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NASA NTRS1984

Computer modeling results on all-Si cascade solar cells

The properties of a cascade solar cell made entirely of silicon are investigated numerically with the goal of developing an optimal silicon solar cell grown by molecular-beam epitaxy. The cascade cell is modeled as two standard back-surface field cells with abrupt junctions connected by a tunnel junction. A cascade cell would have approximately twice the open-circuit voltage of a single cell. If the minority carriers generated in the front cell can be reflected before reaching the tunnel junction, then the cascade cell will show an increase in efficiency over a single cell by a percentage point.

Sparks, P. D.↗

NASA NTRS1986

Modeling and analysis of cascade solar cells

A brief review is given of the present status of the development of cascade solar cells. It is known that photovoltaic efficiencies can be improved through this development. The designs and calculations of the multijunction cells, however, are quite complicated. The main goal is to find a method which is a compromise between accuracy and simplicity for modeling a cascade solar cell. Three approaches are presently under way, among them (1) equivalent circuit approach, (2) numerical approach, and (3) analytical approach. Here, the first and the second approaches are discussed. The equivalent circuit approach using SPICE (Simulation Program, Integrated Circuit Emphasis) to the cascade cells and the cascade-cell array is highlighted. The methods of extracting parameters for modeling are discussed.

Ho, F. D.↗

NASA NTRS1985

Large-scale separation and hysteresis in cascades

An approach using a two-dimensional thin aerofoil, allied with the theory of viscous bluff-body separation, is used to study the initial cross-over from massive separation to an attached flow in a single-row unstaggered cascade. Analytic solutions are developed for the limit of small cascade-spacing. From the analytic solutions several interesting features of the cascade are examined, including multiple-solution branches and multiple regions of hysteresis. In addition, numerical results are presented for several selected aerofoils. Some of the aerofoils are found to contain markedly enlarged regions of hysteresis for certain critical cascade spacings.

Rothmayer, A. P.↗

NASA NTRS1986

Unsteady transonic flow over cascade blades

An attempt is made to develop an efficient staggered cascade blade unsteady aerodynamics model for the neighborhood of March 1, representing the blade row by a rectilinear two-dimensional cascade of thin, flat plate airfoils. The equations of motion are derived on the basis of linearized transonic small perturbation theory, and an analytical solution is obtained by means of the Wiener-Hopf procedure. Making use of the transonic similarity law, the results obtained are compared with those of other linearized cascade analyses. A parametric study is conducted to find the effects of reduced frequency, stagger angle, solidity, and the location of the pitching axis on cascade stability.

Surampudi, S. P.↗

NASA NTRS1984

Unsteady transonic flow in cascades

There is a need for methods to predict the unsteady air loads associated with flutter of turbomachinery blading at transonic speeds. The results of such an analysis in which the steady relative flow approaching a cascade of thin airfoils is assumed to be transonic, irrotational, and isentropic is presented. The blades in the cascade are allowed to undergo a small amplitude harmonic oscillation which generates a small unsteady flow superimposed on the existing steady flow. The blades are assumed to oscillate with a prescribed motion of constant amplitude and interblade phase angle. The equations of motion are obtained by linearizing about a uniform flow the inviscid nonheat conducting continuity and momentum equations. The resulting equations are solved by employing the Weiner Hopf technique. The solution yields the unsteady aerodynamic forces acting on the cascade at Mach number equal to 1. Making use of an unsteady transonic similarity law, these results are compared with the results obtained from linear unsteady subsonic and supersonic cascade theories. A parametric study is conducted to find the effects of reduced frequency, solidity, stagger angle, and position of pitching axis on the flutter.

Surampudi, S. P.↗

NASA NTRS1984

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed.

Weinberg, B. C.↗

NASA NTRS1985

Turbine Vane External Heat Transfer. Volume 2. Numerical Solutions of the Navier-stokes Equations for Two- and Three-dimensional Turbine Cascades with Heat Transfer

The application of the time-dependent ensemble-averaged Navier-Stokes equations to transonic turbine cascade flow fields was examined. In particular, efforts focused on an assessment of the procedure in conjunction with a suitable turbulence model to calculate steady turbine flow fields using an O-type coordinate system. Three cascade configurations were considered. Comparisons were made between the predicted and measured surface pressures and heat transfer distributions wherever available. In general, the pressure predictions were in good agreement with the data. Heat transfer calculations also showed good agreement when an empirical transition model was used. However, further work in the development of laminar-turbulent transitional models is indicated. The calculations showed most of the known features associated with turbine cascade flow fields. These results indicate the ability of the Navier-Stokes analysis to predict, in reasonable amounts of computation time, the surface pressure distribution, heat transfer rates, and viscous flow development for turbine cascades operating at realistic conditions.

Yang, R. J.↗

NASA NTRS1987

Numerical simulations of unsteady, viscous, transonic flow over isolated and cascaded airfoils using a deforming grid

A compressible, unsteady, full Navier-Stokes, finite difference code was developed for modeling transonic flow through two-dimensional, oscillating cascades. The procedure introduces a deforming grid technique to capture the motion of the airfoils. Results using a deforming grid are presented for both isolated and cascaded airfoils. The load histories and unsteady pressure distributions are predicted for the NASA 64A010 isolated airfoil and compared with existing experimental data. Results show that the deforming grid technique can be used to successfully predict the unsteady flow properties around an oscillating airfoil. The deforming grid technique was extended for modeling unsteady flow in a cascade. The use of a deforming grid simplifies the specification of boundary conditions. Unsteady flow solutions similar to the isolated airfoil predictions are found for a NACA 0012 cascade with zero interblade phase angle and zero stagger. Experimental data for these cases are not available for code validation, but computational results are presented to show sample predictions from the code. Applications of the code to typical turbomachinery flow conditions will be presented in future work.

Huff, Dennis L.↗

NASA NTRS1987

Numerical simulations of unsteady, viscous, transonic flow over isolated and cascaded airfoils using a deforming grid

Huff, Dennis L.↗

NASA NTRS1987

Output control using feedforward and cascade controllers

An open-loop solution to the output control problem in SISO (single-input, single-output) systems by means of feedforward and cascade controllers is investigated. A simple characterization of feedforward controllers, which achieve steady-state disturbance rejection, is given in a transfer-function setting. Cascade controllers which cause steady-state command tracking are characterized. Disturbance decoupling and command matching controllers are identified. Conditions for existence of feedforward and cascade controllers are given. For unstable systems, it is shown that a stabilizing feedback controller can be used without affecting the feedforward and cascade controllers used for output control; hence, the three controllers can be designed independently. Output control by a combination of feedforward and feedback is discussed.

Seraji, H.↗

NASA NTRS1988

Experimental investigation of the performance of a supersonic compressor cascade

Results are presented from an experimental investigation of a linear, supersonic, compressor cascade tested in the supersonic cascade wind tunnel facility at the DFVLR in Cologne, Federal Republic of Germany. The cascade design was derived from the near-tip section of a high-through-flow axial flow compressor rotor with a design relative inlet Mach number of 1.61. Test data were obtained over a range of inlet Mach numbers from 1.23 to 1.71, and a range of static pressure ratios and axial-velocity-density ratios (AVDR) at the design inlet condition. Flow velocity measurements showing the wave pattern in the cascade entrance region were obtained using a laser transit anemometer. From these measurements, some unique-incidence conditions were determined, thus relating the supersonic inlet Mach number to the inlet flow direction. The influence of static pressure ratio and AVDR on the blade passage flow and the blade-element performance is described, and an empirical correlation is used to show the influence of these two (independent) parameters on the exit flow angle and total-pressure loss for the design inlet condition.

Tweedt, D. L.↗

NASA NTRS1989

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and nonzero interblade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions were coded for the inlet and exit boundary conditions. Sample unsteady solutions were performed for an oscillating cascade and compared to experimental data. Also, test cases were run for a flat plate cascade to compare with the unsteady, small-perturbation, subsonic analyis. The predictions for oscillating cascades with nonzero interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. The zero degree interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus nonreflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions.

Huff, Dennis L.↗

NASA NTRS1989

Experimental investigation of transonic oscillating cascade aerodynamics

Fundamental experiments are performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate the subsonic and transonic aerodynamics of cascaded airfoils executing torsion mode oscillations at realistic values of reduced frequency. In particular, an unsteady aerodynamic influence coefficient technique is developed and utilized. In this technique, only one airfoil in the cascade is oscillated at a time, with the resulting airfoil surface unsteady pressure distribution measured on one dynamically-instrumented reference airfoil. The unsteady aerodynamics of an equivalent cascade with all airfoils oscillating at any specified interblade phase angle are then determined through a vector summation of these data.

Buffum, Daniel H.↗

NASA NTRS1989

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and nonzero interblade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the perioidic boundary conditions. Approximate nonreflecting boundary conditons were coded for the inlet and exit boundary conditions. Sample unsteady solutions were performed for an oscillating cascade and compared to experimental data. Also, test cases were run for a flat plate cascade to compare with the unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with nonzero interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. The zero degree interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus nonreflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distribution for certain flow conditions.

Huff, Dennis L.↗

NASA NTRS1989

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and non-zero inter-blade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions have been coded for the inlet and exit boundary conditions. Sample unsteady solutions have been performed for an oscillating cascade and compared to experimental data. Also, test cases were fun for a flat plate cascade to compare with an unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with non-zero inter-blade phase angles are in good agreement with experimental data and small-perturbation theory. The zero degree inter-blade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus non-reflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions. This code is expected to be used as a tool for reviewing simpler models that do not include the full nonlinear aerodynamics or as a final check for designs against flutter in turbomachinery.

Huff, Dennis L.↗

NASA NTRS1991

Wind tunnel wall effects in a linear oscillating cascade

Experiments in a linear oscillating cascade reveal that the wind tunnel walls enclosing the airfoils have, in some cases, a detrimental effect on the oscillating cascade aerodynamics. In a subsonic flow field, biconvex airfoils are driven simultaneously in harmonic, torsion-mode oscillations for a range of interblade phase angle values. It is found that the cascade dynamic periodicity - the airfoil to airfoil variation in unsteady surface pressure - is good for some values of interblade phase angle but poor for others. Correlation of the unsteady pressure data with oscillating flat plate cascade predictions is generally good for conditions where the periodicity is good and poor where the periodicity is poor. Calculations based upon linearized unsteady aerodynamic theory indicate that pressure waves reflected from the wind tunnel walls are responsible for the cases where there is poor periodicity and poor correlation with the predictions.

Buffum, Daniel H.↗

NASA NTRS1990

The aerodynamics of an oscillating cascade in a compressible flow field

Fundamental experiments are performed in the NASA Lewis Research Center Transonic Oscillating Cascade Facility to investigate and quantify the aerodynamics of a cascade of bioconvex airfoils executing torsion mode oscillations at realistic reduced frequency values. Both steady and unsteady airfoil surface pressures are measured at two inlet Mach numbers, 0.65 and 0.80, and two incidence angles, 0 and 7 deg, with the harmonic torsional airfoil cascade oscillations at realistic high reduced frequency and unsteady data obtained at several interblade phase angle values. The time-variant pressures are analyzed by means of discrete Fourier transform techniques, with these unique data compared with predictions from a linearized unsteady cascade model. The experimental results indicate that the interblade phase angle has a major effect on the chordwise distributions of the airfoil surface unsteady pressure, with the effect of reduced frequency, incidence angle, and Mach numbers somewhat less significant.

Buffum, D. H.↗

NASA NTRS1990

Experimental investigation of oscillating cascade aerodynamics

A series of experiments are performed in the NASA Lewis Transonic Oscillating Cascade Facility to provide fundamental data quantifying the high subsonic and transonic steady and oscillating aerodynamics of a biconvex airfoil cascade at realistic reduced frequency values for all interblade phase angles. This is accomplished by developing and utilizing an unsteady aerodynamic influence-coefficient technique in which only one cascaded airfoil is oscillated at a time. The vector summation of the resulting airfoil-surface unsteady pressures (measured on a dynamically instrumented airfoil) makes it possible to determine the unsteady aerodynamics of an equivalent cascade with all airfoils oscillating at any specified interblade phase angle.

Buffum, Daniel H.↗