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Analytical method for predicting stability and control characteristics of large elastic airplanes at subsonic and supersonic speeds
Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.
A method of operating an oxygen transport membrane based reforming system employing one or more packs of thermally coupled panels of reformer tubes and oxygen transport membrane ("OTM") reactors close to thermo-neutral point is provided. The method produces syngas by converting a hydrocarbon-containing feed, such as natural gas in the reformer tubes of a pack by endothermic steam reforming reactions. The heat required for endothermic reforming reactions is provided by exothermic oxidizing reactions occurring inside the OTM reactors of the pack. At a thermo-neutral point the heat released by exothermic reactions matches the heat required to support endothermic reactions and heat losses in the pack. The method modulates the flow rate of hydrocarbon-containing feed and/or steam-to-carbon ratio of the combined feed to the pack to maintain the surface temperature of oxygen transport membrane reactors below a target maximum temperature. The syngas product oxygen-to-carbon ratio is maintained within a desired target range such that the OTM based reforming system is operated close to thermo-neutral point.
A method to evaluate the lateral ride quality of a B-1 aircraft subjected to a reduction in lateral static stability is developed. Ride quality is then found for three different relaxed static stability configurations which are augmented by yaw rate feedback to restore specified handling qualities. These cases are compared to the ride quality of the unrelaxed aircraft with the same handling qualities.
A method of measuring foaming volume is described and investigated to establish the critical factors in its operation. Data on foaming volumes and foam stabilities are given for a series of hydrocarbons and for a range of concentrations of aqueous ethylene-glycol solutions. It is shown that the amount of foam formed depends on the machinery of its production as well as on properties of the liquid, whereas the stability of the foam produced, within specified mechanical limitations, is primarily a function of the liquid.
A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.
This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.
Abstract The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.
In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.
A recently developed noniterative method for the solution of the transient fluid flow equations at all speed is extended to handle chemical reacting flows. The species conservation equations are loosely coupled into the predictor/multicorrector sequence of the solution procedure. A split-operator method separates the chemical kinetics terms from the fluid-dynamical terms, as well as an implicit differencing method enhance the numerical stability. The method was applied for turbulent diffusion flame calculations and for the analyses of high pressure, axisymmetric turbulent hypersonic nozzle flows. The diffusion flame results were compared with a similar pressure method for fast chemistry integration scheme without operator-splitting. Simulations of the nozzle flow indicated that the nonideal intermolecular effects must be included in the analysis and design of high pressure hypersonic nozzle.
A method for forming a stabilized bed of magneto-caloric material is provided. The method includes aligning magneto-caloric particles within the casing while a magnetic field is applied to the magneto-caloric particles and then fixing positions of the magneto-caloric particles within the casing. A related stabilized bed of magneto-caloric material is also provided.
A technique based on the Galerkin approximation is developed to remove spurious roots arising when Chebyshev spectral methods are used to solve eigenvalue problems in hydrodynamic stability. The derivation of Galerkin-Chebyshev approximations is explained, and numerical results for the Orr-Sommerfeld equations of plane Poiseuille flow and a Blasius profile are presented in tables and compared with those obtained by the method of Zebib (1984). It is pointed out that the present method does not increase the size of the algebraic system to be solved.
Approximate method of stability analysis for equilibrium in elastic continuums subjected to follower type surface traction
The stability is considered of the solution differential-difference equations of the retarded type with constant coefficients and two constant time delays. A method that makes use of analytical expressions to determine stability boundaries, and the stability of the system, is derived. The method was applied to a system represented by a second-order differential equation with constant coefficients and time delays in the velocity and displacement terms. The results obtained is in agreement with those obtained by other investigators.
A brief summary is made of methods available to the helicopter designer for obtaining desired stability characteristics by modifications to the airframe design. The discussion is based on modifications made during the establishment of flying-qualities criteria and includes sample indications of theoretical studies of additional methods.
Part I of this report presents a brief review of methods available to the helicopter designer for obtaining desired stability characteristics by modifications to the airframe design. The discussion is based on modifications made during the establishment of flying-qualities criteria and includes sample results of theoretical studies of additional methods. The conclusion is reached that it is now feasible to utilize combinations of methods whereby stability-parameter values are realized which in turn provide the desired stability characteristics. Part II reviews some of the methods of predicting rotor stability derivatives. The procedures by which these rotor derivatives are employed to estimate helicopter stability characteristics have been summarized.
Longitudinal stability derivatives prediction for rigid and elastic airplanes, using influence coefficient method
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