Aerothermal Optimization Research Articles

Aerothermal Optimization of Film Cooling Hole Locations on the Squealer Tip of an HP Turbine Blade

Abstract This article presents a time-efficient method to optimize the positions of film cooling holes on a gas turbine blade's squealer tip for cooling and aerodynamic performance. A computational approach is employed for the optimization, including validations against experiments. Five discrete film cooling holes are considered, and two different blowing ratios of 0.4 and 1.0 are studied. The positions of cooling holes on the tip along the tangential direction are varied as the input parameters of optimization. The multi-objective optimization uses an algorithm with an artificial neural network for fast fitness function predictions. The best cooling configuration found by the optimization achieves a 13.43% reduction in total heat flux and a 0.4% increase in aerodynamic loss when the blowing rate is 1.0. Including the casing relative motion in the computations results in a total pressure loss coefficient increase of about 8% for both blowing ratios. For M = 1.0, imposing the casing's motion results in a 10.2% reduction in total heat transfer to the tip compared to the stationary casing. For the lower blowing rate of 0.4, the total heat flux reduction to the tip is 12.0% because of the imposed casing motion. Hence, the cooling effectiveness can be improved by employing the particular position optimization method presented in this study. The results suggest that experimental and computational heat transfer studies on cooled turbine blade tips, especially in cascade arrangements, need to consider the relative motion of the blade tip.

Aerothermal optimization of turbine cascade squealer tip with non-uniform squealer height

The squealer tip has significant influence on both the aerodynamic and heat transfer characteristics of the high-pressure turbine blade. However, due to the complexity of parameterization and meshing of the squealer and the complicated flow structure within the over-tip region, the existing squealer designs in the open literature have constant squealer heights. In this paper, the design space to the squealer height with non-uniform squealer height is extended and the new flow features it may bring are investigated. A parameterization system specifically designed for the non-uniform squealer height using five control parameters is implemented to automatically generate the geometry and hybrid meshes. Combining it with the multi-objective optimization system using genetic algorithms, a transonic turbine cascade squealer tip is optimized employing Reynolds-averaged Navier–Stokes k–ω shear stress transport model. The main objective of this study is to obtain a squealer configuration with the lowest total pressure loss coefficient and heat transfer coefficient. The optimum configuration with non-uniform squealer height achieves improvements in both the aerodynamic efficiency and the heat transfer performance, relative to the baseline conventional squealer tip geometry with the constant squealer height. Additionally, this work demonstrates that a flow structure in which the main flow forms a “blanket” below the leakage flow in the squealer is beneficial for aerothermal performance, especially reducing heat transfer losses, which provides valuable insight into the squealer tip design of advanced high-pressure turbines.

An Artificial Neural Network (Ann) Based Aerothermal Optimization of Film Cooling Hole Locations on the Squealer Tip of an Hp Turbine Blade

An Artificial Neural Network (Ann) Based Aerothermal Optimization of Film Cooling Hole Locations on the Squealer Tip of an Hp Turbine Blade

Aero-thermal optimization of a gas turbine blade endwall with non-axisymmetric contouring and purge flow

With the ever-increasing turbine inlet temperature and blade loadings, the thermal management for the endwall of gas turbines is gaining wide attention. Specifically, the increasing blade loadings intensify the cross flows and the blade-endwall interactions, making the design of turbine endwalls operating in such harsh thermal environments a really challenging problem. To resolve such a problem, we propose a novel non-axisymmetric endwall, which is shaped both near the blade leading edge and between the two adjacent blades. The effectiveness of the proposed non-axisymmetric endwall is well demonstrated on a typical large-turning-angle gas turbine with a purge slot. More specifically, in order to obtain a solution that can achieve a good balance between the gas turbine aerodynamic and thermal performance, we carry out three separate optimizations for the non-axisymmetric endwall. The aerodynamic loss, the film cooling effectiveness and the heat transfer coefficient are taken as the objective functions, respectively, for the optimization process. The optimal solution aiming to minimize the heat transfer coefficient achieves the most desirable performance. This solution substantially reduces both the aerodynamic loss and thermal loads at the turbine endwall, since it is effective to suppress both the horseshoe vortex and the cross flows. Furthermore, through a fundamental flow-thermal analysis of the three optimal solutions, an insight into the effects of non-axisymmetric endwall on gas turbine aero-thermal performance is obtained and guidelines for the aero-thermal design of non-axisymmetric endwalls are provided.

Aero-thermal optimization of the rim seal cavity to enhance rotor platform thermal protection

Abstract The flow field in the rotor-stator rim cavity is controlled by both the instantaneous distortion caused by rotor and stator airfoils. Naturally one would then assume that the design of optimal rim seal geometries would require full unsteady turbine stage simulations, that would then require an experimental assessment. This manuscript presents a reduced-order approach, neglecting the obvious unsteady interaction effects, to optimize the cavity geometry with a two-dimensional axisymmetric approach, making it possible to explore a wide range of geometries followed by an experimental assessment in a linear cascade. Two parameterization strategies are presented, coupled with a genetic optimizer to maximize thermal protection to the rotor rear platform while minimizing the cooling massflow required. This reduced-order optimization scheme was then assessed at different levels of sophistication to assess the effect of rotation, the vanes, and the rotor geometry with a series of increasing levels of fidelity to the real turbine conditions. Finally, this paper demonstrated the sensitivity of the optimal geometries to variations in the axial gap and purge coolant total pressure.

Aerothermal Optimization of Turbine Squealer Tip Geometries With Arbitrary Cooling Injection

Abstract The optimization of the turbine rotor tip geometry remains a vital opportunity to create more efficient and durable engines. Balancing the aerodynamic and thermal aspects, while maintaining the mechanical integrity, is key to reshape one of the most vulnerable and life-determining parts of the entire turbine. The ever-increasing turbine gas temperatures, combined with the difficulty of cooling the tip and the aerodynamically penalizing nature of the overtip leakage vortex, make the design of the tip a truly multidisciplinary challenge. While many earlier efforts focused on uncooled geometries or studied the aerothermal impact with a fixed cooling configuration, the current paper presents the outcome of a multi-objective optimization where both the squealer rim geometry and the cooling injection pattern were allowed to vary simultaneously. This study explores a significantly wider design space, seeking a further synergistic aerothermal benefit through the combination of a quasi-fully arbitrary cooling arrangement, with mutating squealer rim structures. Specifically, the current manuscript presents the results of over 330 cooled and uncooled squealer tip geometries. The high-pressure turbine tip was automatically altered using a novel parametrization strategy adopting a maximum of 40 design variables to vary the squealer rim structures, as well as the size and location of the various cooling holes. The aerodynamic and thermal characteristics of every design were evaluated through Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) simulations with the k–ω shear-stress transport (SST) model for the turbulence closure, adopting an unstructured hexahedral grid typically containing more than 8 × 106 cells. A multi-objective differential evolution algorithm was used to obtain a Pareto front of designs which maximize the aerodynamic efficiency, while minimizing the overtip thermal loads. Eventually, a detailed investigation and robustness study was performed on a set of prime squealer geometries, to further investigate the aerodynamic flow topology and the effect of various cooling injection schemes on the heat transfer patterns.

Aerothermal Optimization of Bladeless Turbines

Abstract The harnessing of mechanical power from supersonic flows is constrained by physical limitations and substantial aerodynamic losses. Bladeless axial turbines are a viable alternative to extract power in such harsh conditions without restricting the operating conditions. In this paper, we present a shape optimization of the wavy surface of bladeless turbines to maximize the power extraction, while minimizing convective heat flux and pressure losses. First, a baseline geometry was defined and an experimental campaign was carried out on the baseline wavy surface of the bladeless turbine at supersonic conditions. Pressure, heat flux, and skin friction measurements were compared with the Reynolds averaged Navier–Stokes results. Afterward, an evaluation routine which consisted of the geometry and grid generation, solving, and postprocessing was implemented within a multi-objective optimization routine to maximize the pressure force and minimize heat flux and pressure loss. Finally, a three-dimensional assessment in terms of power, heat load, and pressure drop was performed for the best performing geometry with the commercial solver cfd++ of Metacomp.

Multi-objective optimization of three rows of film cooling holes by genetic algorithm

Aero-thermal optimization on multi-rows of film cooling over a flat plate has been performed to optimize the inclination angles. Hence three cylindrical holes with injection angles of ?, ?, and ? have been considered. The cooling hole has a 3 mm diameter and an inclined angle between 25-35?. Numerical simulations were performed at a fixed density ratio of 1.25 and blowing ratio of 0.5. The control-volume method with a SIMPLEC algorithm has been used to solve the steady-state RANS equations with SST k-? turbulent model. The injection angles of the holes are selected as the design variables to perform the optimization of three rows of film cooling. In order to evaluate the performance of holes arrangement, two objective functions are defined based on aerodynamic losses and adiabatic film cooling effectiveness. The curve fitting method is used to find the optimal point of objective functions. The optimizations have been performed using the genetic algorithm method. Results of the present study show that the best performance of three rows of cooling holes was achieved in inclined angles 25.45, 32.85, and 33.1.

DAFoam: An Open-Source Adjoint Framework for Multidisciplinary Design Optimization with OpenFOAM

The adjoint method is an efficient approach for computing derivatives that allow gradient-based optimization to handle systems parameterized with a large number of design variables. Despite this advantage, implementing the adjoint method for a partial-differential-equation-based primal solver is a time-consuming task. To lower the barrier for adjoint implementations, an object-oriented framework (DAFoam) is proposed to rapidly implement the discrete adjoint method for any steady-state OpenFOAM primal solver by adding or modifying only a few hundred lines of source code. In this paper, the DAFoam framework is introduced and the proposed object-oriented adjoint development process is illustrated. Using this strategy, the adjoint method is implemented for eight primal solvers, five turbulence models, and one radiation model in OpenFOAM. Excellent adjoint speed and scalability, with up to 10 million cells and 1536 CPU cores, and an average error in the adjoint derivatives of less than 0.1% are achieved. Finally, the implemented adjoint solvers and models are integrated into a gradient-based optimization framework, and four distinct design optimizations (multipoint aerodynamic optimization of a low-speed unmanned-aerial-vehicle wing, aerodynamic optimization of a transonic aircraft configuration, aerothermal optimization of a turbine internal cooling passage, and aerostructural optimization of a compressor rotor) are shown. DAFoam is available under an open-source license and is a powerful tool for the high-fidelity multidisciplinary design optimization of engineering systems, such as aircraft, ground vehicles, marine vessels, and turbomachinery.

A genetic algorithm based aerothermal optimization of tip carving for an axial turbine blade

In turbomachines, a properly dimensioned gap between the rotating blade tip and the stationary casing is required in order to avoid mechanical failures due to blade rubbing. Maintaining a tip gap allows the relative motion of the blade, however a leakage flow almost always exists due to the strong pressure differentials existing near the tip airfoil boundaries. Tip leakage flow which is a 3-dimensional and highly complex flow system is responsible from a considerable amount of total pressure loss in a turbine stage. Besides, tip leakage flows induce adverse thermal effects near the blade tip, eventually causing an increase in cooling demand. Various passive control methods exist to weaken the adverse effects of tip leakage flows, in an effort to increase turbine stage efficiency. In this paper, a novel tip carving approach is applied to mitigate the undesired aerothermal effects of the tip leakage flow. A numerical investigation is carried out to obtain the optimum shape of the carved blade tip with an objective function to minimize both heat transfer and leakage loss. A genetic algorithm is used for the optimization, integrated with a meta model which predicts the objective functions quickly. Various meta-models such as Artificial Neural Network (ANN), Extreme Learning Machine (ELM) and Support Vector Machine (SVM) are tested for this purpose. An initial database consisting of 55 blade tip geometries is created for meta-model training using “Sobol design of experiments” methodology. This database is then successively enlarged using a coarse-to-fine approach in order to improve the prediction capabilities of the meta-models. Once a sufficient level of prediction error and a proper consistency is achieved, the optimization process is terminated. Current results indicate that carved blade tip designs are likely to achieve a considerable improvement in aero-thermal performance of axial turbine stages. Multi-objective optimization of the blade tip surface of the carved type is a promising approach in gas turbines since it paves the way for undiscovered blade tip designs for further performance improvements.

Aerothermal optimization of a ribbed U-bend cooling channel using the adjoint method

Aerothermal optimization is a powerful technique for automating the design of turbine internal cooling passages, where both pressure loss and heat transfer are considered. Existing optimization studies commonly adopt gradient-free algorithms, which can handle only a few design variables. However, to enhance heat transfer, internal cooling designs use complex geometries consisting of ribbed serpentine channels, which need to be parameterized by using a large number of design variables. To address this need, we develop herein an approach for aerothermal optimization that uses a gradient-based optimizer in conjunction with a discrete adjoint method to efficiently compute the required gradients with respect to numerous design variables. We apply this approach to the design of a ribbed U-bend channel, which is representative of a section of turbine internal cooling passages. The objective function combines heat transfer and pressure loss as a weighted sum. We find the Pareto front for these two objectives by running five optimizations with different weights. We consider both a rib-free and a ribbed U-bend configuration. For the rib-free configuration, we use 113 design variables to parameterize the U-bend shape. We compare our optimization results with those from gradient-free methods and demonstrate that the proposed method leads to lower pressure loss while enhancing heat transfer. For the ribbed configuration, we use 146 design variables and allow the ribs to change their arrangement independently (shape, height, pitch, and angle). Each rib adopts a requisite arrangement to balance heat transfer and aerodynamics, depending on the local flow conditions. Optimizing the U-bend shape is shown to be more effective for improving overall heat transfer than optimizing the rib arrangement. However, optimizing ribs is more effective for improving local heat transfer. The results demonstrate that the proposed optimization framework has the potential to handle general turbine heat transfer designs, not only for internal cooling but also for other design problems, such as film cooling and jet impingement cooling.

Aerothermal Optimization of Fully Cooled Turbine Blade Tips

Optimal turbine blade tip designs have the potential to enhance aerodynamic performance while reducing the thermal loads on one of the most vulnerable parts of the gas turbine. This paper describes a novel strategy to perform a multi-objective optimization of the tip geometry of a cooled turbine blade. The parameterization strategy generates arbitrary rim shapes around the coolant holes on the blade tip. The tip geometry performance is assessed using steady Reynolds-averaged Navier–Stokes simulations with the k–ω shear stress transport (SST) model for the turbulence closure. The fluid domain is discretized with hexahedral elements, and the entire optimization is performed using identical mesh characteristics in all simulations. This is done to ensure an adequate comparison among all investigated designs. Isothermal walls were imposed at engine-representative levels to compute the convective heat flux for each case. The optimization objectives were a reduction in heat load and an increase in turbine row efficiency. The multi-objective optimization is performed using a differential evolution strategy. Improvements were achieved in both the aerodynamic efficiency and heat load reduction, relative to a conventional squealer tip arrangement. Furthermore, this work demonstrates that the inclusion of over-tip coolant flows impacts the over-tip flow field, and that the rim–coolant interaction can be used to create a synergistic performance enhancement.

AEROTHERMAL OPTIMIZATION OF SQUEALER GEOMETRY IN AXIAL FLOW TURBINES USING GENETIC ALGORITHM

In turbomachines, a tip gap is required in order to allow the relative motion of the blade and to prevent the blade tip surface from rubbing. This gap which lay out between the blade tip surface and the casing, results in fluid leakage due to the pressure difference between the pressure side and the suction side of the blade. The tip leakage flow causes almost one third of the aerodynamic loss and unsteady thermal loads over the blade tip. Previous experimental and numerical studies revealed that the squealer blade tip arrangements are one of the effective solutions in increasing the aerothermal performance of the axial flow turbines. In this paper the tip leakage flow is examined and optimized with the squealer geometry as a means to control those losses related with the tip clearance. The squealer height and width have been selected as design parameters and the corresponding computational domain was obtained parametrically. Numerical experiments with such parametrically generated multizone structured grid topologies paved the way for the aerothermal optimization of the high pressure turbine blade tip region. Flow within the linear cascade model has been numerically simulated by solving Reynolds Averaged Navier-Stokes (RANS) equations in order to produce a database. For the numerical validation a well-known test case, Durham cascade is investigated in end wall profiling studies has been used. Sixteen different squealer tip geometries have been modeled parametrically and their performance have been compared in terms of both aerodynamic loss and convective heat transfer coefficient at blade tip. Also, these two values have been introduced as objective functions in the optimization studies. A state of the art multi-objective optimization algorithm, NSGA-II, coupled with an Artificial Neural Network is used to obtain the optimized squealer blade tip geometries for reduced aerodynamic loss and minimum heat transfer coefficient. Optimization results are verified using CFD.

Optimization and analysis of hypersonic leading edge geometries

An aerothermal optimization study of two-dimensional hypersonic leading edge geometries has been performed using both genetic algorithm and particle swarm optimization. The accuracy of a simplified model and a reduced order numerical model was assessed through comparison to simulations of the compressible Navier–Stokes equations performed in OpenFOAM. Specifically, the estimated surface pressure and laminar convective heating distributions have been compared. The simplified model was found to have compromised accuracy in regions of high and low surface curvature. The reduced order numerical model was found to give accurate results with significantly reduced computational cost compared to complete Navier–Stokes simulations. Optimizations were then performed using the simplified analysis technique, and the reduced order numerical model. The performance of the optimized hypersonic leading edge geometries was analyzed using OpenFOAM. The results show that both methods achieve a similar geometric result. However, the quality of the optimization is improved by using the reduced order numerical model. An analysis was performed in the design space immediately surrounding the optimized geometry to assess the impact of small geometric changes on aerothermal performance. The results show that even small changes in leading edge geometry can have a significant influence on aerothermal performance.

Optimization of a high pressure turbine blade tip cavity with conjugate heat transfer analysis

The current study aims to understand the aero-thermal performance of a cooled cavity tip in a single stage transonic turbine. The squealer tip of the uncooled turbine blade was reduced to an aerodynamic loss with suppressing leakage flow. However, the aerodynamic loss study of the cooled turbine blade tip is rare. It is necessary to study the tip cavity of the cooled turbine blade. Depth, front blend radius and aft blend radius of the cavity were set as design variables, and 30 cases were chosen using design of experiments. These cases were calculated with conjugate heat transfer method. Approximation model was made using the Kriging method, and tip cavity shape was optimized with multidisciplinary design optimization. Average total pressure loss behind the trailing edge and cooling effectiveness of blade tip surface were set to the objective function. The aerodynamic optimization model decreased 1.6 % of total pressure loss, the heat transfer optimization model increased 1.3 % point of cooling effectiveness and aero-thermal optimization model were found. Volume of tip cavity becomes larger when three design variables are grown. Amount of tip leakage flow and its distribution over the tip region increases and total pressure loss and cooling effectiveness increase. In terms of heat transfer, blade tip without cavity is advantageous. Total pressure loss coefficient, however, also increases over 5 %. To improve both aero-thermal characteristics of cooled blade tip, the design using the multidisciplinary design optimization is recommended.

Aero-thermal optimization on multi-rows film cooling of a realistic marine high pressure turbine vane

Aero-thermal optimizations on multi-rows film cooling of a realistic marine high pressure turbine vane are performed in this paper. Firstly, a full three-dimensional optimization platform for film-cooled turbines, which consists of the parametric modeling, automatic mesh generation, the CFD numerical calculation and the optimization strategy is established. The design variables are selected based on the considerations of hole-to-hole interactions and invalid coverage of cooling film. Two objective functions of aerodynamic efficiency and adiabatic film cooling effectiveness are adopted to evaluate the overall performance of film-cooled turbine vane. Bothe single objective and multi-objective optimization are adopted to optimize the configurations of multi rows film cooling holes, and the Multi-Island Genetic Algorithm and The response surface approximation with the Non-dominated Sorting Genetic Algorithm (NSGA-II) are selected to conduct the optimizations. The objective of the present study is to use a numerical optimization method to find the optimal cooling structure configurations that yields better cooling performance with an acceptable aerodynamic penalty. The results show that the film cooling effectiveness of multi-objective optimization is increased by 11.4%, and average temperature of the blade surface is reduced by 75K.

Aero-Thermal Optimization of a Heat Sink using Variable Neighbourhood Search

Aero-Thermal Optimization of a Heat Sink using Variable Neighbourhood Search

Aero-thermal optimization of in-flight electro-thermal ice protection systems in transient de-icing mode

Even if electro-thermal ice protection systems (IPS) consume less energy when operating in de-icing mode than in anti-icing mode, they still need to be optimized for energy usage. The optimization, however, should also take into account the effect of the de-icing system on the aerodynamic performance. The present work offers an optimization framework in which both thermal and aerodynamic viewpoints are taken into account in formulating various objective and constraint functions by considering the energy consumption, the thickness, the volume, the shape and the location of the accreted ice on the surface as the key parameters affecting the energy usage and the aerodynamic performance. The design variables include the power density and the activation time of the electric heating blankets. A derivative-free technique, called the mesh adaptive direct search (MADS) method, is used to carry out the optimization process, which would normally need a large number of unsteady conjugate heat transfer (CHT) calculations for the IPS simulation. To avoid such prohibitive computations, reduced-order modeling (ROM) is used to construct simplified low-dimensional CHT models. The approach is illustrated through several test cases, in which different combinations of objective and constraint functions, design variables and cycling sequence patterns are examined. In these test cases, the energy consumption is significantly reduced compared to the experiments by improving the spatial and temporal distribution of the thermal energy usage. The results show the benefits of the approach in bringing energy, safety and aerodynamic considerations together in designing de-icing systems.

Aerothermal Optimization and Experimental Verification for Discrete Turbine Airfoil Film Cooling

The optimization aims to maximize the film cooling performance while minimizing the corresponding aerodynamic penalty. The cooling performance is assessed using the adiabatic film cooling effectiveness, while the aerodynamic penalty is measured with a mass-averaged total pressure loss coefficient. Two design variables are selected: the coolant-to-mainstream temperature ratio and the coolant-to-mainstream total pressure ratio. Two staggered rows of discrete cylindrical film cooling holes on the suction surface of a turbine vane are considered. A nondominated sorting genetic algorithm (NSGA-II) is coupled with an artificial neural network (ANN) to perform a multiple-objective optimization of the coolant flow parameters on the vane suction surface. Three-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations are employed to construct the ANN network that produces low-fidelity predictions of the objective functions during the optimization. The effect of varying the coolant flow parameters on the adiabatic film cooling effectiveness and the aerodynamic loss is analyzed using the optimization method and RANS simulations. The computational fluid dynamics predictions of the adiabatic film cooling effectiveness and aerodynamic performance are assessed and validated against corresponding experimental measurements. The optimal solutions are reproduced in the experimental facility and the Pareto front is substantiated with experimental data.

Design and Optimization of the Internal Cooling Channels of a High Pressure Turbine Blade—Part I: Methodology

This first paper describes the conjugate heat transfer (CHT) method and its application to the performance and lifetime prediction of a high pressure turbine blade operating at a very high inlet temperature. It is the analysis tool for the aerothermal optimization described in a second paper. The CHT method uses three separate solvers: a Navier–Stokes solver to predict the nonadiabatic external flow and heat flux, a finite element analysis (FEA) to compute the heat conduction and stress within the solid, and a 1D aerothermal model based on friction and heat transfer correlations for smooth and rib-roughened cooling channels. Special attention is given to the boundary conditions linking these solvers and to the stability of the complete CHT calculation procedure. The Larson–Miller parameter model is used to determine the creep-to-rupture failure lifetime of the blade. This model requires both the temperature and thermal stress inside the blade, calculated by the CHT and FEA. The CHT method is validated on two test cases: a gas turbine rotor blade without cooling and one with five cooling channels evenly distributed along the camber line. The metal temperature and thermal stress distribution in both blades are presented and the impact of the cooling channel geometry on lifetime is discussed.