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NASA NTRS1993

Dynamic stall of an oscillating wing. Part 1: Evaluation of turbulence models

Unsteady flowfields of a two-dimensional oscillating wing are calculated using an implicit, finite-difference, Navier-Stokes numerical scheme using five widely used turbulence models. The objective of this study is to identify an appropriate turbulence model for accurate simulation of three-dimensional dynamic stall. Three unsteady flow conditions corresponding to attached flow, light-stall, and deep-stall of an oscillating wing experiment were chosen as test cases for computations. Results of unsteady airload hysteresis curves, harmonics of unsteady pressures, and instantaneous flow pictures are presented. Comparison of unsteady airloads with experiment show that all models are deficient in some sense and not a single model predicts all airloads consistently and in agreement with experiment for all flow conditions. For the attached flow condition, the Renormalization Group Theory (RNG), the Johnoson-King (J-K), and the Spalart-Allmaras (S-A) models have better performance. The Baldwin-Lomax (B-L) and the Baldwin-Barth (B-B) models fair poorly. At the light-stall condition, the results for the RNG, the J-K, and S-A models are in agreement with experiment for the upstroke but they all over predict the separation shown by the experiment and therefore have bigger hysteresis loops than experimental results. The B-B model results are also in good agreement for upstroke but have poor lift hysteresis for downstroke. It has superior drag and pitching-moment predictions. For deep-stall conditions, the airloads for the RNG, the B -B, and the S-A models have fair agreement with experiment, but the B-B model performed better at the extreme deep-stall condition. Overall, the RNG model provides significant improvement over the B-L model in all flow regimes with no additional computational cost. The Baldwin-Barth model is the most expensive of the models considered here, costing about 2.5 times that of the Baldwin-Lomax model. Finally, a brief discussion of the effects of grid density, time-step size, and numerical dissipation on the unsteady solutions are also presented.

Srinivasan, G. R.↗

NASA NTRS1999

Continuum Modeling of the Dynamics of Externally Injection-locked Coupled Oscillator Arrays

Mutually injection-locked arrays of electronic oscillators provide a novel means of controlling the aperture phase of a phased-array antenna, thus achieving the advantages of spatial power combining while retaining the ability to steer the radiated beam. In a number of design concepts, one or more of the oscillators are injection locked to a signal from an external master-oscillator. The behavior of such a system has been analyzed by numerical solution of a system of nonlinear differential equations which, due to its complexity, yields limited insight into the relationship between the injection signals and the aperture phase. In this paper, we develop a continuum model, which results in a single partial differential equation for the aperture phase as a function of time. Solution of the equation is effected by means of the Laplace transformation and yields detailed information concerning the dynamics of the array under the influence of the external injection signals.

injection locked↗

NASA NTRS1986

Energy broadening due to space-charge oscillations in high current electron beams

During electron beam accelerator operation on Spacelab I, substantial fluxes of electrons were observed with energies greater than the initial beam energy. Numerical calculations are performed for the emission of an unneutralized, one-dimensional electron beam. These calculations show clearly that space charge oscillations, which are associated with the charge buildup on the emitter, strongly modify the beam and cause the returning beam particles to have a distribution of kinetic energies ranging from half to over twice the initial energy.

Katz, I.↗

NASA NTRS1990

An evaluation of the structure of tropical intraseasonal oscillations in three general circulation models

The attributes for the simulation of tropical intraseasonal oscillations in the 30 to 60 day range by three GCMs are compared with analyses of the European Center for Medium-Range Weather Forecasts. Models under consideration include the Goddard Laboratory of Atmospheric sciences (GLAS), Goddard Laboratory for Atmospheres (GLA), and UCLA GCMs. They are characterized by the same resolutions of four degrees latitude by five degrees longitude with 9 levels. Observations reveal that the eastward traveling planetary scale structure becomes more stationary over the Indonesian region and accelerates over the Central Pacific. In the tropics a Kelvin wave-type structure is found to be dominant near the center of the oscillation. The simulated winds are realistic although the meridional component is too strong, especially in the GLA GCM. The differences in the structure of the oscillation in the GLAS GCM and GLA GCM are considered to be a consequence of the different numerical schemes used. The GCMs are characterized by preferred zones for diabatic heating, with a turn-on heating occurring when the rising branch of the intraseasonal oscillation passes over these convective regions.

Park, Chung-Kyu↗

NASA NTRS2010

Guidelines for Computing Longitudinal Dynamic Stability Characteristics of a Subsonic Transport

A systematic study is presented to guide the selection of a numerical solution strategy for URANS computation of a subsonic transport configuration undergoing simulated forced oscillation about its pitch axis. Forced oscillation is central to the prevalent wind tunnel methodology for quantifying aircraft dynamic stability derivatives from force and moment coefficients, which is the ultimate goal for the computational simulations. Extensive computations are performed that lead in key insights of the critical numerical parameters affecting solution convergence. A preliminary linear harmonic analysis is included to demonstrate the potential of extracting dynamic stability derivatives from computational solutions.

Thompson, Joseph R.↗

NASA NTRS1982

Numerical simulations of unsteady transonic flow in diffusers

Forced and naturally occurring, self-sustaining oscillations of transonic flows in two-dimensional diffusers were computed using MacCormack's hybrid method. Depending upon the shock strengths and the area ratios, the flow was fully attached or separated by either the shock or the adverse pressure gradient associated with the enlarging diffuser area. In the case of forced oscillations, a sinusoidal plane pressure wave at frequency 300 Hz was prescribed at the exit. A sufficiently large amount of data were acquired and Fourier analyzed. The distrbutions of time-mean pressures, the power spectral density, and the amplitude with phase angle along the top wall and in the core region were determined. Comparison with experimental results for the forced oscillation generally gave very good agreement; some success was achieved for the case of self-sustaining oscillation despite substantial three-dimensionality in the test. An observation of the sequence of self-sustaining oscillations was given.

Liou, M.-S.↗

NASA NTRS1999

Generation of Electron Suprathermal Tails in the Upper Solar Atmosphere: Implications for Coronal Heating

We present a mechanism for the generation of non-Maxwellian electron distribution function in the upper regions of the solar atmosphere in the presence of collisional damping. It is suggested that finite amplitude, low frequency, obliquely propagating electromagnetic waves can carry a substantial electric field component parallel to the mean magnetic field that can be significantly larger than the Dreicer electric field. This long wavelength electric fluctuation is capable of generating high frequency electron plasma oscillations and low frequency ion acoustic-like waves. The analysis has been performed using 1-1/2D Vlasov and PIC numerical simulations in which both electrons and ions are treated kinetically and self consistently. The simulation results indicate that high frequency electron plasma oscillations and low frequency ion acoustic-like waves are generated. The high frequency electron plasma oscillation drives electron plasma turbulence, which subsequently is damped out by the background electrons. The turbulence damping results in electron acceleration and the generation of non-Maxwellian suprathermal tails on time scales short compared to collisional damping. Bulk heating also occurs if the fluctuating parallel electric field is strong enough. This study suggests that finite amplitude, low frequency, obliquely propagating, electromagnetic waves can play a significant role in the acceleration and heating of the solar corona electrons and in the coupling of medium and small-scale phenomena.

Vinas, Adolfo F.↗

NASA NTRS1979

Calculated global conditions for the unsteady Euler's flow equations

This paper considers the numerical solution of a fluid dynamical system with time-dependent oscillating boundaries. The problem detailed, a compressible and inviscid flow in a one-dimensional pipe with vibrating ends, is examined to develop techniques needed to solve the more complex unsteady flows in turbomachine cascades. The problem is shown to be mathematically ill-posed but by complementing the governing equations with energy conservation, a unique solution is obtained. An artificial damping term is introduced into the governing equations to improve the performance of the time-marching integration.

Kuzo, D. M.↗

NASA NTRS1982

Transient phenomena of shock-induced turbulent separation for a spikebody and stalling airfoil at transonic and supersonic speeds

The time-dependent, compressible, Reynolds-averaged, full Navier-Stokes equations are applied to solve an axisymmetric flow around a forward-facing stepbody (spikebody) at supersonic speeds and a stalling airfoil at transonic speeds. Important transient and unsteady phenomena, not yet well understood, are examined, and significant new findings of the present solution to the phenomena are discussed. The phenomena described in detail are as follows: The evolution of the shock wave pressure built up by the impact of the pressure waves, one from the trailing edge; the separation of the flow as influenced by the shock wave; the location of the reversed flow, the separation point, and the reattachment point; and the transient (or unsteady) phenomena of the flow pulsation, oscillation, and stalling of the body and airfoil wake flow. The numerical results show that the transient flow instability is caused by a supersonic jet induced in the separation bubble by the shock-bifurcation (lambda shock) mechanism between the separation shock and the reflected shock. Pulsation and stall phenomena are caused by a sudden increase in the leading-edge pressure due to the jet and the separation bubble interacting along the stagnation point flow.

Yoshikawa, K. K.↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

Implicit total variation diminishing (TVD) schemes for steady-state calculations

Yee, H. C.↗

NASA NTRS1985

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.

Yee, H. C.↗

NASA NTRS1991

The computation of standard solar models

Procedures for calculating standard solar models with the usual simplifying approximations of spherical symmetry, no mixing except in the surface convection zone, no mass loss or gain during the solar lifetime, and no separation of elements by diffusion are described. The standard network of nuclear reactions among the light elements is discussed including rates, energy production and abundance changes. Several of the equation of state and opacity formulations required for the basic equations of mass, momentum and energy conservation are presented. The usual mixing-length convection theory is used for these results. Numerical procedures for calculating the solar evolution, and current evolution and oscillation frequency results for the present sun by some recent authors are given.

Ulrich, Roger K.↗

NASA NTRS1996

Stability Limits and Dynamics of Nonaxisymmetric Liquid Bridges

Theoretical and experimental investigation of the stability of nonaxisymmetric and axisymmetric bridges contained between equal and unequal radii disks as a function of Bond and Weber number with emphasis on the transition from unstable axisymmetric to stable nonaxisymmetric shapes. Numerical analysis of the stability of nonaxisymmetric bridges between unequal disks for various orientations of the gravity vector Experimental and numerical investigation of bridge stability (nonaxisymmetric and axisymmetric), large amplitude (nonaxisymmetric) oscillations and breaking.

Alexander, J. Iwan D.↗

NASA NTRS2002

A Solar Model with g-Modes

Good evidence is assembled showing that the Suit's core arid surface vary on time scales from a month to a decade arid that a number of scales are similar. The most plausible source for numerous long time scales and periodicities is long-lived global oscillations. This suggests g-modes (oscillations restored mainly by buoyancy) because they particularly affect the core and base of the convective envelope, which then indirectly modulates the surface. Also, standing g-modes have rotational properties that match many observed periodicities. But the standard solar model (SSM) has a static core and excites few if any g-modes. making new interior structures worth exploring. The model outlined here assumes two well mixed shells near 0.18 and 0.68 R, (13 = solar radius) where sound speed data shows sharp deviations from the SSM. Mixing is sustained by flows driven by the oscillations. The shells form a cavity that excludes g-modes from their main damping region below 0.1 R, assisting their net excitation and increasing their oscillation periods by at least a factor of two and probably much more. In terms of the solar luminosity L, the modes transport up through the cavity a power approx. 0.004 L as a lower limit and 0.11 L as all upper limit. The modes dissipate energy in the outer shell and cool the inner shell, asymmetrically in each case, and this stimulates occasional convective events whose response time is typically 0.8 years longer near the inner shell. Such events cool the core and reduce neutrino flux while heating the envelope and increasing solar activity. This gives a physical basis for a well mixed Sun with low neutrino flux and basis for the observed anticorrelation and lag of neutrino behind surface activity.

Wolff, Charles L.↗

NASA NTRS2004

Multi-d CFD Modeling of a Free-piston Stirling Convertor at NASA Glenn

A high efficiency Stirling Radioisotope Generator (SRG) is being developed for possible use in long duration space science missions. NASA s advanced technology goals for next generation Stirling convertors include increasing the Carnot efficiency and percent of Carnot efficiency. To help achieve these goals, a multidimensional Computational Fluid Dynamics (CFD) code is being developed to numerically model unsteady fluid flow and heat transfer phenomena of the oscillating working gas inside Stirling convertors. Simulations of the Stirling convertors for the SRG will help characterize the thermodynamic losses resulting from fluid flow and heat transfer between the working gas and solid walls. The current CFD simulation represents approximated 2-dimensional convertor geometry. The simulation solves the Navier Stokes equations for an ideal helium gas oscillating at low speeds. The current simulation results are discussed.

Wilson, Scott D.↗

NASA NTRS2006

Experimental and Computational Analysis of Unidirectional Flow Through Stirling Engine Heater Head

A high efficiency Stirling Radioisotope Generator (SRG) is being developed for possible use in long-duration space science missions. NASA s advanced technology goals for next generation Stirling convertors include increasing the Carnot efficiency and percent of Carnot efficiency. To help achieve these goals, a multi-dimensional Computational Fluid Dynamics (CFD) code is being developed to numerically model unsteady fluid flow and heat transfer phenomena of the oscillating working gas inside Stirling convertors. In the absence of transient pressure drop data for the zero mean oscillating multi-dimensional flows present in the Technology Demonstration Convertors on test at NASA Glenn Research Center, unidirectional flow pressure drop test data is used to compare against 2D and 3D computational solutions. This study focuses on tracking pressure drop and mass flow rate data for unidirectional flow though a Stirling heater head using a commercial CFD code (CFD-ACE). The commercial CFD code uses a porous-media model which is dependent on permeability and the inertial coefficient present in the linear and nonlinear terms of the Darcy-Forchheimer equation. Permeability and inertial coefficient were calculated from unidirectional flow test data. CFD simulations of the unidirectional flow test were validated using the porous-media model input parameters which increased simulation accuracy by 14 percent on average.

Wilson, Scott D.↗

NASA NTRS2004

Global variability of precipitation according to the Tropical Rainfall Measuring Mission

Numerous studies have documented the effect of El Nino-Southern Oscillation (ENSO) on rainfall in many regions of the globe. The question of whether ENSO is the single most important factor in interannual rainfall variability has received less attention, mostly because the kind of data that would be required to make such an assessment were simply not available. Until 1979 the evidence linking El Nino with changes in rainfall around the world came from rain gauges measuring precipitation over land masses and a handful of islands. From 1980 until the launch of the Tropical Rainfall Measuring Mission (TRMM) in November 1997 the remote sensing evidence was confined to ocean rainfall because of the very poor sensitivity of the instruments over land. In this paper we summarize the results of a principal component analysis of TRMM's 60-month (January 1998 to December 2002) global land and ocean remote-sensing record of monthly rainfall accumulations. Contrary to the first principal component of the rainfall itself, the first three indices of the anomaly are most sensitive to precipitation over the ocean rather than over the land. With the help of archived surface station data the first TRMM rain anomaly index is extended back several decades. Comparison of the extended index with the Southern Oscillation Index confirms that the first principal component of the rainfall anomaly is strongly correlated with the ENSO indices.

rainfall↗