Research in stability and control theory
Linear and nonlinear systems, and differential equations for control and stability theory
Gunderson, R. W.↗
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Results for “stability theory”
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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Uncertainty bounds using sector theory
An approach based on sector-stability theory can furnish a description of the uncertainty associated with the frequency response of a model, given sector-bounds on the individual parameters of the model. The application of the sector-based approach to the formulation of useful uncertainty descriptions for linear, time-invariant multivariable systems is presently explored, and the approach is applied to two generic forms of parameter uncertainty in order to investigate its advantages and limitations. The results obtained show that sector-uncertainty bounds can be used to evaluate the impact of parameter uncertainties on the frequency response of the design model.
Waszak, Martin R.↗
Solutal Convection in a Magnetic Fluid
A theoretical and experimental study is presented on the stability of solutal convection of a magnetized fluid in the presence of a magnetic field. The total force on the fluid is derived and equilibrium positions are computed establishing the field necessary to counter fluid buoyancy. The requirements for stability are developed and compared with experiments with a paramagnetic fluid. The experiments are in good agreement not only with the theoretical predictions for equilibrium but also verify the stability theory which predicts both horizontal and vertical stability. Analogous to results for levitation, the theory indicates that solutal convection in paramagnetic fluids cannot be completely stabilized while that in diamagnetic liquid are possible.
Leslie, Fred↗
The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers
During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.
Chang, Chau-Lyan↗
Boundary Layer Stability and Transition in a Chemically Reacting Martian Atmosphere Using LASTRAC
The Thermal Protection System (TPS) is a significant portion of the mass of reentry vehicles, planetary probes, and Martian entry vehicles. Reducing this mass has benefits in terms of decreased fuel requirements and increased payload; however, due to the high risk and uncertainty, the TPS or heat shields are designed conservatively by assuming fully turbulent flow. Laminar flow results in reduced heat flux, and improved transition prediction has the potential to reduce TPS mass and uncertainty in aerothermodynamic predictions. Limited previous research exists examining the problem of transition prediction for Martian atmospheric entry, with studies available on transition on the Mars Science Laboratory TPS. Although transition was demonstrated in wind-tunnel tests, uncertainty in the transition location resulted in a TPS designed for fully turbulent flow, and therefore greater mass than required for a partially laminar condition. In this work, we extend the boundary layer stability code LASTRAC, recently modified to include chemical and thermal nonequilibrium capabilities, to a model of the Martian atmosphere. LASTRAC provides Parabolized Stability Equations (PSE) as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semi-empirical e(sup N) methods. Results included in this work compare disturbance growth characteristics between air and Martian atmosphere at similar non-dimensional freestream conditions on a simple flat plate geometry. Both chemical nonequilibrium and thermochemical nonequilibrium, as well as both PSE and LST, are used.
Kline, H. L.↗
Boundary Layer Stability and Laminar-Turbulent Transition Analysis with Thermochemical Nonequilibrium Applied to Martian Atmospheric Entry
As Martian atmospheric entry vehicles increase in size to accommodate larger payloads, transitional ow may need to be taken into account in the design of the heat shield in order to reduce heat shield mass. The mass of the Thermal Protection System (TPS) comprises a significant portion of the vehicle mass, and a reduction of this mass would result in fuel savings. The current techniques used to design entry shields generally assume fully turbulent flow when the vehicle is large enough to expect transitional flow, and while this worst-case scenario provides a greater factor of safety it may also result in overdesigned TPS and unnecessarily high vehicle mass. Greater accuracy in the prediction of transition would also reduce uncertainty in the thermal and aerodynamic loads. Stability analysis, using e(sup N) -based methods including Linear Stability Theory (LST) and the Parabolized Stability Equations (PSE), offers a physics-based method of transition prediction that has been thoroughly studied and applied in perfect gas flows, and to a more limited extent in reacting and nonequilibrium flows. These methods predict the amplification of a known disturbance frequency and allow identification of the most unstable frequency. Transition is predicted to occur at a critical amplification or N Factor, frequently determined through experiment and empirical correlations. The LAngley Stability and TRansition Analysis Code (LASTRAC), with modifications for thermochemically reacting flows and arbitrary gas mixtures, will be presented with LST results on a simulation of a high enthalpy CO2 gas wind tunnel test relevant to Martian atmospheric entry. The results indicate transition caused by modified Tollmien-Schlichting waves on the leeward side, which are predicted to be more stable and cause transition slightly downstream when thermochemical nonequilibrium is included in the stability analysis for the same mean flow solution.
Transition↗
Three-Dimensional Nonequilibrium Boundary Layer Stability & Transition Analysis For Martian Entry
In this work, we apply the boundary layer stability code LASTRAC, modified to include chemical and thermal nonequilibrium capabilities, to a simulated test case based on literature, with three-dimensional effects. LASTRAC provides Parabolized Stability Equations (PSE)as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semiempirical eN methods. Tests of the Mars Science Laboratory (MSL)indicated a range of laminar to transitional flow conditions. In order to reduce the weight of Thermal Protection Systems (TPS), reliable prediction of transition and an understanding of the environmental factors that contribute to transition are necessary. This work is a step towards addressing this need, including the effects of thermochemical nonequilibrium but neglecting radiation, ablation, and ionization effects. Our results indicate that an oblique first mode produces maximum N-Factors on the symmetry plane, however with N-Factors too small to explain transition. Although we are able to show nonequilibrium three-dimensional PSE results inCO2, further study with improved mean flow solutions, accounting for some of the uncertainties inherent in this analysis, or evaluation of alternative transition mechanisms is needed to explain transition in the wind tunnel cases examined here.
H L Kline↗
Boundary Layer Stability and Transition in a Chemically Reacting Martian Atmosphere using LASTRAC
The Thermal Protection System (TPS) is a significant portion of the mass of reentry vehicles, planetary probes, and Martian entry vehicles. Reducing this mass has benefits in terms of decreased fuel requirements and increased payload; however, due to the high risk and un-certainty, the TPS or heat shields are designed conservatively by assuming fully turbulent flow. Laminar flow results in reduced heat flux, and improved transition prediction has the potential to reduce TPS mass and uncertainty in aerothermodynamic predictions. Limited previous research exists examining the problem of transition prediction for Martian atmospheric entry, with studies available on transition on the Mars Science Laboratory TPS. Although transition was demonstrated in wind-tunnel tests, uncertainty in the transition location resulted in a TPS designed for fully turbulent flow, and therefore greater mass than required for a partially-laminar condition. In this work, we extend the boundary layer stability code LASTRAC, recently modified to include chemical and thermal nonequilibrium capabilities, to a model of the Martian atmosphere. LASTRAC provides Parabolized Stability Equations (PSE) as well as Linear Stability Theory (LST) to predict the stability of a boundary layer and transition with semi-empirical eN methods. Results included in this work compare disturbance growth characteristics between air and Martian atmosphere at similar nondimensional freestream conditions on a simple flat plate geometry. Both chemical nonequilibrium and thermochemical nonequilibrium, as well as both PSE and LST, are used.
Heather L Kline↗
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↗
Stability and instability of thermocapillary convection in models of float-zone crystal growth
The energy-stability theory has been used to study the stability properties of thermocapillary convection in a half-zone model of the float-zone crystal-growth process. It is concluded that the energy theory provides a sufficient condition for stability to disturbances of arbitrary amplitude. Results of the computation of energy-stability limits are found to be in good agreement with experimentally measured bounds for oscillatory thermocapillary convection.
Neitzel, G. P.↗
Some new stability results in the theory of whirling.
Stability in whirl theory, considering internal damping role on motion of elastic shaft
ANGULAR MOTION↗
Qualitative theory of differential equations and structural stability.
Qualitative theory for differential equations, considering structural stability and role of first integrals
Peixoto, M. M.↗
Digital signal processing and control and estimation theory -- Points of tangency, area of intersection, and parallel directions
A number of current research directions in the fields of digital signal processing and modern control and estimation theory were studied. Topics such as stability theory, linear prediction and parameter identification, system analysis and implementation, two-dimensional filtering, decentralized control and estimation, image processing, and nonlinear system theory were examined in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines. An extensive bibliography is included.
Willsky, A. S.↗
Convective effects in float-zone and Czochralski melts
The hydrodynamics of crystal-growth melts is a relatively new research area. Numerical modeling of these processes is necessary. The work discussed herein is in two parts: numerical simulations of the flow in a Czochralski melt, and also of that in a float zone. In addition, for the float-zone case, energy stability theory will be used to determine stability bounds for the onset of oscillatory thermo-capillary flow. Convective effects in crystal-growth melts arise from a variety of mechanisms. Temperature gradients both in the direction of gravity and normal to it give rise to convection due to buoyancy effects. Rotation of the crucible and/or crystal causes a forced convection which may augment or oppose the buoyancy-driven flow. Finally, thermo-capillary forces (due to the variation of surface tension with temperature) drive surface motions which in turn generate convection in the bulk fluid. All of these mechanisms are present in either Czochralski or float-zone growth. The objective of the Czochralski modeling is to develop an accurate numerical simulation of the flow in a Czochralski silicon melt and to investigate the effects of various parameters on the flow properties. Like some earlier investigations, the intent is to simulate the effects of buoyancy, forced and thermo-capillary convection, including unsteady effects. Unlike earlier work, the aim is to include the effects of a variable free surface and freezing interface and, possibly incorporate nonaxisymmetric effects.
Neitzel, G. P.↗
Transition control
A unified view of the different control methods available or contemplated to delay or advance transition is presented. Emphasis is placed on two-dimensional incompressible flows, although more complex situations are also briefly covered. The governing equations are developed first, the routes to transition are mapped, and elements of the linear stability theory are outlined. The four basic stability modifiers - wall motion, suction, shaping, and wall heat transfer - are discussed, along with wave cancellation. The benefits as well as drawbacks of each approach are considered.
Gad-El-hak, Mohamed↗
Thermocapillary convection instability in microgravity crystal growth
Energy and linear stability theories are applied to study the stability properties of thermocapillary convection in a half zone model of the float zone crystal growth process. The analyses yield results which provide sufficient conditions for both stability and instability, respectively, and therefore, lower and upper bounds for the Marangoni numbers at which oscillatory thermocapillary convection will appear. The results of the analyses are compared with available experimental and numerical data.
Neitzel, G. P.↗
Spurious frequencies as a result of numerical boundary treatments
The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues is a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a 2-D cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. A more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions is reported.
Abarbanel, Saul↗
Effect of Surface Waviness on Transition in Three-Dimensional Boundary-Layer Flow
The effect of a surface wave on transition in three-dimensional boundary-layer flow over an infinite swept wing was studied. The mean flow computed using interacting boundary-layer theory, and transition was predicted using linear stability theory coupled with the empirical eN method. It was found that decreasing the wave height, sweep angle, or freestream unit Reynolds number, and increasing the freestream Mach number or suction level all stabilized the flow and moved transition onset to downstream locations.
Masad, Jamal A.↗