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NASA NTRS1991

Computation of supersonic and low subsonic cascade flows using an explicit Navier-Stokes technique and the kappa-epsilon turbulence model

A fully explicit two-dimensional flow solver, based on a four-stage Runge-Kutta scheme, was developed and utilized to predict two-dimensional viscous flow through turbomachinery cascades for which experimental data is available. The formulation is applied to the density averaged Navier-Stokes equations. Several features of the technique improve the ability of the code to predict high Reynolds number flows on highly stretched grids. These include a low Reynolds number compressible form of the k-epsilon turbulence model, anisotropic scaling of artificial dissipation terms and locally varying timestep evaluation based on hyperbolic and parabolic stability considerations. Comparisons between computation and experiment are presented for both a supersonic and a low-subsonic compressor cascade. These results indicate that the code is capable of predicting steady two-dimensional viscous cascade flows over a wide range of Mach numbers in reasonable computational times.

Kunz, R. F.↗

NASA NTRS1991

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time-marching Full-Potential cascade solver are developed and verified. In the first method, the Influence Coefficient method, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response method, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers using both flat plates and actual airfoils.

Bakhle, Milind A.↗

NASA NTRS1990

Numerical simulations of supersonic flow through oscillating cascade sections

A finite difference code has been developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model 'real' airfoils that have thickness and camber. Sample predictions are presented for a cascade of loaded airfoils and show appreciable differences in the unsteady surface pressure distributions when compared with the flat plate results.

Huff, Dennis L.↗

NASA NTRS1991

Variable soft X-ray excesses in active galactic nuclei from nonthermal electron-positron pair cascades

In the present study of the formation of steep soft X-ray excesses that are superposed on flatter, hard X-ray power-law spectra in nonthermal electron-positron pair cascade sources, the soft excess in pair-cascade AGN models appears as a steep power law superposed on the tail of the UV bump and the flat nonthermal (hard X-ray) power law. The model-parameter space in which an excess in soft X-rays is visible is ascertained, and the time-variability of soft excesses in pair cascade models is examined. It is established that the parameter space in which soft excesses appear encompasses the range of preferred input parameters for a recently development Compton reflection model of UV and X-ray emission from the central engine of an AGN.

Zdziarski, Andrzej A.↗

NASA NTRS1991

Gust response analysis for cascades operating in nonuniform mean flows

The linearized unsteady aerodynamic response of a cascade of airfoils subjected to entropic, vortical, and acoustic gusts is analyzed. Field equations for the first-order unsteady perturbation flow are obtained by linearizing the full time-dependent mass, momentum, and energy conservation equations about a nonlinear, isentropic, and irrotational mean or steady flow. A splitting technique is then used to decompose the unsteady velocity field into irrotational and rotational parts leading to field equations for the unsteady entropy, rotational velocity, and irrotational velocity fluctuations that are coupled only sequentially. The entropic and rotational velocity fluctuations can be described in terms of the mean-flow drift and stream functions which can be computed numerically. The irrotational unsteady velocity is described by an inhomogeneous linearized potential equation which contains a source term that depends on the rotational velocity field. This equation is solved via a finite difference technique. Results are presented to indicate the status of the numerical solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described leads to very efficient predictions of cascade unsteady aerodynamics phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Hall, Kenneth C.↗

NASA NTRS1991

Design of transonic compressor cascades using hodograph method

The use of the Hodograph Method in the design of a transonic compressor cascade is discussed. The design of the flow mode in the transonic compressor cascade must be as follows: the flow in the nozzle part should be uniform and smooth; the location of the sonic line should be reasonable; and the aerodynamic character of the flow canal in the subsonic region should be met. The rate through cascade may be determined by the velocity distribution in the subsonic region (i.e., by the numerical solution of the Chaplygin equation). The supersonic sections A'C' and AD are determined by the analytical solution of the Mixed-Type Hodograph equation.

Chen, Zuoyi↗

NASA NTRS1991

The aerodynamic effect of fillet radius in a low speed compressor cascade

The aerodynamic effects of fillet size in a low speed compressor cascade were experimentally studied. Two blade profiles were used during the experiment, namely a controlled diffusion blade and a double circular arc blade. Cascades were tested with three fillet radii and two boundary layer thicknesses over a large range of incidence angles. The cascade performance was determined by extensive downstream flow measurements using a two head, 5 hole pressure probe. Results differ significantly between the two types of blades tested. As fillet radius increases secondary flows and total pressure losses were found to increase for the controlled diffusion blades; whereas, for the double circular arc blades the losses decrease, particularly at high incidence angles.

Curlett, Brian P.↗

NASA NTRS1991

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time marching Full Potential cascade solver are developed and verified. In the first method, the Influence Coefficient, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier Transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers.

Bakhle, M. A.↗

NASA NTRS1992

Analysis of cascades using a two dimensional Euler aeroelastic solver

A two-dimensional unsteady aerodynamic Euler solver based on a flux differencing scheme is being developed to analyze oscillating cascades. The cascades can have subsonic, transonic, or supersonic flow with either subsonic or supersonic axial velocity. The aerodynamic solver is coupled with a typical section structural model for each blade of the cascade. Flutter analysis methods both in time and frequency domains are then implemented into the resulting aeroelastic solver. Methods that reduce computational time for calculating the unsteady aerodynamic coefficients, namely the influence coefficient method and the pulse response method, are also implemented and validated. The present solver showed good correlation with published results for all the flow regimes. It is shown that grid coarsening improved the accuracy of the predictions. A representative flutter calculation showed that both the frequency domain and time domain methods are implemented correctly into the aeroelastic solver.

Reddy, T. S. R.↗

NASA NTRS1993

Cascaded VLSI Chips Help Neural Network To Learn

Cascading provides 12-bit resolution needed for learning. Using conventional silicon chip fabrication technology of VLSI, fully connected architecture consisting of 32 wide-range, variable gain, sigmoidal neurons along one diagonal and 7-bit resolution, electrically programmable, synaptic 32 x 31 weight matrix implemented on neuron-synapse chip. To increase weight nominally from 7 to 13 bits, synapses on chip individually cascaded with respective synapses on another 32 x 32 matrix chip with 7-bit resolution synapses only (without neurons). Cascade correlation algorithm varies number of layers effectively connected into network; adds hidden layers one at a time during learning process in such way as to optimize overall number of neurons and complexity and configuration of network.

Duong, Tuan A.↗

NASA NTRS1952

Effect of Mach Number on the Flow and Application of Compressibility Corrections in a Two-Dimensional Subsonic-Transonic Compressor Cascade Having Varied Porous-Wall Suction at the Blade Tips

A cascade of 65-(12)10 compressor blades was tested at one geometric setting over a range of inlet Mach number from 0.12 to 0.89. Two groups of data are presented and compared: the first from the cascade operating conventionally with no boundary-layer control, and the second with the boundary layer controlled by a combination of upstream slot suction and porous-wall suction at the blade tips. A criterion for two-dimensionality was used to specify the degree of boundary-layer control by suction to be applied. The data are presented and an analysis is made to show the effect of Mach number on turning angle, blade wake, pressure distribution about the blade profile and static-pressure rise. The influence of boundary-layer control on these parameters as well as on the secondary losses is illustrated. A system of correlating the measured static-pressure rise through the cascade with the theoretical isentropic values is presented which gives good agreement with the data. The pressure distribution about the blade profile for an inlet Mach number of 0.21 is corrected with the Prandtl-Glauert, Karman-Tsien, and vector-mean velocity - contraction coefficient compressibility correction factors to inlet Mach numbers of 0.6 and 0.7. The resulting curves are compared with the experimental pressure distributions for inlet Mach numbers of 0.6 and 0.7 so that the validity of applying the three corrections can be evaluated.

Briggs, William B.↗

NASA NTRS1954

A Visualization Study of Secondary Flows in Cascades

Flow-visualization techniques are employed to ascertain the streamline patterns of the nonpotential secondary flows in the boundary layers of cascades, and thereby to provide a basis for more extended analyses in turbomachines. The three-dimensional deflection of the end-wall boundary layer results in the formation of a vortex within each cascade passage. The size and tightness of the vortex generated depend upon the main-flow turning in the cascade passage. Once formed, a vortex resists turning in subsequent blade rows, with consequent unfavorable angles of attack and possible flow disturbances on the pressure surfaces of subsequent blade rows when the vortices impinge on these surfaces. Two major tip-clearance effects are observed, the formation of a tip-clearance vortex and the scraping effect of a blade with relative motion past the wall boundary layer. The flow patterns indicate methods for improving the blade tip-loading characteristics of compressors and of low- and high-speed turbulence.

Herzig, Howard Z↗

NASA NTRS1951

Systematic Two-Dimensional Cascade Tests of NACA 65-Series Compressor Blades at Low Speeds

The performance of NACA 65-series compressor blade section in cascade has been investigated systematically in a low-speed cascade tunnel. Porous test-section side walls and for high-pressure-rise conditions, porous flexible end walls were employed to establish conditions closely simulating two-dimensional flow. Blade sections of design lift coefficients from 0 to 2.7 were tested over the usable angle-of-attack range for various combinations of inlet-flow angle. A sufficient number of combinations were tested to permit interpolation and extrapolation of the data to all conditions within the usual range of application. The results of this investigation indicate a continuous variation of blade-section performance as the major cascade parameters, blade camber, inlet angle, and solidity were varied over the test range. Summary curves of the results have been prepared to enable compressor designers to select the proper blade camber and angle of attack when the compressor velocity diagram and desired solidity have been determined.

Herrig, L. Joseph↗

NASA NTRS1994

Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. Volume 1: Theory development and parametric studies

Typical analytical models for interaction between rotor and stator in a turbofan analyze the effect of wakes from the rotor impinging on the stator, producing unsteady loading, and thereby generating noise. Reflection/transmission characteristics of the rotor are sometimes added in a separate calculation. In those models, there is a one-to-one relationship between wake harmonics and noise harmonics; that is, the BPF (blade passing frequency) wake harmonic causes only the BPF noise harmonic, etc. This report presents a more complete model in which flow tangency boundary conditions are satisfied on two cascades in relative motion for several harmonics simultaneously. By an extension of S.N. Smith's code for two dimensional flat plate cascades, the noise generation/frequency scattering/blade row reflection problem is solved in a single matrix inversion. It is found that the BPF harmonic excitation of the stator scatters considerable energy in the higher BPF harmonics due to relative motion between the blade rows. Furthermore, when swirl between the rotor and stator is modeled, a 'mode trapping' effect occurs which explains observations on fans operating at rotational speeds below BFP cuton: the BPF mode amplifies between blade rows by multiple reflections but cannot escape to the inlet and exit ducts. However, energy scattered into higher harmonics does propagate and dominates the spectrum at two and three times BPF. This report presents the complete derivation of the theory, comparison with a previous (more limited) coupled rotor/stator interaction theory due to Kaji and Okazaki, exploration of the mode trapping phenomenon, and parametric studies showing the effects of vane/blade ratio and rotor/stator interaction. For generality, the analysis applies to stages where the rotor is either upstream or downstream of the stator and to counter rotation stages. The theory has been coded in a FORTRAN program called CUP2D, documented in Volume 2 of this report. It is concluded that the new features of this analysis - unsteady coupling, frequency scattering, and flow turning between rotor and stator - have a profound effect on noise generation caused by rotor/stator interaction. Treating rotors and stators as isolated cascades is not adequate for noise analysis and prediction.

Hanson, Donald B.↗

NASA NTRS1995

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.↗

NASA NTRS1993

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.↗

NASA NTRS1994

Very high energy gamma rays from active galactic nuclei: Cascading on the cosmic background radiation fields and the formation of pair halos

Recent high-energy gamma-ray observations (E(sub gamma) greater than 100 MeV) of blazar Active Galactic Nuclei (AGNs) show emission spectra with no clear upper energy cutoff. AGNs, considered to be possible sources for the observed flux of cosmic rays beyond 10(exp 19) eV, may well have emission extending into the very high energy (VHE), (E(sub gamma) greater than 100 GeV) domain. Because VHE gamma-rays are absorbed by pair production on the intergalactic background radiation fields, much of this emission may not be directly visible. The electromagnetic cascades initiated by absorbed VHE gamma-rays, however, may be observable. Since, most probably, the velocities of (e(+), e(-)) pairs produced in a cascade are quickly isotropized by an ambient random magnetic field, extended 'halos' (R greater than 1 Mpc) of pairs will be formed around AGNs with VHE emission. The cascade radiation from these pair halos is emitted isotropically and should be observable at energies below a few TeV. The halo radiation can be distinguished by its characteristic variation in spectrum and intensity with angular distance from the central source. This variation depends weakly on the details of the central source model, e.g., the orientation and beaming/opening angle of an emitting jet. Limiting or determining the intensity of the pair halo can thus serve as a model-independent bound on or measure of the VHE power of AGNs. Next-generation Cherenkov telescopes may be able to image a pair halo.

Aharonian, F. A.↗

NASA NTRS1996

Endwall Heat Transfer Measurements in a Transonic Turbine Cascade

Turbine blade endwall heat transfer measurements are given for a range of Reynolds and Mach numbers. Data were obtained for Reynolds numbers based on inlet conditions of 0.5 and 1.0 x 106, for isentropic exit Mach numbers of 1.0 and 1.3, and for freestream turbulence intensities of 0.25% and 7.0%. Tests were conducted in a linear cascade at the NASA Lewis Transonic Turbine Blade Cascade Facility. The test article was a turbine rotor with 136' of turning and an axial chord of 12.7 cm. The large scale allowed for very detailed measurements of both flow field and surface phenomena. The intent of the work is to provide benchmark quality data for computational fluid dynamics (CFD) code and model verification. The flow field in the cascade is highly three-dimensional as a result of thick boundary layers at the test section inlet. Endwall heat transfer data were obtained using a steady-state liquid crystal technique.

Giel, P. W.↗