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NASA NTRS1977

Generalized Theodorsen solution for singular integral equations of the airfoil class

A class of singular integral equations is considered which arise in various two-dimensional mixed boundary-value problems with simple harmonic time variation. A problem typical of this class is that of determining the lifting pressure distribution on an oscillating airfoil in an unbounded incompressible potential flow. It is shown that Theodorsen's (1935) solution to this problem, with some modification, is valid for a general class of unsteady kernel functions. The technique employed is to consider an equivalent steady problem and then show that the unsteady resolvent and unsteady homogeneous solution can be written directly in terms of the steady solutions and a single frequency-dependent function which reduces to the Theodorsen function for the steady kernel.

Williams, M. H.↗

NASA NTRS1981

Preliminary investigation of acoustic oscillations in an H2-O2 fired Hall generator

Burner pressure oscillations and interelectrode voltage oscillations measured in an open-cycle supersonic flow Hall generator are presented. The ionized gas for the channel was supplied by seeding the approximately 1 lb/sec of hydrogen-oxygen combustion products with cesium. Since both the burner and the channel were located within magnetic fields exceeding 4 Tesla during operation, an infinite probe pressure measurement technique was used to measure burner pressure oscillations. Calibration of the burner pressure transducer using a resonance tube technique is presented. Evidence is presented for the existence of the first longitudinal mode of oscillations (5000 Hz) within the burner. Interelectrode voltage oscillations were simultaneously measured at two separate axial stations. The magnitude change and the phase shift between the two signals was interpreted as a decaying magnetoacoustic wave driven by the burner that propagates at local gas plus sonic velocities. The amplitude of the electrical voltage oscillations at the start of the power producing region of the channel varied with the magnetic field. This variation is compared with the results of a simple perturbation analysis. Arguments are presented for using an unsteady model for analyzing wave processes in channels.

Phillips, B.↗

NASA NTRS1982

Unsteady lifting-line theory with applications

Unsteady lifting-line theory is developed for a flexible unswept wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The theory is formulated in terms of the acceleration potential and treated by the method of matched asymptotic expansions. The wing displacements are prescribed and the pressure field, airloads, and unsteady induced downwash are obtained in closed form. Sample numerical calculations are presented. The present work identifies and resolves errors in the unsteady lifting-line theory of James and points out a limitation in that of Van Holten. Comparison of the results of Reissner's approximate unsteady lifting-surface theory with those of the present work shows favorable agreement. The present work thus provides some formal justification for Reissner's ad hoc theory. For engineering purposes, the region of applicability of the theory in the reduced frequency-aspect ratio domain is identified approximately and found to cover most cases of practical interest.

Ahmadi, A. R.↗

NASA NTRS1985

Unsteady lifting-line theory as a singular-perturbation problem

Unsteady lifting-line theory is developed for a wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The wing is assumed to have a rigid chord but a flexible span. Use of the method of matched asymptotic expansions reduces the problem from a singular integral equation to quadrature. The pressure field and airloads, for a prescribed wing shape and motion, are obtained in closed form as expansions in inverse aspect ratio. A rigorous definition of unsteady induced downwash is also obtained. Numerical calculations are presented for an elliptic wing in pitch and heave; compared with numerical lifting-surface theory, computation time is reduced significantly. The present work also identifies and resolves errors in the unsteady lifting line theory of James (1975), and points out a limitation in that of Van Holten (1975, 1976, 1977).

Ahmadi, A.↗

NASA NTRS1988

The gasdynamics of compact relativistic jets

The gasdynamics of compact relativistic jets is explored by analyzing a specific idealized flow problem using the method of characteristics. The basic flow pattern of the gas and pressure waves within a jet experiencing a drop in external pressure is calculated, with analytic expressions given for many of the important parameters. Scaling laws which relate the intrinsic properties of the jet to the pressure of the surrounding medium are obtained and discussed. The physical properties of the jet depend critically on the value and abruptness of the decrease in external pressure, as well as on the initial Lorentz factor of the flow. A variety of the flow patterns can result, including jets of oscillating cross section, jets with standing shocks, and broad, nearly hollow beams which can break up into multiple jets. These results are discussed in relation to the observed characteristics of superluminal radio sources in general and the superluminal quasar 4C 39.25 in particular.

Daly, Ruth A.↗

NASA NTRS1991

Inviscid steady/unsteady flow calculations

The solution of the Euler equations using a flux splitting procedure is considered for low subsonic to high supersonic flows. Steady and unsteady, internal and external flow fields, are computed. For transient flows, a direct sparse matrix solver is applied to compute the flow field at each instant of time. Oscillation free normal and oblique shocks are captured. Unstart and restart of a simplified two-dimensional inlet is investigated.

Pordal, H. S.↗

NASA NTRS1991

Extratropical aspects of the 40-50 day oscillation in length-of-day and atmospheric angular momentum

The 40-50-d oscillation in length-of-day (LOD) and AAM is investigated using the 12-yr overlap between two records: AAM data, compiled from the NMC, and LOD variation from the JPL Kalman-filtered earth rotation series. The NMC records are analyzed by latitude belts, in the light of the UCLA GCM results, in order to identify possibly distinct sources of the AAM oscillation in the midlatitudes and the tropics. Results suggest that two intraseasonal oscillations exist in the earth-atmosphere system: a tropical 50-d oscillation associated with the convectively driven waves of the type first described by Madden and Julian (1971) and a midlatitude 40-d oscillation associated with the interaction of nonzonal flow with topography.

Dickey, J. O.↗

NASA NTRS1993

Effect of wind tunnel acoustic modes on linear oscillating cascade aerodynamics

The aerodynamics of a biconvex airfoil cascade oscillating in torsion is investigated using the unsteady aerodynamic influence coefficient technique. For subsonic flow and reduced frequencies as large as 0.9, airfoil surface unsteady pressures resulting from oscillation of one of the airfoils are measured using flush-mounted high-frequency-response pressure transducers. The influence coefficient data are examined in detail and then used to predict the unsteady aerodynamics of a cascade oscillating at various interblade phase angles. These results are correlated with experimental data obtained in the traveling-wave mode of oscillation and linearized analysis predictions. It is found that the unsteady pressure disturbances created by an oscillating airfoil excite wind tunnel acoustic modes which have detrimental effects on the experimental data. Acoustic treatment is proposed to rectify this problem.

Buffum, Daniel H.↗

NASA NTRS1994

Effect of wind tunnel acoustic modes on linear oscillating cascade aerodynamics

The aerodynamics of a biconvex airfoil cascade oscillating in torsion is investigated using the unsteady aerodynamic influence coefficient technique. For subsonic flow and reduced frequencies as large as 0.9, airfoil surface unsteady pressures resulting from oscillation of one of the airfoils are measured using flush-mounted high-frequency-response pressure transducers. The influence coefficient data are examined in detail and then used to predict the unsteady aerodynamics of a cascade oscillating at various interblade phase angles. These results are correlated with experimental data obtained in the traveling-wave mode of oscillation and linearized analysis predictions. It is found that the unsteady pressure disturbances created by an oscillating airfoil excite wind tunnel acoustic modes, which have detrimental effects on the experimental results. Acoustic treatment is proposed to rectify this problem.

Buffum, D. H.↗

NASA NTRS1996

A Hybrid Boundary Element-Finite Volume Method for Unsteady Transonic Airfoil Flows

A hybrid boundary element finite volume method for unsteady transonic flow computation has been developed. In this method, the unsteady Euler equations in a moving frame of reference are solved in a small embedded domain (inner domain) around the airfoil using an implicit finite volume scheme. The unsteady full-potential equation, written in the same frame of reference and in the form of the Poisson equation. is solved in the outer domain using the integral equation boundary element method to provide the boundary conditions for the inner Euler domain. The solution procedure is a time-accurate stepping procedure, where the outer boundary conditions for the inner domain are updated using the integral equation -- boundary element solution over the outer domain. The method is applied to unsteady transonic flows around the NACA0012 airfoil undergoing pitching oscillation and ramp motion. The results are compared with those of an implicit Euler equation solver, which is used throughout a large computational domain, and experimental data.

Hu, Hong↗

NASA NTRS2000

Decadal Variability and Temperature Trends in the Middle Atmosphere From Historical Rocketsonde Data

Observational studies were performed using historical rocketsonde data to investigate long-term temperature trends, solar-cycle variations, and interactions between tropical and extratropical latitudes in the middle atmosphere. Evidence from tropical, subtropical, and midlatitude North American rocketsonde stations indicated a consistent downward trend over 25 years, with a solar cycle component superposed. The trend is about -1.4 to -2.0 K per decade and the amplitude of the decadal oscillation is about 1.1 K. Prior to trend derivation it was necessary for us to correct temperatures for aerodynamic heating in the early years. The empirically derived correction profile agrees well with a theoretical profile of Krumins and Lyons. A study was also performed of the correlation between equatorial winds and north polar temperatures in winter, showing that the entire stratospheric wind profile near the equator -- including the quasi-biennial oscillation (QBO) and stratopause semiannual oscillation (SAO) -- is important to the extratropical flow, not merely the QBO component as previously thought. A strong correlation was discovered between winter polar temperatures and equatorial winds in the upper stratosphere during the preceding September, suggesting a role for the second cycle of the SAO.

Dunkerton, Timothy J.↗

NASA NTRS1999

Decoupling the Roles of Inertia and Gravity on Particle Dispersion

Inertial and gravitational forces determine a particle's motion in a turbulent flow field. Gravity plays the dominant role in this motion by pulling the particles through adjacent regions of fluid turbulence. To better understand and model how a particle's inertia effects its displacement, one must examine the dispersion in a turbulent flow in the absence of gravity. In this paper, we present the particle experiments planned for NASA's KC-135 Reduced-Gravity Aircraft, which generates microgravity conditions for about 20 seconds. We also predict the particle behavior using simulation and ground-based experiments. We will release particles with Stokes numbers of 0.1, 1, and 10 into an enclosed tank of near-isotropic, stationary, and homogenous turbulence. These particle Stoke numbers cover a broad range of flow regimes of interest. Two opposed grids oscillating back and forth generate the turbulent field in the tank with a range of turbulence scales that covers about three orders of magnitude and with turbulence intensities of about ten times the mean velocity. The motion of the particles will be tracked using a stereo image velocimetry technique.

Groszmann, D. E.↗

NASA NTRS1995

Simulations Of On Demand Vortex Generators

The development of a two-dimensional viscous incompressible flow generated by an off center thin oscillating bd on top of a cavity is studied computationally as a prototype of vortex generators. The lid is placed asymmetrically over the cavity so that the gap size is different on either side of the cavity. An adaptive numerical scheme, based on high resolution viscous vortex methods, is used to integrate the vorticity/velocity formulation of the Navier-Stokes equations with the no-slip boun.lary condition enforced on the lid and cavity walls. Depending on the a amplitude and frequency of the oscillation as well as the the gap size, vorticity is ejected in the fluid above the cavity either from the large and/or the small gap. The results of the computations complement ongoing experimental work.

Koumoutsakos, P.↗

NASA NTRS2004

A Resonant Pulse Detonation Actuator for High-Speed Boundary Layer Separation Control

A variety of different types of actuators have been previously investigated as flow control devices. Potential applications include the control of boundary layer separation in external flows, as well as jet engine inlet and diffuser flow control. The operating principles for such devices are typically based on either mechanical deflection of control surfaces (which include MEMS flap devices), mass injection (which includes combustion driven jet actuators), or through the use of synthetic jets (diaphragm devices which produce a pulsating jet with no net mass flow). This paper introduces some of the initial flow visualization work related to the development of a relatively new type of combustion-driven jet actuator that has been proposed based on a pulse detonation principle. The device is designed to utilize localized detonation of a premixed fuel (Hydrogen)-air mixture to periodically inject a jet of gas transversely into the primary flow. Initial testing with airflow successfully demonstrated resonant conditions within the range of acoustic frequencies expected for the design. Schlieren visualization of the pulsating air jet structure revealed axially symmetric vortex flow, along with the formation of shocks. Flow visualization of the first successful sustained oscillation condition is also demonstrated for one configuration of the current test section. Future testing will explore in more detail the onset of resonant combustion and the approach to conditions of sustained resonant detonation.

Beck, B. T.↗

NASA NTRS2005

Transient Three-Dimensional Analysis of Nozzle Side Load in Regeneratively Cooled Engines

Three-dimensional numerical investigations on the start-up side load physics for a regeneratively cooled, high-aspect-ratio nozzle were performed. The objectives of this study are to identify the three-dimensional side load physics and to compute the associated aerodynamic side load using an anchored computational methodology. The computational methodology is based on an unstructured-grid, pressure-based computational fluid dynamics formulation, and a transient inlet condition based on an engine system simulation. Computations were performed for both the adiabatic and cooled walls in order to understand the effect of boundary conditions. Finite-rate chemistry was used throughout the study so that combustion effect is always included. The results show that three types of shock evolution are responsible for side loads: generation of combustion wave; transitions among free-shock separation, restricted-shock separation, and simultaneous free-shock and restricted shock separations; along with oscillation of shocks across the lip. Wall boundary conditions drastically affect the computed side load physics: the adiabatic nozzle prefers free-shock separation while the cooled nozzle favors restricted-shock separation, resulting in higher peak side load for the cooled nozzle than that of the adiabatic nozzle. By comparing the computed physics with those of test observations, it is concluded that cooled wall is a more realistic boundary condition, and the oscillation of the restricted-shock separation flow pattern across the lip along with its associated tangential shock motion are the dominant side load physics for a regeneratively cooled, high aspect-ratio rocket engine.

Wang, Ten-See↗

NASA NTRS2021

Self-Consistent Implementation of a Zero-Equation Transport Model Into a Predictive Model for a Hall Effect Thruster

The performance of an axisymmetric multi-fluid Hall thruster code that incorporates a self-consistent, data-driven closure model for the anomalous electron transport is investigated. Five different operating conditions of the H9 magnetically shielded Hall thruster are simulated with the Jet Propulsion Laboratory’s Hall2De. In order to capture the inherent uncertainty associated with the closure model, O(100) simulations are run for each condition, each of using a coefficient set sampled randomly from a probability distribution. The results of these simulations provide probabilistic predictions of thruster performance quantities including thrust, and discharge current, as well as several component efficiencies and centerline plasma properties. The model is found to yield converged solutions at all conditions, with large 10 kHzrange oscillations and performance trends with voltage and flow rate similar to experiment. The model under-predicts the thrust by 15-25% and over-predicts the discharge current by 20% on average compared to experiments at the same discharge voltage and mass flow rate. This performance discrepancy is due to lower beam utilization, mass utilization, and divergence efficiency than experiment, resulting from high Hall parameters in the acceleration region, which lead to a protracted ion acceleration region. The physical processes underlying this result are discussed in the context of future data-driven modeling efforts.

Jorns, Benjamin A.↗

NASA NTRS1975

Numeric calculation of unsteady forces over thin pointed wings in sonic flow

A fast and reasonably accurate numerical procedure is proposed for the solution of a simplified unsteady transonic equation. The approach described takes into account many of the effects of the steady flow field. The resulting accuracy is within a few per cent and can be carried out on a computer in less than one minute per case (one frequency and one mode of oscillation). The problem concerns a rigid pointed wing which performs harmonic pitching oscillations of small amplitude in a steady uniform transonic flow. Wake influence is ignored and shocks must be weak. It is shown that the method is more flexible than the transonic box method proposed by Rodemich and Andrew (1965) in that it can easily account for variable local Mach number and rather arbitrary planform so long as the basic assumptions are fulfilled.

Kimble, K. R.↗

NASA NTRS1987

Stability and resonance in grooved-channel flows

Numerical simulation using the spectral element method is used to study the stability and resonant response of incompressible moderate-Reynolds-number flows in periodically-grooved channels. For Reynolds numbers below a critical value, the flow is shown to approach a stable steady-state, and the least stable modes resemble Tollmien-Schlichting channel waves. For Reynolds numbers greater than the critical value, self-sustained oscillations result. Oscillatory perturbation of the grooved-channel flow at the frequency of the least stable mode of the linearized system is found to result in subcritical resonant excitation as the critical Reynolds number is approached. The importance of nonhomogeneous geometry in the forced response of the flow is discussed.

Ghaddar, Nasreen K.↗