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

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Tom Verstraete ◽  
Sergio Amaral ◽  
René Van den Braembussche ◽  
Tony Arts
Keyword(s):  
High Pressure ◽  
Radial Basis Function Network ◽  
Computational Cost ◽  
Optimization Procedure ◽  
Material Model ◽  
Computational Effort ◽  
Internal Cooling ◽  
Optimization System ◽  
Cooling Channels ◽  
Cooling Flow

This second paper presents the aerothermal optimization of the first stage rotor blade of an axial high pressure (HP) turbine by means of the conjugate heat transfer (CHT) method and lifetime model described in Paper I. The optimization system defines the position and diameter of the cooling channels leading to the maximum lifetime of the blade while limiting the amount of cooling flow. It is driven by the results of a CHT and subsequent stress analysis of each newly designed geometry. Both temperature and stress distributions are the input for the Larson–Miller material model to predict the lifetime of the blade. The optimization procedure makes use of a genetic algorithm (GA) and requires the aerothermal analysis of a large number of geometries. Because of the large computational cost of each CHT analysis, this results in a prohibitive computational effort. The latter has been remediated by using a more elaborate optimization system, in which a large part of the CHT analyzes is replaced by approximated predictions by means of a metamodel. Two metamodels, an artificial neural network and a radial basis function network, have been tested and their merits have been discussed. It is shown how this optimization procedure based on CHT calculations, a GA, and a metamodel can lead to a considerable extension of the blade lifetime without an increase in the amount of cooling flow or the complexity of the cooling geometry.

Design and Optimization of the Internal Cooling Channels of a HP Turbine Blade: Part II—Optimization

2008 ◽  
Author(s):  
Tom Verstraete ◽  
Sergio Amaral ◽  
Rene´ Van den Braembussche ◽  
Tony Arts
Keyword(s):  
Computational Cost ◽  
Optimization Procedure ◽  
Material Model ◽  
Computational Effort ◽  
Internal Cooling ◽  
Rbf Network ◽  
Design And Optimization ◽  
Optimization System ◽  
Cooling Channels ◽  
Cooling Flow

This second paper presents the aerothermal optimization of the first stage rotor blade of an axial HP turbine by means of the conjugate heat transfer method (CHT) and lifetime model described in paper 1. The optimization system defines the position and diameter of the cooling channels leading to the maximum lifetime of the blade while limiting the amount of cooling flow. It is driven by the results of a CHT and subsequent stress analysis of each newly designed geometry. Both temperature and stress distributions are the input for the Larson-Miller material model to predict the lifetime of the blade. The optimization procedure makes use of a Genetic Algorithm (GA) and requires the aerothermal analysis of a large number of geometries. Because of the large computational cost of each CHT analysis, this results in a prohibitive computational effort. The latter has been remediated by using a more elaborate optimization system, in which a large part of the CHT analyzes are replaced by approximated predictions by means of a meta-model. Two metamodels, an Artificial Neural Network (ANN) and a Radial Basis Function (RBF) network, have been tested and their merits have been discussed. It is shown how this optimization procedure based on CHT calculations, a GA and a metamodel can lead to a considerable extension of the blade lifetime without increase of the amount of cooling flow or the complexity of the cooling geometry.

scholarly journals Machine Learning for the Development of Data Driven Turbulence Closures in Coolant Systems

2020 ◽  
Author(s):  
James Hammond ◽  
Francesco Montomoli ◽  
Marco Pietropaoli ◽  
Richard D. Sandberg ◽  
Vittorio Michelassi
Keyword(s):  
Heat Transfer ◽  
Complex Geometry ◽  
Gene Expression Programming ◽  
Turbine Blades ◽  
Computational Cost ◽  
Data Driven ◽  
Internal Cooling ◽  
Cooling Channels ◽  
Turbulence Closures ◽  
Improved Model

Abstract This work shows the application of Gene Expression Programming to augment RANS turbulence closure modelling for flows through complex geometry, designed for additive manufacturing. Specifically, for the design of optimised internal cooling channels in turbine blades. One of the challenges in internal cooling design is the heat transfer accuracy of the RANS formulation in comparison to higher fidelity methods, which are still not used in design on account of their computational cost. However, high fidelity data can be extremely valuable for improving current lower fidelity models and this work shows the application of data driven approaches to develop turbulence closures for an internally ribbed duct. Different approaches are compared and the results of the improved model are illustrated; first on the same geometry, and then for an unseen predictive case. The work shows the potential of using data driven models for accurate heat transfer predictions even in non-conventional configurations.

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

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Sergio Amaral ◽  
Tom Verstraete ◽  
René Van den Braembussche ◽  
Tony Arts
Keyword(s):  
Heat Transfer ◽  
High Pressure ◽  
Thermal Stress ◽  
Turbine Blade ◽  
Inlet Temperature ◽  
Analysis Tool ◽  
Internal Cooling ◽  
High Pressure Turbine ◽  
Cooling Channels ◽  
The Impact

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.

Dimensioning a recovery boiler furnace using mathematical optimization

TAPPI Journal ◽  
2015 ◽  
Vol 14 (2) ◽  
pp. 119-129 ◽  
Author(s):  
VILJAMI MAAKALA ◽  
PASI MIIKKULAINEN
Keyword(s):  
Radial Basis Function Network ◽  
High Capacity ◽  
Mathematical Optimization ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Performance Criteria ◽  
Boiler Furnace ◽  
Starting Point ◽  
Recovery Boiler ◽  
Base Design

Capacities of the largest new recovery boilers are steadily rising, and there is every reason to expect this trend to continue. However, the furnace designs for these large boilers have not been optimized and, in general, are based on semiheuristic rules and experience with smaller boilers. We present a multiobjective optimization code suitable for diverse optimization tasks and use it to dimension a high-capacity recovery boiler furnace. The objective was to find the furnace dimensions (width, depth, and height) that optimize eight performance criteria while satisfying additional inequality constraints. The optimization procedure was carried out in a fully automatic manner by means of the code, which is based on a genetic algorithm optimization method and a radial basis function network surrogate model. The code was coupled with a recovery boiler furnace computational fluid dynamics model that was used to obtain performance information on the individual furnace designs considered. The optimization code found numerous furnace geometries that deliver better performance than the base design, which was taken as a starting point. We propose one of these as a better design for the high-capacity recovery boiler. In particular, the proposed design reduces the number of liquor particles landing on the walls by 37%, the average carbon monoxide (CO) content at nose level by 81%, and the regions of high CO content at nose level by 78% from the values obtained with the base design. We show that optimizing the furnace design can significantly improve recovery boiler performance.

scholarly journals Updated Kriging-Assisted Shape Optimization of a Gravity Dam

Water ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 87
Author(s):  
Yongqiang Wang ◽  
Ye Liu ◽  
Xiaoyi Ma
Keyword(s):  
Surrogate Model ◽  
Computational Cost ◽  
Region Of Interest ◽  
Optimization Procedure ◽  
Optimal Shape ◽  
Small Sample ◽  
Gravity Dam ◽  
Kriging Surrogate Model ◽  
Gravity Dams ◽  
Sample Set

The numerical simulation of the optimal design of gravity dams is computationally expensive. Therefore, a new optimization procedure is presented in this study to reduce the computational cost for determining the optimal shape of a gravity dam. Optimization was performed using a combination of the genetic algorithm (GA) and an updated Kriging surrogate model (UKSM). First, a Kriging surrogate model (KSM) was constructed with a small sample set. Second, the minimizing the predictor strategy was used to add samples in the region of interest to update the KSM in each updating cycle until the optimization process converged. Third, an existing gravity dam was used to demonstrate the effectiveness of the GA–UKSM. The solution obtained with the GA–UKSM was compared with that obtained using the GA–KSM. The results revealed that the GA–UKSM required only 7.53% of the total number of numerical simulations required by the GA–KSM to achieve similar optimization results. Thus, the GA–UKSM can significantly improve the computational efficiency. The method adopted in this study can be used as a reference for the optimization of the design of gravity dams.

scholarly journals On the Use of Conformal Cooling in High-Pressure Die-Casting and Semisolid Casting

Technologies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 39
Author(s):  
Anders E. W. Jarfors ◽  
Ruslan Sevastopol ◽  
Karamchedu Seshendra ◽  
Qing Zhang ◽  
Jacob Steggo ◽  
...  
Keyword(s):  
High Pressure ◽  
Die Casting ◽  
Life Extension ◽  
Conformal Cooling ◽  
High Pressure Die Casting ◽  
Cooling Channels ◽  
Die Life ◽  
Die Materials ◽  
Pressure Die Casting ◽  
Semisolid Casting

Today, tool life in high pressure die casting (HPDC) is of growing interest. A common agreement is that die life is primarily decided by the thermal load and temperature gradients in the die materials. Conformal cooling with the growth of additive manufacturing has raised interest as a means of extending die life. In the current paper, conformal cooling channels’ performance and effect on the thermal cycle in high-pressure die casting and rheocasting are investigated for conventional HPDC and semisolid processing. It was found that conformal cooling aids die temperature reduction, and the use of die spray may be reduced and support the die-life extension. For the die filling, the increased temperature was possibly counterproductive. Instead, it was found that the main focus for conformal cooling should be focused to manage temperature around the in-let bushing and possibly the runner system. Due to the possible higher inlet pressures for semisolid casting, particular benefits could be seen.

scholarly journals Optimization Design of Lattice Structures in Internal Cooling Channel with Variable Aspect Ratio of Gas Turbine Blade

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3954
Author(s):  
Liang Xu ◽  
Qicheng Ruan ◽  
Qingyun Shen ◽  
Lei Xi ◽  
Jianmin Gao ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Optimization Model ◽  
Lattice Structure ◽  
Turbine Blades ◽  
Internal Cooling ◽  
Cooling Channel ◽  
Cooling Channels ◽  
Mechanical Performances ◽  
Type Lattice

Traditional cooling structures in gas turbines greatly improve the high temperature resistance of turbine blades; however, few cooling structures concern both heat transfer and mechanical performances. A lattice structure (LS) can solve this issue because of its advantages of being lightweight and having high porosity and strength. Although the topology of LS is complex, it can be manufactured with metal 3D printing technology in the future. In this study, an integral optimization model concerning both heat transfer and mechanical performances was presented to design the LS cooling channel with a variable aspect ratio in gas turbine blades. Firstly, some internal cooling channels with the thin walls were built up and a simple raw of five LS cores was taken as an insert or a turbulator in these cooling channels. Secondly, relations between geometric variables (height (H), diameter (D) and inclination angle(ω)) and objectives/functions of this research, including the first-order natural frequency (freq1), equivalent elastic modulus (E), relative density (ρ¯) and Nusselt number (Nu), were established for a pyramid-type lattice structure (PLS) and Kagome-type lattice structure (KLS). Finally, the ISIGHT platform was introduced to construct the frame of the integral optimization model. Two selected optimization problems (Op-I and Op-II) were solved based on the third-order response model with an accuracy of more than 0.97, and optimization results were analyzed. The results showed that the change of Nu and freq1 had the highest overall sensitivity Op-I and Op-II, respectively, and the change of D and H had the highest single sensitivity for Nu and freq1, respectively. Compared to the initial LS, the LS of Op-I increased Nu and E by 24.1% and 29.8%, respectively, and decreased ρ¯ by 71%; the LS of Op-II increased Nu and E by 30.8% and 45.2%, respectively, and slightly increased ρ¯; the LS of both Op-I and Op-II decreased freq1 by 27.9% and 19.3%, respectively. These results suggested that the heat transfer, load bearing and lightweight performances of the LS were greatly improved by the optimization model (except for the lightweight performance for the optimal LS of Op-II, which became slightly worse), while it failed to improve vibration performance of the optimal LS.

Multidisciplinary Optimization of Airfoil Cooling Structure

2008 ◽  
Author(s):  
Grzegorz Nowak
Keyword(s):  
Cooling System ◽  
Computational Cost ◽  
System Optimization ◽  
Multidisciplinary Optimization ◽  
Internal Cooling ◽  
Technical Problems ◽  
Thermal Boundary Conditions ◽  
Optimization Task ◽  
External Conditions ◽  
Cooling Air

This paper discusses the problem of cooling system optimization within a gas turbine airfoil regarding to thermo-mechanical behavior of the component, as well as some economical aspects of turbine operation. The main goal of this paper is to show the possibilities of evolutionary approach application to the cooling system optimization. This method, despite its relatively high computational cost, seems to be a valuable tool to such technical problems. The analysis involves the optimization of location and size of internal cooling passages within an airfoil. Initially cooling is provided with circular passages and heat is transported by convection. During the optimization the number of channels can vary. The task is approached in 3D configuration. Each passage is fed with cooling air of constant parameters at the inlet. Also a constant pressure drop is assumed along the passage length. The thermal boundary conditions in passages vary with diameter and local vane temperature (passage wall temperature). The analysis is performed by means of the genetic algorithm for the optimization task and FEM for the heat transfer predictions within the component. In the present study the airfoil profile is taken as aerodynamically optimal and the objective of the search procedure is to find cooling structure variant that at given external conditions provides lower stresses, material temperature and indirectly coolant usage.

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

Comparison of 3D Unsteady Transient Conjugate Heat Transfer Analysis on a High Pressure Cooled Turbine Stage With Experimental Data

2017 ◽  
Author(s):  
Jong-Shang Liu ◽  
Mark C. Morris ◽  
Malak F. Malak ◽  
Randall M. Mathison ◽  
Michael G. Dunn
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Flux ◽  
High Pressure ◽  
High Temperature ◽  
Gas Turbine ◽  
Conjugate Heat Transfer ◽  
Turbine Rotor ◽  
Turbine Stage ◽  
Cooling Flow

In order to have higher power to weight ratio and higher efficiency gas turbine engines, turbine inlet temperatures continue to rise. State-of-the-art turbine inlet temperatures now exceed the turbine rotor material capability. Accordingly, one of the best methods to protect turbine airfoil surfaces is to use film cooling on the airfoil external surfaces. In general, sizable amounts of expensive cooling flow delivered from the core compressor are used to cool the high temperature surfaces. That sizable cooling flow, on the order of 20% of the compressor core flow, adversely impacts the overall engine performance and hence the engine power density. With better understanding of the cooling flow and accurate prediction of the heat transfer distribution on airfoil surfaces, heat transfer designers can have a more efficient design to reduce the cooling flow needed for high temperature components and improve turbine efficiency. This in turn lowers the overall specific fuel consumption (SFC) for the engine. Accurate prediction of rotor metal temperature is also critical for calculations of cyclic thermal stress, oxidation, and component life. The utilization of three-dimensional computational fluid dynamics (3D CFD) codes for turbomachinery aerodynamic design and analysis is now a routine practice in the gas turbine industry. The accurate heat-transfer and metal-temperature prediction capability of any CFD code, however, remains challenging. This difficulty is primarily due to the complex flow environment of the high-pressure turbine, which features high speed rotating flow, coupling of internal and external unsteady flows, and film-cooled, heat transfer enhancement schemes. In this study, conjugate heat transfer (CHT) simulations are performed on a high-pressure cooled turbine stage, and the heat flux results at mid span are compared to experimental data obtained at The Ohio State University Gas Turbine Laboratory (OSUGTL). Due to the large difference in time scales between fluid and solid, the fluid domain is simulated as steady state while the solid domain is simulated as transient in CHT simulation. This paper compares the unsteady and transient results of the heat flux on a high-pressure cooled turbine rotor with measurements obtained at OSUGTL.

Sign in / Sign up

Export Citation Format

Share Document