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NASA NTRS1974

Cosmic-ray cascades photographed in scintillator

Light produced by nuclear-electromagnetic cascades in a plastic scintillator can be photographed, and the resulting images on film used to measure both the energy content of the cascades and also the positions at which the cascades passed through the scintillator. The energy content of a cascade can be measured to 20% and its position determined to plus or minus 0.8 cm in each scintillator. Techniques for photographing the cascades and analyzing the film are described. Sample data are presented and discussed.

Barrowes, S. C.↗

NASA NTRS1978

Measurement of the turbulence intensity behind a two-dimensional cascade and in a three-stage axial blower

Turbulence intensity (Tu) measurements were made in two-dimensional and rotating cascades of blades in a low-speed cascade wind tunnel using hot-wire probes as sensors. The local Tu at Re = 1.6x100000 was determined in the wake zone behind a two-dimensional cascade. Then the values were recomputed for a rotating cascade, giving a mean turbulence intensity of 6.5% at 1/10 chord downstream and 2.9% at one chord. Fans were used for measurements on the rotating cascade. Re was equal to 7x100000. Frequency analysis was employed to separate the actual Tu of the entry flow from the effects caused by interaction with the rotor blades, showing that the true Tu increased from a few tenths of a percent to 6.6% in the 1st rotor, and from 7.2 to 9.3% in the 2d rotor. The Tu behind the 3d rotor was equal to 8.9%.

Kiock, R.↗

NASA NTRS1982

An experimental investigation of gapwise periodicity and unsteady aerodynamic response in an oscillating cascade. 1: Experimental and theoretical results

Tests were conducted on a linear cascade of airfoils oscillating in pitch to measure the unsteady pressure response on selected blades along the leading edge plane of the cascade, over the chord of the center blade, and on the sidewall in the plane of the leading edge. The pressure data were reduced to Fourier coefficient form for direct comparison, and were also processed to yield integrated loads and, particularly, the aerodynamic damping coefficient. Results from the unsteady Verdon/Caspar theory for cascaded blades with nonzero thickness and camber were compared with the experimental measurements. The three primary results are: (1) from the leading edge plane blade data, the cascade was judged to be periodic in unsteady flow over the range of parameters tested; (2) the interblade phase angle was found to be the single most important parameter affecting the stability of the oscillating cascade blades; and (3) the real blade theory and the experiment were in excellent agreement for the several cases chosen for comparison.

Carta, F. O.↗

NASA NTRS1986

Application of a linearized unsteady aerodynamic analysis to standard cascade configurations

A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the linearized unsteady aerodynamic response to prescribed blade motions, has been applied to five cascade configurations. These include the first, fifth, eighth and ninth standard configurations proposed as a result of the Second International Symposium on Aeroelasticity in Turbomachines and a NASA Lewis flutter cascade. Selected results from this study, including comparisons between analytical predictions and the experimental measurements submitted for three of the foregoing configurations, are described. The correlation between theory and experiment for the first standard configuration (a compressor cascade operating at low Mach number and frequency) is quite good. Moreover, the predictions and measurements for the NASA Lewis cascade of symmetric biconvex airfoils show good qualitative agreement. However, wide discrepancies exist between the theoretical predictions and the experimental measurements for the fifth standard configuration (a subsonic transonic fan tip cascade). These can be partially attributed to conditions being imposed in the experiment which differ from those commonly used in unsteady aerodynamic analyses.

Verdon, J. M.↗

NASA NTRS1986

The boundary layer on compressor cascade blades

The purpose of NASA Research Grant NSG-3264 is to characterize the flowfield about an airfoil in a cascade at chord Reynolds number(R sub C)near 5 x 10 to the 5th power. The program is experimental and combines laser Doppler velocimeter (LDV) measurements with flow visualization techniques in order to obtain detailed flow data, e.g., boundary layer profiles, points of separation and the transition zone, on a cascade of highly-loaded compressor blades. The information provided by this study is to serve as benchmark data for the evaluation of current and future compressor cascade predictive models, in this way aiding in the compressor design process. Summarized is the research activity for the period 1 December 1985 through 1 June 1986. Progress made from 1 June 1979 through 1 December 1985 is presented. Detailed measurements have been completed at the initial cascade angle of 53 deg. (incidence angle 5 degrees). A three part study, based on that data, has been accepted as part of the 1986 Gas Turbine Conference and will be submitted for subsequent journal publication. Also presented are data for a second cascade angle of 45 deg (an incidence angle of 3 degrees).

Deutsch, S.↗

NASA NTRS1986

On the application of a linearized unsteady potential-flow analysis to fan-tip cascades

A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the unsteady response to prescribed blade motions, has been applied to five two-dimensional cascade configurations. These include a flat-plate cascade and three cascades which are representative of the tip sections of current fan designs. Here the blades are closely spaced, highly staggered, and operate at low mean incidence. The fifth configuration is a NASA Lewis cascade of symmetric biconvex airfoils for which experimental measurements are available. Numerical solutions are presented that clearly illustrate the effects and importance of blade geometry and mean blade loading on the linearized unsteady response at high subsonic inlet Mach number and high blade-vibrational frequency. In addition, a good qualitative agreement is shown between the analytical predictions and experimental measurements for the cascade of symmetric biconvex airfoils. Finally, recommendations on the research needed to extend the range of application of linearized unsteady aerodynamic analyses are provided.

Usab, W. J., Jr.↗

NASA NTRS1989

Time domain unsteady incompressible cascade airfoil theory for helicopter rotors in hover

A detailed derivation of a finite-time arbitrary-motion incompressible cascade theory is presented for both Laplace and frequency domains. The generalized cascade lift deficiency function is shown to be consistent with the generalized Theodorsen's lift deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity; it also yields a correct value for the zero reduced frequency limit. Efficient numerical procedures are presented for the evaluation of the cascade lift deficiency function. Numerical examples comparing the cascade lift deficiency function with Loewy's (1957) rotary-wing lift deficiency function in frequency domain are presented. Pade approximants of the cascade lift deficiency function are constructed using a Bode plot approach that allows for complex poles. A general-purpose optimization program is used to determine the coefficients of the approximant.

Dinyavari, M. A. H.↗

NASA NTRS1990

Time domain flutter analysis of cascades using a full-potential solver

A time domain approach is used to determine the dynamic aeroelastic stability of a cascade of blades. The structural model for each blade is a typical section with two degrees of freedom. The aerodynamic model is the unsteady, two-dimensional, full-potential flow through the cascade of airfoils. The unsteady equations of motion for the structure and the fluid are integrated simultaneously in time starting with the steady flowfield and a small initial disturbance applied to the airfoils. The motion of each blade is analyzed to determine the aeroelastic stability of the cascade. The effect of interblade phase angle is included in the analysis by allowing each blade to have an independent motion and considering a number of blade passages. Calculations are made using an airfoil section and structural parameters that are representative of a propfan. The results are compared with those from a separate frequency domain analysis. Good agreement between the results is observed. With the time domain approach, it is possible to consider nonlinear structural models and nonlinear force-displacement relations. The method allows a realistic simulation of the motion of the fluid and the cascade blades for a better physical understanding and it also has the potential for saving computational time when compared to the frequency domain approach for the flutter analysis of cascades.

Bakhle, Milind A.↗

NASA NTRS1991

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

Huff, Dennis L.↗

NASA NTRS1991

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

A compressible flow code that can predict the nonlinear unsteady aerodynamic associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

Huff, Dennis L.↗

NASA NTRS1992

Aerodynamics of loaded cascades in subsonic flows subject to unsteady three-dimensional vortical disturbances

A highly efficient numerical method is developed for three-dimensional, periodic, vortical flows around a cascade of loaded airfoils. The method linearizes Euler's equations about the mean flow of the cascade and thus fully accounts for the effects of distortion of the vortical disturbances as they propogate and interact with the cascade mean flow. The numerical scheme is based on splitting the unsteady velocity into vortical and potential parts. The latter is governed by a non-constant coefficient inhomogeneous convective wave equation. A new and computationally suitable out-flow conditions are derived and avoid the difficulties associated with the singular velocity downstream. Solutions were obtained in the frequency domain by using a body-fitted coordinate system. Results are presented to demonstrate the effects of the out-flow boundary conditions, cascade spacing, mean blade loading and gust upstream conditions on the aerodynamics response and unsteady pressure field of a cascade.

Fang, J.↗

NASA NTRS1993

A statistical analysis of mesoscale rainfall as a random cascade

The paper considers the random cascade theory for spatial rainfall. Particular attention was given to the following four areas: (1) the relationship of the random cascade theory of rainfall to the simple scaling and the hierarchical cluster-point-process theories, (2) the mathematical foundations for some of the formalisms commonly applied in the develpment of statistical cascade theory, (3) the empirical evidence for a random cascade theory of rainfall, and (4) the way of using data for making estimates of parameters and for making statistical inference within this theoretical framework. An analysis of space-time rainfall data is presented. Cascade simulations are carried out to provide a comparison with methods of analysis that are applied to the rainfall data.

Gupta, Vijay K.↗

NASA NTRS1994

Multipoint inverse design of an infinite cascade of airfoils

This paper describes a method for the design of an infinite cascade in incompressible flow. The method is based on conformal mapping and does not allow for multipoint design. The cascade blade is to determined is divided into a number of segments. Over each segment, the velocity distribution is prescribed together with an inlet or outlet flow angle at which this velocity distributions is to be achieved. In this way multipoint design requirements can be met. It is necessary to satisfy several conditions that arise to guarantee compatibility with the inlet and outlet flow as well as closure of the cascade blade. Satisfaction of these conditions does not necessarily result in a cascade with all of the desired characteristucs. For example, the cascade blades may be bulbous or crossed. Through Newtonian iteration, however, the desired characteristics may be prescribed directly. Four examples will be illustrated to demonstrate the capability of the method.

Selig, M. S.↗

NASA NTRS1996

A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems

A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.

Patnaik, Surya N.↗

NASA NTRS1996

Three-Dimensional Flow Field Measurements in a Transonic Turbine Cascade

Three-dimensional flow field measurements are presented for a large scale transonic turbine blade cascade. Flow field total pressures and pitch and yaw flow angles were measured at an inlet Reynolds number of 1.0 x 10(exp 6) and at an isentropic exit Mach number of 1.3 in a low turbulence environment. Flow field data was obtained on five pitchwise/spanwise measurement planes, two upstream and three downstream of the cascade, each covering three blade pitches. Three-hole boundary layer probes and five-hole pitch/yaw probes were used to obtain data at over 1200 locations in each of the measurement planes. Blade and endwall static pressures were also measured at an inlet Reynolds number of 0.5 x 10(exp 6) and at an isentropic exit Mach number of 1.0. 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 deg of turning and an axial chord of 12.7 cm. The flow field in the cascade is highly three-dimensional as a result of thick boundary layers at the test section inlet and because of the high degree of flow turning. 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 CFD code and model verification.

Giel, P. W.↗

DOE OSTI2024

Analysis and Mitigation of Cascading Outages Using an Interaction Graph Addressing Transient Stability

Cascading outages of power systems pose great threats to system security and reliability, potentially leading to large-scale blackouts. For analysis and mitigation of cascading outages, this paper proposes a transient stability-incorporated interaction graph. This graph statistically quantifies the interactions among line outages and instabilities of generators, which can model propagation paths and patterns of cascading outages. Compared with an interaction graph that only models line outages, this new interaction graph provides important insights on how transient instability occurs along with cascading outages. It also offers more effective strategies for mitigating outage propagation. The proposed interaction graph can be constructed from datasets of historical or simulated cascading events. It is demonstrated on an NPCC 140-bus system with mitigation strategies.

Guo, Zhenping↗

NASA NTRS2018

Scale-Resolving Simulations of Low-Pressure Turbine Cascades with Wall Roughness Using A Spectral-Element Method

The accurate prediction of wall-roughness effects in turbomachinery is becoming critical as turbine designers address airfoil surface quality and degradation concerns arising from the shift to advanced ceramic matrix composite (CMC) or additively-manufactured airfoils operating in higher temperature environments. In this paper, a recently developed computational capability for accurate and efficient scale-resolving simulations of turbomachinery is extended to analyze the boundary- layer separation and transition characteristics in a rough-wall low-pressure turbine (LPT) cascade. The computational capability is based on an entropy-stable discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in an efficient manner for a modern high performance computer architecture. Results from the scale-resolving simulations of both smooth and rough airfoil cascades are presented and compared to previous experiments and numerical simulations. The results show that the suction surface boundary layer undergoes laminar separation, transition, and turbulent reattachment for the smooth airfoil cascade, while in the presence of roughness the separation and transition behavior of the suction surface boundary layer is substantially modified. The differences between the smooth and rough airfoil cascades are then highlighted by a detailed analysis of their respective turbulent flow fields.

Spectral-Element↗

NASA NTRS2019

The State of Remote Sensing Capabilities of Cascading Hazards over High Mountain Asia

Cascading hazard processes refer to a primary trigger such as heavy rainfall, seismic activity, or snow melt, followed by a chain or web of consequences that can cause subsequent hazards influenced by a complex array of preconditions and vulnerabilities. These interact in multiple ways and can have tremendous impacts on populations proximate to or downstream of these initial triggers. High Mountain Asia (HMA) is extremely vulnerable to cascading hazard processes given the tectonic, geomorphologic, and climatic setting of the region, particularly as it relates to glacial lakes. Given the limitations of in situ surveys in steep and often inaccessible terrain, remote sensing data are a valuable resource for better understanding and quantifying these processes. The present work provides a survey of cascading hazard processes impacting HMA and how these can be characterized using remote sensing sources. We discuss how remote sensing products can be used to address these process chains, citing several examples of cascading hazard scenarios across HMA. This work also provides a perspective on the current gaps and challenges, community needs, and view forward towards improved characterization of evolving hazards and risk across HMA.

Glacial lake outburst floods↗