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The performance of turbomachinery is largely affected by the nonuniform boundary conditions caused by the coupling between neighboring parts, such as the inlet distortion and hot streak. Existing works study this problem by comparing the flow fields with uniform and nonuniform boundary conditions, which is cost extensive. In this work a new and efficient method is developed by computing the sensitivities of arbitrary performance metric relative to the boundary conditions and this method quantitatively describes how the disturbance on the boundary surface affects the performance. The adjoint method popular in the design optimization is extended to current field for the efficient computation of the sensitivity. The extra cost is independent of the number of parameters describing the nonuniform distribution. Accuracy of the adjoint boundary sensitivity is validated against analytical results for a converging–diverging nozzle case. Its applications in a representative case are detailed and discussed in this paper. Current method provides a new tool, also direct guides to minimize the negative effect and improve the performance utilizing the adjoint boundary sensitivity.

An optimization framework is developed for the film cooling hole shape design to achieve highest film cooling effectiveness with affordable cost. A key to this design method is the development and applications of a multi-fidelity model (MFM) to improve the efficiency of surrogate model construction. To construct multi-fidelity model, empirical correlations from existing literature are utilized as low-fidelity data and Reynolds-Averaged Navier-Stokes (RANS) simulations provide high-fidelity data. Compared with single-fidelity surrogate models, multi-fidelity model developed in this work combines vast existing knowledge about shaped film cooling hole and three dimensional numerical simulation. As a result, the computation cost has been substantially decreased by 64.5% while accuracy is maintained with similar level, which provides a firm basis for the optimization. Considering three geometric parameters as design variables, i.e. laidback angel, lateral angle, and hole length-diameter ratio, the shaped hole is optimized with genetic algorithm (GA) combined with sequential quadratic programming (SQP) algorithm. After the optimization, an experiment campaign is further carried out to validate the optimization result using pressure sensitive paint (PSP) technology. With current multi-fidelity model, the spatially averaged film cooling effectiveness has been improved by 39 % compared to the baseline, which is an already well-designed shaped hole and the improvement is also verified by experiment. This work verifies the effectiveness of current multi-fidelity model for the design and optimization of shaped film cooling hole for better performance.

In modern aero-engine and gas turbine, the hot streak and residual swirl caused by the combustor have strong impact on both aero and thermal performances of the high-temperature turbine. Due to different design philosophies of combustors and turbine, one combustor usually matches two or more vanes and the resultant mismatching effect is numerically investigated with unsteady simulation where one nonuniform core faces two Nozzle Guide Vane (NGV) blades. Results indicate that the nonuniformity clocking position dominates the averaged-temperature, while the swirl orientation dominates the radial distribution. The mismatching effect strongly impacts both time-averaged and instantaneous performances, in that neighboring blades of NGV have averaged-temperature difference of 10.5 K, and it also halves the base frequency and amplifies unsteady variation in the rotor passage. By analyzing both aero and thermal results from a matrix of four cases, the LE-pos configuration has the best performance. The complex transportation of the nonuniformity in the LE-pos case is detailed and the unsteady interactions between the inlet nonuniformity and the complex flow topology are analyzed. The residual swirl carries the hot streak fluctuating radially in rotor passages and redistributes the temperature on rotor surface. Results from this work highlight the necessity of considering the mismatching effect in gas turbine design optimization.

In modern aero-engine and gas turbine, the highly loaded turbine leads to strong secondary flow by which the main flow and the film cooling jets are driven from the pressure side to the suction side. As a result, the cross flow has considerable influences on the performance of film cooling jets in the endwall region. In this work, the effects of cross flow on the shaped-hole film cooling performance are investigated both experimentally and numerically. Experimental studies are conducted in a curved channel which simulates the real turbine blade environment with the blowing ratio from 0.5 to 2.5. Numerical studies are also conducted to obtain detailed information about vortical structures. Results show that the cross flow changes the relative position of the two pairs of kidney vortices generated at the outlet of the shaped hole. The negative kidney vortices are stuck to the endwall due to the lift force and they decay faster downstream. The coolant is driven by the cross flow to migrate along the radial pressure gradient direction. And the coolant near the endwall migrates further. The peak value of the cooling effectiveness is suppressed; however, the laterally averaged cooling effectiveness is increased, especially at high blowing ratio. An analytical model describing the flow topology about coolant jets with cross flow is proposed and results from this work may help to understand the film cooling behaviour affected by real complicated flow structures in the engine environment.

The swirl generator is widely used in lean-burn combustor to guarantee flame stability and reduce NOx emissions. Thus, the non-uniformities induced by the swirler would affect and damage film-cooling effectiveness on the turbine components, even blow-off coolant coverage, to some certain extent. The arrangement of film-cooling holes was normally designed to be perpendicular to the axial direction and in standard straight row. In this work we experimentally studied the effects of inlet swirl and mass flow ratio on traditional film cooling holes arrangement and a new arrangement pattern whose holes are located along the isobars. Results indicated that the swirl perturbation would damage film coverage. The film-cooling effect of endwall on which the holes are along the isobars, is invariably more promising than that of endwall on which hole arrangement is perpendicular to axial with the same mass flow of coolant, whether the inlet conditions is uniform or not. Keywords: Films-cooling, Holes locating, Isobaric, Swirling flow, Turbine design

This work develops a new and effective method to predict the 2-D cooling effectiveness distribution. The assumption in the existing 1-D method is abandoned and replaced by a scalar diffusion equation to model the lateral spreading of the coolant. The proposed model can be used for predicting 2-D multi-row cooling performance and is validated over four arrangements of double-row cooling holes against in-house experimental data. The paper further presents the advantages of the current method over the classic 1-D method. 2-D distributions for different multi-row configurations are successfully obtained and the relative error is reduced to 19.77% as opposed to that of 45.65% with the 1-D model. The time consumption by the proposed method is on the order of 1 × 1 0 − 3 s which is exceedingly efficient for the cooling design process. To sum up, the proposed method is accurate, capable of 2-D multi-row modeling and of simple form and high efficiency. Hence it is potentially an effective tool for film cooling design.

Strong secondary flow results in substantial aerodynamic loss for highly-loaded turbine. Accurate prediction of the complicated flow structures proposes challenges to the widely used Reynolds Average Navier-Stokes (RANS) approach. This work employs the hybrid RANS/Large Eddy Simulation (LES) method to study the unsteady flows for a highly-loaded turbine blade, with both flat endwall and optimized contoured endwall. Evolution of the unsteady flows in the endwall region is analyzed, with emphasis on the loss generation mechanism. Results show that for the flat endwall, the horseshoe vortex system is highly unsteady and is a significant source of unsteadiness in both the passage and the wake region. It contributes to the unsteady passage vortex, also the earlier breakdown of the trailing edge shedding vortex. The Probability Density Function (PDF) histogram of velocity in the wake region is bimodal, implying the perturbations from two mechanisms. For the contoured endwall, the unsteady evolution of the horseshoe vortex is blocked, which results in significantly reduced unsteadiness, also the merge between the horseshoe vortex with the passage vortex is prevented. Effect of the flow unsteadiness on the loss generation is assessed based on the entropy generation rates contributed by the time-averaged flow and the fluctuations. The effect of unsteadiness is two-fold: unsteady perturbations trigger the vortex breakdown into small-scale structures and thus weakened wake velocity deficit and loss generation; however, in both the passage and the wake region the entropy generation by the fluctuations are remarkable. For the contoured endwall, due to the reduced flow unsteadiness, loss generation contributed by the fluctuations are much smaller compared to the flat endwall. The results highlight the importance of including the loss generation by the fluctuations, also a possible mechanism to reduce the secondary loss by attenuating the flow unsteadiness with the contoured endwall.

Film cooling is an important cooling method for the high-temperature components of modern aero-engines. There have been many previous studies on the influences of compound angle on film cooling performance, most of which are conducted in the ideal flat plate environment with zero pressure gradient, and the results indicate that at high blowing ratios, a large compound angle tends to improve the film cooling performance. However, in this work, it is found that a large compound angle tends to decrease the film cooling performance significantly with the influences of endwall lateral pressure gradient. A curved tunnel with constant width is employed to generate lateral pressure gradient similar to that in the endwall region of real turbine blade. It is shown that the crossflow near the endwall surface is the most obvious flow characteristic in this flow environment. Based on this discovery, we further conduct research on the influences of compound angles on film cooling performance in a curved tunnel both with numerical and experimental approaches. A well-designed laidback fan-shaped film cooling hole is used in this work. The experimental results show that for a film cooling hole with a large compound angle under blowing ratios ranging from 1.0 to 3.0, film cooling performance is reduced significantly under the environment of endwall lateral pressure gradient compared with zero pressure gradient environment. Detailed numerical results further indicate that due to the interaction between endwall crossflow and the strong single kidney vortex created by the large compound angle hole, large amounts of coolant are lifted away from endwall surface, which results in poor cooling performance. A topological model on the interaction between endwall crossflow and kidney vortices is proposed to help illustrate this phenomenon. The results of this work suggest that turbine cooling designers carefully consider the negative influence of large compound angles on endwall film cooling due to the lateral pressure gradient.

Film cooling is an important technology in protecting the turbine blade of modern aero-engine and gas turbine. Besides the widely studied parameters including the cooling hole geometry and blowing ratio, film cooling effectiveness is also affected by the crossflow in the internal cooling channel, which causes off-design inflow directions of the cooling hole. In-hole counter-rotating vortex pair is observed which accounts for the effect of internal crossflow on the film cooling. The current paper numerically studies the effect of internal channel flow on the film cooling performance by comparing the results of three configurations. A theoretical model about the boundary layer deformation is proposed to explain the formation of in-hole vortices based on the vortex dynamics, and two comparative cases with slip and no-slip channel wall respectively are used to highlight the importance of internal channel flow boundary conditions. By comparing adiabatic film cooling effectiveness under varying blowing ratios and internal crossflow velocities, it is shown that internal crossflow plays an important role in film cooling performance. Enhanced cooling effectiveness can be obtained at internal co-flow conditions where in-hole vortices has the opposite direction with downstream kidney vortices. Due to the competitive effects of distorted velocity profile and in-hole vortices, an optimal velocity of internal crossflow can be found at given blowing ratio and the optimal velocity magnitude slightly increases with increasing blowing ratio.

The strong secondary flow and the interaction between multiple vortices result in substantial aerodynamic losses in the endwall region of the highly-loaded turbine. Accurate predictions of complex turbulence characteristics propose severe challenges to the widely used Reynolds-Averaged Navier-Stokes (RANS) approach. This work adopts a high accuracy hybrid RANS/Large Eddy Simulation (LES) method on a highly-loaded turbine blade for which the Reynolds number is 611,000 and the exit Mach number is 0.8. Results verify that, in contrast with the RANS method, the hybrid method can provide more accurate predictions and detailed small-scale flow structures than the RANS simulation. Analysis of the Reynolds stresses predicted by the hybrid method reveals the complex turbulence characteristics in the endwall region and highlights shortcomings of Reynolds stresses predictions existing in the RANS method in the highly-loaded turbine blade environment. To analyze turbulence characteristics near the blade endwall, the Lumley triangle method is applied to quantify the turbulence anisotropy degree. Based on fine flow field structures, the proper orthogonal decomposition (POD) method is used to extract the dominant flow structures from the unsteady hybrid method results. The turbulence kinetic energy budget is employed to study dominant terms in turbulent flow. The total pressure loss coefficient based on the first law of thermodynamics and the entropy generation rate (EGR) based on the second law of thermodynamics are both used to study the loss generation mechanism in the endwall region. Predicted turbulence characteristics and flow mechanism can provide guide towards low loss design and flow control of the turbine blade.

In this paper we explore a new hybrid method for the near-wall treatment of turbulent flow computation with Cartesian mesh. Cloud of points are generated to resolve the boundary layer and they are generated along wall-normal directions. Special attention is paid at the treatment of singular point for the use of current method for complex geometry. Multiple marching directions are defined for enough resolution and smooth transition between near-wall and off-wall solvers. These points demonstrate one dimensional structure in the wall-normal direction and it offers the opportunity of improved accuracy. By exploring this property, a hybrid methodology combines high order scheme in the wall-normal direction and meshless method in the streamwise direction is proposed. Also a hybrid LU-SGS/line-implicit time integration method is developed based on this property. The use of high order scheme for the wall-normal flow derivative significantly improves the overall accuracy, especially in the area with curved solid surface. The current hybrid method is verified using Method of Manufactured Solution (MMS) and a series of turbulent test cases. Results indicate good agreement with available experimental values and improved predictions and robustness compared to the meshless method.