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A basis is provided for examining the stability of so-called 'shooting methods' and to examine the stability of the method successfully applied by Nachtsheim and Green (1970) to boundary-layer flow with large injection and heat transfer. The stability of that method is examined and confirmed.
The fundamental processes controlling lean combustion were observed for better understanding, with particular emphasis on the formation and measurement of gas-phase pollutants, the stability of the combustion process (blowout limits), methods of improving stability, and the application of probe and optical diagnostics for flow field characterization, temperature mapping, and composition measurements. The following areas of investigation are described in detail: (1) axisymmetric, opposed-reacting-jet-stabilized combustor studies; (2) stabilization through heat recirculation; (3) two dimensional combustor studies; and (4) spectroscopic methods. A departure from conventional combustor design to a premixed/prevaporized, lean combustion configuration is attractive for the control of oxides of nitrogen and smoke emissions, the promotion of uniform turbine inlet temperatures, and, possibly, the reduction of carbon monoxide and hydrocarbons at idle.
Launch vehicle attitude control system for lateral drift minimization and prevention of structural load limit exceeding maneuvers, presenting stability analysis
A method of determining the stability of linear systems with many constant time delays is developed. This technique, an extension of the tau-decomposition method, is used to examine not only the stability but also the relative stability of retarded systems with many delays and a class of neutral equations with one delay. Analytical equations are derived for partitioning the delay space of a retarded system with two time delays. The stability of the system in each of the regions defined by the partitioning curves in the parameter plane is determined using the extended tau-decomposition method. In addition, relative stability boundaries are defined using the extended tau-decompositon method in association with parameter plane techniques. Several applications of the extended tau-decomposition method are presented and compared with stability results obtained from other analyses. In all cases the results obtained using the method outlined herein coincide with and extend those of previous investigations. The extended tau-decomposition method applied to systems with time delays requires less computational effort and yields more complete stability analyses than previous techniques.
The method of multiple scales is used to describe a formally correct method based on the nonparallel linear stability theory, that examines the two and three dimensional stability of compressible boundary layer flows. The method is applied to the supersonic flat plate layer at Mach number 4.5. The theoretical growth rates are in good agreement with experimental results. The method is also applied to the infinite-span swept wing transonic boundary layer with suction to evaluate the effect of the nonparallel flow on the development of crossflow disturbances.
Methods and apparatuses for stabilizing the strain-temperature response for a shape memory alloy are provided. To perform stabilization of a second sample of the shape memory alloy, a first sample of the shape memory alloy is selected for isobaric treatment and the second sample is selected for isothermal treatment. When applying the isobaric treatment to the first sample, a constant stress is applied to the first sample. Temperature is also cycled from a minimum temperature to a maximum temperature until a strain on the first sample stabilizes. Once the strain on the first sample stabilizes, the isothermal treatment is performed on the second sample. During isothermal treatment, different levels of stress on the second sample are applied until a strain on the second sample matches the stabilized strain on the first sample.
Methods and apparatuses for stabilizing the strain-temperature response for a shape memory alloy are provided. To perform stabilization of a second sample of the shape memory alloy, a first sample of the shape memory alloy is selected for isobaric treatment and the second sample is selected for isothermal treatment. When applying the isobaric treatment to the first sample, a constant stress is applied to the first sample. Temperature is also cycled from a minimum temperature to a maximum temperature until a strain on the first sample stabilizes. Once the strain on the first sample stabilizes, the isothermal treatment is performed on the second sample. During isothermal treatment, different levels of stress on the second sample are applied until a strain on the second sample matches the stabilized strain on the first sample.
Methods and apparatuses for stabilizing the strain-temperature response for a shape memory alloy are provided. To perform stabilization of a second sample of the shape memory alloy, a first sample of the shape memory alloy is selected for isobaric treatment and the second sample is selected for isothermal treatment. When applying the isobaric treatment to the first sample, a constant stress is applied to the first sample. Temperature is also cycled from a minimum temperature to a maximum temperature until a strain on the first sample stabilizes. Once the strain on the first sample stabilizes, the isothermal treatment is performed on the second sample. During isothermal treatment, different levels of stress on the second sample are applied until a strain on the second sample matches the stabilized strain on the first sample.
Two methods for polarization stabilization of an internal-mirror 3.39-micron He-Ne laser are reported. The first relies on a concurrently lasing 1.15-micron transition by fixing the relative amplitude of two orthogonally polarized longitudinal modes that are split by a Rochon prism and detected with separate Si photodiodes. In the second method, two spatially separated orthogonally polarized adjacent 3.39-micron modes are optically balanced, differentially chopped, and recombined on a single InSb photodiode for phase-sensitive detection. The dual-wavelength scheme has been tested by beating against a methane-stabilized 3.39-micron He-Ne laser, which yields maximum excursions of less than 0.5 MHz over several hours and comparable reproducibility. The polarization-stabilized He-Ne laser has been used as a reference for a tunable color-center laser molecular-beam optothermal spectrometer and provides a precision of better than 2 MHz.
Here, this paper presents a variational multiscale (VMS) based finite element method where the stabilization parameter is computed dynamically. The current dynamic procedure takes in a general structure/form of the stabilization parameter with unknown coefficients and computes them dynamically in a local fashion resulting in a dynamic VMS-based finite element method. Thus, a static stabilization parameter with pre-defined coefficients is not needed. A variational Germano identity (VGI) based local procedure suitable for unstructured meshes is developed to perform the dynamic computation in a local fashion. The local VGI based procedure is applied for each interior vertex in the mesh and unknown coefficients are first determined locally at each vertex, and subsequently, for each element a maximum value is taken over the vertices of the element. To make the current procedure practical, a coarser secondary solution is constructed from the primary coarse-scale solution, which is done locally over a patch of elements around each interior vertex. Further, averaging steps are employed to make the local dynamic procedure robust. Currently, the new dynamic VMS formulation is applied to steady problems governed by the advection-diffusion and incompressible Navier-Stokes equations in both 1D and 2D to demonstrate its efficacy and effectiveness.
The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.
Method of stationkeeping for lenticular gravity gradient satellites
Liapunov or energy restraint methods for dynamic stabilization in two body motion perturbation problems are considered. Results of computerized orbital stabilization estimates show that the application of energy restraint prevents the occurrence of consistent timing errors in the stepwise integration of equations of motion for a nearly circular orbit.
A method of estimating frequency drift rate and removing its effect from Allan variance plots is given. When tried on a test of hydrogen masers, the methods gives consistent results. An error in the previous Allan variance computation algorithm is corrected.
Approximation methods for determining stability of structurally orthotropic cylindrical panels subjected to shearing stresses and internal pressures
We present here a Lagrangian discontinuous Galerkin (DG) hydrodynamic method that is up to third-order accurate using subcell mesh stabilization (SMS) for compressible flows on quadratic meshes in two-dimensional (2D) Cartesian coordinates. Similar to the second-order accurate Lagrangian DG method with linear meshes, the physical evolution equations for the specific volume, velocity, and specific total energy are discretized using a modal DG method with Taylor series polynomials. The Riemann velocity at the vertices of a curvilinear cell, and the corresponding surface forces, are calculated by solving a multidirectional approximate Riemann problem. Curvilinear cells (e.g., quadratic quadrilateral meshes in this work) have many deformational degrees of freedom, and with these cells, they can deform in unphysical ways. Likewise, the Riemann solution at an edge vertex differs from the one at the corner of a cell. With SMS, each quadratic quadrilateral cell is decomposed into four quadrilateral subcells, that move in a Lagrangian manner. The edge vertex is surrounded by four subcells so that it is similar to the vertex at the cell corner. SMS can detect inconsistent density fields between the cell and subcells. The difference between these two density fields is used to correct the stress (pressure) input to the Riemann solver. This SMS scheme enables stable mesh motion and accurate solutions in the context of a Lagrangian high-order DG method that is up to third-order with quadratic cells. We also present effective limiting strategies that ensure monotonicity of the primitive variables with the high-order DG method. This Lagrangian DG hydrodynamic method with SMS conserves mass, momentum, and total energy. A suite of test problems are calculated to demonstrate the designed order of accuracy (up to third-order accurate) of this method, and that the Lagrangian DG method using SMS preserves cylindrical symmetry on 1D radial flow problems with an equal-angle polar quadratic mesh.
The flutter model represented the aft fuselage and empennage of a proposed supersonic transport airplane and had an all movable horizontal tail with a geared elevator. It was tested mounted from a sting in the transonic dynamics tunnel. Symmetric flutter boundaries were determined experimentally at Mach numbers from 0.7 to 1.14 for a geared elevator configuration (gear ratio of 2.8 to 1.0) and an ungeared elevator configuration (gear ratio of 1.0 to 1.0). Gearing the elevator increased the experimental flutter dynamic pressures about 20 percent. Flutter calculations were made for the geared elevator configuration by using two analytical methods based on subsonic lifting surface theory. Both methods analyzed the stabilizer and elevator as a single, deforming surface, but one method also allowed the elevator to be analyzed as hinged from the stabilizer. All analyses predicted lower flutter dynamic pressures than experiment with best agreement (within 12 percent) for the hinged elevator method. Considering the model as mounted from a flexible rather than rigid sting in the analyses, had only a slight effect on the flutter results but was significant in that a sting related vibration mode was identified as a potentially flutter critical mode.
Free flight and free oscillation methods for wind tunnel dynamic stability testing