A mathematical analysis of the stability of a lunar flying vehicle with manual controls
Mathematical analysis of stability of lunar flying vehicle with manual controls
Hall, D.↗
SEARCH · Engineering Papers
Results for “stability analysis”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems
Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.
42 ENGINEERING↗
Recent Progress in Heliogyro Solar Sail Structural Dynamics
Results from recent National Aeronautics and Space Administration (NASA) research on the structural dynamics and control characteristics of heliogyro solar sails are summarized. Specific areas under investigation include coupled nonlinear finite element analysis of heliogyro membrane blade with solar radiation pressure effects, system identification of spinning membrane structures, solarelastic stability analysis of heliogyro solar sails, including stability during blade deployment, and results from small-scale in vacuo dynamics experiments with spinning high-aspect ratio membranes. A low-cost, rideshare payload heliogyro technology demonstration mission concept, used as a mission context for these heliogyro structural dynamics and solarelasticity investigations, is also described.
Wilkie, William K.↗
Aeroelastic stability and response of horizontal axis wind turbine blades
The coupled flap-lag-torsion equations of motion of an isolated horizontal axis wind turbine blade are formulated. Quasi-steady blade-element strip theory was applied to derive the aerodynamic operator which includes boundary layer type gradient winds. The final equations which have periodic coefficients were solved in order to obtain the aeroelastic response and stability of large horizontal axis wind turbine blade. A new method of generating an appropriate time-dependent equilibrium position (required for the stability analysis) has been implemented. Representative steady-state responses and stability boundaries, applicable mainly to an existing blade design (NASA/-ERDA MOD-0), are presented. The results indicate that the MOD-0 configuration is a basically stable design and that blade stability is not sensitive to offsets between blade elastic axis and aerodynamic center. Blade stability appears to be sensitive to precone. The tower shadow (or wake) has a considerable effect on the flap response but leaves blade stability unchanged. Finally, it was found that non linear terms in the equations of motion can significantly affect the linearized stability boundaries, however, these terms have a negligible effect on blade response at operating conditions.
Kottapalli, S. B. R.↗
Effects of heat release on the structure and stability of a coflowing, chemically reacting jet
It is shown how linear stability analysis and full simulations can be used to study the stability and structure of reacting flows. The small effect of gravity on steady laminar flame heights can be modeled if allowance is made for the density variations due to heat release. It is found that cold transitional jet simulations yield perturbation growth rates which are consistent with the predictions of the inviscid stability theory.
Mahalingam, S.↗
Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints
In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.
Orr, Jeb S.↗
Rotordynamic Feasibility of a Conceptual Variable-Speed Power Turbine Propulsion System for Large Civil Tilt-Rotor Applications
A variable-speed power turbine concept is analyzed for rotordynamic feasibility in a Large Civil Tilt-Rotor (LCTR) class engine. Implementation of a variable-speed power turbine in a rotorcraft engine would enable high efficiency propulsion at the high forward velocities anticipated of large tilt-rotor vehicles. Therefore, rotordynamics is a critical issue for this engine concept. A preliminary feasibility study is presented herein to address this concern and identify if variable-speed is possible in a conceptual engine sized for the LCTR. The analysis considers critical speed placement in the operating speed envelope, stability analysis up to the maximum anticipated operating speed, and potential unbalance response amplitudes to determine that a variable-speed power turbine is likely to be challenging, but not impossible to achieve in a tilt-rotor propulsion engine.
Howard, Samuel↗
Effect of outer-cylinder rotation on the radially heated Taylor–Couette flow
A Taylor–Couette setup with radial heating is considered where a Boussinesq fluid is sheared in the annular region between two concentric, independently rotating cylinders maintained at different temperatures. Linear stability analysis is performed to determine the Taylor number for the onset of instability. Two radius ratios corresponding to wide and thin gaps with several rotation rate ratios are considered. The rotation of the outer cylinder is found to have a general stabilizing effect on the stability threshold as compared to pure inner-cylinder rotation, with a few exceptions. The radial heating sets up an axial flow which breaks the reflection symmetry of isothermal Taylor–Couette flow in the axial coordinate. This symmetry breaking separates linear stability thresholds, and we find the fastest growing modes with both positive and negative azimuthal numbers for different parameters. Another important finding of the current study is the discovery of unstable modes in the Rayleigh-stable regime. Furthermore, closed disconnected neutral curves (CDNCs) are observed for both wide and thin gaps which can separate from or merge into open neutral–stability curves. Alternatively, CDNCs can also morph into open neutral stability curves as the rotation rate ratio is changed. CDNCs are observed to be sensitive to changes in control parameters, and their appearance/disappearance is shown to induce discontinuous jumps in the critical Taylor number. Finally, for both wide and thin gaps, the fastest-growing modes found in the pure corotation case are shown to have their origins in the instability islands at smaller values of rotation rate ratios.
97 MATHEMATICS AND COMPUTING↗
Accretion onto magnetized neutron stars - Normal mode analysis of the interchange instability at the magnetopause
Results are reported for a linearized hydromagnetic stability analysis of the magnetopause of an accreting neutron star. The magnetosphere is assumed to be slowly rotating, and the plasma just outside the magnetopause is assumed to be weakly magnetized. The plasma layer is assumed to be bounded above by a shock wave and to be thin compared with the radius of the magnetosphere. Under these circumstances, the growing modes are shown to be localized in the direction parallel to the zero-order magnetic field, but the structure of the modes is still similar to the flute mode. An expression for the growth rate at each magnetic latitude is obtained in terms of the magnitude of the gravitational acceleration normal to the surface, the azimuthal mode number, the radius of the magnetosphere, the height of the shock above the magnetopause, and the effective Atwood number which embodies the stabilizing effects of favorable curvature and magnetic tension. The effective Atwood number is calculated, and the stabilizing effects of viscosity and aligned flow parallel to the magnetopause are discussed.
Arons, J.↗
Transition Analysis for the CRM-NLF Wind Tunnel Configuration
This paper reports the results of a comprehensive linear stability analysis of the boundary layer flow over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a recent wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. Previous work has shown that the measured onset of laminar-turbulent transition during the experiments can be correlated with the linear amplification of Tollmien-Schlichting (TS) and stationary crossflow (CF) instabilities in the swept wing boundary layer. However, a significant scatter ( N ∈ (4,9)) was observed in the values of the logarithmic amplification factor along the measured transition front. This previous analysis was based on an approximate basic state (based on a boundary layer code with conical flow approximation) and parallel stability computations without surface curvature effects. Here, we examine the effects of these various approximations with the goal of quantifying the resulting changes in the N-factor correlations. Specifically, both linear stability theory (LST) and the parabolized stability equations (PSE)are used in conjunction with an accurate definition of the laminar boundary layer flow as computed with a Navier-Stokes solver with a Reynolds-Averaged-Navier-Stokes (RANS) based turbulence model within the turbulent parts of the flow. Furthermore, the effects of instability wave propagation within a fully three-dimensional boundary layer are also evaluated by integrating the disturbance growth rates along suitably chosen, curvilinear (i.e., nonplanar) propagation trajectories. The results of this analysis are also used in an accompanying paper by Venkatachari et al. to develop improved, physics based transition predictions for the same CRM-NLF configuration.
Boundary layer transition↗
The stability of expanding reactive shocks in a van der Waals fluid
Despite the extensive literature accumulated since the pioneering works of D'yakov and Kontorovich in the 1950s, the stability of steady shocks is still an open question when realistic boundary conditions are accounted. The consideration of a supporting mechanism, which is indeed a necessary condition for shock steadiness, modifies the perturbation shock dynamics in the unstable range. The Noh problem is a suitable example to form steady expanding shocks. This configuration is of great interest to the high-energy-density-physics community because of its direct application to inertial confinement fusion and astrophysics, for which the stagnation of a supersonically converging material via an accretion shock front is ubiquitous. Here in this work, we extend the generalized Noh problem, both base-flow solution and linear stability analysis, to conditions where endothermic or exothermic transformations undergo across the shock. Within the spontaneous acoustic emission conditions found for a van der Waals gas, we find that cylindrical and spherical expanding shocks become literally unstable for sufficiently high mode numbers. Counterintuitively, the effect of exothermicity or endothermicity across the shock is found to be stabilizing or destabilizing, respectively.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Explaining the lack of power degradation of energy confinement in wide pedestal quiescent H-modes via transport modeling
Wide pedestal quiescent H (WPQH)-mode is an attractive scenario for future burning plasmas as they operate without ELMs. WPQH is characterized by formation of a wider and higher pedestal (than quiescent H-mode), and broadband fluctuations in the pedestal. Unlike conventional H-modes, where the energy confinement time reduces with increasing heating power, the WPQH plasmas reported in this paper do not show power degradation of the energy confinement. As the injected neutral beam power was increased, reduced core (ρ ≤ 0.45) transport calculated by transp, as well as increased core temperatures, pressure gradient and diamagnetic E × B shear rate were observed. The reduction in the heat transport and rapid decrease in the ion temperature gradient scale length suggest the formation of an ion internal transport barrier (ITB) that was accompanied by increased stored energy in the core. Quasilinear turbulent transport modeling using the trapped gyro Landau fluid (tglf) code was used to predict the ITB and its turbulence stability properties. By using profiles and equilibria produced by matching the transp transport fluxes with the tglf transport model within the tgyro transport solver, the energy confinement time captures the experimentally observed insensitivity to the increased PNBI. Linear stability analysis reveals that drift-wave instabilities in the core are stabilized by E × B shear, T i /T e ratio and Shafranov shift; the latter was found to have the strongest effect on the turbulence suppression at the highest heating level.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Bi-stability and period-doubling cascade of frequency combs in exceptional-point lasers
Abstract Recent studies have demonstrated that a laser can self-generate frequency combs when tuned near an exceptional point (EP), where two cavity modes coalesce. These EP combs induce periodic modulation of the population inversion in the gain medium, and their repetition rate is independent of the laser cavity’s free spectral range. In this work, we perform a stability analysis that reveals two notable properties of EP combs, bi-stability and a period-doubling cascade. The period-doubling cascade enables halving of the repetition rate while maintaining the comb’s total bandwidth, presenting opportunities for the design of highly compact frequency comb generators.
exceptional points↗
Electro-mechanical Modeling of Wind Turbine and Energy Storage Systems with Enhanced Inertial Response
In this paper, a coordinated control scheme for wind turbine generator (WTG) and supercapacitor energy storage system (ESS) is proposed for temporary frequency supports. Inertial control is designed by using generator torque limit considering the security of WTG system, while ESS releases its energy to compensate the sudden active power deficit during the recovery process of turbine rotor. WTG is modeled using the fatigue, aerodynamic, structure, turbulence (FAST) code, which identifies the mechanical loadings of the turbine and addresses electro-mechanical interactions in the wind energy system. A damping controller is augmented to the inertial control to suppress severe mechanical oscillations in the shaft and tower of the turbine during frequency supports. Furthermore, the result of small-signal stability analysis shows that the WTG-ESS tends to improve the stability of the whole multi-energy power grid. The major contributions of this paper will be validated by utilizing the proposed control method that combines the grid support capability and maintaining the integrity of structural design of the turbine for normal operations.
17 WIND ENERGY↗
Embedded mesh solution of the 2-D Euler equations - Evaluation of interface formulations
Solution of the steady 2-D Euler equations using mesh embedding, or local grid refinement, with a cell-centered finite volume scheme is investigated. Embedded regions which are topologically similar to the global grid are considered. An isoenergetic model for the governing equations is used in Jameson's finite volume multistage scheme with modifications to the boundary conditions and smoothing. A detailed study of the embedding interface flux and smoothing formulations is conducted. Taylor expansion analysis reveals that local second order spatial accuracy is not possible if a conservative interface flux formulation is used. The analysis also gives constraints for local first order accuracy. An energy stability analysis indicates that downwind weighting of interface fluxes causes local instabilities. Analysis shows that conservative interface smoothing formulations must have a locally convective component, but that correct interface formulations allow globally dissipative smoothing. Embedded mesh solutions obtained with this scheme are presented for a transonic airfoil. They show that if embedding interfaces are close to the shocks, then small modifications in the interface location can have large effects on converge and solution accuracy.
Allmaras, S. R.↗
Nonlinear Systems- The Parameter Analysis and Design.
Book on nonlinear systems analysis and design covering parameter mapping, symmetrical, transient and forced oscillations and stability analysis
Siljak, D. D.↗
Topology property analysis and application of stable time-delay regions for linear multiple time-delay systems
This study examines the relationship between the topology of stable time-delay regions and the stability analysis of an linear multiple time delay system. To analyze the topology of stable time-delay regions, we construct a function with a value equal to zero for the time-delay points on the boundaries of stable time-delay regions. The function is continuous and differentiable in the whole defining field with a global minimum of zero so that we can locate the boundaries by minimizing the value of the function. Based on the topology analysis, we proposed a performance validation approach for controllers that are designed to stabilize the system using feedback signals with time delays. The method based on the topology analysis is simple and reliable so that can deal with a linear time-invariant system with high order and multiple time delays (more than 3). The example case study shows that the above method is reliable and enables ultra-low latency coordination and control for the future power grid with ubiquitous power electronics.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Impact of Increased Inverter-Based Resources on Power System Small-Signal Stability
The transformation of the power system to include more distributed energy resources (DER) implies an increase in the number of inverter-based resources deployed on the grid. Envisioning future scenarios, this paper presents a small-signal stability analysis for a power grid comprising synchronous generators and inverter-based resources. Three types of inverter control are considered: grid following, droop-controlled grid forming, and virtual oscillator control grid forming. Although small-signal stability of power systems is a widely studied topic, systematic analysis of mixed machine-inverter systems with detailed control models at various inverter levels are limited. This paper addresses the gap with numerical simulations tailored to the IEEE 39-bus system. Results show the system may become unstable at high inverter level of grid-following inverters, and grid-forming inverter control can potentially improve system stability, thereby enabling very high level of DERs.
grid-following inverter↗