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NASA NTRS1986

Stress waves in isotropic elastic plate excited by circular transducer

Steady state harmonic stress waves in an isotropic elastic plate excited on one face by a circular transducer are analyzed theoretically. The transmitting transducer transforms an electrical voltage into a uniform normal stress at the top of the plate. To solve the boundary value problem,the radiation into a half-space is considered. The receiving transducer produces an electrical voltage proportional to the average spatially integrated normal stress over its face due to an incident wave. A numerical procedure is given to evaluate the frequency response at a receiving point due to a multiply reflected wave in the near field. Its stability and convergence are discussed. Parameterization plots which determine the particular wave whose frequency response has maximum magnitude compared with other multiple reflected waves are given for a range of values of dimensionless parameters. The effects of changes in the values of the parameters are discussed.

Williams, J. H., Jr.↗

NASA NTRS1985

A robust nonlinear attitude control law for space stations with flexible structural components

In this paper, a nonlinear attitude control law for space stations with flexible structural components is derived using a rigid-body model. This control law, depending on the Cayley-Rodriguez parameters, globally stabilizes the equilibrium of the rigid-body model. The effect of elastic deformations of the flexible structural components on the resulting feedback system dynamics is analyzed. It is found that the system's stability property is highly robust with respect to structural vibrations and inertial variations. The time-domain behavior of the feedback system is studied numerically using a model of a typical space station with flexible solar panels.

Wang, P. K. C.↗

NASA NTRS1987

The Jeffcott equations in nonlinear rotordynamics

The Jeffcott equations are a system of coupled differential equations representing the behavior of a rotating shaft. This is a simple model which allows investigation of the basic dynamic behavior of rotating machinery. Nolinearities can be introduced by taking into consideration deadband, side force, and rubbing, among others. The properties of the solutions of the Jeffcott equations with deadband are studied. In particular, it is shown how bounds for the solution of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solutions, we are also able to predict the onset of destructive vibrations. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots. This study offers insight into a possible detection method to determine pump stability margins during flight and hot fire tests, and was motivated by the need to explain a phenomenon observed in the development phase of the cryogenic pumps of the Space Shuttle, during hot fire ground testing; namely, the appearance of vibrations at frequencies that could not be accounted for by means of linear models.

Zalik, R. A.↗

NASA NTRS1992

Micro weather stations for in situ measurements in the Martian planetary boundary layer

Viking Lander meteorology measurements show that the Martian planetary boundary layer (PBL) has large diurnal and seasonal variations in pressure, wind velocity, relative humidity, and airborne dust loading. An even larger range of conditions was inferred from remote sensing observations acquired by the Mariner 9 and Viking orbiters. Numerical models indicate that these changes may be accompanied by dramatic vertical and horizontal wind shears (100 m/s/km) and rapid changes in the static stability. In-situ measurements from a relatively small number surface stations could yield global constraints on the Martian climate and atmospheric general circulation by providing ground truth for remote sensing instruments on orbiters. A more complete understanding of the meteorology of the PBL is an essential precursor to manned missions to Mars because this will be their working environment. In-situ measurements are needed for these studies because the spatial and temporal scales that characterize the important meteorological processes near the surface cannot be resolved from orbit. The Mars Environmental Survey (MESUR) Program will provide the first opportunity to deploy a network of surface weather stations for a comprehensive investigation of the Martian PBL. The feasibility and utility of a network of micro-weather stations for making in-situ meteorological measurements in the Martian PBL are assessed.

Crisp, D.↗

NASA NTRS1992

A generalized gamma(s)-family of self-starting algorithms for computational structural dynamics

A generalized gamma(s)-family of self-starting single-step formulations are presented in order to provide simplified yet effective dynamic attributes to include features towards eliminating the need to involve accelerations in the computational process for structural dynamic problems. By appropriately selecting the parameters pertaining to gamma(s)(s = 1, 2, 3), both explicit and implicit formulations are obtained. The stability and accuracy characteristics of the gamma(s)-family of representations are presented to validate the robustness of the formulations for structural dynamic problems. Numerous illustrative examples are described and the results are in excellent agreement and validate the applicability of these formulations for structural dynamic computations.

Namburu, Raju R.↗

NASA NTRS1999

A Numerical Study of Low-Reynolds-Number Separation Bubbles

The present study uses two dimensional numerical simulations to study unsteady low-Reynolds-number separation bubbles. The numerical study is in two parts: (1) a two dimensional time-accurate Navier-Stokes solver is used to simulate flows over the APEX airfoil, and (2) a numerical procedure is developed for localized simulations of transitional separation bubbles. The 2-D computations of flow over the APEX airfoil show that the flow is unsteady with periodic vortex shedding. A linear stability analysis of the separated flow shows that the vortex shedding is caused due to the instability of the separated flow. For transonic flows over the APEX airfoil the vortex shedding is additionally influenced by the presence of shocks. The flowfield has two characteristic time scales, one corresponding to the vortex shedding and another corresponding to the movement of the shocks. The two dimensional (2-D) airfoil simulations also showed the presence of nonlinear effects in the separated region. To better understand the characteristics of separation bubbles a numerical procedure has been developed for localized separation bubble calculations. This procedure is used to perform computations for a flat plate separation bubble test case. The separation bubble is induced by specifying a velocity gradient in the freestream. The growth of disturbances in the separation bubble is analyzed by introducing disturbances upstream of the separation bubble.

Tatineni, Mahidhar↗

NASA NTRS1999

Disturbance Dynamics in Transitional and Turbulent Flows

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. First the decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow. Second, homogeneous shear flow, where disturbances can be described by rapid distortion theory (RDT), is studied. The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.

Grosch, Chester E.↗

NASA NTRS2000

On the Modeling of Shells in Multibody Dynamics

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems involving shell components. The proposed schemes are designed to meet four specific requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the, constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed approach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation.

Bauchau, Olivier A.↗

NASA NTRS1999

Modeling the Dynamics of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

Thacker, W. D.↗

NASA NTRS2001

Aeroelastic Stability Computations for Turbomachinery

This paper describes an aeroelastic analysis program for turbomachines. Unsteady Navier-Stokes equations are solved on dynamically deforming, body fitted, grid to obtain the aeroelastic characteristics. Blade structural response is modeled using a modal representation of the blade and the work-per-cycle method is used to evaluate the stability characteristics. Nonzero interblade phase angle is modeled using phase-lagged boundary conditions. Results obtained showed good correlation with existing experimental, analytical, and numerical results. Numerical analysis also showed that given the computational resources available today, engineering solutions with good accuracy are possible using higher fidelity analyses.

Srivastava, R.↗

NASA NTRS2005

Experimental Study of Large-Amplitude Faraday Waves in Rectangular Cylinders

Experiment on single-mode Faraday waves having two, thee, and four wavelengths across a rectangular cylinder of high aspect ratio is the subject of discussion. Previous experiments recently done by Henderson & Miles (1989) and by Lei Jiang et. a1 (1996) focused on Faraday waves with one and two wavelengths across rectangular cylinders. In this experimental study the waves steepness ranges from small at threshold levels to a large amplitude which according to Penny & Price theory (1952) approaches the maximum sustainable amplitude for a standing wave. The waves characteristics for small amplitudes are evaluated against an existing well known linear theory by Benjamin & Ursell (l954) and against a weakly nonlinear theory by J. Miles (1984) which includes the effect of viscous damping. The evaluation includes the wave neutral stability and damping rate. In addition, a wave amplitude differential equation of a linear theory including viscous effect by Cerda & Tirapegui (1998) is solved numerically to yield prediction of temporal profiles of both wave damping and wave formation at the threshold. An interesting finding from this exercise is that the fluid kinematic viscosity needs to increase ten times in order to obtain good agreement between the theoretical prediction and the experimental data for both wave damping and wave starting. For large amplitude waves, the experimental data are evaluated against the theory of Penny & Price which predicts wave characteristics of any amplitude up to the point at which the wave reaches its maximum amplitude attainable for a standing wave. The theory yields two criteria to show the maximum wave steepness, the vertical acceleration at the wave crest of half the earth gravity field acceleration and the including angle at the crest of 90 degrees. Comparison with experimental data shows close agreement for the wave crest acceleration but a large discrepancy for the including angle. Additional information is included in the original extended abstract.

Iek, Chanthy↗

NASA NTRS2010

Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature

The streamwise lift distribution of a wing-canard-stabilator-body configuration was varied to study its effect on the near-field sonic boom signature. The investigation was carried out via solving the three-dimensional Euler equation with the OVERFLOW-2 flow solver. The computational meshes were created using the Chimera overset grid topology. The lift distribution was varied by first deflecting the canard then trimming the aircraft with the wing and the stabilator while maintaining constant lift coefficient of 0.05. A validation study using experimental results was also performed to determine required grid resolution and appropriate numerical scheme. A wide range of streamwise lift distribution was simulated. The result shows that the longitudinal wave propagation speed can be controlled through lift distribution thus controlling the shock coalescence.

Yoo, Seung Yeun (Paul)↗

NASA NTRS2015

The Magnetospheric Multiscale Constellation

The Magnetospheric Multiscale (MMS) mission is the fourth mission of the Solar Terrestrial Probe (STP) program of the National Aeronautics and Space Administration (NASA). The MMS mission was launched on March 12, 2015. The MMS mission consists of four identically instrumented spin-stabilized observatories which are flown in formation to perform the first definitive study of magnetic reconnection in space. The MMS mission was presented with numerous technical challenges, including the simultaneous construction and launch of four identical large spacecraft with 100 instruments total, stringent electromagnetic cleanliness requirements, closed-loop precision maneuvering and pointing of spinning flexible spacecraft, on-board GPS based orbit determination far above the GPS constellation, and a flight dynamics design that enables formation flying with separation distances as small as 10 km. This paper describes the overall mission design and presents an overview of the design, testing, and early on-orbit operation of the spacecraft systems and instrument suite.

Space mission design↗

NASA NTRS1985

Steady inviscid three-dimensional flows

The present analysis combines some of the theoretical concepts suggested by Hawthorne (1955) with a numerical integration procedure suggested by Martin (1978). The resulting algorithm is for inviscid subsonic flows. Thus, it is restricted to high Reynolds number flows. Chang and Adamczyk (1983) have provided a detailed derivation of the present algorithm along with a discussion of its stability bounds. The present paper represents a summary of this work. The integration of the continuity equation is considered along with an evaluation of the entropy, total temperature, and vorticity field. Attention is given to the shear-flow algorithm construction, and an application to a shear flow in a turning channel. A description of numerical results is also provided. The discussed algorithm represents a new procedure for solving inviscid subsonic three-dimensional rotational flows.

Adamczyk, J. J.↗

NASA NTRS2013

Saturn's F Ring Core: Calm in the Midst of Chaos

The long-term stability of the narrow F Ring core has been hard to understand. Instead of acting as "shepherds", Prometheus and Pandora together stir the vast preponderance of the region into a chaotic state, consistent with the orbits of newly discovered objects like S/2004S6. We show how a comb of very narrow radial locations of high stability in semimajor axis is embedded within this otherwise chaotic region. The stability of these semimajor axes relies fundamentally on the unusual combination of rapid apse precession and long synodic period which characterizes the region. This situation allows stable "antiresonances" to fall on or very close to traditional Lindblad resonances which, under more common circumstances, are destabilizing. We present numerical integrations of tens of thousands of test particles over tens of thousands of Prometheus orbits that map out the effect. The stable antiresonance zones are most stable in a subset of the region where Prometheus first-order resonances are least cluttered by Pandora resonances. This region of optimum stability is paradoxically closer to Prometheus than a location more representative of "torque balance", helping explain a longstanding paradox. One stable zone corresponds closely to the currently observed semimajor axis of the F Ring core. While the model helps explain the stability of the narrow F Ring core, it does not explain why the F Ring material all shares a common apse longitude; we speculate that collisional damping at the preferred semimajor axis (not included in the current simulations) may provide that final step. Essentially, we find that the F Ring core is not confined by a combination of Prometheus and Pandora, but a combination of Prometheus and precession.

Planetary Rings↗

NASA NTRS1991

A comparison of numerical methods for the Rayleigh equation in unbounded domains

A second-order finite difference and two spectral methods, including a Chebyshev tau and a Chebyshev collocation method were implemented to determine the linear hydrodynamic stability of an unbounded shear flow. The velocity profile of the basic flow in the stability analysis mimicks that of a one-stream free mixing layer. Local and global eigenvalue solution methods are used to determine individual eigenvalues and the eigenvalue spectrum, respectively. The calculated eigenvalue spectrum includes a discrete mode, a continuous spectrum associated with the equation singularity and a continuous spectrum associated with the domain unboundedness. The efficiency and the accuracy of these discretization methods in the prediction of the eigensolutions of the discrete mode were evaluated by comparison with a conventional shooting procedure. Their capabilities in mapping out the continuous eigenvalue spectra are also discussed.

Liou, W. W.↗

NASA NTRS1990

Direct numerical study of crossflow instability

Disturbances in the swept Hiemenz flow are calculated by solving the Navier-Stokes equations. The spatially-evolving base flow is treated exactly, allowing a check of the 'local' stability theories. Different types of disturbances such as random noise, waves, and wave packets, are input near the attachment line, develop in space, and exit through an outflow boundary. They all generate streamwise vortices. The effect of the Reynolds number, of the time-dependence of the noise, and of nonlinearity, are investigated.

Spalart, P. R.↗

NASA NTRS1988

Numerical modeling of multidimensional flow in seals and bearings used in rotating machinery

The rotordynamic behavior of turbomachinery is critically dependent on fluid dynamic rotor forces developed by various types of seals and bearings. The occurrence of self-excited vibrations often depends on the rotor speed and load. Misalignment and rotor wobbling motion associated with differential clearance were often attributed to stability problems. In general, the rotative character of the flowfield is a complex three dimensional system with secondary flow patterns that significantly alter the average fluid circumferential velocity. A multidimensional, nonorthogonal, body-fitted-grid fluid flow model is presented that describes the fluid dynamic forces and the secondary flow pattern development in seals and bearings. Several numerical experiments were carried out to demonstrate the characteristics of this complex flowfield. Analyses were performed by solving a conservation form of the three dimensional Navier-Stokes equations transformed to those for a rotating observer and using the general-purpose computer code PHOENICS with the assumptions that the rotor orbit is circular and that static eccentricity is zero. These assumptions have enabled a precise steady-state analysis to be used. Fluid injection from ports near the seal or bearing center increased fluid-film direct dynamic stiffness and, in some cases, significantly increased quadrature dynamic stiffness. Injection angle and velocity could be used for active rotordynamic control; for example, injection, when compared with no injection, increased direct dynamic stiffness, which is an important factor for hydrostatic bearings.

Hendricks, R. C.↗