Three-Dimensional Navier-Stokes Analysis of Turbine Rotor and Tip-Leakage Flowfield

The 3-D viscous flowfield in the rotor passage of a single-stage turbine, including the tip-leakage flow, is computed using a Navier-Stokes procedure. A grid-generation code has been developed to obtain embedded H grids inside the rotor tip gap. The blade tip geometry is accurately modeled without any “pinching”. Chien’s low-Reynolds-number k-ε model is employed for turbulence closure. Both the mean-flow and turbulence transport equations are integrated in time using a four-stage Runge-Kutta scheme. The computational results for the entire turbine rotor flow, particularly the tip-leakage flow and the secondary flows, are interpreted and compared with available data. The predictions for major features of the flowfield are found to be in good agreement with the data. Complicated interactions between the tip-clearance flows and the secondary flows are examined in detail. The effects of endwall rotation on the development and interaction of secondary and tip-leakage vortices are also analyzed.

A Practical Compressor Casing Treatment

A three stage compressor test incorporating casing inserts comprised of compound angled honeycomb cells demonstrated up to 10% higher stall margin than circumferential grooves casing treatment. This is attributed to effective tip flow energization resulting from the unsteady flow induced in and out of the cells as the blade tip sweeps by the cell openings. The rationale for selecting the cell inclination angles both relative to the normal and the tangential directions is discussed. The design intent of the cell orientation is to induce a high cell exit velocity as well as to impart a degree of flow alignment to the injected jets. A first order calculation of cell exit velocity variation based on the cell pressure/volume dynamics is indicative of unsteady blowing which is theorized to effectively mix the tip suction side flow and to enhance the tip flow streamwise momentum. This theory is partially substantiated by the presented compressor test results showing improved radial total pressure profiles, stage characteristics, and stall margin. Since a few unhealthy stages of a multi-stage compressor could make it stall prone, casing treatment of those weak stages could dramatically increase stall margin with negligible impact on overall adiabatic efficiency. In addition to the aerodynamic effectiveness, the mechanical suitability of this casing treatment to multistage compressors, based on its demonstrated abradability and packageability, is discussed.

Grid Dependency Study for the NASA Rotor 37 Compressor Blade

The NASA Rotor 37 has been computed by several authors in the last few years with relative success. The aim of this work is to present a systematic grid dependency study in order to quantify the amount of uncertainty that comes from the grid density. The computational domain is divided onto several regions (i.e. leading edge, trailing edge, shear layer …) and for each of them, the impact of the grid density is investigated. By means of this analysis, substantial improvement has been obtained in the prediction of efficiency and exit angle. On the contrary, the improvement achieved in total pressure and total temperature ratio is less remarkable. It is believed that only after a systematic grid dependency study can the contribution of turbulence modeling, laminar-turbulent transition, and boundary conditions be analyzed with success.

The Aerodynamics of Trailing-Edge-Cooled Transonic Turbine Blades: Part 2 — Theoretical and Computational Approach

A theoretical and computational study into the aerodynamics of trailing-edge-cooled transonic turbine blades is described in this part of the paper. The theoretical study shows that, for unstaggered blades with coolant ejection, the base pressure and overall loss can be determined exactly by a simple control volume analysis. This theory suggests that a thick, cooled trailing edge with a wide slot can be more efficient than a thin, solid trailing edge. An existing time-marching finite volume method is adapted to calculate the transonic flow with trailing edge coolant ejection on a structured, quasi-orthogonal mesh. Good overall agreement between the present method, inviscid and viscous, and experimental evidence is obtained.

Investigation of Tip Leakage Effects in Transonic Flow Using a Parallel Unstructured Navier-Stokes Code

Calculated results for tip flow around two different blade configurations are presented and compared with experimental data. The first configuration (case number 1) is a flat-plate profile tested in a linear transonic tunnel — the profile is an idealized representation of the aft-section of some highly curved turbine blades. The second configuration (case number 2) originates from the outer profile on the last-stage-blade of a steam turbine, however it is also reminiscient of a section from a turbine blade with supersonic exit flow. This configuration was tested in an annular cascade at Mach numbers representative of engine operating conditions. The computed results were obtained using a parallel 3D unstructured Navier-Stokes code. The code runs on a work-station cluster, as well as being optimized for the 256 processor Cray T3D at EPFL: the code is capable of gigaflop performance using more than 3 million cells — adaptive mesh refinement thus allows enhanced resolution within the tip gap region. For each configuration we have calculated two Runs. In both cases, Run-1 is similar to the experimental conditions, so that direct comparison between measured and calculated results is possible. With case number 1/Run-2 we re-calculated the flow without imposing a prescribed inflow boundary-layer along the sidewall. Comparison between the two runs helped reveal how free-stream total pressure can establish itself within the tip gap region. For the second configuration — in the annular cascade — we were interested in observing the influence of relative movement between the blade tip and adjacent sidewall. Hence for case number 2/Run-2 we imposed a circumferential velocity on the adjacent sidewall. This modified the effective sidewall boundary-layer and had a noticeable influence on the development of the tip-leakage flow.

Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

A 3D Rotating Stall Stability Model for Axial Flow Compressor

Rotating stall phenomenon is usually characterized by 3D aerodynamic stability behavior. The earlier models mainly considered the flow effects in terms of 1D and 2D spatial variables. In order to involve the characteristics of the 3D flow of the compressor, it is necessary to improve the existing rotating stall stability models and further develop the models to consider the effects of the 3D disturbance. In this paper, a new aerodynamic stability model concerning the effects of a radial disturbance produced by the compressor, and explaining more mechanisms about the aerodynamic stability of compressor is presented. Using the developed rotating stall stability model, the stall margins are calculated and compared to experimental data for two axial flow compressors. The calculated results show that the developed 3D rotating stall stability model gives better stall margin prediction than that by the 2D model.

Economics and Design Approaches for Small Commercial Turbogenerators

The successful development of small commercial turbogenerators for automotive and other applications presents a major economic challenge. Current aerospace turbogenerators in the 60 kilowatt power range sell for around $500 per kilowatt. Volume automotive turbogenerators prices must be $30 per kilowatt, or less — a 94% reduction. Turbogenerators for aerospace applications have drastically different requirements on almost all important criteria from automotive turbogenerators. The production of commercial turbogenerators requires a radically different organizational setting, mindset, and overhead structure from that necessary for the aerospace industry. Ground up designs which take an integrated approach to material selection, method of operation, fabrication techniques, supplier base, assembly methods, and low cost overheads will be necessary for commercial success. Significant innovation and simplification, and the natural effects of high volume production are also required. Success will likely require lean, agile, innovative, and specialized organizations.

Analysis of Separated Flows Inside an Annular Compressor Cascade Using a Low-Re-Number k-ϵ and an Algebraic Reynolds-Stress-Model

The flow field inside an annular compressor cascade is numerically investigated. The mean flow features are complex three-dimensional zones of turbulent separation at hub and shroud at high inflow angles. The flow field is investigated with an implicit three-dimensional Navier-Stokes code. To predict turbulent effects the flow solver includes two different variants of a Low-Re-number k-ϵ-model and an algebraic Reynolds-stress-model. Using the Low-Re-number model the structure of the regions of separated flow are fairly well predicted. However, intensity and size of these zones are too small compared with the experimental data. Better results are produced using the anisotropic algebraic Reynolds-stress-model combined with a stagnation point modification of the turbulent production term. Stucture and intensity of the vortex systems are simulated in more detail. Static pressure distributions and loss contours are in a very good agreement with the experiments.

Predicting Bypass Transition: A Physical Model Versus Empirical Correlations

A boundary layer transition model is presented which relates the near wall velocity fluctuations to the formation of turbulent spots. This model is used to determine the turbulent intermittency within a boundary layer integral code. Comparisons are made between the code predictions and established empirical correlations for the adverse pressure gradient transition experiments performed by Gostelow and co-workers. Similarly good accuracy was achieved by both the model and empirical correlation for start of transition. However, empirical correlations were less reliable than the model for predicting end of transition. The model was also able to predict the evolution of the measured intermittency considerably more accurately than the Narasimha empirical correlation. The current modelling approach is thus demonstrated to be more reliable than empirical correlation for the modelling of transitional boundary layers.