Computation of Three-Dimensional, Rotational Flow Through Turbomachinery Blade Rows for Improved Aerodynamic Design Studies

The performance of a three dimensional computer code developed for predicting the flowfield in stationary and rotating turbomachinery blade rows is described in this study. The four stage Runge-Kutta numerical integration scheme is used for solving the governing flow equations and yields solution to the full, three dimensional, unsteady Euler equations in cylindrical coordinates. This method is fully explicit and uses the finite volume, time marching procedure. In order to demonstrate the accuracy and efficiency of the code, steady solutions were obtained for several cascade geometries under widely varying flow conditions. Computed flowfield results are presented for a fully subsonic turbine stator and a low aspect ratio, transonic compressor rotor blade under maximum flow and peak efficiency design conditions. Comparisons with Laser Anemometer measurements and other numerical predictions are also provided to illustrate that the present method predicts important flow features with good accuracy and can be used for cost effective aerodynamic design studies.

Aeroelastic Behavior of Low Aspect Ratio Metal and Composite Blades

The aeroelastic stability of titanium and composite blades of low aspect ratio is examined over a range of design parameters, using a Rayleigh-Ritz formulation. The blade modes include a plate-type mode to account for chordwise bending. Chordwise flexibility is found to have a significant effect on the unstalled supersonic flutter of low aspect ratio blades, and also on the stability of tip sections of shrouded fan blades. For blades with a thickness of less than approximately four percent of chord, the chordwise, second bending, and first torsion branches are all unstable at moderately high supersonic Mach numbers. For composite blades, the important structural coupling between bending and torsion cannot be modeled properly unless chordwise bending is accounted for. Typically, aft fiber sweep produces beneficial bending-torsion coupling that is stabilizing, whereas forward fiber sweep has the opposite effect. By using crossed-ply laminate configurations, critical aeroelastic modes can be stabilized.

The Effect of Reynolds Number and Velocity Distribution on LP Turbine Cascade Performance

Because of the laminar boundary-layer’s inability to withstand moderate adverse pressure gradients without separating, profile losses in LP turbines operating at low Reynolds numbers can be high. The choice of design pressure distribution for the blading is thus of great importance. Three sub-sonic LP turbine nozzle-guide-vane cascade profiles have been tested over a wide range of incidence, Mach number and Reynolds number. The three profiles are of low, medium and high deflection and, as such, display significantly different pressure distributions. The tests include detailed boundary-layer traverses, trailing-edge base-pressure monitoring and oil-flow visualisation. It is shown that the loss variation with Reynolds number is a function of pressure distribution and that the trailing-edge loss component is dominant at low Reynolds number. The importance of achieving late flow transition — rather than separation — in the suction-surface trailing-edge region is stressed. The paper concludes by remarking on the advantages and practical implications of each loading design.

Three-Dimensional Boundary Layer on a Compressor Rotor Blade at Peak Pressure Rise Coefficient

A comprehensive study of the three-dimensional turbulent boundary layer on a compressor rotor blade at peak pressure rise coefficient is reported in this paper. The measurements were carried out at various chordwise and radial locations on a compressor rotor blade using a rotating miniature “V” configuration hot-wire probe. The data are compared with the measurement at the design condition. Substantial changes in the blade boundary layer characteristics are observed, especially in the outer sixteen percent of the blade span. The increased chordwise pressure gradient and the leakage flow at the peak pressure coefficient have a cumulative effect in increasing the boundary layer growth on the suction surface. The leakage flow has a beneficial effect on the pressure surface. The momentum and boundary layer thicknesses increase substantially from those at the design condition, especially near the outer radii of the suction surface.

The Dynamics of Suspended Solid Particles in a Two Stage Gas Turbine

Gas turbine engines operating in dusty environments are exposed to erosion and performance deterioration. In order to provide the basis for calculating the erosion and performance deterioration of turbines using pulverized coal, an investigation is undertaken to determine the three dimensional particle trajectories in a two stage turbine. The solution takes into account the influence of the variation in the three dimensional flow field. The change in particle momentum due to their collision with the turbine blades and casings is modeled using empirical equations derived from experimental Laser Doppler Velocimetry (LDV) measurements. The results show the three dimensional trajectory characteristics of the solid particles relative to the turbine blades. The results also show that the particle distribution in the flow field are determined by particle-blade impacts. The results obtained from this study indicate the turbine blade locations which are subjected to more blade impacts and hence more erosion damage.

Determination of the Flow Field in LP Steam Turbines

Up to now the determination of flow conditions across the entire circumference in LP steam turbines appears to be a difficult undertaking. The difficulties are mainly caused by the condensing medium steam and by the limited access to the stage from outside. The Last Stage Test Stand at the University of Stuttgart is a suitable facility for flow measurements in the LP part of steam turbines. Besides a short description of the test stand itself, the measuring equipment and the newly developed methods for data acquisition and evaluation are presented. Finally the flow field behind the last stage is shown and the results interpreted.

An Accurate and Efficient Euler Solver for Three-Dimensional Turbomachinery Flows

Accurate and efficient Euler equation numerical solution techniques are presented for analysis of three-dimensional turbomachinery flows. These techniques include an efficient explicit hopscotch numerical scheme for solution of the 3-D time-dependent Euler equations and an O-type body-conforming grid system. The hopscotch scheme is applied to the conservative form of the Euler equations written in general curvilinear coordinates. The grid is constructed by stacking from hub to shroud 2-D O-type grids on equally spaced surfaces of revolution. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy of the analysis method.

Secondary Losses in a Large Deflection Annular Turbine Cascade: Effect of the Entry Boundary Layer Thickness

The paper presents the results of three dimensional flow measurements behind the trailing edges of an impulse turbine blade row of 120° deflection in an annular cascade. The entry boundary layer thickness was systematically varied on the hub and casing walls separately and its effect on secondary flows and losses is investigated. With the increase of entry boundary layer thickness, it has been found that (i) the contours of local loss coefficient show that the magnitude of the hub loss core increased, (ii) the loss cores near the hub and casing wall are convected away from the walls, (iii) the spanwise variation of the pitchwise averaged losses indicate that the position of large loss peak near the hub wall remains the same, but the magnitude of the loss increases, (iv) the exit static pressure increases and the exit velocity in general decreases, (v) the degree of underturning of flow increases and (vi) the net secondary losses do not change appreciably.

Flow Visualization of Secondary Flows in Three Curved Ducts

Secondary flows were experimentally examined in three 90° curved ducts with square cross sections and different radii of curvature. Dean numbers were from 1.5 × 104 to 3.6 × 104 and radius ratios of 0.5, 2.3, and 3.0 were used. Streak photography flow measurements were made and general developing secondary flow patterns were studied for three cross sections in each bend: the inlet (0° plane), the midpoint (45° plane), and the outlet (90° plane). At the 0° plane, stress driven secondary flows were found to consist of flow toward the duct corners from the center, balanced by return flow at the side bisectors. This resulted in eight symmetric flow patterns at the inlet. After a rapid transition region, the pressure driven secondary flow patterns were found to be characterized by flow moving toward the outer curved wall at the axial midplane and returning to the inner wall along the duct walls. At the 45° and 90° planes two symmetric flow patterns were observed. Secondary flow velocities in the test elbow with the smallest radius of curvature, where centrifugal forces are greater, were as much as 27% higher than secondary flows in the more gradual turns examined in this study. Also, the pressure driven secondary flows at the exit were higher than the stress driven flows at the inlet by as much as 39%. The elbow with a radius ratio of 0.5 was found to influence the upstream inlet conditions the most and the secondary flow velocities at the inlet were as much as 56% higher than for the larger radii of curvature.

Turbulence Measurements in a Straight Walled Two Dimensional Diffuser

Turbulent flow field of a straight walled two dimensional diffuser Is experimentally studied using a hot wire anemometer (X-probe type). The diffuser flow Is tested at the optimum angle corresponding to maximum pressure recovery and consequently at conditions of attached flow. Diffuser side walls are made of different materials to study the effect of wall roughness. Measurements of static pressure, flow velocity, turbulence intensity and turbulent shear stress are carried out at six cross-sections distributed along the axial length of the diffuser. At each cross-section measurements were taken at nine planes distributed along the diffuser width between the parallel walls. Variations of boundary layer displacement thicknesses are studied through their relations to turbulence intensity. The present detailed experimental results are intended as an input to a turbulence model for prediction of diffuser flow.