Due to their exceptional static and dynamic properties along with high-temperature resistance, liquid metal bearings are extensively employed in challenging environments. This paper carried out a multi-objective optimization work for spiral groove journal liquid metal bearings (JLMB) by using a NSGA-II. The clearance of bearing C, spiral angle a, groove depth hg, groove ridge ratio β, groove number N, and groove spacing P were chosen as design variables to maximize the load-carrying capacity and the effective stiffness of liquid metal bearing. During optimization process, the Latin hypercube sampling was adopted to generate 41 sample points, and the Kriging surrogate model was used to establish the correlations between design variables and objective functions. The Pareto front with optimal structures was obtained after optimization. Subsequently, optimal parameters were determined from the Pareto front by using the TOPSIS decision method. Finally, a comparative analysis of bearing performance was conducted between the journal liquid metal bearings with optimal parameters and the original parameters. The results indicated that the optimal JLMB parameters are given as follows: C = 10 μm, a = 26°, hg = 5.2 μm, β = 0.7, P = 11.1 mm, N = 10. The static and dynamic performance of optimized JLMB has been significantly improved. Specifically, the load carrying capacity increased to 2781.2N, making a 1313% enhancement over the JLMB with original parameters. While the effective stiffness of the optimized JLMB surged to 1.86 × 108 N/m, a more than 20-fold increase.

Vortex generators can boost heat transfer performance greatly, although they are always linked with significant pressure drops. In this article, to reduce the pressure drop while improving the thermal efficiency simultaneously, traditional delta winglet pair vortex generators (DWPVG) with slits are installed in the rectangular channel. Besides, the effects of slits on DWPVG on pressure drops and heat transfer performances for different Reynolds numbers are studied. To reveal the fluid flow characteristics, three-dimensional calculations using a confirmed turbulence model are undertaken and the underlying thermo-fluid processes are exposed for the various investigated cases. To reveal the overall thermal performance of different cases, two overall thermal performance factors Nuave/Nu0/(f/f0) and Nuave/Nu0/(f/f0)1/3 are used. The findings suggest that when the fluid flows through slits, induced vortices are located closer to the bottom surface, generating an improvement of the local Nusselt number behind DWPVG. Furthermore, DWPVG with slits can decrease the pressure drop, but also make the local thermal efficiency improve in the channel with a high blocking ratio. Moreover, the increase in the overall thermal performance of the slit DWPVG channel with a high blocking ratio is enlarged with the Reynolds number raise. Besides, the highest heat transfer enhancement is provided by opening slits on five DWPVGs in the rectangular channel.

This paper conducted a multi-objective optimization work for a composite internal and film cooling structure. The pitch-to-height ratio of the ribs, the inclination angle of the ribs, and the inclination angle of the film hole are chosen as the three design variables to enhance the heat transfer performance, improve the film cooling effectiveness and reduce the pressure loss of the internal channel flow. During the optimization process, the Latin hypercube sampling method is adopted to select 26 sample points from the design space. The response values with higher fidelity at the sample points are calculated using computational fluid dynamics (CFD) simulations. Among the 26 sample points, 21 are used to construct a surrogate model of each objective function while the rest of them are adopted to validate the correctness of the established surrogate model. By combining the Kriging surrogate model with a nondominated sorting genetic algorithm, the Pareto optimal front is obtained after the optimization process. Finally, comparison and analysis are conducted with respect to the cooling performance and mechanisms between the reference model and the selected three representative optimized models. Results show that the optimized three models can not only improve the film cooling effectiveness but also reduce the pressure loss of the channel flow and enhance the heat transfer. In addition, it is found that the optimized model induces an anticlockwise rotating vortex, which entrains more coolant near the target surface. The inclined ribs of the optimized models induce a secondary flow along the inclined ribs, which enhances the flow mixing and augments the heat transfer performance.

This paper presents three-dimensional numerical simulations with the established realizable k−ε model to clarify the underlying and interacting mechanisms between the film cooling and the internal cooling. On the one hand, the effects of three different internal cooling channels, i.e., smooth channel, continuous ribbed channel, and truncated ribbed channel, on the film cooling effectiveness and the discharge coefficients are investigated. On the other hand, the influences of three different film cooling holes, i.e., cylindrical hole, two elliptical holes and two circular-to-elliptical holes, on the heat transfer performances and pressure loss of the internal cooling channel are revealed. Especially, the suction effects of the film cooling holes are analyzed through setting up baselines with only internal cooling channels. Results show that the placement of ribs in the internal channel has different influences on the film cooling effectiveness with respect to different hole shapes depending on the blowing ratio. The discharge coefficient of the film hole can be improved by introducing ribs to the internal channel. Suction of film hole is helpful for enhancing the heat transfer performance and reducing the pressure loss of the internal channel. Besides, ribs instead of the suction effect of film hole play a major role to enhance the heat transfer performance in the internal cooling channel.

Attempts for higher output power and thermal efficiency of gas turbines make the inlet temperature of turbine to be far beyond the material melting temperature. Therefore, to protect the airfoil in gas turbine from hot gas and eventually prolong the lifetime of the blade, internal and film cooling structures with better thermal performance and cooling effectiveness are urgently needed. However, the traditional way of proceeding involves numerous simulations, additional experiments, and separate trials. Optimization of turbine cooling structures is an effective way to achieve better structures with higher overall performances while considering the multiple objectives, disciplines or subsystems. In this context, this paper reviews optimization research works on film cooling structures and internal cooling structures in gas turbines by means of various optimization methods. This review covers the following aspects: (A) optimization of film cooling conducted on flat plates and on turbine blades or vanes; (B) optimization of jet impingement cooling structures; (C) optimization of rib shapes, dimple shapes, pin–fin arrays in the cooling channels; (D) optimization of U-bend shaped cooling channels, and internal cooling systems of turbine blades or vanes. The review shows that through a reliable and accurate optimization procedure combined with conjugate heat transfer analysis, higher overall thermal performance can be acquired for single-objective or multi-objectives balanced by other constrained conditions. Future ways forward are pointed out in this review.

This work experimentally tests and numerically investigates the heat transfer augmentation, the flow characteristics and the overall thermal performance of truncated ribs in a rectangular channel with an aspect ratio of 1:4 designed by using the constructal theory. The liquid crystal thermography (LCT) method in steady-state is adopted and the three-dimensional CFD numerical simulations with an established transition k-kl-ω model are conducted to reveal the underlying thermo-fluid mechanisms. Seven cases with novel truncated ribs designed by using constructal theory are designed to improve the heat transfer performances compared with the case with continuous ribs. Among them, ribs with different cross sections, different arrangements and different cut-off angles are studied, based on which, two ways to improve the heat transfer performances with respect to the truncated ribs are given. In addition, two indexes, i.e., Nu/Nu0/(f/f0) and Nu/Nu0/(f/f0)1/3, are considered to study the overall thermal hydraulic performance of the considered cases. Results show that with respect to the factor Nu/Nu0/(f/f0), the designed cases can improve the overall thermal performance up to 38.21%, and with respect to the factor Nu/Nu0/(f/f0)1/3, the designed cases can improve the overall thermal performance up to 12.16%. By analyzing the flow characteristics, the underlying mechanisms about such thermal performance enhancements of the designed cases are revealed. Finally, the augmentation entropy generation number of each case is calculated to evaluate the effect of augmentation on irreversibility.

Film cooling is one of the most efficient and widely used cooling methods for high-temperature components. The interaction between the film cooling jet and main flow creates the counter-rotating vortex pair (CRVP), which enhances the mixing between coolant and hot stream and lifts the coolant film off the protected surface. The desire to overcome the unfavorable effects of CRVP and thus efficiently improve cooling effectiveness promotes various new combined-hole designs for film cooling. In this review paper, a summary of previous progress on film cooling and a special focus on recent literature related to the combined-hole film cooling designs with less difficulty in machining are provided. The underlying mechanisms of the enhancement in cooling effectiveness and film coverage due to antikidney vortex structure by combined holes are analyzed. Some perspectives on future prospects are finally addressed.

Purpose In this study, numerical simulations are performed to compare the adiabatic film cooling effectiveness and reveal the difference of film cooling mechanisms of two models with the same geometries and cross-section areas of film holes’ exits at three typical blowing ratios (M = 0.5, 1 and 1.5). The two models are an elliptical model and a cylindrical model with 90° compound angle, respectively. Design/methodology/approach Three different cases are considered in this work and the baseline is the model with a cylindrical film hole. The same boundary conditions and a validated turbulence model (realizable k-ε) are adopted for all cases. Findings The results show that both the elliptical and cylindrical models with 90° compound angle can enhance the film cooling effectiveness compared with the baseline. However, the elliptical model performs well at lower blowing ratios and in the near region at each blowing ratio because of the wider width of the film hole’s exit. The cylindrical model with 90° compound angle provides better film cooling effectiveness in the further downstream area of the film hole at higher blowing ratio because of the less lift-off and better coolant coverage in the larger x/D region along the mainstream direction. Originality/value Overall, it can be concluded that although the elliptical and cylindrical models with 90° compound angle have identical hole exits, the different inlet direction and cross-sectional geometry affect the flow structures when the coolant enters, moves through and exits the hole and finally different film cooling results appear.

在给定通道雷诺数的条件下,实验研究了矩形内冷通道中截断肋片在6种不同排布方式下的换热特性,并结合三维数值模拟方法,基于流动特征深入分析了其中的对流换热机理.研究表明:6种不同排布方式下,结构2?3?5?9通道的换热性能最好,结构2?5?3?9通道的换热性能最差;结构2?3?5?9通道的压力损失最大,结构2?5?9?3通道的压力损失最小.就总体热性能而言,结构2?9?5?3的最好,结构2?3?5?9的次之,结构2?5?3?9的最差.对流动特征的分析可知,肋片截断区域诱导的横向涡增强主流与边界层流体的掺混,强化了受热壁面与流体间的换热;截断肋片的不同方式排布使通道中流动特征不尽相同,但截断区域的涡结构基本相似.

This work numerically and experimentally studies the heat transfer performances and flow characteristics of vortex generators (VGs) in a high aspect ratio rectangular ribbed channel with the Reynolds number ranging from 20000 to 100000. The steady liquid crystal thermography (LCT) method is adopted to link the images captured by experiments and the Nusselt numbers. Four different cases combining ribs and VGs are considered, and they are compared with a case with five continuous ribs in the channel. For the first time, the effect of winglet VGs and the tetrahedral VGs on heat transfer performance are compared. Simultaneously, two different arrangements of VGs, i.e. common-flow-down VGs and common-flow-up VGs are also studied to figure out which arrangement is better for improving the heat transfer performance. Simulations are conducted to systematically compare the fluid flow and local heat transfer characteristics to reveal the underlying thermo-fluid mechanisms of the considered cases by using three-dimensional CFD numerical simulations with a verified turbulence model, i.e., the SST k-omega model in the transition state. Results indicate that in the range of 0 < x/P < 1, the Nusselt number is enhanced to a large extent due to larger space for the flow reattachment. In addition, it is found that the winglet VGs perform better than the tetrahedral VGs. The winglet VGs with the common-flow-down arrangement give the best overall thermal performance at all Reynolds numbers in most cases. More specifically, the heat transfer performance can be improved up to 5.51% by adopting the common-flow-down VGs compared with the case having five continuous ribs. Furthermore, the flow characteristics reveal that longitudinal VGs can generate vortices to disturb the boundary layers, which can enhance the flow mixing and augment the heat transfer performance.

Endwall film cooling is a significant cooling method to protect the endwall region and the junction region of endwall and a turbine vane, where usually a relatively high temperature load exists. This work aims to find the optimized arrangement of film cooling holes on the endwall and improve the film cooling in some difficult regions on the endwall, such as pressure side-endwall junction region. Several ideas for film cooling hole arrangement design are proposed, based on the pressure coefficient distribution, the streamline distribution, and the heat transfer coefficient (HTC) distribution, respectively. Four specified designs are built and compared. The results are obtained by numerical calculations with a well-validated turbulence model, the k-omega shear stress transport (SST) model. From this work, the designs based on the pressure coefficient distribution (designs 1 and 2) force the flow from the pressure side to the suction side (SS), especially in design 2, which adopts compound angle holes. The designs based on pressure coefficients have benefit in the cooling of the SS but give worse coolant coverage on the pressure side. In addition, designs 1 and 2 have little influence on the original pressure field. The design based on the streamline distributions (design 3) has larger coolant coverage on the endwall and provides good coolant coverage on the endwall and pressure side junction region. The design based on the HTC distribution provides large overall film cooling effectiveness on both the pressure side and the SS. More film cooling holes are placed on the high temperature regions, which is more effective in practice.

Existing researches on two-row film cooling mainly focused on double-jet film cooling. However, researches on the effects by combining different kinds of hole shapes on film cooling performance are quite limited. In order to improve the film cooling effectiveness, the three-dimensional numerical method is utilized to investigate the effects of a novel structure composed of two-row holes with different shapes and arrangements on the adiabatic film cooling effectiveness with the blowing ratio of M = 1.5. To achieve this purpose, 30 different cases with two-row holes are designed and their film cooling effectiveness are compared with those of other seven cases with a single hole. Cases with two-row holes are designed by setting cylindrical, elliptical, or super-elliptical holes as the first-row, and arranging cylindrical holes with 30 deg, 45 deg, 60 deg, and 90 deg compound angles as the second row. The realizable k–ɛ turbulence model with enhanced wall function is utilized for all cases under identical boundary conditions. Similar film cooling performances are observed for cases with elliptical and super-elliptical holes being the first row, since the maximum deviation of film cooling effectiveness is less than 10%. It is found that the case integrates both a cylindrical hole and a cylindrical hole with 90 deg compound angle can greatly improve the film cooling performance with a higher discharge coefficient. However, the staggered case with an elliptical hole as both first- and second row gives the best film cooling effectiveness and the worst discharge coefficient due to the biggest resistance for the coolant flowing into the film hole.

In this study, the effects of elliptical and super-elliptical film holes on the adiabatic film cooling effectiveness under a density ratio of 2 and blowing ratios 0.5 and 1 are studied. Five different cases are designed by considering various length-to-width ratios and the baseline is the model with cylindrical film hole. The DES with the Realizable k-ε model is adopted for the five cases to investigate the cooling performance and clarify the film cooling mechanisms for all considered cases. The results show that with the increase of the blowing ratio, the vertical mixing between the hot gas and cooling jet becomes stronger due to the higher jet momentum and the promoted normal penetration into the mainstream. Therefore, the laterally averaged film cooling effectiveness for all cases is decreased at the higher blowing ratio. This phenomenon is most obvious for the baseline along the whole mainstream direction, while this phenomenon only becomes obvious near the hole region for the elliptical and super-elliptical models with the higher length-to-width ratio. Besides, it is found that the cases with the higher length-to-width ratio result in a better laterally averaged cooling performance compared with those with the lower length-to-width ratio at each blowing ratio. In addition, under the same length-to-width ratio, the elliptical model and super-elliptical model present similar film cooling performances. The model possessing a better cooling performance depends on the blowing ratio and the actual position along the streamwise direction.

Purpose This study aims to clarify the mechanism of film hole location at the span-wise direction of an internal cooling channel with crescent ribs on the adiabatic film cooling performance, three configurations are designed to observe the effects of the distance between the center of the ellipse and the side wall(Case 1, l = w/2, Case 2, l = w/3 and for Case 3, l = w/4). Design/methodology/approach Numerical simulations are conducted under two blowing ratios (i.e. 0.5 and 1) and a fixed cross-flow Reynolds number (Rec = 100,000) with a verified turbulence model. Findings It is shown that at low blowing ratio, reducing the distance increases the film cooling effectiveness but keeps the trend of the effectiveness unchanged, while at high blowing ratio, the characteristic is a little bit different in the range of 0 = x/D = 10. Research limitations/implications These features could be explained by the fact that shrinking the distance between the hole and side wall induces a much smaller reserved region and vortex downstream the ribs and a lower resistance for cooling air entering the film hole. Furthermore, the spiral flow inside the hole is impaired. Originality/value As a result, the kidney-shaped vortices originating from the jet flow are weakened, and the target surface can be well covered, resulting in an enhancement of the adiabatic film cooling performance.

Modern film cooling is an essential method to protect the turbine blade from the hot gas, and the issue about how to improve the film cooling performance has attracted much attention. In this study, a tree-shaped film cooling structure is carried out to improve the overall effectiveness and better decrease the metal temperature of the blade at the same time. To validate the superiority of the proposed structure, a series of numerical simulation cases are conducted under a typical blowing ratio of M = 0.764. The first case is a film cooling channel with a single film hole which with a diameter of 5 mm and is inclined by α = 45° relative to the mainstream direction. The other three cases are tree-shaped structures with one level, two levels and three levels of bifurcations. For all cases, the same boundary conditions and turbulence model (Realizable k-ε) are adopted, and three-dimensional numerical simulations are used as well to test the thermal performance of the models. It is found from the computing results that the overall effectiveness of the tree-shaped structure is improved more than 50% compared to the case with a single film hole, and the results also demonstrate that the more levels of the structure the lower the metal temperatures. Therefore, it is indicated that this research will make a contribution to a higher performance gas turbine.

在吹风比M为0.5,1.0和1.5的3种情况下数值研究了超椭圆孔型对气膜绝热冷却效率的影响,并基于流动特征深入分析了其冷却机制.结果表明:相比于基准的圆形孔模型,吹风比为0.5时超椭圆模型I(长宽比为2)在x/D<5区域内气膜绝热冷却效率较高,吹风比为1.0时在x/D<17.35区域内气膜绝热冷却效率较高,吹风比为1.5时,在整个流向上都具有较高的气膜绝热冷却效率.由于气膜在展向的覆盖范围较大,超椭圆模型II(长宽比为4)在3种不同的吹风比下相比于圆形孔模型和超椭圆模型I具有最佳的气膜绝热冷却效率,且吹风比越大,其优势越明显.

This study explores the effects of crescent ribs mounted in an internal cooling channel on the external adiabatic film cooling performance to evaluate the advantage of crescent ribs in gas turbine blade cooling. Three ribs including a transverse rib, a crescent rib concave to the stream-wise direction, and a crescent rib convex to the stream-wise direction are considered. For a fixed mainstream flow Reynolds number, two cross-flow Reynolds numbers and two blowing ratios are taken into account. The results show that the case with a crescent rib concave to the stream-wise direction provides higher film cooling effectiveness both at the lower cross-flow Reynolds number and at the higher cross-flow Reynolds number with higher blowing ratio while the case with a crescent rib convex to the stream-wise direction performs worst at any condition. It is found that the longitudinal vortices produced by crescent ribs concave to the stream-wise direction can promote the cooling air entering the film hole while that induced by the other crescent ribs are nonbeneficial for the cooling air entering the hole. The results indicated that a lower spiral intensity leads to counter-rotating vortices with lower intensity and thus results in better cooling effectiveness. However, it makes a narrow coverage of the target surface by the coolant, which leads to disadvantages upon the cooling performance. The relative merits among the cases at different cross-flow Reynolds numbers and blowing ratios are investigated based on the dominating mechanism.

For modern high-efficiency gas turbines, film cooling is an essential method to protect the turbine blade from the hot gas, and the issue about how to improve the film cooling performance has attracted much attention. This study presents a new design concept used for film cooling in gas turbine to improve the overall cooling effectiveness and better decrease the metal temperature of the blade at the same time. A tree-shaped film cooling structure is considered. To validate the superiority of the proposed structure, a series of numerical simulation cases are conducted at three typical blowing ratios (i.e. 0.5, 0.764, and 0.9). The first case is a film cooling channel with a single film hole with a diameter of 5mm and it is inclined by =45 degrees relative to the mainstream direction and the other three cases are tree-shaped structures with one level, two levels and three levels of bifurcations. Moreover, the same boundary conditions and turbulence model (realizable k-epsilon) are adopted, and three-dimensional numerical simulations are used for all cases. The computed results show that the higher the blowing ratio, the better is the overall effectiveness downstream the film holes of the tree-shaped structures, whereas the opposite is valid for the case with a single film hole. Additionally, the overall effectiveness of the tree-shaped structures is improved more than 50% compared with Case 1 with a single film hole, and the results also demonstrate that the more levels of the structure, the lower the metal temperatures will be. Therefore, it is indicated that this research will make a contribution to a higher performance gas turbine.

Reduced order model constitutes an efficient option to decrease the high computational cost of dynamical systems governed by partial differential equations (PDE). The technique based on proper orthogonal decomposition (POD) was first presented in the article [1] to generate a reduced set of basis functions for Galerkin representation of PDEs which results in approximate the simulation at any time point by solving an ODEs of time dependent coefficients. Our approach in this article targets the development of a non-intrusive reduction technique. We keep the same manner of obtaining basis functions, while approximating the time dependent coefficients using Kriging based surrogate model. The proposed method is then illustrated with an application to the simulations of heat diffusion systems on a thin rod and on a square plate. The numerical results illustrate the simulation using the proposed idea.