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NASA NTRS1994

Convection in the Physical Vapor Transport Process: Thermal - 1

The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra(sub tau) ranging from 1.80 x 10 to 1.92 x 10(exp 6). Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is to increase the threshold of instability. For typical ground based conditions, time dependent oscillatory convection can occur. This results in unsteady transport, and non-uniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows parametric regions exhibiting both an oscillatory approach to steady state and a chaotic transient to a periodic state. Low gravity conditions stabilize the flow field. Convective effects are effectively reduced, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Duval, Walter M. B.↗

NASA NTRS1994

Convection in the Physical Vapor Transport Process-I: Thermal

The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra, ranging from 1.80 x 10 to 1.92 x 10(exp 6). Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is to increase the threshold of instability. For typical ground based conditions, time dependent oscillatory convection can occur. This results in unsteady transport, and non- uniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows parametric regions exhibiting both an oscillatory approach to steady state and a chaotic transient to a periodic state. Low gravity conditions stabilize the flow field. Convective effects are effectively reduced, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Duval, Walter M. B.↗

NASA NTRS1994

Convection in the Physical Vapor Transport Process: Thermosolutal - Part 2

We consider the effect of an inert gas on the diffusive-convective physical vapor transport process. We investigate the case when the temperature gradient is stabilizing and the concentration gradient is destabilizing for a wide parametric range. When an inert gas is present, the thermal and solutal convection oppose each other. The solutal field is destabilizing while the thermal field and the advective-diffusive flux stabilize the flow field. When the pressure of the inert component is increased, the stabilizing effect of the advective-diffusive flux is decreased. The intensity of convection as well as the oscillatory transient time increases. Below, the critical Rayleigh number, the nonlinear dynamics of the flow field show an oscillatory approach to steady state. For parametric values in the neighborhood of the critical Rayleigh number, the flow field undergoes a chaotic transient which settles to a periodic state. The asymptotic state of the flow field shows that growth and amalgamation of cells yields an overturning motion which results in an asymmetric cellular structure. The low gravity environment yields the stabilizing advective-diffusive flow which results in uniform temperature and concentration gradients near the crystal interface.

Duval, Walter M. B.↗

NASA NTRS1996

Unsteady, Transonic Flow Around Delta Wings Undergoing Coupled and Natural Modes Response: A Multidisciplinary Problem

The unsteady, three-dimensional Navier-Stokes equations coupled with the Euler equations of rigid-body dynamics are sequentially solved to simulate and analyze the aerodynamic response of a high angle of attack delta wing undergoing oscillatory motion. The governing equations of fluid flow and dynamics of the multidisciplinary problem are solved using a time-accurate solution of the laminar, unsteady, compressible, full Navier- Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. The primary model under consideration consists of a 65 deg swept, sharp-edged, cropped delta wing of zero thickness at 20 deg angle of attack. In a freestream of Mach 0.85 and Reynolds number of 3.23 x 10(exp 6), the flow over the upper surface of the wing develops a complex shock system which interacts with the leading-edge primary vortices producing vortex breakdown. The effect of the oscillatory motion of the wing on the vortex breakdown and overall aerodynamic response is detailed to provide insight to the complicated physics associated with unsteady flows and the phenomenon of wing rock. Forced sinusoidal single and coupled mode rolling and pitching motion is presented for the wing in a transonic freestream. The Reynolds number, frequency of oscillation, and the phase angle are varied. Comparison between the single and coupled mode forced rolling and pitching oscillation cases illustrate the effects of coupling the motion. This investigation shows that even when coupled, forced rolling oscillation at a reduced frequency of 2(pi) eliminates the vortex breakdown which results in an increase in lift. The coupling effect for in phase forced oscillations show that the lift coefficient of the pitching-alone case and the rolling-moment coefficient of the rolling-alone case dominate the resulting response. However, with a phase lead in the pitching motion, the coupled motion results in a non-periodic response of the rolling moment. The second class of problems involve releasing the wing in roll to respond to the flowfield. Two models of sharp-edged delta wings, the previous 65 deg swept model and an 80 deg swept, sharp-edged delta wing, are used to observe the aerodynamic response of a wing free to roll in a transonic and subsonic freestream, respectively. These cases demonstrate damped oscillations, self-sustained limit cycle oscillations, and divergent rolling oscillations. Ultimately, an active control model using a mass injection system was applied on the surface of the wing to suppress the self-sustained limit cycle oscillation known as wing rock. Comparisons with experimental investigations complete this study, validating the analysis and illustrating the complex details afforded by computational investigations.

Menzies, Margaret Anne↗

NASA NTRS1997

Performance and Vibratory Loads Data From a Wind-Tunnel Test of a Model Helicopter Main-Rotor Blade With a Paddle-Type Tip

An investigation was conducted in the Langley Transonic Dynamics Tunnel to obtain data to permit evaluation of paddle-type tip technology for possible use in future U.S. advanced rotor designs. Data was obtained for both a baseline main-rotor blade and a main-rotor blade with a paddle-type tip. The baseline and paddle-type tip blades were compared with regard to rotor performance, oscillatory pitch-link loads, and 4-per-rev vertical fixed-system loads. Data was obtained in hover and forward flight over a nominal range of advance ratios from 0.15 to 0.425. Results indicate that the paddle-type tip offers no performance improvements in either hover or forward flight. Pitch-link oscillatory loads for the paddle-type tip are higher than for the baseline blade, whereas 4-per-rev vertical fixed-system loads are generally lower.

Yeager, William T., Jr.↗

NASA NTRS1995

On the Oscillation of Combustion of a Laminar Spray

A spray combustor, with flow velocities in the laminar range, exhibits a unique operating mode where large amplitude, self-induced oscillations of the flame shape occur. The phenomenon, not previously encountered, only occurs when fuel is supplied in the form of fine liquid droplets and does not occur when fuel is supplied in gaseous form. Several flow mechanisms are coupled in such a fashion as to trigger and maintain the oscillatory motion of the flame. These mechanisms include heat transfer and evaporation processes, dynamics of two-phase flows, and effects of gravity (buoyancy forces). An interface volume, lying between the fuel nozzle and the flame was found to be the most susceptible to gravity effects, and postulated to be responsible for inducing the oscillatory motion. Heptane fuel was used in the majority of the tests.

Levy, Yeshayahou↗

NASA NTRS1998

Confined States in Large-Aspect-Ratio Thermosolutal Convection

Two-dimensional thermosolutal convection with no-slip boundary conditions is studied using numerical simulations in a periodic domain. The domain is large enough to follow the evolution of phase instabilities of fully nonlinear traveling waves. In the parameter regime studied these instabilities evolve, without loss of phase or hysteresis, into a series of confined states or pulses characterized by locally enhanced heat and solute transport. The wavelength and phase velocity of the traveling rolls within a pulse differ substantially from those in the background. The pulses drift in the same direction as the convection rolls on which they ride but more slowly, and are characterized by an exponential leading front and an oscillatory trailing end. Multiple, apparently stable, states are found for identical parameter values. The qualitative properties of the pulses are in good agreement with the predictions of a third-order phase equation which accounts for the relation between wave number and phase velocity, the oscillatory tails and the multiplicity of states. These properties of the pulses are shown to be a consequence of Shil'nikov dynamics in the spatial domain.

Spina, Alejandro↗

NASA NTRS1959

Dynamic Longitudinal and Directional Stability Derivatives for a 45 deg. Sweptback-Wing Airplane Model at Transonic Speeds

An investigation was made at transonic speeds to determine some of the dynamic stability derivatives of a 45 deg. sweptback-wing airplane model. The model was sting mounted and was rigidly forced to perform a single-degree-of-freedom angular oscillation in pitch or yaw of +/- 2 deg. The investigation was made for angles of attack alpha, from -4 deg. to 14 deg. throughout most of the transonic speed range for values of reduced-frequency parameter from 0.015 to 0.040 based on wing mean aerodynamic chord and from 0.04 to 0.14 based on wing span. The results show that reduced frequency had only a small effect on the damping-in-pitch derivative and the oscillatory longitudinal stability derivative for all Mach numbers M and angles of attack with the exception of the values of damping coefficient near M = 1.03 and alpha = 8 deg. to 14 deg. In this region, the damping coefficient changed rapidly with reduced frequency and negative values of damping coefficient were measured at low values of reduced frequency. This abrupt variation of pitch damping with reduced frequency was a characteristic of the complete model or wing-body-vertical-tail combination. The damping-in-pitch derivative varied considerably with alpha and M for the horizontal-tail-on and horizontal-tail-off configurations, and the damping was relatively high at angles of attack corresponding to the onset of pitch-up for both configurations. The damping-in-yaw derivative was generally independent of reduced frequency and M at alpha = -4 deg. to 4 deg. At alpha = 8 deg. to 14 deg., the damping derivative increased with an increase in reduced frequency and alpha for the configurations having the wing, whereas the damping derivative was either independent of or decreased with increase in reduced frequency for the configuration without the wing. The oscillatory directional stability derivative for all configurations generally decreased with an increase in the reduced-frequency parameter, and, in some instances, unstable values were measured for the model configuration with the horizontal tail removed.

Bielat, Ralph P.↗

NASA NTRS1996

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗

NASA NTRS1998

Estimation of Aircraft Nonlinear Unsteady Parameters From Wind Tunnel Data

Aerodynamic equations were formulated for an aircraft in one-degree-of-freedom large amplitude motion about each of its body axes. The model formulation based on indicial functions separated the resulting aerodynamic forces and moments into static terms, purely rotary terms and unsteady terms. Model identification from experimental data combined stepwise regression and maximum likelihood estimation in a two-stage optimization algorithm that can identify the unsteady term and rotary term if necessary. The identification scheme was applied to oscillatory data in two examples. The model identified from experimental data fit the data well, however, some parameters were estimated with limited accuracy. The resulting model was a good predictor for oscillatory and ramp input data.

Klein, Vladislav↗

NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗

NASA NTRS1996

The Dynamics of Ultrasonically Levitated Drops in an Electric Field

Ultrasonic and electrostatic levitation techniques have allowed the experimental investigation of the nonlinear oscillatory dynamics of free droplets with diameter between 0.1 and 0.4 cm. The measurement of the resonance frequencies of the first three normal modes of large amplitude shape oscillations in an electric field of varying magnitude has been carried out with and without surface charges for weakly conducting liquids in air. These oscillations of nonspherical levitated drops have been driven by either modulating the ultrasonic field or by using a time-varying electric field, and the free decay from the oscillatory state has been recorded. A decrease in the resonance frequency of the driven fundamental quadrupole mode has been measured for increasing oblate deformation in the absence of an electric field. Similarly, a decrease in this frequency has also been found for increasing DC electric field magnitude. A soft nonlinearity exists in the amplitude dependence of the resonant mode frequencies for freely decaying as well as ultrasonically and electrically driven uncharged drops. This decrease in resonance frequency is accentuated by the presence of free surface charge on the drop. Subharmonic resonance excitation has been observed for drops in a time-varying electric field, and hysteresis exists for resonant modes driven to large amplitude. Mode coupling from lower-order resonances to higher-order modes has been found to be very weak, even for fairly large amplitude shape oscillations. Most of these results are in general agreement with predictions from recent analytical and numerical investigations.

Trinh, E. H.↗

NASA NTRS2000

Laboratory and Field Measurements of Raindrop Oscillations

This study presents new measurements of raindrop oscillations in laboratory and field conditions. A 2-D video disdrometer is used to detect the shape of oscillating raindrops. The studies that were conducted to examine the oscillatory behavior of drops reveal that there is a lack of observations of the large drop oscillations. Yet, these drops have significant importance on radar rain estimation. Therefore, the new laboratory study is particularly designed to expand our knowledge on oscillatory behavior of large raindrops. The preliminary laboratory tests indicate that the drops are less oblate than the equilibrium shapes. Regarding the field studies, a large sample of raindrops was collected in several tropical field campaigns. The raindrops are mostly distorted and canted due to the environmental wind. An algorithm that determines the drop orientation and canting angle is added to the current system. This would reveal one of the most comprehensive data set on the oscillating behavior of raindrops in natural rain. The role of the oscillating raindrops on polarimetric parameters and subsequent rain estimation will be added to the discussion.

Tokay, A.↗

NASA NTRS1999

Fluid Physics in a Fluctuating Acceleration Environment

Our program of research aims at developing a stochastic description of the residual acceleration field onboard spacecraft (g-jitter) to describe in quantitative detail its effect on fluid motion. Our main premise is that such a statistical description is necessary in those cases in which the characteristic time scales of the process under investigation are long compared with the correlation time of g-jitter. Although a clear separation between time scales makes this approach feasible, there remain several difficulties of practical nature: (i), g-jitter time series are not statistically stationary but rather show definite dependences on factors such as active or rest crew periods; (ii), it is very difficult to extract reliably the low frequency range of the power spectrum of the acceleration field. This range controls the magnitude of diffusive processes; and (iii), models used to date are Gaussian, but there is evidence that large amplitude disturbances occur much more frequently than a Gaussian distribution would predict. The lack of stationarity does not constitute a severe limitation in practice, since the intensity of the stochastic components changes very slowly during space missions (perhaps over times of the order of hours). A separate analysis of large amplitude disturbances has not been undertaken yet, but it does not seem difficult a priori to devise models that may describe this range better than a Gaussian distribution. The effect of low frequency components, on the other hand, is more difficult to ascertain, partly due to the difficulty associated with measuring them, and partly because they may be indistinguishable from slowly changing averages. This latter effect is further complicated by the lack of statistical stationarity of the time series. Recent work has focused on the effect of stochastic modulation on the onset of oscillatory instabilities as an example of resonant interaction between the driving acceleration and normal modes of the system, and on cavity flow as an example of how an oscillatory response under periodic driving becomes diffusive if the forcing is random instead. This paper describes three different topics that illustrate behavior that is peculiar to a stochastic acceleration field. In the first case, we show that g-jitter can induce effective attractive or repulsive forces between a pair of spherical particles that are suspended in an incompressible fluid of different density provided that the momentum diffusion length is larger than the interparticle separation (as in the case in most colloidal suspensions). Second, a stochastic modulation of the control parameter in the vicinity of a pitchfork or supercritical bifurcation is known not to affect the location of the threshold. We show, however, that resonance between the modulation and linearly stable modes close to onset can lead to a shift in threshold. Finally, we discuss the classical problem of vorticity diffusion away from a plane boundary that is being vibrated along its own plane. Periodic motion with zero average vorticity production results in an exponential decay of the vorticity away from the boundary. Random vibration, on the other hand, results in power law decay away from the boundary even if vorticity production averages to zero.

Drolet, Francois↗

NASA NTRS1964

Theory of Tumbling Bodies Entering Planetary Atmospheres with Application to Probe Vehicles and the Australian Tektites

The tumbling motion of aerodynamically stable bodies entering planetary atmospheres is analyzed considering that the tumbling, its arrest, and the subsequent oscillatory motion are governed by the equation for the fifth Painleve' transcendent. Results based on the asymptotic behavior of the transcendent are applied to study (1) the oscillatory behavior of planetary probe vehicles in relation to aerodynamic heating and loads and (2) the dynamic behavior of the Australian tektites on entering the Earth's atmosphere, under the hypothesis that their origin was the Moon.

Tobak, Murray↗

NASA NTRS2001

Ocean-Science Mission Needs: Real-Time AUV Data for Command, Control, and Model Inputs

Predictive models for tides, hydrodynamics, and bio-optical properties affecting the visibility and buoyancy of coastal waters are needed to evaluate the safety of personnel and equipment engaged in maritime operations under potentially hazardous conditions. Predicted currents can be markedly different for two-layer systems affected by terrestrial runoff than for well-mixed conditions because the layering decouples the surface and bottom Ekman layers and rectifies the current response to oscillatory upwelling-and downwelling-favorable winds. Standard ocean models (e.g. Princeton Ocean Model) require initial-and boundary data on the physical and optical properties of the multilayered water column to provide accurate simulations of heat budgets and circulation. Two observational systems are designed to measure vertically structured conditions on the West Florida Shelf (WFS): a tethered buoy network and an autonomous underwater vehicle (AUV) observational system. The AUV system is described with a focus on the observational systems that challenge or limit the communications command and control network for various types of measurement programs. These include vertical oscillatory missions on shelf transects to observe the optical and hydrographic properties of the water column, and bottom-following missions for measuring the bottom albedo. Models of light propagation, absorption, and conversion to heat as well as determination of the buoyancy terms for physical models require these measurements. High data rates associated with video bottom imagery are the most challenging for the real-time, command and control communications system, but they are met through a combination of loss-less and lossy data-compression methods, depending upon the data-rate of the radio links.

Carder, Kendall L.↗

NASA NTRS2001

Simulation of Flow Control Using Deformable Surfaces

The goal of this investigation is to numerically simulate the effects of oscillatory actuators placed on the leading edge of an airfoil, and to quantify the effects of oscillatory blowing on an airfoil stall behavior. It has been demonstrated experimentally that periodic blowing can delay flow separation at high angle of attack. The computations are to be performed for a TAU 0015 airfoil at a high Reynolds number of approx. 1 x 10(exp 6) with turbulent flow conditions. The two-equation Wilcox k - w turbulence model has been shown to provide reliable descriptions of transition and turbulence at high Reynolds numbers. The results are to be compared to Seifert's experimental data.

Truman, C. Randall↗

NASA NTRS1996

Navier-Stokes Simulation of the Canard-Wing-Body Longitudinal Dynamic Stability Characteristics

Many modern aircraft are canard-configured for aircraft control and improved aerodynamic performance. Canards can often enhance aircraft cruise performance, maneuverability and agility. For close-coupled canard configurations, the aerodynamic interaction between the canard and wing significantly changes the flow characteristics of the wing. In unsteady flow, such changes in the flow structure and performance of wings can be quite pronounced. Accurate modeling of the unsteady aerodynamics is essential for potential CFD design and analysis of such configurations. A time-accurate numerical simulation is performed to study the unsteady aerodynamic interaction between a canard and wing with emphasis on the effects of the canard on the configuration's dynamic response characteristics. The thin-layer Reynolds-averaged Navier-Stokes Equations with various turbulence models are used in this study. Computations are made on a generic, analytically-defined, close-coupled canard-wing-body configuration which has been the subject of numerous previously published experimental studies during the 1970's to mid-80's. More recently, a series of steady-flow simulations has been performed and published by the author. In the current study, the configuration is given prescribed ramp and oscillatory motions in order to predict characteristics such as the damping-in-pitch and oscillatory longitudinal stability parameters. The current computations are made at high-subsonic and transonic Mach numbers, moderate angles-of- attack from -4 to 20 degrees, and at various pitch rates and reduced frequencies. Comparisons of pressures and integrated force quantities (e.g. lift, drag, pitching moment and selected dynamic parameters) are made with other published computational results and available experimental data. Results showing the unsteady effects of the canard on surface pressures, integrated forces, canard-wing vortex interaction and vortex breakdown will be presented.

Tu, Eugene L.↗