Compound Angle Research Articles

Deep learning method for fast prediction of film cooling performance

This study examines the predictive capability of deep learning method for adiabatic film cooling effectiveness distribution with variable operating conditions and geometric layouts. A conditional generative adversarial network is trained to establish nonlinear mapping from input to output. We embed the boundary condition information directly into the input tensor, thereby imparting the capability to address variable operating conditions. The processed input tensors include different blowing ratios M, incoming turbulence intensity Tu, geometry profile controlled by the inclination angle ϕ, compound angle θ, number of hole rows n, pitch between hole rows Px, and span-wise hole pitch Py. The output data are adiabatic film cooling effectiveness fields generated by Reynolds-averaged Navier–Stokes simulations. The prediction results are in good agreement with the computational fluid dynamics results in terms of various statistical assessments. Furthermore, compared with conventional methods of solving Navier–Stokes equations, predictions based on deep learning result in better response times. Therefore, the method proposed in this study is of high significance in the early design of cooling structures for turbine blades.

Predicting and optimizing multirow film cooling with trenches using gated recurrent unit neural network

The film cooling of cylindrical holes embedded in transverse trenches under superposition has shown promise for protecting the critical components of a high-pressure turbine from thermal damage. To optimize the relevant parameters and provide a suitable film cooling strategy, it is important to predict the effectiveness of lateral-averaged adiabatic film cooling with the trench effect on the surface of a blade. However, high-fidelity semi-empirical correlations for film cooling under superposition conditions with a trench have rarely been examined. This study establishes a gated recurrent unit (GRU) neural network model to predict the effectiveness of lateral-averaged film cooling under multiple-row superposition conditions with a trench. In general, a GRU neural network model is built with a large sequence of one-dimensional parameters, including the depth and width of the trench, compound angle, location of the hole, and blowing ratio. The computational fluid dynamics (CFD) method is used to provide a training dataset for the model. After careful testing and validation, the results predicted by the GRU agreed well with the CFD results. Moreover, the performance and robustness of the GRU were better than those of other recurrent neural network models, such as the long short-term memory model. Integrated with the GRU model, the sparrow search algorithm was adopted to optimize the parameters of the trench. The film cooling effectiveness of the optimized case improved by 1.6% compared with the best case, 28.5% compared with the worst case in dataset, and 23.5% compared with the no-trench case.

Effects of hole arrangement and trenched hole on multirow film cooling

Multirow film cooling is an advanced cooling method to provide effective surface cooling for gas turbine components exposed to high temperature. In this paper, the performance of multirow film cooling under different configurations is investigated numerically. The geometrical parameters, including the hole arrangement, hole orientation, and trenched hole, are considered. The numerical setup is validated before the performances of different cooling configurations are compared. The flow and heat transfer characteristics of the various cooling configurations are analyzed, and the different row-to-row interactions are revealed. For the configurations with standard holes, the staggered arrangement of simple angle holes achieves better cooling efficiency than the counterpart with inline configuration, while the inline arrangement with opposite compound angle holes provides the best cooling efficiency. For the configurations with trenched holes, the trench promotes the coolant uniform mixing, and the coolant stays more close to the effusion plate. Thus, the multirow cooling efficiency with trenched holes is better than the cooling configurations with standard holes.

Effect of Coolant Crossflow on Film Cooling Effectiveness of Diffusion Slot Hole With and Without Ribs

Abstract The coolant flow condition at the film hole entrance has a notable effect on film cooling effectiveness. The previous studies about internal ribbed crossflow effects are the hole with a circular inlet cross section. In this study, a diffusion slot hole with a race-track inlet cross section is examined in a low-speed wind tunnel by the pressure-sensitive paint (PSP) technique. The film cooling effectiveness of three different hole configurations are investigated: a normal diffusion slot hole, a compound angle diffusion slot hole, and a lateral inclination angle diffusion slot hole. Two internal perpendicular crossflow conditions with and without ribs for the 45 deg inline crossflow and the 135 deg counter crossflow are discussed. The blowing ratios are varied from 0.5 to 2.5 at a constant crossflow-to-mainstream velocity ratio of 0.36. A detailed method for the uncertainty analysis of the PSP is also presented. It is found that the normal diffusion slot hole always shows the best cooling performance than other holes. The ribs under the crossflow condition have a positive effect on the film cooling effectiveness for the normal diffusion slot hole even though the compound angle changes the hole’s orientation. However, the ribs have a negative effect on the film cooling effectiveness for the geometrically asymmetric diffusion slot hole.

Second law analysis of aerodynamic characteristics with flow temperature variations of simple angle and compound angle full coverage film cooling

The present investigation employs entropy generation to quantify aerodynamic characteristics with flow temperature variations, and the associated second law losses, which are present within a film cooled boundary layer produced by a unique full-coverage compound angle hole configuration. With this arrangement, an alternating sign for the compound angle β is employed from one streamwise row of holes to another, such that compound angle β is +30° in one row of holes, followed by −30° in the next row of holes. Entropy change distributions, entropy generation distributions, and mass-averaged overall exergy destruction from this compound angle arrangement are compared to results from a simple angle arrangement with β = 0°. These quantities are determined from flow field measurements of local flow temperature variations, and local stagnation pressure variations with film cooling. Within the investigation, full-coverage film cooling blowing ratio values range from 2.9 to 6.0, mainstream Reynolds numbers Rems range from 127,000 to 142,000, and effusion flow Reynolds numbers range from about 7000 to approximately 13,000. Distributions of local entropy generation and mass-averaged overall exergy destruction (both relative to freestream flow) are determined using three analysis approaches, which account for local flow temperature variations only, local flow stagnation pressure variations only, and variations of stagnation pressure and local flow temperature together. Similar qualitative trends of local entropy generation for the three different types of data are observed, which mean that temperature and stagnation pressure within the flow experience similar rearrangements by secondary advection and diffusion phenomena for the two film cooling arrangements. From a quantitative perspective, values associated with flow temperature variations only, are consistently larger than values associated with stagnation pressure variations only. Important local variations of local entropy generation are observed for the compound angle arrangement, which are due to skewed and non-symmetric film distributions, along with the associated tilted horseshoe-shaped vortex, which forms around each film coolant concentration.

Film cooling performance of blade pressure side with three-row film holes under rotating condition

Film cooling is an essential cooling method for high-temperature components of turbines. The film cooling performance on the pressure side of turbine blades with three-row film holes is investigated experimentally and numerically at a rotating speed of 600 rpm. Three test models composed of two types of hole arrangement (in-line and staggered) and two compound angles (β = 0° and 45°) are studied at five blowing ratios (M = 0.5, 0.75, 1.0, 1.25, and 1.5). The film trajectories on the pressure side are short, dissipate quickly, and deflected to the upper and lower sides. Upstream of the pressure side, the coolant coverage is poor near the tip due to the rotating effect, and no coolant is ejected near the hub at low M due to insufficient internal pressure. The best film cooling performance is at M = 0.75 for all three models in this study. Because of the large row space, the difference in film cooling effectiveness (η) between cases with the in-line and staggered arrangement is not significant at M = 0.5. When M ≥ 0.75, η is generally higher for the case with the staggered arrangement. Furthermore, the case with β = 45° shows a higher η than cases with β = 0°

Comparisons of Cooling Performance and Flow Characteristics of a Combustor Liner Plate with Compound Angle and Simple Angle Effusion Holes

Comparisons of Cooling Performance and Flow Characteristics of a Combustor Liner Plate with Compound Angle and Simple Angle Effusion Holes

Experimental study of combined influences of wall curvature and compound angle on film cooling effectiveness of a fan-shaped film-hole

Deep discussions of the combined influences of compound angle (CA), wall curvature and cooling air flowrate on the film effectiveness of a typical fan-shaped-hole as well as the cooling unsteadiness level were conducted, to acquire the proper cooling schemes in different regions of turbine blade. Typical CAs of 0°, 30° and 60° were designed at convex, concave, and flat walls. Blowing ratio (BR) of coolant-to-mainstream varied from 0.5 to 3.0. Both the turbulent dissipation and vorticity of secondary vortices determine the CA effect on film effectiveness. The 30°-jet can achieve the highest film effectiveness, and such trend is non-sensitive to the BR and wall curvature. The CA-induced largest increment can reach about 50%. The wall curvature effects on film effectiveness can be obviously changed by the CA. Relative to the flat wall, the angled jet at convex wall can generate the largest increments of 26%. In general, the fan-shaped-hole with CA = 30° is strongly proposed at the convex wall, due to the highest film effectiveness and the lowest cooling unsteadiness level. However, the angled-holes at the concave wall can produce a negative influence on the durability, due to the increment in unsteadiness-level above 20% relative to the other walls.

Effect of length-to-diameter ratio on film cooling and heat transfer performances of simple and compound cylindrical-holes in transverse trenches with various depths

Advances in trenched-hole film cooling result in a fact that short-holes exposing in a transverse trench have a significantly large potential for application in designs of future double-wall cooled blade. In present work, combined influences of hole-length, trench-depth, compound angle and cooling air flowrate on the film effectiveness and heat transfer features of trenched-holes were discussed deeply. Film effectiveness and heat transfer coefficient were measured by an infrared thermal imaging system. Numerical simulation as an auxiliary tool was conducted to provide necessary flow details. Two typical length-to-diameter ratios of L/D = 2 and 5, three trench-depths of H = 0.5D, 0.75D and 1.0D and two compound-angles of film-hole of 0° and 45° were designed. Cooling air flowrate was controlled in a relatively large range from 0.5 to 4.0 in averaged blowing ratio (BR). The results revealed the various jet-mechanisms caused by L/D while relatively regular variations of turbulent intensity of jets. Thus, the complicated trends in film effectiveness while regular trends in heat transfer coefficient can be clearly captured. The combined influences of trends above can bring to the more undesirable thermal protections for the short-hole jet. The L/D-induced decrement in area-averaged net heat flux reduction (NHFR) can reach 60% at most. To effectively improve film coverage and NHFR, the short-holes were properly embedded in the deeper trench. And the sensitivity analysis of trench-depth to discharge coefficient showed the negligible variation below 5%. The NHFR of the shallowest trench can be improved through application of compound angle, inducing an enlarged aerodynamic loss below 10%.

Large Eddy Simulation of Film Cooling Involving Compound Angle Hole with Bulk Flow Pulsation

The effects of pulsations in the main flow on film cooling from a cylindrical hole with a spanwise injection angle (orientation angle) are analyzed using numerical methods. The hole is located on a flat plate with a 35° inclined injection angle, and the compound angle denotes the orientation and inclination angles. The film cooling flow fields for the sinusoidal flow pulsation of 36 Hz from a cylindrical hole with 0° and 30° orientation angles at the time-averaged blowing ratio of M = 0.5 are simulated via large eddy simulation (LES). The CFD results are validated using the experimental data and compared to the Reynolds-averaged Navier–Stokes (RANS) and URANS results. The results reveal that if the pulsation frequency goes from 0 to 36 Hz, the adiabatic film cooling effectiveness decreases regardless of the compound angle; however, the film cooling for the 30° orientation angle exhibits better performance than that for a simple angle (0°). Moreover, if 36 Hz pulsation is applied, the film cooling effectiveness obtained by unsteady RANS exhibits a large deviation from the experimental data, unlike the LES results. The credibility of the LES results relative to the experimental data is demonstrated by comparing the time-averaged η and the phase-averaged temperature contours. The LES results demonstrate that LES can more accurately predict η than the experimental data; in contrast, URANS results are highly overpredicted around the centerline of the coolant spreading. Thus, LES results are more consistent with the experimental results for the time- and phase-averaged temperature contours than the URANS results.

Effects of Holes Arrangement on the Superposition Characteristics of Film Cooling Effectiveness

The purpose of the current research is to test and analyze the applicability of the Sellers model in different arrangements and configurations of film cooling holes and then to modify the Sellers model to improve the accuracy of the superposition prediction. The film cooling effectiveness distributions at different blowing ratios are obtained using the infrared thermometry technology. The flat plate experiments are completed in a low-speed closed-loop wind tunnel facility. The mainstream Reynolds number based on the film hole diameter is 6300, and the blowing ratios range from 0.8 to 1.8. The superposition characteristics are described in three different cases: double rows of cylindrical holes in an inline arrangement, double rows of cylindrical holes in a staggered arrangement, and double rows of compound angle holes in an inline arrangement. The results indicate that the Sellers model cannot accurately predict the film cooling effectiveness in certain conditions, which is mainly attributed to the interaction between counter-rotating vortex pairs of the adjacent rows and the increasing momentum of mainstream near the wall surface. For all cases, the corresponding modified superposition prediction methods are given in this paper.

Direct and Inverse Model for Single-Hole Film Cooling With Machine Learning

Abstract The direct prediction model for adiabatic film cooling effectiveness distribution and inverse prediction model for design parameters are studied in this article. Convolutional neural networks (CNNs) are trained on a set of simulated adiabatic film cooling effectiveness contours parameterized by blowing ratio, density ratio, mainstream turbulence intensity, injection angle, and compound angle. The direct model and the inverse model are able to approximate the data in the test set with plausible accuracy. The absolute error of spatial averaged effectiveness no larger than 0.03 could be obtained in the test set by a direct model with time consumption less than 1 ms for a single case. The inverse model is the first model of its kind, which accomplished the inverse mapping from contours to parameters. It has been demonstrated that the concatenation of inverse model with the pretrained direct model, which can be treated as a complex loss function, has preferable approximation performance compared with simple mean squared error (MSE) loss function in the training of the inverse model, thus confirming the necessity of adopting specialized modeling strategies for inverse problems.

Influence of Biot number and geometric parameters on the overall cooling effectiveness of double wall structure with pins

In this paper, the overall cooling effectiveness of double wall cooling structures with pins is experimentally investigated on the low-speed wind tunnel. The analysis of the single cooling technology contributions to improve the double wall cooling performance is provided. The effect of Biot number (Bi = 0.03, 0.32, 2.25) and the film hole size (de= 2 mm, 3 mm, 5 mm) on the overall cooling effectiveness are also studied. In order to further improve the overall cooling performance, the present study proposes two new shapes of film hole patterns with compound angles (compound configuration, double configuration). By numerically analyzing the cooling effectiveness of the outer film cooling and the heat transfer performance of the inner target wall, the mechanism by which film hole size and new film hole patterns affect the overall cooling performance of double wall structures is clarified. The results show that the area-averaged overall cooling effectiveness of the double cooling technology is more than 30% higher than that of the two single cooling technologies and the contribution of impingement cooling is higher than that of effusion cooling at high blowing ratios. The cooling performance of the double wall structure is greatly influenced by the Biot number of effusion plates. Low Biot number means higher thermal conductivity, resulting in higher overall cooling effectiveness under the same thermal load conditions. Increasing the film hole size could enhance the film cooling performance outside of the effusion plate, suppressing the unfavorable results of lower heat transfer performance at the inner side. The fitting correlation equation obtained using the binary linear regression method agrees well with the experimental results, with a maximum deviation of less than 4%. Both of the two compound structures can effectively improve the overall cooling performance of the double wall structure. The double configuration has the best cooling performance and the area-averaged cooling effectiveness improves by 15.1% compared to the reference configuration under the condition of M = 1.5. The experimental results provide a vital database for the future double wall cooling design.

Second Law Analysis of Aerodynamic Gains Associated with Simple Angle and Compound Angle Full Coverage Film Cooling

Second Law Analysis of Aerodynamic Gains Associated with Simple Angle and Compound Angle Full Coverage Film Cooling

Investigations of improved cooling effectiveness for ramp film cooling with compound angle film cooling jets

PurposeThis paper aims to investigate the film cooling effectiveness (FCE) and mixing flow characteristics of the flat surface ramp model integrated with a compound angled film cooling jet.Design/methodology/approachThree-dimensional numerical simulation is performed on a flat surface ramp model with Reynolds Averaged Navier-Stokes approach using a finite volume solver. The tested model has a fixed ramp angle of 24° and a ramp width of two times the diameter of the film cooling hole. The coolant air is injected at 30° along the freestream direction. Three different film hole compound angles oriented to freestream direction at 0°, 90° and 180° were investigated for their performance on-ramp film cooling. The tested blowing ratios (BRs) are in the range of 0.9–2.0.FindingsThe film hole oriented at a compound angle of 180° has improved the area-averaged FCE on the ramp test surface by 86.74% at a mid-BR of 1.4% and 318.75% at higher BRs of 2.0. The 180° film hole compound angle has also produced higher local and spanwise averaged FCE on the ramp test surface.Originality/valueAccording to the authors’ knowledge, this study is the first of its kind to investigate the ramp film cooling with a compound angle film cooling hole. The improved ramp model with a 180° film hole compound angle can be effectively applied for the end-wall surfaces of gas turbine film cooling.

Large eddy simulation of compound angle effects on cooling effectiveness and flow structure of fan-shaped holes

Large eddy simulation (LES) was utilized to investigate the influence of applying various compound angle (CA), on film-cooling effectiveness and turbulent flow structures. The baseline cooling hole was a 7-7-7 laidback fan-shaped hole, where this hole is located at a flat plate surface with a pitchwise spacing of 6D, and the hole was inclined at 30-degrees with respect to the mainstream hot-gas flow. Five different cooling hole orientations (CA0, CA15, CA30, CA45 and CA60) were numerically simulated using a constant density ratio of 1.5 and two blowing ratios (M = 1.0 and 3.0). The time-averaged computational results for the thermal and flow fields were validated by comparison with experimental data from previous literature. The simulation results revealed that under a low blowing ratio (M = 1.0), cooling performance was not affected significantly by the compound angle, but at the higher blowing ratio there was a considerable improvement of 40% for the CA60 hole over the CA0 hole, this improvement was especially pronounced in the lateral direction. The vorticity-field investigation showed that as the compound angle increased, the magnitude of the streamwise vorticity also increased while it becoming more asymmetric. In addition, time-space evaluation and spectral analysis of the velocity fluctuations indicates higher unsteadiness and greater turbulent statistics when using holes with larger compound angles.

Heat Transfer Coefficient Augmentation for a Shaped Film Cooling Hole at a Range of Compound Angles

Abstract Film cooling holes with shaped diffusers are used to efficiently deliver coolant to the surface of a gas turbine part to keep metal temperatures low. Reducing the heat flux into a component, relative to a case with no coolant injection, is the ultimate goal of film cooling. This reduction in heat flux is primarily achieved via a lower driving temperature at the wall for convection, represented by the adiabatic effectiveness. Another important consideration, however, is how the disturbance to the flowfield and thermal field caused by the injection of coolant augments the heat transfer coefficient. The present study examines the spatially resolved heat transfer coefficient augmentation, measured using a constant heat flux foil and infrared (IR) thermography, for a shaped film cooling hole at a range of compound angles. Results show that the heat transfer coefficient increases with the compound angle and the blowing ratio. Due to the unique asymmetric flowfield of a compound angle hole, a significant amount of augmentation occurs to the side of the film cooling jet, where the very little coolant is present. This causes local regions of increased heat flux, which is counter to the goal of film cooling. Heat transfer results are compared with adiabatic effectiveness and flowfield measurements from a previous study.

Large Eddy Simulation of Film Cooling with Forward Expansion Hole: Comparative Study with LES and RANS Simulations

The forward expansion hole improves the film cooling effectiveness by reducing the penetration of the coolant jet into the main flow compared to the cylindrical holes. In addition, compound angles improve the film cooling effectiveness by promoting the lateral spreading of the coolant on a wall. Evidently, the combination of a compound angle and shaped hole further improves the adiabatic film cooling effectiveness. The film cooling flow with a shaped hole with 15° forward expansion, a 35° inclination angle, and 0° and 30° compound angles at 0.5 and 1.0 blowing ratios was numerically simulated with Large Eddy Simulations (LES) and Reynolds-averaged Navier–Stokes (RANS) simulations. The results of the time-averaged film cooling effectiveness, temperature, velocity, and root-mean-square (rms) values of the fluctuating velocity and temperature profiles were compared with the experimental data by Lee et al. (2002) to verify how the LES improves the results compared to those of the RANS. For the forward expansion hole, the velocity and temperature fluctuations in the LES contours are smaller than those of the cylindrical hole; thus, the turbulence and mixing intensity of the forward expansion hole are weaker and lower than those of the cylindrical hole, respectively. This leads to the higher film cooling effectiveness of the forward expansion hole. By contrast, the RANS contours do not exhibit velocity or temperature fluctuations well. These results are discussed in detail in this paper.

Investigation on flow field and heat transfer characteristics of film cooling with different swirling directions for coolant flow

In this paper, a hexagonal prism inlet chamber is used to form a swirling flow for the film cooling, and three kinds of compound angle of film hole ( γ = 10°, 20°, 30°) with clockwise swirling or counterclockwise swirling are used for numerical simulation studies. The influence of different compound angles of film hole and the swirling directions for the film cooling effectiveness are obtained. The results show that the film cooling effectiveness and spanwise cooling coverage range of the clockwise swirling or counterclockwise swirling flow both are low when the compound angle of film hole is 10°. With the increasing compound angle of film hole, the kidney shaped vortex of film hole exit gradually weakens until it disappears, which reduces the entrainment effect by the coolant jet. So that the spanwise coverage range of two swirling modes is obviously improved. When the compound angle of film hole is 30° compared to 10°, the average spanwise film cooling effectiveness of clockwise swirling and counterclockwise swirling are increased by about 133.75 and 212.6%, respectively. The average spanwise film cooling effectiveness on the downstream of film hole for counterclockwise swirling is increased by about 140% compared with clockwise swirling.

Numerical investigation on the effect of upstream ramps on film cooling performance with compound angles

Numerical investigation on the effect of upstream ramps on film cooling performance with compound angles