Effects of impingement gap and hole arrangement on overall cooling effectiveness for impingement/effusion cooling
Introduction
In order to achieve higher thermal efficiency for the modern aero engines and heavy-duty gas turbine, higher pressure ratio as well as turbine inlet temperature are required. Typical turbine materials cannot resist the higher inlet temperature, which may result in structural failure due to high temperature and thermal stress. Thus, the hybrid cooling techniques, combined external film cooling and internal cooling, are used to make the turbine work properly. The impingement/effusion cooling system is a typically hybrid cooling contained impingement and film cooling. Coolant supplied from the compressor flows through the perforated plate, then impinges on a parallel plate with effusion hole (film plate). After cooling the film plate, the spent coolant ejects into the mainstream through the neighboring film hole and forms the protective film. The effused way of the spent coolant in this hybrid cooling system is quite different from the impingement cooling alone.
Numerous researches have investigated the effect of relative position of impingement hole and effusion hole on the heat transfer of impingement/effusion cooling. Hollworth and Dagan [1], Hollworth et al., [2] measured the heat transfer of staggered impingement where the coolant is effused through film hole, which produced higher heat transfer intensity, about 20–30%, compared with impingement alone. Two arrangements of holes, in-line (the impingement jet opposite film hole) and staggered, were also employed. They found that the circulation of spent coolant, which lead to the preheat of impingement jet, is suppresses due to the suction effect of film hole with staggered arrangement through the flow visualization. The effect of relative position of impingement hole and film hole on the distribution of heat transfer was also addressed by Cho and Rhee [3]. They shifted the impingement plate to obtain different relative positions of impingement and film hole. The distributions of Sherwood number indicated that the staggered hole arrangement provided better heat/mass transfer performance. An area with low momentum flow was found in shifted hole arrangement which results in low heat transfer. They further investigated the heat transfer for similar hole arrangements with small jet to jet pitch [4]. The area averaged heat transfer of staggered and shifted arrays was nearly same and the heat transfer distribution of former arrangement was more uniform. Recently, Andreini et al. [5] experimentally and numerically assessed the impingement/effusion cooling with various diameters and arrangements of holes. The investigation indicated that the heat transfer of impingement is more sensitive to the relative position between film hole and impingement hole for configuration with smaller hole to hole pitch.
The other geometrical parameters were also studied by previous researches. Dabagh et al. [6] tried to obtain the optimum number of impingement holes for fixed number of film holes. Rhee et al. [7] investigated the effect of existence of effusion holes (film holes) on heat transfer of impingement. The experimental results showed that the heat transfer with film hole was enhanced significantly at small impingement gap, compared with the impingement alone. The enchantment of heat transfer was not obvious for large gap distance (H/D ≥ 4). Huber and Viskanta [8] also studied the influences of impingement gap and hole to hole spacing on the heat transfer on the impingement target surface where the spent air effuses through film hole. The results of local heat transfer indicated better uniformity and higher intensity for small impingement gap.
Through the above description, the convective heat transfer of impingement/effusion cooling has been widely investigated with various geometrical parameters. However, a conjugate heat transfer occurs in the hybrid cooling system. It is also important for the normal operation of the turbine in terms of the hot spot and thermal stress [9]. For the designer, it will be helpful to the optimization of cooling system if the surface temperature of turbine can be obtained in laboratory condition through reliable analogy methods. The turbine surface temperature can be converted to non-dimensional parameter, as shown in Eq. (1):Where Tg,Tc, i and Tw are the recovery temperature of mainstream, reference temperature of coolant and local surface temperature, respectively. According to the Eq. (1), the overall cooling effectiveness, obtained from conjugate test in laboratory condition, can be converted to the turbine surface temperature by using corresponding temperatures in turbine condition.
The experimental results by Martiny et al. [10] and Jung et al. [11] both showed the strong effect of Biot number on conjugate heat transfer, where the h,δ and k are heat transfer coefficient on the surface, characteristic length and thermal conductivity of plate. Matching mainstream side Biot number is considered as an important and convenient analogy principle. Panda and Prasad [12] experimentally and numerically studied the ϕ on parallel orifice plates. Tan et al [13] measured the ϕ of flat plate with different geometrical parameters, including impingement gap (H/D = 2~4) and two hole arrangements (staggered and shifted). The results showed that the smaller impingement gap and hole-to-hole spacing produced better cooling performance. Mensch and Thole [14] also investigated the effect of the impingement on conjugate heat transfer of gas turbine endwall through experiment and numerical simulation. Actually, most of these conjugate heat transfer researches were performed based on this analogy principle.
In hybrid cooling system, it is not rigorous to match mainstream side Bi only because the relationship between the coolant side heat transfers and mainstream side heat transfers is not considered. Thus, Albert et al. [15], Albert and Bogard [16] proposed analogy parameters on airfoil wall through a brief one-dimensional analysis. The improved analogy theory included two new parameters, adiabatic cooling effectiveness (η) and heat transfer coefficient ratio (hg/hc), mainstream side to coolant side). The further improved analogy theory was presented by Nathan et al. [17]. The equation of the analogy theory can be presented as follows.Li et al. [18] also presented similar analogy parameters through theoretical analysis based on energy equilibrium. They also found that the warming factor (χ) has little effect on the ϕ compared the others parameters through the partial derivative analysis.
Nathan et al. [17] proposed that scaled overall cooling effectiveness can be obtained in laboratory by matching the key analogy parameters based on the Eq. (2). Considering that many researches of conjugate heat transfer have been performed by only matching mainstream side Biot number, these researches did not mention how to match the analogy parameters in laboratory condition to that in turbine condition. Thus, based on the previous analogy theories and impingement/effusion cooling system, the authors discussed the matching principles of analogy parameters in detail [19], which can be concluded as follows:
- 1.
The mainstream side Biot number (Big) can be scaled by scaling the thermal conductivities ratio of metal and mainstream (kg/ks), which can be achieved by changing solid material and mainstream temperature.
- 2.
In impingement/effusion cooling, the changes of adiabatic cooling effectiveness (η) and heat transfer coefficient ratio (hg/hc) are interrelated. The analogy principles for simultaneously matching the η and hg/hc are different for different temperature ratios (Tg/Tc).
- 3.
If the Tg/Tc is matched between turbine and laboratory conditions, the theoretical analysis indicated that the analogy parameters, includingBig,ηand hg/hc, can be simultaneously matched by matching and blowing ratio (M). If the Tg/Tc is mismatched, the theoretical analysis [19] showed that matching momentum flux ratio (I) is a key principle to reduce the influence of mismatched temperature ratio.
According to previous literatures, the heat transfer of hybrid cooling was influenced by a series of geometrical parameters [1], [2], [3], [4], [5], [6], [7], [8], [9]. Considering the overall cooling effectiveness reflects the conjugate heat transfer of convection and conduction, current study focuses on the overall cooling effectiveness in hybrid cooling scheme with various parameters, including the relative position of impingement hole and film hole, impingement gap distance, as well as the blowing ratio (momentum flux ratio). Due to the difficulty for matching the temperature ratio of turbine condition, about 2, in laboratory condition, it is necessary to experimentally validate the above match principles of analogy parameters for overall cooling effectiveness. The approach to evaluate the matching principles is similar to Ramachandran and Shih [20] and Liu et al. [19]. Two temperature ratios were employed to evaluate the performance of matching principles. The numerical simulation was also carried out to analyze the flow field and compare with the experimental results.
Section snippets
Experimental facility
In this paper, all the flat plate experiments were conducted in a low speed wind tunnel facility depicted in Fig. 1(a). The details of test section are presented in Fig. 1(b).
The mainstream was supplied by a centrifugal blower. The velocity of mainstream was adjusted by a valve before entering 250 KW air heater. The mainstream temperature was maintained by the air heater with a PID controller. The heated mainstream passed through the expanded section and two contraction sections to ensure the
Numerical simulation approach
The experimental setups in this paper, including the geometrical parameters of test section and operating conditions, were almost identical with the previous numerical simulation [19]. The detailed discussion for numerical accuracy and validation had been presented in the previous paper [19].
The CFD software ANSYS CFX Ver. 16.0 was chosen to solve the steady Reynolds-averaged Navier–Stokes (RANS) equations with SST k-ω turbulence model. The previous numerical research [5], [12], [14] showed
Results and discussion
In this paper, the study focuses on the effects of geometrical parameters, including the relative position of the projection of impingement hole and inlet of film holes, impingement gap distance, on the overall cooling effectiveness (ϕ) of impingement/effusion cooling scheme. Matching principles of analogy parameters for overall cooling effectiveness are also investigated with different geometrical structures. Note that, due to the different optical diameters of IR windows, the available IR
Conclusions
In this study, the effects of geometrical parameters on the overall cooling effectiveness were experimentally investigated on the flat plate with impingement and effusion cooling. Geometrical parameters investigated included two relative position of impingement and effusion holes (staggered arrangement and overlapped arrangement) and three impingement gap distances (H/D = 2.5, 5 and 7.5). The numerical simulation was employed to predict the effect of gap distance in a wider range. The specific
CRediT authorship contribution statement
Gang Xie: Conceptualization, Methodology, Investigation, Writing - original draft. Cun-liang Liu: Supervision. Lin Ye: Software. Rui Wang: Validation. Jiajia Niu: Investigation. Yingni Zhai: Supervision.
Declaration of Competing Interest
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.
Acknowledgments
The authors are grateful for the financial support from Project supported by the National Natural Science Foundation of China (grant no. 51776173) and the Innovation Capacity Support Plan in Shaanxi Province of China (grant no. 2019KJXX-065) and Scientific Research Plan Project of Key Laboratory of Shaanxi Provincial Education Department (17JS070).
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