Plane Cascade Research Articles

Experimental Investigation and Theoretical Predication of Flutter Behavior of a Plane Cascade in Low Speed Flow

The Institute of Aeroelasticity operates a test facility which enables aeroelastic investigations of plane cascades in low-speed flow. The test stand serves as a pilot facility to develop tools for analogous investigations in transonic flow. Eleven blades are elastically suspended in a windtunnel with a 1 × 0.2 m2 cross section. This paper describes the experimental method of determining the flutter boundary by extrapolation of the results measured in subcritical flow. A two-dimensional theoretical model of the 11 blades, including the windtunnel walls, permits the computation of unsteady pressures, forces, and moments in close relation to the experiment. The prediction of flutter is compared with experimental results. In the present investigation, the motion of the blades is constrained to pitch around mid-chord. The vibrating blades are mechanically uncoupled. Any interaction between the blades is effected by the air stream, leading to a sensitive dependence on the aerodynamic forces.

Measurements and Prediction of the Effects of Surface Roughness on Profile Losses and Deviation in a Turbine Cascade

Measurements of pressure distributions, profile losses, and flow deviation were carried out on a planar turbine cascade in incompressible flow to assess the effects of partial roughness coverage of the blade surfaces. Spanwise-oriented bands of roughness were placed at various locations on the suction and pressure surfaces of the blades. Roughness height, spacing between roughness elements, and band width were varied. A computational method based on the inviscid/viscous interaction approach was also developed; its predictions were in good agreement with the experimental results. This indicates that good predictions can be expected for a variety of cascade and roughness configurations from any two-dimensional analysis that couples an inviscid method with a suitable rough surface boundary-layer analysis. The work also suggests that incorporation of the rough wall skin-friction law into a three-dimensional Navier–Stokes code would enable good predictions of roughness effects in three-dimensional situations. Roughness was found to have little effect on static pressure distribution around the blades and on deviation angle, provided that it does not precipitate substantial flow separation. Roughness on the suction surface can cause large increases in profile losses; roughness height and location of the leading edge of the roughness band are particularly important. Loss increments due to pressure-surface roughness are much smaller than those due to similar roughness on the suction surface.

Flow Visualization in a Linear Turbine Cascade of High Performance Turbine Blades

Multiple smoke wires are used to investigate the secondary flow near the endwall of a plane cascade with blade shapes used in high-performance turbine stages. The wires are positioned parallel to the endwall and ahead of the cascade, within and outside the endwall boundary layer. The traces of the smoke generated by the wires are visualized with a laser light sheet illuminating various cross sections around the cascade. During the experiment, a periodically fluctuating horseshoe vortex system of varying number of vortices is observed near the leading edge of the cascade. A series of photographs and video tapes was taken in the cascade to trace these vortices. The development and evolution of the horseshoe vortex and the passage vortex are clearly resolved in the photographs. The interation between the suction side leg of the horseshoe vortex and the passage vortex is also observed in the experiment. A vortex induced by the passage vortex, starting about one-fourth of the curvilinear distance along the blade on the suction surface, is also found. This vortex stays close to the suction surface and above the passage vortex in the laminar flow region on the blade. From this flow visualization, a model describing the secondary flows in a cascade is proposed and compared with previous published models. Some naphthalene mass transfer results from a blade near an endwall are cited and compared with the current model. The flows inferred from the two techniques are in good agreement.

Time of Concentration and Peak Discharge Formulas for Planes in Series

Based on the kinematic-wave equations, a time of concentration formula for overland flow over a series of planes is derived. The formula is applicable to a cascade of planes, to planes of different roughnesses, to planes of different flow regimes, to planes of different soil types and infiltration rates resulting in different net intensities, to planes subject to different rainfall intensities, and to planes with a combination of all these variables. For practical applications, the formula is developed in terms of the Manning resistance coefficient that is applicable to turbulent or near turbulent flow only. For the series of planes subject to uniform rainfall excess, under the full-area contribution, the corresponding peak discharge formula in terms of the Manning resistance coefficient is derived. This formula can also be used to estimate the peak discharge under the partial-area contribution. The derived formulas are all consistent with the published formulas for a single plane.

Minimum-drag cascade design for an “impeller-directing vanes-unchoked convergent nozzle” system

The variational problem of designing the slender airfoils of the plane cascade of an “impeller-directing vanes-unchoked convergent nozzle” system in a supersonic ideal (inviscid and non-heat-conducting) gas flow with a subsonic normal velocity component is solved in the linear approximation. The minimized functional is the axial component of the force acting on the system. The conditions to be met by the optimized airfoils include the specification of the projection of the force applied to the cascade onto the axis running parallel to its front, and the free stream condition. Flows past rather sparse cascades, whose “discontinuous characteristics” departing from the lower surface of an airfoil, do not impinge on the upper surface of the adjacent airfoil are considered.

CVBEM Formulation for Multiple Profiles and Cascades

A numerical algorithm based on the CVBEM (from Complex Variable Boundary Element Method) for plane incompressible potential flow around aerofoils and cascades is described. The method is based on the representation of the complex disturbance velocity by means of a Cauchy-type integral around the foil. The Cauchy density function is approximated piecewise linearly and a linear system on the nodal values is obtained by collocation at the nodes. The Kutta condition is imposed via a Lagrange multiplier, in contrast with the least-squares formulation used in a previous work. For cascades, the problem is conformally mapped by a simple hyperbolic function (exponential or hyperbolic tangent) to a related problem with only one profile and one or two poles. Thus, the cascade problem is accurately solved with minor modifications to the single profile code and at the same cost of a single profile computation. Finally, several numerical examples are shown: single Joukowski and NACA profiles, interference coefficients for the flat plate cascade and a plane cascade at the external cylindrical section of an industrial fan.

Minimum-drag cascade design for supersonic flow with subsonic normal velocity component

The variational problem of designing the slender profile of a plane cascade in a supersonic ideal (inviscid and nonheat-conducting) gas flow with a subsonic normal velocity component is solved in the linear approximation. The optimum profiles constructed differ fundamentally from the “closest analog” — the supersonic single profile creating minimum wave drag for given lift. Following [1], it is easy to show that in this case the optimum profile is a plate at an angle of attack determined by the given lift.

Calculation of a three-dimensional turbulent cascade flow

A three-dimensional steady incompressible viscous flow through a plane cascade of turbine blades has been analyzed through a numerical method based on the Navier-Stokes equation. Particular attention is paid to the prediction of secondary flows occurring due to the endwall boundary layer and the blade geometry. A standard k-e model is used for the modelling of Reynolds stress and boundary-fitted coordinates are adopted to represent the complex blade geometry accurately. Two differencing schemes are applied to the convective terms to investigate the effect of numerical diffusion. Experimental data obtained for the flows through the Langston cascade are selected for code validation. Computed results for the velocity vectors and static pressure distributions are in good agreement with presious measurements and provide validity of this numerical method. Three-dimensional viscous flow phenomena and the distribution of total pressure loss caused by secondary flows are also reasonably well predicted.

Determination of Watershed Features for Surface Runoff Models

This paper presents a new algorithm to identify watershed features like channels, ridges, and overland flow planes from a digitized elevation‐location data of discrete points of a catchment. The lateral inflow to the channels are the outflow from the planes bordering the channels. The flow of water is shown to follow distinct paths across these planes and an algorithm is developed to find out the slope, width, average length, and number of the cascade of planes contributing to a particular channel segment. A model catchment is used to demonstrate the steps of the algorithm and a real catchment is also analyzed to demonstrate the application of the algorithms developed. The data generated can be easily stored to be used in numerically based surface runoff models.

Design of plane channels and cascades without flow separation

Design of plane channels and cascades without flow separation

Aerodynamic Performance of a Transonic Low Aspect Ratio Turbine Nozzle

This paper presents detailed information on the three-dimensional flow field in a realistic turbine nozzle with an aspect ratio of 0.65 and a turning angle of 76 deg. The nozzle has been tested in a large-scale planar cascade over a range of exit Mach numbers from 0.3 to 1.3. The experimental results are presented in the form of nozzle passage Mach number distributions and spanwise distribution of losses and exit flow angle. Details of the flow field inside the nozzle passage are examined by means of surface flow visualization and Schlieren pictures. The performance of the nozzle is compared to the data obtained for the same nozzle tested in an annular cascade and a stage environment. Excellent agreement is found between the measured pressure distribution and the prediction of a three-dimensional Euler flow solver.

Three BEM schemes for the calculating of subsonic compressible plane cascade flow

This paper reports research work on the calculation of slightly perturbed two-dimensional subsonic compressible potential flow through a cascade by direct boundary element methods. The work has been performed in three schemes: 1. Scheme 1. Orthotropic medium method. 2. Scheme 2. Equivalent cascade method. 3. Scheme 3. Compressibility correction method. Using the above three schemes, six slightly perturbed cases of 2D subsonic compressible potential flow through a cascade composed of K-7 compressor-blades has been calculated. The results obtained according to these three schemes are compared with each other, and with results of experiments performed by the authors. Satisfactory coincidence has been obtained.

Effects of Simulated Rotation on Tip Leakage in a Planar Cascade of Turbine Blades: Part II—Downstream Flow Field and Blade Loading

This paper and its companion paper present experimental results on the effects of simulated rotation on the tip leakage in a linear turbine cascade test. Part II examines the downstream flow field. For clearance sizes of 2.4 and 3.8 percent of the blade chord, measurements were made in two planes downstream of the trailing edge using a seven-hole pressure probe. Significant changes in the tip leakage vortex and passage vortex structures are observed with the introduction of relative motion. The effects of clearance size and rotation on the relationship between bound circulation and tip-vortex circulation are discussed. The validity of a previously developed tip-vortex model for the case of rotation is examined in the light of the measurements. Finally, for clearances of 1.5, 2.4, and 3.8 percent of the blade chord, the effects of rotation on blade loading are studied through static pressure measurements on the blade surfaces. The distortion of the surface pressure field near the tip is found to be reduced with increasing wall speed. This is consistent with the reduced strength of the tip-leakage vortex as wall speed is increased. For all measurements two wall speeds are considered and the results are compared with the case of no rotation.

SHIFT: a distributed runoff model using irregular triangular facets

SHIFT (Sistema HIdrológico de Facetas Triangulares) is a computational system that allows for the: (1) creation, editing and visualization of a watershed Digital Elevation Model (DEM), based on the Triangular Irregular Network (TIN) concepts; (2) input and interpolation of soil, river-bed, and rainfall data; and (3) calculation and routing of runoff in all the facets and reaches. The TIN DEM model is constructed from a set of points, where the slope changes abruptly. Afterwards, the drainage network is automatically identified and an interactive editor allows the addition or deletion of points to eliminate network discontinuities. Rainfall data are interpolated by means of a procedure based on the minimization of the bending energy of a thin plate. In order to calculate and route the runoff, the system determines the routing sequence of river segments and for each one: identifies the facets forming the contributing area; and determines a cascade of overland flow planes. Then, for each element and time interval, the system calculates the infiltration and routes the resultant runoff by a numerical solution of the kinematic wave equations. This information is saved and the user can see the hydrograph for any facet or reach.

Development of the Tip-Leakage Flow Downstream of a Planar Cascade of Turbine Blades: Vorticity Field

The paper presents detailed measurements of the tip-leakage flow emerging from a planar cascade of turbine blades. Four clearances of from 1.5 to 5.5 percent of the blade chord are considered. Measurements were made at the trailing edge plane, and at two main planes 1.0 and 1.56 axial chord lengths downstream of the cascade. The results give insight into several aspects of the leakage flow, including the size and strength of the leakage vortex in relation to the size of the tip gap and the bound circulation of the blade, and the evolution of the components of vorticity as the vortex diffuses laterally downstream of the blade row. The vortex was found to have largely completed its roll-up into a nearly axisymmetric structure even at the trailing edge of the cascade. As a result, it was found that the vortex could be modeled surprisingly well with a simple model based on the diffusion of a line vortex.

An efficient method for solving the mixed direct-inverse problem of the transonic rotational flow in plane casades

The method in [1] has been extended to the case of rotational flow in this paper. A new method for dealing with the shock wave is presented. This method has the advantages of both the shock-fitting and the shock capturing methods. The direct problem and the mixed direct-inverse problem of the rotational flow in a transonic plane cascade at both design and off design conditions are solved, and the results show that the present method has rapid convergence rate and high accuracy even for the flow with moderately strong shocks.

Flow Field in the Tip Gap of a Planar Cascade of Turbine Blades

Measurements are presented for the flow in the tip gap of a planar cascade of turbine blades. Three clearances of from 2.0 to 3.2 percent of the blade chord were considered. Detailed surveys of the velocity magnitude, flow direction, and total pressure within the gap were supplemented by blade surface and endwall static pressure measurements. The results help to clarify the relationship between the leakage mass flow rate distribution and the driving pressure differences. It was found that even for the present relatively large clearances, fluid near the endwall experiences a pressure difference that is comparable with the blade pressure difference. It is also shown that a simple model can predict with good accuracy the mass flow rate distribution and the magnitude and direction of the velocity vectors within the gap.

Comparison of Lumped and Distributed Models for Chemical Transport by Surface Runoff

AbstractA simple, complete mixing model is used to evaluate the degree of distortion involved in modeling chemical exchange and transport at the soil surface as a lumped rather than a distributed process. A complete mixing model was coupled to the kinematic cascade model, KINEROS, to provide a distributed representation of chemical exchange and transport. A lumped model was developed by ignoring spatial variations of chemical concentration in overland flow and in the mixing zone. Chemical concentration and transport predicted by the alternative approaches were evaluated for total transport, arrival time, peak concentration time, and peak concentration. Total chemical transport was virtually unaffected by model form. However, significant differences were found in arrival and peak concentration times as well as peak concentrations when chemical was placed only in the upper plane of a two plane cascade. The lumped model predicted significantly lower peak chemical concentrations and arrival times that were too short. A lumped model provides a good approximation for transport from a single plane, but caution should be used when a lumped model is used to describe chemical exchange and transport on a cascade of planes.

Computation of rotational transonic flows using a decomposition method

Any vector field may be decomposed, in a unique way, into an irrotational and a rotational part, if appropriate boundary conditions are imposed to the scalar and vector potentials introduced by the above decomposition. In the present work, the transformation is applied to the mass flux vector, in order to calculate two-dimensional, steady, rotational, transonic flows in arbitrarily shaped ducts and plane cascades. The whole procedure is discussed from an analytical and a numerical point of view, while finite difference-finite volume schemes are used to derive numerical results.

Experimental Investigations of Flows Through a Plane Cascade at Large Angles of Attack With Separations

Measurements of various parameters in the flows through a cascade at different angles of attack have been performed. The parameters, such as Reynolds stresses (uu/U2, vv/U2, and uv/U2), pressure distribution on the blade surface, velocity distribution in the blade passage, position of the separation point, and so on, are measured at a large angle of attack with separations. In addition, the development of wake is also investigated. A new formula with second-order accuracy has been developed to analyze hot-wire signals in flows with high turbulence intensity. The hot-wire data are compared with those by conventional measurement techniques and by flow visualizations. The results are satisfactory.