Andrea Arnone

Rotor-stator interaction analysis using the Navier-Stokes equations and a multigrid method

A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully implicit discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor-stator interaction in the first stage of a modern gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

Analysis and Optimization of Transonic Centrifugal Compressor Impellers Using the Design of Experiments Technique

The turbomachine industry is increasingly interested in developing automated design procedures that are able to summarize current design experience, to take into account manufacturing limitations and to define new rules for improving machine performance. In this paper, a strategy for the parametric analysis and optimization of transonic centrifugal impellers was developed, using the technique of the design of experiments coupled with a three dimensional fluid-dynamic solver. The geometrical parameterization was conducted using Bezier curves and a few geometrical parameters, which were chosen after a screening analysis in order to determine the most significant ones. The range of variation of the parameters was defined taking into account the manufacturing requirements. The analysis of the influence of such parameters on the main impeller performance was subdivided into two steps: first, the effect of the parameters acting on the blade shape was investigated and an optimum configuration was chosen, then the influence of three functional parameters was analyzed, fixing the already optimized variables. The whole strategy aimed at an industrial design approach, and attention was focused on the time required in the design process. From the present analysis it was possible not only to define an optimum geometry, but also to understand the influence of the input parameters on the main machine performance.

Numerical Investigation of Airfoil Clocking in a Three-Stage Low-Pressure Turbine

A quasi-three-dimensional, blade-to-blade, time-accurate, viscous solver was used for a three-stage LP turbine study. Due to the low Reynolds number, transitional computations were performed. Unsteady analyses were then carried out by varying the circumferential relative position of consecutive vanes and blade rows to study the effects of clocking on the turbines performance. A clocking strategy developed in order to limit the number of configurations to be analyzed is discussed. The optimum analytically-determined clocking position is illustrated for two different operating conditions, referred to as cruise and takeoff. The effects of clocking on wake interaction mechanisms and unsteady blade loadings is presented and discussed. For low Reynolds number turbine flows, the importance of taking transition into account in clocking analysis is demonstrated by a comparison with a fully turbulent approach.

Real Gas Effects in Turbomachinery Flows: A Computational Fluid Dynamics Model for Fast Computations

A numerical model was included in a three-dimensional viscous solver to account for real gas effects in the compressible Reynolds averaged Navier-Stokes (RANS) equations. The behavior of real gases is reproduced by using gas property tables. The method consists of a local fitting of gas data to provide the thermodynamic property required by the solver in each solution step. This approach presents several characteristics which make it attractive as a design tool for industrial applications. First of all, the implementation of the method in the solver is simple and straightforward, since it does not require relevant changes in the solver structure. Moreover, it is based on a low-computational-cost algorithm, which prevents a considerable increase in the overall computational time. Finally, the approach is completely general, since it allows one to handle any type of gas, gas mixture or steam over a wide operative range. In this work a detailed description of the model is provided. In addition, some examples are presented in which the model is applied to the thermo-fluid-dynamic analysis of industrial turbomachines.

Prediction of Turbine Blade Passage Heat Transfer Using a Zero and a Two-Equation Turbulence Model

Predictions of the heat transfer rates on the hot surfaces of a turbine cascade blade passage as influenced by the turbulence models was examined. A zero equation turbulence model supplemented by a bypass transition model and a two equation low Reynolds number model were chosen for this study. The experimental data of Graziani et. al. were used for comparison. The comparisons suggest that at least for the experimental data considered in this work the use of a two-equation model does not provide an overall more accurate solution than the zero equation model. This conclusion is strengthened if one takes into account the relative economy of computations with the algebraic model.Copyright

Development of Secondary Flow Field in a Low Solidity Diffuser in a Transonic Centrifugal Compressor Stage

In the present paper, the flow structure inside a low-solidity diffuser of a transonic compressor was investigated in detail. Steady computations were carried out and compared to experimental data. The secondary flow development inside the diffuser was analyzed and the reason for the stall inception was detected. Unsteady calculations were performed for two operating points, one close to the choke and the other one close to the stall of the compressor, in order to assess the effect of the unsteadiness in the diffuser secondary flow development.Copyright

Parametric Optimization of a High-Lift Turbine Vane

Numerical optimization techniques are increasingly used in the aerodynamic design of turbomachine blades. In the present paper, an existing three-dimensional high-lift turbine cascade was redesigned by means of CFD analyses and optimization techniques, based on the blade geometrical parameterization. A new parametric design tool was developed for this purpose. Blade geometry was handled in a fully three dimensional way, using Bezier curves and surfaces for both camber-surface and thickness distribution. In the optimization procedure different techniques were adopted: a Genetic Algorithm (GA) strategy made it possible to considerably reduce two-dimensional profile losses, while the optimal stacking line was found based on a successive Design of Experiments (DOE) analysis. As a result, a new high-lift blade with higher performance was obtained; in addition, the effect of hub/tip leaning was presented and discussed.Copyright

Navier-Stokes turbine heat transfer predictions using two-equation turbulence closures

Navier-Stokes calculations were carried out in order to predict the heat transfer rates on turbine blades. The calculations were performed using TRAF2D which is a two-dimensional, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using q-omega and k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a non-periodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the Rocketdyne Space Shuttle Main Engine (SSME) high pressure fuel turbine. The comparison with the experimental results, although generally favorable, serves to highlight the weaknesses of the turbulence models and the possible areas of improving these models for use in turbomachinery heat transfer calculations.

A Redesign Strategy to Improve the Efficiency of a 17-Stage Steam Turbine

A three-dimensional Reynolds averaged Navier–Stokes solver was applied to the aerodynamic redesigning of a 17-stage steam turbine. The redesign procedure was divided into three steps. In the first one, a single embedded stage was considered, and an optimization of stator lean and rotor twist was carried out by applying suitable repeating inlet/outlet boundary conditions. In the second step, a proper geometrical transformation between the original reference stage and the optimized one was identified and then applied to all other turbine stages, thus leading to a first approximation of the redesigned turbine. Finally, a neural-network-based refinement of the stator and rotor twist of each stage was performed to account for its actual position and operating conditions within the meridional channel. In this work, a detailed description of the redesign procedure is provided, and the aerodynamic characteristics of the optimized geometry are discussed and compared with the original ones.

An assessment of the laminar kinetic energy concept for the prediction of high-lift, low-Reynolds number cascade flows

The laminar kinetic energy (LKE) concept has been applied to the prediction of low-Reynolds number flows, characterized by separation-induced transition, in high-lift airfoil cascades for aeronautical low-pressure turbine applications. The LKE transport equation has been coupled with the low-Reynolds number formulation of the Wilcoxs k − ω turbulence model. The proposed methodology has been assessed against two high-lift cascade configurations, characterized by different loading distributions and suction-side diffusion rates, and tested over a wide range of Reynolds numbers. The aft-loaded T106C cascade is studied in both high- and low-speed conditions for several expansion ratios and inlet freestream turbulence values. The front-loaded T108 cascade is analysed in high-speed, low-freestream turbulence conditions. Numerical predictions with steady inflow conditions are compared to measurements carried out by the von Kármán Institute and the University of Cambridge. Results obtained with the proposed model show its ability to predict the evolution of the separated flow region, including bubble-bursting phenomenon and the formation of open separations, in high-lift, low-Reynolds number cascade flows.