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NASA NTRS1982

CAS22 - FORTRAN program for fast design and analysis of shock-free airfoil cascades using fictitious-gas concept

A user-oriented computer program, CAS22, was developed that is applicable to aerodynamic analysis and transonic shock-free redesign of existing two-dimensional cascades of airfoils. This FORTRAN program can be used: (1) as an analysis code for full-potential, transonic, shocked or shock-free cascade flows; (2) as a design code for shock-free cascades that uses Sobieczky's fictitious-gas concept; and (3) as a shock-free design code followed automatically by the analysis in order to confirm that the newly obtained cascade shape provides for an entirely shock-free transonic flow field. A four-level boundary-conforming grid of an O type is generated. The shock-free design is performed by implementing Sobieczky's fictitious-gas concept of elliptic continuation from subsonic into supersonic flow domains. Recomputation inside each supersonic zone is performed by the method of characteristics in the rheograph plane by using isentropic gas relations. Besides converting existing cascade shapes with multiple shocked supersonic regions into shock-free cascades, CAS22 can also unchoke previously choked cascades and make them shock free.

Dulikravich, D. S.↗

NASA NTRS1982

Environmental solid particle effects on compressor cascade performance

The effect of suspended solid particles on the performance of the compressor cascade was investigated experimentally in a specially built cascade tunnel, using quartz sand particles. The cascades were made of NACA 65(10)10 airfoils. Three cascades were tested, one accelerating cascade and two diffusing cascades. The theoretical analysis assumes inviscid and incompressible two dimensional flow. The momentum exchange between the fluid and the particle is accounted for by the interphase force terms in the fluid momentum equation. The modified fluid phase momentum equations and the continuity equation are reduced to the conventional stream function vorticity formulation. The method treats the fluid phase in the Eulerian system and the particle phase in Lagrangian system. The experimental results indicate a small increase in the blade surface static pressures, while the theoretical results indicate a small decrease. The theoretical analysis, also predicts the loss in total pressure associated with the particulate flow through the cascade.

Tabakoff, W.↗

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. These influence coefficient determined oscillating cascade data were correlated with: (1) data obtained in this cascade with all airfoils oscillating at several interblade phase angle values; and (2) predictions from a classical linearized unsteady cascade model.

Buffum, Daniel H.↗

NASA NTRS1992

Lumley's energy cascade dissipation rate model for boundary-free turbulent shear flows

True dissipation occurs mainly at the highest wavenumbers where the eddy sizes are comparatively small. These high wavenumbers receive their energy through the spectral cascade of energy starting with the largest eddies spilling energy into the smaller eddies, passing through each wavenumber until it is dissipated at the microscopic scale. However, a small percentage of the energy does not spill continuously through the cascade but is instantly passed to the higher wavenumbers. Consequently, the smallest eddies receive a certain amount of energy almost immediately. As the spectral energy cascade continues, the highest wavenumber needs a certain time to receive all the energy which has been transferred from the largest eddies. As such, there is a time delay, of the order of tau, between the generation of energy by the largest eddies and the eventual dissipation of this energy. For equilibrium turbulence at high Reynolds numbers, there is a wide range where energy is neither produced by the large eddies nor dissipated by viscosity, but is conserved and passed from wavenumber to higher wavenumbers. The rate at which energy cascades from one wavenumber to another is proportional to the energy contained within that wavenumber. This rate is constant and has been used in the past as a dissipation rate of turbulent kinetic energy. However, this is true only in steady, equilibrium turbulence. Most dissipation models contend that the production of dissipation is proportional to the production of energy and that the destruction of dissipation is proportional to the destruction of energy. In essence, these models state that the change in the dissipation rate is proportional to the change in the kinetic energy. This assumption is obviously incorrect for the case where there is no production of turbulent energy, yet energy continues to cascade from large to small eddies. If the time lag between the onset on the energy cascade to the destruction of energy at the microscale can be modeled, then there will be a better representation of the dissipation process. Development of an energy cascade time scale equation is discussed.

Duncan, B. S.↗

NASA NTRS1951

Effect of Tunnel Configuration and Testing Technique on Cascade Performance

An investigation has been conducted to determine the influence of aspect ratio, boundary-layer control by means of slots and porous surfaces, Reynolds number, and tunnel end-wall condition upon the performance of airfoils in cascades. A representative compressor-blade section (the NACA 65-(12)(10) of aspect ratios of 1, 2, and 4 has been tested at low speeds in cascades with solid and with porous side walls. Two-dimensional flow was established in porous-wall cascades of each of the three aspect ratios tested; the flow was not two-dimensional in any of the solid-wall cascades. Turbine-blade sections of aspect ratio 0.83 were tested in cascades with solid and porous side walls and blade sections of aspect ratio 3.33 were tested in cascades with solid wall. No particular advantage was observed in the use of porous walls for the turbine cascades tested.

Erwin, John R↗

NASA NTRS1992

Flutter analysis of supersonic axial flow cascades using a high resolution Euler solver. Part 1: Formulation and validation

This report presents, in two parts, a dynamic aeroelastic stability (flutter) analysis of a cascade of blades in supersonic axial flow. Each blade of the cascade is modeled as a typical section having pitching and plunging degrees of freedom. Aerodynamic forces are obtained from a time accurate, unsteady, two-dimensional cascade solver based on the Euler equations. The solver uses a time marching flux-difference splitting (FDS) scheme. Flutter stability is analyzed in the frequency domain. The unsteady force coefficients required in the analysis are obtained by harmonically oscillating (HO) the blades for a given flow condition, oscillation frequency, and interblade phase angle. The calculated time history of the forces is then Fourier decomposed to give the required unsteady force coefficients. An influence coefficient (IC) method and a pulse response (PR) method are also implemented to reduce the computational time for the calculation of the unsteady force coefficients for any phase angle and oscillation frequency. Part 1, this report, presents these analysis methods and their validation by comparison with results obtained from linear theory for a selected flat plate cascade geometry. A typical calculation for a rotor airfoil is also included to show the applicability of the present solver for airfoil configurations. The predicted unsteady aerodynamic forces for a selected flat plate cascade geometry and flow conditions correlated well with those obtained from linear theory for different interblade phase angles and oscillation frequencies. All the three methods of predicting unsteady force coefficients, namely, HO, IC, and PR, showed good correlations with each other. It was established that only a single calculation with four blade passages is required to calculate the aerodynamic forces for any phase angle for a cascade consisting of any number of blades, for any value of the oscillation frequency. Flutter results, including mistuning effects, for a cascade of stator airfoils are presented in Part 2 of the report.

Reddy, T. S. R.↗

NASA NTRS2002

Methodology of Blade Unsteady Pressure Measurement in the NASA Transonic Flutter Cascade

In this report the methodology adopted to measure unsteady pressures on blade surfaces in the NASA Transonic Flutter Cascade under conditions of simulated blade flutter is described. The previous work done in this cascade reported that the oscillating cascade produced waves, which for some interblade phase angles reflected off the wind tunnel walls back into the cascade, interfered with the cascade unsteady aerodynamics, and contaminated the acquired data. To alleviate the problems with data contamination due to the back wall interference, a method of influence coefficients was selected for the future unsteady work in this cascade. In this approach only one blade in the cascade is oscillated at a time. The majority of the report is concerned with the experimental technique used and the experimental data generated in the facility. The report presents a list of all test conditions for the small amplitude of blade oscillations, and shows examples of some of the results achieved. The report does not discuss data analysis procedures like ensemble averaging, frequency analysis, and unsteady blade loading diagrams reconstructed using the influence coefficient method. Finally, the report presents the lessons learned from this phase of the experimental effort, and suggests the improvements and directions of the experimental work for tests to be carried out for large oscillation amplitudes.

Lepicovsky, J.↗

NASA NTRS2012

Cascade Storage and Delivery System for a Multi Mission Space Exploration Vehicle (MMSEV)

NASA is developing a Multi Mission Space Exploration Vehicle (MMSEV) for missions beyond Low Earth Orbit (LEO). The MMSEV is a pressurized vehicle used to extend the human exploration envelope for Lunar, Near Earth Object (NEO), and Deep Space missions. The Johnson Space Center is developing the Environmental Control and Life Support System (ECLSS) for the MMSEV. The MMSEV s intended use is to support longer sortie lengths with multiple Extra Vehicular Activities (EVAs) on a higher magnitude than any previous vehicle. This paper presents an analysis of a high pressure oxygen cascade storage and delivery system that will accommodate the crew during long duration Intra Vehicular Activity (IVA) and capable of multiple high pressure oxygen fills to the Portable Life Support System (PLSS) worn by the crew during EVAs. A cascade is a high pressure gas cylinder system used for the refilling of smaller compressed gas cylinders. Each of the large cylinders are filled by a compressor, but the cascade system allows small cylinders to be filled without the need of a compressor. In addition, the cascade system is useful as a "reservoir" to accommodate low pressure needs. A regression model was developed to provide the mechanism to size the cascade systems subject to constraints such as number of crew, extravehicular activity duration and frequency, and ullage gas requirements under contingency scenarios. The sizing routine employed a numerical integration scheme to determine gas compressibility changes during depressurization and compressibility effects were captured using the Soave-Redlich-Kwong (SRK) equation of state. A multi-dimensional nonlinear optimization routine was used to find the minimum cascade tank system mass that meets the mission requirements. The sizing algorithms developed in this analysis provide a powerful framework to assess cascade filling, compressor, and hybrid systems to design long duration vehicle ECLSS architecture. 1

Yagoda, Evan↗

NASA NTRS1971

Measurement of the nuclear electromagnetic cascade development in glass at energies above 200 GeV

The longitudinal development of nuclear-electromagnetic cascades with energies greater than 200 GeV was measured in a low-Z (glass) absorber. This was done in the course of operating an ionization spectrometer at mountain altitude in an experiment to study the properties of gamma rays emitted from individual interactions at energies around 10,000 GeV. The ionization produced by a cascade is sampled by 20 sheets of plastic scintillator spaced uniformly in depth every 2.2 radiation lengths. Adjacent pairs of scintillators are viewed by photomultipliers which measure the mean ionization produced by an individual cascade in 10 layers each 1.1 interaction length (4.4 radiation lengths) thick. The longitudinal development of the cascades was measured for about 250 cascades having energies ranging from 200 GeV to 2500 GeV. The observations are compared with the predictions of calculations made for this specific spectrometer using a three-dimensional Monte Carlo model of the nuclear-electromagnetic cascade.

Gillespie, C. R.↗

NASA NTRS1974

Results from cascade thrust reverser noise and suppression experiments

Results from experimental work on model scale cascade reversers with cold airflow are presented. Sound power level directivity and spectral characteristics for cascade reversers are reported. Effect of cascade exit area ratio, vane profile shape, and emission arc are discussed. Model equivalent diameters varied from 3 to 5 inches, pressure ratios range from 1.15 to 3.0. Depending on the reverser type, acoustic power was proportional to the 4 1/2 to 6th power of ideal jet velocity. Reverser noise peaked at higher frequency and was more omnidirectional than nozzle-alone jet noise. Appreciable reduction in sideline noise was obtained from plane shields. Airfoil-vaned cascades were the most aerodynamically efficient and least noisy reversers. Scaling of cascade reverser data to example aircraft engines showed all cascades above the 95 PNdB sideline goal from STOL aircraft. However, the airfoil-vaned reverser has a good potential for meeting this goal for high-bypass (low pressure ratio) exhausts.

Gutierrez, O. A.↗

NASA NTRS1992

Multi-point inverse design of an infinite cascade of airfoils

This paper describes a practical method for the design of an infinite cascade in incompressible flow. The method is based on conformal mapping, and as a result it allows for multi-point design. The cascade blade to be determined is divided into a desired number of segments. Over each segment, the velocity distribution is prescribed together with an inlet or outlet flow angle at which this velocity distribution is to be achieved. In this way multi-point 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 the desired characteristics. For example, the cascade blades may be bulbous or crossed. Through Newton iteration, however, the desired characteristics may be prescribed by allowing for the adjustment of the design parameters that define the mathematical problem through conformal mapping. Several examples will be illustrated to demonstrate the capability of the method. It will be shown that the method is limited to the design of cascades with solidities of up to one.

Selig, Michael S.↗

NASA NTRS1992

Flutter analysis of a supersonic cascade in time domain using an ADI Euler solver

The aeroelastic stability of a two-dimensional cascade oscillating in supersonic axial flow is analyzed in the time domain. The aeroelastic model consists of a single degree of freedom typical section structural model for each blade of the cascade and an unsteady two-dimensional cascade aerodynamic model based on the Euler equations. The Euler equations are solved using a time accurate Alternating Direction Implicit (ADI) solution scheme. The aeroelastic equations are integrated in time. The effect of interblade phase angle is included in the aeroelastic analysis by an appropriate choice of initial and boundary conditions. Flutter predictions are obtained from the time response of a flat plate cascade in single degree of freedom pitching motion. The results correlate well with those obtained from a separate frequency domain flutter analysis for all values of interblade phase angles considered. Flutter results are then presented for cascades having airfoil sections representative of a supersonic throughflow fan. The validity of the time integration method for a cascade of airfoils at various interblade phase angles is demonstrated.

Reddy, T. S. R.↗

NASA NTRS1994

Statistical analysis of mesoscale rainfall: Dependence of a random cascade generator on large-scale forcing

Under the theory of independent and identically distributed random cascades, the probability distribution of the cascade generator determines the spatial and the ensemble properties of spatial rainfall. Three sets of radar-derived rainfall data in space and time are analyzed to estimate the probability distribution of the generator. A detailed comparison between instantaneous scans of spatial rainfall and simulated cascades using the scaling properties of the marginal moments is carried out. This comparison highlights important similarities and differences between the data and the random cascade theory. Differences are quantified and measured for the three datasets. Evidence is presented to show that the scaling properties of the rainfall can be captured to the first order by a random cascade with a single parameter. The dependence of this parameter on forcing by the large-scale meteorological conditions, as measured by the large-scale spatial average rain rate, is investigated for these three datasets. The data show that this dependence can be captured by a one-to-one function. Since the large-scale average rain rate can be diagnosed from the large-scale dynamics, this relationship demonstrates an important linkage between the large-scale atmospheric dynamics and the statistical cascade theory of mesoscale rainfall. Potential application of this research to parameterization of runoff from the land surface and regional flood frequency analysis is briefly discussed, and open problems for further research are presented.

Over, Thomas, M.↗

NASA NTRS2012

The Impact of Electromagnetic Cascades of Very-high Energy Gamma Rays on the Extragalactic Gamma-ray Background

As very high energy (VHE) photons propagate through the extragalactic background light (EBL), they interact with the soft photons of the EBL and initiate electromagnetic cascades of photons and electrons. The collective intensity of a cosmological population emitting at VHEs (such as blazars) will be attenuated at the highest energies through interactions with the EBL and enhanced at lower energies by the resulting cascade. As such, depending on the space density and spectra of the sources and the model of the EBL, cascade radiation can provide a significant contribution to the extragalactic gamma-ray background (EGB). Through deflections of the charged particles of the cascade, an intergalactic magnetic field (IGMF) may leave an imprint on the anisotropy properties of the EGB. The impact of a strong IGMF is to isotropize lower energy cascade photons, inducing a modulation in the anisotropy energy spectrum of the EGB. We discuss the implications of cascade radiation for the origins of the EGB and the nature of the IGMF, as well as insight that will be provided by data from the Fermi Large Area Telescope in the upcoming years.

Venters, Tonia↗

DOE OSTI2025

Insights from designing an artificial cascade catalysis system using principles from substrate channeling in enzymes

Generalizing the key requirements of highly-selective, multi-step chemical conversions involving spatially separated reaction centers remains one of the grand challenges of chemistry. Much work towards this effort has focused on decomposing multi-step conversions into their constituent reactions, whose intermediates are successively upgraded in a chemical cascade via diffusion from center to center. This approach for synthesizing more complex molecules takes its cues from biochemical networks, where near-unit conversion of even complex carbohydrates is achieved by upgrading chemical precursors via enzymatic cascades. In this computational study we examine a simple cascade involving coupled Ag and Cu catalysts that sequentially converts CO2 to CO and then CO2 and CO to reduced products, generically named CO2Product and COProduct. The system architecture is inspired by the phenomenon of biological substrate channeling, and components are examined to evaluate their effects on conversion efficiency in the cascade. Aside from a substrate channel linking two reaction centers, we find efficient cascades must also incorporate directional substrate diffusion, compartmentalization of the reaction centers, and proper timing of substrate arrival at the active center. We make explicit linkages between these requirements and chemical conversion in known biological systems, revealing additional control elements that could be incorporated.

CO 2 reduction↗

NASA NTRS1944

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↗

DOE OSTI2026

Finite-element-based simulations of electrodes for CO 2 cascade reduction reactions

The multielectron reduction of CO 2 to liquid fuels could be a path to scalable energy storage, but reaching this goal requires major advances in catalysis and systems engineering. Cascade catalysis, which couples sequential reactions without isolating intermediates, has emerged as a promising route to enhance selectivity and efficiency in CO 2 reduction (CO 2 R). In this review, we examine how finite-element-based simulations of continuum model [finite element method (FEM)] approaches are being used to analyze and guide CO 2 R cascade systems. We first outline the fundamentals of cascade catalysis and recent advances in catalytic materials (metallic, molecular, and hybrid architectures). We then focus on FEM developments at the electrode and device scales, emphasizing how these models capture transport phenomena, local microenvironments, and geometry-dependent effects. To clarify design principles, we present case studies of cascade electrodes organized in systems without and with integrated semiconductors. We further emphasize the integration of FEM with multiscale frameworks (density functional theory, molecular dynamics, kinetic Monte Carlo) and its role in bridging atomic-level insights with device-level performance. Finally, we identify current limitations and future prospects, including improved boundary conditions, coupling with operando experiments, and machine learning-accelerated model development. Together, these insights provide design principles for next-generation CO 2 R cascade systems for efficient solar fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗