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Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall
International Journal of Heat and Mass Transfer xxx (xxxx) xxx
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Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall Xin Li a, Gongnan Xie a,⇑, Jian Liu a,b, Bengt Sunden b a b
School of Marine Science and Technology, Northwestern Polytechnical University, P.O. Box 24, Xi’an 710072, China Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden
a r t i c l e
i n f o
Article history: Received 7 March 2019 Received in revised form 3 June 2019 Accepted 8 July 2019 Available online xxxx Keywords: Cooling channel Slit ribs Heat transfer Flow characteristics Thermal performance
a b s t r a c t Augmentation of heat transfer must always be judged against an additional pressure loss. To this context, this paper explores slitted ribs on the turbulent flow and heat transfer characteristics in rectangular cooling channels with an aspect ratio of 4:1. A verified v2f turbulence model is applied in the present numerical simulations in the Reynolds number range from 20,000 to 80,000. The flow and thermal performance of various geometrical structures for the ratios of slit-length-to-rib-length (Rl = 0, 0.20, 0.35 and 0.50) and the rib heights (e = 10 mm, 15 mm and 20 mm) are comprehensively compared and evaluated. Special thermal behaviors are carefully observed and analyzed with slits on ribs of different height. It is found that strip slits in low-height ribs provide both lower Nusselt number and friction factors than the corresponding solid ribs, while an opposite effect is captured for strip slits on high-height ribs. The present results suggest that introducing a short-length strip slit in ribs could be a beneficial way to enhance heat transfer of cooling channels with high-height ribs. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Turbomachinery is used in industries and military applications for many years because the high power output. Moreover, a more advanced turbomachinery technology is required for further development. It has been widely accepted that raising the inlet gas temperature is a feasible way to improve the turbomachinery efficiency. However, the high temperature of the working fluid generally produces a negative effect on the turbine blades. Therefore, a successful and practical cooling technology is indispensable to ensure the turbomachinery to operate normally [1–3]. In the previous studies, various cooling methods such as rib turbulators [4–6], dimpled/protruded surfaces [7–9], film cooling [10–12] and jet impingement [13,14] have been developed and documented in the available literatures. As a traditional cooling method, the internal cooling channel with various rib turbulators has been extensively investigated. Kaewchoothong et al. [15] studied the effect of different rib angles of attack (a) in a stationary square channel by experiment. It was found that V-shape ribs with attack angle 60° created highest average heat transfer coefficient and largest friction factor among all rib cases. Yongsiri et al. [16] numerically investigated a similar
⇑ Corresponding author. Te.l: +86-29-88492611; fax: +86-29-88495278.
topic. Instead of changing the horizontal angle of attack, they inclined the ribs in the vertical direction, and recirculation zones were observed in cases where the vertical angle a ranged from 45° to 150°. Experiments were conducted by Jansangsuk et al. [17] to study the heat transfer enhancement in a rectangular channel with triangular V-shape ribs. Their research indicated that the thermal performance was enhanced as wavy baffles were used in the cooling passage, particularly the ribs with rib-to-channel height e/H = 0.2, rib pitch to channel height P/H = 3 led to the largest thermal enhancement factor. Xie et al. [18] numerically studied the flow and heat transfer characteristics produced by various half-size and same-size rib configurations in a square channel. Different recirculating flow areas were discovered when a half-size rib was inserted between two big ribs at various positions. In addition, the highest Nusselt number and highest friction factor were captured when a half-size rib was set at the middle position. Furthermore, the thermal behavior of a square channel with inclined ribs and grooves was also measured by Liu et al. [19]. They discovered that creating grooves on the surface between two ribs enhanced the heat transfer to varying degrees. In contrast to arranging ribs on one surface, the thermal performance of the cooling passage with ribs arranged on two opposite walls is discussed in [20–26] as well. Satta et al. [20] and Yang et al. [21] performed experiments, respectively, to analyze the flow and heat transfer characteristics of a cooling channel. They discov-
E-mail address: [email protected] (G. Xie). https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Nomenclature Dh e f f0 H Hs h Ld Lr Ls Lt Lu Nu Nu0 Nuave P p q Rl Re Tf Tw u W Wr
hydraulic diameter (m) height of rib (mm) friction factor friction factor of smooth channel height of computational domain (mm) height of slit (mm) heat transfer coefficient (W/m2K) length of downstream extended section (mm) length of rib (mm) length of slit (mm) length of test section (mm) length of upstream extended section (mm) Nusselt number of rib channels Nusselt number of smooth channel average Nusselt number on the heated surface pitch distance (mm) pressure (Pa) wall heat flux density (W/m2) ratio between the length of slit and rib Reynolds number fluid temperature (K) wall temperature (K) mainstream velocity (m/s) width of computational domain (mm) width of rib (mm)
ered that the two-side ribbed passage had a higher heat transfer coefficient than the one-side ribbed channel. Manca et al. [23] numerically investigated the effect of inclined ribs in turbulent flow. The rectangular ribs were set on two opposite heated surfaces, the angles between the flow direction and the ribbed surface ranged from 0° to 33°. It was found that the heat transfer coefficients and friction factors increased as the inclination angle was increased. Furthermore, ribs with different section shapes were studied and the influences of the working fluid were taken into account [24,25]. The results indicated that the changing trend of Nusselt numbers and friction factors were very similar when utilizing air and water as the working fluid, respectively, but water seemed to be a better coolant than air because the Nusselt numbers were larger. The researches also indicated that various values of P/e (pitch-to-rib height) were required to obtain best performances for cases with different shaped ribs and the triangular ribs with Wr/e = 2 provided the best thermal behavior among all the cases. Numerical calculations were also conducted by Desrues et al. [26] to investigate the pressure drop and heat transfer in the channels with alternated ribs arranged on two opposed walls at low Reynolds number. They predicted that the channel with complex geometry structures provided higher heat transfer enhancement and larger friction factor compared to a straight smooth channel. Moreover, the application of complex geometry benefitted to the miniaturization of the heat exchangers as well. In addition, a better thermodynamic performance is expected in a passage with perforated ribs because this kind of ribs produce less pressure drop than solid ribs. Thus Hwang et al. [27] experimentally examined the thermal behavior of a perforated rib channel with an open-area ratio equal to 0.5. The ribs were arranged on two opposite walls in a rectangular channel alternately in their research. It was found that perforated ribs compared to solid ribs brought a slight increase in heat transfer coefficient and a remarkable decrease in pressure drop. Hence the heat transfer performance of the cooling channel is improved. Subsequently, five different types of perforated ribs have been investigated by Buchlin
x, y, z y+
Cartesian coordinates (m) dimensionless wall distance+
Greek symbols h open-area ratio Dp pressure drop (Pa) k thermal conductivity (W/mK) l dynamic viscosity of fluid (Pas) q fluid density (kg/m3) Subscripts ave the average value d the downstream section f fluid h hydraulic u the upstream section l length r rib s slit t the test section w wall 0 smooth cooling channel
[28]. He found that the Chevron-type turbulators had the most efficient enhancement on heat transfer and Column-type was the second. It has been reported in the research literature [29] that the holetype perforated rib channel has higher heat transfer enhancement than the slit-type rib channel. Nevertheless, it is still meaningful to investigate the flow and heat transfer characteristics of a slit rib channel because the lower friction losses the slit ribs provide. Hwang et al. [30] and Yang et al. [31] performed experiments and numerical simulations, respectively, to study the thermal performance in the slit rib channels with various rib open-area ratio (b) and rib pitch-to-height ratio. They discovered that the average Nusselt number increased and the friction factor decreased as the open-area ratio became greater. Similar experiments were conducted by Tariq et al. [32]. In the work by Hwang et al. several slits were opened on one rib while in the work by Tariq et al. there are only one slit on a rib. Specific conclusions were drawn such that the slit rib channel provided higher heat transfer augmentation than the solid rib channel, but the enhancement was not always strengthened as the open area ratio increase. An optimum openarea ratio with the value, b = 20%, was captured under the experimental conditions. Furthermore, Sharma et al. [33] discussed heat transfer and friction factor characteristics in details for a rectangular channel with different configurations of solid and convergingslit ribs. It was found that a converging-slit rib configuration led to decreases of both friction factor ratio and reattachment area. Thus, the thermal performance had been improved compared with the solid rib configuration. In addition, the channel with alternate arrangement of solid and slit ribs has better heat transfer behavior than the channel with slit ribs only. In previous literatures about slit rib channels, most researchers only changed the slit height to investigate the influence of the open-area ratio on heat transfer enhancement, but the effect of other geometric parameters were rarely considered. This paper is focused on the impact of slit length and rib height on the flow and heat transfer characteristics of rectangular cooling channels.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
X. Li et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx
The rib configurations with various length ratio (Rl = 0, 0.20, 0.35, 0.50, as Rl = 0 means solid ribs) and different rib height (e = 10 mm, 15 mm and 20 mm) are numerically studied to evaluate the thermal performance of the rectangular cooling channels. It should be noted that this study mainly focuses on the turbulent flow and heat transfer characteristics produced by various slit ribs in a channel, while the mechanical and thermal stresses are not in the scope of this research. Stress concentration phenomenon may appear at the opening areas of ribs and may impact the structural strength. However, this situation might be solved perfectly by adopting suitable manufacturing and processing technology for slit ribs. In addition, comparing the total stress of a blade, the stress due to the open areas of ribs is very tiny, which will not affect the overall reliability of a blade.
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2. Geometrical models According to the simplified geometry model of the turbine blade mentioned in previous researches [18], a rectangular passage is used to simulate the thermal performance of the rib internal cooling channel in a turbine blade. The computational domain, shown in Fig. 1, has a total length of 1500 mm and the crosssectional area of the channel (W H) is equal to 320 mm 80 mm. Similar to the experimental setup in the literature [34], the whole fluid domain consists of three parts, including a roughened test section with a constant heat flux employed on the bottom surface. To obtain a nearly fully developed flow and eliminate the influence of the exit flow, two extended smooth channels with lengths 600 mm and 400 mm, respectively, are added at the upstream and downstream positions of the test section.
Fig. 1. Computational domain: a rectangular channel with an array of slit ribs on the bottom of the heated section. The slit ribs have different rib height (e = 10 mm, 15 mm and 20 mm) and slit length (Ls/Lr = 0, 0.20, 0.35, 0.50).
Fig. 2. Diagram and geometrical parameters of slit rib configurations on the heated surface. The slit is asymmetrically arranged on the rib center and the slit height Hs = 0.4e.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Table 1 Geometry parameters of various rib configurations. Cases
e/P
e/H
Hs/e
Ls/Lr
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4
0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.20 0.20 0.20 0.20
0.125 0.125 0.125 0.125 0.1875 0.1875 0.1875 0.1875 0.25 0.25 0.25 0.25
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
0 0.20 0.35 0.50 0 0.20 0.35 0.50 0 0.20 0.35 0.50
Ribs with length 320 mm and width 10 mm are placed on the bottom of the test section. A slit with constant height ratio (Hs/ e = 0.4) is opened horizontally at the middle region of every rib. In addition, the variable Rl is defined as the ratio of slit length (Ls) to rib length (Lr) in order to illustrate the different open-area ratio of slit ribs conveniently. Fig. 2 shows a picture of the slit ribs placed on the bottom surface of the cooling channel. A slit with constant slit-height to rib-height ratio was asymmetrically arranged at the center of the rib. Twelve different cases based on various values of rib height and slit length, as listed in Table 1, are studied to analyze the influence of slit length and rib height on flow structures and thermal performance in the passages. Besides, the heat transfer coefficient in a totally smooth rectangular channel (defined as Case 0) is also calculated at Re in the range of 20,000–80,000.
ble because unavoidable deviations to obtain data near ribs both in experiments and simulations. Although there is a larger deviation between the experimental data and the simulation results calculated by v2f model for the perforated rib case when compared with the solid rib case, it is found that the v2f model provides the smallest deviations among all tested turbulence models. Therefore, the v2f model is suggested as suitable in this research, and it is chosen in the following study. Apart from turbulence models, the grid quality can also influence the accuracy of the calculation results greatly. For this reason, four mesh systems, respectively, 5 M, 6 M, 7 M, 8 M, are tested at Re = 80,000 for Case A1. The typical structured meshes at the inlet boundary and in the rib regions are shown in Fig. 4. In order to satisfy the requirement of employing the turbulence model, the grids near walls are pretty dense to maintain y+ values at a low level. Fig. 5 exhibits the distributions of spanwise average Nusselt number simulated for different mesh systems. The results indicate that the distinctions between the four mesh systems are not very obvious, especially the results of the 7 M and 8 M mesh systems are almost identical. Therefore, considering the accuracy and economy of the calculations, the 7 M mesh system is deemed to be the best choice among all the four systems.
600
RNG kRealizable kv2f
300
SST kStandard k-
200
Experimental data SST kRNG kStandard k-
100 0
a)
0.2
0.4
v2f Realizable kStandard k-
0.6
0.8
1.0
x/P
500
Standard k-
perforated rib case
3.1. Mesh independence and model validation 400
RNG k-
Realizable kv2f
300
SST k-
Nu
It is recognized that the selection of various turbulence models can lead to different accuracy of the calculation results [35]. Thus one should be cautious when choosing an appropriate model for CFD simulation of turbulent flow and heat transfer. In order to obtain a suitable turbulence model for the further study, different kinds of turbulence models such as Standard k-e, realizable k-e, RNG k-e, Standard k-x, SST k-x, and v2f model are used to simulate the heat transfer of the ribbed channel presented in Ref. [34] at Re = 80,000. The distributions of Nusselt number between the 3rd and 4th row ribs along streamwise direction are displayed in Fig. 3. Compared with other models, the predictions by the v2f model exhibit the best agreement with the experimental data for the solid rib case. The deviations of the results is less than 10% in the middle region of 0.1 x/P 0.95, though larger differences exist in the region near two ribs. The deviation of area weighted average Nusselt number in the region of 0.12 x/P 0.32 is equal to 14.2%, while the difference in the region of 0.12 x/P 0.97 is 7.12%. This indicates that the deviations of the results are mainly focused in the region near ribs. These differences are considered to be tolera-
Standard k-
400
3. Details of numerical simulations To clarify the flow and heat transfer features in the slit rib channels, three-dimensional numerical computations are carried out by the simulation software FLUENT 15.0. The commercial software ICEM CFD 15.0 is used to generate high quality grids for the simulations. Details about model validation, mesh independence and solution settings are provided in this section.
solid rib case
500
Nu
4
Standard k-
200
Experimental data Standard kRealizable kRNG k-
100
b)
0 0.0
0.2
0.4
0.6
v2f Standard kSST k0.8
1.0
x/P
Fig. 3. Comparison of Nusselt number distributions along streamwise direction between 3rd and 4th row ribs at Re = 80,000. The Nusselt number in every x coordinate is the average value in the spanwise direction in the range of 0.12 m y 0.20 m. (a) solid rib case in Ref. [31]; (b) case 2a in Ref. [31].
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 4. Typical structured meshes of the inlet, near rib region and slit region. The grids are denser near the wall surfaces in order to gain a low level of y+ and ensure the accuracy of calculation.
400 350 300
Nu
250 200 150
8M grids 7M grids 6M grids 5M grids
100 50 0.0
0.2
0.4
0.6
0.8
1.0
x/P Fig. 5. Comparison of spanwise average Nusselt number distributions along the streamwise direction of a rectangular channel with solid ribs calculated for different grid systems.
3.2. Solution scheme In order to imitate the heat transfer between the cooling channel and turbine blade in the actual operation condition, suitable boundary conditions should be applied at the computational domain boundaries. According to the previous research, a heat flux density q = 1000 W/m2 is imposed on the bottom face of the test section in the ribbed channels while on the smooth test section (Case 0) a heat flux density q = 900 W/m2 is applied to keep the same heating power for all cases studied in this paper. In order to have an agreement with the experimental settings, other walls of the computational domain, including the rib faces [36], are treated as adiabatic, no slip boundaries. A uniform velocity, based on
the Reynolds number range from 20,000 to 80,000, is adopted as the velocity-inlet boundary conditions, and a turbulence intensity level of 3% and the hydraulic diameter 0.128 m are fixed at the inlet. Moreover, the outlet of the channel is defined as an outflow boundary condition, The working fluid is considered to be incompressible dry air with constant thermal-physical properties at 300 K. The flow process is assumed to be three dimensional, turbulent and steady. The pressure-based and steady solver is selected to get the flow and heat transfer features in the various passages. To set the v2f model, the SIMPLEC scheme is chosen for the pressure-velocity coupling. Second order difference formulae are applied for spatial discretization of turbulent kinetic energy, turbulent dissipation rate, velocity variance scale and energy equations to get more accuracy results. The convergence residual are set as 108 for the energy equations and 105 for others. In addition, several surface monitors are created at the significant sections to observe the temperature, pressure and velocity values. 3.3. Parameter definitions To analyze and compare the calculation results of different rib configurations, some dimensionless parameters are defined as follows. The Reynolds number is defined as:
Re ¼
quDh l
ð1Þ
where q is fluid density, u is the inlet velocity, Dh is hydraulic diameter of the channel, and l is the fluid dynamic viscosity at 300 K. The local Nusselt number of every cell is introduced by:
NuðiÞ ¼
q Dh T w ðiÞ T f k
ð2Þ
where q is the heat flux imposed on the bottom surface of the test section, k is the air thermal conductivity, Tw(i) is the local wall tem-
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 6. Temperature distributions on the heated surface of the test section for various rib configurations at Re = 80,000.
350
f ¼ e=15 mm
e=10 mm
300
e=20 mm
Dp D h 2qu2 Lt
ð3Þ
where Dp is the pressure drop between inlet and outlet of the test section, and Lt is the length of the test section.
Nuave
250
4. Results and discussion 200
4.1. Heat transfer enhancement 150
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
100 50
2
4
6
8 2
4
6
8 2
4
6
8
Re×10-4 Fig. 7. Comparison of the average Nusselt numbers on heated surface for models as Re ranges from 20,000 to 80,000.
perature, and Tf is the mean temperature between the inlet and outlet of the passage. The friction factor, f, is defined as:
Temperature and the Nusselt number distributions on the heated surface are calculated to analyze the heat transfer performance in different rib channels. Fig. 6 exhibits the temperature fields of the heated surface for various slit rib channels at Re = 80,000. High-temperature zones are captured downstream of the ribs along the flow direction while low-temperature area appears in the upstream region. The high-temperature zones extend obviously as the rib height increases. Furthermore, the surface temperature changes periodically in all rib configurations and a declining trend of temperature is observed on the surface between neighboring ribs along the mainstream direction. It is noticed that the temperature in the center region between adjacent ribs increases because the existence of slits on the ribs, and
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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X. Li et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx
100 500
e=15 mm
e=10 mm
e=10 mm
e=20 mm
80
p (Pa)
Nu
400
300
0
60
40
200
100
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
row 3
0.0
0.2
0.4
0.6
0.8
20 row 4
0
1.0
2
4
6
8 2
4
x/P
(a) 500
e=15 mm
150
Nu
130 300
110
4
6
8
1st row
5th row
e=10 mm
90
200
0
8 2
Fig. 9. Comparison of pressure drops for channels with various rib configurations, the pressure drop value is from the inlet and outlet sections at x = 0.6 m and x= 1.1 m, respectively.
400
100
6
Re×10-4
70 Solid ribs Rl=0.20 Rl=0.35 row 4 Rl=0.50
row 3
0.0
0.2
0.4
0.6
0.8
50 30 10
1.0
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
150
x/P
130
(b)
p (Pa)
110
500 e=20 mm 400
90 70 50 30 10
Nu
300
e=15 mm
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
150 130
200
100
0
Solid ribs Rl=0.20 Rl=0.35 row 4 Rl=0.50
row 3 0.0
0.2
0.4
0.6
0.8
1.0
x/P
(c) Fig. 8. Comparison of Nusselt number distributions along the streamwise direction between two row ribs at Re = 80,000. The Nusselt number at every point is an average value in the spanwise direction: (a) the height of ribs e = 10 mm; (b) e = 15 mm; (c) e = 20 mm.
the longer the slits are, the larger the temperature increase region will be. According to the definition of the Nusselt number shown in Eq. (2), it can be inferred that the value of Nu is only related to the wall temperature because dry air with constant properties was selected as the working fluid in this research. Thus, the Nu distributions can be illustrated by the wall temperature distributions, a
110
e=20 mm
90 70 50 30 10 0.0
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
0.2
0.4
0.6
0.8
1.0
1.2
1.4
x (m) Fig. 10. Pressure values along the streamwise direction on the geometric center line of the channel of y = 0.16 m and z = 0.04 m at Re = 80,000. The vertical broken lines indicate the positions of ribs.
low local wall temperature also means a high local Nusselt number. The average Nusselt numbers (Nuave) on the heated surface are displayed in Fig. 7. The value of Nuave is given by:
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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X. Li et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx
Nuav e ¼
NudA ¼ A
Pn
i¼1 NuðiÞjAðiÞj
A
ð4Þ
where A is the total area of the heated surface, A(i) is the facet area. The results indicate clear distinctions for cases with the same open-area ratio but different blockage ratio (e/H). As shown in Figs. 6 and 7, opening slits on ribs cause an increase in wall temperature and a decrease in Nusselt number in these cases with small blockage ratio (e = 10 mm). However, slit ribs do not always lead to poorer heat transfer behavior than solid ribs. The average Nusselt number of the channel with high ribs, for example e = 20 mm, becomes larger due to the addition of slits on ribs. At the same time, it also can be seen clearly that the heat transfer of the cooling passage is enhanced as the Reynolds number increase, and the maximum Nusselt number appears for the case with e = 20 mm and Rl = 0.20 at Re = 80,000. Moreover, an extension of the slit will bring a decrease in the average Nusselt number. In order to have an intuition about the heat transfer features on the heated surface, the spanwise average Nusselt number distributions along streamwise direction between the 3rd and 4th row ribs at Re = 80,000 are depicted in Fig. 8. The value of the mean Nusselt number is calculated by following equation:
RW NuðxÞ ¼
0
NuðyÞdy W
ð5Þ
It is discovered the best heat transfer area is present at the middle region between neighboring ribs or in the upstream of the ribs. Different rib structures produce various distribution features of the Nusslet number. The maximum local average Nusselt number is captured in the solid rib channel among the cases with low ribs, but for the cases with higher blockage ratio such as e = 15 mm or 20 mm, the maximum appears in the slit rib configurations with Rl = 0.20. The slit ribs bring an increase of Nusselt number at the upstream of the ribs and also contributes to creating a lower temperature in this area compared to solid rib configuration. From the discussion above, the simulation results suggest that the heat transfer characteristics in the various slit rib channels depend on at least two parameters, the rib height and the slit length. It is found that an opening slit on low ribs will weaken the heat transfer of the cooling passages, but a positive effect will be provided when slits are created on the higher ribs. 4.2. Pressure drop and friction factors To investigate the flow resistance performance of the cooling passages, the pressure distributions and friction factors in the channels with various slit ribs are discussed in this part. The pressure drops between inlet and outlet sections of the heated channel are compared in Fig. 9. It is easy to understand that increase of Reynolds number and blockage ratio lead to higher pressure drop. In contrast, a longer slit is helpful to decrease the pressure drop in the duct with slit ribs. However, the distinctions of flow resistance features between slit rib channel and solid rib channel for various blockage ratio are unexpected. Compared to solid rib configurations, the existence of slits on low ribs slightly reduces the pressure drop in the cooling passage, but an opposite phenomenon is observed if short slits are opened on higher ribs. The largest pressure drop appears in the channel with Rl = 0.20 and e = 20 mm at Re = 80,000. To obtain more details about the flow resistance in the channel, the pressure distributions on the center line of the duct along the main flow direction are presented in Fig. 10. This figure suggests that there are no differences of the pressure values at the range 0 x 0.5 as there is a smooth channel only. The influence of slit rib configurations on pressure mainly appears in the test section and the downstream extended section. A sharper decrease is cap-
0.10
0.08
0.06
f
R
0.04
Case A1 Case B1 Case C1
0.02
0.00
2
3
Case A2 Case B2 Case C2 4
5
Case A3 Case B3 Case C3 6
Case A4 Case B4 Case C4 7
8
Re×10-4 Fig. 11. Friction factors for channels with various rib configurations for Reynolds number ranging from 20,000 to 80,000.
tured in the channels with higher blockage ratio. Furthermore, the largest pressure gradient appears around the first row rib, which also brings the minimum local pressure value in the region between the first and second row ribs. An unexpected result is indicated by Fig. 10, where it is shown that the slit rib channel with high blockage ratio produces a larger total pressure drop than the solid rib configuration though the pressure drop created by every single slit rib is smaller. The friction factors (f) defined by Eq. (3) are calculated and compared in Fig. 11, in order to evaluate flow resistance characteristics of different rib configurations at various Reynolds number. A higher flow resistance is observed as the Reynolds number increases, but the value of the friction factor almost remains constant when Re exceeds 40,000. However, the slit rib channel with e = 20 mm and Rl = 0.20 provides the largest friction factor among all cases studied in this paper. 4.3. Flow characteristics Various flow conditions in the channel might be a reason for the differences between different rib configurations regarding the thermal behavior, so the flow structures are investigated to gain a clearer understanding about the friction and heat transfer features provided by different slit ribs. Fig. 12 depicts the streamlines and x velocity distributions on the section of y = 0.16 m in cases of e = 10 mm or e = 20 mm at Re = 80,000. A wider range of x velocity values is observed in channels with higher ribs, and a separation vortex is formed downstream of ribs in the solid rib channel. It is observed that, for the channels with low ribs (e = 10 mm), a large vortex fills the area between the first and second row ribs, but the vortex regions become smaller and reattachment regions are observed on the heated surface after the second rib. However, in the solid rib channel with e = 20 mm, regions between every two adjacent ribs are almost filled by a vortex, and it might be responsible for the lower average Nusselt number compared to the solid rib configuration with e = 10 mm as shown in Fig. 7. From the comparison of streamlines in solid rib channels with different blockage ratio, a conclusion can be drawn that the higher solid ribs lead to a larger vortex than low ribs. It is also can be seen clearly that the separation vortex can be reduced by creating a slit on ribs, but with a slit extension the vortex size is enlarged slightly. The relation between Nusselt number distributions and flow structures can be explained by the theory in Ref. [21]. The flow field on the bottom face between adjacent ribs can be divided into
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 12. Surface streamlines and x velocity contours on the vertical cross sections at the middle position of ribs of y = 0.16 m for cases e = 10 mm and e = 20 mm at Re = 80,000.
three parts, the separation vortex region, the reattachment region and the flow over a flat region. In general, the convective heat transfer is mainly enhanced by the separation vortex behind ribs and the reattachment to the channel bottom. For ducts with low solid ribs, there are a vortex region and a reattachment region on the heated surface. These provide a considerable enhancement of the heat transfer in the channel. However, the effect of the separation vortex and reattachment flow is constrained while the flow over the flat region is enlarged due to the existence of a slit on ribs. As a result, new boundary layers are developed in the flat flow region and the convective heat transfer is weakened. The impact of slit ribs is completely different in the channels with high blockage ratio. In contrast to the cases with low ribs, there are only separation vortex regions existing in the area between neighboring ribs in the high blockage ratio cases (e = 20 mm). When a slit is
opened on this kind of ribs, the vortex is destroyed and a more complex flow structure, which contributes to the mixing of fluid, is observed in the region between adjacent ribs. To obtain a clearer recognition of the complex flow structures caused by slit ribs, the turbulent kinetic energy distributions and streamlines on the middle section of the ribs are depicted in Fig. 13. It is discovered that several eddies are formed and the impingement on the upwind surfaces of ribs is strengthened when slits are opened on ribs. The different flow structures in adjacent slit region and no-slit region are features of the slit rib cases. Eddies and impingement, which intensify the local turbulent flow and fluid mixture, always happen in the adjacent no-slit regions. Consequently, the heat transfer in these regions is enhanced. However, opposite effects are captured in the adjacent slit region. Backward flow is observed downstream of the ribs in the solid rib case. This
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 13. Surface streamlines and turbulent kinetic energy distributions on the middle section of ribs for cases with P = 100 mm and e = 20 mm at Re = 80,000. The section is a xy plane where z = 0.01 m.
indicates that there are recirculation zones in this region. However, for the slit rib cases, the air is flowing forward through the slit. The recirculation flow in the adjacent slit region is restricted, thus there is not enough time for the coolant to cool the heated surface or mix with the hot fluid sufficiently. As a result, the wall temperature in this region is higher than for the solid rib case as shown in Fig. 6. Furthermore, as the slits are extended, the circulation area is enlarged and the flow resistance decreases. More air flows through the slits and the impingement on the rib surfaces is weakened. This results in expansion of the high temperature regions downstream the slits. Fig. 14 shows the turbulent kinetic energy and streamlines on the section near the heated surface (z = 0.0005 m) at Re = 80,000. It is interesting to observe that the fluid flows in two opposite directions in the middle regions between adjacent ribs, except for the first and second ribs, in the cases with low ribs (e = 10 mm). These curves where the air is separated into two directions, might be the boundary of the separation vortex regions and the reattachment flow regions as indicated in Fig. 12. However, for the cases with e = 20 mm, no similar characteristics are observed. Most of the fluid flows in an opposite direction to the main stream. This might be because the ribs are too high so that the rib spacing is not large enough to let the fluid reattach on the surface again. Furthermore, a convergence phenomenon is captured at the upstream of the first row rib in the slit rib channels while a parallel flow is observed in the passage with solid ribs. This fact confirms that the flow characteristics on the horizontal cross section is changed greatly when a slit is opened on the ribs. The relationships between the turbulent kinetic energy and the Nusselt number can be inferred from Fig. 14. The distributions of the turbulent kinetic energy agree with the wall temperature distributions (shown in Fig. 6). It is discovered that a large local turbulent kinetic energy and local heat transfer are provided in the zone between adjacent no-slit regions, because powerful impingement happens at the upwind surfaces of the ribs. For the cases with e = 10 mm, the fluid impacts on the heated surfaces due to the sep-
aration of the vortex flow and reattachment flow. The turbulent kinetic energy is very high near the boundary of the vortex and reattachment regions and the local heat transfer is enhanced. However, when slits are created on the low ribs, the impingement as well as the convective heat transfer are weakened because the vortex is restrained. Nevertheless, the turbulent flow upstream the ribs is enhanced if slits are opened on the ribs with e = 20 mm, though the turbulent kinetic energy downstream slits is reduced. It is indicated that the flow structures become more complex and corner vortices are formed in the region between the first and second row ribs as slits exist on ribs. In addition, compared to the low ribs (e = 10 mm), the higher ribs can produce stronger impingement and secondary flow, which leads to heat transfer enhancement upstream of the rib. For the cases with high ribs (e = 20 mm), a lower temperature appears upstream of the slit ribs. This suggests that opening a slit on the ribs can reinforce the convection heat transfer on the heated surface, though the temperature at the middle region increases slightly as the turbulent kinetic energy is weakened. In addition, the change of flow structures also indicates the difference of pressure structures in various cooling passages. It is accepted that the lower blockage ratio channels have less flow resistance and larger circulation area which are helpful in decreasing the pressure drop in the ducts. Furthermore, the circulation area can also be increased by opening a slit or hole on the ribs. However, the different flow conditions and mass transport features created by slit ribs with various rib-height can evidently influence the flow resistance features in the passage as well. As mentioned above, different size recirculation zones are captured behind the ribs in the solid rib cases with various rib-height. In the solid rib case with e = 20 mm, the regions between adjacent ribs are filled with recirculation flow. Thus, the mass transport of fluid between the mainstream and the recirculation zones is very small and a great deal of the air is trapped in these regions. Due to less mixing with the trapped air, the fluid in the mainstream region flows through the channel at a high velocity. However, it is observed that
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 14. Surface streamlines and turbulent kinetic energy distributions on the xy cross section near the heated surface of the channel of z = 0.0005 m at Re = 80,000.
1.9
Case A1 Case B1 Case C1
1.8
Case A2 Case B2 Case C2
Case A3 Case B3 Case C3
Case A4 Case B4 Case C4
1.7
Nuave/Nu0
several vortex zones are formed in the adjacent no-slit regions when creating slits on this kind of ribs as indicated in Fig. 13. The complex vortex structures are effective to improve the mixture of the fluid in the mainstream and the adjacent rib regions. Furthermore, the vortex structures also contribute to the intensification of the mass transport in the air in these regions and the shearing drag in the fluid is strengthened as well. Therefore, the momentum loss and the pressure drop in the case with e = 20 mm and Rl = 0.20 increase, although the flow area is extended as slits are opened on the ribs. This effect might be the real reason which causes the increase of the pressure drop when slits are opened on ribs in the cases with e = 20 mm as shown in Fig. 9. For the low solid rib configuration (e = 10 mm), the recirculation zones behind the ribs are smaller and the air trapped in the recirculation zones is less than for the solid rib case with e = 20 mm. Thus, the mass transport between the mainstream and the adjacent rib regions is larger. The impact of different slit rib configurations on the flow field is weak and the increase of circulation area is more significant than the momentum loss when slits are created on the ribs. Therefore, the slit rib cases with
1.6 1.5 1.4 1.3 1.2
2
3
4
5
6
7
8
Re×10-4 Fig. 15. Normalized Nusselt numbers for all rib configurations as the Re range of 20,000 Re 80,000. The value of each normalized Nusselt number is defined as the ratio of Nusselt number of rib channel to that of smooth channel.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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22 20 18 16
f/f0
14 12 10 8 6 4
Case A1 Case B1 Case C1
2 0
2
3
Case A2 Case B2 Case C2 4
Case A3 Case B3 Case C3
5
6
Re×10
Case A4 Case B4 Case C4 7
8
-4
Fig. 16. Normalized friction factors for all rib configurations as the Re range of 20,000 Re 80,000. The value of each normalized friction factor is defined as the ratio of friction factor of rib channel to that of smooth channel.
e = 10 mm provide a smaller pressure drop than the solid rib configuration. In addition, the influence of the circulation area on the flow resistance is enhanced and the pressure drop is reduced as the slits are extended. Accordingly, the slit rib channel (e = 20 mm, Rl = 0.50) and the solid rib channel (e = 20 mm, Rl = 0) have equal pressure drops as exhibited in Fig. 9. 4.4. Overall thermal performance To obtain a comprehensive estimate about the behavior of slit rib channels the overall thermal performance of various cooling passages is compared and analyzed in this part. Case 0 is designed to represent the Nusselt number and friction factor in a smooth channel without any ribs. Fig. 15 displays the comparison of normalized Nusselt number (Nuave/Nu0) for all rib configurations studied in this paper. This figure indicates that the normalized Nusselt number decreases as the
0.24
Reynolds number is increasing from 20,000 to 40,000, but it increases slightly as the Re continues to increase. The minimum value (about 1.3) of Nuave/Nu0 appears in the channel with e = 10 mm and Rl = 0.50 at Re = 40,000 while the maximum value (about 1.75) is captured in the case with e = 20 mm and Rl = 0.20 at Re = 20,000. An evident distinction is discovered, namely as the rib height increases, the convection heat transfer is weakened in the solid rib channels, but an opposite effect is observed in the slit ribs configurations, and the longer the slit is, the smaller the normalized Nusselt number will be. To compare the flow resistance features in different rib ducts, the normalized friction factor is exhibited in Fig. 16. It is found that the distribution of normalized friction factor is analogous to that of the normalized Nusselt number. The rib configuration which provides the best heat transfer also leads to the largest friction factor, and the maximum normalized friction factor is about 21 while the minimum value is around 5. In addition, the blockage ratio is also a significant parameter which influences the flow resistance of the channel greatly. The channel with higher blockage ratio has a larger normalized friction factor as well. Two thermal enhancement factors, (Nuave/Nu0)/(f/f0) and (Nuave/ Nu0)/(f/f0)1/3, are presented in Fig. 17 to conduct a comprehensive evaluation of various slit rib channels. This figure suggests that the influence of slit length on (Nuave/Nu0)/(f/f0) is negligible, but the rib height and the Reynolds number impact the (Nuave/Nu0)/ (f/f0) considerably. The value rises but then drops with the increase of Reynolds number and higher ribs always lead to a smaller (Nuave/Nu0)/(f/f0). However, the other thermal enhancement factor (Nuave/Nu0)/(f/f0)1/3 remains almost constant in most cases as the Reynolds number changes from 20,000 to 80,000. The rib height and the slit length are the two major factors which impact the Table 2 Geometry parameters of Case D1–D4, with P = 50 mm and e = 10 mm.
e=10 mm
Rl=0.35 Rl=0.50
e/H
Hs/e
Ls/Lr
0.2 0.2 0.2 0.2
0.125 0.125 0.125 0.125
0.4 0.4 0.4 0.4
0 0.20 0.35 0.50
0.84
Solid ribs Rl=0.20
Rl=0.35 Rl=0.50
0.16
Solid ribs Rl=0.20
Rl=0.35 Rl=0.50
0.14
e=15 mm
0.12
e=20 mm
0.76
( Nuave/Nu0 /( f/f0)1/3
Solid ribs Rl=0.20
(
0.20
(
( Nuave/Nu0 /(f/f0)
e/P
D1 D2 D3 D4
0.80
0.22
0.10
Cases
e=10 mm
0.72 0.76
Rl=0.35 Rl=0.50
Solid ribs Rl=0.20 e=15 mm
0.72 0.68 0.64
e=20 mm
0.64 0.60
0.08
Rl=0.35 Rl=0.50
Solid ribs Rl=0.20
0.06 2
4
6
Re×10-4
8
0.56
Rl=0.35 Rl=0.50
Solid ribs Rl=0.20
0.52 2
4
6
8
Re×10-4
Fig. 17. Overall thermal performance for cases with different rib height and slit length as the Re range of 20,000 Re 80,000.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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22
1.60 18
1.50
16 14
1.45
f/f0
Nuave/Nu0
20
1.55
1.40
10
1.35
8
1.25
a)
6
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
1.30
0.0
0.1
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
12
4 2
0.2
0.3
0.4
0.5
b)
Rl
0.0
0.1
0.2
0.3
0.4
0.5
Rl
0.24 0.80 0.75
(Nuave/Nu0)/(f/f0)1/3
(Nuave/Nu0)/(f/f0)
0.20
0.16
0.12
0.08
c)
0.0
0.1
0.65 0.60 0.55
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
0.04
0.70
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
0.50
0.2
0.3
0.4
0.5
Rl
d)
0.0
0.1
0.2
0.3
0.4
0.5
Rl
Fig. 18. Comparison of normalized Nusselt number, normalized friction factor, (Nuave/Nu0)/(f/f0) and (Nuave/Nu0)/(f/f0)1/3 for cases with various values of rib-height and ribpitch as Rl ranges from 0 to 0.50.
thermal performance of the channel remarkably, and the lower rib and shorter slit can provide a better thermal behavior of the cooling passage. The influences of various height of slit ribs on the heat transfer performance are completely different. The thermal performance is improved when a slit is opened on high ribs, but an opposite effect is observed if a slit is created on lower ribs. The best thermal behavior is provided by the solid ribs with e = 10 mm while the solid rib configuration with e = 20 mm has the worst performance among all cases studied in this paper. To have a more comprehensive understanding of the effect of creating slits on ribs, additional four cases (Case D1–D4) with e = 10 mm and P = 50 mm at Re = 80,000 were investigated to take the rib-pitch into account. Details about the four cases are listed in Table 2 and the comparison of the performance indices is displayed in Fig. 18. It is found that the values of the normalized Nusselt number, (Nuave/Nu0)/(f/f0) and (Nuave/Nu0)/(f/f0)1/3 of cases (P = 50 mm and e = 10 mm) are close to the values in the cases with the same rib-height. A common decrease of the normalized Nusselt number is observed when slits are opened on ribs with e = 10 mm, while an opposite effect is provided if slits are created on the higher ribs (e = 20 mm). From the discussion we can infer that the rib-height might be the main factor which influences the heat transfer performance of the cooling channel.
5. Conclusions Three-dimensional numerical simulations were applied to investigate the flow and heat transfer characteristics in a rectangular internal cooling channel with different height slit ribs. Slit ribs with various rib height and slit length were designed. The wall temperature, Nusselt number, friction factor and flow structure in the channels were analyzed in order to evaluate the thermal performance of the passages. Based on the results, the following conclusions are drawn: (1) The solid rib channel with e = 10 mm has the best overall thermal performance among all cases studied in this research. However, the highest heat transfer enhancement is provided by the slit rib configuration with e = 20 mm and Rl = 0.20, and the channel with the highest solid ribs has the poorest thermal performance because of the lowest heat transfer enhancement and the high friction factor in this case. (2) It is found that producing slit on ribs can constrain the formation of a separation vortex, but various effects are captured while the slit is opened on ribs with different height. For the cases studied in this paper, the values of Nusselt
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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number and friction factor decrease when a slit is created on low ribs, however, a contrary phenomenon is observed while opening a slit on high ribs. In addition there is a decreasing trend of the normalized Nusselt number and normalized friction factor as the slit is extended, and the higher solid ribs always lead to a larger pressure drop in the channel. (3) The comparison of overall thermal performance indicates that ribs with short slit provide better thermal performance than ribs with long slit under the same pumping power condition. Creating a slit on high ribs can enhance the convection heat transfer in the cooling channel but a negative effect is observed when a slit is opened on low ribs. This finding suggests that opening short slit on high ribs is a beneficial way to improve thermal performance of the rectangular cooling channel.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgment This research was supported by the National Natural Science Foundation of China (51676163), and the National 111 Project (B18041). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046. References [1] H. Zhang, L. Li, X. Tang, Z. Huang, Review of heavy-duty gas turbine blade cooling technology, Gas Turb. Technol. 30 (2017) 1–7. [2] Z. Liu, X. Yang, Z. Feng, Study on heat transfer and cooling in gas turbine blade: Internal cooling, Therm. Turb. 42 (2013) 265–275. [3] Phil Ligrani, Heat transfer augmentation technologies for internal cooling of turbine components of gas turbine engines, Int. J. Rotating Mach. 2013 (2013), Article ID 275653. [4] C. Nonino, G. Comini, Convective heat transfer in ribbed square channels, Int. J. Numer. Methods Heat Fluid Flow 12 (2002) 610–628. [5] B. Cukurel, T. Arts, C. Selcan, Conjugate heat transfer characterization in cooling channels, J. Therm. Sci. 21 (2012) 286–294. [6] K.Y. Kim, Y.M. Lee, Design optimization of internal cooling passage with Vshape ribs, Numer. Heat Transf.-Part A 51 (2007) 1103–1118. [7] A. Perwez, S. Shreyak, R. Kumar, Heat transfer and friction factor characteristic of spherical and inclined teardrop dimple channel subjected to forced convection, Exp. Heat Transfer 32 (2019) 159–178. [8] T. Pirasaci, M. Sivrioglu, Experimental investigation of laminar mixed convection heat transfer from arrays of protruded heat sources, J. Faculty Eng. Archit. Gazi Univ. 27 (2012) 765–773. [9] J. Park, P.M. Ligrani, Numerical predictions of heat transfer and fluid flow characteristics for seven different dimpled surfaces in a channel, Numer. Heat Transfer-Part A 47 (2005) 209–232. [10] R.S. Bunker, A review of shaped hole turbine film-cooling technology, ASME J. Heat Transfer 127 (2005) 441–453. [11] J.Y. Jeong, W. Kim, J.S. Kwak, J.S. Park, Heat transfer coefficient and film cooling effectiveness on the partial cavity tip of a gas turbine blade, ASME J. Turbomach. 141 (2019), https://doi.org/10.1115/1.4042647. [12] M.K. Kelishami, E. Lakzian, Optimization of the blowing ratio for film cooling on a flat plate, Int. J. Numer. Methods Heat Fluid Flow 27 (2017) 104–119.
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Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall Xin Li a, Gongnan Xie a,⇑, Jian Liu a,b, Bengt Sunden b a b
School of Marine Science and Technology, Northwestern Polytechnical University, P.O. Box 24, Xi’an 710072, China Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden
a r t i c l e
i n f o
Article history: Received 7 March 2019 Received in revised form 3 June 2019 Accepted 8 July 2019 Available online xxxx Keywords: Cooling channel Slit ribs Heat transfer Flow characteristics Thermal performance
a b s t r a c t Augmentation of heat transfer must always be judged against an additional pressure loss. To this context, this paper explores slitted ribs on the turbulent flow and heat transfer characteristics in rectangular cooling channels with an aspect ratio of 4:1. A verified v2f turbulence model is applied in the present numerical simulations in the Reynolds number range from 20,000 to 80,000. The flow and thermal performance of various geometrical structures for the ratios of slit-length-to-rib-length (Rl = 0, 0.20, 0.35 and 0.50) and the rib heights (e = 10 mm, 15 mm and 20 mm) are comprehensively compared and evaluated. Special thermal behaviors are carefully observed and analyzed with slits on ribs of different height. It is found that strip slits in low-height ribs provide both lower Nusselt number and friction factors than the corresponding solid ribs, while an opposite effect is captured for strip slits on high-height ribs. The present results suggest that introducing a short-length strip slit in ribs could be a beneficial way to enhance heat transfer of cooling channels with high-height ribs. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Turbomachinery is used in industries and military applications for many years because the high power output. Moreover, a more advanced turbomachinery technology is required for further development. It has been widely accepted that raising the inlet gas temperature is a feasible way to improve the turbomachinery efficiency. However, the high temperature of the working fluid generally produces a negative effect on the turbine blades. Therefore, a successful and practical cooling technology is indispensable to ensure the turbomachinery to operate normally [1–3]. In the previous studies, various cooling methods such as rib turbulators [4–6], dimpled/protruded surfaces [7–9], film cooling [10–12] and jet impingement [13,14] have been developed and documented in the available literatures. As a traditional cooling method, the internal cooling channel with various rib turbulators has been extensively investigated. Kaewchoothong et al. [15] studied the effect of different rib angles of attack (a) in a stationary square channel by experiment. It was found that V-shape ribs with attack angle 60° created highest average heat transfer coefficient and largest friction factor among all rib cases. Yongsiri et al. [16] numerically investigated a similar
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topic. Instead of changing the horizontal angle of attack, they inclined the ribs in the vertical direction, and recirculation zones were observed in cases where the vertical angle a ranged from 45° to 150°. Experiments were conducted by Jansangsuk et al. [17] to study the heat transfer enhancement in a rectangular channel with triangular V-shape ribs. Their research indicated that the thermal performance was enhanced as wavy baffles were used in the cooling passage, particularly the ribs with rib-to-channel height e/H = 0.2, rib pitch to channel height P/H = 3 led to the largest thermal enhancement factor. Xie et al. [18] numerically studied the flow and heat transfer characteristics produced by various half-size and same-size rib configurations in a square channel. Different recirculating flow areas were discovered when a half-size rib was inserted between two big ribs at various positions. In addition, the highest Nusselt number and highest friction factor were captured when a half-size rib was set at the middle position. Furthermore, the thermal behavior of a square channel with inclined ribs and grooves was also measured by Liu et al. [19]. They discovered that creating grooves on the surface between two ribs enhanced the heat transfer to varying degrees. In contrast to arranging ribs on one surface, the thermal performance of the cooling passage with ribs arranged on two opposite walls is discussed in [20–26] as well. Satta et al. [20] and Yang et al. [21] performed experiments, respectively, to analyze the flow and heat transfer characteristics of a cooling channel. They discov-
E-mail address: [email protected] (G. Xie). https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Nomenclature Dh e f f0 H Hs h Ld Lr Ls Lt Lu Nu Nu0 Nuave P p q Rl Re Tf Tw u W Wr
hydraulic diameter (m) height of rib (mm) friction factor friction factor of smooth channel height of computational domain (mm) height of slit (mm) heat transfer coefficient (W/m2K) length of downstream extended section (mm) length of rib (mm) length of slit (mm) length of test section (mm) length of upstream extended section (mm) Nusselt number of rib channels Nusselt number of smooth channel average Nusselt number on the heated surface pitch distance (mm) pressure (Pa) wall heat flux density (W/m2) ratio between the length of slit and rib Reynolds number fluid temperature (K) wall temperature (K) mainstream velocity (m/s) width of computational domain (mm) width of rib (mm)
ered that the two-side ribbed passage had a higher heat transfer coefficient than the one-side ribbed channel. Manca et al. [23] numerically investigated the effect of inclined ribs in turbulent flow. The rectangular ribs were set on two opposite heated surfaces, the angles between the flow direction and the ribbed surface ranged from 0° to 33°. It was found that the heat transfer coefficients and friction factors increased as the inclination angle was increased. Furthermore, ribs with different section shapes were studied and the influences of the working fluid were taken into account [24,25]. The results indicated that the changing trend of Nusselt numbers and friction factors were very similar when utilizing air and water as the working fluid, respectively, but water seemed to be a better coolant than air because the Nusselt numbers were larger. The researches also indicated that various values of P/e (pitch-to-rib height) were required to obtain best performances for cases with different shaped ribs and the triangular ribs with Wr/e = 2 provided the best thermal behavior among all the cases. Numerical calculations were also conducted by Desrues et al. [26] to investigate the pressure drop and heat transfer in the channels with alternated ribs arranged on two opposed walls at low Reynolds number. They predicted that the channel with complex geometry structures provided higher heat transfer enhancement and larger friction factor compared to a straight smooth channel. Moreover, the application of complex geometry benefitted to the miniaturization of the heat exchangers as well. In addition, a better thermodynamic performance is expected in a passage with perforated ribs because this kind of ribs produce less pressure drop than solid ribs. Thus Hwang et al. [27] experimentally examined the thermal behavior of a perforated rib channel with an open-area ratio equal to 0.5. The ribs were arranged on two opposite walls in a rectangular channel alternately in their research. It was found that perforated ribs compared to solid ribs brought a slight increase in heat transfer coefficient and a remarkable decrease in pressure drop. Hence the heat transfer performance of the cooling channel is improved. Subsequently, five different types of perforated ribs have been investigated by Buchlin
x, y, z y+
Cartesian coordinates (m) dimensionless wall distance+
Greek symbols h open-area ratio Dp pressure drop (Pa) k thermal conductivity (W/mK) l dynamic viscosity of fluid (Pas) q fluid density (kg/m3) Subscripts ave the average value d the downstream section f fluid h hydraulic u the upstream section l length r rib s slit t the test section w wall 0 smooth cooling channel
[28]. He found that the Chevron-type turbulators had the most efficient enhancement on heat transfer and Column-type was the second. It has been reported in the research literature [29] that the holetype perforated rib channel has higher heat transfer enhancement than the slit-type rib channel. Nevertheless, it is still meaningful to investigate the flow and heat transfer characteristics of a slit rib channel because the lower friction losses the slit ribs provide. Hwang et al. [30] and Yang et al. [31] performed experiments and numerical simulations, respectively, to study the thermal performance in the slit rib channels with various rib open-area ratio (b) and rib pitch-to-height ratio. They discovered that the average Nusselt number increased and the friction factor decreased as the open-area ratio became greater. Similar experiments were conducted by Tariq et al. [32]. In the work by Hwang et al. several slits were opened on one rib while in the work by Tariq et al. there are only one slit on a rib. Specific conclusions were drawn such that the slit rib channel provided higher heat transfer augmentation than the solid rib channel, but the enhancement was not always strengthened as the open area ratio increase. An optimum openarea ratio with the value, b = 20%, was captured under the experimental conditions. Furthermore, Sharma et al. [33] discussed heat transfer and friction factor characteristics in details for a rectangular channel with different configurations of solid and convergingslit ribs. It was found that a converging-slit rib configuration led to decreases of both friction factor ratio and reattachment area. Thus, the thermal performance had been improved compared with the solid rib configuration. In addition, the channel with alternate arrangement of solid and slit ribs has better heat transfer behavior than the channel with slit ribs only. In previous literatures about slit rib channels, most researchers only changed the slit height to investigate the influence of the open-area ratio on heat transfer enhancement, but the effect of other geometric parameters were rarely considered. This paper is focused on the impact of slit length and rib height on the flow and heat transfer characteristics of rectangular cooling channels.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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The rib configurations with various length ratio (Rl = 0, 0.20, 0.35, 0.50, as Rl = 0 means solid ribs) and different rib height (e = 10 mm, 15 mm and 20 mm) are numerically studied to evaluate the thermal performance of the rectangular cooling channels. It should be noted that this study mainly focuses on the turbulent flow and heat transfer characteristics produced by various slit ribs in a channel, while the mechanical and thermal stresses are not in the scope of this research. Stress concentration phenomenon may appear at the opening areas of ribs and may impact the structural strength. However, this situation might be solved perfectly by adopting suitable manufacturing and processing technology for slit ribs. In addition, comparing the total stress of a blade, the stress due to the open areas of ribs is very tiny, which will not affect the overall reliability of a blade.
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2. Geometrical models According to the simplified geometry model of the turbine blade mentioned in previous researches [18], a rectangular passage is used to simulate the thermal performance of the rib internal cooling channel in a turbine blade. The computational domain, shown in Fig. 1, has a total length of 1500 mm and the crosssectional area of the channel (W H) is equal to 320 mm 80 mm. Similar to the experimental setup in the literature [34], the whole fluid domain consists of three parts, including a roughened test section with a constant heat flux employed on the bottom surface. To obtain a nearly fully developed flow and eliminate the influence of the exit flow, two extended smooth channels with lengths 600 mm and 400 mm, respectively, are added at the upstream and downstream positions of the test section.
Fig. 1. Computational domain: a rectangular channel with an array of slit ribs on the bottom of the heated section. The slit ribs have different rib height (e = 10 mm, 15 mm and 20 mm) and slit length (Ls/Lr = 0, 0.20, 0.35, 0.50).
Fig. 2. Diagram and geometrical parameters of slit rib configurations on the heated surface. The slit is asymmetrically arranged on the rib center and the slit height Hs = 0.4e.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Table 1 Geometry parameters of various rib configurations. Cases
e/P
e/H
Hs/e
Ls/Lr
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4
0.1 0.1 0.1 0.1 0.15 0.15 0.15 0.15 0.20 0.20 0.20 0.20
0.125 0.125 0.125 0.125 0.1875 0.1875 0.1875 0.1875 0.25 0.25 0.25 0.25
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
0 0.20 0.35 0.50 0 0.20 0.35 0.50 0 0.20 0.35 0.50
Ribs with length 320 mm and width 10 mm are placed on the bottom of the test section. A slit with constant height ratio (Hs/ e = 0.4) is opened horizontally at the middle region of every rib. In addition, the variable Rl is defined as the ratio of slit length (Ls) to rib length (Lr) in order to illustrate the different open-area ratio of slit ribs conveniently. Fig. 2 shows a picture of the slit ribs placed on the bottom surface of the cooling channel. A slit with constant slit-height to rib-height ratio was asymmetrically arranged at the center of the rib. Twelve different cases based on various values of rib height and slit length, as listed in Table 1, are studied to analyze the influence of slit length and rib height on flow structures and thermal performance in the passages. Besides, the heat transfer coefficient in a totally smooth rectangular channel (defined as Case 0) is also calculated at Re in the range of 20,000–80,000.
ble because unavoidable deviations to obtain data near ribs both in experiments and simulations. Although there is a larger deviation between the experimental data and the simulation results calculated by v2f model for the perforated rib case when compared with the solid rib case, it is found that the v2f model provides the smallest deviations among all tested turbulence models. Therefore, the v2f model is suggested as suitable in this research, and it is chosen in the following study. Apart from turbulence models, the grid quality can also influence the accuracy of the calculation results greatly. For this reason, four mesh systems, respectively, 5 M, 6 M, 7 M, 8 M, are tested at Re = 80,000 for Case A1. The typical structured meshes at the inlet boundary and in the rib regions are shown in Fig. 4. In order to satisfy the requirement of employing the turbulence model, the grids near walls are pretty dense to maintain y+ values at a low level. Fig. 5 exhibits the distributions of spanwise average Nusselt number simulated for different mesh systems. The results indicate that the distinctions between the four mesh systems are not very obvious, especially the results of the 7 M and 8 M mesh systems are almost identical. Therefore, considering the accuracy and economy of the calculations, the 7 M mesh system is deemed to be the best choice among all the four systems.
600
RNG kRealizable kv2f
300
SST kStandard k-
200
Experimental data SST kRNG kStandard k-
100 0
a)
0.2
0.4
v2f Realizable kStandard k-
0.6
0.8
1.0
x/P
500
Standard k-
perforated rib case
3.1. Mesh independence and model validation 400
RNG k-
Realizable kv2f
300
SST k-
Nu
It is recognized that the selection of various turbulence models can lead to different accuracy of the calculation results [35]. Thus one should be cautious when choosing an appropriate model for CFD simulation of turbulent flow and heat transfer. In order to obtain a suitable turbulence model for the further study, different kinds of turbulence models such as Standard k-e, realizable k-e, RNG k-e, Standard k-x, SST k-x, and v2f model are used to simulate the heat transfer of the ribbed channel presented in Ref. [34] at Re = 80,000. The distributions of Nusselt number between the 3rd and 4th row ribs along streamwise direction are displayed in Fig. 3. Compared with other models, the predictions by the v2f model exhibit the best agreement with the experimental data for the solid rib case. The deviations of the results is less than 10% in the middle region of 0.1 x/P 0.95, though larger differences exist in the region near two ribs. The deviation of area weighted average Nusselt number in the region of 0.12 x/P 0.32 is equal to 14.2%, while the difference in the region of 0.12 x/P 0.97 is 7.12%. This indicates that the deviations of the results are mainly focused in the region near ribs. These differences are considered to be tolera-
Standard k-
400
3. Details of numerical simulations To clarify the flow and heat transfer features in the slit rib channels, three-dimensional numerical computations are carried out by the simulation software FLUENT 15.0. The commercial software ICEM CFD 15.0 is used to generate high quality grids for the simulations. Details about model validation, mesh independence and solution settings are provided in this section.
solid rib case
500
Nu
4
Standard k-
200
Experimental data Standard kRealizable kRNG k-
100
b)
0 0.0
0.2
0.4
0.6
v2f Standard kSST k0.8
1.0
x/P
Fig. 3. Comparison of Nusselt number distributions along streamwise direction between 3rd and 4th row ribs at Re = 80,000. The Nusselt number in every x coordinate is the average value in the spanwise direction in the range of 0.12 m y 0.20 m. (a) solid rib case in Ref. [31]; (b) case 2a in Ref. [31].
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 4. Typical structured meshes of the inlet, near rib region and slit region. The grids are denser near the wall surfaces in order to gain a low level of y+ and ensure the accuracy of calculation.
400 350 300
Nu
250 200 150
8M grids 7M grids 6M grids 5M grids
100 50 0.0
0.2
0.4
0.6
0.8
1.0
x/P Fig. 5. Comparison of spanwise average Nusselt number distributions along the streamwise direction of a rectangular channel with solid ribs calculated for different grid systems.
3.2. Solution scheme In order to imitate the heat transfer between the cooling channel and turbine blade in the actual operation condition, suitable boundary conditions should be applied at the computational domain boundaries. According to the previous research, a heat flux density q = 1000 W/m2 is imposed on the bottom face of the test section in the ribbed channels while on the smooth test section (Case 0) a heat flux density q = 900 W/m2 is applied to keep the same heating power for all cases studied in this paper. In order to have an agreement with the experimental settings, other walls of the computational domain, including the rib faces [36], are treated as adiabatic, no slip boundaries. A uniform velocity, based on
the Reynolds number range from 20,000 to 80,000, is adopted as the velocity-inlet boundary conditions, and a turbulence intensity level of 3% and the hydraulic diameter 0.128 m are fixed at the inlet. Moreover, the outlet of the channel is defined as an outflow boundary condition, The working fluid is considered to be incompressible dry air with constant thermal-physical properties at 300 K. The flow process is assumed to be three dimensional, turbulent and steady. The pressure-based and steady solver is selected to get the flow and heat transfer features in the various passages. To set the v2f model, the SIMPLEC scheme is chosen for the pressure-velocity coupling. Second order difference formulae are applied for spatial discretization of turbulent kinetic energy, turbulent dissipation rate, velocity variance scale and energy equations to get more accuracy results. The convergence residual are set as 108 for the energy equations and 105 for others. In addition, several surface monitors are created at the significant sections to observe the temperature, pressure and velocity values. 3.3. Parameter definitions To analyze and compare the calculation results of different rib configurations, some dimensionless parameters are defined as follows. The Reynolds number is defined as:
Re ¼
quDh l
ð1Þ
where q is fluid density, u is the inlet velocity, Dh is hydraulic diameter of the channel, and l is the fluid dynamic viscosity at 300 K. The local Nusselt number of every cell is introduced by:
NuðiÞ ¼
q Dh T w ðiÞ T f k
ð2Þ
where q is the heat flux imposed on the bottom surface of the test section, k is the air thermal conductivity, Tw(i) is the local wall tem-
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 6. Temperature distributions on the heated surface of the test section for various rib configurations at Re = 80,000.
350
f ¼ e=15 mm
e=10 mm
300
e=20 mm
Dp D h 2qu2 Lt
ð3Þ
where Dp is the pressure drop between inlet and outlet of the test section, and Lt is the length of the test section.
Nuave
250
4. Results and discussion 200
4.1. Heat transfer enhancement 150
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
100 50
2
4
6
8 2
4
6
8 2
4
6
8
Re×10-4 Fig. 7. Comparison of the average Nusselt numbers on heated surface for models as Re ranges from 20,000 to 80,000.
perature, and Tf is the mean temperature between the inlet and outlet of the passage. The friction factor, f, is defined as:
Temperature and the Nusselt number distributions on the heated surface are calculated to analyze the heat transfer performance in different rib channels. Fig. 6 exhibits the temperature fields of the heated surface for various slit rib channels at Re = 80,000. High-temperature zones are captured downstream of the ribs along the flow direction while low-temperature area appears in the upstream region. The high-temperature zones extend obviously as the rib height increases. Furthermore, the surface temperature changes periodically in all rib configurations and a declining trend of temperature is observed on the surface between neighboring ribs along the mainstream direction. It is noticed that the temperature in the center region between adjacent ribs increases because the existence of slits on the ribs, and
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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100 500
e=15 mm
e=10 mm
e=10 mm
e=20 mm
80
p (Pa)
Nu
400
300
0
60
40
200
100
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
row 3
0.0
0.2
0.4
0.6
0.8
20 row 4
0
1.0
2
4
6
8 2
4
x/P
(a) 500
e=15 mm
150
Nu
130 300
110
4
6
8
1st row
5th row
e=10 mm
90
200
0
8 2
Fig. 9. Comparison of pressure drops for channels with various rib configurations, the pressure drop value is from the inlet and outlet sections at x = 0.6 m and x= 1.1 m, respectively.
400
100
6
Re×10-4
70 Solid ribs Rl=0.20 Rl=0.35 row 4 Rl=0.50
row 3
0.0
0.2
0.4
0.6
0.8
50 30 10
1.0
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
150
x/P
130
(b)
p (Pa)
110
500 e=20 mm 400
90 70 50 30 10
Nu
300
e=15 mm
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
150 130
200
100
0
Solid ribs Rl=0.20 Rl=0.35 row 4 Rl=0.50
row 3 0.0
0.2
0.4
0.6
0.8
1.0
x/P
(c) Fig. 8. Comparison of Nusselt number distributions along the streamwise direction between two row ribs at Re = 80,000. The Nusselt number at every point is an average value in the spanwise direction: (a) the height of ribs e = 10 mm; (b) e = 15 mm; (c) e = 20 mm.
the longer the slits are, the larger the temperature increase region will be. According to the definition of the Nusselt number shown in Eq. (2), it can be inferred that the value of Nu is only related to the wall temperature because dry air with constant properties was selected as the working fluid in this research. Thus, the Nu distributions can be illustrated by the wall temperature distributions, a
110
e=20 mm
90 70 50 30 10 0.0
Solid ribs Rl=0.20 Rl=0.35 Rl=0.50
0.2
0.4
0.6
0.8
1.0
1.2
1.4
x (m) Fig. 10. Pressure values along the streamwise direction on the geometric center line of the channel of y = 0.16 m and z = 0.04 m at Re = 80,000. The vertical broken lines indicate the positions of ribs.
low local wall temperature also means a high local Nusselt number. The average Nusselt numbers (Nuave) on the heated surface are displayed in Fig. 7. The value of Nuave is given by:
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Nuav e ¼
NudA ¼ A
Pn
i¼1 NuðiÞjAðiÞj
A
ð4Þ
where A is the total area of the heated surface, A(i) is the facet area. The results indicate clear distinctions for cases with the same open-area ratio but different blockage ratio (e/H). As shown in Figs. 6 and 7, opening slits on ribs cause an increase in wall temperature and a decrease in Nusselt number in these cases with small blockage ratio (e = 10 mm). However, slit ribs do not always lead to poorer heat transfer behavior than solid ribs. The average Nusselt number of the channel with high ribs, for example e = 20 mm, becomes larger due to the addition of slits on ribs. At the same time, it also can be seen clearly that the heat transfer of the cooling passage is enhanced as the Reynolds number increase, and the maximum Nusselt number appears for the case with e = 20 mm and Rl = 0.20 at Re = 80,000. Moreover, an extension of the slit will bring a decrease in the average Nusselt number. In order to have an intuition about the heat transfer features on the heated surface, the spanwise average Nusselt number distributions along streamwise direction between the 3rd and 4th row ribs at Re = 80,000 are depicted in Fig. 8. The value of the mean Nusselt number is calculated by following equation:
RW NuðxÞ ¼
0
NuðyÞdy W
ð5Þ
It is discovered the best heat transfer area is present at the middle region between neighboring ribs or in the upstream of the ribs. Different rib structures produce various distribution features of the Nusslet number. The maximum local average Nusselt number is captured in the solid rib channel among the cases with low ribs, but for the cases with higher blockage ratio such as e = 15 mm or 20 mm, the maximum appears in the slit rib configurations with Rl = 0.20. The slit ribs bring an increase of Nusselt number at the upstream of the ribs and also contributes to creating a lower temperature in this area compared to solid rib configuration. From the discussion above, the simulation results suggest that the heat transfer characteristics in the various slit rib channels depend on at least two parameters, the rib height and the slit length. It is found that an opening slit on low ribs will weaken the heat transfer of the cooling passages, but a positive effect will be provided when slits are created on the higher ribs. 4.2. Pressure drop and friction factors To investigate the flow resistance performance of the cooling passages, the pressure distributions and friction factors in the channels with various slit ribs are discussed in this part. The pressure drops between inlet and outlet sections of the heated channel are compared in Fig. 9. It is easy to understand that increase of Reynolds number and blockage ratio lead to higher pressure drop. In contrast, a longer slit is helpful to decrease the pressure drop in the duct with slit ribs. However, the distinctions of flow resistance features between slit rib channel and solid rib channel for various blockage ratio are unexpected. Compared to solid rib configurations, the existence of slits on low ribs slightly reduces the pressure drop in the cooling passage, but an opposite phenomenon is observed if short slits are opened on higher ribs. The largest pressure drop appears in the channel with Rl = 0.20 and e = 20 mm at Re = 80,000. To obtain more details about the flow resistance in the channel, the pressure distributions on the center line of the duct along the main flow direction are presented in Fig. 10. This figure suggests that there are no differences of the pressure values at the range 0 x 0.5 as there is a smooth channel only. The influence of slit rib configurations on pressure mainly appears in the test section and the downstream extended section. A sharper decrease is cap-
0.10
0.08
0.06
f
R
0.04
Case A1 Case B1 Case C1
0.02
0.00
2
3
Case A2 Case B2 Case C2 4
5
Case A3 Case B3 Case C3 6
Case A4 Case B4 Case C4 7
8
Re×10-4 Fig. 11. Friction factors for channels with various rib configurations for Reynolds number ranging from 20,000 to 80,000.
tured in the channels with higher blockage ratio. Furthermore, the largest pressure gradient appears around the first row rib, which also brings the minimum local pressure value in the region between the first and second row ribs. An unexpected result is indicated by Fig. 10, where it is shown that the slit rib channel with high blockage ratio produces a larger total pressure drop than the solid rib configuration though the pressure drop created by every single slit rib is smaller. The friction factors (f) defined by Eq. (3) are calculated and compared in Fig. 11, in order to evaluate flow resistance characteristics of different rib configurations at various Reynolds number. A higher flow resistance is observed as the Reynolds number increases, but the value of the friction factor almost remains constant when Re exceeds 40,000. However, the slit rib channel with e = 20 mm and Rl = 0.20 provides the largest friction factor among all cases studied in this paper. 4.3. Flow characteristics Various flow conditions in the channel might be a reason for the differences between different rib configurations regarding the thermal behavior, so the flow structures are investigated to gain a clearer understanding about the friction and heat transfer features provided by different slit ribs. Fig. 12 depicts the streamlines and x velocity distributions on the section of y = 0.16 m in cases of e = 10 mm or e = 20 mm at Re = 80,000. A wider range of x velocity values is observed in channels with higher ribs, and a separation vortex is formed downstream of ribs in the solid rib channel. It is observed that, for the channels with low ribs (e = 10 mm), a large vortex fills the area between the first and second row ribs, but the vortex regions become smaller and reattachment regions are observed on the heated surface after the second rib. However, in the solid rib channel with e = 20 mm, regions between every two adjacent ribs are almost filled by a vortex, and it might be responsible for the lower average Nusselt number compared to the solid rib configuration with e = 10 mm as shown in Fig. 7. From the comparison of streamlines in solid rib channels with different blockage ratio, a conclusion can be drawn that the higher solid ribs lead to a larger vortex than low ribs. It is also can be seen clearly that the separation vortex can be reduced by creating a slit on ribs, but with a slit extension the vortex size is enlarged slightly. The relation between Nusselt number distributions and flow structures can be explained by the theory in Ref. [21]. The flow field on the bottom face between adjacent ribs can be divided into
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 12. Surface streamlines and x velocity contours on the vertical cross sections at the middle position of ribs of y = 0.16 m for cases e = 10 mm and e = 20 mm at Re = 80,000.
three parts, the separation vortex region, the reattachment region and the flow over a flat region. In general, the convective heat transfer is mainly enhanced by the separation vortex behind ribs and the reattachment to the channel bottom. For ducts with low solid ribs, there are a vortex region and a reattachment region on the heated surface. These provide a considerable enhancement of the heat transfer in the channel. However, the effect of the separation vortex and reattachment flow is constrained while the flow over the flat region is enlarged due to the existence of a slit on ribs. As a result, new boundary layers are developed in the flat flow region and the convective heat transfer is weakened. The impact of slit ribs is completely different in the channels with high blockage ratio. In contrast to the cases with low ribs, there are only separation vortex regions existing in the area between neighboring ribs in the high blockage ratio cases (e = 20 mm). When a slit is
opened on this kind of ribs, the vortex is destroyed and a more complex flow structure, which contributes to the mixing of fluid, is observed in the region between adjacent ribs. To obtain a clearer recognition of the complex flow structures caused by slit ribs, the turbulent kinetic energy distributions and streamlines on the middle section of the ribs are depicted in Fig. 13. It is discovered that several eddies are formed and the impingement on the upwind surfaces of ribs is strengthened when slits are opened on ribs. The different flow structures in adjacent slit region and no-slit region are features of the slit rib cases. Eddies and impingement, which intensify the local turbulent flow and fluid mixture, always happen in the adjacent no-slit regions. Consequently, the heat transfer in these regions is enhanced. However, opposite effects are captured in the adjacent slit region. Backward flow is observed downstream of the ribs in the solid rib case. This
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 13. Surface streamlines and turbulent kinetic energy distributions on the middle section of ribs for cases with P = 100 mm and e = 20 mm at Re = 80,000. The section is a xy plane where z = 0.01 m.
indicates that there are recirculation zones in this region. However, for the slit rib cases, the air is flowing forward through the slit. The recirculation flow in the adjacent slit region is restricted, thus there is not enough time for the coolant to cool the heated surface or mix with the hot fluid sufficiently. As a result, the wall temperature in this region is higher than for the solid rib case as shown in Fig. 6. Furthermore, as the slits are extended, the circulation area is enlarged and the flow resistance decreases. More air flows through the slits and the impingement on the rib surfaces is weakened. This results in expansion of the high temperature regions downstream the slits. Fig. 14 shows the turbulent kinetic energy and streamlines on the section near the heated surface (z = 0.0005 m) at Re = 80,000. It is interesting to observe that the fluid flows in two opposite directions in the middle regions between adjacent ribs, except for the first and second ribs, in the cases with low ribs (e = 10 mm). These curves where the air is separated into two directions, might be the boundary of the separation vortex regions and the reattachment flow regions as indicated in Fig. 12. However, for the cases with e = 20 mm, no similar characteristics are observed. Most of the fluid flows in an opposite direction to the main stream. This might be because the ribs are too high so that the rib spacing is not large enough to let the fluid reattach on the surface again. Furthermore, a convergence phenomenon is captured at the upstream of the first row rib in the slit rib channels while a parallel flow is observed in the passage with solid ribs. This fact confirms that the flow characteristics on the horizontal cross section is changed greatly when a slit is opened on the ribs. The relationships between the turbulent kinetic energy and the Nusselt number can be inferred from Fig. 14. The distributions of the turbulent kinetic energy agree with the wall temperature distributions (shown in Fig. 6). It is discovered that a large local turbulent kinetic energy and local heat transfer are provided in the zone between adjacent no-slit regions, because powerful impingement happens at the upwind surfaces of the ribs. For the cases with e = 10 mm, the fluid impacts on the heated surfaces due to the sep-
aration of the vortex flow and reattachment flow. The turbulent kinetic energy is very high near the boundary of the vortex and reattachment regions and the local heat transfer is enhanced. However, when slits are created on the low ribs, the impingement as well as the convective heat transfer are weakened because the vortex is restrained. Nevertheless, the turbulent flow upstream the ribs is enhanced if slits are opened on the ribs with e = 20 mm, though the turbulent kinetic energy downstream slits is reduced. It is indicated that the flow structures become more complex and corner vortices are formed in the region between the first and second row ribs as slits exist on ribs. In addition, compared to the low ribs (e = 10 mm), the higher ribs can produce stronger impingement and secondary flow, which leads to heat transfer enhancement upstream of the rib. For the cases with high ribs (e = 20 mm), a lower temperature appears upstream of the slit ribs. This suggests that opening a slit on the ribs can reinforce the convection heat transfer on the heated surface, though the temperature at the middle region increases slightly as the turbulent kinetic energy is weakened. In addition, the change of flow structures also indicates the difference of pressure structures in various cooling passages. It is accepted that the lower blockage ratio channels have less flow resistance and larger circulation area which are helpful in decreasing the pressure drop in the ducts. Furthermore, the circulation area can also be increased by opening a slit or hole on the ribs. However, the different flow conditions and mass transport features created by slit ribs with various rib-height can evidently influence the flow resistance features in the passage as well. As mentioned above, different size recirculation zones are captured behind the ribs in the solid rib cases with various rib-height. In the solid rib case with e = 20 mm, the regions between adjacent ribs are filled with recirculation flow. Thus, the mass transport of fluid between the mainstream and the recirculation zones is very small and a great deal of the air is trapped in these regions. Due to less mixing with the trapped air, the fluid in the mainstream region flows through the channel at a high velocity. However, it is observed that
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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Fig. 14. Surface streamlines and turbulent kinetic energy distributions on the xy cross section near the heated surface of the channel of z = 0.0005 m at Re = 80,000.
1.9
Case A1 Case B1 Case C1
1.8
Case A2 Case B2 Case C2
Case A3 Case B3 Case C3
Case A4 Case B4 Case C4
1.7
Nuave/Nu0
several vortex zones are formed in the adjacent no-slit regions when creating slits on this kind of ribs as indicated in Fig. 13. The complex vortex structures are effective to improve the mixture of the fluid in the mainstream and the adjacent rib regions. Furthermore, the vortex structures also contribute to the intensification of the mass transport in the air in these regions and the shearing drag in the fluid is strengthened as well. Therefore, the momentum loss and the pressure drop in the case with e = 20 mm and Rl = 0.20 increase, although the flow area is extended as slits are opened on the ribs. This effect might be the real reason which causes the increase of the pressure drop when slits are opened on ribs in the cases with e = 20 mm as shown in Fig. 9. For the low solid rib configuration (e = 10 mm), the recirculation zones behind the ribs are smaller and the air trapped in the recirculation zones is less than for the solid rib case with e = 20 mm. Thus, the mass transport between the mainstream and the adjacent rib regions is larger. The impact of different slit rib configurations on the flow field is weak and the increase of circulation area is more significant than the momentum loss when slits are created on the ribs. Therefore, the slit rib cases with
1.6 1.5 1.4 1.3 1.2
2
3
4
5
6
7
8
Re×10-4 Fig. 15. Normalized Nusselt numbers for all rib configurations as the Re range of 20,000 Re 80,000. The value of each normalized Nusselt number is defined as the ratio of Nusselt number of rib channel to that of smooth channel.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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22 20 18 16
f/f0
14 12 10 8 6 4
Case A1 Case B1 Case C1
2 0
2
3
Case A2 Case B2 Case C2 4
Case A3 Case B3 Case C3
5
6
Re×10
Case A4 Case B4 Case C4 7
8
-4
Fig. 16. Normalized friction factors for all rib configurations as the Re range of 20,000 Re 80,000. The value of each normalized friction factor is defined as the ratio of friction factor of rib channel to that of smooth channel.
e = 10 mm provide a smaller pressure drop than the solid rib configuration. In addition, the influence of the circulation area on the flow resistance is enhanced and the pressure drop is reduced as the slits are extended. Accordingly, the slit rib channel (e = 20 mm, Rl = 0.50) and the solid rib channel (e = 20 mm, Rl = 0) have equal pressure drops as exhibited in Fig. 9. 4.4. Overall thermal performance To obtain a comprehensive estimate about the behavior of slit rib channels the overall thermal performance of various cooling passages is compared and analyzed in this part. Case 0 is designed to represent the Nusselt number and friction factor in a smooth channel without any ribs. Fig. 15 displays the comparison of normalized Nusselt number (Nuave/Nu0) for all rib configurations studied in this paper. This figure indicates that the normalized Nusselt number decreases as the
0.24
Reynolds number is increasing from 20,000 to 40,000, but it increases slightly as the Re continues to increase. The minimum value (about 1.3) of Nuave/Nu0 appears in the channel with e = 10 mm and Rl = 0.50 at Re = 40,000 while the maximum value (about 1.75) is captured in the case with e = 20 mm and Rl = 0.20 at Re = 20,000. An evident distinction is discovered, namely as the rib height increases, the convection heat transfer is weakened in the solid rib channels, but an opposite effect is observed in the slit ribs configurations, and the longer the slit is, the smaller the normalized Nusselt number will be. To compare the flow resistance features in different rib ducts, the normalized friction factor is exhibited in Fig. 16. It is found that the distribution of normalized friction factor is analogous to that of the normalized Nusselt number. The rib configuration which provides the best heat transfer also leads to the largest friction factor, and the maximum normalized friction factor is about 21 while the minimum value is around 5. In addition, the blockage ratio is also a significant parameter which influences the flow resistance of the channel greatly. The channel with higher blockage ratio has a larger normalized friction factor as well. Two thermal enhancement factors, (Nuave/Nu0)/(f/f0) and (Nuave/ Nu0)/(f/f0)1/3, are presented in Fig. 17 to conduct a comprehensive evaluation of various slit rib channels. This figure suggests that the influence of slit length on (Nuave/Nu0)/(f/f0) is negligible, but the rib height and the Reynolds number impact the (Nuave/Nu0)/ (f/f0) considerably. The value rises but then drops with the increase of Reynolds number and higher ribs always lead to a smaller (Nuave/Nu0)/(f/f0). However, the other thermal enhancement factor (Nuave/Nu0)/(f/f0)1/3 remains almost constant in most cases as the Reynolds number changes from 20,000 to 80,000. The rib height and the slit length are the two major factors which impact the Table 2 Geometry parameters of Case D1–D4, with P = 50 mm and e = 10 mm.
e=10 mm
Rl=0.35 Rl=0.50
e/H
Hs/e
Ls/Lr
0.2 0.2 0.2 0.2
0.125 0.125 0.125 0.125
0.4 0.4 0.4 0.4
0 0.20 0.35 0.50
0.84
Solid ribs Rl=0.20
Rl=0.35 Rl=0.50
0.16
Solid ribs Rl=0.20
Rl=0.35 Rl=0.50
0.14
e=15 mm
0.12
e=20 mm
0.76
( Nuave/Nu0 /( f/f0)1/3
Solid ribs Rl=0.20
(
0.20
(
( Nuave/Nu0 /(f/f0)
e/P
D1 D2 D3 D4
0.80
0.22
0.10
Cases
e=10 mm
0.72 0.76
Rl=0.35 Rl=0.50
Solid ribs Rl=0.20 e=15 mm
0.72 0.68 0.64
e=20 mm
0.64 0.60
0.08
Rl=0.35 Rl=0.50
Solid ribs Rl=0.20
0.06 2
4
6
Re×10-4
8
0.56
Rl=0.35 Rl=0.50
Solid ribs Rl=0.20
0.52 2
4
6
8
Re×10-4
Fig. 17. Overall thermal performance for cases with different rib height and slit length as the Re range of 20,000 Re 80,000.
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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22
1.60 18
1.50
16 14
1.45
f/f0
Nuave/Nu0
20
1.55
1.40
10
1.35
8
1.25
a)
6
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
1.30
0.0
0.1
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
12
4 2
0.2
0.3
0.4
0.5
b)
Rl
0.0
0.1
0.2
0.3
0.4
0.5
Rl
0.24 0.80 0.75
(Nuave/Nu0)/(f/f0)1/3
(Nuave/Nu0)/(f/f0)
0.20
0.16
0.12
0.08
c)
0.0
0.1
0.65 0.60 0.55
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
0.04
0.70
P/e=10,e=10 mm P/e=5,e=20 mm P/e=5,e=10 mm
0.50
0.2
0.3
0.4
0.5
Rl
d)
0.0
0.1
0.2
0.3
0.4
0.5
Rl
Fig. 18. Comparison of normalized Nusselt number, normalized friction factor, (Nuave/Nu0)/(f/f0) and (Nuave/Nu0)/(f/f0)1/3 for cases with various values of rib-height and ribpitch as Rl ranges from 0 to 0.50.
thermal performance of the channel remarkably, and the lower rib and shorter slit can provide a better thermal behavior of the cooling passage. The influences of various height of slit ribs on the heat transfer performance are completely different. The thermal performance is improved when a slit is opened on high ribs, but an opposite effect is observed if a slit is created on lower ribs. The best thermal behavior is provided by the solid ribs with e = 10 mm while the solid rib configuration with e = 20 mm has the worst performance among all cases studied in this paper. To have a more comprehensive understanding of the effect of creating slits on ribs, additional four cases (Case D1–D4) with e = 10 mm and P = 50 mm at Re = 80,000 were investigated to take the rib-pitch into account. Details about the four cases are listed in Table 2 and the comparison of the performance indices is displayed in Fig. 18. It is found that the values of the normalized Nusselt number, (Nuave/Nu0)/(f/f0) and (Nuave/Nu0)/(f/f0)1/3 of cases (P = 50 mm and e = 10 mm) are close to the values in the cases with the same rib-height. A common decrease of the normalized Nusselt number is observed when slits are opened on ribs with e = 10 mm, while an opposite effect is provided if slits are created on the higher ribs (e = 20 mm). From the discussion we can infer that the rib-height might be the main factor which influences the heat transfer performance of the cooling channel.
5. Conclusions Three-dimensional numerical simulations were applied to investigate the flow and heat transfer characteristics in a rectangular internal cooling channel with different height slit ribs. Slit ribs with various rib height and slit length were designed. The wall temperature, Nusselt number, friction factor and flow structure in the channels were analyzed in order to evaluate the thermal performance of the passages. Based on the results, the following conclusions are drawn: (1) The solid rib channel with e = 10 mm has the best overall thermal performance among all cases studied in this research. However, the highest heat transfer enhancement is provided by the slit rib configuration with e = 20 mm and Rl = 0.20, and the channel with the highest solid ribs has the poorest thermal performance because of the lowest heat transfer enhancement and the high friction factor in this case. (2) It is found that producing slit on ribs can constrain the formation of a separation vortex, but various effects are captured while the slit is opened on ribs with different height. For the cases studied in this paper, the values of Nusselt
Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046
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number and friction factor decrease when a slit is created on low ribs, however, a contrary phenomenon is observed while opening a slit on high ribs. In addition there is a decreasing trend of the normalized Nusselt number and normalized friction factor as the slit is extended, and the higher solid ribs always lead to a larger pressure drop in the channel. (3) The comparison of overall thermal performance indicates that ribs with short slit provide better thermal performance than ribs with long slit under the same pumping power condition. Creating a slit on high ribs can enhance the convection heat transfer in the cooling channel but a negative effect is observed when a slit is opened on low ribs. This finding suggests that opening short slit on high ribs is a beneficial way to improve thermal performance of the rectangular cooling channel.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgment This research was supported by the National Natural Science Foundation of China (51676163), and the National 111 Project (B18041). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046. References [1] H. Zhang, L. Li, X. Tang, Z. Huang, Review of heavy-duty gas turbine blade cooling technology, Gas Turb. Technol. 30 (2017) 1–7. [2] Z. Liu, X. Yang, Z. Feng, Study on heat transfer and cooling in gas turbine blade: Internal cooling, Therm. Turb. 42 (2013) 265–275. [3] Phil Ligrani, Heat transfer augmentation technologies for internal cooling of turbine components of gas turbine engines, Int. J. Rotating Mach. 2013 (2013), Article ID 275653. [4] C. Nonino, G. Comini, Convective heat transfer in ribbed square channels, Int. J. Numer. Methods Heat Fluid Flow 12 (2002) 610–628. [5] B. Cukurel, T. Arts, C. Selcan, Conjugate heat transfer characterization in cooling channels, J. Therm. Sci. 21 (2012) 286–294. [6] K.Y. Kim, Y.M. Lee, Design optimization of internal cooling passage with Vshape ribs, Numer. Heat Transf.-Part A 51 (2007) 1103–1118. [7] A. Perwez, S. Shreyak, R. Kumar, Heat transfer and friction factor characteristic of spherical and inclined teardrop dimple channel subjected to forced convection, Exp. Heat Transfer 32 (2019) 159–178. [8] T. Pirasaci, M. Sivrioglu, Experimental investigation of laminar mixed convection heat transfer from arrays of protruded heat sources, J. Faculty Eng. Archit. Gazi Univ. 27 (2012) 765–773. [9] J. Park, P.M. Ligrani, Numerical predictions of heat transfer and fluid flow characteristics for seven different dimpled surfaces in a channel, Numer. Heat Transfer-Part A 47 (2005) 209–232. [10] R.S. Bunker, A review of shaped hole turbine film-cooling technology, ASME J. Heat Transfer 127 (2005) 441–453. [11] J.Y. Jeong, W. Kim, J.S. Kwak, J.S. Park, Heat transfer coefficient and film cooling effectiveness on the partial cavity tip of a gas turbine blade, ASME J. Turbomach. 141 (2019), https://doi.org/10.1115/1.4042647. [12] M.K. Kelishami, E. Lakzian, Optimization of the blowing ratio for film cooling on a flat plate, Int. J. Numer. Methods Heat Fluid Flow 27 (2017) 104–119.
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Please cite this article as: X. Li, G. Xie, J. Liu et al., Parametric study on flow characteristics and heat transfer in rectangular channels with strip slits in ribs on one wall, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.046