Numerical investigations on flow and heat transfer of swirl and impingement composite cooling structures of turbine blade leading edge

International Journal of Heat and Mass Transfer 144 (2019) 118625

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Numerical investigations on flow and heat transfer of swirl and impingement composite cooling structures of turbine blade leading edge Fan Wu a, Liang Li a,b,⇑, Jiefeng Wang a, Xiaojun Fan a, Changhe Du a a b

School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China Shaanxi Engineering Laboratory of Turbomachinery and Power Equipment, Xi’an 710049, China

a r t i c l e

i n f o

Article history: Received 27 March 2019 Received in revised form 16 August 2019 Accepted 22 August 2019

Keywords: Swirl and impingement composite cooling Mass flow rate Flow and heat transfer Numerical method

a b s t r a c t In this paper, four swirl and impingement composite cooling structures are established to deeply study the flow and heat transfer characteristics, where the swirl nozzles and impingement nozzles are reasonably arranged. Numerical simulation is conducted by solving the Reynolds Averaged Navier-Stokes (RANS) equations with the standard k-x model. Meanwhile, numerical results are compared with the cooling behaviors of swirl cooling and impingement cooling under the same condition. Results revealed that the pressure distribution of four composite cooling structures is quite different from that of swirl cooling and impingement cooling. Hence, the nozzle mass flow ratio distribution of composite cooling structures displays a large fluctuation with the variation of the nozzle location, which has an influence on the flow and heat transfer characteristics. Moreover, the heat transfer characteristics of swirl and impingement composite cooling combine the advantages of impingement cooling and swirl cooling, where there both exists extremely high local heat transfer regions and uniform heat transfer regions. As for composite cooling 3 and composite cooling 4, the alternate locations of impingement nozzles and swirl nozzles could effectively increase the band-shaped high heat transfer area. Meanwhile, the low heat transfer area caused by the continuous arrangement of impingement nozzles is reduced. Among four composite cooling structures, the composite cooling 4 has the highest average heat transfer coefficient and the minimum pressure loss. The globally average heat transfer of composite cooling 4 is 3.49% lower than swirl cooling but is 19.12% higher than impingement cooling. Its total pressure loss is 4.29% lower than swirl cooling and is slightly lower compared with impingement cooling. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction In order to improve the efficiency and power of modern gas turbine engines, the turbine inlet gas temperature has a great increase, which is far more beyond the blade material thermal resisting limitation. As the blade leading edge surface is directly exposed to a very high temperature, it requires more complex cooling schemes. Hence, various cooling methods have been developed over the years to keep the turbine blade leading edge temperature below critical levels. The impingement cooling, which provides an effective possibility to significantly enhance the local heat transfer coefficient, is widely used in blade leading edge cooling systems. The swirl cooling as a novel blade leading edge cooling method exhibits excellent performance for its high heat transfer coefficient and uniform thermal distribution.

⇑ Corresponding author. E-mail address: [email protected] (L. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118625 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

A number of studies have been reported on the mechanism of impingement cooling on a semicircular concave surface. Chupp et al. [1] experimentally studied the impingement of a single row of circular jets on a semicircular concave surface. Results indicated that the dependence of Nusselt number on Reynolds number, geometry and chordwise location on the blade leading region. Tabakoff et al. [2] conducted an experimental investigation of the heat transfer performance of air jets impinging on the blade leading edge inner surface. They found that the round jet array configurations have the highest heat transfer rate compared to the row of round jets and slot jets. Yang et al. [3] experimentally investigated the effects of nozzle shapes and Reynolds numbers on jet impingement cooling on a semicircular concave surface. Results showed that the averaged heat transfer rates for impingement on the concave surface are more enhanced compared with the existing experimental results. Choi et al. [4] experimentally studied the impingement cooling characteristics on a semicircular concave surface and the distribution of mean velocity and velocity fluctuation were measured by using a Laser Doppler Anemometer.

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F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

Nomenclature L Re V Nu Nuac Ps Pto Tw P

length of swirl chamber Reynolds number velocity magnitude Nusselt number globally average Nusselt number total pressure loss coefficient the outlet total pressure the target temperature Static pressure

Greek symbols q coolant air density k thermal conductivity

Kayansayan et al. [5] presented an experimental study of a concave channel impingement cooling. The experimental data of velocity at the wall jets are consistent with numerical solution results at a low Reynolds number range. Taslim et al. [6–9] systematically investigated the heat transfer characteristics of impingement cooling on a concave surface under the effects of smooth and roughness wall, jet to target wall spacing, showerhead and cross flow using experimental and numerical methods. They found that the heat transfer is enhanced by the roughness wall surface while is reduced by the cross flow. Many studies of impingement cooling on the blade leading edge were performed. Rajamani et al. [10] numerically studied three different profiles in the cooling passage of the blade leading edge. Their results indicated that the cross flow and vortex formation have a significant influence on heat transfer performance. Liu et al. [11–12] numerically investigated the flow and heat transfer characteristics of impingement cooling on the internal blade leading edge. The influences of jet nozzle position, jet Mach number and jet nozzle diameter were studied, respectively. Numerical results indicated that the heat transfer increased with the increase of impinging jets Mach number and jet nozzles diameter, but it increased with the decrease of the distance between jet nozzles center and the pressure side. Liu et al. [13] conducted an experimental study that the flow behaviors and aerodynamic parameters of a confined channel with a staggered jet array were investigated. They found that the mass flow distribution, static pressure and discharge coefficient were dominated by the ratio of passage height to impingement holes diameter. Li et al. [14] experimentally investigated the effect of film holes on impingement cooling in a 2/3 cylinder leading edge model, and the numerical simulation with SST k-x model was verified with experimental data. Their results showed that the film suction could enhance the local heat transfer. Moreover, the position and angle of film hole affect the heat transfer behaviors as well. With regard to the swirl cooling basic mechanism, many researches have been performed. Kreith et al. [15] first investigated the flow and heat transfer performance of the swirling flow in a circular tube. They found that the swirling flow could bring about a thinner thermal boundary layer. Hay and West et al. [16] experimentally studied the heat transfer of free swirling flow with tangential injections in a circular pipe. Results revealed that the heat transfer was highly depended on the swirling intensity. Chang and Dhir [17] presented an experimental study on the turbulent swirling flow with tangential injections. They explained that the heat transfer enhancement was closely related to the increasing tangential momentum ratio. Ligrani et al. [18] experimentally pointed out Görtler vortex pairs could contribute to high heat

Dh ReD qw Nusp y+ Ptj Tin X,
Y, Z V out

l s

diameter of swirl chamber Reynolds number based on hydraulic diameter of the swirl chamber heat flux spanwise average Nusselt number wall coordinate normal to wall the inlet total pressure the inlet total temperature cartesian coordinates the outlet averaged velocity dynamic viscosity coefficient stress tensor

transfer characteristics of swirl cooling. Hedlund et al. [19] experimentally explored the local flow pattern and heat transfer performance at various Reynolds numbers. They found that the Görtler vortex pairs became more numerous while their sizes decreased relatively with the increase of Reynolds number. Researchers have considered many factors influencing heat transfer behaviors of swirl cooling. Ling et al. [20] experimentally measured the swirl cooling heat transfer coefficients and numerically studied the vortex flow field in a circular cooling passage. Besides, a careful comparison on the heat transfer was carried out with former studies. Du et al. [21–23] systematically studied the effects of nozzle geometric parameters such as aspect ratio, axial number and inject angle in a semicircular swirl cooling configuration by numerical method. Furthermore, aerodynamic parameters such as inlet Reynolds number and temperature ratio were studied as well. Fan et al. [24] conducted an experiment to investigate the flow and heat transfer behaviors of swirl cooling with a semicircular swirl chamber, 5 nozzles and a coolant inlet chamber. Their results showed that the heat transfer coefficient increased with the increasing Reynolds number and the decreasing temperature ratio. Several studies have been conducted to investigate the novel swirl cooling configuration. Kusterer et al. [25–27] first proposed a new swirl cooling configuration named double swirl chambers (DSC) and experimentally studied the cooling effectiveness of a modified DSC structure. They concluded that the DSC structure had a higher heat transfer coefficient than swirl cooling and impingement cooling. Luan et al. [28] numerical compared the flow and heat transfer characteristics of swirl cooling with three different inlet chambers. The results presented that the alternation of inlet chambers changed the flow structure and heat transfer distribution. It is noteworthy that all previous internal cooling researches of the blade leading edge were based on independent impingement cooling and swirl cooling. Nevertheless, almost no attention was paid to the combination of these two cooling methods. From the above discussion, swirl cooling has the advantages of uniform heat transfer distribution and strong anti-cross flow ability while its pressure loss is relatively high; impingement cooling has the advantages of high local heat transfer potential while it is greatly affected by the cross flow. To make full use of the advantages of strong anti-cross flow ability of swirl cooling and high local heat transfer of impingement cooling, meanwhile, to avoid the poor resistance of the impingement cooling against the cross flow, a swirl and impingement composite cooling structure is proposed to provide a better choice for blade leading edge cooling. In the present study, four swirl and impingement composite cooling

F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

configurations were established, where the relative positions and numbers of impingement nozzles and swirl nozzles were reasonably arranged. In order to meet the actual blade with internal cooling passage, the coolant inlet chamber was added. Under the constant geometric and aerodynamic parameters, swirl and impingement composite cooling flow and heat transfer behaviors were analyzed using numerical method. Meanwhile, for the purpose of obtaining the optimum heat transfer coefficient composite cooling structure, numerical results were compared with impingement cooling and swirl cooling under the same condition. In the end, this paper seeks to provide a suggestion for turbine blade leading edge cooling design.

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2. Numerical method 2.1. Geometrical details The swirl cooling configuration for the present study is extracted and modified from the geometry of Fan et al. [24]. To deeply investigate the flow and thermal characteristics of swirl and impingement composite cooling, four composite cooling models were established. In these structures, the relative positions and numbers of impingement nozzles and swirl nozzles are reasonably arranged. Because Taslim et al. [9] have already confirmed that the impingement cooling is significantly affected by the cross flow and

(a) composite cooling 1

(b) composite cooling 2

(c) composite cooling 3

(d) composite cooling 4 Fig. 1. Configuration parameters of swirl and impingement composite cooling models.

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2.3. Governing equations A commercial software ANSYS CFX is applied to perform this simulation. The solutions are obtained by solving the turbulent steady viscous compressible RANS equations with two equation turbulence model. And a second order format with high resolution correction is used to discretize the convection term. The overall accuracy of this numerical simulation is second order. Because high velocity compressible cooling air is forced into the internal cooling passage, compressibility effects are concerned as well. Whereas, effects of the radiation heat transfer, buoyancy as well as external momentum sources are neglected. Considering these assumptions, the details of transport equations are expressed as follows. The continuity equation:

Fig. 2. Three dimensional geometry of composite cooling 1.

Rao et al. [29] pointed out that the heat transfer of swirl cooling is little affected at the downstream, the impingement nozzles were located at the upstream of these composite cooling models. Besides, the heat transfer distribution of swirl cooling is more uniform than impingement cooling, so that there are more swirl nozzles arranged in these composite cooling structures. As shown in Fig. 1, the two-dimensional geometry of these models and geometric dimensions are indicated, where the unit is mm. Every structure consists of one swirl chamber, one inlet chamber, two impingement nozzles and four swirl nozzles. The only difference in these four composite cooling structures exists in the variation of impingement nozzles and swirl nozzles relative position. Meanwhile, the inlet cross sectional area of impingement nozzles and swirl nozzles is kept unchanged. For the sake of a clearer understanding, the three dimensional geometry of composite cooling 1 is shown in Fig. 2. As for impingement cooling and swirl cooling, the nozzle type is merely changed, while the geometric parameter of nozzles remained unchanged. The cooing air injects from six inlet nozzles into the swirl chamber after the mass flow allocation at the inlet chamber, and then flows out through the outlet. 2.2. Parameter definition Several parameters are defined to evaluate and analyze the flow and heat transfer performance of swirl and impingement composite cooling. (1) The Reynolds number is based on the hydraulic diameter of swirl chamber.

ReD ¼ qV y Dh =l

r  ðqUÞ ¼ 0

ð4Þ

The momentum equation:

r  ðqU  UÞ ¼
rp þ r  s þ SM where



ð5Þ

s is the total enthalpy, related to the strain rate by 2 3



s ¼ l rU þ ðrUÞT
dr  U

ð6Þ

The total energy equation:

r  ðqUhtot Þ ¼ r  ðkrT Þ þ r  ðU  sÞ þ SE

ð7Þ

where htot is the total enthalpy, SE is the energy source. 2.4. Turbulence model The suitable turbulence model is of great importance on the numerical results accuracy. However, almost no experimental measurement on the swirl and impingement composite cooling has been carried out currently. Actually, turbulence model applicability is closely related to the flow behavior, and the flow patterns of composite cooling structures are vortex flow and impinging jets. Hence, the swirl cooling and impingement cooling are selected to validate the turbulence model, respectively. Figs. 3 and 4 show a comparison of the target wall spanwisely averaged Nusselt number of swirl cooling and impingement cooling, respectively. Fan et al. [24] have already conducted an experiment on swirl cooling in a semicircular swirl chamber with an inlet chamber, and experimental results were compared with corresponding numerical results. They have confirmed that the standard k-x model has the best

ð1Þ

where Vy is mean axial velocity, q is the coolant density, l is the dynamic viscosity coefficient and Dh is the hydraulic diameter of swirl chamber. (2) Nusselt number. The Nusselt number is usually used to evaluate the heat intensity and its definition is as follows.

Nu ¼ qw Dh =ðT w
T in Þk

ð2Þ

where qw is the target heat flux; k is the thermal conductivity; Tin and Tw are the inlet temperature and the target temperature. (3) To investigate the flow penalty, the total pressure drop coefficient is defined as follows.

Ps ¼ ðPtj
Pto Þ=Ptj

ð3Þ

where Ptj is the inlet total pressure and Pto is the outlet total pressure.

Fig. 3. Comparison of the spanwisely averaged Nusselt number on the target wall with the experimental data from Fan et al. [24].

F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

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Fig. 5. Three dimensional mesh of composite cooling 1. Fig. 4. Comparison on spanwise area weight average Nusselt number along the target plane of experimental results [30].

solution accuracy compared with the standard k-e model, RNG k-e model and SST k-x model, as shown in Fig. 3. And the averaged deviation between the numerical computation s and the experimental data is about 10%, which is reasonably acceptable. Liu et al. [30] showed that both the standard k-x model and SST k-x model provide a lower simulating error for impingement cooling, and the SST k-x model is slightly better than k-x model, as is indicated in Fig. 4. Furthermore, Fan et al. [31] present that the standard k-x model is most appropriate for the calculation on both high Reynolds number flow and low Reynolds number flow. Thus, this study applies the standard k-x model to investigate the composite cooling flow and thermal characteristics. 2.5. Boundary conditions The cooling fluid is air ideal gas for all cases. The velocity is specified to keep ReD = 10,000 at the inlet with the total temperature of 350 K, and the turbulence intensity of the inlet flow is set to be 5% in all cases. As for the outlet, the average static pressure is 0.11 MPa. The target wall of the swirl chamber is set to be a constant temperature of 500 K, the rest wall are adiabatic surface. In addition, all walls have non-slip velocity conditions. The convergence of this simulation is accomplished until all the root mean square residuals of the mass, energy and momentum equation are lower than 10-5.

1.43 million, 2.48 million, 3.12 million, 5.24 million and 6.36 million are selected. The mesh refinement is synchronously conducted on each mesh in three coordinate directions, and the standard k-x model is employed. Fig. 6 shows the spanwise-averaged Nusselt number Nusp distribution versus dimensionless parameters YL-1 for five different meshes. It can be seen that the Nusp distribution on the target wall is almost the same when the grid number is greater than 3.12 million. Furthermore, the target wall globallyaveraged Nusselt number Nuac obtained by five different meshes are presented in Table 1. The extrapolation value is calculated by using the Richardson extrapolation method [32] with the results of 5.24 million grids and 6.36 million grids. Provided that the calculated Nusselt number is a baseline solution, the relative error is less than 1.5% when the grid number is larger than 3.12 million. Hence, the grid number has a little influence on numerical results. Considering the simulation time, the grids with 5.24 million are employed in the present study, and the same grid size definition is adopted for the other cases. 3. Results and discussion For the sake of a convenient analysis, it is suggested that the impingement nozzle and swirl nozzle are numbered from 1 to 6 along the Y direction. And the XY section indicates this section

2.6. Mesh procedure The software ICEM CFD is used to generate the hexahedral structured grids for this numerical calculation. Fig. 5 presents mesh details of the swirl chamber and inlet chamber. As shown in Fig. 5, the inlet chamber, swirl nozzles and the outlet are discretized by H-type grids. O-type grids are used to discretize impingement nozzles, while C- type grids are used to discretize the swirl chamber. In order to satisfy the requirements of the turbulence model, all grids around walls are encrypted. Hence, the y+ value of the first cell is lower than 1 in all cases. 2.7. Grid independence analysis Proper grid numbers can guarantee the accuracy of the numerical simulation and reduce the use of computer resources. The configuration of composite cooling 1 is selected to validate grid independence. Five different meshes with the grid number of

Fig. 6. The distribution of spanwise-averaged Nusselt number for five different meshes.

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Table 1 The globally-averaged Nusselt number for the five different meshes. Node number, million

Nuac

Relative error

1.43 2.48 3.12 5.24 6.36 Extrapolation

180.9 178.627 174.597 172.351 172.04 169.89

6.48% 5.14% 2.77% 1.44% 1.26% –

parallel to the inlet jet section while the YZ section indicates it perpendicular to the inlet section. In this section, simulations are conducted with the same geometric and aerodynamic parameters. 3.1. Flow field The allocation of mass flow is closely related to flow structures at the swirl chamber. Owing to the introduction of the inlet chamber, the practical mass flow ratio distribution of nozzles can be obtained. Fig. 7 gives the mass flow ratio allocation distribution of jet nozzles for 6 cooling structures. It clearly shows that various arrangements of jet nozzles have a great impact on mass flow ratio distribution. For impingement cooling and swirl cooling, the mass flow ratio of nozzles increases gradually along the axial direction due to the large pressure drop from upstream to downstream. As for composite cooling structures, the mass flow ratio distribution of nozzles varies with the relative position of impingement nozzles and swirl nozzles, which is different from that of swirl cooling and impingement cooling. It can be seen that the mass flow ratio of some swirl nozzles has a sudden decrease, which is mainly caused by the difference of pressure distribution of the swirl chamber. Additionally, the mass flow ratio distribution of composite cooling 4 is more uniform compared with other cooling structures. Fig. 8 provides the YZ/XY section coolant pressure distribution contours of 6 cooling structures. As can be seen, the overall coolant pressure decreases gradually along the axial direction. Besides, the high pressure occurs in the near wall region while a relative low pressure exists in the chamber core. This is mostly because of the increasing axial velocity in the swirl chamber and the local lower near-wall circumferential velocity, which are discussed in detail in [29,33]. Furthermore, it should be noted that the pressure gradient of swirl cooling is the largest among these cooling structures. For swirl cooling and impingement cooling, since jet nozzles are arranged on the same axial line and the pressure in inlet chamber is weakly changed, the increasing pressure difference contributes

Fig. 7. Mass flow ratio of each jet nozzles for 6 cooling structures.

to an increase in mass flow ratio of nozzles along the axial direction. With regard to composite cooling, it is obvious that the pressure distribution is quite different owing to the various relative positions of impingement nozzles and swirl nozzles. The suction effect of impingement nozzles would increase the inlet velocity, which brings a relative low pressure distribution just below the impingement nozzles at XY section, as shown in Fig. 8. However, it is worth noting that the pressure just below some swirl nozzles adjoined to impingement nozzles is relative high. Hence, the mass flow ratio distribution of four composite cooling structures has a sudden drop, which is showed in Fig. 7. To deeply investigate the flow phenomena of four composite cooling configurations, Fig. 9 presents the streamline and velocity contours at 6 XZ section that corresponding to the location of each nozzle. Regarding swirl cooling, it can be seen that the high velocity occurs in the near wall region accompanied with a low velocity in the chamber core. The magnitude of velocity decreases continuously along the circumferential direction due to the friction and dissipation. For impingement cooling, the cooling jet of No.1 nozzle impinges onto the target wall directly, and the Coanda effect makes the jets flow toward both sides, forming two large scale vortices. Whereas, the cooling jets of downstream nozzles could not impinge onto the target wall directly due to the cross flow. Compared with impingement cooling and swirl cooling, it is obvious that different arrangements of impingement nozzles and swirl nozzles of composite cooling change the upstream coolant streamline distribution. Whereas, as the air flow develops downstream, the streamline distribution is little affected. As for composite cooling 1, the cooling jet of No.1 nozzle spreads to both sides more obviously than impingement cooling, forming two different scale vortices. However, the intensity of jets impinge on the target wall is weaker than impingement cooling. Besides, the corner vortices are clearly observed as well, which is mainly caused by the streamline deflection. As cooling airs of No.1 nozzle flow toward downstream and through from both sides of No.2 nozzle impinging jets, two small vortices are generated near the top region. However, the vortex number has a decrease compared with impingement cooling. Because the cooling air can flow in free directions around the wall, the upstream axial flows have a strong interference on the development of the cooling jets tangential flow of No.3 nozzle. Hence, the vortex deviates away from the center of XZ section and moves to the left side, as shown in Fig. 9(a). As the upstream spent air passes through the core region at each downstream nozzle, the swirl intensity at the near wall region is almost unchanged. For composite cooling 2, when the swirling air of No.1 nozzle flows along the target wall and passes through the right side of No.2 nozzle, it directly encounters with the impinging jets and contributes to a high momentum loss. Therefore, the air velocity of No.2 nozzle is significantly attenuated at the right side and part of impinging jets are entrained by upstream swirling airs, forming a large scale vortex. Besides, another part of impinging jets flow toward the left side and a small scale vortex is generated because of the cross flow. The streamline and velocity distribution of No.3 nozzle are similar with that of No.2 nozzle of composite cooling 1, which is mainly owing to the similarity of the location of impingement nozzles. Differently, the vortex number in the left side of is more numerous than that of composite cooling 1. This is mostly because of the convergence of the upstream swirling flow and impinged jets. With regard to composite cooling 3, the upstream streamline and velocity distribution is similar to the composite cooling 2 because of the similarity of their geometrical structure. Differently, the streamline of No.4 nozzle is strongly affected by the upstream flow. As Fig. 9(c) shown, the impinging jets are entrained by upstream spent airs, and the entraining effect will become stronger

F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

(a) impingement cooling

(c) composite cooling 1

(e) composite cooling 3

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(b) swirl cooling

(d) composite cooling 2

(f) composite cooling 4

Fig. 8. The YZ/XY section coolant pressure distribution contours of 6 cooling structures.

along the circumferential direction. Hence, a vortex is generated in the right side. For composite cooling 4, a larger mass flow ratio of No.1 nozzle brings about a slower velocity attenuation of impinging jets and the coolant forms a large scale vortex on both sides. In addition, the streamline distribution of No.3 nozzle is similar to that of No.4 nozzle of composite cooling 3. The only difference is that the confluence of the spent air and the impinging jet from No.3 nozzle are squeezed, forming a small scale vortex at the bottom of the target wall. Fig. 10 shows the streamline and axial velocity VY contours in YZ section of 6 cooling structures. Generally, for 6 cooling structures the axial velocity increases from upstream to downstream due to the fact that more jet flows enter the swirl chamber. It can be seen that there exists backflow regions, while the backflow velocity decreases with the increase of axial position. Differently, for composite cooling 4, the area of low-velocity backflow regions is reduced and the velocity distribution is more uniform compared with other composite cooling structures. It presents that the alternate arrangement of impingement nozzles and swirl nozzles is beneficial to decrease the area of low-velocity backflow regions caused by the continuous arrangement of impingement nozzles. It should be noted that the high axial velocity region of composite cooling and swirl cooling is located in the swirl chamber core at the fifth and sixth inlet nozzle positions. This is mainly because a vortex occurs in the bottom wall and thus reduces the cross-sectional area. However, the high axial velocity region of impingement cooling is located in the swirl chamber bottom at each nozzle position. Furthermore, the magnitude of the high axial velocity of composite cooling structures is larger than swirl cooling and impingement

cooling. This is mainly because there simultaneously exists two vortices near the top and bottom wall and thus the air flow from the upstream is further accelerated in the swirl chamber center, especially for composite cooling 2. When the swirl nozzle is located at the first position such as composite cooling 2 and composite cooling 3, several alternating vortices are observed at the upstream. The unsymmetrical inlet nozzle causes these vortices, which are explained by Biegger et al. [33]. The vorticity is useful to analyze the rotation of fluid and is presented to show the swirling intensity in the chamber as introduced in Liu et al. [34]. The Non-dimensional vorticity in the axial direc


tion can be expressed as xY ¼ @u
@w Dh = V out , where the V out is @Z @X the averaged velocity at the outlet of the swirl chamber. Fig. 11 shows the axial vorticity contours at 5 XZ section between each nozzles. For swirl cooling, it can be seen that the maximum of the vorticity occurs in the near wall region, while the negative value appears near the chamber core. Furthermore, the high vorticity region also appears at the chamber corner because of the existence of corner vortices. Regarding impingement cooling, the magnitude of the vorticity is obviously smaller than swirl cooling which is due to the free flow of the spent impinging jets. In composite cooling structures, it is obvious that the magnitude of the vorticity is declined compared with swirl cooling, and the vorticity distribution becomes more complex. The high negative vorticity region decreases and deviates from the chamber core, indicating that the swirling intensity in the chamber core is suppressed. This is mainly because the upstream air passes through the chamber core region, as shown in Fig. 10. Moreover, the high vorticity region at the chamber corner is reduced.

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(a) composite cooling 1

(b) composite cooling 2

(c) composite cooling 3

(d) composite cooling 4

(e) impingement cooling

(f) swirl cooling Fig. 9. Streamline and velocity contours in XZ section of 6 cooling structures.

F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

(a) composite cooling 1

(b) composite cooling 2

(c) composite cooling 3

(d) composite cooling 4

(e) impingement cooling

(f) swirl cooling Fig. 10. Streamline and axial velocity contours in YZ section of 6 cooling structures.

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F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

(a) composite cooling 1

(b) composite cooling 2

(c) composite cooling 3

(d) composite cooling 4

(e) impingement cooling

(f) swirl cooling Fig. 11. The axial vorticity contours at 5 XZ section between each nozzles.

3.2. Heat transfer performance For a better view of the Nu contours, the target is transferred from three dimensions to two dimensions along the Y direction, which shown in Fig. 12. Fig. 13 illustrates the Nu contours of swirl

cooling, impingement cooling and 4 composite cooling structures. As can be seen, the heat transfer characteristics of composite cooling structures combine the advantages of swirl cooling and impingement cooling. For composite cooling structures, most of regions are maintained a relative high heat transfer and an even

F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

Fig. 12. Two dimensional expansion schematic of the target.

(a) impingement cooling

(b) swirl cooling

(c) composite cooling 1

11

temperature gradient, meanwhile, there exists very high local heat transfer region as well. Compared with impingement cooling, the anti-cross-flow ability of composite cooling structures is enhanced because the impingement nozzles are located at the upstream. For composite cooling 3 and composite cooling 4, the alternate arrangement of impingement nozzles and swirl nozzles contributes to the decreasing area of low Nu region located between the impingement nozzles. This is because that the tangential movement of the swirling flow effectively reduces the momentum loss caused by the collision between two adjacent impinging jets. Compared with swirl cooling, the area of banded high Nu regions of composite cooling is increased, which is because of the different mass flow ratio allocation of nozzles, as shown in Fig. 7. It is worth to mention that a smaller mass flow ratio of some swirl nozzles brings about a higher Nu and a relative high mass flow ratio of impingement nozzles enhance the anti-cross flow impacts, which effectively strengthen the local heat transfer, such as composite cooling 2 and composite cooling 3. However, the area of low Nu regions of composite cooling is increased a little as well. Overall, the extremely high heat transfer region and the relative uniform heat transfer region are simultaneously observed in composite cooling structures, which is beneficial to deal with various temperature field distribution of the blade leading edge. Fig. 14 shows the Nusp distribution along the axial direction. It clearly shows that the overall Nusp distribution gets changed because of the alternation of nozzles. As observed in Fig. 14, the high value of Nusp corresponds to the location of inlet nozzles and the variation of mass flow ratio of nozzles greatly changes the value of Nusp. For example, the Nusp for composite cooling 4 is higher than others at the position of No.1 nozzle, while it turns lower at the position of No.3 nozzle. When the impingement nozzles are arranged adjacently, such as composite cooling 1 and composite cooling 2, it was found that the lowest value of Nusp decreases dramatically. It can be explained by the decreasing velocity of cooling jets after impinged on the target wall. For composite cooling 3, as the impinging jets of No.4 nozzle are greatly affected by the cross flow, the amplitude of Nusp peak decreases dramatically and deflects toward downstream, which is corresponding to the flow phenomena of the Fig. 10. In Fig. 15, the target wall spanwise-averaged heat flux distribution is illustrated along the axial direction. Obviously, the high heat flux region is corresponding to the location of inlet nozzles. It is noteworthy that the maximum value of heat flux of the composite cooling 4 is higher than swirl cooling and impingement cooling at

(d) composite cooling 2

(e) composite cooling 3

(f) composite cooling 4 Fig. 13. The target Nussrlt number contour of 6 cooling structures.

Fig. 14. The spanwise-averaged Nusselt number along the streamwise direction.

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F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625 Table 2 Comparison of the Nuac and Ps of different cooling structures.

Fig. 15. The spanwise-averaged heat flux distribution along the streamwise direction.

Configurations

ReD

Nuac

Ps

swirl cooling impingement cooling composite cooling 1 composite cooling 2 composite cooling 3 composite cooling 4

10265.5 10299.2 10281.9 10290.7 10242.1 10325.6

182.9 148.177 172.351 175.017 172.787 176.517

0.1772 0.1728 0.1716 0.1718 0.1705 0.1696

are both the largest and the Nuac of impingement cooling is the least. As for 4 composite cooling structures, different arrangements of impingement nozzles and swirl nozzles bring about different flow and heat transfer characteristics. The composite cooling 4 has the highest heat transfer coefficient and the least pressure loss among 4 composite cooling structures. Compared with swirl cooling, although its globally averaged heat transfer coefficient is slightly reduced, the pressure loss is obviously decreased. It is beneficial for the arrangement of film holes on the blade leading edge. 4. Conclusion

Fig. 16. The circumferential averaged heat flux distribution.

the upstream, which is mostly due to the larger mass flow ratio. Fig. 16 provides the average heat flux distribution over the circumference (characterized by the angle) on the curve surface of the target wall. The impingement spots are characterized by the local maximum heat flux for the impingement cooling at the center position of target (angle = 90 deg), while the maximum value of heat flux of swirl cooling is located at the left side of the target wall. As for composite cooling, the maximum value of heat flux is observed at the center region of the target wall, where the heat flux distribution is similar to the swirl cooling. The composite cooling 4 has the local highest heat flux among 4 composite cooling structures. Besides, the heat flux of composite cooling 4 is obviously larger than swirl cooling at the center region of the target wall and is larger than impingement cooling at the left and right side of the target wall. Indeed, the high temperature stagnation zone of practical gas turbine blade leading edge is mostly located at the central region of the target wall. Hence, the composite cooling 4 could take more heat flux away at the central region and keep a relative high heat transfer at other regions, which would be suitable to the application in the blade leading edge cooling. In order to deeply compare the flow and heat transfer characteristics, the target wall globally-averaged Nusselt number Nuac and the total pressure loss coefficient Ps are listed in Table 2. It can be seen that the ReD is almost unchanged in all cases to ensure the fairness for this comparison. The Nuac and Ps of swirl cooling

In this paper, four swirl and impingement composite cooling configurations are established by reasonably arranging the position of impingement nozzles and swirl nozzles, and an inlet chamber is introduced to improve the models. Numerical simulation is performed to investigate the swirl and impingement composite cooling characteristics by using the commercial software ANSYS CFX, with the application of RANS equations and the k-x turbulence model. Furthermore, results are compared with swirl cooling and impingement cooling under the same geometric and aerodynamic parameters. The nozzle mass flow ratio distribution of composite cooling structures varies with the relative position of impingement nozzles and swirl nozzles, where the mass flow ratio of some swirl nozzles has a sudden decrease due to the varied pressure distribution in swirl chamber. The various arrangements of impingement nozzles and swirl nozzles of composite cooling have some effects on the upstream streamline distribution. As the convergence of the upstream swirling flow and impinged jets passes through the core region of each downstream nozzle, the high axial velocity region exists in the swirl chamber core at the fifth and sixth inlet nozzle positions. Hence, the axial vorticity distribution in the core region is affected greatly, while the maximum value of the vorticity occurred in the near wall region is less affected. The heat transfer of composite cooling structures combine the advantages of swirl cooling and impingement cooling, and both the extremely high local heat transfer regions and uniform heat transfer regions are simultaneously obtained. As for composite cooling 3 and composite cooling 4, the alternate arrangement of impingement nozzles and swirl nozzles can increase the bandshaped high heat transfer area. In addition, the composite cooling 4 could take more heat flux away at the central region of the target wall and keep a relative high heat transfer at other region, which is suitable to the application in the blade leading edge cooling. Among 4 composite cooling structures, composite cooling 4 has the highest averaged heat transfer coefficient and the lowest pressure loss, and the alternate arrangement of impingement nozzles and swirl nozzles is beneficial to decrease the area of lowvelocity regions caused by the continuous arrangement of impingement nozzles. Compared with swirl cooling, the Nuac of composite cooling 4 is reduced by 3.49%, while its Ps is reduced by 4.29%. It is beneficial for the arrangement of film holes on the blade leading edge. Compared with impingement cooling, the Nuac of composite cooling 4 is increased by 19.12%, and its Ps is slightly

F. Wu et al. / International Journal of Heat and Mass Transfer 144 (2019) 118625

lower. Hence, if a maximum averaged heat transfer with a high pressure loss is desired, one should choose the swirl cooling. If one is interested in a minimum pressure loss with a relative low averaged heat transfer and could flexibly deal with the hot spots, the composite cooling 4 would be the best choice. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgement The authors gratefully acknowledge financial support from National Science and Technology Major Project (2017-I-00090010). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118625. References [1] R.E. Chupp, H.E. Helms, P.W. McFadden, Evaluation of internal heat transfer coefficients for impingement cooled turbine airfoils, J. Aircraft 6 (1969) 203– 208. [2] W. Tabakoff, W. Clevenger, Gas turbine blade heat transfer augmentation by impingement of air jets having various configurations, J. Eng. Power 94 (1972) 51–58. [3] G. Yang, M. Choi, J.S. Lee, An experimental study of slot jet impingement cooling on concave surface: effects of nozzle configuration and curvature, Int. J. Heat Mass Transf. 42 (1999) 2199–2209. [4] M. Choi, H.S. Yoo, G. Yang, J.S. Lee, D.K. Sohn, Measurements of impinging jet flow and heat transfer on a semi-circular concave surface, Int. J. Heat Mass Transf. 43 (2000) 1811–1822. [5] N. Kayansayan, S. Küçüka, Impingement cooling of a semi-cylindrical concave channel by confined slot-air-jet, Exp. Therm. Fluid Sci. 25 (2001) 383–396. [6] M.E. Taslim, L. Setayeshgar, S.D. Spring, An experimental evaluation of advanced leading edge impingement cooling concepts, ASME J. Turbomach. 123 (2001) 147–153. [7] M.E. Taslim, K. Bakhtari, H. Liu, Experimental and numerical investigation of impingement on a rib-roughened leading-edge wall, ASME J. Turbomach. 125 (2003) 682–691. [8] M.E. Taslim, A. Khanicheh, Experimental and numerical study of impingement on an airfoil leading edge with and without showerhead and gill film holes, ASME J. Turbomach. 128 (2006) 310–320. [9] M.E. Taslim, D. Bethka, Experimental and numerical impingement heat transfer in an airfoil leading-edge cooling channel with cross-flow, ASME J. Turbomach. 131 (2009) 011–021. [10] K. Rajamani, M. Ganesh, K. Paramanandam, C. Jayamurugan, et al., Cooling efficiency enhancement using impingement cooling technique for turbine blades, ASME 2013 Gas Turbine India Conference. American Society of Mechanical Engineers, 2013, pp. V001T04A014–V001T04A014. [11] Z. Liu, Z. Feng, L. Song, Numerical study of flow and heat transfer of impingement cooling on model of turbine blade leading edge, Proceedings of GT2010, ASME Turbo Expo 2010, Paper No. GT2010-23711, 2010. [12] Z. Liu, Z. Feng, Numerical simulation on the effect of jet nozzle position on impingement cooling of gas turbine blade leading edge, Int. J. Heat Mass Transf. 54 (2011) 4949–4959. [13] H.Y. Liu, S.L. Liu, H.F. Qiang, et al., Aerodynamic investigation of impingement cooling in a confined channel with staggered jet array arrangement, Exp. Therm. Fluid Sci. 48 (2013) 184–197.

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