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At least 217 records · Page 12

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NASA NTRS1988

Simulation of 2-dimensional viscous flow through cascades using a semi-elliptic analysis and hybrid C-H grids

A semi-elliptic formulation, termed the interacting parabolized Navier-Stokes (IPNS) formulation, is developed for the analysis of a class of subsonic viscous flows for which streamwise diffusion is neglible but which are significantly influenced by upstream interactions. The IPNS equations are obtained from the Navier-Stokes equations by dropping the streamwise viscous-diffusion terms but retaining upstream influence via the streamwise pressure-gradient. A two-step alternating-direction-explicit numerical scheme is developed to solve these equations. The quasi-linearization and discretization of the equations are carefully examined so that no artificial viscosity is added externally to the scheme. Also, solutions to compressible as well as nearly compressible flows are obtained without any modification either in the analysis or in the solution process. The procedure is applied to constricted channels and cascade passages formed by airfoils of various shapes. These geometries are represented using numerically generated curilinear boundary-oriented coordinates forming an H-grid. A hybrid C-H grid, more appropriate for cascade of airfoils with rounded leading edges, was also developed. Satisfactory results are obtained for flows through cascades of Joukowski airfoils.

Ramamurti, R.↗

NASA NTRS1989

The measurement of boundary layers on a compressor blade in cascade. Volume 1: Experimental technique, analysis and results

Measurements were made of the boundary layers and wakes about a highly loaded, double-circular-arc compressor blade in cascade. These laser Doppler velocimetry measurements have yielded a very detailed and precise data base with which to test the application of viscous computational codes to turbomachinery. In order to test the computational codes at off-design conditions, the data were acquired at a chord Reynolds number of 500,000 and at three incidence angles. Moreover, these measurements have supplied some physical insight into these very complex flows. Although some natural transition is evident, laminar boundary layers usually detach and subsequently reattach as either fully or intermittently turbulent boundary layers. These transitional separation bubbles play an important role in the development of most of the boundary layers and wakes measured in this cascade and the modeling or computing of these bubbles should prove to be the key aspect in computing the entire cascade flow field. In addition, the nonequilibrium turbulent boundary layers on these highly loaded blades always have some region of separation near the trailing edge of the suction surface. These separated flows, as well as the subsequent near wakes, show no similarity and should prove to be a challenging test for the viscous computational codes.

Zierke, William C.↗

NASA NTRS1990

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 aerodynamic phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Hall, Kenneth C.↗

NASA NTRS1990

Numerical simulations of supersonic flow through oscillating cascade sections

A finite difference code was 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 NTRS1990

Development of a linearized unsteady aerodynamic analysis for cascade gust response predictions

A method for predicting the unsteady aerodynamic response of a cascade of airfoils to entropic, vortical, and acoustic gust excitations is being developed. Here, the unsteady flow is regarded as a small perturbation of a nonuniform isentropic and irrotational steady background flow. A splitting technique is used to decompose the linearized unsteady velocity into rotational and irrotational parts leading to equations for the complex amplitudes of the linearized unsteady entropy, rotational velocity, and velocity potential that are coupled only sequentially. The entropic and rotational velocity fluctuations are described by transport equations for which closed-form solutions in terms of the mean-flow drift and stream functions can be determined. The potential fluctuation is described by an inhomogeneous convected wave equation in which the source term depends on the rotational velocity field, and is determined using finite-difference procedures. The analytical and numerical techniques used to determine the linearized unsteady flow are outlined. Results are presented to indicate the status of the 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 herein leads to very efficient predictions of cascade unsteady aerodynamic response phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Verdon, Joseph M.↗

NASA NTRS1988

The unsteady aerodynamics of an oscillating cascade in a compressible flow field

Fundamental experiments were performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate and quantify the unsteady aerodynamics of a cascade of biconvex airfoils executing torsion-mode oscillations at realistic reduced frequencies. Flush-mounted, high-response miniature pressure transducers were used to measure the unsteady airfoil surface pressures. The pressures were measured for three interblade phase angles at two inlet Mach numbers, 0.65 and 0.80, and two incidence angles, 0 and 7 deg. The time-variant pressures were analyzed by means of discrete Fourier transform techniques, and these unique data were then compared with predictions from a linearized unsteady cascade model. The experimental results indicate that the interblade phase angle had a major effect on the chordwise distributions of the airfoil surface unsteady pressure, and that reduced frequency, incidence angle, and Mach number had a somewhat less significant effect.

Buffum, Daniel H.↗

NASA NTRS1990

Cascade aerodynamic gust response including steady loading effects

To predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first-order model is formulated. The flow is analyzed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body-fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analyzing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.

Chiang, Hsiao-Wei D.↗

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, Milind A.↗

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

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.↗