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NASA NTRS1990

Numerical experiments in supersonic boundary-layer stability

The three-dimensional (3-D) time-dependent compressible Navier-Stokes equations are numerically solved by a Fourier-Chebyshev collocation method to study the stability of supersonic flows over a flat plate. Several direct simulations carried out in this study suggest the existence of a secondary instability that might provide a route to transition. The interaction of the modes involved in the secondary instability is possibly amenable to a Floquet-type analysis. Pertinent differences between this instability and the analogous incompressible K-type secondary instability are pointed out. Some preliminary results of a 2-D direct simulation of the nonlinear evolution of a second mode perturbation wave are also discussed.

Erlebacher, Gordon↗

NASA NTRS1990

Stabilization of Taylor-Couette flow due to time-periodic outer cylinder oscillation

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly. The critical Reynolds numbers calculated from linear stability theory agree well with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: a truncated Fourier series representation in time, and a fundamental solution matrix based on a Chebyshev pseudospectral representation in space. For large amplitude, low frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent region followed by rapid change in the perturbed flow velocities.

Murray, B. T.↗

NASA NTRS1991

Instability of multi-layer fluid configurations in the presence of time-dependent accelerations in a microgravity environment

The increasing number of research opportunities in a microgravity environment will benefit not only fundamental studies in fluid dynamics, but also technological applications such as those involving materials processing. In particular, fluid configurations which involve fluid-fluid interfaces would occur in a variety of experimental investigations. This work investigates the stability of a configuration involving fluid-fluid interfaces in the presence of a time-dependent forcing. Both periodic (g-jitter) and nonperiodic accelerations are considered. The fluid configuration is multilayered, and infinite in extent. The analysis is linear and inviscid, and the acceleration vector is oriented perpendicular to each interface. A Floquet analysis is employed in the case of the periodic forcing. In the problem of nonperiodic forcing, the resulting system of equations are integrated in time. Specific nondimensional parameters appear in each problem. The configuration behavior is investigated for a range of parameter values.

Lyell, M. J.↗

NASA NTRS1991

802GHz integrated horn antennas imaging array

Pattern measurements at 802GHz of a single element in 256-element integrated horn imaging array are presented. The integrated-horn antenna consists of a dipole-antenna suspended on a 1-micron dielectric membrane inside a pyramidal cavity etched in silicon. The theoretical far-field patterns, calculated using reciprocity and Floquet-modes representation of the free-space field, agree well with the measured far-field patterns at 802GHz. The associated directivity for a 1.40 lambda horn aperture, calculated from the measured E and H-plane patterns is 12.3dB + or - 0.2dB. This work demonstrates that high-efficiency integrated-horn antennas are easily scalable to terahertz frequencies and could be used for radio-astronomical and plasma-diagnostic applications.

Ali-Ahmad, Walid Y.↗

NASA NTRS1991

Secondary instability of high-speed flows and the influence of wall cooling and suction

El-Hady, Nabil M.↗

NASA NTRS1992

Secondary instability of high-speed flows and the influence of wall cooling and suction

The periodic streamwise modulation of the supersonic and hypersonic boundary layers by a two dimensional first mode or second mode wave makes the resulting base flow susceptible to a broadband spanwise-periodic three dimensional type of instability. The principal parametric resonance of this instability (subharmonic) was analyzed using Floquet theory. The effect of Mach number and the effectiveness of wall cooling or wall suction in controlling the onset, the growth rate, and the vortical nature of the subharmonic secondary instability are assessed for both a first mode and a second mode primary wave. Results indicate that the secondary subharmonic instability of the insulated wall boundary layer is weakened as Mach number increases. Cooling of the wall destabilizes the secondary subharmonic of a second mode primary wave, but stabilizes it when the primary wave is a first mode. Suction stabilizes the secondary subharmonic at all Mach numbers.

El-Hady, Nabil M.↗

NASA NTRS1992

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

Jin, Jian-Ming↗

NASA NTRS1991

Dynamics of helicopters with dissimilar blades

The dynamics of helicopters with dissimilar rotor blades is investigated for hingeless rotors in hover. An elastic blade model with finite element formulation is used. Hub motions are included by modeling the fuselage as a rigid body with pitch and roll degrees of freedom. The aeromechanical stability solution is solved in the fixed frame via Floquet theory. A parametric study of the effects of dissimilarity among blades' structural stiffness, mass, and damping on aeromechanical stability is presented. It is found that a slight reduction in the lag stiffness of one blade stabilizes the regressing lag mode instability.

Wang, James M.↗

NASA NTRS1991

On the reflectivity of complex mesh surfaces

Poorer than expected surface reflectivity was observed in an early Tracking and Data Relay Satellite System antenna utilizing a tricot mesh weave. This poor reflectivity was determined to be caused by inadequate electrical contact at wire crossover points. A proper mathematical and numerical approach to assess the impact of wire junctions on reflectivity performance is developed. A mathematical method is presented for computing the surface reflectivity of complex mesh configurations like those on unfurlable-type spacecraft antennas. The method is based on the Floquet mode expansion to establish an integral equation for mesh wire currents. The equation is solved using the method of moments with triangular basis functions. It is observed that it is necessary to give special attention to the junction treatment among different branches of the mesh configurations. A vector junction current approach that resulted in satisfactory solutions for the current is described. The results of numerical simulations are compared against measured data and excellent agreement is observed.

Imbriale, William A.↗

NASA NTRS1992

Effects of g-jitter and cross-diffusion on the onset of convection in doubly diffusive systems

The effects of a modulated gravity field in doubly diffusive layers with and without cross-diffusion are studied. Attention is focused on the determination of linear stability criteria for such systems. Floquet theory is used to establish the stability criteria by a systematic analysis of the topology of the neutral curves from which stability boundaries can be constructed. Convective stability boundaries for gravity-modulated doubly cross-diffusive systems are presented for the cases of dynamically free and rigid boundaries. Two physically different forms of layer stratification are considered: (1) imposed independent gradients of two components and (2) a solute gradient induced by a fixed temperature gradient.

Terrones, Guillermo↗

NASA NTRS1992

Secondary instability of high-speed flows and the influence of wall cooling and suction

The periodic streamwise modulation of the supersonic and hypersonic boundary layers by a two-dimensional first-mode or second-mode wave makes the resulting base flow susceptible to a broadband spanwise-periodic three-dimensional type of instability. The principal parametric resonance of this instability (subharmonic) has been analyzed using Floquet theory. The effect of Mach number and the effectiveness of wall cooling or wall suction in controlling the onset, the growth rate, and the vortical structure of the subharmonic secondary instability are assessed for both a first-mode and a second-mode primary wave. Results indicate that the secondary subharmonic instability of an insulated wall boundary layer is weakened as Mach number increases. Cooling of the wall destabilizes the secondary subharmonic of a second-mode primary wave, but stabilizes it when the primary wave is a first mode. Suction stabilizes the secondary subharmonic at all Mach numbers.

El-Hady, Nabil M.↗

NASA NTRS1990

Bearingless rotor aeromechanical stability measurements and correlations using nonlinear aerodynamics

The aeromechanical stability of a 1/8th Froude scaled bearingless rotor model was investigated experimentally in a wind tunnel. Both shaft-fixed and shaft-free conditions were examined to study the aeroelastic stability of a bearingless rotor without the incorporation of auxiliary dampers. This wind tunnel investigation generated a set of stability data for four different advance ratios, and a wide range of collective pitch settings. Theoretical analysis was performed using the newly developed University of Maryland Advanced Rotorcraft Code (UMARC). For analysis, the blade is modeled as an elastic beam undergoing flap bending, lag bending, elastic twist, and axial deformation. Blade response is calculated using a finite element method in time. Nonlinear aerodynamic effects are included by using a semiempirical stall modeling. The linearized periodic rotor perturbation equations in the nonrotating frame are solved for stability roots using Floquet transition matrix theory, as well as constant coefficient approximation. The predicted results are compared with the experimental data.

Wang, James M.↗

NASA NTRS1992

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

Saunders, B. V.↗

NASA NTRS1992

Interface stability of a fluid column subject to periodic accelerations normal to the longitudinal axis of the column

This project investigates the interface stability of an inviscid fluid column in the presence of a periodic acceleration field which has a component normal to the longitudinal axis of the column. A ramification of this configuration is that perturbations cannot be considered axisymmetric. The column is taken to be infinite in length. Floquet analysis will be utilized in the stability investigation.

Lyell, M. J.↗

NASA NTRS1993

Comprehensive analysis of bearingless rotors - Model development and experimental correlation of modes, response, trim and stability

A generic mathematical model that is capable of accurately modeling the multiple load path bearingless rotor blade is developed. A comprehensive, finite element based solution for the natural vibration of the rotor blade is developed. An iterative scheme based on harmonic balance is used to evaluate the nonlinear response of the rotor to control inputs and a Newton-Raphson procedure is employed to evaluate the trim of rotorcraft. Linearized perturbation model of the nonlinear system are presented. The model is validated by comparing with existing whirl tower, wind tunnel and flight test results of BMR/BO-105 helicopter. Frequencies of two bearingless rotor blades compare well with results from experiments. Nonlinear response and trim results are presented for the bearingless BMR/BO-105 rotor. Aeroelastic stability in forward flight, evaluated using floquet theory agrees with test data in general.

Jambunathan, V.↗

NASA NTRS1993

Fluid column stability in the presence of periodic accelerations

The interface stability of fluid columns in the presence of a periodic acceleration field with a component normal to the longitudinal axis of the isothermal cylinder was investigated. Floquet theory was used in the investigation and the column was taken as infinite. The finite length case was also studied and axisymmetric and nonaxisymmetric oscillations were considered. Results for the infinite length case were good approximations to those for the finite length column.

Lyell, M. J.↗

NASA NTRS1993

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy-driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time-periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time-periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically employing two distinct computational implementations of Floquet theory. Results are presented for materials with large Schmidt number, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, B. T.↗

NASA NTRS1993

On the dispersion relations for parametric instabilities of parallel-propagating Alfven waves

We consider the dispersion relation for the parametric instabilities of large-amplitude circularly polarized Alfven waves propagating parallel to the ambient magnetic field. A linear perturbation analysis is employed, and the perturbations are taken to propagate along the ambient field. We present an analysis based on Floquet's theorem. The result is a hierarchy of dispersion relations. However, all the dispersion relations are found to be equivalent to the one obtained via the standard analysis; the differences between them are due only to how ca and k are defined. Thus we conclude that physically there is really only one dispersion relation, namely the 'electrostatic dispersion relation', which is in agreement with earlier works. However, we disagree with Vinas and Goldstein (1991), who obtained additional dispersion relations which they have called the 'electromagnetic dispersion relations'. Their additional dispersion relations are a consequence of first truncating the dispersion relation for obliquely propagating perturbations and then taking the limit of parallel-propagating perturbations.

Yajanti, Venku↗