Analytical Evaluation of Aerodynamic Characteristics of Turbines with Nontwisted Rotor Blades
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FLOW - AIRFOILS - CASCADES↗
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Numerical simulation of transonic propeller flow using a 3-dimensional small disturbance code employing novel helical coordinates
The numerical simulation of three-dimensional transonic flow about propeller blades is discussed. The equations for the unsteady potential flow about propellers is given for an arbitrary coordinate system. From this the small disturbance form of the equation is derived for a new helical coordinate system. The new coordinate system is suited to propeller flow and allows cascade boundary conditions to be applied straightforward. A numerical scheme is employed which solves the steady flow as an asymptotic limit of unsteady flow. Solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an eight bladed cascade. Both high and low advance ratio cases are given which include a lifting case as well as nonlifting cases. The nonlifting cases are compared to solutions from a Euler code.
Snyder, Aaron↗
Numerical simulation of transonic propeller flow using a three-dimensional small disturbance code employing novel helical coordinates
The numerical simulation of three-dimensional transonic flow about propeller blades is discussed. The equations for the unsteady potential flow about propellers is given for an arbitrary coordinate system. From this the small disturbance form of the equation is derived for a new helical coordinate system. The new coordinate system is suited to propeller flow and allows cascade boundary conditions to be applied straightforward. A numerical scheme is employed which solves the steady flow as an asymptotic limit of unsteady flow. Solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an eight bladed cascade. Both high and low advance ratio cases are given which include a lifting case as well as nonlifting cases. The nonlifting cases are compared to solutions from a Euler code.
Snyder, Aaron↗
Flutter analysis of cascades using a two dimensional Euler solver
Flutter analysis of a cascade of blades in compressible flow is presented, with each blade of the cascade modeled as a typical section having pitching and plunging degrees of freedom. The aerodynamic forces are obtained from an unsteady, 2-D cascade solver based on the Euler equations. To reduce the computational time, an influence coefficient technique and a pulse response technique are also used to obtain the unsteady force coefficients for any frequency and phase angle. The predicted steady and unsteady aerodynamic forces for selected cascade geometries and flow conditions correlate well with the available experimental and analytical data.
Reddy, T. S. R.↗
Prediction of turbine rotor-stator interaction using Navier-Stokes methods
Flows in turbomachinery are generally complex and do not easily lend themselves to numerical computation. The flows are three-dimensional and inherently unsteady. Complicated blade geometries and flow phenomena such as separation and periodic transition from laminar to turbulent flow add to the numerical complexity. Nevertheless, the accurate numerical analysis of such flows is a problem of considerable interest and practical importance to the turbomachinery community. Much of the early work in turbomachinery flow prediction focussed on airfoil cascades. While such analyses of flows in isolated airfoil rows have helped improve understanding of the flow phenomena and have gained widespread acceptance in the industrial community as a design tool, they do not yield any information regarding the unsteady effects arising out of rotor-stator aerodynamic interaction. These interaction effects become increasingly important as the distance between successive stator and rotor rows is decreased. Thus, the need exists for analytical tools that treat the rotor and stator airfoils as a system and provide information regarding the magnitude and the impact of the unsteady effects. The focus a three-dimensional, time-accurate, thin-layer Navier-Stokes code that was recently developed to study rotor-stator interaction problems. A system of patched and overlaid grids that move relative to each other is used to discretize the flow field and the governing equations are integrated using a third-order upwind scheme set in an iterative, implicit framework. The code was used to simulate subsonic flow through an axial turbine configuration for which considerable experimental data exists. Grid refinement studies were also conducted as part of the code validation process. The current status of the research, along with planned future directions, are also discussed.
Madavan, Nateri K.↗
A Solution of the Direct and Inverse Potential Problems for Arbitrary Cascades of Airfoils
Methods are given of determining the potential flow plast an arbitrary cascade of airfoils and the inverse problem of determining an airfoil having a prescribed velocity distribution in cascade. Results indicated that Cartesian mapping function method may be satisfactorily extended to include cascades. Numerical calculation for computing cascades by Cartesian mapping function method is considerably greater than for single airfoils but much less than hitherto required for cascades. Detailed results are presented graphically.
PRESSURE DISTRIBUTION - AIRFOILS↗
A calculation procedure for viscous flow in turbomachines, volume 1
A method for analyzing the nonadiabatic viscous flow through turbomachine rotors is presented. The field analysis is based upon the numerical integration of the full incompressible stream function vorticity form of the Navier-Stokes equations, together with the energy equation, over the rotor blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. A numerical scheme is used to carry out the necessary integration of the elliptic governing equations. The flow characteristics within the rotor of a radial inflow turbine are investigated over a wide range of operating conditions. The calculated results are compared to existing experimental data. The flow in a radial compressor is analyzed in order to study the behavior of viscous flow in diffusing cascades. The results are compared qualitatively to known experimental trends. The solution obtained provides insight into the flow phenomena in this type of turbomachine. It is concluded that the method of analysis is quite general and gives a good representation of the actual flow behavior within turbomachine passages.
Khalil, I.↗
Measurement of Gust Response on a Turbine Cascade
The paper presents benchmark experimental data on a gust response of an annular turbine cascade. The experiment was particularly designed to provide data for comparison with the results of a typical linearized gust-response analysis. Reduced frequency, Mach number, and incidence were varied independently. Except for the lowest reduced frequency, the gust velocity distribution was nearly sinusoidal. For the high inlet-velocity series of tests, the cascade was near choking. The mean flow was documented by measuring blade surface pressures and the cascade exit flow. High-response pressure transducers were used to measure the unsteady pressure distribution. Inlet-velocity components and turbulence parameters were measured using hot wire. In addition to the synchronous time-average pressure spectra, typical power spectra are included for several representative conditions.
Kurkov, A. P.↗
Measurement of Gust Response on a Turbine Cascade
This in-house experiment on the gust response of an annular turbine cascade was particularly designed to provide data to compare with the results of a typical, linearized gust-response analysis. Reduced frequency, Mach number, and incidence were varied independently. Except for the lowest reduced frequency, the gust velocity distribution was nearly sinusoidal. For the high inlet-velocity series of tests, the cascade was near choking. The mean flow was documented by measuring blade surface pressures and the cascade exit flow, and high-response pressure transducers were used to measure the unsteady pressure distribution. Inlet-velocity components and turbulence parameters were measured using hot wire anemometry. In addition to the synchronous time-averaged pressure spectra, typical power spectra are included for several representative conditions.
Kurkov, Anatole P.↗
Resistance of cascade of airfoils in gas stream at subsonic velocity
A method of computing the resistance of a cascade of airfoils in a viscous compressible gas flow is described.
BOUNDARY LAYER - AIRFOILS - CASCADES↗
Three-dimensional Navier-Stokes analysis and redesign of an imbedded bellmouth nozzle in a turbine cascade inlet section
Experimental measurements in the inlet of a transonic turbine blade cascade showed unacceptable pitchwise flow non-uniformity. A three-dimensional, Navier-Stokes computational fluid dynamics (CFD) analysis of the imbedded bellmouth inlet in the facility was performed to identify and eliminate the source of the flow non-uniformity. The blockage and acceleration effects of the blades were accounted for by specifying a periodic static pressure exit condition interpolated from a separate three-dimensional Navier-Stokes CFD solution of flow around a single blade in an infinite cascade. Calculations of the original inlet geometry showed total pressure loss regions consistent in strength and location to experimental measurements. The results indicate that the distortions were caused by a pair of streamwise vortices that originated as a result of the interaction of the flow with the imbedded bellmouth. Computations were performed for an inlet geometry which eliminated the imbedded bellmouth by bridging the region between it and the upstream wall. This analysis indicated that eliminating the imbedded bellmouth nozzle also eliminates the pair of vortices, resulting in a flow with much greater pitchwise uniformity. Measurements taken with an installed redesigned inlet verify that the flow non-uniformity has indeed been eliminated.
VanFossen, G. J.↗
Secondary vorticity in axial compressor blade rows
A theoretical investigation of secondary flow in compressor blade rows is presented. Formulas for calculating secondary flows in annular cascade blade passages are derived. The influence of the relative rotation vector on secondary velocity perturbations, using recent developments in shear-flow theory, is examined. A method of calculating the flow through successive blade rows is given and a comparison is made with experimental results.
Dixon, S. L.↗
Incompressible lifting-surface aerodynamics for a rotor-stator combination
Current literature on the three dimensional flow through compressor cascades deals with a row of rotor blades in isolation. Since the distance between the rotor and stator is usually 10 to 20 percent of the blade chord, the aerodynamic interference between them has to be considered for a proper evaluation of the aerothermodynamic performance of the stage. A unified approach to the aerodynamics of the incompressible flow through a stage is presented that uses the lifting surface theory for a compressor cascade of arbitrary camber and thickness distribution. The effects of rotor stator interference are represented as a linear function of the rotor and stator flows separately. The loading distribution on the rotor and stator flows separately. The loading distribution on the rotor and stator blades and the interference factor are determined concurrently through a matrix iteration process.
Ramachandra, S. M.↗
Detailed computational procedure for design of cascade blades with prescribed velocity distributions in compressible potential flows
A detailed step-by-step computational outline is presented for the design of two-dimensional cascade blades having a prescribed velocity distribution on the blade in a potential flow of the usual compressible fluid. The outline is based on the assumption that the magnitude of the velocity in the flow of the usual compressible nonviscous fluid is proportional to the magnitude of the velocity in the flow of a compressible nonviscous fluid with linear pressure-volume relation.
Costello, George R↗
Three-dimensional Navier-Stokes analysis and redesign of an imbedded bellmouth nozzle in a turbine cascade inlet section
Verification of proposed turbopump blading performance will involve evaluation of candidate blades in cascade test facilities. It is necessary to be able to predict the flow fields within these cascades for the results to be applicable to actual engine environments. This work presents the results of a study to predict the flow field for the NASA Lewis Transonic Turbine Blade Cascade Facility, which is similar to those used to evaluate rocket propulsion turbines. A pitchwise nonuniform total pressure distribution was observed at the blade row leading edge plane. A CFD analysis was used to show that the cause of the flow nonuniformity was a pair of vortices that originated in an embedded bellmouth inlet. Further CFD analysis was used to verify that a redesigned inlet section resulted in a flow with acceptable uniformity. A computational analysis was chosen because physical accessibility to the inlet section was limited, and because a computational approach also allows one to examine design changes cheaper and more quickly than an experimental approach would. The PARC code, a general purpose, three-dimensional, Navier-Stokes code with multiblock solution capability, was chosen for the present study. Results are presented detailing the computational requirements needed to accurately predict flows of this nature. Calculations of the original geometry showed total pressure loss regions consistent in strength and in location to experimental measurements. An examination of the results shows that the distortions are caused by a pair of vortices that originate as a result of the interaction of the flow with the imbedded bellmouth. Computations were performed for an inlet geometry which eliminated the imbedded bellmouth by bridging the region between it and the upstream wall. This analysis indicated that eliminating the imbedded bellmouth eliminates the troublesome pair of vortices, resulting in a flow with much greater pitchwise uniformity.
Giel, P. W.↗
Aerodynamic Design of Axial Flow Compressors
An overview of 'Aerodynamic systems design of axial flow compressors' is presented. Numerous chapters cover topics such as compressor design, potential and viscous flow in two dimensional cascades, compressor stall and blade vibration, and compressor flow theory. Theoretical aspects of flow are also covered. This work is based substantially on a three-volume Confidential Research Memorandum f h t issued by the National Advisory Committee for Aeronautics in 1956 and declassified in .1958 for release to the general public. The material, which was of a fundamental character, has been updated for the present edition in the light of subsequent developments in the field and has been carefully reexamined for current validity by members of the staff of the NASA Lewis Research Center, Cleveland, Ohio. It is now published for the first time in a single volume to meet continuing demand for the information and to make it readily available in convenient form to the engineering community both within and outside the National Aeronautics and Space Administration.
Axial flow compressor↗
Velocity distribution on symmetrical airfoils in closed tunnels by conformal mapping
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WIND TUNNEL TESTS - CORRECTIONS↗
Nonuniform flow field generation for supersonic compressor stator development: Design and preliminary results
Design and preliminary results are given for a technique which can generate a nonuniform flow similar to the discharge of an impulse supersonic compressor rotor. The technique utilizes a carefully contoured, two-dimensional blunt body in a conventional hypersonic wind tunnel to generate the required flow field. To show the effects of the flow vorticity, a cascade of impulse-type blades was tested in this test stream. Some preliminary performance data are given along with comparison with previously determined uniform flow results.
Lipfert, F. W.↗