press, New York, NY, USA, 1971.
2. R. J. Margason, “Fifty years of jet in cross-flow research,” Computational and Experimental Assessment of Jets in Cross Flow, vol. 41, pp. 7–34, 1993.
3. J. C. Han, S. Dutta, and S. V. Ekkad, Gas Turbine Heat Transfer and Cooling Technology, Taylor and Francis, New York, NY, USA, 2000.
4. Z. L. Yu, T. Xu, J. L. Li, L. Ma, and T. S. Xu, “Comparison of a series of double chamber model with various hole angles for enhancing cooling effectiveness,” International Communications in Heat and Mass Transfer, vol. 44, pp. 38–44, 2013.
5. N. Kayansayan and S. Küçüka, “Impingement cooling of a semi-cylindrical concave channel by confined slot-air-jet,” Experimental Thermal and Fluid Science, vol. 25, no. 6, pp. 383–396, 2001.
6. M. Choi, H. S. Yoo, G. Yang, J. S. Lee, and D. K. Sohn, “Measurements of impinging jet flow and heat transfer on a semi-circular concave surface,” International Journal of Heat and Mass Transfer, vol. 43, no. 10, pp. 1811–1822, 2000.
7. M. E. Taslim and D. Bethka, “Experimental and numerical impingement heat transfer in an airfoil leading-edge cooling channel with cross-flow,” ASME Journal of Turbomachinery, vol. 131, no. 1, pp. 1–7, 2009.
8. D. Rhee, P. Yoon, and H. Cho, “Local heat/mass transfer and flow characteristics of array impinging jets with effusion holes ejecting spent air,” International Journal of Heat and Mass Transfer, vol. 46, no. 6, pp. 1049–1061, 2003.
9. N. Souris, H. Liakos, and M. Founti, “Impinging jet cooling on concave surfaces,” AIChE Journal, vol. 50, no. 8, pp. 1672–1683, 2004.
10. B. V. N. R. Kumar and B. V. S. S. S. Prasad, “Computational flow and heat transfer of a row of circular jets impinging on a concave surface,” Heat and Mass Transfer, vol. 44, no. 6, pp. 667–678, 2008.
11. L. Zhao and Z. P. Feng, “Numerical simulation on the effect of jet nozzle position on impingement cooling of gas turbine blade leading edge,” International Journal of Heat and Mass Transfer, vol. 54, no. 23-24, pp. 4949–4959, 2011.
12. Z. L. Yu, T. Xu, J. L. Li, H. Xiu, and Y. Li, “Numerical simulation on the effect of turbulence models on impingement cooling of double chamber model,” Mathematical Problems in Engineering, vol. 2013, Article ID 170317, 8 pages, 2013.
13. H. Wei, D. Chiang, and H. L. Li, “Jet impingement and forced convection cooling experimental study in rotating turbine blades,” in Proceedings of GT2000, ASME Turbo Expo, Paper No. GT2009-59795, Munich, Germany, 2000.
14. Z. L. Yu, T. Xu, J. L. Li, T. S. Xu, and T. Yoshino, “Computational analysis of droplet mass and size effect on mist/air impingement cooling performance,” Advances in Mechanical Engineering, vol. 2013, Article ID 181856, 8 pages, 2013.
15. X. Li, J. L. Gaddis, and T. Wang, “Mist/steam cooling by a row of impinging jets,” International Journal of Heat and Mass Transfer, vol. 46, no. 12, pp. 2279–2290, 2003.
16. X. Li, J. L. Gaddis, and T. Wang, “Mist/steam heat transfer with jet impingement onto a concave surface,” ASME Journal of Heat Transfer, vol. 125, no. 3, pp. 438–446, 2003.
17. X. Li and T. Wang, “Computational analysis of surface curvature effect on mist film cooling performance,” ASME Journal of Heat Transfer, vol. 130, no. 12, Article ID 121901, p. 10, 2008.
18. T. S. Dhanasekaran and T. Wang, “Simulation of mist film cooling on rotating gas turbine blades,” ASME Journal of Heat Transfer, vol. 134, no. 1, Article ID 011501, p. 11, 2012.
19. S. K. Aggarwal and T. W. Park, “Dispersion of evaporating droplets in a swirling axisymmetric jet,” AIAA journal, vol. 37, no. 12, pp. 1578–1587, 1999.
20. X. Q. Chen and J. C. F. Pereira, “Prediction of evaporating spray in anisotropically turbulent gas flow,” Numerical Heat Transfer A, vol. 27, no. 2, pp. 143–162, 1995.
21. T.-H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, “A new κ-ε eddy viscosity model for high reynolds number turbulent flows,” Computers & Fluids, vol. 24, no. 3, pp. 227–238, 1995.
22. ANSYS FLUENT 12.1 Documentation, ANSYS.