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A numerical study is made of the stability of weak and strong shocks attached to wedges and cones. The stability is shown to depend on the boundary conditions imposed, in good agreement with the experimental observations and the principle of minimum entropy. The behavior of the solutions is explained by quasi-static considerations.
The present investigation is concerned with the applicability of the vertical temperature gradient, DT, as a dispersion parameter for urban area sources. Data on DT were tabulated from temperature measurements at 5 m and 30 m obtained on 30 m towers at 12 stations. DT was obtained by subtracting the value at 5 m from that at 30 m. Positive DT values represent an inversion. Accuracy of the DT data is 0.1 K. Hourly measurements of DT along with concentrations of the primary pollutants, CO, NO, and total hydrocarbons (THC), are available from the 1976 RAPS data base for St. Louis. Linear correlations between a given pollutant species concentration and DT are developed from that data set. It could be confirmed that a strong positive correlation exists at night between the thermal stability of the lowest part of the boundary layer and the urban concentration of the primary pollutants CO, NO, and hydrocarbons.
The present investigation is concerned with a fourth order accurate finite difference method and its application to the study of the temporal and spatial stability of the three-dimensional compressible boundary layer flow on a swept wing. This method belongs to the class of compact two-point difference schemes discussed by White (1974) and Keller (1974). The method was apparently first used for solving the two-dimensional boundary layer equations. Attention is given to the governing equations, the solution technique, and the search for eigenvalues. A general purpose subroutine is employed for solving a block tridiagonal system of equations. The computer time can be reduced significantly by exploiting the special structure of two matrices.
The experimental and theoretical program at NASA Langley to develop high-speed low-disturbance wind tunnels for transition research is reviewed. Design and operational details of three new low-disturbance wind tunnels - the Mach-18 quiet helium, Mach-8 variable density, and Mach-3.5/Mach-6 high-speed low-disturbance tunnels, are presented. Focus is placed on the high-speed low-disturbance wind tunnel, which will have relatively large mass flows and run times from about 6 to 25 minutes. This facility is designed to provide direct simulation of low-disturbance flight conditions in the atmosphere. The Mach-8 facility will provide uniform flow conditions suitable for validation of aerodynamic codes, while the helium facility will be used for validation of boundary-layer and free shear-layer stability and transition prediction codes.
Titanium and nickel aluminides of nonequilibrium microstructures and in thin gauge thickness were identified, characterized and produced for potential high temperature applications. A high rate sputter deposition technique for rapid surveillance of the microstructures and nonequilibrium phase is demonstrated. Alloys with specific compositions were synthesized with extended solid solutions, stable dispersoids, and specific phase boundaries associated with different heat treatments. Phase stability and mechanical behavior of these nonequilibrium alloys were investigated and compared.
An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.
The evolution of minor planets in the outer part of the asteroid belt is considered. In the framework of the semi-averaged elliptic restricted three-dimensional three-body model, the boundary of regions of the Hill's stability is found. As was shown in our work, the Jacobian integral exists.
The linear stability of a fully three-dimensional boundary layer formed over a general aviation fuselage was investigated. The location of the onset of transition was estimated using the N-factor method. The results were compared with existing experimental data and indicate N-factors of approximately 8.5 on the side of the fuselage and 3.0 near the top. Considerable crossflow existed along the side of the body, which significantly affected the unstable modes present in the boundary layer. Fair agreement was found between the predicted frequency range of linear instability modes and available experimental data concerning the spectral content of the boundary layer.
Two-dimensional, incompressible, spatially developing mixing layer simulations are performed at Re = 10(exp 2) and 10(exp 4) with two classes of perturbations applied at the inlet boundary; combinations of discrete modes from linear stability theory, and a broad spectrum of modes derived from experimentally measured velocity spectra. The effect of the type and strength of inlet perturbations on vortex dynamics and time-averaged properties are explored. Two-point spatial velocity and autocorrelations are used to estimate the size and lifetime of the resulting coherent structures and to explore possible feedback effects. The computed time-averaged properties such as mean velocity profiles, turbulent statistics, and spread rates show good agreement with experimentally measured values. It is shown that by forcing with a broad spectrum of modes derived from an experimental energy spectrum many experimentally observed phenomena can be reproduced by a 2-D simulation. The strength of the forcing merely affected the length required for the dominant coherent structures to become fully-developed. Thus intensities comparable to those of the background turbulence in many wind tunnel experiments produced the same results, given sufficient simulation length.
Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.
Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.
Buffet boundaries, buffeting-load increments for the stabilizers and elevators, and buffeting bending-moment increments for the stabilizers and wings as measured in gradual maneuvers for a jet-powered bomber airplane are presented. The buffeting-load increments were determined from strain-gage measurements at the roots or hinge supports of the various surfaces considered. The Mach numbers of the tests ranged from 0.19 to 0.78 at altitudes close to 30,000 feet. The predominant buffet frequencies were close to the natural frequencies of the structural components. The buffeting-load data, when extrapolated to low-altitude conditions, indicated loads on the elevators and stabilizers near the design limit loads. When the airplane was held in buffeting, the load increments were larger than when recovery was made immediately.
Recent investigations have examined observations in an attempt to determine when and how the ocean forces the atmosphere, and vice versa. These studies focus primarily on relationships between sea surface temperature anomalies and the turbulent and radiative surface heat fluxes. It has been found that both positive and negative feedbacks, which enhance or reduce sea surface temperature anomaly amplitudes, can be generated through changes in the surface boundary layer. Consequent changes in sea surface temperature act to change boundary layer characteristics through changes in static stability or turbulent fluxes. Previous studies over the global oceans have used coarse-resolution observational and model products such as ICOADS and the NCEP Reanalysis. This study focuses on documenting the atmosphere ocean feedbacks that exist in recently produced higher resolution products, namely the SeaFlux v1.0 product and the NASA Modern Era Retrospective-Analysis for Research and Applications (MERRA). It has been noted in recent studies that evidence of oceanic forcing of the atmosphere exists on smaller scales than the usually more dominant atmospheric forcing of the ocean, particularly in higher latitudes. It is expected that use of these higher resolution products will allow for a more comprehensive description of these small-scale ocean-atmosphere feedbacks. The SeaFlux intercomparisons have revealed large scatter between various surface flux climatologies. This study also investigates the uncertainty in surface flux feedbacks based on several of these recent satellite based climatologies
A detailed study of the chevron-shaped dark spots on the strong southern equatorial wind jet near 7.5 S planetographic latitude shows variations in velocity with longitude and time. The presence of the large anticyclonic South Equatorial Disturbance (SED) has a profound effect on the chevron velocity, causing slower velocities to its east and accelerations over distance from the disturbance. The chevrons move with velocities near the maximum wind jet velocity of approx 140 m/s, as deduced by the history of velocities at this latitude and the magnitude of the symmetric wind jet near 7 N latitude. Their repetitive nature is consistent with a gravity-inertia wave (n = 75 to 100) with phase speed up to 25 m/s, relative to the local flow, but the identity of this wave mode is not well constrained. However, for the first time, high spatial resolution movies from Cassini images show that the chevrons oscillate in latitude with a 6.7 +/- 0.7-day period. This oscillating motion has a wavelength of approx 20 and a speed of 101 +/- 3 m/s, following a pattern similar to that seen in the Rossby wave plumes of the North Equatorial Zone, and possibly reinforced by it. All dates show chevron latitude variability, but it is unclear if this larger wave is present during other epochs, as there are no other suitable time series movies that fully delineate it. In the presence of mUltiple wave modes, the difference in dominant cloud appearance between 7 deg N and 7.5 deg S is likely due to the presence of the Great Red Spot, either through changes in stratification and stability or by acting as a wave boundary.
A detailed study of the chevron-shaped dark spots on the strong southern equatorial wind jet near 7.5 deg S planetographic latitude shows variations in velocity with longitude and time. The chevrons move with velocities near the maximum wind jet velocity of approx.140 m/s, as deduced by the history of velocities at this latitude and the magnitude of the symmetric wind jet near 7 deg N latitude. Their repetitive nature is consistent with an inertia-gravity wave (n = 75-100) with phase speed up to 25 m/s, relative to the local flow, but the identity of this wave mode is not well constrained. However, high spatial resolution movies from Cassini images show that the chevrons oscillate in latitude with a approx.7-day period. This oscillating motion has a wavelength of approx.20 deg and a speed of approx.100 m/s, following a pattern similar to that seen in the Rossby wave plumes of the North Equatorial Zone, and possibly reinforced by it, though they are not perfectly in phase. The transient anticyclonic South Equatorial Disturbance (SED) may be a similar wave feature, but moves at slower velocity. All data show chevron latitude variability, but it is unclear if this Rossby wave is present during other epochs, without time series movies that fully delineate it. In the presence of multiple wave modes, the difference in dominant cloud appearance between 7 deg N and 7.5 deg S may be due to the presence of the Great Red Spot, either through changes in stratification and stability or by acting as a wave boundary.
A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.
A concerted effort has been underway over the past several years to evolve computational capabilities for modeling aircraft loss-of-control under the NASA Aviation Safety Program. A principal goal has been to develop reliable computational tools for predicting and analyzing the non-linear stability & control characteristics of aircraft near stall boundaries affecting safe flight, and for utilizing those predictions for creating augmented flight simulation models that improve pilot training. Pursuing such an ambitious task with limited resources required the forging of close collaborative relationships with a diverse body of computational aerodynamicists and flight simulation experts to leverage their respective research efforts into the creation of NASA tools to meet this goal. Considerable progress has been made and work remains to be done. This paper summarizes the status of the NASA effort to establish computational capabilities for modeling aircraft loss-of-control and offers recommendations for future work.
A wind tunnel investigation has been conducted to evaluate the aerodynamic performance, stability, and control characteristics of a full-scale general aviation aircraft equipped with an advanced natural laminar flow wing. Force and moment data were measured over wide angle-of-attack and sideslip ranges and at Reynolds numbers from 1.4 million to 2.4 million based on the mean aerodynamic chord. Additional measurements determined the condition of the wing boundary layer and the wing stalling characteristics. The results showed that large regions of natural laminar flow existed on the wing which would significantly enhance the cruise performance of the configuration. Artificially tripping the boundary layer did not significantly affect the lift, stability, and control characteristics. Leading-edge modifications were effective in improving the stall resistance of the configuration, and resulted in only minor penalties in calculated cruise performance.