Wahid Ghaly

Single and Multipoint Shape Optimization of Gas Turbine Blade Cascades

*† A multipoint shape optimization method for the aerodynamic performance of gas turbine blade cascades is presented and is applied to the design of a transonic and a subsonic compressor rotor. The optimization method uses a Genetic Algorithm (GA), which is combined with an Artificial Neural Network (ANN) that uses a back propagation algorithm, so as to design two-dimensional gas turbine cascades. The ANN is used to build a low fidelity model that approximates the optimization objective and constraints. The latter are to achieve a better aerodynamic performance over the full operating range of gas turbine cascades by varying the blade profile, which is described by the blade camber line and thickness distribution. The blade geometry is parameterized using a Non-Rational B-Splines (NURBS) representation. To reduce computation time the optimization scheme was parallelized on an SGI 2000 computer using Message Passing Interface (MPI). The cascade aerodynamic performance, which is used in computing the objective function and in training/testing the ANN, is determined by solving the two-dimensional Reynolds-Averaged Navier-Stokes equations using a cell-vertex finite volume method on an unstructured triangular mesh and turbulence is modeled using the Baldwin-Lomax model. The chosen objective function and optimization methodology results in a significant improvement in terms of efficiency and pressure ratio, and the use of ANN results in a ten-fold speed-up of the design process.

A Strategy for Multi-Point Shape Optimization of Turbine Stages in Three-Dimensional Flow

This paper presents an effective and practical shape optimization strategy for turbine stages so as to minimize the adverse effects of three-dimensional flow features on the turbine performance. The optimization method combines a genetic algorithm (GA), with a Response Surface Approximation (RSA) of the Artificial Neural Network (ANN) type. During the optimization process, the individual objectives and constraints are approximated using ANN that is trained and tested using a few three-dimensional CFD flow simulations; the latter are obtained using the commercial package Fluent. The optimization objective is a weighted sum of individual objectives such as isentropic efficiency, streamwise vorticity and is penalized with a number of constraints. To minimize three-dimensional effects, the stator and rotor stacking curves are taken as the design variable. They are parametrically represented using a quadratic rational Bezier curve (QRBC) whose parameters are related to the blade lean, sweep and bow, which are used as the design variables. The described strategy was applied to single and multipoint optimization of the E/TU-3 turbine stage. This optimization strategy proved to be successful, flexible and practical, and resulted in an improvement of around 1% in stage efficiency over the turbine operating range with as low as 5 design variables. This improvement is attributed to the reduction in secondary flows, in stator hub choking, and in the transonic region and the associated flow separation.Copyright

An inverse blade design method for subsonic and transonic viscous flow in compressors and turbines

An inverse blade design method applicable to two- and three-dimensional inviscid and viscous flow in turbomachinery cascades is presented and is applied to design cascades in two-dimensional viscous flow. The pressure distribution along the blade surfaces is prescribed and is reached by modifying the initial guess of the blade geometry. The geometry modification is computed from a virtual velocity distribution derived from the difference between the current and the target pressure along the blade surfaces. The inverse method is implemented into and is consistent with the unsteady Reynolds-averaged Navier-Stokes (RANS) equations where an arbitrary Lagrangian–Eulerian (ALE) formulation on a moving and deforming grid is used. The grid velocities are determined from the space conservation law (SCL), which ensures a fully conservative computational procedure. The unsteady RANS equations are discretized using a cell-vertex finite volume method and the time accuracy is achieved using a dual time stepping scheme. An algebraic Baldwin–Lomax model is used for turbulence closure. The design method is first validated, and then its robustness, flexibility and usefulness are demonstrated on the redesign of recent compressor and turbine blade geometries used in modern gas turbine engines.

Aerodynamic Inverse Design for Viscous Flow in Turbomachinery Blading

An inverse design method for turbomachinery blading based on a time-accurate solution of the compressible viscous flow equations on a time-varying geometry is presented. The blade pressure loading and thickness distributions are the prescribed design parameters. The blade profile is modified as it moves at a virtual velocity distribution that would make the momentum flux on the blade surfaces equal to the flux corresponding to the prescribed loading distribution. The unsteady flow due to the blade motion is simulated by solving the Reynolds-averaged Navier-Stokes equations that are discretized using a cell-vertex finite volume method in which an arbitrary Lagrangian-Eulerian formulation is used to account for the mesh movement and deformation during the design procedure. The method is first verified by inversely designing an existing blade using its loading distribution as the design target and starting from a profile that has a different camberline. The robustness, flexibility, and usefulness of this design method are demonstrated by redesigning a subsonic turbine and a transonic compressor blade for which, for the latter case, the conventional quasi-steady approach failed. The redesign cases demonstrate that the blade aerodynamic performance can be improved by carefully tailoring the target loading distribution.

Conjugate mass transfer modeling for VOC source and sink behavior of porous building materials : When to apply it?

Volatile organic compounds (VOC) are major indoor air pollutants. Physical models have been developed to predict VOC source (emission) and sink behavior (sorption) of building materials. They frequently adopt the conventional convection approach using a third-kind boundary condition. This conventional convection approach in conjunction with the commonly used Sherwood number correlation is based on the assumptions of constant wall concentration at the material-air interface and quasi-steady convective mass transfer in the fluid (air). In this study, the validity of these assumptions is theoretically investigated. An analytical model using the conventional convection approach and a numerical conjugate mass transfer model are developed. The conjugate mass transfer models consider unsteady two-dimensional laminar forced convection over a flat plate coupled with unsteady one-dimensional diffusion and sorption within the porous solid through the concentration and the flux continuities at the material-air interface. The simulation results indicate that the assumptions can lead to a significant overestimation of the wall concentration especially in the early transfer phase. When the effect on the VOC source/sink behavior is quantified by the total transfer time, which is the time required to emit/absorb 99% of the maximum transferable VOC mass, the analytical model results in less than 5% error in the predicted value when VOC transfer is controlled by internal diffusion, i.e., Biot number larger than 9 for (ε + K) 100.

Aerodynamic Design of Gas Turbine Cascades Using Global Optimizers and Artificial Neural Networks

A simulation-based optimization scheme for gas turbine cascades is developed and is implemented using Computational Fluid Dynamics (CFD) for the flow simulation coupled with Genetic Algorithm (GA), Simulated Annealing (SA) and Artificial Neural Networks (ANN) for the optimization process. It is parallelized and tested for a cascade of compressor blades with the goal of improving their aerodynamic performance over their entire operating range by properly reshaping their profile, which is parameterized using a NURBS approximation. The validity and effectiveness of the developed optimization method is demonstrated on the redesign of a compressor rotor.

Aero-Thermal Optimization and Experimental Verification for the Discrete Film Cooling of a Turbine Airfoil

The optimization aims to maximize the film cooling performance while minimizing the corresponding aerodynamic penalty. The film 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 total pressure ratio. Two staggered rows of discrete cylindrical film cooling holes on the suction surface of a turbine vane are considered. 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 three-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations. The CFD 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. A non-dominated sorting genetic algorithm (NSGA-II) is coupled with an artificial neural network (ANN) to perform a multiple objective optimization of the film coolant flow parameters on the suction surface of a high pressure gas turbine vane. The numerical predictions are employed to construct the artificial neural network that produces low-fidelity predictions of the objectives during the optimization. The Pareto front of optimal solutions is generated by the optimization methodology.Copyright

Aerodynamic inverse design of turbomachinery cascades using a finite volume method on unstructured meshes

A recently developed aerodynamic inverse design method for turbomachinery cascades is presented and is implemented in a cell-vertex finite volume method on unstructured triangular meshes. In this design method, the mass-averaged swirl schedule and the blade thickness distribution are prescribed. The design method then provides the blade shape that would accomplish this loading by imposing the appropriate pressure jump across the blades and satisfying the blade boundary condition, the latter implies that the flow is tangent to the blade surfaces. The method is first validated for a compressor cascade. It is then used to design an impulse cascade and to redesign the ONERA cascade.

Aerothermal shape optimization for a double row of discrete film cooling holes on the suction surface of a turbine vane

A multiple-objective optimization is implemented for a double row of staggered film holes on the suction surface of a turbine vane. The optimization aims to maximize the film cooling performance, which is assessed using the cooling effectiveness, while minimizing the corresponding aerodynamic loss, which is measured with a mass-averaged total pressure coefficient. Three geometric variables defining the hole shape are optimized: the conical expansion angle, compound angle and length to diameter ratio of the non-diffused portion of the hole. The optimization employs a non-dominated sorting genetic algorithm coupled with an artificial neural network to generate the Pareto front. Reynolds-averaged Navier–Stokes simulations are employed to construct the neural network and investigate the aerodynamic and thermal optimum solutions. The optimum designs exhibit improved performance in comparison to the reference design. The optimization methodology allowed investigation into the impact of varying the geometric variables on the cooling effectiveness and the aerodynamic loss.

Optimization of Film Cooling Holes on the Suction Surface of a High Pressure Turbine Blade

This paper aims to optimize film coolant flow parameters on the suction surface of a high-pressure gas turbine blade in order to obtain an optimum compromise between a high film cooling effectiveness and a low aerodynamic loss. An optimization algorithm coupled with three-dimensional Reynolds-averaged Navier Stokes (RANS) analysis is used to determine the optimum film cooling configuration. The VKI blade with two staggered rows of axially oriented, conically flared, film cooling holes on its suction surface is considered. Two design variables are selected; the coolant to mainstream temperature ratio and total pressure ratio. The effect of varying these coolant flow parameters on the film cooling effectiveness and the aerodynamic loss is analyzed using an optimization method and three dimensional steady CFD simulations. The optimization process involves a genetic algorithm and a response surface approximation of the artificial neural network type to provide low-fidelity predictions of the objective function. The CFD simulations are performed using the commercial software CFX. The numerical predictions of the aerodynamics and wall heat transfer are validated against experimental data. The optimization objective consists of maximizing the spatially averaged film cooling effectiveness and minimizing the aerodynamic penalty produced by film cooling. The results of this optimization are reported in terms of the aerodynamic loss and adiabatic cooling effectiveness.Copyright