- Email: [email protected]
Effusion Cooling
Chinese
Journal of Aeronautics Chinese Journal of Aeronautics 22(2009) 343-348
www.elsevier.com/locate/cja
Numerical Study of Flow and Heat Transfer Characteristics of Impingement/Effusion Cooling Zhang Jingzhoua,*, Xie Haoa,b, Yang Chengfenga a
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b
College of Power Engineering, Nanjing Normal University, Nanjing 210042, China Received 16 June 2008; accepted 24 October 2008
Abstract Three-dimensional numerical simulation is carried out to investigate the flow and heat transfer characteristics of impingement/effusion cooling systems. The impingement/effusion holes are arranged on two parallel perforated plates respectively in a staggered manner. Every effusion hole has an inclined angle of 30° with respect to the surface. The two parallel plates are spaced three times the diameter of the effusion hole. The ratio of center-to-center spacing of adjacent holes to the diameter of the effusion hole is set to be 3.0, 4.0 and 5.0 respectively. The flow field, temperature field and wall film cooling effectiveness are calculated for different blowing ratios ranging from 0.5 to 1.5. In general, the wall cooling effectiveness increases as the center-to-center spacing of adjacent holes decreases or the blowing ratio increases. Keywords: impingement/effusion; blowing ratio; cooling effectiveness; heat transfer; numerical simulation
1. Introduction1 With the further development of aeroengines, designing the combustion chamber is facing the increasing challenges from higher working temperature and heat capacity than ever. This undoubtedly leads to a series of problems, such as the match between oil and air, the control of temperature distribution of combustion and the effective cooling of the combustor liner, and so on. In order to improve the reliability of the combustor liner at ever-increasing temperatures, there are two methods for choice. One is to employ the materials with more advanced heat-resistant characteristics to make combustor liner, and the other is to devise more efficacious combustor liner cooling systems, to which the impingement/effusion cooling system belongs. A lot of researches were dedicated to the impingement jet cooling[1-7] and effusion cooling[8-14]. However, the investigations on the flow and heat transfer characteristics of impingement/effusion composite cooling systems are comparatively less till now. In this respect, to name but a few, Q. H. Xu, et al.[15] and Y. Z. Lin, et *Corresponding author. Tel.: +86-25-84895909. E-mail address: [email protected] Foundation items: National Natural Science Foundation of China (50876041); Aeronautical Science Foundation of China (2008ZB2014) 1000-9361/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/S1000-9361(08)60109-0
al.[16] have studied local and average convection heat transfer coefficients inside the effusion holes in the impingement/effusion cooling schemes and concluded that the pressure distribution exerts significant influences on the heat transfer enhancement inside the effusion hole entrance. H. H. Cho, et al.[17] and D. H. Rhee, et al.[18-20] have investigated the effects of gap distance, Reynolds number and hole arrangement on the heat/mass transfer characteristics near the effusion hole. They discovered very weak interaction between adjacent impinging jets with small gap distance and the Sherwood number increasing monotonically with Reynolds number which implies that the patterns of heat/mass transfer are similar to those of all tested Reynolds numbers. To deepen understanding of the flow and heat transfer characteristics in impingement/effusion cooling system, this article calculates the flow field, temperature field and wall film cooling effectiveness for different blowing ratios ranging from 0.5 to 1.5. 2. Computation Scheme Fig.1 shows the schematic structure of an impingement/effusion cooling scheme. Let the diameters of impinging hole di and effusion hole dm be 1.5 mm and 1.0 mm respectively and the thickness of impingement and effusion plates ti be
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Fig.1
Zhang Jingzhou et al. / Chinese Journal of Aeronautics 22(2009) 343-348
Schematic structure of impingement/effusion cooling scheme.
1.8 mm. The ratios of center-to-center spacing of adjacent holes to the diameter of the effusion hole in x-direction and y-direction are designated as Sm /dm (or Si /di) and Pm /dm (or Pi /di) respectively, and Pm = 2Sm. In this article, Sm and Pm equal to Si and Pi respectively. The ratio of the gap between two perforated plates to the effusion hole diameter H/dm is 3. Both sorts of holes are arranged in a staggered manner on the two parallel perforated plates and the effusion holes have an inclined angle D of 30° to the surface. The computational region contains 19 rows of holes in x-direction. According to the flow similarity in y-direction, the computational model may be simplified by defining symmetric boundary conditions. Thus, the center-to-center spacing of adjacent holes Pi is set to be the width of computational region. Table 1 lists the parameters of three systems to be studied with different center-to-center spacings of adjacent holes, the blowing ratio M set to be 0.5, 1.0 and 1.5 and the blowing ratio M defined as M
U 2U 2 UfU f
(1)
where U2 and Uf denote the density of the secondary flow, and the primary flow respectively, and U2 and Uf the velocity of them. Table 1 Parameters of three systems Cases
Pm /dm
Sm /dm
M
CJ-FS-P3
3.0
1.5
0.5
CJ-FS-P4
4.0
2.0
1.0
CJ-FS-P5
5.0
2.5
1.5
Both primary and secondary flows are assumed to be of incompressible ideal gas. The boundary conditions of inlets of the primary and secondary flows are defined as velocity-inlet and the conditions of outlets of both flows as pressure-outlet. The primary flow has
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an inlet temperature T, of 800 K with a velocity Uf of 80 m/s; the secondary flow has a temperature T2, of 300 K with a velocity calculated based on the blowing ratio. Both the impingement and effusion plates are assumed to be made from the same alloy steel with heat conductivity of 16.27 W/(mgK). The two sidefaces of the calculation domain are set to be with symmetric boundary conditions. The surfaces on the effusion plate are viewed as the fluid-solid coupling wall, and surfaces on the impingement plate are defined as adiabatic wall boundary conditions. The computation domain grids are divided by the non-uniform meshes with finer grids in the regions near walls. To reduce the amount of grids and calculation time, the symmetric boundary conditions are applied to the cell boundary. Three-dimensional (3D) numerical simulation is carried out with Fluent-CFD software. The first order upwind is selected for discreteness of the governing equations, and the standard k-H turbulence model is applied. It is necessary to control the speed of calculation by under-relaxation. The calculation continues until the convergence criterion of 105 is met. 3. Verification with an Example To verify the proposed computation, an example of multi-holes film cooling is made of the cooling configuration[10], in which Pm /dm = 4, Sm /dm = 8, D = 30q. In order to characterize adiabatic wall cooling effectiveness, the adiabatic wall cooling effectiveness is defined as Tf Taw Kad (2) Tf T2 where Taw is adiabatic wall temperature at the multihole surface subject to the primary flow. Fig.2 compares the adiabatic wall cooling effectiveness in terms of experimental data and the computed results in the case of M =1.94. For both types of hole arrangements ü either inline or staggered, the computed results are consistent with the experimental data.
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Fig.2
Zhang Jingzhou et al. / Chinese Journal of Aeronautics 22(2009) 343-348
Comparison of computed and experimental results.
4. Results and Discussion The impingement/effusion cooling process can be viewed as the interactive outgrowth of three different effects: ķ the convective heat transfer from the hot primary flow to the wall surface is reduced by the secondary flow which blows over the effusion plate surface; ĸ the cooling by secondary flow impinging on the backside of the effusion plate; Ĺ the absorption of heat from the wall by the secondary flow passing through the holes. The wall cooling effectiveness is defined as
K
Tf Tw Tf T2
(3)
where Tw is wall temperature at the effusion surface subject to the primary flow. 4.1. Effects of center-to-center spacing of adjacent holes Fig.3 shows the influences of ratio of centerto-center spacing of adjacent holes to hole diameter on the local wall film cooling effectiveness at M =1.0. For the front rows of effusion holes at x/dm<10, the local wall cooling effectiveness K is relatively lower, which
Fig.3
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Distribution of wall cooling effectiveness at M =1.0.
means a poorer aforesaid effect due to an insufficient coverage of coolant film over the spanwise region. At y/Pm=0, K shows obvious fluctuation, and, at y/Pm = 1/4, K is lower than that at y/Pm = 0, indicating that the local wall cooling effectiveness near the effusion holes is superior to other regions. The spanwise average wall film cooling effectiveness K , curve runs nearly in line with the local K curve at the position between centerlines of adjacent columns of effusion holes in the streamwise direction. It can be observed that higher wall cooling effectiveness is gained in the case of smaller center-to-center spacing of adjacent holes. When Pm/dm decreases from 5 to 3, K increases almost by 18% at x/dm = 20. 4.2. Effects of blowing ratio Fig.4 shows the changes of distribution of wall cooling effectiveness when M equals 0.5, 1.0 and 1.5. It displays the general trend of K as M varies. When M increases, the average cooling effectiveness gradually improves; however, it exerts minor influences on wall cooling effectiveness if M >1.0. 4.3. Flow feature The impingement/effusion cooling flow is characterized by sheer complexities. First, when the coolant ejected from the impinging holes cools the backside surface of effusion plate, a couple of kidney-shaped vortices form between adjacent two impinging holes (see Fig.5) with the flow characteristics similar to the conventional jet impingement cooling, but, compared to it, the heat transfer on the target plate with effusion holes is remarkably enhanced because the coolant is attracted strongly by effusion holes. Second, the coolant which enters, passes through and then discharges from the effusion holes forms a coolant film near the surface of effusion plate subject to the primary hot flow.
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From the effusion holes, the coolant discharges at an angle of 30° and mixes with primary flow directly. To investigate the interaction between the secondary and the primary flows, the velocity components of secondary flow from effusion holes can be divided into two parts: the tangent velocity in primary flow direction and the normal velocity in impinging direction. As the momentum of primary flow in the tangential direction is much stronger than that of secondary flow, the coolant is forced to flow over the surface of the effusion plate. In the normal direction, the opposite is the case, where the coolant discharges into the primary flow. Fig.6 shows cross sections of velocity field near the effusion holes at different sites in streamwise direction. In the upstream region, as the secondary flow from adjacent effusion holes does not mix together, the effusion cooling process is similar to single-row film cooling scheme. In the midstream region, the coolant from adjacent effusion holes begins to mix together. Although the coolant penetration is almost the same as that from the front effusion, the coolant coverage is significantly upgraded, resulting in the increase of wall cooling effectiveness. This looks clearer in the downstream region.
Fig.4
Distribution of wall cooling effectiveness at Pm/dm= 5.0.
Fig.6 Cross sections of velocity fields at Pm/dm = 4.0, M = 1.0.
4.4. Temperature feature Fig.5
Flow fields at symmetric plane y/Pm = 1/2 at Pm/dm = 4.0, M =1.0.
Fig.7 shows the temperature field at the selected plane (y/Pm = 1/2) when Pm/dm = 5.0 and M =1.5. It can
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Zhang Jingzhou et al. / Chinese Journal of Aeronautics 22(2009) 343-348
be seen that a remarkable temperature gradient exists near the gas-solid intercoupling side, especially near the upstream region because of strong heat transfer taking place between the primary flow and the hot side of effusion plate. In the streamwise direction, the surface temperature is getting close to the seconday flow temperature, and at about the 8th row of effusion holes, the surface temperature approaches the secondary flow temperature of 300 K.
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centerlines due to the different thickness of film. The difference between peaks and valleys contracts gradually streamwise due to development of the boundary layer from decelerating flow. In conclusion, the total heat flux is larger on the hot side than on the cold side of the effusion plate, which is attributed to the fact that a portion of heat flux on the hot side is absorbed by the secondary flow in the effusion holes.
Fig.8
Surface heat flux on both sides of effusion plate.
5. Conclusions
Unit: K
Fig.7 Temperature contour plots at selected plane (y/Pm = 1/2).
Fig.8 shows the surface heat flux on both sides of the effusion plate. On the cold side of the plate, the distribution of heat flux is relatively even. Higher heat flux is observed in the upstream region devoid of film cooling protection. As the x/dm increases, heat flux gradually decreases because of more secondary flow discharging out of effusion holes. On the hot side of effusion plate, surface heat flux presents the similar pattern in the streamwise direction. In spanwise direction, surface heat flux takes on an appearance of alternating peaks and valleys with the peaks in the centerlines of effusion holes and the valleys in the middle of adjacent
The effects of the center-to-center spacing of adjacent holes and the blowing ratio on the impingement/effusion cooling system have been studied. The flow patterns, temperature characteristics and heat flux have been investigated through numerical calculation. The results are summarized as follows: Decreasing center-to-center spacing of adjacent holes could increase wall cooling effectiveness. In addition, enhancing the blowing ratio could also gradually increase the average wall cooling effectiveness. However, the blowing ratio exerts minor influences on the wall cooling effectiveness if M >1.0. Different from the conventional impingement cooling system, the impingement/effusion cooling scheme is characterized by remarkable enhancement of the heat transfer in effusion plate, which is credited to the strong attraction of secondary flow by effusion holes. The discharge of secondary flow into the primary flow almost keeps unchanged at different sites in the streamwise direction, but the secondary flow from adjacent effusion holes begins to mix together in midstream region, thus obviously improving coolant coverage leading to the increase of wall cooling effectiveness. A significant temperature gradient appears near the gas-solid intercoupling side, especially near the upstream region because of strong heat transfer taking place between the primary flow and hot side of effusion plate. The surface temperature is getting close to the secondary flow temperature in streamwise direction. The total heat flux is larger on the hot side than on the cold side of the effusion plate. This can be attri-
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buted to absorption of a portion of heat flux from the hot side by the secondary flow in the effusion holes. References [1]
Goldstein R J, Timmers J F. Visualization of heat transfer from arrays of impinging jets. International Journal of Heat and Mass Transfer 1982; 25: 18571868. [2] Behbahani A I, Goldstein R J. Local heat transfer to staggered arrays of impinging circular air jets ASME. 27th International Gas Turbine Conference and Exhibit. 1982; 18-22. [3] van Treuren K W, Wang Z, Ireland P T, et al. Detailed measurements of local heat transfer coefficient and adiabatic wall temperature beneath an array of impinging jets. Journal of Turbomachinery 1994; 116(2): 269-274. [4] Huang Y Z, Ekkad S V, Han J C. Detailed heat transfer distribution under an array of orthogonal impinging jets. Journal of Thermophysics and Heat Transfer 1998; 12(1): 73-79. [5] Zhang J Z, Li L G. High-resolution heat transfer coefficients measurement for jet impingement using thermochromic liquid crystals. Chinese Journal of Aeronautics 2001; 14(4): 205-209. [6] Zhang J Z, Li Y K, Tan X M, et al. Numerical computation and experimental investigation on local convective heat transfer characteristics for jet array impingement. Acta Aeronautica et Astronautica Sinica 2004; 25(4): 339-342. [in Chinese] [7] Facchini B, Surace M, Tarchi L. Impingement cooling for modern combustors: experimental analysis of heat transfer and effectiveness. Experiments in Fluids 2006; 40(4): 601-611. [8] Andrews G E, Khalifa I M, Asere A A, et al. Full coverage effusion film cooling with inclined holes. ASME Paper 95-GT-274, 1995. [9] Fric T F, Campbell R P, Rettig M G. Quantitative visualization of full-coverage discrete-hole film cooling. The 1997 International Gas Turbine and Aeroengine Congress and Exposition. 1997. [10] Song B, Lin Y Z, Liu G E, et al. An investigation on flim cooling effectiveness of inclined-multiholes walls with different patterens. Journal of Aerospace Power 1999; 14(1): 91-94. [in Chinese] [11] Harrington M K, McWaters M A, Bogard D G, et al. Full-coverage film cooling with short normal injection holes. Journal of Turbomachinery 2001; 123(4): 798-
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805. [12] Pieter E. Comparison of cooling film development calculation for transpiration cooled plates with different turbulence model. ASME 2001-GT-0132, 2001. [13] Leger B, Miron P, Emidio J M. Geometric and aerothermal influences on multiholed plate temperature: application on combustor wall. International Journal of Heat and Mass Transfer 2003; 46(7): 1215-1222. [14] Zhong F Q, Brown G L. A three-dimensional, coupled heat transfer model for multi-hole cooling and comparisons with experiments. AIAA-2006-595, 2006. [15] Xu Q H, Lin Y Z, Liu G E. Heat transfer coefficient of impingement/effusion double wall cooling method. Journal of Dalian University of Technology 2001; 41(S1): 63-66. [in Chinese] [16] Lin Y Z, Yu W L, Liu G E, et al. Influence of pressure drop distribution on the convection heat transfer inside the inclined hole of impingement/effusion cooling. Acta Aeronautica et Astronautica Sinica 2003; 24(2): 97-102. [in Chinese] [17] Cho H H, Rhee D H. Local heat/mass transfer measurement on the effusion plate in impingement/effusion cooling systems. Journal of Turbomachinery 2001; 123(3): 601-608. [18] Rhee D H, Yoon P H, Cho H H. Local heat/mass transfer and flow characteristics of array impinging jets with effusion holes ejecting spent air. International Journal of Heat and Mass Transfer 2003; 46(6): 10491061. [19] Rhee D H, Choi J H, Cho H H. Heat (mass) transfer on effusion plate in impingement/effusion cooling systems. Journal of Thermophysics and Heat Transfer 2003; 17(1): 95-102. [20] Rhee D H, Choi J H, Cho H H. Flow and heat (mass) transfer characteristics in an impingement/effusion cooling system with crossflow. Journal of Turbomachinery 2003; 125(1): 74-82.
Biography: Zhang Jingzhou Born in 1964, he received B.S. degree from Tsinghua University in 1986, M.S. degree from Southeast University in 1989 and Ph.D. degree from Nanjing University of Aeronautics and Astronautics in 1992. He has done a lot of researches on mixer-ejector and enhanced heat transfer, and published several scientific papers in various periodicals. E-mail: [email protected]
Journal of Aeronautics Chinese Journal of Aeronautics 22(2009) 343-348
www.elsevier.com/locate/cja
Numerical Study of Flow and Heat Transfer Characteristics of Impingement/Effusion Cooling Zhang Jingzhoua,*, Xie Haoa,b, Yang Chengfenga a
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b
College of Power Engineering, Nanjing Normal University, Nanjing 210042, China Received 16 June 2008; accepted 24 October 2008
Abstract Three-dimensional numerical simulation is carried out to investigate the flow and heat transfer characteristics of impingement/effusion cooling systems. The impingement/effusion holes are arranged on two parallel perforated plates respectively in a staggered manner. Every effusion hole has an inclined angle of 30° with respect to the surface. The two parallel plates are spaced three times the diameter of the effusion hole. The ratio of center-to-center spacing of adjacent holes to the diameter of the effusion hole is set to be 3.0, 4.0 and 5.0 respectively. The flow field, temperature field and wall film cooling effectiveness are calculated for different blowing ratios ranging from 0.5 to 1.5. In general, the wall cooling effectiveness increases as the center-to-center spacing of adjacent holes decreases or the blowing ratio increases. Keywords: impingement/effusion; blowing ratio; cooling effectiveness; heat transfer; numerical simulation
1. Introduction1 With the further development of aeroengines, designing the combustion chamber is facing the increasing challenges from higher working temperature and heat capacity than ever. This undoubtedly leads to a series of problems, such as the match between oil and air, the control of temperature distribution of combustion and the effective cooling of the combustor liner, and so on. In order to improve the reliability of the combustor liner at ever-increasing temperatures, there are two methods for choice. One is to employ the materials with more advanced heat-resistant characteristics to make combustor liner, and the other is to devise more efficacious combustor liner cooling systems, to which the impingement/effusion cooling system belongs. A lot of researches were dedicated to the impingement jet cooling[1-7] and effusion cooling[8-14]. However, the investigations on the flow and heat transfer characteristics of impingement/effusion composite cooling systems are comparatively less till now. In this respect, to name but a few, Q. H. Xu, et al.[15] and Y. Z. Lin, et *Corresponding author. Tel.: +86-25-84895909. E-mail address: [email protected] Foundation items: National Natural Science Foundation of China (50876041); Aeronautical Science Foundation of China (2008ZB2014) 1000-9361/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/S1000-9361(08)60109-0
al.[16] have studied local and average convection heat transfer coefficients inside the effusion holes in the impingement/effusion cooling schemes and concluded that the pressure distribution exerts significant influences on the heat transfer enhancement inside the effusion hole entrance. H. H. Cho, et al.[17] and D. H. Rhee, et al.[18-20] have investigated the effects of gap distance, Reynolds number and hole arrangement on the heat/mass transfer characteristics near the effusion hole. They discovered very weak interaction between adjacent impinging jets with small gap distance and the Sherwood number increasing monotonically with Reynolds number which implies that the patterns of heat/mass transfer are similar to those of all tested Reynolds numbers. To deepen understanding of the flow and heat transfer characteristics in impingement/effusion cooling system, this article calculates the flow field, temperature field and wall film cooling effectiveness for different blowing ratios ranging from 0.5 to 1.5. 2. Computation Scheme Fig.1 shows the schematic structure of an impingement/effusion cooling scheme. Let the diameters of impinging hole di and effusion hole dm be 1.5 mm and 1.0 mm respectively and the thickness of impingement and effusion plates ti be
· 344 ·
Fig.1
Zhang Jingzhou et al. / Chinese Journal of Aeronautics 22(2009) 343-348
Schematic structure of impingement/effusion cooling scheme.
1.8 mm. The ratios of center-to-center spacing of adjacent holes to the diameter of the effusion hole in x-direction and y-direction are designated as Sm /dm (or Si /di) and Pm /dm (or Pi /di) respectively, and Pm = 2Sm. In this article, Sm and Pm equal to Si and Pi respectively. The ratio of the gap between two perforated plates to the effusion hole diameter H/dm is 3. Both sorts of holes are arranged in a staggered manner on the two parallel perforated plates and the effusion holes have an inclined angle D of 30° to the surface. The computational region contains 19 rows of holes in x-direction. According to the flow similarity in y-direction, the computational model may be simplified by defining symmetric boundary conditions. Thus, the center-to-center spacing of adjacent holes Pi is set to be the width of computational region. Table 1 lists the parameters of three systems to be studied with different center-to-center spacings of adjacent holes, the blowing ratio M set to be 0.5, 1.0 and 1.5 and the blowing ratio M defined as M
U 2U 2 UfU f
(1)
where U2 and Uf denote the density of the secondary flow, and the primary flow respectively, and U2 and Uf the velocity of them. Table 1 Parameters of three systems Cases
Pm /dm
Sm /dm
M
CJ-FS-P3
3.0
1.5
0.5
CJ-FS-P4
4.0
2.0
1.0
CJ-FS-P5
5.0
2.5
1.5
Both primary and secondary flows are assumed to be of incompressible ideal gas. The boundary conditions of inlets of the primary and secondary flows are defined as velocity-inlet and the conditions of outlets of both flows as pressure-outlet. The primary flow has
No.4
an inlet temperature T, of 800 K with a velocity Uf of 80 m/s; the secondary flow has a temperature T2, of 300 K with a velocity calculated based on the blowing ratio. Both the impingement and effusion plates are assumed to be made from the same alloy steel with heat conductivity of 16.27 W/(mgK). The two sidefaces of the calculation domain are set to be with symmetric boundary conditions. The surfaces on the effusion plate are viewed as the fluid-solid coupling wall, and surfaces on the impingement plate are defined as adiabatic wall boundary conditions. The computation domain grids are divided by the non-uniform meshes with finer grids in the regions near walls. To reduce the amount of grids and calculation time, the symmetric boundary conditions are applied to the cell boundary. Three-dimensional (3D) numerical simulation is carried out with Fluent-CFD software. The first order upwind is selected for discreteness of the governing equations, and the standard k-H turbulence model is applied. It is necessary to control the speed of calculation by under-relaxation. The calculation continues until the convergence criterion of 105 is met. 3. Verification with an Example To verify the proposed computation, an example of multi-holes film cooling is made of the cooling configuration[10], in which Pm /dm = 4, Sm /dm = 8, D = 30q. In order to characterize adiabatic wall cooling effectiveness, the adiabatic wall cooling effectiveness is defined as Tf Taw Kad (2) Tf T2 where Taw is adiabatic wall temperature at the multihole surface subject to the primary flow. Fig.2 compares the adiabatic wall cooling effectiveness in terms of experimental data and the computed results in the case of M =1.94. For both types of hole arrangements ü either inline or staggered, the computed results are consistent with the experimental data.
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Fig.2
Zhang Jingzhou et al. / Chinese Journal of Aeronautics 22(2009) 343-348
Comparison of computed and experimental results.
4. Results and Discussion The impingement/effusion cooling process can be viewed as the interactive outgrowth of three different effects: ķ the convective heat transfer from the hot primary flow to the wall surface is reduced by the secondary flow which blows over the effusion plate surface; ĸ the cooling by secondary flow impinging on the backside of the effusion plate; Ĺ the absorption of heat from the wall by the secondary flow passing through the holes. The wall cooling effectiveness is defined as
K
Tf Tw Tf T2
(3)
where Tw is wall temperature at the effusion surface subject to the primary flow. 4.1. Effects of center-to-center spacing of adjacent holes Fig.3 shows the influences of ratio of centerto-center spacing of adjacent holes to hole diameter on the local wall film cooling effectiveness at M =1.0. For the front rows of effusion holes at x/dm<10, the local wall cooling effectiveness K is relatively lower, which
Fig.3
· 345 ·
Distribution of wall cooling effectiveness at M =1.0.
means a poorer aforesaid effect due to an insufficient coverage of coolant film over the spanwise region. At y/Pm=0, K shows obvious fluctuation, and, at y/Pm = 1/4, K is lower than that at y/Pm = 0, indicating that the local wall cooling effectiveness near the effusion holes is superior to other regions. The spanwise average wall film cooling effectiveness K , curve runs nearly in line with the local K curve at the position between centerlines of adjacent columns of effusion holes in the streamwise direction. It can be observed that higher wall cooling effectiveness is gained in the case of smaller center-to-center spacing of adjacent holes. When Pm/dm decreases from 5 to 3, K increases almost by 18% at x/dm = 20. 4.2. Effects of blowing ratio Fig.4 shows the changes of distribution of wall cooling effectiveness when M equals 0.5, 1.0 and 1.5. It displays the general trend of K as M varies. When M increases, the average cooling effectiveness gradually improves; however, it exerts minor influences on wall cooling effectiveness if M >1.0. 4.3. Flow feature The impingement/effusion cooling flow is characterized by sheer complexities. First, when the coolant ejected from the impinging holes cools the backside surface of effusion plate, a couple of kidney-shaped vortices form between adjacent two impinging holes (see Fig.5) with the flow characteristics similar to the conventional jet impingement cooling, but, compared to it, the heat transfer on the target plate with effusion holes is remarkably enhanced because the coolant is attracted strongly by effusion holes. Second, the coolant which enters, passes through and then discharges from the effusion holes forms a coolant film near the surface of effusion plate subject to the primary hot flow.
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Zhang Jingzhou et al. / Chinese Journal of Aeronautics 22(2009) 343-348
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From the effusion holes, the coolant discharges at an angle of 30° and mixes with primary flow directly. To investigate the interaction between the secondary and the primary flows, the velocity components of secondary flow from effusion holes can be divided into two parts: the tangent velocity in primary flow direction and the normal velocity in impinging direction. As the momentum of primary flow in the tangential direction is much stronger than that of secondary flow, the coolant is forced to flow over the surface of the effusion plate. In the normal direction, the opposite is the case, where the coolant discharges into the primary flow. Fig.6 shows cross sections of velocity field near the effusion holes at different sites in streamwise direction. In the upstream region, as the secondary flow from adjacent effusion holes does not mix together, the effusion cooling process is similar to single-row film cooling scheme. In the midstream region, the coolant from adjacent effusion holes begins to mix together. Although the coolant penetration is almost the same as that from the front effusion, the coolant coverage is significantly upgraded, resulting in the increase of wall cooling effectiveness. This looks clearer in the downstream region.
Fig.4
Distribution of wall cooling effectiveness at Pm/dm= 5.0.
Fig.6 Cross sections of velocity fields at Pm/dm = 4.0, M = 1.0.
4.4. Temperature feature Fig.5
Flow fields at symmetric plane y/Pm = 1/2 at Pm/dm = 4.0, M =1.0.
Fig.7 shows the temperature field at the selected plane (y/Pm = 1/2) when Pm/dm = 5.0 and M =1.5. It can
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Zhang Jingzhou et al. / Chinese Journal of Aeronautics 22(2009) 343-348
be seen that a remarkable temperature gradient exists near the gas-solid intercoupling side, especially near the upstream region because of strong heat transfer taking place between the primary flow and the hot side of effusion plate. In the streamwise direction, the surface temperature is getting close to the seconday flow temperature, and at about the 8th row of effusion holes, the surface temperature approaches the secondary flow temperature of 300 K.
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centerlines due to the different thickness of film. The difference between peaks and valleys contracts gradually streamwise due to development of the boundary layer from decelerating flow. In conclusion, the total heat flux is larger on the hot side than on the cold side of the effusion plate, which is attributed to the fact that a portion of heat flux on the hot side is absorbed by the secondary flow in the effusion holes.
Fig.8
Surface heat flux on both sides of effusion plate.
5. Conclusions
Unit: K
Fig.7 Temperature contour plots at selected plane (y/Pm = 1/2).
Fig.8 shows the surface heat flux on both sides of the effusion plate. On the cold side of the plate, the distribution of heat flux is relatively even. Higher heat flux is observed in the upstream region devoid of film cooling protection. As the x/dm increases, heat flux gradually decreases because of more secondary flow discharging out of effusion holes. On the hot side of effusion plate, surface heat flux presents the similar pattern in the streamwise direction. In spanwise direction, surface heat flux takes on an appearance of alternating peaks and valleys with the peaks in the centerlines of effusion holes and the valleys in the middle of adjacent
The effects of the center-to-center spacing of adjacent holes and the blowing ratio on the impingement/effusion cooling system have been studied. The flow patterns, temperature characteristics and heat flux have been investigated through numerical calculation. The results are summarized as follows: Decreasing center-to-center spacing of adjacent holes could increase wall cooling effectiveness. In addition, enhancing the blowing ratio could also gradually increase the average wall cooling effectiveness. However, the blowing ratio exerts minor influences on the wall cooling effectiveness if M >1.0. Different from the conventional impingement cooling system, the impingement/effusion cooling scheme is characterized by remarkable enhancement of the heat transfer in effusion plate, which is credited to the strong attraction of secondary flow by effusion holes. The discharge of secondary flow into the primary flow almost keeps unchanged at different sites in the streamwise direction, but the secondary flow from adjacent effusion holes begins to mix together in midstream region, thus obviously improving coolant coverage leading to the increase of wall cooling effectiveness. A significant temperature gradient appears near the gas-solid intercoupling side, especially near the upstream region because of strong heat transfer taking place between the primary flow and hot side of effusion plate. The surface temperature is getting close to the secondary flow temperature in streamwise direction. The total heat flux is larger on the hot side than on the cold side of the effusion plate. This can be attri-
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Biography: Zhang Jingzhou Born in 1964, he received B.S. degree from Tsinghua University in 1986, M.S. degree from Southeast University in 1989 and Ph.D. degree from Nanjing University of Aeronautics and Astronautics in 1992. He has done a lot of researches on mixer-ejector and enhanced heat transfer, and published several scientific papers in various periodicals. E-mail: [email protected]